So what is the proper way to remove acyclic nails?
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It's based on a DAG, or directed acyclic graph, a system in which data spreads laterally instead of being stacked in blocks.
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The Finney will allow users to share computational resources over a distributed ledger based on the cryptocurrency IOTA, which uses a controversial directed acyclic graph (DAG) architecture different from a blockchain.
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The acyclic chromatic number of McGee graph is 3. In graph theory, an acyclic coloring is a (proper) vertex coloring in which every 2-chromatic subgraph is acyclic. The acyclic chromatic number A(G) of a graph G is the fewest colors needed in any acyclic coloring of G. Acyclic coloring is often associated with graphs embedded on non-plane surfaces.
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To emphasize that DAGs are not the same thing as directed versions of undirected acyclic graphs, some authors call them acyclic directed graphs or acyclic digraphs.
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Cyclic and acyclic acetals on acetalated dextran which degrades to dextran, acetone, and ethanol. During the synthesis of acetalated dextran both acyclic and cyclic acetals are formed. The acyclic acetals degrade into an acetone and an alcohol, whereas cyclic acetals degrade into acetone. The ratio of cyclic to acyclic acetals varies with reaction time since acyclic acetals are kinetically favored and cyclic acetals are the thermodynamically favored.
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The corresponding concept for undirected graphs is a forest, an undirected graph without cycles. Choosing an orientation for a forest produces a special kind of directed acyclic graph called a polytree. However, there are many other kinds of directed acyclic graph that are not formed by orienting the edges of an undirected acyclic graph. Moreover, every undirected graph has an acyclic orientation, an assignment of a direction for its edges that makes it into a directed acyclic graph.
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Many natural problems are actually promise problems. For instance, consider the following problem: Given a directed acyclic graph, determine if the graph has a path of length 10. The yes instances are directed acyclic graphs with a path of length 10, whereas the no instances are directed acyclic graphs with no path of length 10. The promise is the set of directed acyclic graphs.
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Cofibrations can be characterized as the maps which have the left lifting property with respect to acyclic fibrations, and acyclic cofibrations are characterized as the maps which have the left lifting property with respect to fibrations. Similarly, fibrations can be characterized as the maps which have the right lifting property with respect to acyclic cofibrations, and acyclic fibrations are characterized as the maps which have the right lifting property with respect to cofibrations.
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A cyclic directed network is one with a closed loop of edges. An acyclic directed network does not contain such loop. Since a self-edge – an edge connecting a vertex to itself – is considered a cycle, it is therefore absent from any acyclic network. :A Bayesian network is an example of an acyclic directed network.
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1232 pages. However, the IUPAC recommends using the name "alkene" only for acyclic hydrocarbons with just one double bond; alkadiene, alkatriene, etc., or polyene for acyclic hydrocarbons with two or more double bonds; cycloalkene, cycloalkadiene, etc. for cyclic ones; and "olefin" for the general class — cyclic or acyclic, with one or more double bonds.
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Any undirected graph may be made into a DAG by choosing a total order for its vertices and directing every edge from the earlier endpoint in the order to the later endpoint. The resulting orientation of the edges is called an acyclic orientation. Different total orders may lead to the same acyclic orientation, so an -vertex graph can have fewer than acyclic orientations. The number of acyclic orientations is equal to , where is the chromatic polynomial of the given graph.. condensation of the blue directed graph.
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And in an acyclic orientation, every face must have at least one sink. Therefore, an acyclic orientation is a unique sink orientation if and only if there is no other acyclic orientation with a smaller sum. Additionally, a k-regular subgraph of the given graph forms a face of the polytope if and only if its vertices form a lower set for at least one acyclic unique sink orientation. In this way, the face lattice of the polytope is uniquely determined from the graph .
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The thiosulfinate group can occur in cyclic as well as acyclic structures.
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The acyclic dependencies principle (ADP) is a software design principle defined by Robert C. Martin that states that "the dependency graph of packages or components should have no cycles". This implies that the dependencies form a directed acyclic graph.
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A molecule containing no rings is called an acyclic or open-chain compound.
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This representation allows the compiler to perform common subexpression elimination efficiently.. At a higher level of code organization, the acyclic dependencies principle states that the dependencies between modules or components of a large software system should form a directed acyclic graph..
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The abstract framework for defining cohomology and derived functors does not need them. However, in most concrete situations, resolutions by acyclic sheaves are often easier to construct. Acyclic sheaves therefore serve for computational purposes, for example the Leray spectral sequence.
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R. vannielii produces acyclic and aliphatic cyclic carotenoids like anhydrorhodovibrin, rhodovibrin, spirilloxanthin and rhodopin.
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We can test in linear time if a hypergraph is α-acyclic. Note that α-acyclicity has the counter-intuitive property that adding hyperedges to an α-cyclic hypergraph may make it α-acyclic (for instance, adding a hyperedge containing all vertices of the hypergraph will always make it α-acyclic). Motivated in part by this perceived shortcoming, Ronald Fagin defined the stronger notions of β-acyclicity and γ-acyclicity. We can state β-acyclicity as the requirement that all subhypergraphs of the hypergraph are α-acyclic, which is equivalent to an earlier definition by Graham.
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In algebraic topology, a discipline within mathematics, the acyclic models theorem can be used to show that two homology theories are isomorphic. The theorem was developed by topologists Samuel Eilenberg and Saunders MacLane.S. Eilenberg and S. Mac Lane (1953), "Acyclic Models." Amer.
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A graph that has a topological ordering cannot have any cycles, because the edge into the earliest vertex of a cycle would have to be oriented the wrong way. Therefore, every graph with a topological ordering is acyclic. Conversely, every directed acyclic graph has at least one topological ordering. Therefore, this property can be used as an alternative definition of the directed acyclic graphs: they are exactly the graphs that have topological orderings.
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In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is acyclic. A polytree is an example of an oriented graph.
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A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest.
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Kuich,ed, pages 77–88. Springer-Verlag, 1992. or acyclic context-sensitive grammar is NP-complete.
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Acyclic spaces occur in topology, where they can be used to construct other, more interesting topological spaces. For instance, if one removes a single point from a manifold M which is a homology sphere, one gets such a space. The homotopy groups of an acyclic space X do not vanish in general, because the fundamental group \pi_1(X) need not be trivial. For example, the punctured Poincaré homology sphere is an acyclic, 3-dimensional manifold which is not contractible.
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In the area of database theory, his contributions include the initiation of the study of acyclic databases and of non-two-phase locking. Acyclic database schemes are schemes that contain a single acyclic join dependency (a join dependency is a relationship governing the joining of tables of the database ) and a collection of functional dependencies;Catriel Beeri , Ronald Fagin , David Maier , Alberto Mendelzon , Jeffrey Ullman , Mihalis Yannakakis, Properties of acyclic database schemes, Proceedings of the thirteenth annual ACM symposium on Theory of computing, p.355-362, 11–13 May 1981. a number of researchers, including Yannakakis, pointed out the usefulness of these schemes by demonstrating the many useful properties they had: for example, the ability to solve many acyclic-scheme based problems in polynomial time, whereas the problem could easily have been NP-complete for other schemes.
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106°, whilst the angle of the acyclic carbene is 121°, both greater than those seen for imidazol-2-ylidenes.
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A directed acyclic graph (regardless of planarity) has a dominance drawing if and only if the partially ordered set of its vertices, ordered by reachability, has order dimension two. The (rotated) dominance drawing of a transitively reduced directed acyclic graph may be used as a Hasse diagram of the corresponding partial order.
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PMEG (9-[2-(phosphonomethoxy)ethyl] guanine) is an acyclic nucleoside phosphonate. Acyclic nucleoside phosphonates can have significant antiviral, cytostatic and antiproliferative activities. PMEG can inhibit cell proliferation and cause genotoxicity. PMEG is active against leukemia and melanoma in animal tumor models, and also has antiviral activities against herpes viruses in murine models.
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The first approach assumes that preferences are at least acyclic (which is necessary and sufficient for the preferences to have a maximal element on any finite subset). For this reason, it is closely related to relaxing transitivity. The second approach drops the assumption of acyclic preferences. Kumabe and Mihara adopt this approach.
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Robbins' theorem can be restated as saying that a graph has a totally cyclic orientation if and only if it does not have a bridge. Totally cyclic orientations are dual to acyclic orientations (orientations that turn into a directed acyclic graph) in the sense that, if is a planar graph, and orientations of are transferred to orientations of the planar dual graph of by turning each edge 90 degrees clockwise, then a totally cyclic orientation of corresponds in this way to an acyclic orientation of the dual graph and vice versa... The number of different totally cyclic orientations of any graph is where is the Tutte polynomial of the graph, and dually the number of acyclic orientations is .. As a consequence, Robbins' theorem implies that the Tutte polynomial has a root at the point if and only if the graph has a bridge. If a strong orientation has the property that all directed cycles pass through a single edge st (equivalently, if flipping the orientation of an edge produces an acyclic orientation) then the acyclic orientation formed by reversing st is a bipolar orientation. Every bipolar orientation is related to a strong orientation in this way.
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In fact, a deterministic finite state automaton is acyclic if and only if it recognizes a finite set of strings.
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A directed acyclic graph must be planar in order to have an upward planar drawing, but not every planar acyclic graph has such a drawing. Among the planar directed acyclic graphs with a single source (vertex with no incoming edges) and sink (vertex with no outgoing edges), the graphs with upward planar drawings are the st-planar graphs, planar graphs in which the source and sink both belong to the same face of at least one of the planar embeddings of the graph. More generally, a graph G has an upward planar drawing if and only if it is directed and acyclic, and is a subgraph of an st-planar graph on the same vertex set., pp. 111–112; , 6.1 "Inclusion in a Planar st-Graph", pp.
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The strings "tap", "taps", "top", and "tops" stored in a trie (left) and a DAFSA (right), stands for End-of-word. In computer science, a deterministic acyclic finite state automaton (DAFSA),Jan Daciuk, Stoyan Mihov, Bruce Watson and Richard Watson (2000). Incremental construction of minimal acyclic finite state automata. Computational Linguistics 26(1):3-16.
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A tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.
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This conjecture was disproved in 1995 by Arduengo's group, who obtained a derivative of dihydroimidazol-2-ylidene, lacking the double bond. The thermodynamical stability in this compound, and the role of steric protection in preventing dimerization, has been a topic of some dispute. Bis(diisopropylamino) carbene, the first acyclic stable carbene The first acyclic persistent carbene was reported in 1996, thus showing that a cyclic backbone was not necessary for their stability. Unlike the cyclic derivatives, the acyclic carbenes are flexible with respect to rotation of the bonds to the carbenic atom.
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A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree.
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Other data structures used to represent Boolean functions include negation normal form (NNF), Zhegalkin polynomials, and propositional directed acyclic graphs (PDAG).
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Acyclic coloring. Every graph G with acyclic chromatic number k has \chi_g(G) \le k(k+1). Marking game. For every graph G, \chi_g(G) \le col_g(G), where col_g(G) is the game coloring number of G. Almost every known upper bound for the game chromatic number of graphs are obtained from bounds on the game coloring number.
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Scheme 6. Stetter reaction with acyclic α-diketones In addition, they showed the atom economy and utility of using a cyclic α-diketone to generate the Stetter product with a tethered ethyl ester. The reaction precedes through the same mechanism as the acyclic version, but the ester generated by attack of ethanol remains tethered to the product.
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A directed acyclic graph may be used to represent a network of processing elements. In this representation, data enters a processing element through its incoming edges and leaves the element through its outgoing edges. For instance, in electronic circuit design, static combinational logic blocks can be represented as an acyclic system of logic gates that computes a function of an input, where the input and output of the function are represented as individual bits. In general, the output of these blocks cannot be used as the input unless it is captured by a register or state element which maintains its acyclic properties.. Electronic circuit schematics either on paper or in a database are a form of directed acyclic graphs using instances or components to form a directed reference to a lower level component.
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However, it has a linear time solution for directed acyclic graphs, which has important applications in finding the critical path in scheduling problems.
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A directed acyclic graph G has an upward planar drawing if and only if G is a subgraph of an st-planar graph..
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RecCC is a constructive neural network approach to deal with tree domains with pioneering applications to chemistry and extension to directed acyclic graphs.
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In graph theory, a moral graph is used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm, used in belief propagation on graphical models. The moralized counterpart of a directed acyclic graph is formed by adding edges between all pairs of non- adjacent nodes that have a common child, and then making all edges in the graph undirected. Equivalently, a moral graph of a directed acyclic graph is an undirected graph in which each node of the original is now connected to its Markov blanket.
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The Cram's rule of asymmetric induction developed by Donald J. Cram in 1952Studies in Stereochemistry. X. The Rule of "Steric Control of Asymmetric Induction" in the Syntheses of Acyclic Systems Donald J. Cram, Fathy Ahmed Abd Elhafez J. Am. Chem. Soc.; 1952; 74(23); 5828–5835. Abstract is an early concept relating to the prediction of stereochemistry in certain acyclic systems.
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This gives a repertoire of examples, since the first homology group is the abelianization of the fundamental group. With every perfect group G one can associate a (canonical, terminal) acyclic space, whose fundamental group is a central extension of the given group G. The homotopy groups of these associated acyclic spaces are closely related to Quillen's plus construction on the classifying space BG.
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Acetamiprid has an acyclic group instead of a second heterocyclic ring and is therefore much less toxic to honey bees than nitro- substituted compounds.
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A simple maze in which the maze walls and the free space between the walls form two interdigitating trees A spanning tree may be defined as a set of edges that, together with all of the vertices of the graph, forms a connected and acyclic subgraph. But, by cut-cycle duality, if a set of edges in a planar graph is acyclic (has no cycles), then the set of edges dual to has no cuts, from which it follows that the complementary set of dual edges (the duals of the edges that are not in ) forms a connected subgraph. Symmetrically, if is connected, then the edges dual to the complement of form an acyclic subgraph. Therefore, when has both properties – it is connected and acyclic – the same is true for the complementary set in the dual graph.
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Cyclic perfluorocarbons, such as perfluoromethylhexane and perfluoro-1,3-dimethylcyclohexane, are generally believed to be better than acyclic ones as they can be detected at lower levels.
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Phytol is likely the most abundant acyclic isoprenoid compound present in the biosphere and its degradation products have been used as biogeochemical tracers in aquatic environments.
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Acyclic nucleoside phosphonates prodrugs require further phosphorylation in the cell in order to become the active metabolite. Once PMEG is phosphorylated into its triphosphate form, host or viral DNA polymerases can use it a substrate during DNA synthesis. Since it is an acyclic nucleoside, lacking a 3'-OH moiety, to further extension of the DNA strand occurs. Thus this agent uses the classical mechanism of DNA chain terminator.
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It is NP-complete to determine whether A(G) ≤ 3. showed that the decision variant of the problem is NP-complete even when G is a bipartite graph. demonstrated that every proper vertex coloring of a chordal graph is also an acyclic coloring. Since chordal graphs can be optimally colored in O(n + m) time, the same is also true for acyclic coloring on that class of graphs.
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In constraint satisfaction, a decomposition method translates a constraint satisfaction problem into another constraint satisfaction problem that is binary and acyclic. Decomposition methods work by grouping variables into sets, and solving a subproblem for each set. These translations are done because solving binary acyclic problems is a tractable problem. Each structural restriction defined a measure of complexity of solving the problem after conversion; this measure is called width.
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Although the nomenclature is not followed widely, according to IUPAC, an alkene is an acyclic hydrocarbon with just one double bond between carbon atoms. Olefins comprise a larger collection of cyclic and acyclic alkenes as well as dienes and polyenes. To form the root of the IUPAC names for straight-chain alkenes, change the -an- infix of the parent to -en-. For example, CH3-CH3 is the alkane ethANe.
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A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet. A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional independence with a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms.
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Since 2018, nakamo.to is part of the Advanced Blockchain AG. The main aim is to develop DLT further to use it as a solution to decentralize tasks, for example in manufacturing or the automotive industry. The new project peaq, cofounded by Küfner, is focusing on further development of directed acyclic graphs. Through the project the Dagchain was invented as an alternative approach to reach consensus within directed acyclic graphs.
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Similar principles guide the lowest energy conformations of larger ring systems. Along with the acyclic stereocontrol principles outlined below, subtle interactions between remote substituents in large rings, analogous to those observed for 8-10 membered rings, can influence the conformational preferences of a molecule. In conjunction with remote substituent effects, local acyclic interactions can also play an important role in determining the outcome of macrocyclic reactions.Deslongchamps, P. Pure Appl. Chem.
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Catriel Beeri , Ronald Fagin , David Maier , Mihalis Yannakakis, On the Desirability of Acyclic Database Schemes, Journal of the ACM, v.30 n.3, p.479-513, July 1983.
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Lecture Notes Comp. Sci. 6795, Springer, 478−479. # S. Kitaev and S. Seif. Word problem of the Perkins semigroup via directed acyclic graphs, Order 25 (2008), 177−194.
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ACID and Transactions in Hive Internally, a compiler translates HiveQL statements into a directed acyclic graph of MapReduce, Tez, or Spark jobs, which are submitted to Hadoop for execution.
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For real-time data (cyclic data and alarms), the Profinet Real-Time (RT) telegrams are transmitted directly via Ethernet. UDP/IP is used for the transmission of acyclic data.
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That is in any application represented by a directed acyclic graph there is a causal structure, either an explicit order or time in the example or an order which can be derived from graph structure. This follows because all directed acyclic graphs have a topological ordering, i.e. there is at least one way to put the vertices in an order such that all edges point in the same direction along that order.
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A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is acyclic. Some authors restrict the phrase "directed forest" to the case where the edges of each connected component are all directed towards a particular vertex, or all directed away from a particular vertex (see branching).
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See . (or directed tree or oriented treeSee .See . or singly connected networkSee .) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees.
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Different functionality in Maple requires numerical data in different formats. Symbolic expressions are stored in memory as directed acyclic graphs. The standard interface and calculator interface are written in Java.
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In the Laniatores, Gonyleptoidea produce alkylated benzoquinones and phenols, and Travunioidea produce mainly terpenoids. In the Eupnoi, the Sclerosomatidae secrete short-chain acyclic ketones and alcohols, and the Phalangiidae, naphthoquinones.
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This class of molecules tends to be slightly more stable than the acyclic analogues as there is a stabilization through the delocalization of the unpaired electrons within the π-system.
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The Coxian distribution is extremely important as any acyclic phase-type distribution has an equivalent Coxian representation. The generalised Coxian distribution relaxes the condition that requires starting in the first phase.
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Besifovir (INN) is an investigational medication to treat hepatitis B virus (HBV) infection. It is a novel and potent acyclic nucleotide phosphonate with a similar chemical structure to adefovir and tenofovir.
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"The complexity of acyclic conjunctive queries". Journal of the ACM 48 (3): 431–498. . Acyclicity of conjunctive queries is a structural property of queries that is defined with respect to the query's hypergraph: a conjunctive query is acyclic if and only if it has hypertree-width 1. For the special case of conjunctive queries in which all relations used are binary, this notion corresponds to the treewidth of the dependency graph of the variables in the query (i.e.
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In any directed bipartite graph, all cycles have a length that is divisible by two. Therefore, no directed bipartite graph can be aperiodic. In any directed acyclic graph, it is a vacuous truth that every k divides all cycles (because there are no directed cycles to divide) so no directed acyclic graph can be aperiodic. And in any directed cycle graph, there is only one cycle, so every cycle's length is divisible by n, the length of that cycle.
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The key difference from the more recent Barabási–Albert model is that the Price model produces a graph with directed edges while the Barabási–Albert model is the same model but with undirected edges. The direction is central to the citation network application which motivated Price. This means that the Price model produces a directed acyclic graph and these networks have distinctive properties. For example, in a directed acyclic graph both longest paths and shortest paths are well defined.
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A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic. Some authors restrict the phrase "directed tree" to the case where the edges are all directed towards a particular vertex, or all directed away from a particular vertex (see arborescence).
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In solution, reducing monosaccharides exist in equilibrium between their acyclic and cyclic forms with less than 1% in the acyclic form. The open chain form can close to give the pyranose and furanose with both the α- and β-anomers present for each. The equilibrium population of conformers depends on their relative energies which can be determined to a rough approximation using steric and stereoelectronic arguments. It has been shown that cations in solution can shift the equilibrium.
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An annulation is defined as a transformation of one or more acyclic precursors resulting in the fusion of a new ring via two newly generated bonds. These strategies can be used to create aromatic systems from acyclic precursors in a single step, with many substituents already in place.Danheiser, R L., Brisbois, R G. James, J. Kowalczyk, Miller, R. F. “An Annulation Method for the Synthesis of Highly Substituted Polycyclic Aromatic and Heteroaromatic Compounds.” J. Am. Chem. Soc.
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A food web is often acyclic, with few exceptions such as adults preys on juveniles and parasitism.Newman, Mark E. J. “Chapter 5.3 Ecological Networks”. Networks: an Introduction. Oxford: Oxford UP, 2010. p.
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In the other direction, if an orientation with outdegree k is given, an ordering with coloring number k + 1 can be obtained as a topological ordering of the resulting directed acyclic graph.
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Nevertheless, if X is an acyclic CW complex, and if the fundamental group of X is trivial, then X is a contractible space, as follows from the Whitehead theorem and the Hurewicz theorem.
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The following statements are equivalent for a tournament T on n vertices: # T is transitive. # T is a strict total ordering. # T is acyclic. # T does not contain a cycle of length 3.
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In such a graph, the longest path from the first milestone to the last one is the critical path, which describes the total time for completing the project. Longest paths of directed acyclic graphs may also be applied in layered graph drawing: assigning each vertex v of a directed acyclic graph G to the layer whose number is the length of the longest path ending at v results in a layer assignment for G with the minimum possible number of layers..
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Synthesised cyclic and acyclic diaminocarbenes Unlike the aromatic imidazol-2-ylidenes or triazol-5-ylidenes, these carbenes appear not to be thermodynamically stable, as shown by the dimerisation of some unhindered cyclic and acyclic examples. Studies suggest that these carbenes dimerise via acid catalysed dimerisation (as in the Wanzlick equilibrium). Diaminocarbenes have diagnostic 13C NMR chemical shift values between 230–270 ppm for the carbenic atom. The X-ray structure of dihydroimidazole-2-ylidene shows a N-C-N bond angle of ca.
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Several cases of the conjecture have been proven to be true—for instance, it is known to be true for graphs with a prime number of vertices.—but the full conjecture remains open. Variants of the problem for randomized algorithms and quantum algorithms have also been studied. Bender and Ron have shown that, in the same model used for the evasiveness conjecture, it is possible in only constant time to distinguish directed acyclic graphs from graphs that are very far from being acyclic.
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The aromatization of acyclic precursors is rarer in organic synthesis, although it is a significant component of the BTX production in refineries. Among acyclic precursors, alkynes are relatively prone to aromatizations since they are partially dehydrogenated. The Bergman cyclization is converts an enediyne to a dehydrobenzene intermediate diradical, which abstracts hydrogen to aromatize. The enediyne moiety can be included within an existing ring, allowing access to a bicyclic system under mild conditions as a consequence of the ring strain in the reactant.
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The star chromatic number \chi_s(G) of G is the fewest colors needed to star color G. One generalization of star coloring is the closely related concept of acyclic coloring, where it is required that every cycle uses at least three colors, so the two-color induced subgraphs are forests. If we denote the acyclic chromatic number of a graph G by \chi_a(G), we have that \chi_a(G) \leq \chi_s(G), and in fact every star coloring of G is an acyclic coloring. The star chromatic number has been proved to be bounded on every proper minor closed class by . This results was further generalized by to all low-tree-depth colorings (standard coloring and star coloring being low-tree-depth colorings with respective parameter 1 and 2).
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Main path analysis is implemented in Pajek, a widely used social network analysis software written by Vladimir Batagelj and Andrej Mrvar of University of Ljubljana, Slovenia. To run main path analysis in Pajek, one needs to first prepare a citation network and have Pajek reads in the network. Next, in the Pajek main menu, computes the traversal counts of all links in the network applying one of the following command sequences (depending on the choice of traversal counts). Network → Acyclic Network → Create Weighted Network + Vector → Traversal Weights → Search Path Link Count (SPC), or Network → Acyclic Network → Create Weighted Network + Vector → Traversal Weights → Search Path Link Count (SPLC), or Network → Acyclic Network → Create Weighted Network + Vector → Traversal Weights → Search Path Node Pairs (SPNP) After traversal counts are computed, the following command sequences find the main paths.
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In contrast with ordinary undirected graphs for which there is a single natural notion of cycles and acyclic graphs, there are multiple natural non-equivalent definitions of acyclicity for hypergraphs which collapse to ordinary graph acyclicity for the special case of ordinary graphs. A first definition of acyclicity for hypergraphs was given by Claude Berge: a hypergraph is Berge- acyclic if its incidence graph (the bipartite graph defined above) is acyclic. This definition is very restrictive: for instance, if a hypergraph has some pair v eq v' of vertices and some pair f eq f' of hyperedges such that v, v' \in f and v, v' \in f', then it is Berge-cyclic. Berge-cyclicity can obviously be tested in linear time by an exploration of the incidence graph.
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Mirsky's theorem can be restated in terms of directed acyclic graphs (representing a partially ordered set by reachability of their vertices), as the statement that there exists a graph homomorphism from a given directed acyclic graph G to a k-vertex transitive tournament if and only if there does not exist a homomorphism from a (k + 1)-vertex path graph to G. For, the largest path graph that has a homomorphism to G gives the longest chain in the reachability ordering, and the sets of vertices with the same image in a homomorphism to a transitive tournament form a partition into antichains. This statement generalizes to the case that G is not acyclic, and is a form of the Gallai–Hasse–Roy–Vitaver theorem on graph colorings and orientations .
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Mihalis Yannakakis: Algorithms for Acyclic Database Schemes . Proc. VLDB 1981: 82-94. The query evaluation, and thus query containment, is LOGCFL-complete and thus in polynomial time.Georg Gottlob, Nicola Leone, and Francesco Scarcello (2001).
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A polytree. In mathematics, and more specifically in graph theory, a polytree. (also called directed tree, oriented tree. or singly connected network.) is a directed acyclic graph whose underlying undirected graph is a tree.
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The graph application is for manipulating directed and undirected graphs. Some the standard graph functions exist (like for adjacency and cliques) together with combinatorial functions like computing the lattice represented by a directed acyclic graph.
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A graphoid is termed DAG-induced if there exists a directed acyclic graph D such that I(X,Z,Y) \Leftrightarrow \langle X,Z,Y\rangle_D where \langle X,Z,Y\rangle_D stands for d-separation in D. d-separation (d-connotes "directional") extends the notion of vertex separation from undirected graphs to directed acyclic graphs. It permits the reading of conditional independencies from the structure of Bayesian networks. However, conditional independencies in a DAG cannot be completely characterized by a finite set of axioms.
