"There's a freeness and playfulness in the clothes," she says.
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We can only focus on the freeness and the fairness of our elections.
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She speaks unreservedly, dipping between subjects and trains of thought with a casual freeness.
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She'll still make mistakes, but her intentions are wonderful, so there's a lightness and a freeness.
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You can feel the freeness of it and yet you feel the control there as well — that's dance.
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At first I was told it would take one or two billing cycles before the "freeness" would kick in.
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What we do know is that Putin has been elected… We can only focus on the freeness and fairness of our elections.
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In a huge country with prolonged, phased elections, minimum standards of behavior are essential for peace, freeness and fairness of the process.
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There is a freeness there, an ability to ambulate and move around it and breathe with the work, and that is what continues its relevance.
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Or at the very least, throughout history the care-freeness of youth has been sapped by the stark anxieties of a world ever hurtling toward entropy.
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"We are not asking the administration or anyone to take sides, but to merely demand the same level of freeness and fairness," Ballard lobbyist Jamie Rubin told Reuters.
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For example, when Afrobaromer's researchers turned to experts to compare opinions on the freeness and fairness of the last election, they found that ordinary Ghanaians were significantly more critical than the human rights experts at Freedom House.
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Owen Bush declared, "People don't know how to deal with free, and they can't handle it … The freeness is turning people into beasts," while for the performer David Leslie, the point was the intensity itself, the feeling engendered by such rare, socially sanctioned abandon.
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No matter the bigness of the data, the vastness of the Web, the freeness of speech, nothing could be less well settled in the twenty-first century than whether people know what they know from faith or from facts, or whether anything, in the end, can really be said to be fully proved.
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Eisenbud, Theorem 14.4 Generic freeness is proved using Grothendieck's technique of dévissage. See Noether's normalization lemma#Illustrative application : generic freeness for a proof of a version of generic freeness.
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Intra-personal fairness (such as envy-freeness) are relevant only as a secondary criterion.
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Esso, Starbucks, etc.). Before the procedure, each participant was shown all the 64 possible allocations, and was asked to grade the satisfaction and fairness of each of them between 0 (bad) and 100 (good). Then, they were taught seven different procedures, with different levels of fairness guarantees: Strict Alternation and Balanced Alternation (no guarantees), Divide and Choose (only envy-freeness), Compensation Procedure and Price Procedure (envy-freeness and Pareto-efficiency), Adjusted Knaster and Adjusted Winner (envy-freeness, Pareto-efficiency and equitability). They practiced each of these against a computer.
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Generic flatness is a consequence of the generic freeness lemma. Generic freeness states that if A is a noetherian integral domain, B is a finite type A-algebra, and M is a finite type B-module, then there exists a non-zero element f of A such that Mf is a free Af-module.EGA IV2, Lemme 6.9.2 Generic freeness can be extended to the graded situation: If B is graded by the natural numbers, A acts in degree zero, and M is a graded B-module, then f may be chosen such that each graded component of Mf is free.
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Envy-freeness becomes easier to attain when it is assumed that agents' valuations are quasilinear in money, and thus transferable across agents. Demange, Gale and Sotomayor showed a natural ascending auction that achieves an envy-free allocation using monetary payments for unit demand bidders (where each bidder is interested in at most one item). Fair by Design is a general framework for optimization problems with envy-freeness guarantee that naturally extends fair item assignments using monetary payments. Cavallo generalizes the traditional binary criteria of envy-freeness, proportionality, and efficiency (welfare) to measures of degree that range between 0 and 1.
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Berliant, Thomson and Dunz introduced the criterion of group envy-freeness, which generalizes both Pareto-efficiency and envy-freeness. They proved the existence of group-envy-free allocations with additive utilities. Later, Berliant and Dunz studied some natural non-additive utility functions, motivated by the problem of land division. When utilities are not additive, a CEEI allocation is no longer guaranteed to exist, but it does exist under certain restrictions.
