Iteratively solve those problems and you should wind up with a solution to the whole problem.
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Perhaps ironically, Giegel stressed the need to move slowly and iteratively as it develops its ultrafast technology.
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So we're continuing to strive for, and iteratively learn, how we can reduce that cycle time going forward.
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As the branches and sub-branches are iteratively eliminated, so too is the amount of data that requires analysis.
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Technology, whether it's our phones, TVs, or computers, is in its adult period, where changes happen slowly and iteratively.
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So by iteratively changing by pixel, we will reach a point that this image becomes highly classified as a banana.
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The tags used and overall approach can be modified iteratively through experimentation and adaptation, which fits the larger agile paradigm well.
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Instead, Italy, Japan or India provide more optimal conditions for understanding customer needs, iteratively developing solutions and selling the vehicles in that segment.
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As I have explained previously, reinforcement learning steals the idea of utility from economists in an effort to quantify and iteratively evaluate decision making.
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He's expecting to see more instances of companies crafting strategic partnerships and iteratively working through a roadmap that eventually lands them at a consolidation.
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AlphaGo itself first learned on a database of millions of individual moves from 160,000 human-played Go games, before iteratively training against itself and improving.
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The iPad Pro will get progressively, iteratively better over time, and I strongly suspect Apple's announcements today will just be another step in that journey.
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"It's been about helping scale the infrastructure that lets Deliveroo continue their growth, and iteratively improving the experience for riders and restaurants," Robinson told Business Insider.
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They should be able to learn like a child, continuously, iteratively and from everything, being able to generalize, apply and extrapolate these learnings in a useful way.
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But here, given our blindness during blinks and saccades, a clever algorithm could repeatedly swap things around you, in real-time, testing your A/B reactions iteratively.
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The chips in these MacBooks are part of a new family of processors from Intel called Kaby Lake, which are iteratively better than their predecessor processors, called Skylake.
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And it turns out that if you take all that technology that's been proven, the big players in the space have been iteratively optimizing the same technology you've had since the 1960s.
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A much more sensible way to improve an algorithm is iteratively, by adjusting the the inputs: improve the incoming data first, and then change the algorithm's analysis to leverage the new information.
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Well, so this all part of the iteratively improving part of AI. So it uses AI to take sensors from around ... It's already got sensors, so why not let it do other things?
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Imagine employing your own secretary who optimizes your schedule, plans your weekends, reminds you about deadlines and iteratively adapts to your preferences and behaviors at a fraction of the cost of a human.
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" Jenny Fielding, NYC, Managing Director, Techstars "This may sound provocative, but I think the most common mistake is that there is a belief in the tech world that branding should be approached iteratively like their approach to product development.
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If that program or piece of code is run iteratively (again and again), the effect is that an increasing amount of physical memory (RAM, generally) is never released back to the OS. This has potentially serious consequences when it comes to performance.
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But I think, in this case, just having passed through it iteratively, I just adore her," Paltrow revealed, following up with some sage wisdom: "I always start to think of the ampersand sign—what else can you bring in, instead of being resistant to or being made insecure by?
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Oh. Well, because it grew, I think, iteratively out of our friendship and the fact that I worked on all of his campaigns, I chaired his finance committee when he ran for Senate, and so in that sense, friends are always your advisers, and I certainly was a mentor to Michelle Obama.
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The researchers said they used methods including dual learning for fact-checking translations; deliberation networks, to repeat translations and refine them; and new techniques like joint training, to iteratively boost English-to-Chinese and Chinese-to-English translation systems; and agreement regularization, which can generate translations by reading sentences both left-to-right and right-to-left.
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The hardware has increased iteratively; but you need an incredible amount of horsepower and very well optimised low-latency engine to drive VR. Neither Unreal nor Unity are particularly well optimised… The big players who have the tech that could make a difference don't see the demographics on VR yet, and the people won't buy it without the killer apps.
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Each method starts by maintaining either continuity of flow or potential, and then iteratively solves for the other.
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The Lanczos algorithm uses a continued fraction expansion to iteratively approximate the eigenvalues and eigenvectors of a large sparse matrix..
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284-287, March 1974. This algorithm is critical to modern iteratively-decoded error-correcting codes including turbo codes and low- density parity-check codes.
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The Autonomic Network Architecture (ANA) project has two complementary objectives that iteratively provide feedback to each other: a scientific objective and a technological one.
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A square system of coupled nonlinear equations can be solved iteratively by Newton's method. This method uses the Jacobian matrix of the system of equations.
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Most of the work on blind deconvolution started in early 1970s. Blind deconvolution is used in astronomical imaging and medical imaging. Blind deconvolution can be performed iteratively, whereby each iteration improves the estimation of the PSF and the scene, or non-iteratively, where one application of the algorithm, based on exterior information, extracts the PSF. Iterative methods include maximum a posteriori estimation and expectation- maximization algorithms.
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The problem can be solved by iteratively merging two of the k arrays using a 2-way merge until only a single array is left. If the arrays are merged in arbitrary order, then the resulting running time is only O(kn). This is suboptimal. The running time can be improved by iteratively merging the first with the second, the third with the fourth, and so on.
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More details about these TV-based approaches – iteratively reweighted l1 minimization, edge-preserving TV and iterative model using directional orientation field and TV- are provided below.
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The Hardy Cross method iteratively corrects for the mistakes in the initial guess used to solve the problem. Subsequent mistakes in calculation are also iteratively corrected. If the method is followed correctly, the proper flow in each pipe can still be found if small mathematical errors are consistently made in the process. As long as the last few iterations are done with attention to detail, the solution will still be correct.
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The second step is to point out sources of waste and to eliminate them. Waste- removal should take place iteratively until even seemingly essential processes and procedures are liquidated.
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Hash functions used for data searches use some arithmetic expression which iteratively processes chunks of the input (such as the characters in a string) to produce the hash value.
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PageRank can be computed either iteratively or algebraically. The iterative method can be viewed as the power iteration method or the power method. The basic mathematical operations performed are identical.
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It can handle the situations when one configuration includes multiple clusters or when holes exist inside clusters. It can also be applied to a cluster iteratively to identify multiple sub-surface layers.
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Recursive waves of depths 1, 2 and 3\. A recursive wave is a self-similar curve in three-dimensional space that is constructed by iteratively adding a helix around the previous curve.
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There are two main approaches to document layout analysis. Firstly, there are bottom-up approaches which iteratively parse a document based on the raw pixel data. These approaches typically first parse a document into connected regions of black and white, then these regions are grouped into words, then into text lines, and finally into text blocks. Secondly, there are top-down approaches which attempt to iteratively cut up a document into columns and blocks based on white space and geometric information.
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Behavior authoring for computer games consists of first writing the behaviors in a programming language, iteratively refining these behaviors, testing the revisions by executing them, identifying new problems and then refining the behaviors again.
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The use of SID may be applied to 2D arrays, by iteratively adding features equidistant from the previously present features, doubling the density with each iteration.K. Oyama et al., Proc. SPIE 9051, 90510V (2014).
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K nearest neighbor query is computed by iteratively performing range queries with an incrementally enlarged search region until k answers are obtained. Another possibility is to employ similar querying ideas in The iDistance Technique.
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Solving Apollonius' problem iteratively in this case leads to the Apollonian gasket, which is one of the earliest fractals to be described in print, and is important in number theory via Ford circles and the Hardy–Littlewood circle method.
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After all words are annotated and disambiguated, they can be used as a training corpus in any standard word embedding technique. In its improved version, MSSA can make use of word sense embeddings to repeat its disambiguation process iteratively.
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Thunar's About screen logo The Thunar interface was developed prior to the coding of its core. A minimally functional software mockup was built in Python. Features were added and UI elements changed iteratively to react to test user input.
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It builds up a picture iteratively, recognizing groups of pixels as objects. It uses the color, shape, texture and size of objects as well as their context and relationships to draw conclusions and inferences, similar to a human analyst.
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Architects iteratively partition system tasks and information into finer, finite subsets that are controllable and efficient. RCS focuses on intelligent control that adapts to uncertain and unstructured operating environments. The key concerns are sensing, perception, knowledge, costs, learning, planning, and execution.
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Natural evolution strategies (NES) are a family of numerical optimization algorithms for black box problems. Similar in spirit to evolution strategies, they iteratively update the (continuous) parameters of a search distribution by following the natural gradient towards higher expected fitness.
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It also allows rigid bodies to be linked with one or two common centers (e.g. peptide planes) by solving rigid body constraints iteratively in the same basic manner that SHAKE is used for atoms involving more than one SHAKE constraint.
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With the VINES Laboratory (Virtual Integrated Nursing Education Simulation) in full operation, IN aims to teach nursing skills iteratively and sequentially without harming patients. It seeks to become the Center for Excellence in Nursing Simulation in the Philippines and Asia.
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Iteratively dividing by the p factors shows that each p has an equal counterpart q; the two prime factorizations are identical except for their order. The unique factorization of numbers into primes has many applications in mathematical proofs, as shown below.
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Affine shape adaptation is a methodology for iteratively adapting the shape of the smoothing kernels in an affine group of smoothing kernels to the local image structure in neighbourhood region of a specific image point. Equivalently, affine shape adaptation can be accomplished by iteratively warping a local image patch with affine transformations while applying a rotationally symmetric filter to the warped image patches. Provided that this iterative process converges, the resulting fixed point will be affine invariant. In the area of computer vision, this idea has been used for defining affine invariant interest point operators as well as affine invariant texture analysis methods.
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See fixed-point theorems in infinite-dimensional spaces. The collage theorem in fractal compression proves that, for many images, there exists a relatively small description of a function that, when iteratively applied to any starting image, rapidly converges on the desired image.
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SCCCs provide performance comparable to other iteratively decodable codes including turbo codes and LDPC codes. They are noted for having slightly worse performance at lower SNR environments (i.e. worse waterfall region), but slightly better performance at higher SNR environments (i.e. lower error floor).
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Execution proceeds by a process of continually matching rules against a history, and firing those rules when antecedents are satisfied. Any instantiated future-time consequents become commitments which must subsequently be satisfied, iteratively generating a model for the formula made up of the program rules.
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This was done by adaptively mapping an predefined "atlas" (layout map of some cells) to an image iteratively using the Expectation Maximization algorithm until convergence. SRS has been shown to reduce over-segmentation and under-segmentation errors compared to usually used watershed segmentation method.
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This double process cycle is iteratively applied until an optimal balance of differences and commonalities between stakeholders are reached that meets the semantic integration requirements. This approach is based on research on community-based ontology engineering () that is validated in European projects, government and industry.
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2\. The deferred-acceptance auction iteratively rejects the lowest-valued agent that can be rejected while keeping an optimal set of active agents. So, Carl is rejected first, then Bob. Alice remains and she is accepted. She pays the threshold value which is $1M.
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Isotonic regression is used iteratively to fit ideal distances to preserve relative dissimilarity order. Isotonic regression is also used in probabilistic classification to calibrate the predicted probabilities of supervised machine learning models. Software for computing isotone (monotonic) regression has been developed for R, Stata, and Python.
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It is an analysis method that focus on the essential elements that whole enterprise needs. It is a scheme that target the innovation and evolution of the capabilities. There is a set of essential steps for the analysis. The activities are dependent and it is conducted iteratively.
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Antoine's necklace is constructed iteratively like so: Begin with a solid torus A0 (iteration 0). Next, construct a "necklace" of smaller, linked tori that lie inside A0. This necklace is A1 (iteration 1). Each torus composing A1 can be replaced with another smaller necklace as was done for A0.
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Boosting approaches add new kernels iteratively until some stopping criteria that is a function of performance is reached. An example of this is the MARK model developed by Bennett et al. (2002) Kristin P. Bennett, Michinari Momma, and Mark J. Embrechts. MARK: A boosting algorithm for heterogeneous kernel models.
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The shifting nth root algorithm is an algorithm for extracting the nth root of a positive real number which proceeds iteratively by shifting in n digits of the radicand, starting with the most significant, and produces one digit of the root on each iteration, in a manner similar to long division.
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Perhaps the most common and straightforward mechanism to build a MGF is to iteratively apply a hash function together with an incrementing counter value. The counter may be incremented indefinitely to yield new output blocks until a sufficient amount of output is collected. This is the approach used in MGF1.
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This sequence culminated with Robins and Zelikovsky's algorithm in 2000 which improved the ratio to 1.55 by iteratively improving upon the minimum cost terminal spanning tree. More recently, however, Jaroslaw Byrka et al. proved an \ln(4) + \varepsilon \le 1.39 approximation using a linear programming relaxation and a technique called iterative, randomized rounding.
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Linear approximations for S-boxes then must be combined with the cipher's other actions, such as permutation and key mixing, to arrive at linear approximations for the entire cipher. The piling-up lemma is a useful tool for this combination step. There are also techniques for iteratively improving linear approximations (Matsui 1994).
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In a linear program a column corresponds to a primal variable. Column generation is a technique to solve large linear programs. It typically works in a restricted problem, dealing only with a subset of variables. By generating primal variables iteratively and on-demand, eventually the original unrestricted problem with all variables is recovered.
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The result would be 0 with regular rounding, but with stochastic rounding, the expected result would be 30, which is the same value obtained without rounding. This can be useful in machine learning where the training may use low precision arithmetic iteratively. Stochastic rounding is a way to achieve 1-dimensional dithering.
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The final hub-authority scores of nodes are determined after infinite repetitions of the algorithm. As directly and iteratively applying the Hub Update Rule and Authority Update Rule leads to diverging values, it is necessary to normalize the matrix after every iteration. Thus the values obtained from this process will eventually converge.
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This is done until a certain small magnitude is reached. Thus graphs with different magnitudes are induced. In the second phase a partition of the graph with the smallest magnitude - the coarsest graph - is computed. In the third and last phase, the computed partition is iteratively projected back to the original graph.
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The multiplicative weights update method is an algorithmic technique most commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design. The simplest use case is the problem of prediction from expert advice, in which a decision maker needs to iteratively decide on an expert whose advice to follow. The method assigns initial weights to the experts (usually identical initial weights), and updates these weights multiplicatively and iteratively according to the feedback of how well an expert performed: reducing it in case of poor performance, and increasing it otherwise. It was discovered repeatedly in very diverse fields such as machine learning (AdaBoost, Winnow, Hedge), optimization (solving linear programs), theoretical computer science (devising fast algorithm for LPs and SDPs), and game theory.
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The music video, directed by Terri Timely, depicts a wedding reception that's initially glum but gets iteratively more lively and majestic as the participants become healthier, happier and more numerous as the scene appears to move backwards through different eras. In the end, the original bridesmaid and mother enter the wedding and attack their replacements.
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Since the CLIQUE problem is intractable, WINNOWER uses a heuristic to solve CLIQUE. It iteratively constructs cliques of larger and larger sizes. If N = mn, then the run time of the algorithm is O(N^{2d+1} ).This algorithm runs in a reasonable amount of time in practice especially for small values of d.
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A method for adapting consists in iteratively "auto-labeling" the target examples. The principle is simple: # a model h is learned from the labeled examples; # h automatically labels some target examples; # a new model is learned from the new labeled examples. Note that there exist other iterative approaches, but they usually need target labeled examples.