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A "bow-tie" diagram, cause-and-effect diagram, Bayesian network (a directed acyclic network) and fault trees are few examples of how network theories can be applied in risk assessment.Rausand, Marvin. Risk Assessment: Theory, Methods, and Applications.
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Several equivalent definitions of a Bayesian network have been offered. For the following, let G = (V,E) be a directed acyclic graph (DAG) and let X = (Xv), v ∈ V be a set of random variables indexed by V.
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Several syntheses of vancosamine have been published.Hauser, F. M., Ellenberger, S. R., Glusker, J. P., Smart, F. J., Carrell, H. L. "Stereoselective Syntheses or +/- Daunosamine, +/- Vancosamine, and +/- Ristosamine from Acyclic Precursors." J. Org. Chem. 1986, 51, 50-57.
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One can therefore say a connected network has only one component. Directed Networks Figure 7. An example of acyclic directed network in epidemiology by CDC. :Networks of which each edge has a direction from one vertex to another.
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Rühlmann-method Usually toluene, dioxane, tetrahydrofuran or acyclic dialkylethers are employed as solvents. Advantageously also N-methyl- morpholine has been used. It allowed in some cases a successful reaction, in which otherwise the reaction failed in less polar media.
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NB: Wright's rules assume a model without feedback loops: the directed graph of the model must contain no cycles, i.e. it is a directed acyclic graph, which has been extensively studied in the causal analysis framework of Judea Pearl.
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The montréalone parent compound has been studied theoretically,Krenske, E. H.; Houk, K. N.; Arndtsen, B. A.; St. Cyr, D. J., Cyclic 1,3-Dipoles or Acyclic Phosphonium Ylides? Electronic Characterization of "Montréalones". J. Am. Chem. Soc. 2008, 130, 10052.
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As a result, the visual representation of a scene is based entirely on a network of interconnecting nodes, depending on each other's information. For the convenience of viewing these networks, there is a dependency and a directed acyclic graph.
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Conversely, every directed acyclic graph that has a bimodal planar embedding with a consistent assignment has an upward planar drawing, that can be constructed from it in linear time., pp. 112–115; , 6.2 "Angles in Upward Drawings", pp. 180–188; ; .
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In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that takes the form of a directed acyclic graph.
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Metallabenzene complexes have been classified into three varieties; in such compounds the parent acyclic hydrocarbon ligand is viewed as the anion C5H5−. The 6 π electrons in the metallacycle conform to the Hückel (4n+2) theory. :Three classes of stable metallabenzenes.
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Given a dominance drawing of a directed acyclic graph D1 = (V, E1), inverting the interpretation of one axis results in a new relation one could call coreachability. Thus a point (xa, ya) could be considered coreachable from a point (xb, yb) whenever xa ≥ xb but ya ≤ yb. In this way, the dominance drawing may be seen to induce a second directed acyclic graph D2 = (V, E2) on the same vertex set. The pairs {≤1, ≤2} of partial orders on a shared ground set that permit such simultaneous representation by a single drawing—interpreted in terms of reachability and coreachability—are called codominant.
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This is the same method of cycle cutset using the definition of cutset for hypergraphs: a cycle hypercutset of a hypergraph is a set of edges (rather than vertices) that makes the hypergraph acyclic when all their vertices are removed. A decomposition can be obtained by grouping all variables of a hypercutset in a single one. This leads to a tree whose nodes are sets of hyperedges. The width of such a decomposition is the maximal size of the sets associated with nodes, which is one if the original problem is acyclic and the size of its minimal hypercutset otherwise.
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Equivalently, a strongly connected component of a directed graph G is a subgraph that is strongly connected, and is maximal with this property: no additional edges or vertices from G can be included in the subgraph without breaking its property of being strongly connected. The collection of strongly connected components forms a partition of the set of vertices of G. The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex. If each strongly connected component is contracted to a single vertex, the resulting graph is a directed acyclic graph, the condensation of G. A directed graph is acyclic if and only if it has no strongly connected subgraphs with more than one vertex, because a directed cycle is strongly connected and every nontrivial strongly connected component contains at least one directed cycle.
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A raffinement on the above definition can be made, resulting in the concept of acyclic agreement forest. An agreement forest for two -trees and is said to be acyclic if each of its tree components can be numbered in such a way that if the root of one component is an ancestor of the root of another component in either or , then the number assigned to is lower than the number assigned to . Another characterization of acyclicity in agreement forest is to consider the directed graph that has vertex set and a directed edge if and only if and at least one of the two following conditions hold: # the root of is an ancestor of the root of in # the root of is an ancestor of the root of in The directed graph is called the inheritance graph associated with the agreement forest , and we call acyclic if has no directed cycle.
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Nodes contain headlines, body text, and other information. Headlines naturally serve as descriptions of the body text. For example, @file nodes are nodes whose headline starts with @file. Leo trees are in fact directed acyclic graphs; nodes may have more than one parent.
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Farnesyl diphosphatase (, FPP phosphatase) is an enzyme with systematic name (2E,6E)-farnesyl-diphosphate diphosphohydrolase. This enzyme catalyses the following chemical reaction : (2E,6E)-farnesyl diphosphate + H2O \rightleftharpoons (2E,6E)-farnesol + diphosphate The enzyme is involved in the biosynthesis of acyclic sesquiterpenoids.
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Citronellol, or dihydrogeraniol, is a natural acyclic monoterpenoid. Both enantiomers occur in nature. (+)-Citronellol, which is found in citronella oils, including Cymbopogon nardus (50%), is the more common isomer. (−)-Citronellol is found in the oils of rose (18–55%) and Pelargonium geraniums.
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Dppp can sometimes be used in palladium-catalyzed arylation under Heck reaction conditions to control regioselectivity.Cabri, Walter; Candiani, Ilaria; Bedeschi Angelo; Penco, Sergio"α-Regioselectivity in Palladium-Catalyzed Arylation of Acyclic Enol Ethers" journal= Journal of Organic Chemistry, 1991, volume 57, p. 1481.
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The result of a WBA is a why–because graph (WBG). The WBG depicts causal relations between factors of an accident. It is a directed acyclic graph where the nodes of the graph are factors. Directed edges denote cause–effect relations between the factors.
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A feature structure can be represented as a directed acyclic graph (DAG), with the nodes corresponding to the variable values and the paths to the variable names. Operations defined on feature structures, e.g. unification, are used extensively in phrase structure grammars. In most theories (e.g.
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The first and general case is the acyclic carbonate group. Organic substituents can be identical or not. Both aliphatic or aromatic substituents are known, they are called dialkyl or diaryl carbonates, respectively. The simplest members of these classes are dimethyl carbonate and diphenyl carbonate.
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Okenone is synthesized in 12 species of Chromatiaceae, spanning eight genera. Other purple sulfur bacteria have acyclic carotenoid pigments like lycopene and rhodopin. However, geochemists largely study okenone because it is structurally unique. It is the only pigment with a 2,3,4 trimethylaryl substitution pattern.
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The mathematical structure of a directed acyclic graph is used to describe the way in which the various realms can influence one other, and even the physical world can function as part of the realm of ideal forms for some worlds "downstream" in the graph.
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Airflow uses directed acyclic graphs (DAGs) to manage workflow orchestration. Tasks and dependencies are defined in Python and then Airflow manages the scheduling and execution. DAGs can be run either on a defined schedule (e.g. hourly or daily) or based on external event triggers (e.g.
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In the mathematical fields of graph theory and combinatorics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. It is one of several graph polynomials studied in algebraic graph theory.
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An efficient total synthesis of pederin is known. Beginning with (+)-benzoylselenopederic acid, Zn(BH4)2 reduction is applied, introducing stereoselective reduction of the acyclic ketone. Michael addition of nitromethane is performed. After several steps of Moffatt oxidation, phenylselenation, hydrolysis, and reduction, pederic acid is reached.
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Curiously, although it was originally designed for acyclic graphical models, it was found that the Belief Propagation algorithm can be used in general graphs. The algorithm is then sometimes called loopy belief propagation, because graphs typically contain cycles, or loops. The initialization and scheduling of message updates must be adjusted slightly (compared with the previously described schedule for acyclic graphs) because graphs might not contain any leaves. Instead, one initializes all variable messages to 1 and uses the same message definitions above, updating all messages at every iteration (although messages coming from known leaves or tree-structured subgraphs may no longer need updating after sufficient iterations).
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Saegusa-Ito oxidation For acyclic substrates the reaction yields the thermodynamic E-olefin product exclusively. Acyclic substrates This discovery was preceded nearly eight years earlier by a report that treatment of unactivated ketones with palladium acetate yielded the same products in low yields. The major improvement provided by Saegusa and Ito was the recognition that the enol form was the reactive species, developing a method based on silyl enol ethers. Benzoquinone is actually not a necessary component for this reaction; its role is to regenerate palladium(II) from its reduced form palladium(0), so that a smaller amount of expensive palladium(II) acetate is required at the beginning.
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Part of Freeciv's technology tree, showing complex dependencies between technologies. For example, astronomy can be reached by first researching ceremonial burial and then mysticism, or by researching masonry followed by mathematics In strategy computer games, a technology, tech, or research tree is a hierarchical visual representation of the possible sequences of upgrades a player can take (most often through the act of research). Because these trees are technically directed and acyclic, they can more accurately be described as a technology directed acyclic graph. The diagram is tree-shaped in the sense that it branches between each 'level', allowing the player to choose one sequence or another.
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ONNX provides definitions of an extensible computation graph model, built-in operators and standard data types, focused on inferencing (evaluation). Each computation dataflow graph is a list of nodes that form an acyclic graph. Nodes have inputs and outputs. Each node is a call to an operator.
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As above, spiroketalization was performed thermodynamically with introduction of acid. Ley's Synthesis of Okadaic Acid. Ley's synthesis of okadaic acid is most unlike its predecessors, although it still contains similar motifs. Like the others, this synthesis divided okadaic acid into three components along the acyclic segments.
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Farnesol is a natural 15-carbon organic compound which is an acyclic sesquiterpene alcohol. Under standard conditions, it is a colorless liquid. It is hydrophobic, and thus insoluble in water, but miscible with oils. Farnesol is produced from 5-carbon isoprene compounds in both plants and animals.
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Directed acyclic graphs may also be used as a compact representation of a collection of sequences. In this type of application, one finds a DAG in which the paths form the given sequences. When many of the sequences share the same subsequences, these shared subsequences can be represented by a shared part of the DAG, allowing the representation to use less space than it would take to list out all of the sequences separately. For example, the directed acyclic word graph is a data structure in computer science formed by a directed acyclic graph with a single source and with edges labeled by letters or symbols; the paths from the source to the sinks in this graph represent a set of strings, such as English words.. Any set of sequences can be represented as paths in a tree, by forming a tree vertex for every prefix of a sequence and making the parent of one of these vertices represent the sequence with one fewer element; the tree formed in this way for a set of strings is called a trie.
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Each cycle in the minimum weight cycle basis has a set of edges that are dual to the edges of one of the cuts in the Gomory–Hu tree. When cycle weights may be tied, the minimum-weight cycle basis may not be unique, but in this case it is still true that the Gomory–Hu tree of the dual graph corresponds to one of the minimum weight cycle bases of the graph.. In directed planar graphs, simple directed cycles are dual to directed cuts (partitions of the vertices into two subsets such that all edges go in one direction, from one subset to the other). Strongly oriented planar graphs (graphs whose underlying undirected graph is connected, and in which every edge belongs to a cycle) are dual to directed acyclic graphs in which no edge belongs to a cycle. To put this another way, the strong orientations of a connected planar graph (assignments of directions to the edges of the graph that result in a strongly connected graph) are dual to acyclic orientations (assignments of directions that produce a directed acyclic graph)..
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In graph theory, the girth of a graph is the length of a shortest cycle contained in the graph.R. Diestel, Graph Theory, p.8. 3rd Edition, Springer- Verlag, 2005 If the graph does not contain any cycles (i.e. it's an acyclic graph), its girth is defined to be infinity.
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Diphenyl carbonate is the organic compound with the formula (C6H5O)2CO. It is classified as an acyclic carbonate ester. It is a colorless solid. It is both a monomer in combination with bisphenol A in the production of polycarbonate polymers and a product of the decomposition of polycarbonates.
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Its ease of human understanding make behavior trees less error prone and very popular in the game developer community. Behavior trees have been shown to generalize several other control architectures. Mathematically, they are directed acyclic graphs. Behavior tree modelling the search and grasp plan of a two-armed robot.
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172–179; ; . In an upward embedding, the sets of incoming and outgoing edges incident to each vertex are contiguous in the cyclic ordering of the edges at the vertex. A planar embedding of a given directed acyclic graph is said to be bimodal when it has this property.
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The bright red pigment lycopene is the acyclic precursor of all carotenoids in cyanobacteria. In myxoxanthophyll synthesis, lycopene is enzymatically converted to 1-hydroxylycoprene, then to intermediates 1'-hydroxy-y-carotene, plectaniaxanthin, and myxol. Finally, the hydroxyl group in myxol is glycosylated at the 2' position to form myxoxanthophyll.
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RCM undergoes a similar mechanistic pathway as other olefin metathesis reactions, such as cross metathesis (CM), ring-opening metathesis polymerization (ROMP), and acyclic diene metathesis (ADMET).Crabtree, R. H. Applications. The Organometallic Chemistry of the Transition Metals, 6th Ed.; John Wiley & Sons, Inc.: New Jersey, 2014, pp.318-322.
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Elimination of selenoxides takes place through an intramolecular syn elimination pathway. The carbon–hydrogen and carbon–selenium bonds are co-planar in the transition state. (2)File:SelenMech1.png The reaction is highly trans-selective when acyclic α-phenylseleno carbonyl compounds are employed. Formation of conjugated double bonds is favored.
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The Hosoya index of a graph G, its number of matchings, is used in chemoinformatics as a structural descriptor of a molecular graph. It may be evaluated as mG(1) . The third type of matching polynomial was introduced by as a version of the "acyclic polynomial" used in chemistry.
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The visualization of orders with Hasse diagrams has a straightforward generalization: instead of displaying lesser elements below greater ones, the direction of the order can also be depicted by giving directions to the edges of a graph. In this way, each order is seen to be equivalent to a directed acyclic graph, where the nodes are the elements of the poset and there is a directed path from a to b if and only if a ≤ b. Dropping the requirement of being acyclic, one can also obtain all preorders. When equipped with all transitive edges, these graphs in turn are just special categories, where elements are objects and each set of morphisms between two elements is at most singleton.
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In some applications, such cycles are undesirable, and we wish to eliminate them and obtain a directed acyclic graph (DAG). One way to do this is simply to drop edges from the graph to break the cycles. Closely related are the feedback vertex set, which is a set of vertices containing at least one vertex from every cycle in the directed graph, and the minimum spanning tree, which is the undirected variant of the feedback arc set problem. A minimal feedback arc set (one that can not be reduced in size by removing any edges) has the additional property that, if the edges in it are reversed rather than removed, then the graph remains acyclic.
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An arbitrary directed graph may also be transformed into a DAG, called its condensation, by contracting each of its strongly connected components into a single supervertex.. When the graph is already acyclic, its smallest feedback vertex sets and feedback arc sets are empty, and its condensation is the graph itself.
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Optimizing an FSM means finding a machine with the minimum number of states that performs the same function. The fastest known algorithm doing this is the Hopcroft minimization algorithm. Other techniques include using an implication table, or the Moore reduction procedure. Additionally, acyclic FSAs can be minimized in linear time.
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Eau de Cologne mint has a strong odor due to the two chemical constituents, linalyl acetate (45%) and linalool (45-50%), which make up around 90% of the oil.Murray, M. J., & Lincoln, D. E. (1970). The Genetic Basis of Acyclic Oil Constituents in MENTHA CITRATA Ehrh. Genetics, 65(3), 457–471.
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The descriptions given so far all specify the number of elements of the universe. Unfortunately most interesting sets of structures are not restricted to a certain size, like all graphs that are trees, are connected or are acyclic. Thus to discriminate a finite number of structures is of special importance.
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Word-representable graphs were introduced by Sergey Kitaev in 2004 based on joint research with Steven SeifS. Kitaev and S. Seif. Word problem of the Perkins semigroup via directed acyclic graphs, Order 25 (2008), 177−194. on the Perkins semigroup, which has played an important role in semigroup theory since 1960.
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His studies have been documented by way of a number of articles and ResearchGate, an online repository of scientific articles has listed 73 of them. He holds two patents, Isolation and purification of shikimic acid from plant sources and Microbial chiral resolution of cyclic and acyclic acetates to enantiomerically pure (R)-alcohols.
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Structure of aminoacetaldehyde. Most members of this class are unstable towards self-condensation, however some important examples do exist as intermediates in biosynthetic pathways e.g. glutamate-1-semialdehyde. The acyclic forms of certain amino sugars also qualify, for instance vancosamine. Aminoacetaldehyde, the simplest member of this subclass, is highly reactive toward self-condensation.
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The traditional name isopentane was still retained in the 1993 IUPAC recommendations,Table 19(a) Acyclic and monocyclic hydrocarbons. Parent hydrocarbons but is no longer recommended according to the 2013 recommendations. The preferred IUPAC name is the systematic name 2-methylbutane. An isopentyl group is a subset of the generic pentyl group.
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Selectivity is high for the radical addition that leads to the more stable adduct radical, and trans lactones are selectively formed from either cis or trans acyclic alkenes.Fristad, W. E.; Peterson, J. R. J. Org. Chem. 1985, 50, 10. (6)File:MnCoupleScope3.png β-Dicarbonyl compounds are useful substrates for the formation of dihydrofurans.
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Structure of Ru(C6H4)(PMe3)4. Transition metal benzyne complexes are organometallic complexes that contain benzyne ligands (C6H4). Unlike benzyne itself, these complexes are less reactive although they undergo a number of insertion reactions.Buchwald, S. L.; Nielsen, R. B. "Group 4 Metal Complexes of Benzynes, Cycloalkynes, Acyclic Alkynes, and Alkenes" Chem. Rev.
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In organometallic chemistry, the pentadienyl anion is a ligand, the acyclic analogue of the more-common cyclopentadienyl anion. The pentadienyl anion is generated by deprotonation of pentadiene. A number of complexes are known, including bis(pentadienyl) iron, Fe(C5H7)2, the "open" analog of ferrocene. Only few pentadienyl complexes feature simple C5H7 ligands.
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Although not practiced under the name, aromatization is a cornerstone of oil refining. One of the major reforming reactions is the dehydrogenation of naphthenes into aromatics. The process, which is catalyzed by platinum, is exemplified in the conversion methylcyclohexane (a naphthene) into toluene (an aromatic). Dehydrocyclization converts paraffins (acyclic hydrocarbons) into aromatics.
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In an elementary form, the dictionary entries represent nodes in a directed acyclic graph (DAG), that describes the actions of the program, as an abstract syntax tree (AST) in tabular form. It uses an intermediate representation (IR), that is based on the encoded abstract syntax tree and symbol table of a program.
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Graphs in which vertices represent events occurring at a definite time, and where the edges are always point from the early time vertex to a late time vertex of the edge, are necessarily directed and acyclic. The lack of a cycle follows because the time associated with a vertex always increases as you follow any path in the graph so you can never return to a vertex on a path. This reflects our natural intuition that causality means events can only affect the future, they never affect the past, and thus we have no causal loops. An example of this type of directed acyclic graph are those encountered in the causal set approach to quantum gravity though in this case the graphs considered are transitively complete.
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The acyclic chromatic index of a graph G, denoted by a'(G), is the smallest number of colors needed to have a proper acyclic edge coloring of G. It has been conjectured that a'(G) \le \Delta + 2 , where \Delta is the maximum degree of G.; Currently the best known bound is a'(G) \le \lceil 3.74 (\Delta -1) \rceil. The problem becomes easier when G has large girth. More specifically, there is a constant c such that if the girth of G is at least c \Delta \log \Delta, then a'(G) \le \Delta + 2. A similar result is that for all \epsilon > 0 there exists an g such that if G has girth at least g, then a'(G) \le (1+\epsilon) \Delta.
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In the presence of merges, the resulting graph is no longer a tree, as nodes can have multiple parents, but is instead a rooted directed acyclic graph (DAG). The graph is acyclic since parents are always backwards in time, and rooted because there is an oldest version. However, assuming that there is a trunk, merges from branches can be considered as "external" to the tree – the changes in the branch are packaged up as a patch, which is applied to HEAD (of the trunk), creating a new revision without any explicit reference to the branch, and preserving the tree structure. Thus, while the actual relations between versions form a DAG, this can be considered a tree plus merges, and the trunk itself is a line.
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Epoxide opening In a ring-opening, the cleaved molecule remains as a single unit. The bond breaks, but the two fragments remain attached by other parts of the structure. For example, an epoxide ring can be opened by heterolytic cleavage of one of the polar carbon–oxygen bonds to give a single acyclic structure.
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X. The Rule of "Steric Control of Asymmetric Induction" in the Syntheses of Acyclic Systems Donald J. Cram, Fathy Ahmed Abd Elhafez J. Am. Chem. Soc.; 1952; 74(23); 5828-5835. Abstract He published over 350 research papers and eight books on organic chemistry, and taught graduate and post-doctoral students from 21 different countries.
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With the interpretation of strings as connected, directed acyclic graphs of maximum degree one, classical definitions of edit distance such as Levenshtein distance, Hamming distance and Jaro–Winkler distance may be interpreted as graph edit distances between suitably constrained graphs. Likewise, graph edit distance is also a generalization of tree edit distance between rooted trees.
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The edges are therefore known as directed edges. Example of such network include a link from the reference section on this page which will leads you to another, but not the other way around. In terms of food web, a prey eaten by a predator is another example. :Directed networks can be cyclic or acyclic.
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In some cases, tasks depend on each other. These interdependencies can be illustrated by a directed acyclic graph. Intuitively, some tasks cannot begin until others are completed. Assuming that the required time for each of the tasks is known in advance, an optimal execution order must lead to the minimization of the total execution time.
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In a comparison with other methods for drawing directed acyclic graphs, the left-right algorithm (together with a planarization preprocessing step) was found to perform well in terms of the area of the drawings it produces, the number of bends, and the aspect ratio of the drawing, but less well in total edge length.
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Juvenile hormones (JHs) are a group of acyclic sesquiterpenoids that regulate many aspects of insect physiology. The first discovery of a JH was by Vincent Wigglesworth. JHs regulate development, reproduction, diapause, and polyphenisms. In insects, JH (formerly called neotenin) refers to a group of hormones, which ensure growth of the larva, while preventing metamorphosis.
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ADMET copolymerization with Ru catalyst Acyclic diene metathesis (ADMET) is similar to ROMP in that subsequent hydrogenation is required. ADMET requires a certain type of diene in order for the polymerization to occur. Ruthenium complexes can once again be used for ADMET polymerization. In this case, an α,ω-diene monomer with functionality is required.
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Phosphate-activated derivatives of farnesol are the building blocks of possibly all,l acyclic sesquiterpenoids. These compounds are doubled to form 30-carbon squalene, which in turn is the precursors for steroids in plants, animals, and fungi. As such, farnesol and its derivatives are important starting compounds for both natural and artificial organic synthesis.
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Finding a small edge set with this property is a key step in layered graph drawing... Sometimes it is desirable to drop as few edges as possible, obtaining a minimum feedback arc set (MFAS), or dually a maximum acyclic subgraph. This is a hard computational problem, for which several approximate solutions have been devised.
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Vanadium catalyzed epoxidations have been shown to be very sensitive to the steric bulk of the vinyl group. 500px Homoallylic alcohols are effective directing groups for epoxidations in both cyclic and acyclic systems for substrates which show hydrogen bonding. However these reactions tend to have lower levels of selectivity.Johnson, M. R.; Kishi, Y. Tetrahedron Lett., 1979, 4347-4350.
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Heterocyclic compounds can be usefully classified based on their electronic structure. The saturated heterocycles behave like the acyclic derivatives. Thus, piperidine and tetrahydrofuran are conventional amines and ethers, with modified steric profiles. Therefore, the study of heterocyclic chemistry focuses especially on unsaturated derivatives, and the preponderance of work and applications involves unstrained 5- and 6-membered rings.
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PROFINET uses the acyclic slots of the PROFINET communications protocol and does not interfere with co-existing automation processes. The commands are based on the following use cases: Brief pauses (say up to one hour) - In general, such pauses are planned - e.g. lunchtime breaks – enabling devices to be routinely switched off. Safety-related functions are protected.
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PFA tubing is commonly used to handle aggressive chemicals Nafion is a fluoroether with a strongly acidic sulfonic acid substituents Acyclic perfluoroethers are known, e.g. O(C2F5)2, the analogue of diethylether. More interesting and more useful are the cyclic ethers, especially, the epoxides. Thus tetrafluoroethyene oxide and hexafluoropropylene oxide are two of the simplest cyclic perfluoroethers.
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The resulting torsional barriers can be quite large and vary from 12-20 kcal/mol. The interactions are thought to be dependent on the torsional preferences (also known as the gauche effect). The nitrogen atom is usually pyramidal, but cyclic and strongly steric hindered acyclic sulfenamides can display a planar arrangement of bonds around the nitrogen atom.
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The idea of a spanning tree can be generalized to directed multigraphs. Given a vertex v on a directed multigraph G, an oriented spanning tree T rooted at v is an acyclic subgraph of G in which every vertex other than v has outdegree 1. This definition is only satisfied when the "branches" of T point towards v.
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Decomposition methods translate a problem into a new one that is easier to solve. The new problem only contains binary constraints; their scopes form a directed acyclic graph. The variables of the new problem represent each a set of variables of the original one. These sets are not necessarily disjoint, but they cover the set of the original variables.
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There are many synonyms for "cycle graph". These include simple cycle graph and cyclic graph, although the latter term is less often used, because it can also refer to graphs which are merely not acyclic. Among graph theorists, cycle, polygon, or n-gon are also often used. The term n-cycle is sometimes used in other settings.
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As a qualitative property, liveness of a FD- DEVS network is decidable by (1) generating RG of the given network, (2) from RG, generating kernel directed acyclic graph (KDAG) in which a vertex is strongly connected component, and (3) checking if a vertex of KDAG contains a state transition cycle which contains a set of liveness states[HZ06b].
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Phytol is an acyclic diterpene alcohol that can be used as a precursor for the manufacture of synthetic forms of vitamin E and vitamin K1. In ruminants, the gut fermentation of ingested plant materials liberates phytol, a constituent of chlorophyll, which is then converted to phytanic acid and stored in fats. In shark liver it yields pristane.