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PAT (Process Analysis Toolkit) is a self-contained framework for composing, simulating and reasoning of concurrent, real-time systems and other possible domains. It comes with user friendly interfaces, featured model editor and animated simulator. Most importantly, PAT implements various model checking techniques catering for different properties such as deadlock-freeness, divergence-freeness, reachability, LTL properties with fairness assumptions, refinement checking and probabilistic model checking. To achieve good performance, advanced optimization techniques are implemented in PAT, e.g.
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In 1983, Terao asked whether the freeness of an arrangement is determined from its intersection lattice.Hiroaki. Terao, The exponents of a free hypersurface, Singularities, Part 2 (Arcata, Calif., 1981), 561–566, Proc. Sympos. Pure Math.
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Ginseng's compiler proves the cons-freeness properties of the entire initial program and of dynamic patches. Later versions of Ginseng also support a notion of transactional safety. This allows developers to annotate a sequence of function calls as a logical unit, preventing updates from violating program semantics in ways that are not detectable by either activeness safety or cons-freeness safety. For example, in two versions of OpenSSH examined by Ginseng's authors, important user verification code was moved between two functions called in sequence.
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Furthermore, while Gershwin's piece is more influenced by big band and swing, Milhaud's and Antheil's works can be seen as reinterpretations of the large freeness of Creole and New Orleans and cutting-edge New York jazz.
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Gal, Mash, Procaccia and Zick, based on their experience with the rent division application in the Spliddit website, note that envy-freeness alone is insufficient to guarantee the satisfaction of the participants. Therefore they build an algorithmic framework, based on linear programming, for calculating allocations that are both envy-free and optimize some criterion. Based on theoretic and experimental tests, they conclude that the maximin criterion - maximizing the minimum utility of an agent subject to envy-freeness - attains optimal results. Note that, since their solution is always EF, it might return negative prices.
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Envy-freeness (EF) is a criterion of fair division. In an envy-free division, every agent feels that their share is at least as good as the share of any other agent, and thus no agent feels envy.
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This proves safety because control can never return to old code that would access new representations of data. Cons-Freeness is another way to prove type safety, where a section of code is considered safe if it does not access state of a given type in a way that requires knowledge of the type representation. This code can be said to not access the state concretely, while it may access the state abstractly. It is possible to prove or disprove cons-freeness for all types in any section of code, and the DSU system Ginseng uses this to prove type safety.
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One may similarly define free products of other algebraic structures than groups, including algebras over a field. Free products of algebras of random variables play the same role in defining "freeness" in the theory of free probability that Cartesian products play in defining statistical independence in classical probability theory.
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In a proportional division, the value of each partner is at least 1/n of the total. In particular, the value of the least fortunate agent (which is called the egalitarian welfare of the division) is at least 1/n. This means that in an egalitarian-optimal division, the egalitarian welfare is at least 1/n, and so an egalitarian-optimal division is always proportional. Hence, the egalitarian price of proportionality (EPOP) is 1: ::::EPOP = 1 Similar considerations apply to the egalitarian price of equitability (EPOQ): ::::EPOQ = 1 The egalitarian price of envy-freeness is much larger: ::::EPOV = n/2 This is an interesting result, as it implies that insistence on the criterion of envy- freeness increases the social gaps and harms the most unfortunate citizens.
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Better Ways to Cut a Cake by Steven J. Brams, Michael A. Jones, and Christian Klamler in the Notices of the American Mathematical Society December 2006. A generalization of the surplus procedure called the equitable procedure (EP) achieves a form of equitability. Equitability and envy-freeness can be incompatible for 3 or more players.
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There is always a graded polynomial subring A ⊂ R (with generators in various degrees) such that R is finitely generated as an A-module. Then R is Cohen–Macaulay if and only if R is free as a graded A-module. Again, it follows that this freeness is independent of the choice of the polynomial subring A.
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What is the importance of intra-personal fairness criteria (such as envy-freeness, where each person compares bundles based only on his own utility-function), vs. inter-personal fairness criteria (such as equitability, where each person views the utilities of all other agents)? Using a free-form bargaining experiment, it was found that inter-personal fairness (e.g. equitability) is more important.