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As there are n elements, the total running time is O(n log k). Note that the operation of replacing the key and iteratively doing decrease-key or sift-down are not supported by many Priority Queue libraries such as C++ stl and Java. Doing an extract-min and insert function is less efficient.
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Glucose can react with bromine in water to form the aldonic acid, which can then undergo oxidative decarboxylation with hydrogen peroxide and iron (III) acetate to form arabinose. This reaction can be conducted iteratively, shortening one carbon at a time to generate sugars with smaller chain lengths. Fig 2: Glucose chain shortening: Ruff degradation.
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To arrive at a set of subsampled values that more closely resembles the original, it is necessary to undo the gamma correction, perform the calculation, and then step back into the gamma-corrected space. More efficient approximations are also possible, such as with a luma-weighted average or iteratively with lookup tables in WebP and sjpeg's "Sharp YUV" feature.
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Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square). In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, .
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Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods.
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Such detectors using a soft Viterbi algorithm or BCJR algorithm are essential in iteratively decoding the low-density parity- check code used in modern HDDs. A single integrated circuit contains the entire read and write channels (including the iterative decoder) as well as all the disk control and interface functions. There are currently two suppliers: Broadcom and Marvell.
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Some types of causative constructions essentially do not permit double causatives, e.g. it would be difficult to find a lexical double causative. Periphrastic causatives however, have the potential to always be applied iteratively (Mom made Dad make my brother make his friends leave the house.). Many Indo-Aryan languages (such as Hindustani) have lexical double causatives.
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Vector generalized linear models are described in detail in Yee (2015). The central algorithm adopted is the iteratively reweighted least squares method, for maximum likelihood estimation of usually all the model parameters. In particular, Fisher scoring is implemented by such, which, for most models, uses the first and expected second derivatives of the log-likelihood function.
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Orthogonal projection of a cantor cube showing a hexaflake. A hexaflake is a fractal constructed by iteratively exchanging hexagons by a flake of seven hexagons;. it is a special case of the n-flake. The hexaflake has 7n−1 hexagons in its nth iteration, each smaller by 1/3 than the hexagons in the previous iteration.
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It is also known as Shotgun hill climbing. It iteratively does hill-climbing, each time with a random initial condition x_0. The best x_m is kept: if a new run of hill climbing produces a better x_m than the stored state, it replaces the stored state. Random-restart hill climbing is a surprisingly effective algorithm in many cases.
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We can further improve upon this algorithm, by iteratively merging the two shortest arrays. It is clear that this minimizes the running time and can therefore not be worse than the strategy described in the previous paragraph. The running time is therefore in O(n log k). Fortunately, in border cases the running time can be better.
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Searching in a binary search tree for a specific key can be programmed recursively or iteratively. We begin by examining the root node. If the tree is null, the key we are searching for does not exist in the tree. Otherwise, if the key equals that of the root, the search is successful and we return the node.
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This problem is sometimes solved iteratively/hierarchically, by first searching for the largest jump and then repeating the search in both sub-sections until they are too small. This does not always produce good results. A direct way to solve the problem is by an efficient optimization method called dynamic programming. Sometimes there are no other stations in the same climate region.
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This allows assignment and review of writing and revision tasks to be performed piecemeal, which enables students to develop work iteratively and focus more on higher-order concerns such as organization and pairing claims with suitable evidence, than surface-level issues such as grammar or spelling. Engagement data is tracked for individual activities and automatically compiled into individual student and aggregate class reports.
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Analysis starts by mapping the distorted 2D pattern on the representative plane of the fiber. This is the plane that contains the cylinder axis in reciprocal space. In crystallography first an approximation of the mapping into reciprocal space is computed that is refined iteratively. The digital method frequently called Fraser correction starts from the Franklin approximation for the tilt angle β.
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J. Y. Bouguet, (2001) . Pyramidal implementation of the affine lucas kanade feature tracker description of the algorithm. Intel Corporation, 5. In order to achieve motion tracking with this method, the flow vector can be iteratively applied and recalculated, until some threshold near zero is reached, at which point it can be assumed that the image windows are very close in similarity.
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Topography is used for monitoring crystal quality and visualizing defects in many different crystalline materials. It has proved helpful e.g. when developing new crystal growth methods, for monitoring growth and the crystal quality achieved, and for iteratively optimizing growth conditions. In many cases, topography can be applied without preparing or otherwise damaging the sample; it is therefore one variant of non-destructive testing.
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However, deriving the set of equations used to update the parameters iteratively often requires a large amount of work compared with deriving the comparable Gibbs sampling equations. This is the case even for many models that are conceptually quite simple, as is demonstrated below in the case of a basic non-hierarchical model with only two parameters and no latent variables.
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MPCA is solved by performing PCA in each mode of the tensor iteratively. MPCA has been applied to face recognition, gait recognition, etc. MPCA is further extended to uncorrelated MPCA, non-negative MPCA and robust MPCA. N-way principal component analysis may be performed with models such as Tucker decomposition, PARAFAC, multiple factor analysis, co-inertia analysis, STATIS, and DISTATIS.
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The regions are iteratively grown by comparison of all unallocated neighboring pixels to the regions. The difference between a pixel's intensity value and the region's mean, \delta, is used as a measure of similarity. The pixel with the smallest difference measured in this way is assigned to the respective region. This process continues until all pixels are assigned to a region.
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In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment. After the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables are often used when constructing this design.
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The added cases, whose conclusions conflicted with the advice of the system were termed "cornerstone cases". Consequently, the data base grew iteratively with each refinement to the knowledge. The data base could then be used to test changes to the knowledge. Knowledge acquisition tools, similar to those provided by Teiresias were developed to find and help modify the conflicting rules.
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Mathematical optimization is used in much modern controller design. High-level controllers such as model predictive control (MPC) or real-time optimization (RTO) employ mathematical optimization. These algorithms run online and repeatedly determine values for decision variables, such as choke openings in a process plant, by iteratively solving a mathematical optimization problem including constraints and a model of the system to be controlled.
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The term deck optimization (or deck tuning) refers to iteratively improving a play deck in a collectible card game. This is usually done through test or trial play sessions, during which the deck's performance is evaluated. After observation and consideration, changes are made to the deck, and its new performance can then be judged. This cycle can be repeated as needed.
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Interactive Visual Analysis of Scientific Data. Steffen Oeltze, Helmut Doleisch, Helwig Hauser, Gunther Weber. Presentation at IEEE VisWeek 2012, Seattle (WA), USA These techniques involve looking at datasets through different, correlated views and iteratively selecting and examining features the user finds interesting. The objective of IVA is to gain knowledge which is not readily apparent from a dataset, typically in tabular form.
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In contrast to LACS and PANAV/PSSI, CheckShift uses secondary structure predicted from high-performance secondary structure prediction programs such as PSIPRED to iteratively adjust 13C and 15N chemical shifts so that their secondary shifts match the predicted secondary structure. These programs have all been shown to accurately identify mis-referenced and properly re-reference protein chemical shifts deposited in the BMRB,.
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The improvement kata is a routine for moving from the current situation to a new situation in a creative, directed, meaningful way. It is based on a four-part model: # In consideration of a vision or direction... # Grasp the current condition. # Define the next target condition. # Move toward that target condition iteratively, which uncovers obstacles that need to be worked on.
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Conceptually, in the Levenberg–Marquardt algorithm, the objective function is iteratively approximated by a quadratic surface, then using a linear solver, the estimate is updated. This alone may not converge nicely if the initial guess is too far from the optimum. For this reason, the algorithm instead restricts each step, preventing it from stepping "too far". It operationalizes "too far" as follows.
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The Z-spread of a bond is the number of basis points (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury forward rates), so that the NPV of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including accrued interest). The spread is calculated iteratively.
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The patterns aim at identifying meanings using the local structural properties of the co- occurrence graph. A randomized algorithm which partitions the graph vertices by iteratively transferring the mainstream message (i.e. word sense) to neighboring vertices is Chinese Whispers. By applying co-occurrence graphs approaches have been shown to achieve the state-of-the-art performance in standard evaluation tasks.
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The interest points obtained from the multi-scale Harris operator with automatic scale selection are invariant to translations, rotations and uniform rescalings in the spatial domain. The images that constitute the input to a computer vision system are, however, also subject to perspective distortions. To obtain an interest point operator that is more robust to perspective transformations, a natural approach is to devise a feature detector that is invariant to affine transformations. In practice, affine invariant interest points can be obtained by applying affine shape adaptation where the shape of the smoothing kernel is iteratively warped to match the local image structure around the interest point or equivalently a local image patch is iteratively warped while the shape of the smoothing kernel remains rotationally symmetric (Lindeberg 1993, 2008; Lindeberg and Garding 1997; Mikolajzcyk and Schmid 2004).
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The blob descriptors obtained from these blob detectors with automatic scale selection are invariant to translations, rotations and uniform rescalings in the spatial domain. The images that constitute the input to a computer vision system are, however, also subject to perspective distortions. To obtain blob descriptors that are more robust to perspective transformations, a natural approach is to devise a blob detector that is invariant to affine transformations. In practice, affine invariant interest points can be obtained by applying affine shape adaptation to a blob descriptor, where the shape of the smoothing kernel is iteratively warped to match the local image structure around the blob, or equivalently a local image patch is iteratively warped while the shape of the smoothing kernel remains rotationally symmetric (Lindeberg and Garding 1997; Baumberg 2000; Mikolajczyk and Schmid 2004, Lindeberg 2008).
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The latter two papers introduced the view of boosting algorithms as iterative functional gradient descent algorithms. That is, algorithms that optimize a cost function over function space by iteratively choosing a function (weak hypothesis) that points in the negative gradient direction. This functional gradient view of boosting has led to the development of boosting algorithms in many areas of machine learning and statistics beyond regression and classification.
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Once the method has been developed, application techniques will be designed to successfully apply the method in stand-alone mode as well as together with other methods. Application techniques constitute the "use" component of the method which continues to evolve and grow throughout the life of the method. The method procedure, language constructs, and application techniques are reviewed and tested to iteratively refine the method.
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100-110, 1999. It can be used for performing semi-supervised learning in cases in which there exist redundancy in features. It may be seen as a combination of co-training and boosting. Each example is available in two views (subsections of the feature set), and boosting is applied iteratively in alternation with each view using predicted labels produced in the alternate view on the previous iteration.
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This is also called the dynamic part of the architecture. It tells organization, how to iteratively develop the elements mentioned above. # Concept for the technical components needed to implement the architecture, for example design tools, internal and externally visible repositories. One element comprised in the third category is a "BII-repository", in which each organization publishes the content of its Business Interoperability Interface (BII) to collaboration partners.
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A hierarchical classifier is a classifier that maps input data into defined subsumptive output categories. The classification occurs first on a low-level with highly specific pieces of input data. The classifications of the individual pieces of data are then combined systematically and classified on a higher level iteratively until one output is produced. This final output is the overall classification of the data.
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In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. It is named after its inventor Edmond Halley. The algorithm is second in the class of Householder's methods, after Newton's method. Like the latter, it produces iteratively a sequence of approximations to the root; their rate of convergence to the root is cubic.
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This procedure can be carried out digitally (by methods of triangulation and projective geometry or iteratively (repeated angle corrections by congruent rays). The accuracy of modern autographs is about 0.001 mm. Well known are the instruments of the companies Wild Heerbrugg (Leica), e.g. analog A7, B8 of the 1980s and the digital autographs beginning in the 1990s, or special instruments of Zeiss and Contraves.
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In a general constraint satisfaction problem, every variable can take a value in a domain. A backtracking algorithm therefore iteratively chooses a variable and tests each of its possible values; for each value the algorithm is recursively run. Look ahead is used to check the effects of choosing a given variable to evaluate or to decide the order of values to give to it.
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They state that there are limits to what a software development team can achieve in terms of safely implementing changes and new functionality. Maturity Models specific to software evolution have been developed to improve processes, and help to ensure continuous rejuvenation of the software as it evolves iteratively. The "global process" that is made by the many stakeholders (e.g. developers, users, their managers) has many feedback loops.
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The pointers are sorted by the value that they point to. In an O(k) preprocessing step the heap is created using the standard heapify procedure. Afterwards, the algorithm iteratively transfers the element that the root pointer points to, increases this pointer and executes the standard decrease key procedure upon the root element. The running time of the increase key procedure is bounded by O(log k).
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The index of an inner node indicates which input array the value comes from. The value contains a copy of the first element of the corresponding input array. The algorithm iteratively appends the minimum element to the result and then removes the element from the corresponding input list. It updates the nodes on the path from the updated leaf to the root (replacement selection).
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Neural Abstraction Pyramid The feed-forward architecture of convolutional neural networks was extended in the neural abstraction pyramid by lateral and feedback connections. The resulting recurrent convolutional network allows for the flexible incorporation of contextual information to iteratively resolve local ambiguities. In contrast to previous models, image-like outputs at the highest resolution were generated, e.g., for semantic segmentation, image reconstruction, and object localization tasks.
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The dynamic mask defines the beam. The beam is focused on the surface of a UV- curable polymer resin through a projection lens that reduces the image to the desired size. Once a layer is polymerized, the stage drops the substrate by a predefined layer thickness, and the dynamic mask displays the image for the next layer on top of the preceding one. This proceeds iteratively until complete.
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In constraint satisfaction, local search is an incomplete method for finding a solution to a problem. It is based on iteratively improving an assignment of the variables until all constraints are satisfied. In particular, local search algorithms typically modify the value of a variable in an assignment at each step. The new assignment is close to the previous one in the space of assignment, hence the name local search.
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A variety of subtly different iteration methods have been implemented and made available in software packages; reviews and comparisons have been useful but generally refrain from choosing a "best" technique. The software package PRRN/PRRP uses a hill-climbing algorithm to optimize its MSA alignment score and iteratively corrects both alignment weights and locally divergent or "gappy" regions of the growing MSA.Mount DM. (2004). Bioinformatics: Sequence and Genome Analysis 2nd ed.
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LOBPCG can be trivially adopted for computing several largest singular values and the corresponding singular vectors (partial SVD), e.g., for iterative computation of PCA, for a data matrix with zero mean, without explicitly computing the covariance matrix , i.e. in matrix-free fashion. The main calculation is evaluation of a function of the product of the covariance matrix and the block-vector that iteratively approximates the desired singular vectors.
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In constraint satisfaction, backmarking is a variant of the backtracking algorithm. Backmarking works like backtracking by iteratively evaluating variables in a given order, for example, x_1,\ldots,x_n. It improves over backtracking by maintaining information about the last time a variable x_i was instantiated to a value and information about what changed since then. In particular: An example, in which search has reached xi=d the first time.
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It does so by iteratively marking as composite, i.e., not prime, the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.
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For many choices of ρ or ψ, no closed form solution exists and an iterative approach to computation is required. It is possible to use standard function optimization algorithms, such as Newton–Raphson. However, in most cases an iteratively re-weighted least squares fitting algorithm can be performed; this is typically the preferred method. For some choices of ψ, specifically, redescending functions, the solution may not be unique.
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The profits for any implementation process being framed in a project management framework are: Clarity An implementation framework offers the process to be detailed in with factors such as time, quality, budget and feasibility. Iterative, incremental approach As explained, the possibility to execute different phases of the implementation process iteratively enables the process to be executed by incrementally aligning the product to be implemented with the end-user (organization).