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Circular dependency example In this UML package diagram, package A depends on packages B and C. Package B in turn depends on package D, which depends on package C, which in turn depends on package B. The latter three dependencies create a cycle, which must be broken in order to adhere to the acyclic dependencies principle.
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Azure Data Lake Analytics is a parallel on-demand job service. The parallel processing system is based on the Microsoft Dryad solution. Dryad can represent arbitrary Directed Acyclic Graphs (DAGs) of computation. Data Lake Analytics provides a distributed infrastructure that can dynamically allocate or de-allocate resources so customers pay for only the services they use.
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Each finite language is generated by a trie automaton, and each trie can be compressed into a deterministic acyclic finite state automaton. Though tries can be keyed by character strings, they need not be. The same algorithms can be adapted to serve similar functions on ordered lists of any construct; e.g., permutations on a list of digits or shapes.
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Note that a resolution proof can be seen as a general directed acyclic graph as opposed to a tree. After the recursive call the clause of the present node is updated. While doing so four different cases can occur. The present pivot variable can occur in both, the left, the right or in none of the parent nodes.
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The cyclic 1,3-dipolar form is detectably or exclusively formed with phosphite and phosphonite-based analogs. Triphenylphosphine-based variants lack sufficient tendency for intramolecular cyclization, and exist as acyclic phosphonium ylides.St. Cyr, D. J.; Arndtsen, B. A., A New Use of Wittig-type Reagents as 1,3-Dipolar Cycloaddition Precursors and in Pyrrole Synthesis. J. Am. Chem. Soc.
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Biological ontologies are directed acyclic graphs of controlled vocabularies. They are designed to capture biological concepts and descriptions in a way that can be easily categorised and analysed with computers. When categorised in this way, it is possible to gain added value from holistic and integrated analysis. The OBO Foundry was an effort to standardise certain ontologies.
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The program evaluation and review technique (PERT) uses DAGs to model the milestones and activities of large human projects, and schedule these projects to use as little total time as possible. Combinational logic blocks in electronic circuit design, and the operations in dataflow programming languages, involve acyclic networks of processing elements. DAGs can also represent collections of events and their influence on each other, either in a probabilistic structure such as a Bayesian network or as a record of historical data such as family trees or the version histories of distributed revision control systems. DAGs can also be used as a compact representation of sequence data, such as the directed acyclic word graph representation of a collection of strings, or the binary decision diagram representation of sequences of binary choices.
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The Coffman–Graham algorithm performs the following steps. #Represent the partial order by its transitive reduction or covering relation, a directed acyclic graph that has an edge from x to y whenever and there does not exist any third element of the partial order for which . In the graph drawing applications of the Coffman–Graham algorithm, the resulting directed acyclic graph may not be the same as the graph being drawn, and in the scheduling applications it may not have an edge for every precedence constraint of the input: in both cases, the transitive reduction removes redundant edges that are not necessary for defining the partial order. #Construct a topological ordering of in which the vertices are ordered lexicographically by the set of positions of their incoming neighbors.
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Time-order between two operations can be represented by an ordered pair of these operations (e.g., the existence of a pair (OP1, OP2) means that OP1 is always before OP2), and a schedule in the general case is a set of such ordered pairs. Such a set, a schedule, is a partial order which can be represented by an acyclic directed graph (or directed acyclic graph, DAG) with operations as nodes and time-order as a directed edge (no cycles are allowed since a cycle means that a first (any) operation on a cycle can be both before and after (any) another second operation on the cycle, which contradicts our perception of Time). In many cases, a graphical representation of such a graph is used to demonstrate a schedule.
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The transition graph T_I of an instance I of a problem L is a directed graph. The nodes represent all elements of the finite set of solutions F_L(I) and the edges point from one solution to the neighbor with strictly better cost. Therefore it is an acyclic graph. A sink, which is a node with no outgoing edges, is a local optimum.
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The Mumm rearrangement is an organic reaction and a rearrangement reaction.Mumm, O. Ber. Dtsch. Chem. Ges. 1910, 43, 886-893Preparation of acyclic isoimides and their rearrangement rates to imides J. S. Paul Schwarz J. Org. Chem.; 1972; 37(18) pp 2906 - 2908; It describes a 1,3(O-N) acyl transfer of an acyl imidate or isoimide group to an imide.
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Usually for acyclic systems trans isomers are more stable than cis isomers. This is typically due to the increased unfavorable steric interaction of the substituents in the cis isomer. Therefore, trans isomers have a less- exothermic heat of combustion, indicating higher thermochemical stability. In the Benson heat of formation group additivity dataset, cis isomers suffer a 1.10 kcal/mol stability penalty.
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The first is the stabilization of the transition state as a result of the hydrogen bonding. The second is the electron-withdrawing nature of the oxygen, which draws electron density away from the alkene, lowering its reactivity. 500px Acyclic allylic alcohols exhibit good selectivity as well. In these systems both A1,2 (steric interactions with vinyl) and A1,3 strain are considered.
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The problem of listing all answers to a non-Boolean conjunctive query has been studied in the context of enumeration algorithms, with a characterization (under some computational hardness assumptions) of the queries for which enumeration can be performed with linear time preprocessing and constant delay between each solution. Specifically, these are the acyclic conjunctive queries which also satisfy a free-connex condition.
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1-Hydroxycarotenoid 3,4-desaturase (, CrtD, hydroxyneurosporene desaturase, carotenoid 3,4-dehydrogenase, 1-hydroxy-carotenoid 3,4-dehydrogenase) is an enzyme with systematic name 1-hydroxy-1,2-dihydrolycopene:acceptor oxidoreductase. This enzyme catalyses the following chemical reaction : 1-hydroxy-1,2-dihydrolycopene + acceptor \rightleftharpoons 1-hydroxy-3,4-didehydro-1,2-dihydrolycopene + reduced acceptor The enzymes from Rubrivivax gelatinosus and Rhodobacter sphaeroides acts primarily on acyclic carotenoids.
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Acyclovir is a synthetic acyclic purine nucleoside that has strong activity against certain members of the herpesvirus group. It is given to birds in the form of oral administration for numerous days or in an IV form. Acyclovir has decreased morbidity and mortality during multiple Pacheco’s disease outbreaks. However, it cannot prevent the establishment of the carrier and latent infections.
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As defined by IUPAC nomenclature of organic chemistry, the classifications for hydrocarbons are: #Saturated hydrocarbons are the simplest of the hydrocarbon species. They are composed entirely of single bonds and are saturated with hydrogen. The formula for acyclic saturated hydrocarbons (i.e., alkanes) is CH. The most general form of saturated hydrocarbons is CH, where r is the number of rings.
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Let G be an acyclic causal graph (a graph in which each node appears only once along any path) with vertex set V and let P be a probability distribution over the vertices in V generated by G. G and P satisfy the Causal Markov Condition if every node X in V is independent of NonDescendants(X) given Parents(X).
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The Hierarchy Open Service Interface Definition (OSID) is an Open Knowledge Initiative specification. OSIDs are programmatic interfaces which comprise a Service Oriented Architecture for designing and building reusable and interoperable software. The Hierarchy OSID which provides a means of creating and traversing hierarchical structures of various types. These types include trees, forests, directed graphs with multiple parents, and directed acyclic graphs.
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MapReduce tasks must be written as acyclic dataflow programs, i.e. a stateless mapper followed by a stateless reducer, that are executed by a batch job scheduler. This paradigm makes repeated querying of datasets difficult and imposes limitations that are felt in fields such as machine learning, where iterative algorithms that revisit a single working set multiple times are the norm.
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Though technically distinct from the alkanes, this class of hydrocarbons is referred to by some as the "cyclic alkanes." As their description implies, they contain one or more rings. Simple cycloalkanes have a prefix "cyclo-" to distinguish them from alkanes. Cycloalkanes are named as per their acyclic counterparts with respect to the number of carbon atoms in their backbones, e.g.
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2003 (Ambleside, UK): Guillaume Marrelec, INSERM, France. G. Marrelec, P. Ciuciu, M. Pélégrini-Issac, H. Benali: Estimation of the hemodynamic response function in event-related functional MRI: directed acyclic graphs for a general Bayesian inference framework. 2005 (Glenwood Springs, Colorado, USA): Duygu Tosun, Johns Hopkins University, Baltimore, USA. D. Tosun, J.L. Prince: Cortical surface alignment using geometry driven multispectral optical flow.
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Dhrupad music is primarily devotional in theme and content. It contains recitals in praise of particular deities. Dhrupad compositions begin with a relatively long and acyclic alap, where the syllables of the following mantra is recited: > "Om Anant tam Taran Tarini Twam Hari Om Narayan, Anant Hari Om Narayan". The alap gradually unfolds into more rhythmic jod and jhala sections.
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Acyclic unsaturated substrates (olefins, ketones, enamines imines) represents the most common prochiral substrates. Substrates that are particularly amenable to asymmetric hydrogenation often feature a polar functional group adjacent to the site to be hydrogenates. In the absence of this functional) group, catalysis often results in low ee's. For unfunctionalized olefins, iridium with P,N-based ligands) have proven successful catalysts.
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Triazane is an inorganic compound with the chemical formula or .IUPAC Goldbook Triazane is the third simplest acyclic azane after ammonia and hydrazine. It can be synthesized from hydrazine but is unstable and cannot be isolated in the free base form, only as salt forms such as triazanium sulfate. Attempts to convert triazanium salts to the free base release only diazene and ammonia.
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As in the above example, there is usually some cost associated with removing an edge. For this reason, we'd like to remove as few edges as possible. Removing one edge suffices in a simple cycle, but in general figuring out the minimum number of edges to remove is an NP-hard problem called the minimum feedback arc set or maximum acyclic subgraph problem.
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Hashgraph is a distributed ledger technology developed by Leemon Baird, the co-founder and CTO of Swirlds, in 2016. It is an asynchronous Byzantine Fault Tolerance (aBFT) consensus algorithm that they consider capable of securing the platform against attacks. It does not use miners to validate transactions, and uses directed acyclic graphs for time-sequencing transactions without bundling them into blocks.
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316-317 These grammars were introduced by Dahlhaus and Warmuth.. Here: p.197-198 They were later shown to be equivalent to the acyclic context-sensitive grammars. Membership in any growing context- sensitive language is polynomial time computable; Here: p.85-86 however, the uniform problem of deciding whether a given string belongs to the language generated by a given growingG.
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Every complete graph is a comparability graph, the comparability graph of a total order. All acyclic orientations of a complete graph are transitive. Every bipartite graph is also a comparability graph. Orienting the edges of a bipartite graph from one side of the bipartition to the other results in a transitive orientation, corresponding to a partial order of height two.
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A graph is formed by vertices and by edges connecting pairs of vertices, where the vertices can be any kind of object that is connected in pairs by edges. In the case of a directed graph, each edge has an orientation, from one vertex to another vertex. A path in a directed graph is a sequence of edges having the property that the ending vertex of each edge in the sequence is the same as the starting vertex of the next edge in the sequence; a path forms a cycle if the starting vertex of its first edge equals the ending vertex of its last edge. A directed acyclic graph is a directed graph that has no cycles.... Adding the red edges to the blue directed acyclic graph produces another DAG, the transitive closure of the blue graph.
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For instance, the number of strong orientations is and the number of acyclic orientations is .. For bridgeless planar graphs, graph colorings with colors correspond to nowhere- zero flows modulo on the dual graph. For instance, the four color theorem (the existence of a 4-coloring for every planar graph) can be expressed equivalently as stating that the dual of every bridgeless planar graph has a nowhere-zero 4-flow. The number of -colorings is counted (up to an easily computed factor) by the Tutte polynomial value and dually the number of nowhere-zero -flows is counted by . An st-planar graph is a connected planar graph together with a bipolar orientation of that graph, an orientation that makes it acyclic with a single source and a single sink, both of which are required to be on the same face as each other.
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This walk is a path if it does not repeat any edges, arcs, or vertices, except possibly the first and last vertices. A path is closed if its first and last vertices are the same, and a closed path is a cycle if it does not repeat vertices, except the first and the last. A mixed graph is acyclic if it does not contain a cycle.
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Work stealing is designed for a "strict" fork–join model of parallel computation, which means that a computation can be viewed as a directed acyclic graph with a single source (start of computation) and a single sink (end of computation). Each node in this graph represents either a fork or a join. Forks produce multiple logically parallel computations, variously called "threads" or "strands". Edges represent serial computation.
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Chemotypes found in Melaleuca quinquenervia M. quinquenervia have been shown to occur in distinct chemical forms. These forms or chemotypes are characterised by the organic compounds terpenes. Chemotype 1 has acyclic foliar terpenes, with concentrations of sesquiterpene E-nerolidol 74–95% of total oil and also monoterpene linalool. Chemotype 2 has high concentration of cyclic foliar terpenes, in particular sesquiterpene viridiflorol with 13-66% of total oil.
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Isoprenoid monoterpenes are present in grape, above all acyclic linalool, geraniol, nerol, citronellol, homotrienol and monocyclic α-terpineol, mostly occurring as glycosides. Carotenoids accumulate in ripening grape berries. Oxidation of carotenoids produces volatile fragments, C13-norisoprenoids. These are strongly odoriferous compounds, such as β-ionone (aroma of viola), damascenone (aroma of exotic fruits), β-damascone (aroma of rose) and β-ionol (aroma of flowers and fruits).
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The formation of the hopene skeleton is one of the most complex single step reactions in biochemistry. In a single step, 13 covalent bonds are broken or formed, 9 chiral centers are established, and 5 rings are produced. Squalene–hopene cyclase catalyses the conversion of the acyclic molecule of squalene into the pentacyclic triterpenes of hopene and hopanol. These products appear in the ratio 5:1.
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Deprotonation of carbene precursor salts with strong bases has proved a reliable route to almost all stable carbenes: Deprotonation of precursor salts to give stable carbenes. Imidazol-2-ylidenes and dihydroimidazol-2-ylidenes, e.g. IMes, have been prepared by the deprotonation of the respective imidazolium and dihydroimidazolium salts. The acyclic carbenes and the tetrahydropyrimidinyl based carbenes were prepared by deprotonation using strong homogeneous bases.
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A polytree, a directed acyclic graph formed by assigning an orientation to each edge of an undirected tree, may be viewed as a special case of a multitree. The set of all vertices connected to any vertex in a multitree forms an arborescence. The word "multitree" has also been used to refer to a series-parallel partial order,. or to other structures formed by combining multiple trees.
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Some, such as dot, neato, twopi, circo, fdp, and sfdp, can read a DOT file and render it in graphical form. Others, such as gvpr, gc, acyclic, ccomps, sccmap, and tred, read DOT files and perform calculations on the represented graph. Finally, others, such as lefty, dotty, and grappa, provide an interactive interface. The GVedit tool combines a text editor with noninteractive image viewer.
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International Union of Pure and Applied Chemistry defines alkanes as "acyclic branched or unbranched hydrocarbons having the general formula n2n+2, and therefore consisting entirely of hydrogen atoms and saturated carbon atoms". However, some sources use the term to denote any saturated hydrocarbon, including those that are either monocyclic (i.e. the cycloalkanes) or polycyclic, despite their having a distinct general formula (i.e. cycloalkanes are CnH2n).
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For example, Java allows a class to implement multiple interfaces, but only inherit from one class. If multiple inheritance is allowed, the hierarchy is a directed acyclic graph (or DAG for short), otherwise it is a tree. The hierarchy has classes as nodes and inheritance relationships as links. Classes in the same level are more likely to be associated than classes in different levels.
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In general, the corresponding graphs may contain cycles. A preorder that is antisymmetric no longer has cycles; it is a partial order, and corresponds to a directed acyclic graph. A preorder that is symmetric is an equivalence relation; it can be thought of as having lost the direction markers on the edges of the graph. In general, a preorder's corresponding directed graph may have many disconnected components.
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Cyclic α,β-unsaturated ketones are the most commonly employed substrates for vicinal difunctionalization. They tend to be more reactive than acyclic analogues and undergo less direct addition than aldehydes. Amides and esters can be used to encourage conjugate addition in cases when direct addition may be competitive (as in the addition of organolithium compounds).Franck, W.; Bhat, V.; Subramanian, S. J. Am. Chem. Soc.
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The name of CH2=CH2 is therefore ethENe. For straight-chain alkenes with 4 or more carbon atoms, that name does not completely identify the compound. For those cases, and for branched acyclic alkenes, the following rules apply: # Find the longest carbon chain in the molecule. If that chain does not contain the double bond, name the compound according to the alkane naming rules.
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They can be pooling, where a group of neurons in one layer connect to a single neuron in the next layer, thereby reducing the number of neurons in that layer. Neurons with only such connections form a directed acyclic graph and are known as feedforward networks. Alternatively, networks that allow connections between neurons in the same or previous layers are known as recurrent networks'.
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If storing dictionary words is all that is required (i.e., storage of information auxiliary to each word is not required), a minimal deterministic acyclic finite state automaton (DAFSA) would use less space than a trie or a ternary search tree. This is because a DAFSA can compress identical branches from the trie which correspond to the same suffixes (or parts) of different words being stored.
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See also Outer automorphism group. Notice that in an exact sequence, the composition fi+1 ∘ fi maps Ai to 0 in Ai+2, so every exact sequence is a chain complex. Furthermore, only fi-images of elements of Ai are mapped to 0 by fi+1, so the homology of this chain complex is trivial. More succinctly: :Exact sequences are precisely those chain complexes which are acyclic.
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3390/molecules25071526 # Yates MK, Chatterjee P, Flint M, et al. Probing the Effects of Pyrimidine Functional Group Switches on Acyclic Fleximer Analogues for Antiviral Activity. Molecules. 2019;24(17):3184. Published 2019 Sep 2. # Ku T, Lopresti N, Shirley M, et al. Synthesis of distal and proximal fleximer base analogues and evaluation in the nucleocapsid protein of HIV-1. Bioorg Med Chem. 2019;27(13):2883‐2892.
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In analogy to Kuratowski's and Wagner's characterizations of the planar graphs as being the graphs that do not contain K5 or K3,3 as a minor, the linklessly embeddable graphs may be characterized as the graphs that do not contain as a minor any of the seven graphs in the Petersen family. In analogy to the characterizations of the outerplanar and planar graphs as being the graphs with Colin de Verdière graph invariant at most two or three, the linklessly embeddable graphs are the graphs that have Colin de Verdière invariant at most four. An upward planar graph is a directed acyclic graph that can be drawn in the plane with its edges as non-crossing curves that are consistently oriented in an upward direction. Not every planar directed acyclic graph is upward planar, and it is NP-complete to test whether a given graph is upward planar.
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Trees are a special case of bipartite graphs, and testing whether a tree is well-covered can be handled as a much simpler special case of the characterization of well- covered bipartite graphs: if is a tree with more than two vertices, it is well-covered if and only if each non-leaf node of the tree is adjacent to exactly one leaf. The same characterization applies to graphs that are locally tree-like, in the sense that low-diameter neighborhoods of every vertex are acyclic: if a graph has girth eight or more (so that, for every vertex , the subgraph of vertices within distance three of is acyclic) then it is well- covered if and only if every vertex of degree greater than one has exactly one neighbor of degree one.; , Theorem 4.1. A closely related but more complex characterization applies to well-covered graphs of girth five or more.
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Grignard reagents are prepared by treating an organic halide (normally organobromine) with magnesium metal. Cyclic or acyclic ethers are required to stabilize the organomagnesium compound. Water and air, which rapidly destroy the reagent by protonolysis or oxidation, are excluded using air-free techniques. Although the reagents still need to be dry, ultrasound can allow Grignard reagents to form in wet solvents by activating the magnesium such that it consumes the water.
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Another difference is that the barrelene reaction requires the triplet excited state while the Mariano and Pratt acyclic dienes used the excited singlet. Thus acetone is used in the barrelene reaction; acetone captures the light and then delivers triplet excitation to the barrelene reactant. In the final step of the rearrangement there is a spin- flip, termed intersystem-crossing (ISC) to provide paired electrons and a new sigma bond. Equation 3.
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In fact, it turns out that the query containment problem for conjunctive queries is exactly the same problem as the query evaluation problem. Since queries tend to be small, NP-completeness here is usually considered acceptable. The query containment problem for conjunctive queries is also equivalent to the constraint satisfaction problem. An important class of conjunctive queries that have polynomial-time combined complexity are the acyclic conjunctive queries.
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Acetamiprid is an alpha-Chloro-N-heteroaromatic compound. It is a neonicotinoid with a chloropyridinyl group and it is comparable to other neonicotinoids such as imidacloprid, nitenpyram and thiacloprid. These substances all have a 6-chloro-3-pyridine methyl group but differ in the nitroguanidine, nitromethylene, or cyanoamidine substituent on an acyclic or cyclic moiety. There are two isomeric forms in acetamiprid with E and Z-configurations of the cyanoimino group.
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This means that there are individuals who belong to the intersection ("collegium") of all decisive coalitions. If there is someone who has a veto, then he belongs to the collegium. If the rule is assumed to be neutral, then it does have someone who has a veto. Finally, Brown's theorem left open the case of acyclic social preferences where the number of alternatives is less than the number of individuals.
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Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled. Both finite impulse and infinite impulse recurrent networks can have additional stored states, and the storage can be under direct control by the neural network.
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After desaturation, lycopene cyclase first forms γ-carotene by converting one of the ψ acyclic ends of the lycopene as a β-ring, then subsequently converts the other to form β-carotene. From β-carotene, hydrolases (blue) are responsible for the inclusion of two 3-hydroxy groups, and ketolases (green) for the addition of two 4-keto groups, forming multiple intermediate molecules until the final molecule, astaxanthin, is obtained.
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ASTs are trees and are thus incapable of representing shared terms. ASGs are usually directed acyclic graphs (DAG), although in some applications graphs containing cycles may be permitted. For example, a graph containing a cycle might be used to represent the recursive expressions that are commonly used in functional programming languages as non-looping iteration constructs. The mutability of these types of graphs, is studied in the field of graph rewriting.
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He has constructed various beautiful examples of topological spaces, e.g. an acyclic, 3-dimensional continuum which admits a fixed point free homeomorphism onto itself; also 2-dimensional, contractible polyhedra which have no free edge. His topological and geometric conjectures and themes stimulated research for more than half a century. Borsuk received his master's degree and doctorate from Warsaw University in 1927 and 1930, respectively; his Ph.D. thesis advisor was Stefan Mazurkiewicz.
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It is NP-hard to determine whether a given graph has a RAC drawing with straight edges, even if the input graph is 1-planar and the output RAC drawing must be 1-planar as well. The RAC drawing problem remains NP-hard for upward drawing of directed acyclic graphs.. However, in the special case of outer-1-planar graphs, a RAC drawing can be constructed in linear time.
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According to Reike, traditional blockchain technology has some shortcomings such as scalability, which led the founders of nakamo.to to focus on their new project peaq that is based on directed acyclic graphs (DAG). DAGs are a DLT System that for example the cryptocurrency IOTA is based on. Reike invested in IOTA as a student and when Robert Küfner first approached him in Berlin, Reike introduced him to IOTA.
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In mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups of a product space X \times Y and those of the spaces X and Y. The theorem first appeared in a 1953 paper in the American Journal of Mathematics by Samuel Eilenberg and Joseph A. Zilber. One possible route to a proof is the acyclic model theorem.
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When measured both in terms of the number n of vertices and the number m of edges in a directed acyclic graph, transitive reductions can also be found in time O(nm), a bound that may be faster than the matrix multiplication methods for sparse graphs. To do so, apply a linear time longest path algorithm in the given directed acyclic graph, for each possible choice of starting vertex. From the computed longest paths, keep only those of length one (single edge); in other words, keep those edges (u,v) for which there exists no other path from u to v. This O(nm) time bound matches the complexity of constructing transitive closures by using depth first search or breadth first search to find the vertices reachable from every choice of starting vertex, so again with these assumptions transitive closures and transitive reductions can be found in the same amount of time.
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It was originally used to describe the complex mixture of petroleum-based acids when the analytical methods available in the early 1900s could identify only a few naphthene-type components with accuracy. Today "naphthenic" acid is used in a more generic sense to refer to all of the carboxylic acids present in petroleum, whether cyclic, acyclic, or aromatic compounds, and carboxylic acids containing heteroatoms such as N and S. Although commercial naphthenic acids often contain a majority of cycloaliphatic acids, multiple studies have shown they also contain straight chain and branched aliphatic acids and aromatic acids; some naphthenic acids contain >50% combined aliphatic and aromatic acids. Naphthenic acids are represented by a general formula CnH2n-z O2, where n indicates the carbon number and z specifies a homologous series. The z is equal to 0 for saturated, acyclic acids and increases to 2 in monocyclic naphthenic acids, to 4 in bicyclic naphthenic acids, to 6 in tricyclic acids, and to 8 in tetracyclic acids.
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Local search usually works on all variables, improving a complete assignment to them. However, local search can also be run on a subset of variables, using some other mechanism for the other variables. A proposed algorithm works on a cycle cutset, which is a set of variables that, if removed from the problem, makes it acyclic. For any assignment of the variables of the cutset, the remaining problem has a forest as primal graph.
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2-Butene is an acyclic alkene with four carbon atoms. It is the simplest alkene exhibiting cis/trans-isomerism (also known as (E/Z)-isomerism); that is, it exists as two geometric isomers cis-2-butene ((Z)-2-butene) and trans-2-butene ((E)-2-butene). It is a petrochemical, produced by the catalytic cracking of crude oil or the dimerization of ethylene. Its main uses are in the production of gasoline (petrol) and butadiene,.
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Mixed graphs are also used as graphical models for Bayesian inference. In this context, an acyclic mixed graph (one with no cycles of directed edges) is also called a chain graph. The directed edges of these graphs are used to indicate a causal connection between two events, in which the outcome of the first event influences the probability of the second event. Undirected edges, instead, indicate a non-causal correlation between two events.
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The naturally occurring form of glucose is -glucose, while -glucose is produced synthetically in comparatively small amounts and is of lesser importance. Glucose is a monosaccharide containing six carbon atoms and an aldehyde group, and is therefore an aldohexose. The glucose molecule can exist in an open-chain (acyclic) as well as ring (cyclic) form. Glucose is naturally occurring and is found in fruits and other parts of plants in its free state.
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An output of a quantitative historical linguistic analysis is normally a tree or a network diagram. This allows summary visualisation of the output data but is not the complete result. A tree is a connected acyclic graph, consisting of a set of vertices (also known as "nodes") and a set of edges ("branches") each of which connects a pair of vertices. An internal node represents a linguistic ancestor in a phylogenic tree or network.