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The procedure requires the agents to rank bundles of items. This is feasible when the number of items is small, but may be difficult when the number of items is large, since the number of bundles grows exponentially with the number of items. The procedure does not guarantee envy-freeness; see envy-free item assignment for procedures that do guarantee it.
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This is not encouraging, since the probability of envy- freeness converges to 0 when the number of partners grows. But it is impossible to do better: in every truthful-in-expectation mechanism, the GPEF is at most 1/n. 3\. Expected Number of Envy-Free partners (ENEF) means that there is a certain integer N such that, if we average the number of partners who do not envy in all possible outcomes of the mechanism, then regardless of the partners' valuations, the expectation is at least N. The ENEF criterion seems more appropriate than the GPEF criterion, because it measures not only the probability of entire envy-freeness, but also the quality of the cases in which the allocation is not entirely envy-free. The maximum ENEF of a truthful-in-expectation mechanism is at most n-1+1/n.
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Google uses a minor variant of GSP to auction off advertisement slots. Potential advertisements may be of varying quality. Suppose that there are two advertisements for eggs. One advertisement simply fills its space with the word “egg” repeated over and over, while the other advertisement shows a picture of eggs, contains branding information, and mentions positive qualities about their eggs, such as cage-freeness.
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A group-envy-free allocation is also envy-free, since X and Y can be groups with a single agent. A group-envy-free allocation is also Pareto efficient, since X and Y can be the entire group of all n agents. Group-envy-freeness is much stronger than the combination of these two criteria, since it applies also to groups of 2, 3, ..., n-1 agents.
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After the release and success of the first album, McMahon then proceeded to compose his second Jack's Mannequin album, The Glass Passenger, which was released in September 2008. Jack's Mannequin's third and final album, People and Things was released in October 2011. He stated that this new album "[would] probably have a bit of freeness" to it, distancing itself from The Glass Passenger."JACK'S BACK".
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For indivisible items, an assignment satisfying proportionality, envy-freeness, or equitability does not always exist (for a simple example, imagine two partners trying to divide a single valuable item). See also fair item allocation. Consequently, in the price of fairness calculations, the instances in which no assignment satisfies the relevant fairness notion are not considered. A brief summary of the results: ::::UPOP = n - 1 + 1/n; for two people: 3/2.
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It says that the characteristic of the style of eating is "its freeness in the arrangement of food on a large dish" People eat Sawachi in the situation of "Enkai" which refers to a gathering of family, friends and relatives. They surround "Sawachi", feasts on large dishes, and take own portions by themselves. The style represents the cultural climate of Kochi prefecture which hates formal arrangements and respect freedom.
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However, no such allocation is PE, since it is Pareto-dominated by the allocation [(4,0);(0,2)] whose utility vector is (4,2). Non-existence remains even if we weaken envy-freeness to no domination -- no agent gets more of each good than another agent. Proposition 8 (Maniquet): There exist 2-good 3-agent division economies with strictly monotonic, continuous and even differentiable preferences, where there is domination at every Pareto efficient allocation.
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Her family was generally supportive of her naturalness and freeness with her body. Schneemann attributed her father's support to the fact that he was a rural physician who had to often deal with the body in various states of health. Schneemann was awarded a full scholarship to New York's Bard College. She was the first woman from her family to attend college, but her father discouraged her from an art education.
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For the definition of E_\infty-ring spectra essentially the same approach works, where one replaces the A_\infty- operad by an E_\infty-operad, i.e. an operad of contractible topological spaces with analogous "freeness" conditions. An example of such an operad can be again motivated by the study of loop spaces. The product of the double loop space \Omega^2X is already commutative up to homotopy, but this homotopy fulfills no higher conditions.
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If a function is proven cons- free, it can be updated even if it is live on the stack, since it will not cause a type error by accessing state using the old representation. Empirical analysis of cons-freeness and activeness safety by Hayden et all show that both techniques permit most correct updates and deny most erroneous updates. However, manually selecting update points results in zero update errors, and still allows frequent update availability.