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The loser of each replayed game is written to the node and the winner is iteratively promoted to the top. When the root is reached, the new overall winner was found and can be used in the next round of merging. The images of the tournament tree and the loser tree in this section use the same data and can be compared to understand the way a loser tree works.
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Repeated iteratively for all transducers. Ultrasound computer tomographs use ultrasound waves for creating images. In the first measurement step a defined ultrasound wave is generated with typically Piezoelectric ultrasound transducers, transmitted in direction of the measurement object and received with other or the same ultrasound transducers. While traversing and interacting with the object the ultrasound wave is changed by the object and carries now information about the object.
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The pairwise exchange or 2-opt technique involves iteratively removing two edges and replacing these with two different edges that reconnect the fragments created by edge removal into a new and shorter tour. Similarly, the 3-opt technique removes 3 edges and reconnects them to form a shorter tour. These are special cases of the k-opt method. The label Lin–Kernighan is an often heard misnomer for 2-opt.
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A similar outcome can be implemented by an immediate acceptance (or forward-greedy) auction. This auction iteratively accepts the highest-valued agent that can still be feasibly selected, and charges them the threshold payments (the smallest bid that they should have made in order to win). In this case, Alice is selected first, so Bob and Carl can no longer be selected. Alice pays her threshold value which is $1M.
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Bootstrapping is a technique used to iteratively improve a classifier's performance. Typically, multiple classifiers will be trained on different sets of the input data, and on prediction tasks the output of the different classifiers will be combined together. Seed AI is a hypothesized type of artificial intelligence capable of recursive self- improvement. Having improved itself, it would become better at improving itself, potentially leading to an exponential increase in intelligence.
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Seppo Linnainmaa in 1970 is said to have developed the Backpropagation Algorithm but the origins of the algorithm go back to the 1960s with many contributors. It is a generalisation of the least mean squares algorithm in the linear perceptron and the Delta Learning Rule. It implements gradient descent search through the space possible network weights, iteratively reducing the error, between the target values and the network outputs.
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Cyber threat hunting is an active cyber defence activity. It is "the process of proactively and iteratively searching through networks to detect and isolate advanced threats that evade existing security solutions." This is in contrast to traditional threat management measures, such as firewalls, intrusion detection systems (IDS), malware sandbox (computer security) and SIEM systems, which typically involve an investigation of evidence-based data after there has been a warning of a potential threat.
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They may find a solution of a problem, but they may fail even if the problem is satisfiable. They work by iteratively improving a complete assignment over the variables. At each step, a small number of variables are changed in value, with the overall aim of increasing the number of constraints satisfied by this assignment. The min- conflicts algorithm is a local search algorithm specific for CSPs and is based on that principle.
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As a scientist, Southwell developed relaxation methods for solving partial differential equations in engineering and theoretical physics during the 1930 and the 1940s. The equations had first to be discretised by the finite difference methods. Then, the values of the function of the grids would have to be iteratively adjusted so that the discretised equation would be satisfied. At the time, digital computers did not exist, and the computations had to be done by hand.
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In mathematics, and specifically the field of partial differential equations (PDEs), a parametrix is an approximation to a fundamental solution of a PDE, and is essentially an approximate inverse to a differential operator. A parametrix for a differential operator is often easier to construct than a fundamental solution, and for many purposes is almost as good. It is sometimes possible to construct a fundamental solution from a parametrix by iteratively improving it.
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Prevalence of online code repositories, documentation, blogs and forums—enables programmers to build applications iteratively searching for, modifying, and combining examples. Using the web is integral to an opportunistic approach to programming when focusing on speed and ease of development over code robustness and maintainability. There is a widespread use of the web by programmers, novices and experts alike, to prototype, ideate, and discover. To develop software quickly programmers often mash up various existing systems.
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Genetic or evolutionary art makes use of genetic algorithms to develop images iteratively, selecting at each "generation" according to a rule defined by the artist. Algorithmic art is not only produced by computers. Wendy Chun explains: The American artist, Jack Ox, has used algorithms to produce paintings that are visualizations of music without using a computer. Two examples are visual performances of extant scores, such as Anton Bruckner's Eighth Symphony and Kurt Schwitters' Ursonate.
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A drawback of this method is that DNS caches hide the end user's IP address. Both redirection methods, HTTP and DNS based, can be performed in the CDNI, either iteratively or recursively. The recursive redirection is more transparent for the end user because it involves only one UE redirection, but it has other dependencies on the interconnection realisation. A single UE redirection may be preferable if the number of interconnected CDNs exceeds two.
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The lack of robustness and slow convergence of these solvers did not make them an interesting alternative in the beginning. The rise of parallel computing in the 1980s however sparked their popularity. Complex problems could now be solved by dividing the problem into subdomains, each processed by a separate processor, and solving for the interface coupling iteratively. This can be seen as a second level domain decomposition as is visualized in the figure.
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The cutting-plane method is an umbrella term for optimization methods which iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are popularly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory and Václav Chvátal.
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The pairs of sequences are then scored. The scoring function favours pairs which are very similar, but disfavours sequences which are very common in the target genome. The 1000 highest scoring pairs are kept, and the others are discarded. Each of these 1000 'seed' motifs are then used to search iteratively search for further sequences of length which maximise the score(a greedy algorithm), until N sequences for that motif are reached.
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In regression problems this can be found in one matrix operation. In classification problems the fixed non-linearity introduced by the sigmoid output function is most efficiently dealt with using iteratively re-weighted least squares. RBF networks have the disadvantage of requiring good coverage of the input space by radial basis functions. RBF centres are determined with reference to the distribution of the input data, but without reference to the prediction task.
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It introduced new swatches, gradients, patterns, shapes and stylistic sets for OpenType fonts. With this version users now can easily convert smart objects to layers and also can adjust 32-bit layers for brightness/contrast and curves. Presets are now more intuitive to use and easier to organize. With the February 2020 update (version 21.1) Photoshop now can iteratively fill multiple areas of an image without having to leave content-aware fill workspace.
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NEMS (National Energy Modeling System) is a long-standing United States government policy model, run by the Department of Energy (DOE). NEMS computes equilibrium fuel prices and quantities for the US energy sector. To do so, the software iteratively solves a sequence of linear programs and nonlinear equations. NEMS has been used to explicitly model the demand-side, in particular to determine consumer technology choices in the residential and commercial building sectors.
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With longer-proportioned rectangles, the squares don't overlap, but with shorter-proportioned ones, they do. In Western cultures that read left to right, attention is often focused inside the left-hand rabatment, or on the line it forms at the right-hand side of the image. When rabatment is used with one side of a golden rectangle, and then iteratively applied to the left-over rectangle, the resulting "whirling rectangles" describe the golden spiral.
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The view factors are used as coefficients in a linear system of rendering equations. Solving this system yields the radiosity, or brightness, of each patch, taking into account diffuse interreflections and soft shadows. Progressive radiosity solves the system iteratively with intermediate radiosity values for the patch, corresponding to bounce levels. That is, after each iteration, we know how the scene looks after one light bounce, after two passes, two bounces, and so forth.
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Space mapping refers to a methodology that employs a "quasi-global" modeling formulation to link companion "coarse" (ideal or low-fidelity) with "fine" (practical or high-fidelity) models of different complexities. In engineering optimization, space mapping aligns (maps) a very fast coarse model with its related expensive-to-compute fine model so as to avoid direct expensive optimization of the fine model. The alignment process iteratively refines a "mapped" coarse model (surrogate model).
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The first approach to splitting large SVM learning problems into a series of smaller optimization tasks was proposed by Bernhard Boser, Isabelle Guyon, Vladimir Vapnik. It is known as the "chunking algorithm". The algorithm starts with a random subset of the data, solves this problem, and iteratively adds examples which violate the optimality conditions. One disadvantage of this algorithm is that it is necessary to solve QP-problems scaling with the number of SVs.
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The Faddeev equations, named after their inventor Ludvig Faddeev, are equations that describe, at once, all the possible exchanges/interactions in a system of three particles in a fully quantum mechanical formulation. They can be solved iteratively. In general, Faddeev equations need as input a potential that describes the interaction between two individual particles. It is also possible to introduce a term in the equation in order to take also three-body forces into account.
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A different approach to this issue is followed in the Espresso algorithm, developed by Brayton et al. at the University of California, Berkeley. Rather than expanding a logic function into minterms, the program manipulates "cubes", representing the product terms in the ON-, DC-, and OFF- covers iteratively. Although the minimization result is not guaranteed to be the global minimum, in practice this is very closely approximated, while the solution is always free from redundancy.
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In this method, the input of each variable is varied with other parameters remaining constant and the effect on the design objective is observed. This is a time-consuming method and improves the performance partially. To obtain the optimal solution with minimum computation and time, the problem is solved iteratively where in each iteration the solution moves closer to the optimum solution. Such methods are known as ‘numerical optimization’ or ‘simulation-based optimization’.
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Given a skew standard or skew semistandard tableau T, one can iteratively apply inward slides to T until the tableau becomes straight-shape (which means no more inward slides are possible). This can generally be done in many different ways (one can freely choose into which cell to slide first), but the resulting straight-shape tableau is known to be the same for all possible choices. This tableau is called the rectification of T.
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Proving existence is relatively straightforward: let be the set of all normal subgroups that can not be written as a product of indecomposable subgroups. Moreover, any indecomposable subgroup is (trivially) the one-term direct product of itself, hence decomposable. If Krull-Schmidt fails, then contains ; so we may iteratively construct a descending series of direct factors; this contradicts the DCC. One can then invert the construction to show that all direct factors of appear in this way.
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In software design, the same schema, business logic and other components are often repeated in multiple different contexts, while each version refers to itself as "Source Code". To address this problem, the concepts of SSOT can also be applied to software development principles using processes like recursive transcompiling to iteratively turn a single source of truth into many different kinds of source code, which will match each other structurally because they are all derived from the same SSOT.
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These methods iteratively update the haplotype estimates of each sample conditional upon a subset of K haplotype estimates of other samples. IMPUTE2 introduced the idea of carefully choosing which subset of haplotypes to condition on to improve accuracy. Accuracy increases with K but with quadratic O(K^2) computational complexity. The SHAPEIT1 method made a major advance by introducing a linear O(K) complexity method that operates only on the space of haplotypes consistent with an individual’s genotypes.
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These half-spaces are used to describe primitives that can be combined to get the final model. Another approach decouples the detection of primitive shapes and the computation of the CSG tree that defines the final model. This approach exploits the ability of modern program synthesis tools to find a CSG tree with minimal complexity. There are also approaches that use genetic algorithms to iteratively optimize an initial shape towards the shape of the desired mesh.
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While boosting is not algorithmically constrained, most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier. When they are added, they are weighted in a way that is related to the weak learners' accuracy. After a weak learner is added, the data weights are readjusted, known as "re-weighting". Misclassified input data gain a higher weight and examples that are classified correctly lose weight.
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The response of the site to the seismic vibrator is measured by sensors (geophones), also placed on the ground surface. Two key-components are required for the profiling based on full-waveform inversion. These components are: a) a computer model for the simulation of elastic waves in semi-infinite domains; and b) an optimization framework, through which the computed response is matched to the measured response, via iteratively updating an initially assumed material distribution for the soil.
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The article then follows the recipe's development, which invariably begins with numerous problems in its original incarnation. The author then describes iteratively modifying the recipe's ingredients and cooking method, each time presenting the recipe to a panel of tasters who provide feedback. At the end of the article, the author reaches a final recipe and lists the ingredients and preparation instructions, often with minor variants. Recipes typically include hand-drawn illustrations of any difficult cuts or other uncommon preparation.
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The Neural network which edits seismic data or pick first breaks was trained by users, who were just selecting and presenting to the network examples of trace edits or refraction picks. The network then changes internal weights iteratively until it can reproduce the examples accurately provided by the users. Fabio Boschetti et al.(1996) introduce a fractal-based algorithm, which detects the presence of a signal by analyzing the variation in fractal dimension along the trace.
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The iterated elimination (or deletion) of dominated strategies (also denominated as IESDS or IDSDS) is one common technique for solving games that involves iteratively removing dominated strategies. In the first step, at most one dominated strategy is removed from the strategy space of each of the players since no rational player would ever play these strategies. This results in a new, smaller game. Some strategies--that were not dominated before--may be dominated in the smaller game.
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Researchers have studied 0-1 quadratic knapsack problems for decades. One focus is to find effective algorithms or effective heuristics, especially those with an outstanding performance solving real world problems. The relationship between the decision version and the optimization version of the 0-1 QKP should not be ignored when working with either one. On one hand, if the decision problem can be solved in polynomial time, then one can find the optimal solution by applying this algorithm iteratively.
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Any surplus points they have are divided among other preferences in successive iteration(s). Similarly, a candidate who falls well short of this criteria during the first count has their points transferred among other preferences in subsequent count(s). This whole exercise is repeated iteratively until all vacant seats are filled. It is pertinent to mention that the points system is only used for senators to be elected from general, women, and technocrat seats in provincial assemblies.
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Through a continual process of stretching and folding, much like in a "baker's map," tracers advected in chaotic flows will develop into complex fractals. The fractal dimension of a single contour will be between 1 and 2. Exponential growth ensures that the contour, in the limit of very long time integration, becomes fractal. Fractals composed of a single curve are infinitely long and when formed iteratively, have an exponential growth rate, just like an advected contour.
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Differential Evolution optimizing the 2D Ackley function. In evolutionary computation, differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as they make few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. However, metaheuristics such as DE do not guarantee an optimal solution is ever found.
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The limit subdivision surface is the surface produced from this process being iteratively applied infinitely many times. In practical use however, this algorithm is only applied a limited, and usually fairly small, number of times. Mathematically, the neighborhood of an extraordinary point (non-4-valent node for quad refined meshes) of a subdivision surface is a spline with a parametrically singular point J. Peters and U. Reif: Subdivision Surfaces, Springer series Geometry and Computing monograph 3, 2008, doi .
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The general idea is to iteratively approach the posterior from the prior through a sequence of target distributions. An advantage of such methods, compared to ABC-MCMC, is that the samples from the resulting posterior are independent. In addition, with sequential methods the tolerance levels must not be specified prior to the analysis, but are adjusted adaptively. It is relatively straightforward to parallelize a number of steps in ABC algorithms based on rejection sampling and sequential Monte Carlo methods.
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As with DSDM, the Prince2 method acknowledges implementation as a phase within the method. Prince2 consists of a set of processes, of which 3 processes are especially meant for implementation. The processes of controlling a stage, managing product delivery and managing stage boundaries enable an implementation process to be detailed in with factors as time and quality. The Prince2 method can be carried out iteratively but is also suitable for a straight execution of the processes.
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Termination: The algorithm terminates once \Delta(m,n,x) is larger than zero for all x,n,m. Different move acceptance strategies can be used. In a first- improvement strategy, any improving relocation can be applied, whereas in a best-improvement strategy, all possible relocations are iteratively tested and only the best is applied at each iteration. The former approach favors speed, whether the latter approach generally favors solution quality at the expense of additional computational time.
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It includes scientific disciplines: Agronomy, Botany, Ecology, Forestry, Geology, Geochemistry, Hydrogeology, and Wildlife Biology. It also draws upon applied sciences: Agricultural & Horticultural Sciences, Engineering Geomorphology, landscape architecture, and Mining, Geotechnical, and Civil, Agricultural & Irrigation Engineering. Landscape engineering builds on the engineering strengths of declaring goals, determining initial conditions, iteratively designing, predicting performance based on knowledge of the design, monitoring performance, and adjusting designs to meet the declared goals. It builds on the strengths and history of reclamation practice.