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For example, "car" is similar to "bus", but is also related to "road" and "driving". Computationally, semantic similarity can be estimated by defining a topological similarity, by using ontologies to define the distance between terms/concepts. For example, a naive metric for the comparison of concepts ordered in a partially ordered set and represented as nodes of a directed acyclic graph (e.g., a taxonomy), would be the shortest- path linking the two concept nodes.
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16 bits are available for cyclic transmission using ASi-5. A cyclic transmission of up to 32 bytes per participant is possible. An acyclic parameter channel with up to 256 bytes is available for each device as well. ASi-5 is to provide a set of up to 1536 binary inputs and 1536 binary outputs per Ethernet address. 1.2 ms cycle time can be achieved by the system for up to 24 participants.
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Device diagnostics provides information about the connected device. The available diagnostics data are determined by the device manufacturer. Diagnostic data can be transmitted via the acyclic services with a data width of up to 256 bytes. The ASi-5 system is open for the use of parameter interfaces such as e.g. IO-Link. IO-Link devices can be efficiently collected over long distances and could be integrated cyclically up to 32 bytes.
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Acyclic diene metathesis or ADMET (distinguish from ADME) is a special type of olefin metathesis used to polymerize terminal dienes to polyenes: ADMET The new double bonds formed can be in cis- or trans-configurations. The exact ratio depends on the identities of the monomer and catalyst. ADMET is a type of step-growth, condensation polymerization. It should be distinguished from ring-opening metathesis polymerization (ROMP), which is a chain-growth, addition polymerization.
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Structure of dicarbonate (PhOC(O)OC6H4)2CMe2 derived from bis(phenol-A) and two equivalents of phenol. Carbonate esters have planar OC(OC)2 cores, which confers rigidity. The unique O=C bond is short (1.173 Å in the depicted example), while the C-O bonds are more ether- like (the bond distances of 1.326 Å for the example depicted). Carbonate esters can be divided into three structural classes: acyclic, cyclic, and polymeric.
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This unique formation of cyclic and acyclic acetals leads to varying degradation time because the two acetal groups hydrolyze at different rates. Acetalated dextran's degradation time can vary from hours to a month or more at pH 7.2. Also, acetalated dextran is unique because it is acid sensitive. Therefore, at lower pH acetalated dextran degrades more rapidly, which results in a polymer that degrades approximately two logs faster at pH 5 compared to pH 7.
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In the resulting graph for the locked pairs, the source corresponds to the winner. A source is bound to exist because the graph is a directed acyclic graph by construction, and such graphs always have sources. In the absence of pairwise ties, the source is also unique (because whenever two nodes appear as sources, there would be no valid reason not to connect them, leaving only one of them as a source).
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One possible generalization of a hypergraph is to allow edges to point at other edges. There are two variations of this generalization. In one, the edges consist not only of a set of vertices, but may also contain subsets of vertices, subsets of subsets of vertices and so on ad infinitum. In essence, every edge is just an internal node of a tree or directed acyclic graph, and vertices are the leaf nodes.
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Microsoft made several preview releases of this technology available as add-ons to Windows HPC Server 2008 R2. An application written for Dryad is modeled as a directed acyclic graph (DAG). The DAG defines the dataflow of the application, and the vertices of the graph defines the operations that are to be performed on the data. The "computational vertices" are written using sequential constructs, devoid of any concurrency or mutual exclusion semantics.
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In computer science, a graph-structured stack (GSS) is a directed acyclic graph where each directed path represents a stack. The graph-structured stack is an essential part of Tomita's algorithm, where it replaces the usual stack of a pushdown automaton. This allows the algorithm to encode the nondeterministic choices in parsing an ambiguous grammar, sometimes with greater efficiency. In the following diagram, there are four stacks: {7,3,1,0}, {7,4,1,0}, {7,5,2,0}, and {8,6,2,0}.
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According to definition from IUPAC ring-opening polymerization is a polymerization in which a cyclic monomer yields a monomeric unit which is acyclic or contains fewer cycles than the monomer. Generally, the ring-opening polymerization is carried out under mild conditions, and the by-product is less than the polycondensation reaction and the high molecular weight polymer is easily obtained. Common ring-opening polymerization products includes polypropylene oxide, polytetrahydrofuran, polyepichlorohydrin, polyoxymethylene, polycaprolactam and polysiloxane.
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The feedback vertex set problem can be solved in polynomial time on graphs of maximum degree at most three.; Note that the problem of deleting as few edges as possible to make the graph cycle-free is equivalent to finding a spanning tree, which can be done in polynomial time. In contrast, the problem of deleting edges from a directed graph to make it acyclic, the feedback arc set problem, is NP-complete.
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Determinant of an integral matrix can be reduced to finding the difference between the number of accepting and rejecting paths on a polynomially sized directed acyclic graph with distinguished start, accept, and reject nodes. Comparing the number of accepting and rejecting paths can be done in PL as follows. Modify the graph to make all paths the same length and for each node to have at most two successors. Take a random path.
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Older techniques for matching strings include: suffix arrays, suffix trees, suffix automata or directed acyclic word graphs, and factor automata (Allauzen, Crochemore, Raffinot, 1999). In 1999, Allauzen, Crochemore, and Raffinot, presented the factor oracle algorithm as a memory efficient improvement upon these older techniques for string matching and compression. Starting in the mid-2000s, factor oracles have found application in computer music, as well.Assayag G., Dubnov S., Using Factor Oracles for Machine Improvisation.
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Abstract Meaning Representation (AMR) is a semantic representation language. AMR graphs are rooted, labeled, directed, acyclic graphs (DAGs), comprising whole sentences. They are intended to abstract away from syntactic representations, in the sense that sentences which are similar in meaning should be assigned the same AMR, even if they are not identically worded. By nature, the AMR language is biased towards English – it is not meant to function as an international auxiliary language.
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Good leaving groups for this process include hydroxide, alkoxides, carboxylates, and enolates. Readily available cyclic starting materials may be used to generate stereodefined acyclic products, which would be difficult to access by other methods. (9)File:SmI2Scope2.png Samarium iodide may be used to reduce ketones and aldehydes to alcohols; however, diastereoselectivity is low and a variety of more stereoselective methods exist. Aldehydes may be selectively reduced in the presence of ketones. (10)File:SmI2Scope3.
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To prove that transitive reduction is as hard as transitive closure, Aho et al. construct from a given directed acyclic graph G another graph H, in which each vertex of G is replaced by a path of three vertices, and each edge of G corresponds to an edge in H connecting the corresponding middle vertices of these paths. In addition, in the graph H, Aho et al. add an edge from every path start to every path end.
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Link/cut trees can be used to solve the dynamic connectivity problem for acyclic graphs. Given two nodes x and y, they are connected if and only if FindRoot(x) = FindRoot(y). Another data structure that can be used for the same purpose is Euler tour tree. In solving the maximum flow problem, link/cut trees can be used to improve the running time of Dinic's algorithm from O(V^2 E) to O(VE \log V).
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So a perfect citation graph is an example of a directed acyclic graph. In practice this is not always true, for instance an academic paper goes through several versions in the publishing process and it may be possible to update bibliographies at different times in such a way to lead to edges that apparently point forward in time. However, in practice it appears such citations are often less than 1% of the total number of links.
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Spheroidene monooxygenase (, CrtA, acyclic carotenoid 2-ketolase, spirilloxantin monooxygenase, 2-oxo-spirilloxanthin monooxygenase) is an enzyme with systematic name spheroidene,reduced-ferredoxin:oxygen oxidoreductase (spheroiden-2-one-forming). This enzyme catalyses the following chemical reaction : spheroidene + reduced ferredoxin + O2 \rightleftharpoons spheroiden-2-one + oxidized ferredoxin + H2O : spirilloxantin + reduced ferredoxin + O2 \rightleftharpoons 2-oxospirilloxanthin + oxidized ferredoxin + H2O : 2'-oxospirilloxanthin + reduced ferredoxin + O2 \rightleftharpoons 2,2'-dioxospirilloxanthin + oxidized ferredoxin + H2O The enzyme is involved in spheroidenone biosynthesis and in 2,2'-dioxospirilloxanthin biosynthesis.
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Example of a non-linear video editing studio Non-linear editing is a form of offline editing for audio, video, and image editing. In offline editing, the original content is not modified in the course of editing. In non-linear editing, edits are specified and modified by specialized software. A pointer- based playlist, effectively an edit decision list (EDL), for video and audio, or a directed acyclic graph for still images, is used to keep track of edits.
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Nano (NANO), formerly RaiBlocks (XRB), is a peer-to-peer digital currency. It is a decentralized, open-source cryptocurrency based on directed acyclic graph (DAG) architecture, and released under the FreeBSD License. It operates without intermediaries by utilizing a distributed ledger with a block-lattice data structure. Nano was launched in October 2015 by Colin LeMahieu, with the aim of addressing blockchain scalability limitations that can result in restrictive fees and increased transaction confirmation times under load.
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Cram and Reetz demonstrated that 1,3-stereocontrol is possible if the reaction proceeds through an acyclic transition state. The reaction of β-alkoxy aldehyde with allyltrimethylsilane showed good selectivity for the anti-1,3-diol, which was explained by the Cram polar model. The polar benzyloxy group is oriented anti to the carbonyl to minimize dipole interactions and the nucleophile attacks anti- to the bulkier (RM) of the remaining two substituents.Leitereg, T.J.; Cram, D.J. J. Am. Chem. Soc.
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It collapses the ancestor tree into a directed acyclic graph. In some cultures, cousins and other relations were permitted, encouraged, or required to marry. This may have been to keep kin bonds, wealth and property within a family (endogamy) or simply because there was a limited number of potential marriage partners available. Among royalty, the frequent requirement to marry only other royals resulted in a reduced gene pool in which most individuals were the result of extensive pedigree collapse.
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In contrast to the group lasso problem, where features are grouped into disjoint blocks, it may be the case that grouped features are overlapping or have a nested structure. Such generalizations of group lasso have been considered in a variety of contexts. For overlapping groups one common approach is known as latent group lasso which introduces latent variables to account for overlap. Nested group structures are studied in hierarchical structure prediction and with directed acyclic graphs.
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When represented as a tree, we can think of innermost reduction as working from the bottom up, while outermost works from the top down. The expression can also be represented as a directed acyclic graph, allowing sub-expressions to be shared: 300px As for trees, outermost and innermost reduction also applies to graphs. Hence we have graph reduction. Now evaluation with outermost graph reduction can proceed as follows: 200px Notice that evaluation now only requires four steps.
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A forest is an undirected graph in which any two vertices are connected by at most one path. Equivalently, a forest is an undirected acyclic graph. Equivalently, a forest is an undirected graph, all of whose connected components are trees; in other words, the graph consists of a disjoint union of trees. As special cases, the order-zero graph (a forest consisting of zero trees), a single tree, and an edgeless graph, are examples of forests.
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A Java 3D scene graph is a directed acyclic graph (DAG). Compared to other solutions, Java 3D is not only a wrapper around these graphics APIs, but an interface that encapsulates the graphics programming using a true object-oriented approach. Here a scene is constructed using a scene graph that is a representation of the objects that have to be shown. This scene graph is structured as a tree containing several elements that are necessary to display the objects.
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IOTA is an open-source distributed ledger and cryptocurrency designed for the Internet of things (IoT). It uses a directed acyclic graph to store transactions on its ledger, motivated by a potentially higher scalability over blockchain based distributed ledgers. IOTA does not use miners to validate transactions, instead, users that issue a new transaction must approve two previous transactions and perform a small amount of proof of work. Transactions can therefore be issued without fees, facilitating microtransactions.
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The basic double auction model involves a single market. It can be extended to handle a supply chain - a chain of markets, in which the buyers in one market become sellers in the next market. E.g., farmers sell fruits in the fruit market; juice makers buy fruits in the fruit market, make juice and sell it in the juice market to consumers. The model can be further extended to handle markets in an arbitrary directed acyclic graph.
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At each point in the decision process, multiple alternatives are offered, each leading to a result or a further choice. The alternatives are commonly called "leads", and the set of leads at a given point a "couplet". Single access keys are closely related to decision trees or self-balancing binary search trees. However, to improve the usability and reliability of keys, many single-access keys incorporate reticulation, changing the tree structure into a directed acyclic graph.
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Logical formulas are discrete structures, as are proofs, which form finite trees or, more generally, directed acyclic graph structures (with each inference step combining one or more premise branches to give a single conclusion). The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e.g., fuzzy logic. Concepts such as infinite proof trees or infinite derivation trees have also been studied, e.g.
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A monosaccharide often switches from the acyclic (open- chain) form to a cyclic form, through a nucleophilic addition reaction between the carbonyl group and one of the hydroxyls of the same molecule. The reaction creates a ring of carbon atoms closed by one bridging oxygen atom. The resulting molecule has a hemiacetal or hemiketal group, depending on whether the linear form was an aldose or a ketose. The reaction is easily reversed, yielding the original open-chain form.
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The closure problem takes as input a directed acyclic graph with weights on its vertices and seeks the minimum (or maximum) weight of a closure, a set of vertices with no outgoing edges. (The problem may be formulated for directed graphs without the assumption of acyclicity, but with no greater generality, because in this case it is equivalent to the same problem on the condensation of the graph.) It may be solved in polynomial time using a reduction to the maximum flow problem..
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Heterogeneous Earliest Finish Time (or HEFT) is a heuristic to schedule a set of dependent tasks onto a network of heterogenous workers taking communication time into account. For inputs HEFT takes a set of tasks, represented as a directed acyclic graph, a set of workers, the times to execute each task on each worker, and the times to communicate the results from each job to each of its children between each pair of workers. It descends from list scheduling algorithms.
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Example bigraph with sharing in which the node of control M is shared by the two nodes of control S. This is represented by M being in the intersection of the two S-nodes. Bigraphs with sharing are a generalisation of Milner's formalisation that allows for a straightforward representation of overlapping or intersecting spatial locations. In bigraphs with sharing, the place graph is defined as a directed acyclic graph (DAG), i.e. prnt is a binary relation instead of a map.
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In this tree, the lowest common ancestor of the nodes and is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) of two nodes and in a tree or directed acyclic graph (DAG) is the lowest (i.e. deepest) node that has both and as descendants, where we define each node to be a descendant of itself (so if has a direct connection from , is the lowest common ancestor).
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A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet. The random variables measured in a general experiment can depend on each other in complicated ways. In the field of causal inference, such dependencies are represented via Bayesian networks: directed acyclic graphs where each node represents a variable and an edge from a variable to another signifies that the former influences the latter and not otherwise, see the figure.
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In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations'. These abstract from a conventional homotopy category of topological spaces or of chain complexes (derived category theory), via the acyclic model theorem. The concept was introduced by . In recent decades, the language of model categories has been used in some parts of algebraic K-theory and algebraic geometry, where homotopy-theoretic approaches led to deep results.
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The traditional name neopentane was still retained in the 1993 IUPAC recommendations,Table 19(a) Acyclic and monocyclic hydrocarbons. Parent hydrocarbons but is no longer recommended according to the 2013 recommendations. The preferred IUPAC name is the systematic name 2,2-dimethylpropane, but the substituent numbers are superfluous because it is the only possible “dimethylpropane”. A neopentyl group attached to a generic group R. A neopentyl substituent, often symbolized by "Np", has the structure Me3C–CH2– for instance neopentyl alcohol (Me3CCH2OH or NpOH).
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A Storm application is designed as a "topology" in the shape of a directed acyclic graph (DAG) with spouts and bolts acting as the graph vertices. Edges on the graph are named streams and direct data from one node to another. Together, the topology acts as a data transformation pipeline. At a superficial level the general topology structure is similar to a MapReduce job, with the main difference being that data is processed in real time as opposed to in individual batches.
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Communication is an equivalence relation, and communicating classes are the equivalence classes of this relation. A communicating class is closed if the probability of leaving the class is zero, namely if i is in C but j is not, then j is not accessible from i. The set of communicating classes forms a directed, acyclic graph by inheriting the arrows from the original state space. A communicating class is closed if and only if it has no outgoing arrows in this graph.
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The Fischer glycosidation reaction is an equilibrium process and can lead to a mixture of ring size isomers, and anomers, plus in some cases, small amounts of acyclic forms. With hexoses, short reactions times usually lead to furanose ring forms, and longer reaction times lead to pyranose forms. With long reaction times the most thermodynamically stable product will result which, owing to the anomeric effect, is usually the alpha anomer. :Fischer glycosidation of glucose to produce methyl glucoside using trimethylsilylchloride as catalyst.
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The bond angles in aziridine are approximately 60°, considerably less than the normal hydrocarbon bond angle of 109.5°, which results in angle strain as in the comparable cyclopropane and ethylene oxide molecules. A banana bond model explains bonding in such compounds. Aziridine is less basic than acyclic aliphatic amines, with a pKa of 7.9 for the conjugate acid, due to increased s character of the nitrogen free electron pair. Angle strain in aziridine also increases the barrier to nitrogen inversion.
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A Directed acyclic graph view of kernel(s) for the PVC programmers A typical image-processing program of the PVC is written in Halide. Currently, it supports just a subset of Halide programming language without floating point operations and with limited memory access patterns. Halide is a widely adopted domain specific language that lets the user decouple the algorithm and the scheduling of its execution. In this way, the developer can write a program that is optimized for the target hardware architecture.
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The acyclic form of xylose has chemical formula HOCH2(CH(OH))3CHO. The cyclic hemiacetal isomers are more prevalent in solution and are of two types: the pyranoses, which feature six-membered C5O rings, and the furanoses, which feature five-membered C4O rings (with a pendant CH2OH group). Each of these rings is subject to further isomerism, depending on the relative orientation of the anomeric hydroxy group. The dextrorotary form, -xylose, is the one that usually occurs endogenously in living things.
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In 1976, Meyers reported the first alkylation reaction of metallated azaenolates of hydrazones with an acyclic amino acid-based auxiliary. Compared with the free carbonyl compounds and the chiral enamine species reported previously, the hydrazones exhibit higher reactivity, regioselectivity and stereoselectivity. Hydrazone alkylation developed by Meyer. The combination of cyclic amino acid derivatives (SAMP and RAMP) and the powerful hydrazone techniques were pioneered by E. J. Corey and D. Enders in 1976, and were independently developed by D. Enders later.
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Every finite connected graph has a spanning tree. However, for infinite connected graphs, the existence of spanning trees is equivalent to the axiom of choice. An infinite graph is connected if each pair of its vertices forms the pair of endpoints of a finite path. As with finite graphs, a tree is a connected graph with no finite cycles, and a spanning tree can be defined either as a maximal acyclic set of edges or as a tree that contains every vertex.
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As regards to the direction, this article adopts the convention that the cited node points to the citing node, signifying the fact that knowledge in the cited node flows to the citing node. Citation network is also by nature acyclic, which means that a node can never chain back to itself if one moves along the links following their direction. Several terms related to a citation network are defined here before proceeding further. Heads are the nodes the direction arrow leads to.
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The translation finds all partial solutions relative to each set of variables. The problem that results from the translation represents the interactions between these local solutions. By definition, a decomposition method produces a binary acyclic problem; such problems can be solved in time polynomial in its size. As a result, the original problem can be solved by first translating it and then solving the resulting problem; however, this algorithm is polynomial-time only if the decomposition does not increase size superpolynomially.
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Unfortunately, the most famous "click reaction," a [3+2] cycloaddition between an azide and an acyclic alkyne, is copper-catalyzed, posing a serious problem for use in vivo due to copper's toxicity. To bypass the necessity for a catalyst, Carolyn R. Bertozzi's lab introduced inherent strain into the alkyne species by using a cyclic alkyne. In particular, cyclooctyne reacts with azido-molecules with distinctive vigor. The most common method of installing bioorthogonal reactivity into a target biomolecule is through metabolic labeling.
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Acyclic tautomer (left) and cyclic hemiketal tautomer (right) X-ray crystallographic studies of warfarin show that it exists in tautomeric form, as the cyclic hemiketal, which is formed from the 4-hydroxycoumarin and the ketone in the 3-position substituent. However, the existence of many 4-hydroxycoumadin anticoagulants (for example phenprocoumon) that possess no ketone group in the 3-substituent to form such a structure, suggests that the hemiketal must tautomerise to the 4-hydroxy form in order for warfarin to be active.
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One of these compounds was formed by the addition of L-selectride to a bulky germanium(II) chloride in ether, while the other was formed by the addition of L-selectride to the same germanium(II) chloride in toluene, followed by filtration and the dropwise addition of PMe3. 370x370px The first stable acyclic germylene hydride was formed from the dissociation of a hydrido-digermene. The initial monomeric germylene chloride was synthesized by the reaction of a bulky lithium amide ligand and GeCl2•dioxane.
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In giving a formal definition of Boolean circuits, Vollmer starts by defining a basis as set B of Boolean functions, corresponding to the gates allowable in the circuit model. A Boolean circuit over a basis B, with n inputs and m outputs, is then defined as a finite directed acyclic graph. Each vertex corresponds to either a basis function or one of the inputs, and there is a set of exactly m nodes which are labeled as the outputs.Vollmer 1999, p. 8.
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A schedule is said to be conflict-serializable when the schedule is conflict-equivalent to one or more serial schedules. Another definition for conflict-serializability is that a schedule is conflict- serializable if and only if its precedence graph/serializability graph, when only committed transactions are considered, is acyclic (if the graph is defined to include also uncommitted transactions, then cycles involving uncommitted transactions may occur without conflict serializability violation). ;G Which is conflict-equivalent to the serial schedule , but not .
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219 . Greater catenation of the Si atoms can be obtained with the halides (SinX2n+2 with n = 14) for the fluorides.A. Earnshaw, N. Greenwood, Chemistry of the Elements, Butterworth-Heinemnann (1997) p. 341 . Thus the polymeric silicon hydrides are formed along with smaller silicon hydride oligomers and hydrogen gas from the spontaneous but slow decomposition, as well as from the accelerated thermolysis, of acyclic and cyclic liquid silanes that are higher in molecular weight than monosilane (SiH4) and disilane (Si2H6).
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Apache Oozie is a server-based workflow scheduling system to manage Hadoop jobs. Workflows in Oozie are defined as a collection of control flow and action nodes in a directed acyclic graph. Control flow nodes define the beginning and the end of a workflow (start, end, and failure nodes) as well as a mechanism to control the workflow execution path (decision, fork, and join nodes). Action nodes are the mechanism by which a workflow triggers the execution of a computation/processing task.
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In the automation of data density to identify clusters, research has also been focused on artificially generating the algorithms. For instance, the Estimation of Distribution Algorithms guarantees the generation of valid algorithms by the directed acyclic graph (DAG), in which nodes represent procedures (building block) and edges represent possible execution sequences between two nodes. Building Blocks determine the EDA's alphabet or, in other words, any generated algorithm. Clustering algorithms artificially generated are compared to DBSCAN, a manual algorithm, in experimental results.
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Circuits over natural numbers are a mathematical model used in studying computational complexity theory. They are a special case of circuits. The object is a labeled directed acyclic graph the nodes of which evaluate to sets of natural numbers, the leaves are finite sets, and the gates are set operations or arithmetic operations. As an algorithmic problem, the problem is to find if a given natural number is an element of the output node or if two circuits compute the same set.
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An arbitrary number of transformations can be performed on the stream. These streams can be arranged as a directed, acyclic dataflow graph, allowing an application to branch and merge dataflows. Flink offers ready-built source and sink connectors with Alluxio, Apache Kafka, Amazon Kinesis, HDFS, Apache Cassandra, and more. Flink programs run as a distributed system within a cluster and can be deployed in a standalone mode as well as on YARN, Mesos, Docker-based setups along with other resource management frameworks.
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Some algorithms become simpler when used on DAGs instead of general graphs, based on the principle of topological ordering. For example, it is possible to find shortest paths and longest paths from a given starting vertex in DAGs in linear time by processing the vertices in a topological order, and calculating the path length for each vertex to be the minimum or maximum length obtained via any of its incoming edges.Cormen et al. 2001, Section 24.2, Single-source shortest paths in directed acyclic graphs, pp. 592–595.
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This is an important measure in citation analysis. Court judgements provide another example as judges support their conclusions in one case by recalling other earlier decisions made in previous cases. A final example is provided by patents which must refer to earlier prior art, earlier patents which are relevant to the current patent claim. By taking the special properties of directed acyclic graphs into account, one can analyse these graphs with techniques not available when analysing the general graphs considered in many studies in network analysis.
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Some factors affecting product composition include steric effects, conjugation, and stability of the forming alkene. For acyclic substrates, the Z-isomer is typically the minor product due to the destabilizing gauche interaction in the transition state, but the selectivity is not usually high. frameless The pyrolysis of N,N-dimethyl-2-phenylcyclohexylamine-N-oxide shows how conformational effects and the stability of the transition state affect product composition for cyclic substrates. frameless In the trans isomer, there are two cis-β-hydrogens that can eliminate.
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The name GADDAG comes from DAG for directed acyclic graph, prefixed by its own reverse. A GADDAG is a specialization of a Trie, containing states and branches to other GADDAGs. It is distinct for its storage of every reversed prefix of every word in a dictionary. This means every word has as many representations as it does letters; since the average word in most Scrabble regulation dictionaries is 5 letters long, this makes the GADDAG about 5 times as big as a simple DAWG.
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The protein-ligand challenges were separated from SAMPL in SAMPL5 (2015-2016) and were distributed as the new Grand Challenges of the Drug Design Data Resource (D3R). SAMPL5 allowed participants to make predictions of the binding affinities of three sets of host–guest systems: an acyclic CB7 derivative and two host from the octa-acid family. Participants were also encouraged to submit predictions for binding enthalpies. A wide array of computational methods were tested, including density functional theory (DFT), molecular dynamics, docking, and metadynamics.
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Decomposition methods generalize join-tree clustering by grouping variables in such a way the resulting problem has a join tree. Decomposition methods directly associate a tree with problems; the nodes of this tree are associated variables and/or constraints of the original problem. By merging constraints based on this tree, one can produce a problem that has a join tree, and this join tree can be easily derived from the decomposition tree. Alternatively, one can build a binary acyclic problem directly from the decomposition tree.
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Instead of a single, monolithic blockchain, Nano uses a block-lattice data structure, where every account has its own blockchain (i.e. transaction and balance history). This is a unique implementation of a directed acyclic graph (DAG), where a "block" is just one transaction, and each transaction contains the account's current balance. Furthermore, account- chains can only be updated by the account owner, which allows the account- chain to be updated immediately and asynchronously from the rest of the block- lattice, resulting in quick transactions.