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When allocating objects among people with different preferences, two major goals are Pareto efficiency and fairness. Since the objects are indivisible, there may not exist any fair allocation. For example, when there is a single house and two people, every allocation of the house will be unfair to one person. Therefore, several common approximations have been studied, such as envy-freeness up to one item (EF1) and proportionality up to one item (PROP1) and Maximin-share fairness (MMS).
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An important feature of all transformational grammars is that they are more powerful than context-free grammars. Chomsky formalized this idea in the Chomsky hierarchy. He argued that it is impossible to describe the structure of natural languages with context-free grammars. His general position on the non-context-freeness of natural language has held up since then, though his specific examples of the inadequacy of CFGs in terms of their weak generative capacity were disproved.
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The important fact is: In Mumford's red book, the theorem is proved by means of Noether's normalization lemma. For an algebraic approach where the generic freeness plays a main role and the notion of "universally catenary ring" is a key in the proof, see Eisenbud, Ch. 14 of "Commutative algebra with a view toward algebraic geometry." In fact, the proof there shows that if f is flat, then the dimension equality in 2. of the theorem holds in general (not just generically).
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PEEF allocations might fail to exist even when all preferences are convex, if there is production and the technology has increasing-marginal-returns. Proposition 6 (Vohra): There exist economies in which all preferences are continuous strongly-monotone and convex, the only source of non-convexity in the technology is due to fixed costs, and there exists no PEEF allocation. Thus, the presence of increasing returns introduces a fundamental conflict between efficiency and fairness. However, envy-freeness can be weakened in the following way.
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Most DSU systems attempt to show some safety properties for updates. The most common variant of safety checking is type safety, where an update is considered safe if it does not result in any new code operating on an old state representation, or vice versa. Type safety is typically checked by showing one of two properties, activeness safety or cons-freeness safety. A program is considered activeness-safe if no updated function exists on the call stack at update time.
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A property that is undecidable already for context-free languages or finite intersections of them, must be undecidable also for conjunctive grammars; these include: emptiness, finiteness, regularity, context-freeness,Given a conjunctive grammar, is its generated language empty / finite / regular / context-free? inclusion and equivalence.Given two conjunctive grammars, is the first's generated language a subset of / equal to the second's? The family of conjunctive languages is closed under union, intersection, concatenation and Kleene star, but not under string homomorphism, prefix, suffix, and substring.
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Ex-ante Envy-Freeness means that no partner envies the lottery of any other partner. This condition is trivial to achieve in a truthful mechanism: randomise over all possible allocations with equal probability and charge each partner 1/n of the total cost. But this condition is not appealing, since there is a large chance that in the final outcome, many partners will be envious. They may not be comforted by the fact that the lottery has been fair. 2\.
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On the other hand, the new division might not be envy free. For example, it is possible that initially both Alice and George received a land-plot which Bob subjectively values as 1/3, but now after the re-division George got all the value (in Bob's eyes) so now Bob envies George. Hence, using envy-freeness as the fairness criterion implies that we must constrain the right of people to voluntary exchanges after the division. Using proportionality as the fairness criterion has no such negative implications.
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Envy-free item allocation (EF allocation) is a fair item allocation problem, in which the fairness criterion is envy-freeness - each agent should receive a bundle that they believe to be at least as good as the bundle of any other agent. Since the items are indivisible, an EF assignment may not exist. The simplest case is when there is a single item and at least two agents: if the item is assigned to one agent, the other will envy. Therefore, the division procedures provide various kinds of relaxations.
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Kitty Empire of The Observer called the album "lively" and said it "finds [the Raconteurs] luxuriating in fancy stuff with kid-in-a-sweetshop enthusiasm. Minimalism is out, bombast is in; the detail, is, as ever, lip-smacking." Commenting on the band's chemistry and freeness, Rolling Stone said the album is "a blissfully stoned conversation between White and Benson about their favorite bands: Led Zeppelin, the Who, Badfinger", though it added, "that freedom is not always satisfying." Austin-American Statesmen said "it's a weirdly overblown and curiously dull album," and complained about its production.