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This eliminates n conditional branches at the cost of the Hn ≈ ln n + γ redundant assignments. Another advantage of this technique is that n, the number of elements in the source, does not need to be known in advance; we only need to be able to detect the end of the source data when it is reached. Below the array a is built iteratively starting from empty, and a.length represents the current number of elements seen.
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Although stochastic computing has a number of defects when considered as a method of general computation, there are certain applications that highlight its strengths. One notable case occurs in the decoding of certain error correcting codes. In developments unrelated to stochastic computing, highly effective methods of decoding LDPC codes using the belief propagation algorithm were developed. Belief propagation in this context involves iteratively reestimating certain parameters using two basic operations (essentially, a probabilistic XOR operation and an averaging operation).
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Hero described a method for iteratively computing the square root of a number. Today, however, his name is most closely associated with Heron's formula for finding the area of a triangle from its side lengths. He also devised a method for calculating cube roots in the 1st century AD. He also designed a shortest path algorithm, Given two points A and B on one side of a line, find C a point on the straight line, that minimizes AC+BC.
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KHOPCA rule 1 The first rule has the function of constructing an order within the cluster. This happens through a node n detects the direct neighbor with the highest weight w, which is higher than the node's own weight w_n. If such a direct neighbor is detected, the node n changes its own weight to be the weight of the highest weight within the neighborhood subtracted by 1. Applied iteratively, this process creates a top-to-down hierarchical cluster structure.
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R now is parameterized by three parameter (s, "ρ", "θ"), where "ρ" is the axis ratio and "θ" the orientation of the ellipse. This modification increases the search space of the previous algorithm from a scale to a set of parameters and therefore the complexity of the affine invariant saliency detector increases. In practice the affine invariant saliency detector starts with the set of points and scales generated from the similarity invariant saliency detector then iteratively approximates the suboptimal parameters.
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Experiments targeting selective phenotypic markers are screened and identified by plating the cells on differential medias. Each cycle ultimately takes 2.5 hours to process, with additional time required to grow isogenic cultures and characterize mutations. By iteratively introducing libraries of mutagenic ssDNAs targeting multiple sites, MAGE can generate combinatorial genetic diversity in a cell population. There can be up to 50 genome edits, from single nucleotide base pairs to whole genome or gene networks simultaneously with results in a matter of days.
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In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character. In evolutionary computation, an initial set of candidate solutions is generated and iteratively updated. Each new generation is produced by stochastically removing less desired solutions, and introducing small random changes.
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Once the forces on the nodes and edges of a graph have been defined, the behavior of the entire graph under these sources may then be simulated as if it were a physical system. In such a simulation, the forces are applied to the nodes, pulling them closer together or pushing them further apart. This is repeated iteratively until the system comes to a mechanical equilibrium state; i.e., their relative positions do not change anymore from one iteration to the next.
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These methods alternate between steps in which one constructs the Voronoi diagram for a set of seed points, and steps in which the seed points are moved to new locations that are more central within their cells. These methods can be used in spaces of arbitrary dimension to iteratively converge towards a specialized form of the Voronoi diagram, called a Centroidal Voronoi tessellation, where the sites have been moved to points that are also the geometric centers of their cells.
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The best-fit curve is often assumed to be that which minimizes the sum of squared residuals. This is the ordinary least squares (OLS) approach. However, in cases where the dependent variable does not have constant variance, a sum of weighted squared residuals may be minimized; see weighted least squares. Each weight should ideally be equal to the reciprocal of the variance of the observation, but weights may be recomputed on each iteration, in an iteratively weighted least squares algorithm.
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Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977. In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option.
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Each new scene involved unique graphics, puzzles, and story elements, so we knew that it wouldn't all be 'figured out' up front. I prefer to work more iteratively and put pieces together to try things out as we go along. PlayFirst's willingness to accept this fact was something that I appreciated in terms of my work style. Not only being able to work this way, but to also be supported in doing it was a great advantage for my team.
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In applied mathematics, K-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. K-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data. K-SVD can be found widely in use in applications such as image processing, audio processing, biology, and document analysis.
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In the Fourier domain or FFT domain the frequency response is corrected according to the desired specs, and the inverse FFT is then computed. In the time-domain, only the first N coefficients are kept (the other coefficients are set to zero). The process is then repeated iteratively: the FFT is computed once again, correction applied in the frequency domain and so on. Software packages like MATLAB, GNU Octave, Scilab, and SciPy provide convenient ways to apply these different methods.
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Interacting stocks and flows generate the dynamic behavior of metrics such as MC and cost. Uncovering leverage points involves understanding feedback loops that link variables, or factors, that cause behavior in other variables. Feedback loops are either self-reinforcing (good or bad) or goal- seeking (seeking equilibrium). Synthesis of improved courses of action arises from mitigating bad (vicious circles) self-reinforcing feedback loops, exploiting good (virtuous circles) and goal-seeking feedback loops, and iteratively optimizing them, typically using parameter-driven simulations.
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As a result, the separators of this merged node are exactly the separators of the two original nodes. As a result, merging a pair of nodes joined by a separator does not change the other separators. As a result, a fixed maximal separator size can be enforced by first calculating all separator sizes and then iteratively merging any pair of nodes having a separator larger than a given amount, and the size of the separators do not need to be recalculated during execution.
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The other way is to assume there is a bias associated with each chromosomal position. The contact map value at each coordinate will be the true signal at that position times bias associated with the two contact positions. An example of algorithms that aim to solve this model of bias is iterative correction, which iteratively regressed out row and column bias from the raw Hi-C contact map. There are a number of software tools available for analysis of Hi-C data.
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Another common method for solving the radiosity equation is "shooting radiosity," which iteratively solves the radiosity equation by "shooting" light from the patch with the most energy at each step. After the first pass, only those patches which are in direct line of sight of a light-emitting patch will be illuminated. After the second pass, more patches will become illuminated as the light begins to bounce around the scene. The scene continues to grow brighter and eventually reaches a steady state.
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The USGS headquarters in Reston, Virginia USGS gauging station 03221000 on the Scioto River below O'Shaughnessy Dam near Dublin, Ohio Earthquake animations from 16 May 2010 to 22 May 2010 Earthquakes around the world, from 23 April 2010 to 23 May 2010 Since 2012, the USGS science focus is directed at topical "Mission Areas" that have continued to evolve iteratively over time. Further organizational structure includes headquarters functions, geographic regions, science and support programs, science centers, labs, and other facilities.
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Another element of Somatic Experiencing therapy is "pendulation", the movement between regulation and dysregulation. The client is helped to move to a state where he or she is dysregulated (i.e. is aroused or frozen, demonstrated by physical symptoms such as pain or numbness) and then iteratively helped to return to a state of regulation. The goal is to allow the client to resolve the physical and mental difficulties caused by the trauma, and thereby to be able to respond appropriately to everyday situations.
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Enabling TCPMUX on a server enables an attacker to easily find out the services running on the host, either by using the "HELP" command or by requesting a large number of services. This has the same effect as port scanning the host for available services iteratively. Because TCPMUX allows someone to use any service only by accessing port number 1, the protocol makes it difficult to apply traditional port-based firewall rules that block access from certain or all hosts to specific services.
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In SURF, the lowest level of the scale space is obtained from the output of the 9×9 filters. Hence, unlike previous methods, scale spaces in SURF are implemented by applying box filters of different sizes. Accordingly, the scale space is analyzed by up-scaling the filter size rather than iteratively reducing the image size. The output of the above 9×9 filter is considered as the initial scale layer at scale s =1.2 (corresponding to Gaussian derivatives with σ = 1.2).
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The idea that continuous functions possess the intermediate value property has an earlier origin. Simon Stevin proved the intermediate value theorem for polynomials (using a cubic as an example) by providing an algorithm for constructing the decimal expansion of the solution. The algorithm iteratively subdivides the interval into 10 parts, producing an additional decimal digit at each step of the iteration.Karin Usadi Katz and Mikhail G. Katz (2011) A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.
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Continuation passing style can be used to implement continuations and control flow operators in a functional language that does not feature first-class continuations but does have first-class functions and tail-call optimization. Without tail-call optimization, techniques such as trampolining, i.e. using a loop that iteratively invokes thunk-returning functions, can be used; without first- class functions, it is even possible to convert tail calls into just gotos in such a loop. Writing code in CPS, while not impossible, is often error-prone.
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Deconvolution of imaged data is essential for accurate 3D reconstructions. Deconvolution is an image restoration approach where 'a priori' knowledge of the optical system in the form of a point spread function (PSF) is used to obtain a better estimate of the object. A point spread function can be either calculated from the actual microscope parameters, measured with beads, or estimated and iteratively refined ([Blind Deconvolution]). PSFs can be adjusted locally to account for variations in refractive characteristics of the tissue with depth and sample characteristics.
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In all three cases the output is a pdb file with atom coordinates of the model or a DeepView project file. The four main steps of homology modelling may be repeated iteratively until a satisfactory model is achieved. The SWISS-MODEL Workspace is accessible via the ExPASy web server, or it can be used as part of the program DeepView (Swiss Pdb-Viewer). As of September 2015 it has been cited 20000 times in scientific literature,Number of results returned from a search in Google Scholar.
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Given a CW complex X there is a dual construction to the Postnikov tower called the Whitehead tower. Instead of killing off all higher homotopy groups, the Whitehead tower iteratively kills off lower homotopy groups. This is given by a tower of CW complexes > \cdots \to X_3 \to X_2 \to X_1 \to X, where # The lower homotopy groups are zero, so \pi_i(X_n) = 0 for i \leq n. # The induced map \pi_i\colon \pi_i(X_n) \to \pi_i(X) is an isomorphism for i > n.
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Psychometrika, 75(2), 292-308. Hence, the conditional log odds does not involve the person parameter \beta_n, which can therefore be eliminated by conditioning on the total score r_n=1. That is, by partitioning the responses according to raw scores and calculating the log odds of a correct response, an estimate \delta_2-\delta_1 is obtained without involvement of \beta_n. More generally, a number of item parameters can be estimated iteratively through application of a process such as Conditional Maximum Likelihood estimation (see Rasch model estimation).
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The general idea for iterative methods is to iteratively combine and revise individual node predictions so as to reach an equilibrium. When updating predictions for individual nodes is a fast operation, the complexity of these iterative methods will be the number of iterations needed for convergence. Though convergence and optimality is not always mathematically guaranteed, in practice, these approaches will typically converge quickly to a good solution, depending on the graph structure and problem complexity. The methods presented in this section are representative of this iterative approach.
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TET processivity can be viewed at three levels, the physical, chemical and genetic levels. Physical processivity refers to the ability of a TET protein to slide along the DNA from one CpG site to another. An in vitro study showed that DNA-bound TET does not preferentially oxidize other CpG sites on the same DNA molecule, indicating that TET is not physically processive. Chemical processivity refers to the ability of TET to catalyze the oxidation of 5mC iteratively to 5caC without releasing its substrate.
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NET-inspired templating engine in which each form element is an object exposing its functionality and state via methods and attributes. QForms maintain page as well as form state, and include the ability to validate fields, trigger events, and associate AJAX calls. QForms bind tightly to the ORM, allowing developers to rapidly and iteratively change any of three components in the model–view–controller (MVC) architecture with little impact to the other components. The Qcodo Package Manager (QPM) was introduced starting with Qcodo v0.4.
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Just as manufacturing engineering is linked with other disciplines, such as mechatronics, multidisciplinary design optimization (MDO) is also being used with other CAE programs to automate and improve the iterative design process. MDO tools wrap around existing CAE processes by automating the process of trial and error method used by classical engineers. MDO uses a computer based algorithm that will iteratively seek better alternatives from an initial guess within given constants. MDO uses this procedure to determine the best design outcome and lists various options as well.
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The Segment-tube detector alternates the optimization of temporal localization and spatial segmentation iteratively. The final output is a sequence of per-frame segmentation masks with precise starting/ending frames denoted with the red chunk at the bottom, while the background are marked with green chunks at the bottom. In action localization applications, object co-segmentation is also implemented as the segment-tube spatio-temporal detector. Inspired by the recent spatio-temporal action localization efforts with tubelets (sequences of bounding boxes), Le et al.
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The locations of the quantiles can then be used to test for differences between samples (in the variables not being split) using the chi-squared test. This was later extended into multiple dimensions in the form of frequency difference gating, a binary space partitioning technique where data is iteratively partitioned along the median. These partitions (or bins) are fit to a control sample. Then the proportion of cells falling within each bin in test samples can be compared to the control sample by the chi squared test.
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Through a multi-criteria spatial decision support system stakeholders were able to voice concerns and work on a compromise solution to have final outcome accepted by majority when siting wind farms. This differs from the work of Higgs et al. in that the focus was on allowing users to learn from the collaborative process, both interactively and iteratively about the nature of the problem and their own preferences for desirable characteristics of solution. This stimulated sharing of opinions and discussion of interests behind preferences.
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The algorithm uses a particle physics simulation in which a set N of randomly oriented unit vectors is generated, resulting in a random, nonuniform distribution of points on the sphere. Each particle then receives a repulsive force from every other particle, proportional to the inverse square of the distance between them. By iteratively displacing the particle in the direction of the resultant forces, the particles rearrange themselves. This system will tend to a stable, minimum energy configuration within approximately 40 iterations, where each particle is maximally separated from its closest neighbors.
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The Hardy Cross method is an application of continuity of flow and continuity of potential to iteratively solve for flows in a pipe network. In the case of pipe flow, conservation of flow means that the flow in is equal to the flow out at each junction in the pipe. Conservation of potential means that the total directional head loss along any loop in the system is zero (assuming that a head loss counted against the flow is actually a head gain). Hardy Cross developed two methods for solving flow networks.
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The output of HHpred and HHsearch is a ranked list of database matches (including E-values and probabilities for a true relationship) and the pairwise query-database sequence alignments. HHblits, a part of the HH-suite since 2001, builds high-quality multiple sequence alignments (MSAs) starting from a single query sequence or a MSA. As in PSI-BLAST, it works iteratively, repeatedly constructing new query profiles by adding the results found in the previous round. It matches against a pre-built HMM databases derived from protein sequence databases, each representing a "cluster" of related proteins.
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All patients are categorized based on tissue and imaging markers collected early and iteratively (a patient's markers may change over time) throughout the trial, so that early insights can guide treatments for later patients. Treatments that show positive effects for a patient group can be ushered to confirmatory clinical trials, while those that do not can be rapidly sidelined. Importantly, confirmatory trials can serve as a pathway for FDA Accelerated Approval. I-SPY 2 can simultaneously evaluate candidates developed by multiple companies, escalating or eliminating drugs based on immediate results.
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Mathematical programming and in particular Mixed integer programming models are another approach to solve MSA problems. The advantage of such optimization models is that they can be used to find the optimal MSA solution more efficiently compared to the traditional DP approach. This is due in part, to the applicability of decomposition techniques for mathematical programs, where the MSA model is decomposed into smaller parts and iteratively solved until the optimal solution is found. Example algorithms used to solve mixed integer programming models of MSA include branch and price and Benders decomposition .