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A dominance drawing Dominance drawing is a style of graph drawing of directed acyclic graphs that makes the reachability relations between vertices visually apparent. In dominance drawing, vertices are placed at distinct points of the Euclidean plane and a vertex v is reachable from another vertex u if and only if both Cartesian coordinates of v are greater than or equal to the coordinates of u. The edges of a dominance drawing may be drawn either as straight line segments, or, in some cases, as polygonal chains.
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Buck requires explicit declaration of dependencies and enforces that by use of a symbolic link tree. Since all dependencies are explicit and Buck has a directed acyclic graph of all source files and build targets, Buck can perform incremental recompilation only building targets downstream of files that have changed. Buck computes a key for each target that is a hash of the contents all the files it depends on. It stores a mapping from that key to the built target in a build cache.
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Squalene-hopene cyclase (SHC) () or hopan-22-ol hydro-lyase is a prokaryotic enzyme in the terpene cyclase/mutase family. It catalyzes the interconversion of an acyclic squalene molecule into a pentacyclic triterpenes hopene and hopanol in the ratio of 5:1. This enzyme catalyses the following chemical reactions. : squalene \rightleftharpoons hop-22(29)-ene : squalene + H2O \rightleftharpoons hopan-22-ol Squalene-hopene cyclase is important because its products, the hopenoids, are very much like sterols in eukaryotes in that they condense lipid membranes and reduce permeability.
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Given a directed graph G, the minimum path cover problem consists of finding a path cover for G having the fewest paths. A minimum path cover consists of one path if and only if there is a Hamiltonian path in G. The Hamiltonian path problem is NP-complete, and hence the minimum path cover problem is NP-hard. However, if the graph is acyclic, the problem is in complexity class P and can therefore be solved in polynomial time by transforming it in a matching problem.
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A variety of acyclic and cyclic thiosulfinates are found in plants, or formed when the plants are cut or crushed. A well-known thiosulfinate is allicin, CH2=CHCH2S(O)SCH2CH=CH2, one of the active ingredients formed when garlic is crushed. Allicin was discovered in 1944 by Chester J. Cavallito and coworkers. Thiosulfinates containing various combinations of the methyl, n-propyl, 1-propenyl, 2-propenyl, n-butyl, 1-butenyl and 2-butenyl groups are formed upon crushing different Allium as well as Brassica species.
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They are used in perfumery for their sweet herbal scent, and are believed to act as plant defense and have anti-fungal properties.SCLabs, Beyond Aroma: Terpenes in cannabis Like the related acyclic terpene myrcene, ocimenes are unstable in air.Karl-Georg Fahlbusch, Franz-Josef Hammerschmidt, Johannes Panten, Wilhelm Pickenhagen, Dietmar Schatkowski, Kurt Bauer, Dorothea Garbe, Horst Surburg "Flavors and Fragrances" in Ullmann's Encyclopedia of Industrial Chemistry, 2002, Wiley-VCH, Weinheim. Like other terpenes, the ocimenes are nearly insoluble in water, but soluble in common organic solvents.
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A context-free grammar G is an SLG if: 1\. for every non-terminal N, there is at most one production rule that has N as its left-hand side, and 2\. the directed graph G=, defined by V being the set of non-terminals and (A,B) ∈ E whenever B appears at the right-hand side of a production rule for A, is acyclic. A mathematical definition of the more general formalism of straight-line context-free tree grammars can be found in Lohrey et al.
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This reaction proceeded with various forms of cyclohexanones. When an acyclic ketone was substituted, the reaction proceeded with low yield, highlighting the thermodynamic favorability of releasing cyclohexanone from the double bonded carbonyl, as it creates unfavorable bond strain in the chair conformation. This represents one of the most convenient constructions of the 1-azaspiro[4,5]decane ring system, a useful natural product. The reaction takes place in refluxing benzene at 80 °C or at room temperature in the presence of Sodium sulfate which activates iminium ion formation.
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This application was the original motivation for Coffman and Graham to develop their algorithm... In the layered graph drawing framework outlined by . the input is a directed graph, and a drawing of a graph is constructed in several stages:. Bastert and Matuszewski also include a description of the Coffman–Graham algorithm; however, they omit the transitive reduction stage of the algorithm. #A feedback arc set is chosen, and the edges of this set reversed, in order to convert the input into a directed acyclic graph.
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Gradle is a build automation tool for multi-language software development. It controls the development process in the tasks of compilation and packaging to testing, deployment, and publishing. The methodology of Gradle builds on the concepts of Apache Ant and Apache Maven, and introduces a Groovy-based domain- specific language, rather than using the XML form used by Maven for declaring the project configuration. Gradle uses a directed acyclic graph to determine the order in which tasks can be run, through providing dependency management.
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Ring-closing metathesis, conversely, usually involves the formation of a five- or six-membered ring, which is enthalpically favorable; although these reactions tend to also evolve ethylene, as previously discussed. RCM has been used to close larger macrocycles, in which case the reaction may be kinetically controlled by running the reaction at high dilutions. The same substrates that undergo RCM can undergo acyclic diene metathesis, with ADMET favored at high concentrations. The Thorpe–Ingold effect may also be exploited to improve both reaction rates and product selectivity.
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A schedule is said to be commitment-ordered (commit-ordered), or commitment-order-serializable, if it obeys the Commitment ordering (CO; also commit-ordering or commit-order-serializability) schedule property. This means that the order in time of transactions' commitment events is compatible with the precedence (partial) order of the respective transactions, as induced by their schedule's acyclic precedence graph (serializability graph, conflict graph). This implies that it is also conflict-serializable. The CO property is especially effective for achieving Global serializability in distributed systems.
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In fact, it has been calculated that the 1,6-hydrogen atom transfer proceeds through a transition that is about 0.8 kcal/mol lower than that of the 1,5. In acyclic systems, δ-hydrogen abstraction is still observed, however, alpha-hydrogen abstraction to form the corresponding ketone competes. In certain cases, particularly nitrites derived from cyclopentyl alcohols, the oxygen-centered radical prefers to react via C-C bond cleavage as opposed to H-atom abstraction. For example, when subjected to Barton conditions, cyclopentyl nitrite forms glutaraldehyde monoxime.
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Semantics, 4: 20), organized as a directed acyclic graph (DAG) created using the open-source OBO-Edit.Smith, B., Ashburner, M., Rosse, C., Bard, J., Bug, W., Ceusters, W., Goldberg, L.J., Eilbeck, K., Ireland, A., Mungall, C.J.; OBI Consortium, Leontis, N., Rocca-Serra, P., Ruttenberg, A., Sansone, S.A., Scheuermann, R.H., Shah, N., Whetzel,P.L,, Lewis, S. (2010): „The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration“, Nat. Biotechnol., 25: 1251–1255 All terms from each level are directly connected the enzyme data in BRENDA.
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Heathcock's synthesis of dihydroprotodaphniphylline features a highly efficient cascade involving two aldehyde/amine condensations, a Prins-like cyclization, and a 1,5-hydride transfer to afford a pentacyclic structure from an acyclic starting material. A cascade reaction, also known as a domino reaction or tandem reaction, is a chemical process that comprises at least two consecutive reactions such that each subsequent reaction occurs only in virtue of the chemical functionality formed in the previous step.Tietze, L. F.; Beifuss, U. Angew. Chem. Int. Ed. 1993, 32, 131–163.
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A directed acyclic word graph saves space over a trie by allowing paths to diverge and rejoin, so that a set of words with the same possible suffixes can be represented by a single tree vertex.. The same idea of using a DAG to represent a family of paths occurs in the binary decision diagram,.. a DAG-based data structure for representing binary functions. In a binary decision diagram, each non-sink vertex is labeled by the name of a binary variable, and each sink and each edge is labeled by a 0 or 1. The function value for any truth assignment to the variables is the value at the sink found by following a path, starting from the single source vertex, that at each non-sink vertex follows the outgoing edge labeled with the value of that vertex's variable. Just as directed acyclic word graphs can be viewed as a compressed form of tries, binary decision diagrams can be viewed as compressed forms of decision trees that save space by allowing paths to rejoin when they agree on the results of all remaining decisions..
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A longest path between two given vertices s and t in a weighted graph G is the same thing as a shortest path in a graph −G derived from G by changing every weight to its negation. Therefore, if shortest paths can be found in −G, then longest paths can also be found in G. For most graphs, this transformation is not useful because it creates cycles of negative length in −G. But if G is a directed acyclic graph, then no negative cycles can be created, and a longest path in G can be found in linear time by applying a linear time algorithm for shortest paths in −G, which is also a directed acyclic graph.. For instance, for each vertex v in a given DAG, the length of the longest path ending at v may be obtained by the following steps: # Find a topological ordering of the given DAG. # For each vertex v of the DAG, in the topological ordering, compute the length of the longest path ending at v by looking at its incoming neighbors and adding one to the maximum length recorded for those neighbors.
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Since commutators in each simple group form a generating set, pairs of commutators form a generating set of the direct product. More generally, a quasisimple group (a perfect central extension of a simple group) which is a non-trivial extension (and therefore not a simple group itself) is perfect but not simple; this includes all the insoluble non- simple finite special linear groups SL(n,q) as extensions of the projective special linear group PSL(n,q) (SL(2,5) is an extension of PSL(2,5), which is isomorphic to A5). Similarly, the special linear group over the real and complex numbers is perfect, but the general linear group GL is never perfect (except when trivial or over F2, where it equals the special linear group), as the determinant gives a non-trivial abelianization and indeed the commutator subgroup is SL. A non-trivial perfect group, however, is necessarily not solvable; and 4 divides its order (if finite), moreover, if 8 does not divide the order, then 3 does. Every acyclic group is perfect, but the converse is not true: A5 is perfect but not acyclic (in fact, not even superperfect), see .
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A Bayesian network (also known as a Bayes network, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.
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The transitive reduction of a DAG is the graph with the fewest edges that represents the same reachability relation as . It is a subgraph of , formed by discarding the edges for which also contains a longer path connecting the same two vertices. Like the transitive closure, the transitive reduction is uniquely defined for DAGs. In contrast, for a directed graph that is not acyclic, there can be more than one minimal subgraph with the same reachability relation.. A Hasse diagram representing the partial order of set inclusion (⊆) among the subsets of a three-element set.
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Preparation of a heterocyclic spiro compound. Each molecule shown in line- angle representation, where each angle (vertex) represents a carbon atom, and each line a bond between atoms (and where necessary hydrogen atoms to fulfill carbon's valence of four are implied). The heterocyclic spiro product, at right of arrow, is a common ketal (acetal) structure prepared from a monocyclic type of ketone and a generally acyclic type of diol (both at left of arrow). The schematic is for the synthesis of the protected 1,4-dioxaspiro[4.5]decane from cyclohexanone and the alcohol, ethanediol.
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Hydrocarbons, being a significant source of energy due to their strong chemical bonds, were a prime source for scientific study in the Aegean Sea oil spill. Chemical markers were placed in a sample of the crude oil spilled, with interesting data revealed. Alkanes and acyclic hydrocarbons, both having single bonds, appeared to have deteriorated in only six months, while triterpane and steranane were still present after years of weathering. Both triterpane and steranane have multiple bonds, which is the reason they were still present after so many years.
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The mechanism of the Barrelene to Semibullvalene transformation 550px The dependence of the success of the Di-pi-Methane rearrangement on singlet versus triplet multiplicity arises primarily from the Free-Rotor Effect The triplet acyclic 1,4-dienes are free to undergo cis- trans interconversion of the diene double bonds (i.e. free-rotation) thus inhibiting the Di-pi-Methane process. The cis-trans isomerization proceeds by weakening of a pi-bond and then twisting. The singlet excited states don't rotate and then are free to undergo the Di-pi-Methane mechanism.
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Specifying a Bayesian network meta-analysis model involves writing a directed acyclic graph (DAG) model for general-purpose Markov chain Monte Carlo (MCMC) software such as WinBUGS. In addition, prior distributions have to be specified for a number of the parameters, and the data have to be supplied in a specific format. Together, the DAG, priors, and data form a Bayesian hierarchical model. To complicate matters further, because of the nature of MCMC estimation, overdispersed starting values have to be chosen for a number of independent chains so that convergence can be assessed.
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SCOP2 prototype was a beta version of Structural classification of proteins and classification system that aimed to more the evolutionary complexity inherent in protein structure evolution. It is therefore not a simple hierarchy, but a directed acyclic graph network connecting protein superfamilies representing structural and evolutionary relationships such as circular permutations, domain fusion and domain decay. Consequently, domains are not separated by strict fixed boundaries, but rather are defined by their relationships to the most similar other structures. The prototype was used for the development of the SCOP version 2 database.
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A GADDAG is a data structure presented by Steven Gordon in 1994, for use in generating moves for Scrabble and other word-generation games where such moves require words that "hook into" existing words. It is often in contrast to move-generation algorithms using a directed acyclic word graph (DAWG) such as the one used by Maven. It is generally twice as fast as the traditional DAWG algorithms, but take about 5 times as much space for regulation Scrabble dictionaries. Quackle, an open-source Scrabble program, uses a GADDAG to generate moves.
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The simplest silene is (the parent molecule) is disilene, . There is no limit to the number of silicon atoms that can be linked together, the only limitation being that the molecule is acyclic, is unsaturated, and is a hydrosilicon. For bridged silenes, the Bredt's rule states that a double bond cannot be placed at the bridgehead of a bridged ring system, unless the rings are large enough (8 or more atoms). Aromatic compounds are often drawn as cyclic silenes, but their structure and properties are different and they are not considered to be silenes.
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Probabilistic graphical models provide a convenient framework for comparing model-based approximations. In this context, value of the process at index x_k \in X can then be represented by a vertex in a directed graph and edges correspond to the terms in the factorization of the joint density of y(X). In general, when no independece relations are assumed, the joint probability distribution can be represented by an arbitrary directed acyclic graph. Using a particular approximation can then be expressed as a certain way of ordering the vertices and adding or removing specific edges.
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Beau and coworkers assembled the core dihydropyran framework of zanamivir congeners via a combination of PBM reaction and Iron(III)-promoted deprotection-cyclization sequence. A stereochemically-defined α-hydroxyaldehyde 2, diallylamine and a dimethylketal-protected boronic acid 1 is coupled to form the acyclic, stereochemically-defined amino-alcohol 3, which then undergoes an Iron(III)-promoted cyclization to form a bicyclic dihydropyran 4. Selective opening of the oxazoline portion of the dihydropyran intermediate 4 with water or timethylsilyl azide then furnish downstream products that have structures resembling the Zanamivir family members. zanamivir core_Beau et al.
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In higher plants, linalool, is an acyclic monoterpenoid. Like the majority of monoterpenes, it starts at the condensation of dimethylallyl diphosphate (DMAPP) and isopentenyl diphosphate (IPP) to form geranyl pyrophosphate (GPP). With the aid of linalool synthase (LIS), water attacks to form the chiral center.LIS appears to show a limonene synthase-type catalysis through a simplified "metal-cofactor-binding domain [where the majority] of the residues involved in substrate...binding [are] in the C-terminal part of the protein" suggesting stereoselectivity and the reasoning behind why some plants have varying levels of each enantiomer.
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Worse there are often errors in the citations introduced at any one of many stages of the process of publishing a document. However, there is a long history of creating a database of citations, also known as a citation index, and so there is lot of information about such problems. In principle each document will have a unique publication date and can only refer to earlier documents. This means that the edges of the graph are not only directed but they are also acyclic, that is there are no loops in the graph.
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This key precursor was in turn accessible biosynthetically via two further thermally allowed sequential 6π electron and 8π electron electrocyclizations. The Nicolaou group therefore sought to synthesize endiandric acid C from an acyclic symmetric diacetylenic diol precursor, 14 (as shown); they began with "mild hydrogenation" in the presence of Lindlar catalyst and quinoline, anticipating tetraene diol 15, cyclooctatriene 16, or the fully cyclized bicyclo[4.2.0]octadiene (bicyclic diol) 17. Remarkably, following this 3-6 hour, 25 °C process, a 45-55% yield of bicyclic diol 17 could be isolated.
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Chiral acyclic alkenes also show diastereoselectivity upon reactions such as epoxidation and enolate alkylation. The substituents around the alkene can favour the approach of the electrophile from one or the other face of the molecule. This is the basis of the Houk's model, based on theoretical work by Kendall Houk, which predicts that the selectivity is stronger for cis than for trans double bonds. :Diastereoselective epoxidation of a cis alkene In the example shown, the cis alkene assumes the shown conformation to minimize steric clash between RS and the methyl group.
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The algorithm considers every possible pair (i, j), 1≤ i, j ≤ n and i ≠ j. For any pair (i, j), every possible pair of l-mers (x, y) is considered (where x is from si and y is from sj). While considering any x and y, the algorithm identifies all the elements of B_d (x)\bigcap B_d (y) that are (l, d, q-2) motifs (with respect to input strings other than si and sj). An acyclic graph is used to represent and explore B_d (x)\bigcap B_d (y).
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The category of topological spaces, Top, admits a standard model category structure with the usual (Serre) fibrations and with weak equivalences as weak homotopy equivalences. The cofibrations are not the usual notion found here, but rather the narrower class of maps that have the left lifting property with respect to the acyclic Serre fibrations. Equivalently, they are the retracts of the relative cell complexes, as explained for example in Hovey's Model Categories. This structure is not unique; in general there can be many model category structures on a given category.
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Based on a proposed biosynthesis pathway of proto-daphniphylline from squalene, Clayton Heathcock and co- workers developed a remarkably elegant and short total synthesis of proto- daphniphylline from simple starting materials. This is an example of how biomimetic synthesis can simplify the total synthesis of a complex natural product. The key step in Heathcock's synthetic route involves a cyclization of acyclic dialdehydes A or B to form proto-daphniphylline. Both dialdehydes (A or B) have carbon skeletons analogous to squalene and can be synthesized from simple starting materials.
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Then, we add the segments from the subdivision, one by one, in random order, refining the trapezoidal decomposition. Using backwards analysis, we can show that the expected number of trapezoids created for each insertion is bounded by a constant. We build a directed acyclic graph, where the vertices are the trapezoids that existed at some point in the refinement, and the directed edges connect the trapezoids obtained by subdivision. The expected depth of a search in this digraph, starting from the vertex corresponding to the bounding box, is O(log n).
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Squalene-hopene cyclase is found in a large number of bacteria but is most readily isolated from the thermophilic bacterium Alicyclobacillus acidocaldarius. It catalyses the conversion of the acyclic molecule of squalene into the pentacyclic triterpenes of hopene and hopanol. Space-filling model of the squalene molecule Squalene-hopene cyclase is thought to be an evolutionary progenitor of many classes of eukaryotic and prokaryotic sterol cyclases. Oxidosqualene cyclases, which are eukaryotic analogs of SHC require oxygen for their reaction demonstrating a much later evolution when the atmosphere began accumulating oxygen.
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After formation of a metal enolate, dissociation of halide generates a positively charged oxyallyl intermediate. This electron-deficient 2π component reacts with electron-rich dienes to give cycloheptenones. Cyclic dienes fare better than the corresponding acyclic dienes because in order to react, the diene must be in the s-cis conformation in the presence of the short-lived oxyallyl cation—cyclic dienes are locked in this reactive conformation. (2)File:43Mech1.png Substituents at the 1 and 3 positions are usually required to stabilize the oxyallyl cation and prevent isomerization to cyclopropanones and allene oxides.
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A high number of hydrogen bond acceptors could decrease permeability across the blood–brain barrier (BBB) due to the polar surface area and needs to be taken into account when designing agonists to target α7 nAChRs. Various cyclic amine groups can act as the basic moiety and potency stays relatively unchanged for example aryl piperazine, piperidine and morpholine. An acyclic tertiary amine is tolerated as the basic moiety but larger steric groups are less tolerated. Many derivatives of quinuclidine such as quinuclidine amide are known to be α7 nAChR agonists.
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In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there is a directed path from vertex u to vertex v and v comes before u in the ordering, then there is also a directed path from vertex v to vertex u. If the graph is a directed acyclic graph (DAG), topological orderings are pre- topological orderings and vice versa. In other cases, any pre-topological ordering gives a partial order.
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More generally, any directed acyclic graph may be used for a feedforward network, with some nodes (with no parents) designated as inputs, and some nodes (with no children) designated as outputs. These can be viewed as multilayer networks where some edges skip layers, either counting layers backwards from the outputs or forwards from the inputs. Various activation functions can be used, and there can be relations between weights, as in convolutional neural networks. Examples of other feedforward networks include radial basis function networks, which use a different activation function.
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The Tangle is the moniker used to describe IOTAs directed acyclic graph (DAG) transaction settlement and data integrity layer. It is structured as a string of individual transactions that are interlinked to each other and stored through a network of node participants. The Tangle does not have miners validating transactions, rather, network participants are jointly responsible for transaction validation, and must confirm two transactions already submitted to the network for every one transaction they issue. Transactions can therefore be issued to the network at no cost, facilitating micropayments.
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The tournament has one vertex for each color in the coloring. For each pair of colors, there is an edge in the colored graph with those two colors at its endpoints, which lends its orientation to the edge in the tournament between the vertices corresponding to the two colors. Incomplete colorings may also be represented by homomorphisms into tournaments but in this case the correspondence between colorings and homomorphisms is not one-to-one. Undirected graphs of bounded genus, bounded degree, or bounded acyclic chromatic number also have bounded oriented chromatic number.
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Katz centrality can be used to compute centrality in directed networks such as citation networks and the World Wide Web. Katz centrality is more suitable in the analysis of directed acyclic graphs where traditionally used measures like eigenvector centrality are rendered useless. Katz centrality can also be used in estimating the relative status or influence of actors in a social network. The work presented in shows the case study of applying a dynamic version of the Katz centrality to data from Twitter and focuses on particular brands which have stable discussion leaders.
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This leads to four possible azaenolate intermediates (A, B, C and D) for the Enders' SAMP/RAMP hydrazone alkylation reaction. Stereoselectivity of the generation of the azaenolates Experiments and calculations show that one specific stereoisomer of the azaenolate is favored over the other three possible candidates. Therefore, although four isomers are possible for the azaenolate, only the one (azaenolate A) with the stereochemistry of its C=C double bonds being E and that of its C-N bond being Z stereochemistry is dominant (EC=CZC-N) for both cyclic and acyclic ketones.
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In combinatorial game theory, for an impartial game given in explicit form as a directed acyclic graph whose vertices represent game positions and whose edges represent valid moves from one position to another, the greedy coloring algorithm (using the reverse of a topological ordering of the graph) calculates the nim-value of each position. These values can be used to determine optimal play in any single game or any disjunctive sum of games.E.g., see Section 1.1 of . For a graph of maximum degree , any greedy coloring will use at most colors.
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Acyclic aliphatic/non-aromatic compound (butane) Cyclic aliphatic/non-aromatic compound (cyclobutane) In organic chemistry, hydrocarbons (compounds composed solely of carbon and hydrogen) are divided into two classes: aromatic compounds and aliphatic compounds (; G. aleiphar, fat, oil), also known as non-aromatic hydrocarbons. Aliphatics can be cyclic; however, hydrocarbons with conjugated pi-systems that obey Hückel's rule are instead considered to be aromatic. Aliphatic compounds can be saturated, like hexane, or unsaturated, like hexene and hexyne. Open-chain compounds (whether straight or branched) contain no rings of any type, and are thus aliphatic.
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Acyclic alkenes, with only one double bond and no other functional groups (also known as mono-enes) form a homologous series of hydrocarbons with the general formula n2n with n being 2 or more (which is two hydrogens less than the corresponding alkane). When n is four or more, there are multiple isomers with this formula, distinguished by the position and conformation of the double bond. Alkenes are generally colorless apolar compounds, somewhat similar to alkanes but more reactive. The first few members of the series are gases or liquids at room temperature.
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In contrast to these polynomial bounds, some drawing styles may exhibit exponential growth in their areas, implying that these styles may be suitable only for small graphs. An example is upward planar drawing of planar directed acyclic graphs, where the area of an n-vertex drawing may be proportional to 2n in the worst case.. Even plane trees may require exponential area, if they are to be drawn with straight edges that preserve a fixed cyclic order around each vertex and must be equally spaced around the vertex..
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A monomer with functionality of 3 or more will introduce branching in a polymer and will ultimately form a cross-linked macrostructure or network even at low fractional conversion. The point at which a tree-like topology transits to a network is known as the gel point because it is signalled by an abrupt change in viscosity. One of the earliest so-called thermosets is known as bakelite. It is not always water that is released in step-growth polymerization: in acyclic diene metathesis or ADMET dienes polymerize with loss of ethene.
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For larger rings, where the bond angles are not as distorted, the stability of the hemiacetals is due to entropy and the proximity of the nucleophile to the carbonyl group. Formation of an acyclic acetal involves a decrease in entropy because two molecules are consumed for every one produced. In contrast, the formation of cyclic hemiacetals involves a single molecule reacting with itself, making the reaction more favorable. Another way to understand the stability of cyclic hemiacetals is to look at the equilibrium constant as the ratio of the forward and backward reaction rate.
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In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext). There is a further group of related concepts applied to sheaves: flabby (flasque in French), fine, soft (mou in French), acyclic. In the history of the subject they were introduced before the 1957 "Tohoku paper" of Alexander Grothendieck, which showed that the abelian category notion of injective object sufficed to found the theory. The other classes of sheaves are historically older notions.
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In graph theory, an arborescence is a directed graph in which, for a vertex u called the root and any other vertex v, there is exactly one directed path from u to v. An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph. Equivalently, an arborescence is a directed, rooted tree in which all edges point away from the root; a number of other equivalent characterizations exist. Every arborescence is a directed acyclic graph (DAG), but not every DAG is an arborescence.
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The number of distinct stereoisomers with the same diagram is bounded by 2c, where c is the total number of chiral carbons. The Fischer projection is a systematic way of drawing the skeletal formula of an acyclic monosaccharide so that the handedness of each chiral carbon is well specified. Each stereoisomer of a simple open-chain monosaccharide can be identified by the positions (right or left) in the Fischer diagram of the chiral hydroxyls (the hydroxyls attached to the chiral carbons). Most stereoisomers are themselves chiral (distinct from their mirror images).
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This directed graph has no cycles: it is not possible to get from any vertex (point) back to that same point, following the connections in the direction indicated by the arrows. A feedback arc set (FAS) or feedback edge set is a set of edges which, when removed from the graph, leaves an acyclic graph. Put another way, it is a set containing at least one edge of every cycle in the graph. In graph theory, a directed graph may contain directed cycles, a closed one-way path of edges.
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While the parameter k in the examples above is chosen as the size of the desired solution, this is not necessary. It is also possible to choose a structural complexity measure of the input as the parameter value, leading to so-called structural parameterizations. This approach is fruitful for instances whose solution size is large, but for which some other complexity measure is bounded. For example, the feedback vertex number of an undirected graph G is defined as the minimum cardinality of a set of vertices whose removal makes G acyclic.