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A hereditary property is a property that is preserved under deletion of vertices. A few important hereditary properties are H-freeness (for some graph H), k-colorability, and planarity. All hereditary properties are testable, and there is a proof of this fact using a version of the graph removal lemma for infinite families of induced subgraphs. In fact, a rough converse of this is also true -- the properties that have oblivious testers with one-sided error are almost hereditary (Alon & Shapira 2008), in a sense which will not be made precise here.
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This situation can be made precise by saying that ΩX is an algebra over the little interval operad. This is an example of an A_\infty- operad, i.e. an operad of topological spaces which is homotopy equivalent to the associative operad but which has appropriate "freeness" to allow things only to hold up to homotopy (succinctly: any cofibrant replacement of the associative operad). An A_\infty-ring spectrum can now be imagined as an algebra over an A_\infty-operad in a suitable category of spectra and suitable compatibility conditions (see May, 1977).
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This theory allows a daseinanalysist to be an objective therapist; therapeutically avoiding bringing previous prejudice into sessions and allowing the analysis to be individualized and not generalized. Boss asserts this freeness in therapy allows daseinsanalysis to become an 'analysis of resistance'. This means that the patient is constantly confronted with the perceived limitations of his own existence and is pushed to the point of rejecting the limitations they are placing upon themselves. The human dasein cannot see these limitations from within itself and needs to be exposed to the freedoms beyond the limitations.
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A group-envy-free division (also known as: coalition-fair division) is a division of a resource among several partners such that every group of partners feel that their allocated share is at least as good as the share of any other group with the same size. The term is used especially in problems of fair division, such as resource allocation and fair cake-cutting. Group-envy- freeness is a very strong fairness requirement: a group-envy-free allocation is both envy-free and Pareto efficient, but the opposite is not true.
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Ginseng is a general-purpose DSU system. It is the only DSU system to use the cons-freeness safety technique, allowing it to update functions that are live on the stack as long as they do not make concrete accesses to updated types. Ginseng is implemented as a source-to-source compiler written using the C Intermediate Language framework in OCaml. This compiler inserts indirection to all function calls and type accesses, enabling Ginseng to lazily transform state at the cost of imposing a constant-time overhead for the entirety of the program execution.
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I.e, the Gap procedure satisfies NN and PE but not EF. Moreover, the Gap Procedure may return non- envy-free allocations, even when EF allocations exist. Brams relates to this problem saying that: "Gap prices do take into account the competitiveness of bidding for goods, which makes the pricing mechanism market-oriented. Although envy-freeness is a desirable property, I prefer a marketlike mechanism when there is a conflict between these two properties; partners should pay more when bids are competitive, even at the sacrifice of causing envy".
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Retrieved from www.jstor.org/stable/41482536 In addition, the Chinese Civil Code from the 1930s gave individuals, including women a great deal of freeness to decide and manage their personal events, including freedom of marriage. According to the Civil Code, whether two people were getting married or divorced, they needed to sign the legal documents in front of two witnesses or a lawyer. This is the first time in Chinese history that women have been granted the right to divorce, it gave Chinese women a chance to leave their miserable marriage legally and freely.
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In the fair random assignment problem, there are n objects and n people with different preferences over the objects. It is required to give an object to each person. To attain fairness, the allocation is randomized: for each (person,object) pair, a probability is calculated, such that the sum of probabilities for each person and for each object is 1. The probabilistic- serial procedure can compute the probabilities such that each agent, looking at the matrix of probabilities, prefers his row of probabilities over the rows of all other people (this property is called envy-freeness).
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Faces are an important class of visual stimuli for humans, and the perception of "faceness" is a critical part of social responsiveness. Because of the importance of the information conveyed by faces for social interaction, humans should therefore have innate preferences for them as a category, with its associated prototype. This prototype's special attractiveness (over the attractiveness of, for instance, the prototypical "chair") is probably related to the evolutionary importance of the mutant-freeness that the prototypical face represents. It has been argued that composite faces are more symmetrical than their original images, and that it is this that accounts for their attractiveness.