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What follows is an example of a Lua function that can be iteratively called to train an `mlp` Module on input Tensor `x`, target Tensor `y` with a scalar `learningRate`: function gradUpdate(mlp, x, y, learningRate) local criterion = nn.ClassNLLCriterion() pred = mlp:forward(x) local err = criterion:forward(pred, y); mlp:zeroGradParameters(); local t = criterion:backward(pred, y); mlp:backward(x, t); mlp:updateParameters(learningRate); end It also has `StochasticGradient` class for training a neural network using Stochastic gradient descent, although the `optim` package provides much more options in this respect, like momentum and weight decay regularization.
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The HIO differs from error reduction only in one step but this is enough to reduce this problem significantly. Whereas the error reduction approach iteratively improves solutions over time the HIO remodels the previous solution in Fourier space applying negative feedback. By minimizing the mean square error in the Fourier space from the previous solution, the HIO provides a better candidate solution for inverse transforming. Although it is both faster and more powerful than error reduction, the HIO algorithm does have a uniqueness problem.Miao J, Kirz J, Sayre D, “The oversampling phasing metod”, Acta Chryst.
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When the observations come from an exponential family and mild conditions are satisfied, least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can also be derived as a method of moments estimator. The following discussion is mostly presented in terms of linear functions but the use of least squares is valid and practical for more general families of functions. Also, by iteratively applying local quadratic approximation to the likelihood (through the Fisher information), the least- squares method may be used to fit a generalized linear model.
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CoBoosting was an attempt by Collins and Singer to improve on previous attempts to leverage redundancy in features for training classifiers in a semi-supervised fashion. CoTraining, a seminal work by Blum and Mitchell, was shown to be a powerful framework for learning classifiers given a small number of seed examples by iteratively inducing rules in a decision list. The advantage of CoBoosting to CoTraining is that it generalizes the CoTraining pattern so that it could be used with any classifier. CoBoosting accomplishes this feat by borrowing concepts from AdaBoost.
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In a posteriori methods, a representative set of Pareto optimal solutions is first found and then the DM must choose one of them. In interactive methods, the decision maker is allowed to iteratively search for the most preferred solution. In each iteration of the interactive method, the DM is shown Pareto optimal solution(s) and describes how the solution(s) could be improved. The information given by the decision maker is then taken into account while generating new Pareto optimal solution(s) for the DM to study in the next iteration.
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Using a standardized format, the FO sends map references and bearing to target, a brief target description, a recommended munition to use, and any special instructions such as "danger close" (the warning that friendly troops are within 600 meters of the target when using artillery, requiring extra precision from the guns). The FO and the battery iteratively "walk" the fire onto the target. The Fire Direction Center (FDC) signals the FO that they have fired and the FO knows to observe fall of shot. He then signals corrections.
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A depth-first search (DFS) is an algorithm for traversing a finite graph. DFS visits the child vertices before visiting the sibling vertices; that is, it traverses the depth of any particular path before exploring its breadth. A stack (often the program's call stack via recursion) is generally used when implementing the algorithm. The algorithm begins with a chosen "root" vertex; it then iteratively transitions from the current vertex to an adjacent, unvisited vertex, until it can no longer find an unexplored vertex to transition to from its current location.
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Rigid bodies are commonly simulated iteratively, with back-tracking to correct error using smaller timesteps. Resting contact between multiple rigid bodies (as is the case when rigid bodies fall into piles or are stacked) can be particularly difficult to handle efficiently and may require complex contact and shock propagation graphs in order to resolve using impulse-based methods. When simulating large numbers of rigid bodies, simplified geometries or convex hulls are often used to represent their boundaries for the purpose of collision detection and response (since this is generally the bottleneck in simulation).
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The hospital set-up closely approximates the standards of the Joint Commission, the leading health care accrediting body in the USA, and other international hospital and infection standards in terms of bed-to-sink ratios, hospital door widths, functionality and work and patient flow. The VINES Laboratory (Virtual Integrated Nursing Education Simulation) is the leading virtual simulation laboratory in the Philippines. It aims to teach nursing skills iteratively and sequentially without harming patients. It seeks to become the Center for Excellence in Nursing Simulation in the Philippines and Asia.
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Swarm behaviour in Dispersive Flies Optimisation Dispersive flies optimisation (DFO) is a bare-bones swarm intelligence algorithm which is inspired by the swarming behaviour of flies hovering over food sources. DFO is a simple optimiser which works by iteratively trying to improve a candidate solution with regard to a numerical measure that is calculated by a fitness function. Each member of the population, a fly or an agent, holds a candidate solution whose suitability can be evaluated by their fitness value. Optimisation problems are often formulated as either minimisation or maximisation problems.
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Random search (RS) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized, and RS can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods. The name "random search" is attributed to Rastrigin who made an early presentation of RS along with basic mathematical analysis. RS works by iteratively moving to better positions in the search-space, which are sampled from a hypersphere surrounding the current position.
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After that, the input signal is further decomposed by a series of 2-D iteratively resampled checkerboard filter banks IRCli(Li)(i=2,3,...,M), where IRCli(Li)operates on 2-D slices of the input signal represented by the dimension pair (n1,ni) and superscript (Li) means the levels of decomposition for the ith level filter bank. Note that, starting from the second level, we attach an IRC filter bank to each output channel from the previous level, and hence the entire filter has a total of 2(L1+...+LN) output channels.
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Scoping reviews are distinct from systematic reviews in a number of important ways. A scoping review is an attempt to search for concepts, mapping the language which surrounds those and adjusting the search method iteratively. A scoping review may often be a preliminary stage before a systematic review, which 'scopes' out an area of inquiry and maps the language and key concepts. As it is a kind of review which should be systematically conducted (the method is repeatable), some academic publishers categorize them as a kind of 'systematic review', which may cause confusion.
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The term block code may also refer to any error-correcting code that acts on a block of k bits of input data to produce n bits of output data (n,k). Consequently, the block coder is a memoryless device. Under this definition codes such as turbo codes, terminated convolutional codes and other iteratively decodable codes (turbo-like codes) would also be considered block codes. A non-terminated convolutional encoder would be an example of a non- block (unframed) code, which has memory and is instead classified as a tree code.
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The resolver now queries the servers referred to, and iteratively repeats this process until it receives an authoritative answer. The diagram illustrates this process for the host that is named by the fully qualified domain name "www.wikipedia.org". This mechanism would place a large traffic burden on the root servers, if every resolution on the Internet required starting at the root. In practice caching is used in DNS servers to off-load the root servers, and as a result, root name servers actually are involved in only a relatively small fraction of all requests.
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Administrators can "live migrate" Xen virtual machines between physical hosts across a LAN without loss of availability. During this procedure, the LAN iteratively copies the memory of the virtual machine to the destination without stopping its execution. The process requires a stoppage of around 60–300 ms to perform final synchronization before the virtual machine begins executing at its final destination, providing an illusion of seamless migration. Similar technology can serve to suspend running virtual machines to disk, "freezing" their running state for resumption at a later date.
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For trees, a concise polynomial canonization algorithm requiring O(n) space is presented by .. Begin by labeling each vertex with the string 01. Iteratively for each non-leaf x remove the leading 0 and trailing 1 from x's label; then sort x's label along with the labels of all adjacent leaves in lexicographic order. Concatenate these sorted labels, add back a leading 0 and trailing 1, make this the new label of x, and delete the adjacent leaves. If there are two vertices remaining, concatenate their labels in lexicographic order.
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Like the models invented before it, the Transformer is an encoder-decoder architecture. The encoder consists of a set of encoding layers that processes the input iteratively one layer after another and the decoder consists of a set of decoding layers that does the same thing to the output of the encoder. The function of each encoder layer is to process its input to generate encodings, containing information about which parts of the inputs are relevant to each other. It passes its set of encodings to the next encoder layer as inputs.
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The structured analysis method can employ IDEF (see figure), is process driven, and starts with a purpose and a viewpoint. This method identifies the overall function and iteratively divides functions into smaller functions, preserving inputs, outputs, controls, and mechanisms necessary to optimize processes. Also known as a functional decomposition approach, it focuses on cohesion within functions and coupling between functions leading to structured data. The functional decomposition of the structured method describes the process without delineating system behavior and dictates system structure in the form of required functions.
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As every policy problem differs from the next, so do the elements involved in a political feasibility analysis. But in order to get started, the analyst works within a basic framework for his/her investigation. These basic steps, as identified by Arnold Meltsner are outlined in the following sections. David Weimer and Aidan Vining argue that in practice analysts should answer the questions iteratively, “moving among them as (the analyst) learn(s) more about the political environment,” meaning that what happens at one stage of the process of identifying political feasibility can affect earlier stages.
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This analysis of SCCC's took place in the 1990s in a series of publications from NASA's Jet Propulsion Laboratory (JPL). The research offered SCCC's as a form of turbo-like serial concatenated codes that 1) were iteratively ('turbo') decodable with reasonable complexity, and 2) gave error correction performance comparable with the turbo codes. Prior forms of serial concatenated codes typically did not use recursive inner codes. Additionally, the constituent codes used in prior forms of serial concatenated codes were generally too complex for reasonable soft-in-soft-out (SISO) decoding.
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The above two criteria are normally applied iteratively until convergence, defined as the point at which no more rotamers or pairs can be eliminated. Since this is normally a reduction in the sample space by many orders of magnitude, simple enumeration will suffice to determine the minimum within this pared-down set. Given this model, it is clear that the DEE algorithm is guaranteed to find the optimal solution; that is, it is a global optimization process. The single-rotamer search scales quadratically in time with total number of rotamers.
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The unknown parameters in each vector βk are typically jointly estimated by maximum a posteriori (MAP) estimation, which is an extension of maximum likelihood using regularization of the weights to prevent pathological solutions (usually a squared regularizing function, which is equivalent to placing a zero-mean Gaussian prior distribution on the weights, but other distributions are also possible). The solution is typically found using an iterative procedure such as generalized iterative scaling, iteratively reweighted least squares (IRLS), by means of gradient-based optimization algorithms such as L-BFGS, or by specialized coordinate descent algorithms.
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28(9): 134-137 (2011). While this provides a simple curve fitting procedure, the resulting algorithm may be biased by excessively weighting small data values, which can produce large errors in the profile estimate. One can partially compensate for this problem through weighted least squares estimation, reducing the weight of small data values, but this too can be biased by allowing the tail of the Gaussian to dominate the fit. In order to remove the bias, one can instead use an iteratively reweighted least squares procedure, in which the weights are updated at each iteration.
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It is common to solve a trajectory optimization problem iteratively, each time using a discretization with more points. A h-method for mesh refinement works by increasing the number of trajectory segments along the trajectory, while a p-method increases the order of the transcription method within each segment. Direct collocation methods tend to exclusively use h-method type refinement, since each method is a fixed order. Shooting methods and orthogonal collocation methods can both use h-method and p-method mesh refinement, and some use a combination, known as hp-adaptive meshing.
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Researchers in the areas of human-computer interaction and cognitive science focus on how people explore for information when interacting with the WWW. This kind of search, sometimes called exploratory search, focuses on how people iteratively refine their search activities and update their internal representations of the search problems.Qu, Yan & Furnas, George. "Model-driven formative evaluation of exploratory search: A study under a sensemaking framework" Existing search engines were designed based on traditional library science theories related to retrieval of basic facts and simple information through an interface.
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In mathematics, the multi-level technique is a technique used to solve the graph partitioning problem. The idea of the multi-level technique is to reduce the magnitude of a graph by merging vertices together, compute a partition on this reduced graph, and finally project this partition on the original graph. In the first phase the magnitude of the graph is reduced by merging vertices. The merging of vertices is done iteratively: of a graph a new coarser graph is created and of this new coarser graph an even more coarse graph is created.
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Ver Hoef and Boveng described the difference between quasi-Poisson (also called overdispersion with quasi-likelihood) and negative binomial (equivalent to gamma-Poisson) as follows: If E(Y) = μ, the quasi-Poisson model assumes var(Y) = θμ while the gamma-Poisson assumes var(Y) = μ(1 + κμ), where θ is the quasi- Poisson overdispersion parameter, and κ is the shape parameter of the negative binomial distribution. For both models, parameters are estimated using Iteratively reweighted least squares. For quasi-Poisson, the weights are μ/θ. For negative binomial, the weights are μ/(1 + κμ).
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The springs and masses do not have to be discrete, they can be continuous (or a mixture), and this method can be easily used in a spreadsheet to find the natural frequencies of quite complex distributed systems, if you can describe the distributed KE and PE terms easily, or else break the continuous elements up into discrete parts. This method could be used iteratively, adding additional mode shapes to the previous best solution, or you can build up a long expression with many Bs and many mode shapes, and then differentiate them partially.
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For combinatorial optimization, the Quantum Approximate Optimization Algorithm (QAOA) briefly had a better approximation ratio than any known polynomial time classical algorithm (for a certain problem), until a more effective classical algorithm was proposed. The relative speed-up of the quantum algorithm is an open research question. The heart of the QAOA relies on the use of unitary operators dependent on 2p angles, where p>1 is an input integer. These operators are iteratively applied on a state that is an equal-weighted quantum superposition of all the possible states in the computational basis.
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The double integration corrects for the -ω² filtering characteristic associated with the nonlinear acoustic effect. This recovers the scaled original spectrum at baseband. The harmonic distortion process has to do with the high frequency replicas associated with each squaring demodulation, for either modulation scheme. These iteratively demodulate and self-modulate, adding a spectrally smeared out and time exponentiated copy of the original signal to baseband and twice the original center frequency each time, with one iteration corresponding to one traversal of the space between the emitter and target.
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The ZMap algorithm was proposed in the academic literature by Byoung K Choi in 2003 as a way of precalculating and storing a regular array of cutter location values in the computer memory. The result is a model of the height map of cutter positions from which in between values can be interpolated. Due to accuracy issues, this was generalized into an Extended ZMap, or EZMap, by the placement of "floating" points in between the fixed ZMap points. The location of the EZMap points are found iteratively when the ZMap is created.
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With these assumptions, the above formula allows computing the cost of all variable evaluations by iteratively proceeding bottom-up from the leaves to the root(s) of the forest. The cost of variable evaluations can be used by local search for computing the cost of a solution. The cost of values of the roots of the forest is indeed the minimal number of violated constraints in the forest for these given values. These costs can therefore used to evaluate the cost of the assignment to the cutset variables and to estimate the cost of similar assignments on the cutset variables.
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Hybrid input-output (HIO) algorithm for phase retrieval is a modification of the error reduction algorithm for retrieving the phases in Coherent diffraction imaging. Determining the phases of a diffraction pattern is crucial since the diffraction pattern of an object is its Fourier transform and in order to properly inverse transform the diffraction pattern the phases must be known. Only the amplitude however, can be measured from the intensity of the diffraction pattern and can thus be known experimentally. This fact together with some kind of support (mathematics) can be used in order to iteratively calculate the phases.
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In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic. In other words, iteratively applying the resolution rule in a suitable way allows for telling whether a propositional formula is satisfiable and for proving that a first-order formula is unsatisfiable. Attempting to prove a satisfiable first-order formula as unsatisfiable may result in a nonterminating computation; this problem doesn't occur in propositional logic. The resolution rule can be traced back to Davis and Putnam (1960); Here: p.