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Constraint satisfaction problems composed of binary constraints only can be viewed as graphs, where the vertices are variables and the edges represent the presence of a constraint between two variables. This graph is called the Gaifman graph or primal constraint graph (or simply primal graph) of the problem. If the primal graph of a problem is acyclic, establishing satisfiability of the problem is a tractable problem. This is a structural restriction, as it can be checked by looking only at the scopes of the constraints, disregarding their relations and the domain.
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The compound is synthesized from acyclic precursors via a mono-pyrrole (porphobilinogen) then a tetrapyrrole (a porphyrinogen, specifically uroporphyrinogen III). This precursor is converted to protoporphyrinogen IX, which is oxidized to protoporphyrin IX.The last step is mediated by the enzyme protoporphyrinogen oxidase. alt=protoporphyrin IX synthesis from protoporphyrinogen-IX Protoporphyrin IX is an important precursor to biologically essential prosthetic groups such as heme, cytochrome c, and chlorophylls. As a result, a number of organisms are able to synthesize this tetrapyrrole from basic precursors such as glycine and succinyl CoA, or glutamate.
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Topological sorting of dependencies depends on the dependency graph being a directed acyclic graph (DAG). In practice, a program may define a dependency graph that has cycles. Usually, reactive programming languages expect such cycles to be "broken" by placing some element along a "back edge" to permit reactive updating to terminate. Typically, languages provide an operator like `delay` that is used by the update mechanism for this purpose, since a `delay` implies that what follows must be evaluated in the "next time step" (allowing the current evaluation to terminate).
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However, uniqueness fails for graphs with (directed) cycles, and for infinite graphs not even existence is guaranteed. The closely related concept of a minimum equivalent graph is a subgraph of D that has the same reachability relation and as few edges as possible. The difference is that a transitive reduction does not have to be a subgraph of D. For finite directed acyclic graphs, the minimum equivalent graph is the same as the transitive reduction. However, for graphs that may contain cycles, minimum equivalent graphs are NP-hard to construct, while transitive reductions can be constructed in polynomial time.
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As Aho et al. show, when the time complexity of graph algorithms is measured only as a function of the number n of vertices in the graph, and not as a function of the number of edges, transitive closure and transitive reduction of directed acyclic graphs have the same complexity. It had already been shown that transitive closure and multiplication of Boolean matrices of size n × n had the same complexity as each other,Aho et al. credit this result to an unpublished 1971 manuscript of Ian Munro, and to a 1970 Russian-language paper by M. E. Furman.
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A function that can be utilized to evaluate any Boolean output in relation to its Boolean input by logical type of calculations. Such functions play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers. The properties of Boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see substitution box). Boolean functions are often represented by sentences in propositional logic, and sometimes as multivariate polynomials over GF(2), but more efficient representations are binary decision diagrams (BDD), negation normal forms, and propositional directed acyclic graphs (PDAG).
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Tenofovir disoproxil is a nucleotide analog reverse-transcriptase inhibitor (NtRTI). It selectively inhibits viral reverse transcriptase, a crucial enzyme in retroviruses such as human immunodeficiency virus (HIV), while showing limited inhibition of human enzymes, such as DNA polymerases α, β, and mitochondrial DNA polymerase γ.Drugbank: Tenofovir In vivo tenofovir disoproxil fumarate is converted to tenofovir, an acyclic analog of deoxyadenosine 5'-monophosphate (d-AMP). Tenofovir lacks a hydroxyl group in the position corresponding to the 3' carbon of the d-AMP, preventing the formation of the 5′ to 3′ phosphodiester linkage essential for DNA chain elongation.
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A relatively recent work (2006) by Fernández and Frenking (2006) summarized the trends in hyperconjugation among various groups of acyclic molecules, using energy decomposition analysis or EDA. Fernández and Frenking define this type of analysis as "...a method that uses only the pi orbitals of the interacting fragments in the geometry of the molecule for estimating pi interactions." For this type of analysis, the formation of bonds between various molecular moieties is a combination of three component terms. ΔEelstat represents what Fernández and Frenking call a molecule’s “quasiclassical electrostatic attractions.” The second term, ΔEPauli, represents the molecule’s Pauli repulsion.
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Graph-theoretic methods, in various forms, have proven particularly useful in linguistics, since natural language often lends itself well to discrete structure. Traditionally, syntax and compositional semantics follow tree-based structures, whose expressive power lies in the principle of compositionality, modeled in a hierarchical graph. More contemporary approaches such as head- driven phrase structure grammar model the syntax of natural language using typed feature structures, which are directed acyclic graphs. Within lexical semantics, especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words; semantic networks are therefore important in computational linguistics.
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In a Binary Decision Diagram, a Boolean function can be represented as a rooted, directed, acyclic graph, which consists of several decision nodes and terminal nodes. In 1993, Shin-ichi Minato from Japan modified Randal Bryant’s BDDs for solving combinatorial problems. His “Zero-Suppressed” BDDs aim to represent and manipulate sparse sets of bit vectors. If the data for a problem are represented as bit vectors of length n, then any subset of the vectors can be represented by the Boolean function over n variables yielding 1 when the vector corresponding to the variable assignment is in the set.
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A major reason for the notion of a good cover is that the Leray spectral sequence of a fiber bundle degenerates for a good cover, and so the Čech cohomology associated with a good cover is the same as the Čech cohomology of the space. (Such a cover is known as a Leray cover.) However, for the purposes of computing the Čech cohomology it suffices to have a more relaxed definition of a good cover in which all intersections of finitely many open sets have contractible connected components. This follows from the fact that higher derived functors can be computed using acyclic resolutions.
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In graph theory, the cycle rank of a directed graph is a digraph connectivity measure proposed first by Eggan and Büchi . Intuitively, this concept measures how close a digraph is to a directed acyclic graph (DAG), in the sense that a DAG has cycle rank zero, while a complete digraph of order n with a self-loop at each vertex has cycle rank n. The cycle rank of a directed graph is closely related to the tree-depth of an undirected graph and to the star height of a regular language. It has also found use in sparse matrix computations (see ) and logic .
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In the case of cyclic nitroxides, five-membered ring systems have been shown to cleave more slowly than six- membered rings and acyclic nitroxides with t-butyl moieties as their R groups cleaved fastest of all. This difference in the rate of cleavage was determined to result not from a difference in C-O bond lengths, but in the difference of C-O-N bond angle in the alkoxyamine. The smaller the bond angle the greater the steric interaction between the nitroxide and the alkyl fragment and the more easily the initiator species broke apart.Moad, G., Rizzardo, E. Macromolecules, 1995, 28, 8722–8728.
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Asymmetric induction by the molecular framework of an acyclic substrate is the idea that asymmetric steric and electronic properties of a molecule may determine the chirality of subsequent chemical reactions on that molecule. This principal is used to design chemical syntheses where one stereocentre is in place and additional stereocentres are required. When considering how two functional groups or species react, the precise 3D configurations of the chemical entities involved will determine how they may approach one another. Any restrictions as to how these species may approach each other will determine the configuration of the product of the reaction.
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Technically, there is a fourth type, Read after Read (RAR or "Input"): Both instructions read the same location. Input dependence does not constrain the execution order of two statements, but it is useful in scalar replacement of array elements. To make sure we respect the three types of dependencies, we construct a dependency graph, which is a directed graph where each vertex is an instruction and there is an edge from I1 to I2 if I1 must come before I2 due to a dependency. If loop-carried dependencies are left out, the dependency graph is a directed acyclic graph.
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This condition however is weaker than asking that every closed loop in the space would bound a disc in the space, all we ask is that any closed loop--and higher dimensional analogue thereof--would bound something like a "two-dimensional surface." The condition of acyclicity on a space X implies, for example, for nice spaces--say, simplicial complexes--that any continuous map of X to the circle or to the higher spheres is null-homotopic. If a space X is contractible, then it is also acyclic, by the homotopy invariance of homology. The converse is not true, in general.
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This technique is used by the Git revision control tool. (Git's recursive merge implementation also handles other awkward cases, like a file being modified in one version and renamed in the other, but those are extensions to its three- way merge implementation; not part of the technique for finding three versions to merge.) Recursive three-way merge can only be used in situations where the tool has knowledge about the total ancestry directed acyclic graph (DAG) of the derivatives to be merged. Consequently, it cannot be used in situations where derivatives or merges do not fully specify their parent(s).
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Judea Pearl and Azaria Paz coined the term "graphoids" after discovering that a set of axioms that govern conditional independence in probability theory is shared by undirected graphs. Variables are represented as nodes in a graph in such a way that variable sets X and Y are independent conditioned on Z in the distribution whenever node set Z separates X from Y in the graph. Axioms for conditional independence in probability were derived earlier by A. Philip Dawid and Wolfgang Spohn. The correspondence between dependence and graphs was later extended to directed acyclic graphs (DAGs) and to other models of dependency.
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Chemical structure of methane, the simplest alkane In organic chemistry, an alkane, or paraffin (a historical name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single. Alkanes have the general chemical formula CnH2n+2. The alkanes range in complexity from the simplest case of methane (CH4), where n = 1 (sometimes called the parent molecule), to arbitrarily large and complex molecules, like pentacontane (C50H102) or 6-ethyl-2-methyl-5-(1-methylethyl) octane, an isomer of tetradecane (C14H30).
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Acyclic alkanes occur in nature in various ways. ;Bacteria and archaea Methanogenic archaea in the gut of this cow are responsible for some of the methane in Earth's atmosphere. Certain types of bacteria can metabolize alkanes: they prefer even-numbered carbon chains as they are easier to degrade than odd-numbered chains. On the other hand, certain archaea, the methanogens, produce large quantities of methane by the metabolism of carbon dioxide or other oxidized organic compounds. The energy is released by the oxidation of hydrogen: :CO2 \+ 4 H2 → CH4 \+ 2 H2O Methanogens are also the producers of marsh gas in wetlands.
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A simple arithmetic circuit. An arithmetic circuit C over the field F and the set of variables x_1, \ldots, x_n is a directed acyclic graph as follows. Every node in it with indegree zero is called an input gate and is labeled by either a variable x_i or a field element in F. Every other gate is labeled by either + or \times; in the first case it is a sum gate and in the second a product gate. An arithmetic formula is a circuit in which every gate has outdegree one (and so the underlying graph is a directed tree).
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A species of bumblebees called B. lucorum in China is not the same species as B. lucorum in Europe. The labial gland secretions of male bumblebees can be divided into two different types according to the biochemical pathways that synthesize the compounds. The two types are PP type secretions that contain only fatty acid derivatives and PP + MAP type secretions that contain fatty acid derivatives and mevalonic acid derivatives in the form of acyclic diterpenes. It was found that the European B. lucorum contains PP type secretions while Chinese B. lucorum contains PP + MAP type secretions.
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Cinnamaldehyde is a naturally-occurring compound that has a conjugated system penta-1,3-diene is a molecule with a conjugated system Diazomethane conjugated pi-system In chemistry, a conjugated system is a system of connected p orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.
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The degree of enantioselectivity depends on numerous factors, namely the structure of the alkene, the nature of the axial donor ligand on the active oxomanganese species and the reaction temperature. Cyclic and acyclic cis-1,2-disubstituted alkenes are epoxidized with almost 100% enantioselectivity whereas trans-1,2-disubstituted alkenes are poor substrates for Jacobsen's catalysts but yet give higher enantioselectivities when Katsuki's catalysts are used. Furthermore, the enantioselective epoxidation of conjugated dienes is much higher than that of the nonconjugated dienes. The enantioselectivity is explained by either a "top-on" approach (Jacobsen) or by a "side-on" approach (Katsuki) of the alkene.
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Neal Stephenson, Clocks, Orreries, etc., acknowledgements for Anathem A major theme of the novel is the many-worlds interpretation of quantum mechanics based on a directed acyclic graph, which accounts for the various "worldtracks" and "narratives" explored by Fraa Orolo and manipulated by Fraa Jad. Another major theme is the recurring philosophical debate between characters espousing mathematical Platonic realism (called "Halikaarnians" in the novel and associated with Incanters) and characters espousing nominalism (called "Procians" in the novel and who are the Rhetors). Stephenson cites the work of Roger Penrose as a major influence on the novel.
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Cyclopentamine is the cyclopentane homolog of propylhexedrine, differing only in terms of the contracted ring size of a cyclopentane, containing one —CH2— unit less than the cyclohexyl group. In terms of the acyclic part of the molecule, both cyclopentamine and propylhexedrine are the same as methamphetamine, all three molecules containing the 2-methylaminopropyl side- chain. The difference between them is that whereas methamphetamine is an aromatic molecule containing a phenyl group, cyclopentamine and propylhexedrine are entirely aliphatic and contain no delocalized electrons at all. The effect that this has on potency is that the reduced alicyclic- alkylamines are weaker than unsaturated (meth)amphetamine.
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Has a BLAS and a partial LAPACK implementation for compatibility. ; MAGMA: Matrix Algebra on GPU and Multicore Architectures (MAGMA) project develops a dense linear algebra library similar to LAPACK but for heterogeneous and hybrid architectures including multicore systems accelerated with GPGPUs. ; PLASMA: The Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) project is a modern replacement of LAPACK for multi- core architectures. PLASMA is a software framework for development of asynchronous operations and features out of order scheduling with a runtime scheduler called QUARK that may be used for any code that expresses its dependencies with a directed acyclic graph.
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A graph with edges colored to illustrate path H-A-B (green), closed path or walk with a repeated vertex B-D-E-F-D-C-B (blue) and a cycle with no repeated edge or vertex H-D-G-H (red). In graph theory, a cycle in a graph is a non- empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices. A graph without cycles is called an acyclic graph.
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Cyclic forms with a seven-atom ring (the same of oxepane), rarely encountered, are called heptoses. Conversion between the furanose, acyclic, and pyranose forms of -glucose Pyranose forms of some pentose sugars Pyranose forms of some hexose sugars For many monosaccharides (including glucose), the cyclic forms predominate, in the solid state and in solutions, and therefore the same name commonly is used for the open- and closed-chain isomers. Thus, for example, the term "glucose" may signify glucofuranose, glucopyranose, the open-chain form, or a mixture of the three. Cyclization creates a new stereogenic center at the carbonyl-bearing carbon.
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GEGL is modelled after a directed acyclic graph, where each node represents an image operation (called "operators" or "ops"), and each edge represents an image. Operations can in general take several input images and give several output images, which corresponds to having several incoming edges (images) and several outgoing edges (images) at a given node (operation). The system uses an on-demand model, doing work only as required. This allows features such as having very quick previews while editing, and once the user has finished making changes, GEGL will repeat the same operations in full resolution for the final image in the background.
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A common application of a trie is storing a predictive text or autocomplete dictionary, such as found on a mobile telephone. Such applications take advantage of a trie's ability to quickly search for, insert, and delete entries; however, if storing dictionary words is all that is required (i.e., storage of information auxiliary to each word is not required), a minimal deterministic acyclic finite state automaton (DAFSA) would use less space than a trie. This is because a DAFSA can compress identical branches from the trie which correspond to the same suffixes (or parts) of different words being stored.
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A pioneer of the "fleximer" class of nucleoside analogs, Seley-Radtke has designed, synthesized and developed a broad range of enzyme inhibitors that have applications as potential therapeutics in treatment of cancer and of infections with viruses. parasites and bacteria. Her lab has identified a series of flexible acyclic nucleosides with prodrug forms which demonstrate activity against coronoviruses, including SARS and MERS, the first known nucleoside analog inhibitors of these viruses. The flexibility of these inhibitors enables binding of the active site as well as amino acid residues out side of the active site which is believed to help reduce emergence of resistance.
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The algorithms treat resolution proofs as directed acyclic graphs, where each node is labeled by a clause and each node has either one or two predecessors called parents. If a node has two parents it is also labeled with a propositional variable called the pivot, which was used to compute the nodes clause using resolution. The following algorithm describes the replacement of nodes. It is assumed that in the resolution proof for all non leaf nodes with two parent nodes, the left parent node contains the positive and the right parent node the negative pivot variable.
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The rate of pseudo-first-order decay of this model enediyne is highly dependent on the solvent hydrogen-donor ability, indicating that the hydrogen abstraction step following biradical formation is kinetically significant in the cycloaromatization of the enediyne, as opposed to acyclic systems, where formation of the biradical itself is known to be the rate-limiting step. It is noteworthy that of the solvents examined, tetrahydrofuran—structurally homologous with deoxyribose—led to comparatively fast decomposition of the 5,9-fused enediyne scaffold (t½ = 68 min); Zein et al. independently remark that deoxyribose 4'-hydrogen abstraction is most likely operative in kedarcidin chromophore bioactivity.
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Whereas a mediator is a factor in the causal chain (1), a confounder is a spurious factor incorrectly suggesting causation (2) Austin Bradford Hill built upon the work of Hume and Popper and suggested in his paper "The Environment and Disease: Association or Causation?" that aspects of an association such as strength, consistency, specificity, and temporality be considered in attempting to distinguish causal from noncausal associations in the epidemiological situation. (See Bradford- Hill criteria.) He did not note however, that temporality is the only necessary criterion among those aspects. Directed acyclic graphs (DAGs) are increasingly used in epidemiology to help enlighten causal thinking.
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Directed acyclic graphs representations of partial orderings have many applications in scheduling for systems of tasks with ordering constraints., p. 469. An important class of problems of this type concern collections of objects that need to be updated, such as the cells of a spreadsheet after one of the cells has been changed, or the object files of a piece of computer software after its source code has been changed. In this context, a dependency graph is a graph that has a vertex for each object to be updated, and an edge connecting two objects whenever one of them needs to be updated earlier than the other.
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Q-systems are a method of directed graph transformations according to given grammar rules, developed at the Université de Montréal by Alain Colmerauer in 1967--70 for use in natural language processing. The Université de Montréal's machine translation system, TAUM-73, used the Q-Systems as its language formalism. The data structure manipulated by a Q-system is a Q-graph, which is a directed acyclic graph with one entry node and one exit node, where each arc bears a labelled ordered tree. An input sentence is usually represented by a linear Q-graph where each arc bears a word (tree reduced to one node labelled by this word).
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To do this, the least sterially bulky R group will rotate to assume the R4 position. Although peracids and metal catalyzed expoidations show different selectivity in acyclic systems, they show relatively similar selectivity in cyclic systems For cyclic ring systems that are smaller seven or smaller or 10 or lager, similar patterns of selectivity are observed. However it has been shown that for medium-sized rings (eight and nine) peracid oxidizers show reverse selectivity, while vanadium catalyzed reactions continue to show formation of the syn epoxide. 1500px Although it is the least reactive metal catalyst for epoxidations, vanadium is highly selective for alkenes with allylic alcohols.
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The former involves enzymic ring expansion- contraction reactions, and the latter is accomplished (biomimetically) or (more frequently) through ring closures of acyclic precursors with more (or fewer) ring atoms than the parent steroid framework. Combinations of these ring alterations are known in nature. For instance, ewes who graze on corn lily ingest cyclopamine (shown) and veratramine, two of a sub-family of steroids where the C- and D-rings are contracted and expanded respectively via a biosynthetic migration of the original C-13 atom. Ingestion of these C-nor- D-homosteroids results in birth defects in lambs: cyclopia from cyclopamine and leg deformity from veratramine.
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The problem of finding the sink in a unique sink orientation of a hypercube was formulated as an abstraction of linear complementarity problems by and it was termed "unique sink orientation" in 2001 . It is possible for an algorithm to determine the unique sink of a -dimensional hypercube in time for , substantially smaller than the time required to examine all vertices. When the orientation has the additional property that the orientation forms a directed acyclic graph, which happens when unique sink orientations are used to model LP-type problems, it is possible to find the sink using a randomized algorithm in expected time exponential in the square root of d .
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A typical Files-11 directory hierarchy: all files are rooted in the Master File Directory; File2 is in two directories All files and directories in a Files-11 file system are contained inside one or more parent directories, and eventually under the root directory, the master file directory (see below). The file system is therefore organised in a directed acyclic graph (DAG) structure. In this example (see right), `File 2` has a directory entry under both `Dir 2` and `Dir 3`; it is "in" both directories simultaneously. Even if removed from one, it would still exist in the other directory until removed from there also.
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The algorithm takes a directed graph as input, and produces a partition of the graph's vertices into the graph's strongly connected components. Each vertex of the graph appears in exactly one of the strongly connected components. Any vertex that is not on a directed cycle forms a strongly connected component all by itself: for example, a vertex whose in-degree or out-degree is 0, or any vertex of an acyclic graph. The basic idea of the algorithm is this: a depth-first search (DFS) begins from an arbitrary start node (and subsequent depth-first searches are conducted on any nodes that have not yet been found).
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A directed graph (blue and black) and its condensation (yellow). The strongly connected components (subsets of blue vertices within each yellow vertex) form the blocks of a partition giving rise to the quotient. The condensation of a directed graph is the quotient graph where the strongly connected components form the blocks of the partition. This construction can be used to derive a directed acyclic graph from any directed graph.. The result of one or more edge contractions in an undirected graph G is a quotient of G, in which the blocks are the connected components of the subgraph of G formed by the contracted edges.
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For directed acyclic graphs whose reachability order has higher dimension, a weak dominance drawing is a drawing in which every edge is oriented upwards, rightwards, or both, but in which there exist pairs of vertices (u, v) for which u dominates v coordinatewise but v is not reachable from u in the graph. We said that a vertex u dominates another vertex v if the coordinates (u_x, u_y) of u are less or equal the coordinates (v_x, v_y) of v, i.e., u_x <= v_x and u_y <= v_y considering a XY-plane. The goal in this style of drawing is to minimize the number of such falsely implied paths.
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These objects can be viewed as collections of smaller components like shapes, which can be viewed as collections of lines, and so on. This coincides directly with the way hierarchical processing works. If a simple unit of the processing hierarchy can classify lines into shapes, then an equivalent unit could process shapes into objects (of course, there are some intermediate steps between these, but the idea is there). Thus, if you arrange these generic classifying units in a hierarchical fashion (using a directed acyclic graph), a full step-by-step classification can ensue from pixels of color all the way up to an abstract label of what is in the picture.
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If a graph G is oriented acyclically with outdegree k, then its edges may be partitioned into k forests by choosing one forest for each outgoing edge of each node. Thus, the arboricity of G is at most equal to its degeneracy. In the other direction, an n-vertex graph that can be partitioned into k forests has at most k(n − 1) edges and therefore has a vertex of degree at most 2k− 1 – thus, the degeneracy is less than twice the arboricity. One may also compute in polynomial time an orientation of a graph that minimizes the outdegree but is not required to be acyclic.
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The mechanism of the Saegusa–Ito oxidation involves coordination of palladium to the enol olefin followed by loss of the silyl group and formation of an oxoallyl-palladium complex. β-hydride elimination yields the palladium hydride enone complex which upon reductive elimination yields the product along with acetic acid and Pd0.Oxidation , Chem 215 lecture notes The reversibility of the elimination step allows equilibration, leading to the thermodynamic E-selectivity in acyclic substrates. It has been shown that the product can form a stable Pd0-olefin complex, which may be responsible for the difficulty with re-oxidation seen in catalytic variants of the reaction.
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Upward planar drawings are particularly important for Hasse diagrams of partially ordered sets, as these diagrams are typically required to be drawn upwardly. In graph-theoretic terms, these correspond to the transitively reduced directed acyclic graphs; such a graph can be formed from the covering relation of a partial order, and the partial order itself forms the reachability relation in the graph. If a partially ordered set has one minimal element, has one maximal element, and has an upward planar drawing, then it must necessarily form a lattice, a set in which every pair of elements has a unique greatest lower bound and a unique least upper bound., 6.7.
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Students with singular needs or disabilities require special teaching approaches, equipment, or care within or outside a regular classroom. Since students with intellectual disabilities are handled separately, schools may treat two students with identical achievements differently, if one of the students is low-performing, but typically developing, and the other student is low-performing due to a disability. Apart from the social promotion, there is the merit promotion, either by mid-term promotion or by using a course-based curriculum with a directed acyclic graph of prerequisites similar to college curricula. This alternative is unique in allowing each student to advance at his or her own pace.
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He served as chair of the University of Michigan's Department of Chemistry from 2002-2004. In 2004 Professor Roush relocated with his group to the Jupiter, Florida campus of the Scripps Research Institute (TSRI) where he is currently an emeritus professor. Roush was active in the field of organic chemistry with research interests including natural product synthesis, methods development and medicinal chemistry. He is known for his stereochemical studies and synthetic applications of the intramolecular Diels-Alder reaction and his work in the area of asymmetric and acyclic diastereoselective synthesis, specifically the use of tartrate ester modified allylboronates and other allylmetal compounds for the aldol-like construction of propionate-derived systems.
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Therefore, the β-keto thioester is formed out of the alcohol by a quadruplet of reactions with respectively N,N′-dicyclohexylcarbodiimide (DCC), N-chlorosuccinimide (NCS), sodium chlorite and 1,1'-carbonyldiimidazole (CDI). With 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) treatment, this β-keto thioester can be converted into an unstable diol, which is the acyclic precursor of the end product. In order to introduce the ring system that characterizes debromoaplysiotoxin in this molecule, hemiketal formation must be achieved between the C.7 ketone and the C.11 hydroxygroup, after which lactone formation can seal the deal. This can be achieved by a method called macrolactonization.
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To prove that transitive reduction is as easy as transitive closure, Aho et al. rely on the already-known equivalence with Boolean matrix multiplication. They let A be the adjacency matrix of the given directed acyclic graph, and B be the adjacency matrix of its transitive closure (computed using any standard transitive closure algorithm). Then an edge uv belongs to the transitive reduction if and only if there is a nonzero entry in row u and column v of matrix A, and there is a zero entry in the same position of the matrix product AB. In this construction, the nonzero elements of the matrix AB represent pairs of vertices connected by paths of length two or more.
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Kharasch- Sosnovsky reaction A modification of the reaction utilizes copper(II) trifluoromethanesulfonate as a catalyst and DBN or DBU as bases to achieve yields up to 80% in the reaction of acyclic olefins with TBPB to allylic benzoates. Substituted oxazolines and thiazolines can be oxidized to the corresponding oxazoles and thiazoles in a modified Kharash-Sosnovsky oxidation with TBPB and a mixture of Cu(I) and Cu(II) salts in suitable yields. Kharasch-Sosnovsky reaction for oxidation of oxazolines and thiazolines The carboalkoxy group at the C-4 position is essential a successful reaction. Benzene and furans can be alkenylated with olefins in an oxidative coupling under palladium salt catalysis, with TBPB as hydrogen acceptor.