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One advantage of the proportionality criterion over envy- freeness and similar criteria is that it is stable with regards to voluntary exchanges. As an example, assume that a certain land is divided among 3 partners: Alice, Bob and George, in a division that is both proportional and envy-free. Several months later, Alice and George decide to merge their land- plots and re-divide them in a way that is more profitable for them. From Bob's point of view, the division is still proportional, since he still holds a subjective value of at least 1/3 of the total, regardless of what Alice and George do with their plots.
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Allowing arbitrary transformations does not meet that goal: they are much too powerful, being Turing complete unless significant restrictions are added (e.g. no transformations that introduce and then rewrite symbols in a context-free fashion). Chomsky's general position regarding the non-context- freeness of natural language has held up since then,. although his specific examples regarding the inadequacy of context-free grammars in terms of their weak generative capacity were later disproved.. Gerald Gazdar and Geoffrey Pullum have argued that despite a few non-context-free constructions in natural language (such as cross-serial dependencies in Swiss German and reduplication in Bambara.), the vast majority of forms in natural language are indeed context-free.
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In 1704 he found, while visiting a member of his flock, a book brought into Scotland by a commonwealth soldier, the Marrow of Modern Divinity, by Edward Fisher, a compendium of the opinions of leading Reformation divines on the doctrine of grace and the offer of the Gospel, which set off the Marrow Controversy. Its object was to demonstrate the unconditional freeness of the Gospel. It cleared away such conditions as repentance, or some degree of outward or inward reformation, and argued that where Christ is heartily received, full repentance and a new life follow. On Boston's recommendation, James Hog of Carnock reprinted The Marrow in 1718; and Boston also published an edition with notes of his own.
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However, the items are discrete and cannot be cut, so an envy- free assignment might be impossible (for example, consider a single item and two agents). The envy-graph procedure aims to achieve the "next-best" option -- envy-freeness up to at most a single good (EF1): it finds an allocation in which the envy of every person towards every other person is bounded by the maximum marginal utility it derives from a single item. In other words, for every two people i and j, there exists an item such that, if that item is removed, i does not envy j. The procedure was presented by Lipton and Markakis and Mossel and Saberi and it is also described in .
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There were three information conditions: (1) Competing Preferences: Players know that the preferences of their co-bargainer are similar to their own; (2) Complementary Preferences: Players know that the preferences of their co-bargainer are diametrically opposed to their own; (3) Unknown (Random) Preferences: Players do not know what their co-bargainer values most relative to their own preferences. In condition (1), the bilateral decisions converge toward efficient outcomes, yet only one-third are "envy-free". In condition (2), while players dramatically misrepresent their true valuation for objects, both efficiency and envy-freeness approach maximum levels. In condition (3), pronounced strategic bidding emerges, yet the result is twice as many envy- free outcomes, with increased levels of efficiency (relative to condition 1).
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In algebraic geometry and commutative algebra, the theorems of generic flatness and generic freeness state that under certain hypotheses, a sheaf of modules on a scheme is flat or free. They are due to Alexander Grothendieck. Generic flatness states that if Y is an integral locally noetherian scheme, is a finite type morphism of schemes, and F is a coherent OX-module, then there is a non-empty open subset U of Y such that the restriction of F to u−1(U) is flat over U.EGA IV2, Théorème 6.9.1 Because Y is integral, U is a dense open subset of Y. This can be applied to deduce a variant of generic flatness which is true when the base is not integral.
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The existence of trapdoor permutations does not by itself imply claw-free permutations exist; however, it has been shown that claw-free permutations do exist if factoring is hard. The general notion of claw-free permutation (not necessarily trapdoor) was further studied by Ivan Damgård in his PhD thesis The Application of Claw Free Functions in Cryptography (Aarhus University, 1988), where he showed how to construct Collision Resistant Hash Functions from claw-free permutations. The notion of claw-freeness is closely related to that of collision resistance in hash functions. The distinction is that claw-free permutations are pairs of functions in which it is hard to create a collision between them, while a collision-resistant hash function is a single function in which it's hard to find a collision, i.e.