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A computationally viable alternative to full analytic response to Kohn-Sham density functional theoretic (DFT) approach, which solves coupled-perturbed Kohn-Sham (CPKS) procedure in non-iteratively has been formulated by Sourav. In the above procedure, the derivative of KS matrix is obtained using finite field and then the density matrix derivative is obtained by single-step CPKS solution followed by analytic evaluation of properties. He has implemented this in deMON2K software and used for calculation of electric properties. Density functional response approach for the linear and non-linear electric properties of molecules K.B. Sophy and Sourav Pal (2003) J.Chem.Phys.
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VoC is derived strictly following its definition as the monetary amount that is big enough to just offset the additional benefit of getting more information. In other words; VoC is calculated iteratively until ::"value of decision situation with perfect information while paying VoC" = "value of current decision situation". A special case is when the decision- maker is risk neutral where VoC can be simply computed as ::VoC = "value of decision situation with perfect information" - "value of current decision situation". This special case is how expected value of perfect information and expected value of sample information are calculated where risk neutrality is implicitly assumed.
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The Gilbert–Johnson–Keerthi distance algorithm is a method of determining the minimum distance between two convex sets. Unlike many other distance algorithms, it does not require that the geometry data be stored in any specific format, but instead relies solely on a support function to iteratively generate closer simplices to the correct answer using the configuration space obstacle (CSO) of two convex shapes, more commonly known as the Minkowski difference. "Enhanced GJK" algorithms use edge information to speed up the algorithm by following edges when looking for the next simplex. This improves performance substantially for polytopes with large numbers of vertices.
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ICM stands for Internal Coordinate Mechanics and was first designed and built to predict low-energy conformations of molecules by sampling the space of internal coordinates (bond lengths, bond angles and dihedral angles) defining molecular geometry. In ICM each molecule is constructed as a tree from an entry atom where each next atom is built iteratively from the preceding three atoms via three internal variables. The rings kept rigid or imposed via additional restraints. ICM also is a programming environment for various tasks in computational chemistry and computational structural biology, sequence analysis and rational drug design.
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It does not require that they do so by any particular method, but the child seeking to learn the language must somehow come to associate words with objects and actions in the world. Second, children must know that there is a strong correspondence between semantic categories and syntactic categories. The relationship between semantic and syntactic categories can then be used to iteratively create, test, and refine internal grammar rules until the child's understanding aligns with the language to which they are exposed, allowing for better categorization methods to be deduced as the child obtains more knowledge of the language.
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Lean startup is a methodology for developing businesses and products that aims to shorten product development cycles and rapidly discover if a proposed business model is viable; this is achieved by adopting a combination of business-hypothesis-driven experimentation, iterative product releases, and validated learning. Central to the lean startup methodology is the assumption that when startup companies invest their time into iteratively building products or services to meet the needs of early customers, the company can reduce market risks and sidestep the need for large amounts of initial project funding and expensive product launches and failures.
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The most common algorithm to compute IFS fractals is called the "chaos game". It consists of picking a random point in the plane, then iteratively applying one of the functions chosen at random from the function system to transform the point to get a next point. An alternative algorithm is to generate each possible sequence of functions up to a given maximum length, and then to plot the results of applying each of these sequences of functions to an initial point or shape. Each of these algorithms provides a global construction which generates points distributed across the whole fractal.
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Traditional model of construction of a wall of rammed earth on a foundation Making rammed earth involves compacting a damp mixture of sub soil that has suitable proportions of sand, gravel, clay, and stabilizer, if any into a formwork (an externally supported frame or mold). Historically, additives such as lime or animal blood were used to stabilize it. Soil mix is poured into the formwork to a depth of and then compacted to approximately 50% of its original volume. The soil is compacted iteratively, in batches or courses, so as to gradually erect the wall up to the top of the formwork.
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The intersection of the unit cube with the cutting plane x_1 + x_2 + x_3 \geq 2. In the context of the Traveling salesman problem on three nodes, this (rather weak) inequality states that every tour must have at least two edges. In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems.
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The primary logical DNS container used to hold DDDS information is the NAPTR record. DDDS is defined in RFC 3401, RFC 3402, RFC 3403, RFC 3404, and RFC 3405. RFC 3401 expresses the system as follows:RFC 3401, M. Mealling, Dynamic Delegation Discovery System (DDDS), IETF (October 2002) > The Dynamic Delegation Discovery System is used to implement lazy binding of > strings to data, in order to support dynamically configured delegation > systems. The DDDS functions by mapping some unique string to data stored > within a DDDS Database by iteratively applying string transformation rules > until a terminal condition is reached.
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The generation must be initiated only when the prime's square is reached, to avoid adverse effects on efficiency. It can be expressed symbolically under the dataflow paradigm as primes = [2, 3, ...] \ p², p²+p, ...] for p in primes], using list comprehension notation with `\` denoting set subtraction of arithmetic progressions of numbers. Primes can also be produced by iteratively sieving out the composites through divisibility testing by sequential primes, one prime at a time. It is not the sieve of Eratosthenes but is often confused with it, even though the sieve of Eratosthenes directly generates the composites instead of testing for them.
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Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization, aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum).
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This behavior is consistent with returning the visually observed speed back toward the preferred speed and suggests that vision is used correctively to maintain walking speed at a value that is perceived to be optimal. Moreover, the dynamics of this visual influence on preferred walking speed are rapid—when visual gains are changed suddenly, individuals adjust their speed within a few seconds. The timing and direction of these responses strongly indicate that a rapid predictive process informed by visual feedback helps select preferred speed, perhaps to complement a slower optimization process that directly senses metabolic rate and iteratively adapts gait to minimize it.
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In (unconstrained) minimization, a backtracking line search, a search scheme based on the Armijo–Goldstein condition, is a line search method to determine the amount to move along a given search direction. It involves starting with a relatively large estimate of the step size for movement along the search direction, and iteratively shrinking the step size (i.e., "backtracking") until a decrease of the objective function is observed that adequately corresponds to the decrease that is expected, based on the local gradient of the objective function. Backtracking line search is typically used for gradient descent, but it can also be used in other contexts.
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Gibbs sampling is a general framework for approximating a distribution. It is a Markov chain Monte Carlo algorithm, in that it iteratively samples from the current estimate of the distribution, constructing a Markov chain that converges to the target (stationary) distribution. The basic idea for Gibbs Sampling is to sample for the best label estimate for y_i given all the values for the nodes in N_i using local classifier f for a fixed number of iterations. After that, we sample labels for each y_i\in Y and maintain count statistics for the number of times we sampled label l for node y_i.
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Evidence_based_assessment (EBA) refers to the use of research and theory to guide the selection of constructs to be used for a specific assessment purpose and to inform the methods and measures used in the assessment process. It involves the recognition that, even with data from psychometrically strong measures, the assessment process is inherently a decision-making task in which the clinician must iteratively formulate and test hypotheses by integrating data that are often incomplete and consistent. EBA has been found to help clinicians in cognitively debiasing their clinical decisions. Evidence-based assessment is part of a larger movement towards evidence-based practices.
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In a function defined by a recursive definition, each value is defined by a fixed first-order formula of other, previously defined values of the same function or other functions, which might be simply constants. A subset of these is the primitive recursive functions. Every such function is provably total: For such a k-ary function f, each value f(n_1, n_2... n_k) can be computed by following the definition backwards, iteratively, and after finite number of iteration (as can be easily proven), a constant is reached. The converse is not true, as not every provably total function is primitive recursive.
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It was invented by David Karger and first published in 1993. The idea of the algorithm is based on the concept of contraction of an edge (u, v) in an undirected graph G = (V, E). Informally speaking, the contraction of an edge merges the nodes u and v into one, reducing the total number of nodes of the graph by one. All other edges connecting either u or v are "reattached" to the merged node, effectively producing a multigraph. Karger's basic algorithm iteratively contracts randomly chosen edges until only two nodes remain; those nodes represent a cut in the original graph.
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J. Numer. Meth. Engng., 52, 2001, p. 139–160Moulinec H., P. Suquet and G. Milton, « Convergence of iterative methods based on Neumann series for composite materials : Theory and practice », Int. J. Numer. Meth. Engng., 2018 (lire en ligne) introduced a numerical method using massively the Fast Fourier Transform (FFT) using only a pixelized image of the study microstructure (without mesh size). By introducing a homogeneous reference medium, the heterogeneity of the medium is transformed into a polarization constraint. The Green operator of the reference medium, known explicitly in Fourier space, can be used to iteratively update the polarization field.
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Hourly averaged iteratively solved surface temperature from BAITSSS (composite surface) compared to measured Infrared Temperature (IRT) and air temperature of corn between 22 May and 28 June 2016 near Bushland, Texas.ET models, in general, need information about vegetation (physical properties and vegetation indices) and environment condition (weather data) to compute water use. Primary weather data requirements in BAITSSS are solar irradiance (R), wind speed (u), air temperature (T), relative humidity (RH) or specific humidity (q), and precipitation (P). Vegetation indices requirements in BAITSSS are leaf area index (LAI) and fractional canopy cover (f), generally estimated from normalized difference vegetation index (NDVI).
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Trajectory optimization is the process of designing a trajectory that minimizes (or maximizes) some measure of performance while satisfying a set of constraints. Generally speaking, trajectory optimization is a technique for computing an open-loop solution to an optimal control problem. It is often used for systems where computing the full closed-loop solution is not required, impractical or impossible. If a trajectory optimization problem can be solved at a rate given by the inverse of the Lipschitz constant, then it can be used iteratively to generate a closed-loop solution in the sense of Caratheodory.
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Dykstra's algorithm is a method that computes a point in the intersection of convex sets, and is a variant of the alternating projection method (also called the projections onto convex sets method). In its simplest form, the method finds a point in the intersection of two convex sets by iteratively projecting onto each of the convex set; it differs from the alternating projection method in that there are intermediate steps. A parallel version of the algorithm was developed by Gaffke and Mathar. The method is named after Richard L. Dykstra who proposed it in the 1980s.
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Relative to oracles, we know that there exist oracles A and B, such that PA = BPPA and PB ≠ BPPB. Moreover, relative to a random oracle with probability 1, P = BPP and BPP is strictly contained in NP and co-NP. There is even an oracle in which BPP=EXPNP (and hence Piteratively constructed as follows. For a fixed ENP (relativized) complete problem, the oracle will give correct answers with high probability if queried with the problem instance followed by a random string of length kn (n is instance length; k is an appropriate small constant).
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In Agile software development, the Fibonacci scale consists of a sequence of numbers used for estimating the relative size of user stories in points. Agile Scrum is based on the concept of working iteratively in short sprints, typically two weeks long, where the requirements and development are continuously being improved. The Fibonacci sequence consists of numbers that are the summation of the two preceding numbers, starting with [0, 1]. Agile uses the Fibonacci sequence to achieve better results by reducing complexity, effort, and doubt when determining the development time required for a task, which can range from a few minutes to several weeks.
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The Beam Propagation Method relies on the slowly varying envelope approximation, and is inaccurate for the modelling of discretely or fastly varying structures. Basic implementations are also inaccurate for the modelling of structures in which light propagates in large range of angles and for devices with high refractive-index contrast, commonly found for instance in silicon photonics. Advanced implementations, however, mitigate some of these limitations allowing BPM to be used to accurately model many of these cases, including many silicon photonics structures. The BPM method can be used to model bi-directional propagation, but the reflections need to be implemented iteratively which can lead to convergence issues.
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Since these holistic problem models could be independently automated and solved due to this closure, they could be blended into higher wholes by nesting one inside of another, in the manner of subroutines. And users could regard them as if they were ordinary subroutines. Yet semantically, this mathematical blending was considerably more complex than the mechanics of subroutines, because an iterative solution engine was attached to each problem model by its calling operator template above it in the program hierarchy. In its numerical solution process, this engine would take control and would call the problem model subroutine iteratively, not returning to the calling template until its system problem was solved.
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The median polish is a simple and robust exploratory data analysis procedure proposed by the statistician John Tukey. The purpose of median polish is to find an additively-fit model for data in a two-way layout table (usually, results from a factorial experiment) of the form row effect + column effect + overall median. Median polish utilizes the medians obtained from the rows and the columns of a two-way table to iteratively calculate the row effect and column effect on the data. The results are not meant to be sensitive to the outliers, as the iterative procedure uses the medians rather than the means.
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CARINE is a first-order classical logic automated theorem prover. CARINE (Computer Aided Reasoning engINE) is a resolution based theorem prover initially built for the study of the enhancement effects of the strategies delayed clause-construction (DCC) and attribute sequences (ATS) in a depth- first search based algorithm [Haroun 2005]. CARINE's main search algorithm is semi-linear resolution (SLR) which is based on an iteratively-deepening depth- first search (also known as depth-first iterative-deepening (DFID) [Korf 1985]) and used in theorem provers like THEO [Newborn 2001]. SLR employs DCC to achieve a high inference rate, and ATS to reduce the search space.
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Second is mining more useful information and can get the corresponding information in test clusters and words clusters. This corresponding information can be used to describe the type of texts and words, at the same time, the result of words clustering can be also used to text mining and information retrieval. Several approaches have been proposed based on the information contents of the resulting blocks: matrix-based approaches such as SVD and BVD, and graph-based approaches. Information-theoretic algorithms iteratively assign each row to a cluster of documents and each column to a cluster of words such that the mutual information is maximized.
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The critical first step in homology modeling is the identification of the best template structure, if indeed any are available. The simplest method of template identification relies on serial pairwise sequence alignments aided by database search techniques such as FASTA and BLAST. More sensitive methods based on multiple sequence alignment – of which PSI-BLAST is the most common example – iteratively update their position-specific scoring matrix to successively identify more distantly related homologs. This family of methods has been shown to produce a larger number of potential templates and to identify better templates for sequences that have only distant relationships to any solved structure.
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After a cytosine is methylated to 5mC, it can be reversed back to its initial state via multiple mechanisms. Passive DNA demethylation by dilution eliminates the mark gradually through replication by a lack of maintenance by DNMT. In active DNA demethylation, a series of oxidations converts it to 5-hydroxymethylcytosine (5hmC), 5-formylcytosine (5fC), and 5-carboxylcytosine (5caC), and the latter two are eventually excised by thymine DNA glycosylase (TDG), followed by base excision repair (BER) to restore the cytosine. TDG knockout produced a 2-fold increase of 5fC without any statistically significant change to levels of 5hmC, indicating 5mC must be iteratively oxidized at least twice before its full demethylation.
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In mathematics, specifically in numerical analysis, the Local Linearization (LL) method is a general strategy for designing numerical integrators for differential equations based on a local (piecewise) linearization of the given equation on consecutive time intervals. The numerical integrators are then iteratively defined as the solution of the resulting piecewise linear equation at the end of each consecutive interval. The LL method has been developed for a variety of equations such as the ordinary, delayed, random and stochastic differential equations. The LL integrators are key component in the implementation of inference methods for the estimation of unknown parameters and unobserved variables of differential equations given time series of (potentially noisy) observations.
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A basic voltage clamp will iteratively measure the membrane potential, and then change the membrane potential (voltage) to a desired value by adding the necessary current. This "clamps" the cell membrane at a desired constant voltage, allowing the voltage clamp to record what currents are delivered. Because the currents applied to the cell must be equal to (and opposite in charge to) the current going across the cell membrane at the set voltage, the recorded currents indicate how the cell reacts to changes in membrane potential. Cell membranes of excitable cells contain many different kinds of ion channels, some of which are voltage-gated.