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With modular programming, concerns are separated such that modules perform logically discrete functions, interacting through well-defined interfaces. Often modules form a directed acyclic graph (DAG); in this case a cyclic dependency between modules is seen as indicating that these should be a single module. In the case where modules do form a DAG they can be arranged as a hierarchy, where the lowest-level modules are independent, depending on no other modules, and higher-level modules depend on lower-level ones. A particular program or library is a top-level module of its own hierarchy, but can in turn be seen as a lower-level module of a higher-level program, library, or system.
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A homopolar generator is a DC electrical generator comprising an electrically conductive disc or cylinder rotating in a plane perpendicular to a uniform static magnetic field. A potential difference is created between the center of the disc and the rim (or ends of the cylinder), the electrical polarity depending on the direction of rotation and the orientation of the field. It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc. The voltage is typically low, on the order of a few volts in the case of small demonstration models, but large research generators can produce hundreds of volts, and some systems have multiple generators in series to produce an even larger voltage.
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Partition of the graph of a rhombic dodecahedron into two linear forests, showing that its linear arboricity is two In graph theory, a branch of mathematics, the linear arboricity of an undirected graph is the smallest number of linear forests its edges can be partitioned into. Here, a linear forest is an acyclic graph with maximum degree two; that is, it is a disjoint union of path graphs. Linear arboricity is a variant of arboricity, the minimum number of forests into which the edges can be partitioned. The linear arboricity of any graph of maximum degree \Delta is known to be at least \lceil\Delta/2\rceil and is conjectured to be at most \lceil(\Delta+1)/2\rceil.
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8-hydroxygeraniol dehydrogenase (, 8-hydroxygeraniol oxidoreductase, CYP76B10, G10H, CrG10H, SmG10H, acyclic monoterpene primary alcohol:NADP+ oxidoreductase) is an enzyme with systematic name (6E)-8-hydroxygeraniol:NADP+ oxidoreductase. This enzyme catalyses the following chemical reaction : (6E)-8-hydroxygeraniol + 2 NADP+ \rightleftharpoons (6E)-8-oxogeranial + 2 NADPH + 2 H+ (overall reaction) : (1a) (6E)-8-hydroxygeraniol + NADP+ \rightleftharpoons (6E)-8-hydroxygeranial + NADPH + H+ : (1b) (6E)-8-hydroxygeraniol + NADP+ \rightleftharpoons (6E)-8-oxogeraniol + NADPH + H+ : (1c) (6E)-8-hydroxygeranial + NADP+ \rightleftharpoons (6E)-8-oxogeranial + NADPH + H+ : (1d) (6E)-8-oxogeraniol + NADP+ \rightleftharpoons (6E)-8-oxogeranial + NADPH + H+ This enzyme contains Zn2+. It catalyses the oxidation of (6E)-8-hydroxygeraniol to (6E)-8-oxogeranial via either (6E)-8-hydroxygeranial or (6E)-8-oxogeraniol.
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The use of metal hydrides (tin, silicon and mercury hydrides) is common in radical cyclization reactions; the primary limitation of this method is the possibility of reduction of the initially formed radical by H-M. Fragmentation methods avoid this problem by incorporating the chain-transfer reagent into the substrate itself—the active chain-carrying radical is not released until after cyclization has taken place. The products of fragmentation methods retain a double bond as a result, and extra synthetic steps are usually required to incorporate the chain- carrying group. Atom-transfer methods rely on the movement of an atom from the acyclic starting material to the cyclic radical to generate the product.
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CC systems can also be defined from pseudoline arrangements, or from sorting networks in which the compare-exchange operations only compare adjacent pairs of elements (as in for instance bubble sort), and every CC system can be defined in this way. This relation is not one-to-one, but the numbers of nonisomorphic CC systems on n points, of pseudoline arrangements with n lines, and of sorting networks on n values, are within polynomial factors of each other. There exists a two-to-one correspondence between CC systems and uniform acyclic oriented matroids of rank 3. These matroids in turn have a 1-1 correspondence to topological equivalence classes of pseudoline arrangements with one marked cell.
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Example history graph of a revision-controlled project; trunk is in green, branches in yellow, and graph is not a tree due to presence of merges (the red arrows). In terms of graph theory, revisions are generally thought of as a line of development (the trunk) with branches off of this, forming a directed tree, visualized as one or more parallel lines of development (the "mainlines" of the branches) branching off a trunk. In reality the structure is more complicated, forming a directed acyclic graph, but for many purposes "tree with merges" is an adequate approximation. Revisions occur in sequence over time, and thus can be arranged in order, either by revision number or timestamp.
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There are two radically different digital compositing workflows: node-based compositing and layer-based compositing. Node-based compositing represents an entire composite as a directed acyclic graph, linking media objects and effects in a procedural map, intuitively laying out the progression from source input to final output, and is in fact the way all compositing applications internally handle composites. This type of compositing interface allows great flexibility, including the ability to modify the parameters of an earlier image processing step "in context" (while viewing the final composite). Node-based compositing packages often handle keyframing and time effects poorly, as their workflow does not stem directly from a timeline, as do layer-based compositing packages.
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First, if the problem has width bounded by a constant then a decomposition of bounded width can be found in polynomial time. Second, the problem obtained by converting the original problem according to the decomposition is not superpolynomially larger than the original problem, if the decomposition has fixed width. While most tractable structural restrictions derive from fixing the width of a decomposition method, others have been developed. Some can be reformulated in terms of decomposition methods: for example, the restriction to binary acyclic problem can be reformulated as that of problem of treewidth 1; the restriction of induced width (which is not defined in terms of a decomposition) can be reformulated as tree clustering.
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We can define a weaker notion of hypergraph acyclicity, later termed α-acyclicity. This notion of acyclicity is equivalent to the hypergraph being conformal (every clique of the primal graph is covered by some hyperedge) and its primal graph being chordal; it is also equivalent to reducibility to the empty graph through the GYO algorithm (also known as Graham's algorithm), a confluent iterative process which removes hyperedges using a generalized definition of ears. In the domain of database theory, it is known that a database schema enjoys certain desirable properties if its underlying hypergraph is α-acyclic. Besides, α-acyclicity is also related to the expressiveness of the guarded fragment of first-order logic.
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The maximum-weight closure of a given graph G is the same as the complement of the minimum-weight closure on the transpose graph of G, so the two problems are equivalent in computational complexity. If two vertices of the graph belong to the same strongly connected component, they must behave the same as each other with respect to all closures: it is not possible for a closure to contain one vertex without containing the other. For this reason, the input graph to a closure problem may be replaced by its condensation, in which every strongly connected component is replaced by a single vertex. The condensation is always a directed acyclic graph.
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Electronic circuits themselves are not necessarily acyclic or directed. Dataflow programming languages describe systems of operations on data streams, and the connections between the outputs of some operations and the inputs of others. These languages can be convenient for describing repetitive data processing tasks, in which the same acyclically-connected collection of operations is applied to many data items. They can be executed as a parallel algorithm in which each operation is performed by a parallel process as soon as another set of inputs becomes available to it.. In compilers, straight line code (that is, sequences of statements without loops or conditional branches) may be represented by a DAG describing the inputs and outputs of each of the arithmetic operations performed within the code.
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Formally, Bayesian networks are directed acyclic graphs (DAGs) whose nodes represent variables in the Bayesian sense: they may be observable quantities, latent variables, unknown parameters or hypotheses. Edges represent conditional dependencies; nodes that are not connected (no path connects one node to another) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) the probability (or probability distribution, if applicable) of the variable represented by the node. For example, if m parent nodes represent m Boolean variables, then the probability function could be represented by a table of 2^m entries, one entry for each of the 2^m possible parent combinations.
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The reachability relationship in any directed acyclic graph can be formalized as a partial order on the vertices of the DAG. In this partial order, two vertices and are ordered as exactly when there exists a directed path from to in the DAG; that is, when is reachable from .. However, different DAGs may give rise to the same reachability relation and the same partial order.. For example, the DAG with two edges and has the same reachability relation as the graph with three edges , , and . Both of these DAGS produce the same partial order, in which the vertices are ordered as . If is a DAG, its transitive closure is the graph with the most edges that represents the same reachability relation.
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Faraday disk, the first homopolar generator A homopolar generator is a DC electrical generator comprising an electrically conductive disc or cylinder rotating in a plane perpendicular to a uniform static magnetic field. A potential difference is created between the center of the disc and the rim (or ends of the cylinder) with an electrical polarity that depends on the direction of rotation and the orientation of the field. It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc. The voltage is typically low, on the order of a few volts in the case of small demonstration models, but large research generators can produce hundreds of volts, and some systems have multiple generators in series to produce an even larger voltage.
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An upward planar drawing This planar DAG has no upward drawing, because its source and sink cannot both be in the same face In graph drawing, an upward planar drawing of a directed acyclic graph is an embedding of the graph into the Euclidean plane, in which the edges are represented as non-crossing monotonic upwards curves. That is, the curve representing each edge should have the property that every horizontal line intersects it in at most one point, and no two edges may intersect except at a shared endpoint.; . In this sense, it is the ideal case for layered graph drawing, a style of graph drawing in which edges are monotonic curves that may cross, but in which crossings are to be minimized.
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Each nonzero cell at each time step represents a position that is occupied by a growing tree branch. At each successive time step, a branch can grow into one of the two cells above it to its left and right only when there is no other branch competing for the same cell. A forest of trees growing according to these rules has exactly the same behavior as Rule 90.. From any initial configuration of Rule 90, one may form a mathematical forest, a directed acyclic graph in which every vertex has at most one outgoing edge, whose trees are the same as the trees in Miller's metaphor. The forest has a vertex for each pair such that cell is nonzero at time .
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The nuclear magnetic resonance database method enables identification of the stereochemistry of chiral molecules, especially polyols. It relies on the observation that NMR spectroscopy data depend only on the immediate environment near an asymmetric carbon, not on the entire molecular structure. All stereoisomers of a certain class of compounds are synthesized, and their proton NMR and carbon-13 NMR chemical shifts and coupling constants are compared. Yoshito Kishi's group at Harvard University has reported NMR databases for 1,3,5-triolsKobayashi, Y.; Tan, C.-H.; Kishi, Y. “Toward Creation of a Universal NMR Database for Stereochemical Assignment: The Case of 1,3,5-Trisubstituted Acyclic Systems” Helv. Chim. Acta 2000, 83, 2562-2571. 1,2,3-triols, 1,2,3,4-tetraols, and 1,2,3,4,5-pentaols.S. Higabayashi, W. Czechtizky, Y. Kobayashi, and Y. Kishi.
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Many important families of combinatorial structures, such as the acyclic orientations of a graph or the adjacencies between regions in a hyperplane arrangement, can be represented as partial cube graphs. An important special case of a partial cube is the skeleton of the permutohedron, a graph in which vertices represent permutations of a set of ordered objects and edges represent swaps of objects adjacent in the order. Several other important classes of graphs including median graphs have related definitions involving metric embeddings . A flip graph is a graph formed from the triangulations of a point set, in which each vertex represents a triangulation and two triangulations are connected by an edge if they differ by the replacement of one edge for another.
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It is equivalent to saying that the prime decomposition of the manifold has no acyclic components, and turns out to be equivalent to the condition that all geometric pieces of the manifold have geometries based on the two Thurston geometries S2×R and S3. In the context that one makes no assumption about the fundamental group whatsoever, Perelman made a further technical study of the limit of the manifold for infinitely large times, and in so doing, proved Thurston's geometrization conjecture: at large times the manifold has a thick-thin decomposition, whose thick piece has a hyperbolic structure, and whose thin piece is a graph manifold. Due to Perelman's and Colding and Minicozzi's results, however, these further results are unnecessary in order to prove the Poincaré conjecture.
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SGA 6 Expo VII uses the following weakened form of the notion of a regular embedding, that agrees with the usual one for Noetherian schemes. First, given a projective module E over a commutative ring A, an A-linear map u: E \to A is called Koszul-regular if the Koszul complex determined by it is acyclic in dimension > 0 (consequently, it is a resolution of the cokernel of u). NB: We follow the terminology of the Stacks project. Then a closed immersion X \hookrightarrow Y is called Koszul-regular if the ideal sheaf determined by it is such that, locally, there are a finite free A-module E and a Koszul-regular surjection from E to the ideal sheaf.
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Main path analysis uncovers the most significant paths, or citation chains, in a citation network. The figure shows the global key-route main paths (in red) for a sample citation network (based on search path count and at key-route 1). Main path analysis is a mathematical tool, first proposed by Hummon and Doreian in 1989, to identify the major paths in a citation network, which is one form of a directed acyclic graph (DAG). The method begins by measuring the significance of all the links in a citation network through the concept of ‘traversal count’ and then sequentially chains the most significant links into a "main path", which is deemed the most significant historical path in the target citation network.
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Allicin, S-benzyl phenylmethanethiosulfinate, and related thiosulfinates show radical-trapping antioxidant activity associated with easy formation of sulfenic acids The acyclic thiosulfinates from Allium and Brassica species possess antimicrobial, antiparasitic, antitumor and cysteine protease inhibitory activity while the natural 1,2-dithiolane-1-oxides are growth inhibitors. The thiosulfinates from Petiveria also exhibit antimicrobial activity. Thiosulfinates feature a S(IV) center linked to a S(II) center, the former being stereogenic. Conversion of simple disulfides to thiosulfinates results in a considerable weakening of the S–S bond from about 70 to 34.5 kcal mol−1 (16.7 to 8.25 kJ mol−1) for the S-S bond in PhS(O)SPh, with the consequence that most thiosulfinates are both unstable and quite reactive.
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Although synthesized from multiple synthetic pathways, reaction of the germylene chloride with L-selectride in toluene at -80 °C most directly gives the orange crystalline hydrido-digermene with 52% yield. This digermene is thought to be in equilibrium with a two-coordinate hydrido-germylene, which can be isolated upon addition of DMAP (dimethylaminopyridine) at 20 °C, giving pale yellow crystals of the three-coordinate germylene hydride in 27% yield. Synthesis of first stable acyclic germylene hydride Similar to the germylene hydrides, the first known example of a germyliumylidene hydride (a germylene hydride cation) was isolated in 2014. This compound can be formed from a two step process, starting with the reaction of potassium bis(NHC)-borate with GeCl2•dioxane to yield a zwitterionic germyliumylidene chloride.
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While family trees are depicted as trees, family relations do not in general form a tree in the sense of graph theory, since distant relatives can mate, so a person can have a common ancestor on their mother's and father's side. However, because a parent must be born before their child is born, a person cannot be their own ancestor, and thus there are no loops, so ancestry forms a directed acyclic graph. The graphs of matrilineal descent ("mother" relationships between women) and patrilineal descent ("father" relationships between men) are trees however. Assuming no common ancestor, an ancestry chart is a perfect binary tree, as each person has exactly one mother and one father, for two parents; these thus have a regular structure.
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Diaryl-strained-cyclooctynes including dibenzylcyclooctyne (DIBO) have also been used to react with 1,3-nitrones in strain-promoted alkyne-nitrone cycloadditions (SPANC) to yield N-alkylated isoxazolines. The SPAAC vs SpANC reaction Because this reaction is metal-free and proceeds with fast kinetics (k2 as fast as 60 1/Ms, faster than both the CuAAC or the SPAAC) SPANC can be used for live cell labeling. Moreover, substitution on both the carbon and nitrogen atoms of the nitrone dipole, and acyclic and endocyclic nitrones are all tolerated. This large allowance provides a lot of flexibility for nitrone handle or probe incorporation.(64) (a) Ning, X.; Temming, R. P.; Dommerholt, J.; Guo, J.; Ania, D.B.; Debets, M. F.; Wolfert, M. A.; Boons, G.-J.
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For instance in certain aldol adducts with 2,6-disubstituted aryl groups the molecular geometry has the vicinal hydrogen atoms in an antiperiplanar configuration both in a crystal lattice (X-ray diffraction) and in solution proton (NMR coupling constants) normally reserved for the most bulky groups i.d. both arenes:Effect of 2,6-Disubstituted Aryl Groups on Acyclic Conformation: Preference for an Antiperiplanar Orientation of the Geminal and Vicinal Hydrogens Paul R. Carlier, Yiqun Zhang, Carla Slebodnick, Michael M.-C. Lo, and Ian D. Williams J. Org. Chem.; 2006; 71(23) pp 8835 - 8841; (Article) Syn-pentane effect in aldol adducts The other contributing factor explaining this conformation is reduction in allylic strain by minimizing the dihedral angle between the arene double bond and the methine proton.
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Sequence graphs can be used to represent multiple sequence alignments with the addition of a new kind of edge representing homology between segments. For a set of genomes, one can create an acyclic breakpoint graph with a thread for each genome. For two segments (a, b) and (c,d), where a,b,c, and d represent the endpoints of the two segments, homology edges can be created from a to c and b to d or from a to d and b to c \- representing the two possible orientations of the homology. The advantage of representing a multiple sequence alignment this way is that it is possible to include inversions and other structural rearrangements that wouldn't be allowable in a matrix representation.
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Tetramethylbutane, sometimes called hexamethylethane, is a hydrocarbon with formula C8H18 or (H3C-)3C-C(-CH3)3. It is the most heavily branched and most compact of the many octane isomers, the only one with a butane (C4) backbone. Because of its highly symmetrical structure, it has a very high melting point and a short liquid range; in fact, it is the smallest saturated acyclic hydrocarbon that appears as a solid at a room temperature of 25 °C. (Among cyclic hydrocarbons, cubane, C8H8 is even smaller and is also solid at room temperature.) The compound can be obtained by reaction of Grignard reagent tert-butylmagnesium bromide with ethyl bromide, or of ethylmagnesium bromide with tert-butyl bromide in the presence of manganese(II) ions.
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Tetra-tert-butylmethane is a hypothetical organic compound with formula C17H36, consisting of four tert-butyl groups bonded to a central carbon atom. It would be an alkane, specifically the most compact branched isomer of heptadecane. Some calculations suggests this compound cannot exist due to the steric hindrance among the closely packed tert-butyl groups, which would make it one of the smallest, if not the smallest itself, saturated and acyclic hydrocarbon that cannot exist. Other calculations suggest that the molecule would be stable, with the C–C bonds to the central ("methane") carbon having a length of 166.1 pm — longer than the typical C−C bond in order to reduce steric effects, but still shorter than those found in some other real molecules.
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While derivations in causal calculus rely on the structure of the causal graph, parts of the causal structure can, under certain assumptions, be learned from statistical data. The basic idea goes back to Sewall Wright's 1921 work on path analysis. A "recovery" algorithm was developed by Rebane and Pearl (1987)Rebane, G. and Pearl, J., "The Recovery of Causal Poly-trees from Statistical Data", Proceedings, 3rd Workshop on Uncertainty in AI, (Seattle) pp. 222–228, 1987 which rests on Wright's distinction between the three possible types of causal substructures allowed in a directed acyclic graph (DAG): # X \rightarrow Y \rightarrow Z # X \leftarrow Y \rightarrow Z # X \rightarrow Y \leftarrow Z Type 1 and type 2 represent the same statistical dependencies (i.e.
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Semi-transitive orientations provide a powerful tool to study word-representable graphs. A directed graph is semi-transitively oriented iff it is acyclic and for any directed path u1→u2→ ...→ut, t ≥ 2, either there is no edge from u1 to ut or all edges ui → uj exist for 1 ≤ i < j ≤ t. A key theorem in the theory of word-representable graphs states that a graph is word-representable iff it admits a semi-transitive orientation . As a corollary to the proof of the key theorem one obtain an upper bound on word-representants: Each non-complete word-representable graph G is 2(n − κ(G))-representable, where κ(G) is the size of a maximal clique in G .
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Both edge and vertex contraction techniques are valuable in proof by induction on the number of vertices or edges in a graph, where it can be assumed that a property holds for all smaller graphs and this can be used to prove the property for the larger graph. Edge contraction is used in the recursive formula for the number of spanning trees of an arbitrary connected graph, and in the recurrence formula for the chromatic polynomial of a simple graph. Contractions are also useful in structures where we wish to simplify a graph by identifying vertices that represent essentially equivalent entities. One of the most common examples is the reduction of a general directed graph to an acyclic directed graph by contracting all of the vertices in each strongly connected component.
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Both checking whether a 2-coloring is valid and checking whether a given odd-length sequence of vertices is a cycle may be performed more simply than testing bipartiteness. Analogously, it is possible to test whether a given directed graph is acyclic by a certifying algorithm that outputs either a topological order or a directed cycle. It is possible to test whether an undirected graph is a chordal graph by a certifying algorithm that outputs either an elimination ordering (an ordering of all vertices such that, for every vertex, the neighbors that are later in the ordering form a clique) or a chordless cycle. And it is possible to test whether a graph is planar by a certifying algorithm that outputs either a planar embedding or a Kuratowski subgraph.
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A Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies ); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies ). The underlying graph of a Markov random field may be finite or infinite. When the joint probability density of the random variables is strictly positive, it is also referred to as a Gibbs random field, because, according to the Hammersley–Clifford theorem, it can then be represented by a Gibbs measure for an appropriate (locally defined) energy function.
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Computer scientist Scott Aaronson analyzed the computational power of the Digi-Comp II. There are several ways to mathematically model the device's computational capabilities. A natural abstraction is a directed acyclic graph in which each internal vertex has an out-degree of 2, representing a toggle cam that routes balls to one of two other vertices. A fixed number of balls are placed at a designated source vertex, and the decision problem is to determine whether any balls ever reach a designated sink vertex. Aaronson showed that this decision problem, given as inputs a description of the DAG and the number of balls to run (encoded in unary), is complete under log-space reduction for CC, the class of problems log-space reducible to the stable marriage problem.
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Notably, this is one of few examples of a diastereoselective intermolecular reductive Heck. In 2018, Engle and coworkers disclosed an intermolecular reductive Heck reaction of diverse terminal alkenes and select internal alkenes utilizing aqueous tetramethylammonium formate as the reductant. This method tolerated an array of functional groups, including reductively labile groups, on both the (hetero)aryl iodide and alkene coupling partners, and was generally regioselective for the anti-Markovnikov product for terminal alkenes. A variety of terminal alkenes were compatible with the conditions, including simple a-olefins, heteroatom-substituted alkenes, and alkene- containing complex molecules such as quinine (49) and various terpenes. In addition, cyclic internal alkenes (45 and 48) were suitable substrates, affording reasonable yields of product; however acyclic internal alkenes were poor substrates for the reaction in terms of yield and regioselectivity.
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In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time.
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The structure of an alpha amino acid in its un-ionized form Amino acids are organic compounds that contain amine (–NH2) and carboxyl (–COOH) functional groups, along with a side chain (R group) specific to each amino acid. The key elements of an amino acid are carbon (C), hydrogen (H), oxygen (O), and nitrogen (N), although other elements are found in the side chains of certain amino acids. About 500 naturally occurring amino acids are known (though only 20 appear in the genetic code) and can be classified in many ways. They can be classified according to the core structural functional groups' locations as alpha- (α-), beta- (β-), gamma- (γ-) or delta- (δ-) amino acids; other categories relate to polarity, pH level, and side chain group type (aliphatic, acyclic, aromatic, containing hydroxyl or sulfur, etc.).
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The acyclicity of G is an essential assumption in the Lindström–Gessel–Viennot lemma; it guarantees (in reasonable situations) that the sums e(a, b) are well-defined, and it advects into the proof (if G is not acyclic, then f might transform a self-intersection of a path into an intersection of two distinct paths, which breaks the argument that f is an involution). Nevertheless, Kelli Talaska's 2012 paper establishes a formula generalizing the lemma to arbitrary digraphs. The sums e(a, b) are replaced by formal power series, and the sum over nonintersecting path tuples now becomes a sum over collections of nonintersecting and non-self-intersecting paths and cycles, divided by a sum over collections of nonintersecting cycles. The reader is referred to Talaska's paper for details.
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DNA uses the deoxynucleotides C, G, A, and T, while RNA uses the ribonucleotides (which have an extra hydroxyl(OH) group on the pentose ring) C, G, A, and U. Modified bases are fairly common (such as with methyl groups on the base ring), as found in ribosomal RNA or transfer RNAs or for discriminating the new from old strands of DNA after replication. Each nucleotide is made of an acyclic nitrogenous base, a pentose and one to three phosphate groups. They contain carbon, nitrogen, oxygen, hydrogen and phosphorus. They serve as sources of chemical energy (adenosine triphosphate and guanosine triphosphate), participate in cellular signaling (cyclic guanosine monophosphate and cyclic adenosine monophosphate), and are incorporated into important cofactors of enzymatic reactions (coenzyme A, flavin adenine dinucleotide, flavin mononucleotide, and nicotinamide adenine dinucleotide phosphate).
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If the double bond of an acyclic mono-ene is not the first bond of the chain, the name as constructed above still does not completely identify the compound, because of cis-trans isomerism. Then one must specify whether the two single C–C bonds adjacent to the double bond are on the same side of its plane, or on opposite sides. For monoalkenes, the configuration is often indicated by the prefixes cis- (from Latin "on this side of" or trans- ("across", "on the other side of") before the name, respectively; as in cis-2-pentene or trans-2-butene. The difference between cis- and trans- isomers More generally, cis-trans isomerism will exist if each of the two carbons of in the double bond has two different atoms or groups attached to it.
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Reactions of linear topology are the most common, and consist of all transformations whose transition states are acyclic, including addition, elimination, substitution, and (some types of) fragmentation reactions. In contrast, in pericyclic reactions, the atoms under chemical change form a closed cycle, and include reactions like the Diels-Alder reaction and Cope rearrangement, among many others. In contrast to these types of reactions, a coarctate reaction is characterized by a doubly cyclic transition state, in which at least one atom undergoes the simultaneous making and breaking of two bonds. Thus, the topology of the transition state of a coarctate reaction is a constricted cycle that meets with itself (resembling a figure eight) while the topology of pericyclic and linear reactions are a circle (or Möbius strip) and line segment, respectively.
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An acyclic graph is a forest, but connectedness is usually assumed; as a result, the condition that is usually considered is that primal graphs are trees. This property of tree-like constraint satisfaction problems is exploited by decomposition methods, which convert problems into equivalent ones that only contain binary constraints arranged as a tree. The variables of these problems correspond to sets of variables of the original problem; the domain of such a variable is obtained by considering some of the constraints of the original problem whose scope is contained in the corresponding original set of variables; constraints of these new problems represent equality of variables that are contained in two sets. If the graph of one such equivalent problem is a tree, the problem can be solved efficiently.