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While the problem is computationally-hard, simulations show that the implementation scales gracefully in terms of running time: even when there are 300 charter schools, it terminates in a few minutes on average. Moreover, while theoretically the algorithm guarantees only 1/4 of the maximum number of allocated classrooms, in the simulations it satisfies on average at least 98% of the maximum number of charter schools that can possibly be satisfied, and allocates on average at least 98% of the maximum number of classrooms that can possibly be allocated. The partial collaboration with the school district lead to several practical desiderata in deploying fair division solutions in practice. First, the simplicity of the mechanism, and the intuitiveness of the properties of proportionality, envy-freeness, Pareto optimality, and strategyproofness, have made the approach more likely to be adopted.
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They compared the procedures performance in terms of efficiency, envy-freeness, equitability and truthfulness. Their conclusions are: (a) The sophisticated mechanisms are advantageous only in the binding case; when renegotiation is possible, their performance drops to the baseline level of DC. (b) The preference for a procedure depends not only on the expected utility calculations of the negotiators, but also on their psychological profile: the more "antisocial" a person is, the more likely he is to opt for a procedure with a compensatory mechanism. The more risk-averse a person is, the more likely he is to opt for a straightforward procedure like DC. (c) The final payoff of a participant in a procedure depends a lot on the implementation. If participants cannot divide the goods under a procedure of their own choice, they are more eager to maximize their payoff.
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As an alternative analysis method against the sampling-based simulation method, an exhaustive generating behavior approach, generally called verification has been applied for analysis of DEVS models. It is proven that infinite states of a given DEVS model (especially a coupled DEVS model ) can be abstracted by behaviorally isomorphic finite structure, called a reachability graph when the given DEVS model is a sub-class of DEVS such as Schedule-Preserving DEVS (SP-DEVS), Finite & Deterministic DEVS (FD- DEVS) [HZ09], and Finite & Real-time DEVS (FRT-DEVS) [Hwang12]. As a result, based on the rechability graph, (1) dead-lock and live-lock freeness as qualitative properties are decidable with SP-DEVS [Hwang05], FD-DEVS [HZ06], and FRT-DEVS [Hwang12]; and (2) min/max processing time bounds as a quantitative property are decidable with SP-DEVS so far by 2012.
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The painting shows the Timurids being lowered in baskets down the cliff face so that they can attack the Georgians that hide in caves carved into the rock. The composition of this scene is more free and flowing than previous images, with a rhythm created through the organic forms of the mounted soldiers and the curves of the rock face (Natif, 218). One explanation for this freeness of composition is that there were very few descriptive elements in the text, so the artist had free rein to depict the scene how he wished (Sims, 261). Some believe that this scene was illustrated because of its “picturesque potential” and propagandistic message of conquering a foreign foe (Sims, 264). The next image breaks from a battle scene and instead shows “The construction of the Great Mosque (Friday Mosque) of Sarnarqand, began on 14 Rarnadan 801/May 20, 1399.” This illustration is also an almost true match to the text that relates to it.
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The envy-free cake-cutting problem is to partition the cake to n disjoint pieces, one piece per agent, such for each agent, the value of his piece is weakly larger than the values of all other pieces (so no agent envies another agent's share). A corollary of the Dubins–Spanier convexity theorem (1961) is that there always exists a "consensus partition" - a partition of the cake to n pieces such that every agent values every piece as exactly 1/n. A consensus partition is of course EF, but it is not PE. Moreover, another corollary of the Dubins–Spanier convexity theorem is that, when at least two agents have different value measures, there exists a division that gives each agent strictly more than 1/n. This means that the consensus partition is not even weakly PE. Envy- freeness, as a criterion for fair allocation, were introduced into economics in the 1960s and studied intensively during the 1970s.
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