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In order to calculate this measure, the original CFG is iteratively reduced by identifying subgraphs that have a single-entry and a single-exit point, which are then replaced by a single node. This reduction corresponds to what a human would do if they extracted a subroutine from the larger piece of code. (Nowadays such a process would fall under the umbrella term of refactoring.) McCabe's reduction method was later called condensation in some textbooks, because it was seen as a generalization of the condensation to components used in graph theory. If a program is structured, then McCabe's reduction/condensation process reduces it to a single CFG node.
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Since every node in B depends on a node in A, this causes the removal of the same fraction 1-p of nodes in B. In network theory, we assume that only nodes which are a part of the largest connected component can continue to function. Since the arrangement of links in A and B are different, they fragment into different sets of connected components. The smaller components in A cease to function and when they do, they cause the same number of nodes (but in different locations) in B to cease to function as well. This process continues iteratively between the two networks until no more nodes are removed.
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In order to handle the changing mathematical structure, the set-valued force laws are commonly written as inequality or inclusion problems. The evaluation of these inequalities/inclusions is commonly done by solving linear (or nonlinear) complementarity problems, by quadratic programming or by transforming the inequality/inclusion problems into projective equations which can be solved iteratively by Jacobi or Gauss–Seidel techniques. The non-smooth approach provides a new modeling approach for mechanical systems with unilateral contacts and friction, which incorporates also the whole classical mechanics subjected to bilateral constraints. The approach is associated to the classical DAE theory and leads to robust integration schemes.
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Particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions.
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As the head/tail breaks method can be used iteratively to obtain head parts of a data set, this method actually captures the underlying hierarchy of the data set. For example, if we divide the array (19, 8, 7, 6, 2, 1, 1, 1, 0) with the head/tail breaks method, we can get two head parts, i.e., the first head part (19, 8, 7, 6) and the second head part (19). These two head parts as well as the original array form a three-level hierarchy: the 1st level (19), the 2nd level (19, 8, 7, 6), and the 3rd level (19, 8, 7, 6, 2, 1, 1, 1, 0).
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Within the basic formulation of COSMO-RS, interaction terms depend on the screening charge density σ. Each molecule and mixture can be represented by the histogram p(σ), the so-called σ-profile. The σ-profile of a mixture is the weighted sum of the profiles of all its components. Using the interaction energy Eint(σ,σ') and the σ-profile of the solvent p(σ'), the chemical potential µs(σ) of a surface piece with screening charge σ is determined as: d\sigma'}} Due to the fact that µs(σ) is present on both sides of the equation, it needs to be solved iteratively.
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Integral equation methods, however, generate dense (all entries are nonzero) linear systems which makes such methods preferable to FD or FEM only for small problems. Such systems require O(n2) memory to store and O(n3) to solve via direct Gaussian elimination or at best O(n2) if solved iteratively. Increasing circuit speeds and densities require the solution of increasingly complicated interconnect, making dense integral equation approaches unsuitable due to these high growth rates of computational cost with increasing problem size. In the past two decades, much work has gone into improving both the differential and integral equation approaches, as well as new approaches based on random walk methods.
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Multiply recursive problems are inherently recursive, because of prior state they need to track. One example is tree traversal as in depth-first search; though both recursive and iterative methods are used, they contrast with list traversal and linear search in a list, which is a singly recursive and thus naturally iterative method. Other examples include divide- and-conquer algorithms such as Quicksort, and functions such as the Ackermann function. All of these algorithms can be implemented iteratively with the help of an explicit stack, but the programmer effort involved in managing the stack, and the complexity of the resulting program, arguably outweigh any advantages of the iterative solution.
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A review of methods for choosing summary statistics is available, which may provide valuable guidance in practice. One approach to capture most of the information present in data would be to use many statistics, but the accuracy and stability of ABC appears to decrease rapidly with an increasing numbers of summary statistics. Instead, a better strategy is to focus on the relevant statistics only—relevancy depending on the whole inference problem, on the model used, and on the data at hand. An algorithm has been proposed for identifying a representative subset of summary statistics, by iteratively assessing whether an additional statistic introduces a meaningful modification of the posterior.
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However, as gradient magnitudes are used for estimation of relative penalty weights between the data fidelity and regularization terms, this method is not robust to noise and artifacts and accurate enough for CS image/signal reconstruction and, therefore, fails to preserve smaller structures. Recent progress on this problem involves using an iteratively directional TV refinement for CS reconstruction. This method would have 2 stages: the first stage would estimate and refine the initial orientation field – which is defined as a noisy point-wise initial estimate, through edge-detection, of the given image. In the second stage, the CS reconstruction model is presented by utilizing directional TV regularizer.
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Hartigan and Wong's method provides a variation of k-means algorithm which progresses towards a local minimum of the minimum sum-of-squares problem with different solution updates. The method is a local search that iteratively attempts to relocate a sample into a different cluster as long as this process improves the objective function. When no sample can be relocated into a different cluster with an improvement of the objective, the method stops (in a local minimum). In a similar way as the classical k-means, the approach remains a heuristic since it does not necessarily guarantee that the final solution is globally optimum.
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In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel who did pioneering research while working for IBM (USA); it is also commonly known as a Feistel network. A large proportion of block ciphers use the scheme, including the US Data Encryption Standard, the Soviet/Russian GOST and the more recent Blowfish and Twofish ciphers. In a Feistel cipher, encryption and decryption are very similar operations, and both consist of iteratively running a function called a "round function" a fixed number of times.
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From Peano's example, it was easy to deduce continuous curves whose ranges contained the n-dimensional hypercube (for any positive integer n). It was also easy to extend Peano's example to continuous curves without endpoints, which filled the entire n-dimensional Euclidean space (where n is 2, 3, or any other positive integer). Most well-known space- filling curves are constructed iteratively as the limit of a sequence of piecewise linear continuous curves, each one more closely approximating the space-filling limit. Peano's ground-breaking article contained no illustrations of his construction, which is defined in terms of ternary expansions and a mirroring operator.
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Tabulation hashing is a technique for mapping keys to hash values by partitioning each key into bytes, using each byte as the index into a table of random numbers (with a different table for each byte position), and combining the results of these table lookups by a bitwise exclusive or operation. Thus, it requires more randomness in its initialization than the polynomial method, but avoids possibly-slow multiplication operations. It is 3-independent but not 4-independent.. Variations of tabulation hashing can achieve higher degrees of independence by performing table lookups based on overlapping combinations of bits from the input key, or by applying simple tabulation hashing iteratively...
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In September 2016, SpaceX announced that development was underway to extend the reusable flight hardware to second stages, a more challenging engineering problem because the vehicle is travelling at orbital velocity. The reusable technology was to have been extended to the 2016 designs of both the tanker and crewed spaceship upper stage variants as well as the first stage of the Interplanetary Transport System, and is considered paramount to the plans Elon Musk is championing to enable the settlement of Mars. In 2016, initial test flights of an Interplanetary Transport System vehicle were expected no earlier than 2020. In 2017 SpaceX was making test flight progress in incrementally and iteratively developing a fairing recovery system.
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In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters.
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It is less clear, however, how and why generalization is observed in infants: It might extend directly from detection and storage of similarities and differences in incoming data, or frequency representations. Conversely, it might be produced by something like general-purpose Bayesian inference, starting with a knowledge base that is iteratively conditioned on data to update subjective probabilities, or beliefs. This ties together questions about the statistical toolkit(s) that might be involved in learning, and how they apply to infant and childhood learning specifically. Gopnik advocates the hypothesis that infant and childhood learning are examples of inductive inference, a general- purpose mechanism for generalization, acting upon specialized information structures ("theories") in the brain.
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After that, the input signal is further decomposed by a series of 2-D iteratively resampled checkerboard filter banks IRCli(Li)(i=2,3,...,M), where IRCli(Li)operates on 2-D slices of the input signal represented by the dimension pair (n1,ni) and superscript (Li) means the levels of decomposition for the ith level filter bank. Note that, starting from the second level, we attach an IRC filter bank to each output channel from the previous level, and hence the entire filter has a total of 2(L1+...+LN) output channels.Lu, Yue M., and Minh N. Do. "Multidimensional directional filter banks and surfacelets", IEEE Transactions on Image Processing. Volume 16 Issue 4, pp. 918–931.
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The first four iterations of the Koch snowflake The first seven iterations in animation Zooming into the Koch curve The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" by the Swedish mathematician Helge von Koch. The Koch snowflake can be built up iteratively, in a sequence of stages. The first stage is an equilateral triangle, and each successive stage is formed from adding outward bends to each side of the previous stage, making smaller equilateral triangles.
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Bundle adjustment boils down to minimizing the reprojection error between the image locations of observed and predicted image points, which is expressed as the sum of squares of a large number of nonlinear, real-valued functions. Thus, the minimization is achieved using nonlinear least-squares algorithms. Of these, Levenberg–Marquardt has proven to be one of the most successful due to its ease of implementation and its use of an effective damping strategy that lends it the ability to converge quickly from a wide range of initial guesses. By iteratively linearizing the function to be minimized in the neighborhood of the current estimate, the Levenberg–Marquardt algorithm involves the solution of linear systems termed the normal equations.
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Despite their poor performance as stand- alone codes, use in Turbo code-like iteratively decoded concatenated coding schemes, such as repeat-accumulate (RA) and accumulate-repeat-accumulate (ARA) codes, allows for surprisingly good error correction performance. Repetition codes are one of the few known codes whose code rate can be automatically adjusted to varying channel capacity, by sending more or less parity information as required to overcome the channel noise, and it is the only such code known for non-erasure channels. Practical adaptive codes for erasure channels have been invented only recently, and are known as fountain codes. Some UARTs, such as the ones used in the FlexRay protocol, use a majority filter to ignore brief noise spikes.
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The bottom- up approaches are the traditional ones, and they have the advantage that they require no assumptions on the overall structure of the document. On the other hand, bottom-up approaches require iterative segmentation and clustering, which can be time consuming. Top-down approaches are newer, and have the advantage that they parse the global structure of a document directly, thus eliminating the need to iteratively cluster together the possibly hundreds or even thousands of characters/symbols which appear on a document. They tend to be faster, but in order for them to operate robustly they typically require a number of assumptions to be made about on the layout of the document.
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Although there are multiple deterministic models to generate scale-free networks, it is common, that they define a simple algorithm of adding nodes, which is then iteratively repeated and thus leads to a complex network. As these models are deterministic, it is possible to get analytic results about the degree distribution, clustering coefficient, average shortest path length, random walk centrality and other relevant network metrics. Deterministic models are especially useful to explain empirically observed phenomena and demonstrate the existence of networks with certain properties. For example, the Barabási-Albert model predicts a decreasing average clustering coefficient as the number of nodes increases,Zadorozhnyi, V.; Yudin, E. Structural properties of the scale-free Barabasi-Albert graph, Automation & Remote Control.
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In evolutionary computation, Minimum Population Search (MPS) is a computational method that optimizes a problem by iteratively trying to improve a set of candidate solutions with regard to a given measure of quality. It solves a problem by evolving a small population of candidate solutions by means of relatively simple arithmetical operations. MPS is a metaheuristic as it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. For problems where finding the precise global optimum is less important than finding an acceptable local optimum in a fixed amount of time, using a metaheuristic such as MPS may be preferable to alternatives such as brute-force search or gradient descent.
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The modern theory of frozen orbits is based on the algorithm given in a 1989 article by Mats Rosengren. For this the analytical expression () is used to iteratively update the initial (mean) eccentricity vector to obtain that the (mean) eccentricity vector several orbits later computed by the precise numerical propagation takes precisely the same value. In this way the secular perturbation of the eccentricity vector caused by the J_2\, term is used to counteract all secular perturbations, not only those (dominating) caused by the J_3\, term. One such additional secular perturbation that in this way can be compensated for is the one caused by the solar radiation pressure, this perturbation is discussed in the article "Orbital perturbation analysis (spacecraft)".
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Small-signal or linear models are used to evaluate stability, gain, noise and bandwidth, both in the conceptual stages of circuit design (to decide between alternative design ideas before computer simulation is warranted) and using computers. A small-signal model is generated by taking derivatives of the current–voltage curves about a bias point or Q-point. As long as the signal is small relative to the nonlinearity of the device, the derivatives do not vary significantly, and can be treated as standard linear circuit elements. An advantage of small signal models is they can be solved directly, while large signal nonlinear models are generally solved iteratively, with possible convergence or stability issues.
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In the Iterative Closest Point or, in some sources, the Iterative Corresponding Point, one point cloud (vertex cloud), the reference, or target, is kept fixed, while the other one, the source, is transformed to best match the reference. The algorithm iteratively revises the transformation (combination of translation and rotation) needed to minimize an error metric, usually a distance from the source to the reference point cloud, such as the sum of squared differences between the coordinates of the matched pairs. ICP is one of the widely used algorithms in aligning three dimensional models given an initial guess of the rigid transformation required. The ICP algorithm was first introduced by Chen and Medioni, and Besl and McKay.
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So far we have neglected the fact that the deformation itself creates a perturbative potential. In order to account for this, we may calculate this perturbative potential, re-calculate the deformation and continue so iteratively. Let us assume the mass density is uniform. Since δ is much smaller than A, the deformation can be treated as a thin shell added to the mass of the Earth, where the shell has a surface mass density ρ δ (and can also be negative), with ρ being the mass density (if mass density is not uniform, then the change of shape of the planet creates differences in mass distribution in all depth, and this has to be taken into account as well).
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As an important special case, which is used as a subroutine in the general algorithm (see below), the Pohlig–Hellman algorithm applies to groups whose order is a prime power. The basic idea of this algorithm is to iteratively compute the p-adic digits of the logarithm by repeatedly "shifting out" all but one unknown digit in the exponent, and computing that digit by elementary methods. (Note that for readability, the algorithm is stated for cyclic groups — in general, G must be replaced by the subgroup \langle g\rangle generated by g, which is always cyclic.) :Input. A cyclic group G of order n=p^e with generator g and an element h\in G. :Output.
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The overall concept of backward averaging was introduced to expedite the convergence process of iteratively solved surface energy balance components which can be time-consuming and can frequently suffer non-convergence, especially in low wind speed. In 2017, the landscape BAITSSS model was scripted in Python shell, together with GDAL and NumPy libraries using NLDAS weather data (~ 12.5 kilometers). The detailed independent model was evaluated against weighing lysimeter measured ET, infrared temperature (IRT) and net radiometer of drought‐tolerant corn at Conservation and Production Research Laboratory in Bushland, Texas by group of scientists from USDA-ARS and Kansas State University between 2017 and 2019. Some later development of BAITSSS includes physically based crop productivity components, i.e.
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In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number , then this root corresponds to a unique root of the same equation modulo any higher power of , which can be found by iteratively "lifting" the solution modulo successive powers of . More generally it is used as a generic name for analogues for complete commutative rings (including p-adic fields in particular) of Newton's method for solving equations. Since p-adic analysis is in some ways simpler than real analysis, there are relatively neat criteria guaranteeing a root of a polynomial.