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In mathematics, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible, such that if there is a (directed) path from vertex v to vertex w in D, then there is also such a path in the reduction. Transitive reductions were introduced by , who provided tight bounds on the computational complexity of constructing them. More technically, the reduction is a directed graph that has the same reachability relation as D. Equivalently, D and its transitive reduction should have the same transitive closure as each other, and its transitive reduction should have as few edges as possible among all graphs with this property. The transitive reduction of a finite directed acyclic graph (a directed graph without directed cycles) is unique and is a subgraph of the given graph.
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If v has no incoming neighbors, set the length of the longest path ending at v to zero. In either case, record this number so that later steps of the algorithm can access it. Once this has been done, the longest path in the whole DAG may be obtained by starting at the vertex v with the largest recorded value, then repeatedly stepping backwards to its incoming neighbor with the largest recorded value, and reversing the sequence of vertices found in this way. The critical path method for scheduling a set of activities involves the construction of a directed acyclic graph in which the vertices represent project milestones and the edges represent activities that must be performed after one milestone and before another; each edge is weighted by an estimate of the amount of time the corresponding activity will take to complete.
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However, every planar graph has an arc diagram in which each edge is drawn as a biarc with at most two semicircles. More strongly, every st-planar directed graph (a planar directed acyclic graph with a single source and a single sink, both on the outer face) has an arc diagram in which every edge forms a monotonic curve, with these curves all consistently oriented from one end of the vertex line towards the other. For undirected planar graphs, one way to construct an arc diagram with at most two semicircles per edge is to subdivide the graph and add extra edges so that the resulting graph has a Hamiltonian cycle (and so that each edge is subdivided at most once), and to use the ordering of the vertices on the Hamiltonian cycle as the ordering along the line.
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Henzinger and King suggest to represent a given tree by keeping its Euler tour in a balanced binary search tree, keyed by the index in the tour. So for example, the unbalanced tree in the example above, having 7 nodes, will be represented by a balanced binary tree with 14 nodes, one for each time each node appears on the tour. We can represent a forest (an acyclic graph) using a collection of ET trees - one ET tree for one forest tree. This representation allows us to quickly answer the question "what is the root of node v?" by just moving to the first node of the ET tree (since nodes in the ET tree are keyed by their location in the Euler tour, and the root is the first and last node in the tour).
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The first examples of the HDDA reaction were reported independently in 1997 by the groups of Ueda and Johnson.Bradley, A. Z.; Johnson, R. P. J. Am. Chem. Soc., 1997, 119, 9917 Cahill, K. J.; Ajaz, A.; Johnson, R. P. Aust. J. Chem., 2010, 63, 1007 Miyawaki, K.; Suzuki, R.; Kawano, T.; Ueda, I. Tetrahedron Lett., 1997, 38, 3943 Johnson and co-workers observed the cyclization of 1,3,8-nonatriyne under flash vacuum thermolysis (600 °C, 10−2 torr) to form two products, indane and the dehydrogenation product indene, in 95% combined yield. Deuterium labeling studies suggested that the product was formed by a [4+2] cycloaddition to a benzyne intermediate, followed by in-situ reduction to form the observed products. Ueda and co-workers observed that acyclic tetraynes cyclized at room temperature to form 5H-fluorenol derivatives.
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If edges (to child nodes) are thought of as references, then a tree is a special case of a digraph, and the tree data structure can be generalized to represent directed graphs by removing the constraints that a node may have at most one parent, and that no cycles are allowed. Edges are still abstractly considered as pairs of nodes, however, the terms and are usually replaced by different terminology (for example, and ). Different implementation strategies exist: a digraph can be represented by the same local data structure as a tree (node with value and list of children), assuming that "list of children" is a list of references, or globally by such structures as adjacency lists. In graph theory, a tree is a connected acyclic graph; unless stated otherwise, in graph theory trees and graphs are assumed undirected.
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A controller on a technological base "Dasphot" marked the starting point for SEA in the business of traffic regulation. Specializing in traffic signaling, the company launched in 1960 electromechanical controllers under the trade name of BC "Block Chalier" that were sold in multiple copies throughout France. In the 1970s, electronics enters the safety equipment. SEA Deloge creates and produces a family of controllers based on CMOS technology, an innovation for its time. Horizon signals that were created in 1976 from a ball of dough, are long remained the best known brand of SEA. The AR 2000, a programmable logic controller is placed on the market. Made in SEA Deloge, this controller has responded to the new traffic requirements (green wave two- way operation acyclic ...) In 1986, AES became Deloge SEA signaling [ref. required] . In that year, the controller becomes AR 2000 LP 2200.
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For each red or blue edge , is reachable from : there exists a blue path starting at and ending at . A vertex of a directed graph is said to be reachable from another vertex when there exists a path that starts at and ends at . As a special case, every vertex is considered to be reachable from itself (by a path with zero edges). If a vertex can reach itself via a nontrivial path (a path with one or more edges), then that path is a cycle, so another way to define directed acyclic graphs is that they are the graphs in which no vertex can reach itself via a nontrivial path.. A topological ordering of a directed graph is an ordering of its vertices into a sequence, such that for every edge the start vertex of the edge occurs earlier in the sequence than the ending vertex of the edge.
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Every directed acyclic graph has a topological ordering, an ordering of the vertices such that the starting endpoint of every edge occurs earlier in the ordering than the ending endpoint of the edge. The existence of such an ordering can be used to characterize DAGs: a directed graph is a DAG if and only if it has a topological ordering. In general, this ordering is not unique; a DAG has a unique topological ordering if and only if it has a directed path containing all the vertices, in which case the ordering is the same as the order in which the vertices appear in the path.. The family of topological orderings of a DAG is the same as the family of linear extensions of the reachability relation for the DAG,. so any two graphs representing the same partial order have the same set of topological orders.
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In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain complexes take their terms in an abelian category, so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi-isomorphism; if we pass to the derived category of complexes, this means that f is an isomorphism there, which recalls the familiar property of maps of groups, modules over a ring, or elements of an arbitrary abelian category that if the kernel and cokernel both vanish, then the map is an isomorphism. If we are working in a t-category, then in fact the cone furnishes both the kernel and cokernel of maps between objects of its core.
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Every transitively reduced st-planar graph, a directed acyclic planar graph with a single source and a single sink, both on the outer face of some embedding of the graph, has a dominance drawing. The left-right algorithm for finding these drawings sets the x coordinate of every vertex to be its position in a depth-first search ordering of the graph, starting with s and prioritizing edges in right-to-left order, and by setting the y coordinate to be obtained in the same way but prioritizing edges in left-to-right order. Typical dominance drawing algorithms include another phase of compaction after this coordinate assignment, shifting vertices down and to the left as much as possible while preserving the properties of a dominance drawing. The resulting drawing lies within an n × n integer grid, and displays many of the symmetries of the underlying topological embedding.
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An individual's preference is single- peaked with respect to this ordering if he has some special place that he likes best along that line, and his dislike for an alternative grows larger as the alternative goes further away from that spot (i.e., the graph of his utility function has a single peak if alternatives are placed according to the linear ordering on the horizontal axis). For example, if voters were voting on where to set the volume for music, it would be reasonable to assume that each voter had their own ideal volume preference and that as the volume got progressively too loud or too quiet they would be increasingly dissatisfied. If the domain is restricted to profiles in which every individual has a single peaked preference with respect to the linear ordering, then simple aggregation rules, which include majority rule, have an acyclic (defined below) social preference, hence "best" alternative.
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371x371px Imines do not form simple cyclic silylene additions: benzo-fused NHSis react with the diimine and ortho carbons of N-tert-butyl phenylimine to form a five-membered ring composed of the NHSi silicon, one carbon and nitrogen of the imine and the ipso and para carbons of the phenyl group, through an intermediate that breaks the phenyl aromaticity. File:NHSi_with_imine.svg NHSis add across nitrile C-N bonds, first forming a three-membered ring, subsequently a second NHSi inserts to complete a 4-membered ring, similar to the reactivity of a alkyne. Alternatively, tert- butyl isocyanide reacts more like an alkyl halide with a single silicon bonding to the tert-butyl fragment and the carbon of the cyanide groups, or with two NHSis to from an acyclic tBu-Si-Si-CN product. There is evidence that the single-silicon NHSi-nitrile interconverts in small quantities to the silicon isonitrile.
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Core to the Shepherd model of user space initialisation is the concept of the extension, a form of composability where services are designed to be layered onto other services, augmenting them with more elaborate or specialised behaviours as desired. This expresses the instantiation-based dependency relationships found in many modern init systems, making the system modular, but also allows services to interact variadically with other services in arbitrary ways. Shepherd also provides so-called virtual services which allow dynamic dispatch over a class of related service objects, such as all those which instantiate a mail transfer agent (MTA) for the system. A system governed via the Shepherd daemon can represent its user space as a directed acyclic graph, with the "system-service" − responsible for early phases of boot and init − as its root, and all subsequently initialised services as extensions to system-service's functionality, either directly or transitively over other services.
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Abilities supply the functional modules for performing specific activities and may activate each other in a hierarchical structure in the same way behaviors use abilities. Both behaviors and abilities are implemented by the same kind of functional modules, but a fundamental difference exists: behaviors are self-activating modules in response to a robot+environment state, whilst abilities are just functional blocks activated and controlled by behaviors for accomplishing their tasks (or by higher-level abilities that have been already activated by a behavior). Behaviors exist for satisfying specific needs, whilst abilities are not related to any need, because they are used by behaviors for accomplishing their tasks, but have no meaning alone. The list of abilities needed by each module (behavior or ability) is represented by its activation tree; the complete set of activation trees can be represented by a system-wide acyclic activation graph.
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Any partial order may be represented (usually in more than one way) by a directed acyclic graph in which there is a path from x to y whenever x and y are elements of the partial order with . The graphs that represent series-parallel partial orders in this way have been called vertex series parallel graphs, and their transitive reductions (the graphs of the covering relations of the partial order) are called minimal vertex series parallel graphs. Directed trees and (two- terminal) series parallel graphs are examples of minimal vertex series parallel graphs; therefore, series parallel partial orders may be used to represent reachability relations in directed trees and series parallel graphs. The comparability graph of a partial order is the undirected graph with a vertex for each element and an undirected edge for each pair of distinct elements x, y with either or .
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Given a purely combinatorial game, there is an associated rooted directed graph whose vertices are game positions and whose edges are moves, and graph traversal starting from the root is used to create a game tree. If the graph contains directed cycles, then a position in the game could repeat infinitely many times, and rules are usually needed to prevent the game from continuing indefinitely. Otherwise, the graph is a directed acyclic graph, and if it isn't a rooted tree, then the game has transpositions. This graph and its topology is important in the study of game complexity, where the state-space complexity is the number of vertices in the graph, the average game length is the average number of vertices traversed from the root to a vertex with no direct successors, and the average branching factor of a game tree is the average outdegree of the graph.
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Typical HMM-based methods work by representing an MSA as a form of directed acyclic graph known as a partial-order graph, which consists of a series of nodes representing possible entries in the columns of an MSA. In this representation a column that is absolutely conserved (that is, that all the sequences in the MSA share a particular character at a particular position) is coded as a single node with as many outgoing connections as there are possible characters in the next column of the alignment. In the terms of a typical hidden Markov model, the observed states are the individual alignment columns and the "hidden" states represent the presumed ancestral sequence from which the sequences in the query set are hypothesized to have descended. An efficient search variant of the dynamic programming method, known as the Viterbi algorithm, is generally used to successively align the growing MSA to the next sequence in the query set to produce a new MSA.
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McClintock also conducted a 1978 study of estrous synchrony in Norway rats (Rattus norvegicus). She reported that the estrous cycles of female rats living in groups of five were more regular than those of rats housed singly. She also reported that social interaction, and more importantly a shared air supply that allowed for olfactory communication enhanced the regularity of the rats’ cycles and synchronized their estrous phases after two or three cycles. McClintock hypothesized that estrous synchrony was caused by pheromones and that a coupled oscillator mechanism produced estrous synchrony in rats This observation of menstrual synchrony in Norway rats is not the same as the Whitten effect because it was the result of the continuous interactions of ongoing cycles within a female group, rather than the result of an exposure to a single external stimulus such as male odor, which in the Whitten effect releases all exposed females simultaneously from an acyclic condition.
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It will paint over the parts that are normally not visible — thus solving the visibility problem — at the cost of having painted invisible areas of distant objects. The ordering used by the algorithm is called a 'depth order', and does not have to respect the numerical distances to the parts of the scene: the essential property of this ordering is, rather, that if one object obscures part of another then the first object is painted after the object that it obscures. Thus, a valid ordering can be described as a topological ordering of a directed acyclic graph representing occlusions between objects.. Overlapping polygons can cause the algorithm to fail The algorithm can fail in some cases, including cyclic overlap or piercing polygons. In the case of cyclic overlap, as shown in the figure to the right, Polygons A, B, and C overlap each other in such a way that it is impossible to determine which polygon is above the others.
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The butterfly network, a multitree used in distributed computation, showing the subtree reachable from one of its vertices. In combinatorics and order- theoretic mathematics, a multitree may describe either of two equivalent structures: a directed acyclic graph (DAG) in which the set of vertices reachable from any vertex induces a tree, or a partially ordered set (poset) that does not have four items a, b, c, and d forming a diamond suborder with and but with b and c incomparable to each other (also called a diamond-free poset.). In computational complexity theory, multitrees have also been called strongly unambiguous graphs or mangroves; they can be used to model nondeterministic algorithms in which there is at most one computational path connecting any two states.. Multitrees may be used to represent multiple overlapping taxonomies over the same ground set.. If a family tree may contain multiple marriages from one family to another, but does not contain marriages between any two blood relatives, then it forms a multitree..
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Much later, it was discovered by Nesterenko and SuslinNesterenko–Suslin 1990 and by TotaroTotaro 1992 that Milnor K-theory is actually a direct summand of the true K-theory of the field. Specifically, K-groups have a filtration called the weight filtration, and the Milnor K-theory of a field is the highest weight-graded piece of the K-theory. Additionally, Thomason discovered that there is no analog of Milnor K-theory for a general variety.Thomason 1992 The first definition of higher K-theory to be widely accepted was Daniel Quillen's.Quillen 1971 As part of Quillen's work on the Adams conjecture in topology, he had constructed maps from the classifying spaces BGL(Fq) to the homotopy fiber of , where ψq is the qth Adams operation acting on the classifying space BU. This map is acyclic, and after modifying BGL(Fq) slightly to produce a new space BGL(Fq)+, the map became a homotopy equivalence.
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These graphs are closely related to partially ordered sets and lattices. The Hasse diagram of a partially ordered set is a directed acyclic graph whose vertices are the set elements, with an edge from x to y for each pair x, y of elements for which x ≤ y in the partial order but for which there does not exist z with x ≤ y ≤ z. A partially ordered set forms a complete lattice if and only if every subset of elements has a unique greatest lower bound and a unique least upper bound, and the order dimension of a partially ordered set is the least number of total orders on the same set of elements whose intersection is the given partial order. If the vertices of an st-planar graph are partially ordered by reachability, then this ordering always forms a two-dimensional complete lattice, whose Hasse diagram is the transitive reduction of the given graph.
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The basic function of the Profinet is the cyclic data exchange between the IO-Controller as producer and several IO-Devices as consumers of the output data and the IO-Devices as producers and the IO-Controller as consumer of the input data. Each communication relationship IO data CR between the IO-Controller and an IO-Device defines the number of data and the cycle times. All Profinet IO-Devices must support device diagnostics and the safe transmission of alarms via the communication relation for alarms Alarm CR. In addition, device parameters can be read and written with each Profinet device via the acyclic communication relation Record Data CR. The data set for the unique identification of an IO-Device, the Identification and Maintenance Data Set 0 (I&M; 0), must be installed by all Profinet IO-Devices. Optionally, further information can be stored in a standardized format as I&M; 1-4.
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If A is a homology 3-sphere not homeomorphic to the standard 3-sphere, then the suspension of A is an example of a 4-dimensional homology manifold that is not a topological manifold. The double suspension of A is homeomorphic to the standard 5-sphere, but its triangulation (induced by some triangulation of A) is not a PL manifold. In other words, this gives an example of a finite simplicial complex that is a topological manifold but not a PL manifold. (It is not a PL manifold because the link of a point is not always a 4-sphere.) Galewski and Stern showed that all compact topological manifolds (without boundary) of dimension at least 5 are homeomorphic to simplicial complexes if and only if there is a homology 3 sphere Σ with Rokhlin invariant 1 such that the connected sum Σ#Σ of Σ with itself bounds a smooth acyclic 4-manifold.
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By the correspondence between stable matchings and lower sets of rotations, the total weight of any matching is then equal to the total weight of its corresponding lower set, plus the weight of the bottom element of the lattice of matchings. The problem of finding the minimum or maximum weight stable matching becomes in this way equivalent to the problem of finding the minimum or maximum weight lower set in a partially ordered set of polynomial size, the partially ordered set of rotations. This optimal lower set problem is equivalent to an instance of the closure problem, a problem on vertex-weighted directed graphs in which the goal is to find a subset of vertices of optimal weight with no outgoing edges. The optimal lower set is an optimal closure of a directed acyclic graph that has the elements of the partial order as its vertices, with an edge from \alpha to \beta whenever \alpha\le\beta in the partial order.
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Still, in most cases, catalysts are necessary for substitution reactions to occur. The cyclopentadienyl anion () with six π electrons is planar and readily generated from the unusually acidic cyclopentadiene (pKa 16), while the corresponding cation with four π electrons is destabilized, being harder to generate than a typical acyclic pentadienyl cations and is thought to be antiaromatic. Similarly, the tropylium cation (), also with six π electrons, is so stable compared to a typical carbocation that its salts can be crystallized from ethanol. On the other hand, in contrast to cyclopentadiene, cycloheptatriene is not particularly acidic (pKa 37) and the anion is considered nonaromatic. The cyclopropenyl cation () and the triboracyclopropenyl dianion () are considered examples of a two π electron system, which are stabilized relative to the open system, despite the angle strain imposed by the 60° bond angles. Planar ring molecules with 4n π electrons do not obey Hückel's rule, and theory predicts that they are less stable and have triplet ground states with two unpaired electrons.
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An open pit mine may be modeled as a set of blocks of material which may be removed by mining it once all the blocks directly above it have been removed. A block has a total value, equal to the value of the minerals that can be extracted from it minus the cost of removal and extraction; in some cases, a block has no extraction value but must still be removed to reach other blocks, giving it a negative value. One may define an acyclic network that has as its vertices the blocks of a mine, with an edge from each block to the blocks above it that must be removed earlier than it. The weight of each vertex in this network is the total value of its block, and the most profitable plan for mining can be determined by finding a maximum weight closure, and then forming a topological ordering of the blocks in this closure.. As cited by .
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The name "entropy compression" was given to this method in a blog posting by Terence Tao. and has since been used for it by other researchers.... Moser's original version of the algorithmic Lovász local lemma, using this method, achieved weaker bounds than the original Lovász local lemma, which was originally formulated as an existence theorem without a constructive method for finding the object whose existence it proves. Later, Moser and Gábor Tardos used the same method to prove a version of the algorithmic Lovász local lemma that matches the bounds of the original lemma.. Since the discovery of the entropy compression method, it has also been used to achieve stronger bounds for some problems than would be given by the Lovász local lemma. For example, for the problem of acyclic edge coloring of graphs with maximum degree Δ, it was first shown using the local lemma that there always exists a coloring with 64Δ colors, and later using a stronger version of the local lemma this was improved to 9.62Δ.
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The two concepts of coloring number and degeneracy are equivalent: in any finite graph the degeneracy is just one less than the coloring number.; , Proposition 1, page 1084. For, if a graph has an ordering with coloring number κ then in each subgraph H the vertex that belongs to H and is last in the ordering has at most κ − 1 neighbors in H. In the other direction, if G is k-degenerate, then an ordering with coloring number k + 1 can be obtained by repeatedly finding a vertex v with at most k neighbors, removing v from the graph, ordering the remaining vertices, and adding v to the end of the order. A third, equivalent formulation is that G is k-degenerate (or has coloring number at most k + 1) if and only if the edges of G can be oriented to form a directed acyclic graph with outdegree at most k.. Such an orientation can be formed by orienting each edge towards the earlier of its two endpoints in a coloring number ordering.
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One of these algorithms, first described by , works by choosing vertices in the same order as the eventual topological sort. First, find a list of "start nodes" which have no incoming edges and insert them into a set S; at least one such node must exist in a non-empty acyclic graph. Then: L ← Empty list that will contain the sorted elements S ← Set of all nodes with no incoming edge while S is not empty do remove a node n from S add n to L for each node m with an edge e from n to m do remove edge e from the graph if m has no other incoming edges then insert m into S if graph has edges then return error (graph has at least one cycle) else return L (a topologically sorted order) If the graph is a DAG, a solution will be contained in the list L (the solution is not necessarily unique). Otherwise, the graph must have at least one cycle and therefore a topological sort is impossible.
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Nakamura's theorem (1979) gives the following necessary (also sufficient if the set of alternatives is finite) condition for a simple game to have a nonempty "core" (the set of socially "best" alternatives) for all profiles of individual preferences: the number of alternatives is less than the Nakamura number of the simple game. Here, the core of a simple game with respect to the profile of preferences is the set of all alternatives x such that there is no alternative y that every individual in a winning coalition prefers to x; that is, the set of maximal elements of the social preference. For the majority game example above, the theorem implies that the core will be empty (no alternative will be deemed "best") for some profile, if there are three or more alternatives. Variants of Nakamura's theorem exist that provide a condition for the core to be nonempty (i) for all profiles of acyclic preferences; (ii) for all profiles of transitive preferences; and (iii) for all profiles of linear orders.
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The following conditions exploit the primal graph of the problem, which has a vertex for each variable and an edge between two nodes if the corresponding variables are in a constraint. The following are conditions on binary constraint satisfaction problems where enforcing local consistency is tractable and allows establishing satisfiability: # enforcing arc consistency, if the primal graph is acyclic; # enforcing directional arc consistency for an ordering of the variables that makes the ordered graph of constraint having width 1 (such an ordering exists if and only if the primal graph is a tree, but not all orderings of a tree generate width 1); # enforcing strong directional path consistency for an ordering of the variables that makes the primal graph having induced width 2. A condition that extends the last one holds for non-binary constraint satisfaction problems. Namely, for all problems for which there exists an ordering that makes the primal graph having induced width bounded by a constant i, enforcing strong directional i-consistency is tractable and allows establishing satisfiability.
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Hence, the reaction is highly diastereoselective, with cis- boronate aryl/vinyl transfer being the predominant pathway. Hydroxypyrrolidines and Hydroxy-γ- and δ-lactams have been shown to react very diastereoselectively, with good to excellent yield. However, such procedures are limited to the usage of vinyl- or electron-rich aryl- boronic acids only. diastereoselective PBM coupling with chiral N-acyliminium ion Batey and coworkers take advantage of the high diastereoselectivity of this reaction to prepare (±)-6-deoxycastanospermine in 7 steps, with an impressive overall yield of 32% (from the vinyl boronic ester). The key acyclic precursor to deoxycastanospermine (A) is formed first by condensing vinyl boronic ester 1 with Cbz-protected hydroxy-pyrrolidine 2 with a PBM coupling, followed by dihydroxylation and TBS protetction. A then undergo intramolecular cyclization via a one-pot imine formation and reduction sequel, followed by TBS deprotection, to afford (±)-6-deoxycastanospermine. Deoxycastanospermine synthesis (Batey et al.) With thiourea catalyst Takemoto and coworkers of Kyoto University recently reported an enantioselective Petasis-type reaction to transform quinolines into respective chiral 1,2-dihydroquinolines (product) using alkenyl boronic acids and chiral thiourea catalyst. Good yields (59–78%) and excellent enantioselectivities (82–96%) are reported.
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At each step one of the subsets and one of the input symbols of the automaton are chosen, and the subsets of states are refined into states for which a transition labeled would lead to , and states for which an -transition would lead somewhere else. When a set that has already been chosen is split by a refinement, only one of the two resulting sets (the smaller of the two) needs to be chosen again; in this way, each state participates in the sets for refinement steps and the overall algorithm takes time , where is the number of initial states and is the size of the alphabet.. Partition refinement was applied by in an efficient implementation of the Coffman–Graham algorithm for parallel scheduling. Sethi showed that it could be used to construct a lexicographically ordered topological sort of a given directed acyclic graph in linear time; this lexicographic topological ordering is one of the key steps of the Coffman–Graham algorithm. In this application, the elements of the disjoint sets are vertices of the input graph and the sets used to refine the partition are sets of neighbors of vertices.
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In the compilation of high-level programming languages, pathwidth arises in the problem of reordering sequences of straight-line code (that is, code with no control flow branches or loops) in such a way that all the values computed in the code can be placed in machine registers instead of having to be spilled into main memory. In this application, one represents the code to be compiled as a directed acyclic graph in which the nodes represent the input values to the code and the values computed by the operations within the code. An edge from node x to node y in this DAG represents the fact that value x is one of the inputs to operation y. A topological ordering of the vertices of this DAG represents a valid reordering of the code, and the number of registers needed to evaluate the code in a given ordering is given by the vertex separation number of the ordering.. For any fixed number w of machine registers, it is possible to determine in linear time whether a piece of straight-line code can be reordered in such a way that it can be evaluated with at most w registers.
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The manifolds with nil geometry all have a unique Seifert fibration, and are characterized by their fundamental groups. The total spaces are all acyclic. {b; (o1, 0); (3, b1), (3, b2), (3, b3)} (b integral, bi is 1 or 2) For b + Σbi/ai= 0 this is an oriented Euclidean 2-torus bundle over the circle, and is the surface bundle associated to an order 3 (trace −1) rotation of the 2-torus. {b; (o1, 0); (2,1), (4, b2), (4, b3)} (b integral, bi is 1 or 3) For b + Σbi/ai= 0 this is an oriented Euclidean 2-torus bundle over the circle, and is the surface bundle associated to an order 4 (trace 0) rotation of the 2-torus. {b; (o1, 0); (2, 1), (3, b2), (6, b3)} (b integral, b2 is 1 or 2, b3 is 1 or 5) For b + Σbi/ai= 0 this is an oriented Euclidean 2-torus bundle over the circle, and is the surface bundle associated to an order 6 (trace 1) rotation of the 2-torus. {b; (o1, 0); (2, 1), (2, 1), (2, 1), (2, 1)} (b integral) These are oriented 2-torus bundles for trace −2 automorphisms of the 2-torus. For b=−2 this is an oriented Euclidean 2-torus bundle over the circle (the surface bundle associated to an order 2 rotation of the 2-torus) and is homeomorphic to {0; (n2, 2);}.
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