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For example, if noise-predictive detection is performed in conjunction with a maximum a posteriori (MAP) detection algorithm such as the BCJR algorithm then NPML and NPML-like detection allow the computation of soft reliability information on individual code symbols, while retaining all the performance advantages associated with noise-predictive techniques. The soft information generated in this manner is used for soft decoding of the error-correcting code. Moreover, the soft information computed by the decoder can be fed back again to the soft detector to improve detection performance. In this way it is possible to iteratively improve the error-rate performance at the decoder output in successive soft detection/decoding rounds.
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This creates the sharp contrast we see between the text and the scroll in the final images of the virtually unwrapped scroll. When the scroll completes a full rotation with respect to the x-ray source, the computer generates a 2D slice of the cross-section, and performing this iteratively allows the computer to build up a 3D volumetric scan describing the density as a function of the position inside the scroll. The only data needed for the virtual unwrapping process is this volumetric scan, so after this point the scroll was safely returned to its protective archive. The density distribution is stored by the computer with corresponding positions, called voxels or volume-pixels.
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Biogeography-based optimization (BBO) is an evolutionary algorithm (EA) that optimizes a function by stochastically and iteratively improving candidate solutions with regard to a given measure of quality, or fitness function. BBO belongs to the class of metaheuristics since it includes many variations, and since it does not make any assumptions about the problem and can therefore be applied to a wide class of problems. BBO is typically used to optimize multidimensional real-valued functions, but it does not use the gradient of the function, which means that it does not require the function to be differentiable as required by classic optimization methods such as gradient descent and quasi-newton methods. BBO can therefore be used on discontinuous functions.
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In computer science, heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to more quickly find the largest element in each step. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case runtime.
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Although further research is necessary on the application of various invariance tests and their respective criteria across diverse testing conditions, two approaches are common among applied researchers. For each model being compared (e.g., Equal form, Equal Intercepts) a χ2 fit statistic is iteratively estimated from the minimization of the difference between the model implied mean and covariance matrices and the observed mean and covariance matrices. As long as the models under comparison are nested, the difference between the χ2 values and their respective degrees of freedom of any two CFA models of varying levels of invariance follows a χ2 distribution (diff χ2) and as such, can be inspected for significance as an indication of whether increasingly restrictive models produce appreciable changes in model-data fit.
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Then it is possible to introduce the unknown branching ratios by hand from a plausible guess. A good guess can be calculated by means of the Statistical Model. Then the procedure to find the feedings is iterative: using the expectation-maximization algorithm to solve the inverse problem, Then the procedure to find the feedings is iterative: using the expectation-maximization algorithm to solve the inverse problem, the feedings are extracted; if they don't reproduce the experimental data, it means that the initial guess of the branching ratios is wrong and has to be changed (of course, it is possible to play with other parameters of the analysis). Repeating this procedure iteratively in a reduced number of steps, the data is finally reproduced.
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In fact, passive-solar design features such as a greenhouse/sunroom/solarium can greatly enhance the livability, daylight, views, and value of a home, at a low cost per unit of space. Much has been learned about passive solar building design since the 1970s energy crisis. Many unscientific, intuition-based expensive construction experiments have attempted and failed to achieve zero energy – the total elimination of heating-and-cooling energy bills. Passive solar building construction may not be difficult or expensive (using off-the-shelf existing materials and technology), but the scientific passive solar building design is a non-trivial engineering effort that requires significant study of previous counter- intuitive lessons learned, and time to enter, evaluate, and iteratively refine the simulation input and output.
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A similar approach searches for the shortest path between two words: the second word is iteratively searched among the definitions of every semantic variant of the first word, then among the definitions of every semantic variant of each word in the previous definitions and so on. Finally, the first word is disambiguated by selecting the semantic variant which minimizes the distance from the first to the second word. An alternative to the use of the definitions is to consider general word-sense relatedness and to compute the semantic similarity of each pair of word senses based on a given lexical knowledge base such as WordNet. Graph-based methods reminiscent of spreading activation research of the early days of AI research have been applied with some success.
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Optimization of a solution involves evaluating the neighbours of a state of the problem, which are new states produced through conservatively altering a given state. For example, in the travelling salesman problem each state is typically defined as a permutation of the cities to be visited, and the neighbors of any state are the set of permutations produced by swapping any two of these cities. The well-defined way in which the states are altered to produce neighboring states is called a "move", and different moves give different sets of neighboring states. These moves usually result in minimal alterations of the last state, in an attempt to progressively improve the solution through iteratively improving its parts (such as the city connections in the traveling salesman problem).
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A popular modularity maximization approach is the Louvain method, which iteratively optimizes local communities until global modularity can no longer be improved given perturbations to the current community state. An algorithm that utilizes the RenEEL scheme, which is an example of the Extremal Ensemble Learning (EEL) paradigm, is currently the best modularity maximizing algorithm. The usefulness of modularity optimization is questionable, as it has been shown that modularity optimization often fails to detect clusters smaller than some scale, depending on the size of the network (resolution limit ); on the other hand the landscape of modularity values is characterized by a huge degeneracy of partitions with high modularity, close to the absolute maximum, which may be very different from each other.
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These solvers applied different numerical methods in the three engine categories, depending upon the nesting context in which they were applied. Some simulation solvers (JANUS, MERCURY, MINERVA, MERLIN and PEGASUS) could not be nested in automatic differentiation contexts of correlation and optimization because they were not overloaded for automatic-differentiation arithmetic. Thus hybrid versions, JANISIS (ISIS or JANUS) and GEMINI (MERLIN or NEPTUNE) were introduced, which would work efficiently in automatic differentiation mode or ordinary arithmetic mode (differentiation internally turned off). This greatly speeded up the iterative searches of solvers like AJAX, MARS, JOVE, ZEUS, and JUPITER, which iteratively called their models many more times in non-differentation mode, when various modes of non- derivative search sub-steps were applied.
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The most common current homology modeling method takes its inspiration from calculations required to construct a three-dimensional structure from data generated by NMR spectroscopy. One or more target-template alignments are used to construct a set of geometrical criteria that are then converted to probability density functions for each restraint. Restraints applied to the main protein internal coordinates – protein backbone distances and dihedral angles – serve as the basis for a global optimization procedure that originally used conjugate gradient energy minimization to iteratively refine the positions of all heavy atoms in the protein. This method had been dramatically expanded to apply specifically to loop modeling, which can be extremely difficult due to the high flexibility of loops in proteins in aqueous solution.
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The second are Coulombic repulsion terms between electrons in a mean-field theory description; a net repulsion energy for each electron in the system, which is calculated by treating all of the other electrons within the molecule as a smooth distribution of negative charge. This is the major simplification inherent in the Hartree–Fock method and is equivalent to the fifth simplification in the above list. Since the Fock operator depends on the orbitals used to construct the corresponding Fock matrix, the eigenfunctions of the Fock operator are in turn new orbitals, which can be used to construct a new Fock operator. In this way, the Hartree–Fock orbitals are optimized iteratively until the change in total electronic energy falls below a predefined threshold.
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The family of CLEAN algorithms, a chapter from the MAPPING software manual The algorithm assumes that the image consists of a number of point sources. It will iteratively find the highest value in the image and subtract a small gain of this point source convolved with the point spread function ("dirty beam") of the observation, until the highest value is smaller than some threshold. Astronomer T. J. Cornwell writes, "The impact of CLEAN on radio astronomy has been immense", both directly in enabling greater speed and efficiency in observations, and indirectly by encouraging "a wave of innovation in synthesis processing that continues to this day." It has also been applied in other areas of astronomy and many other fields of science.
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Without loss of generality, we describe Benson's algorithm for the Black player. Let X be the set of all Black chains and R be the set of all Black- enclosed regions of X. Then Benson's algorithm requires iteratively applying the following two steps until neither is able to remove any more chains or regions: # Remove from X all Black chains with less than two vital Black- enclosed regions in R, where a Black-enclosed region is vital to a Black chain in X if all its empty intersections are also liberties of the chain. # Remove from R all Black-enclosed regions with a surrounding stone in a chain not in X. The final set X is the set of all unconditionally alive Black chains.
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A simplified version of a typical iteration cycle in agile project managementThe basic idea behind this method is to develop a system through repeated cycles (iterative) and in smaller portions at a time (incremental), allowing software developers to take advantage of what was learned during development of earlier parts or versions of the system. Learning comes from both the development and use of the system, where possible key steps in the process start with a simple implementation of a subset of the software requirements and iteratively enhance the evolving versions until the full system is implemented. At each iteration, design modifications are made and new functional capabilities are added. The procedure itself consists of the initialization step, the iteration step, and the Project Control List.
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For example, in the picture, the integrity of data block L2 can be verified immediately if the tree already contains hash 0-0 and hash 1 by hashing the data block and iteratively combining the result with hash 0-0 and then hash 1 and finally comparing the result with the top hash. Similarly, the integrity of data block L3 can be verified if the tree already has hash 1-1 and hash 0. This can be an advantage since it is efficient to split files up in very small data blocks so that only small blocks have to be re-downloaded if they get damaged. If the hashed file is very big, such a hash tree or hash list becomes fairly big.
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Chlorotonil A is synthesized from a type I modular polyketide synthase (PKS). This gene cluster does not have any acyltransferase (AT) domains, indicating that it is a trans-AT PKS; in these systems, there is a tandem-AT domain that loads the extender subunits onto the acyl carrier protein (ACP) and checks the intermediates, rather than individual AT domains in each module. The gene cluster of chlorotonil A is organized so that the initiator, acetyl-CoA, is loaded onto the tandem-AT domain, then is iteratively elongated with malonyl-CoA units to construct the macrolactone backbone. At modules 3 and 7, a double bond shift occurs in the elongation module to allow for the β,γ-unsaturation and α-methylation.
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Robust Principal Component Analysis (RPCA) is a modification of the widely used statistical procedure of principal component analysis (PCA) which works well with respect to grossly corrupted observations. A number of different approaches exist for Robust PCA, including an idealized version of Robust PCA, which aims to recover a low-rank matrix L0 from highly corrupted measurements M = L0 +S0. This decomposition in low-rank and sparse matrices can be achieved by techniques such as Principal Component Pursuit method (PCP), Stable PCP, Quantized PCP, Block based PCP, and Local PCP. Then, optimization methods are used such as the Augmented Lagrange Multiplier Method (ALM), Alternating Direction Method (ADM), Fast Alternating Minimization (FAM), Iteratively Reweighted Least Squares (IRLS ) or alternating projections (AP).
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Next, a binary classification of the input patterns is needed(\circ refers to a pattern which should elicit at least one post synaptic action potential and \bullet refers to a pattern which should have no response accordingly). In the beginning, the neuron does not know which pattern belongs to which classification and has to learn it iteratively, similar to the perceptron . The tempotron learns its tasks by adapting the synaptic efficacy \omega _i. If a \circ pattern is presented and the postsynaptic neuron did not spike, all synaptic efficacies are increased by \Delta \omega _i whereas a \bullet pattern followed by a postsynaptic response leads to a decrease of the synaptic efficacies by \Delta \omega _i with Robert Gütig, Haim Sompolinsky (2006): The tempotron: a neuron that learns spike timing-based decisions, Nature Neuroscience vol.
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33 With location-based service, surveys can take place in the real world, in real time, rather than in halls, in a focus group facility, or on a PC. Mobile survey can be integrated with a marketing campaign; the results of customer satisfaction research can be used iteratively to guide the next campaign. For example, a restaurant that is experiencing increased competition can use the specific database – a collection of small mobile surveys of customers who had used coupons from the LBA in the geographic area – to determine their dining preferences, times, and occasions. Marketers can also use customers' past consumption patterns to forecast future patterns and send special dining offers to the target population at the right place and time, in order to build interest, response, and interaction to the restaurant.
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Fractals are sometimes combined with evolutionary algorithms, either by iteratively choosing good-looking specimens in a set of random variations of a fractal artwork and producing new variations, to avoid dealing with cumbersome or unpredictable parameters, or collectively, as in the Electric Sheep project, where people use fractal flames rendered with distributed computing as their screensaver and "rate" the flame they are viewing, influencing the server, which reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art. Many fractal images are admired because of their perceived harmony. This is typically achieved by the patterns which emerge from the balance of order and chaos. Similar qualities have been described in Chinese painting and miniature trees and rockeries.
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When the model is only nonlinear in fixed effects and the random effects are Gaussian, maximum-likelihood estimation can be done using nonlinear least squares methods, although asymptotic properties of estimators and test statistics may differ from the conventional general linear model. In the more general setting, there exist several methods for doing maximum- likelihood estimation or maximum a posteriori estimation in certain classes of nonlinear mixed-effects models – typically under the assumption of normally distributed random variables. A popular approach is the Lindstrom-Bates algorithm which relies on iteratively optimizing a nonlinear problem, locally linearizing the model around this optimum and then employing conventional methods from linear mixed-effects models to do maximum likelihood estimation. Stochastic approximation of the expectation-maximization algorithm gives an alternative approach for doing maximum-likelihood estimation.
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An example EXIT chart showing two components "right" and "left" and an example decoding (blue) An extrinsic information transfer chart, commonly called an EXIT chart, is a technique to aid the construction of good iteratively-decoded error-correcting codes (in particular low-density parity-check (LDPC) codes and Turbo codes). EXIT charts were developed by Stephan ten Brink, building on the concept of extrinsic information developed in the Turbo coding community.Stephan ten Brink, Convergence of Iterative Decoding, Electronics Letters, 35(10), May 1999 An EXIT chart includes the response of elements of decoder (for example a convolutional decoder of a Turbo code, the LDPC parity- check nodes or the LDPC variable nodes). The response can either be seen as extrinsic information or a representation of the messages in belief propagation.
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In zerotree based image compression scheme such as EZW and SPIHT, the intent is to use the statistical properties of the trees in order to efficiently code the locations of the significant coefficients. Since most of the coefficients will be zero or close to zero, the spatial locations of the significant coefficients make up a large portion of the total size of a typical compressed image. A coefficient (likewise a tree) is considered significant if its magnitude (or magnitudes of a node and all its descendants in the case of a tree) is above a particular threshold. By starting with a threshold which is close to the maximum coefficient magnitudes and iteratively decreasing the threshold, it is possible to create a compressed representation of an image which progressively adds finer detail.
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It is of great importance to assign the NOESY peaks to the correct nuclei based on the chemical shifts. If this task is performed manually it is usually very labor-intensive, since proteins usually have thousands of NOESY peaks. Some computer programs such as PASD/XPLOR-NIH, UNIO, CYANA, ARIA/CNS, and AUDANA/PONDEROSA-C/S in the Integrative NMR platform perform this task automatically on manually pre- processed listings of peak positions and peak volumes, coupled to a structure calculation. Direct access to the raw NOESY data without the cumbersome need of iteratively refined peak lists is so far only granted by the PASD algorithm implemented in XPLOR-NIH, the ATNOS/CANDID approach implemented in the UNIO software package, and the PONDEROSA-C/S and thus indeed guarantees objective and efficient NOESY spectral analysis.
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It is possible to estimate the 3D rotation and translation of a 3D object from a single 2D photo, if an approximate 3D model of the object is known and the corresponding points in the 2D image are known. A common technique for solving this has recently been "POSIT", where the 3D pose is estimated directly from the 3D model points and the 2D image points, and corrects the errors iteratively until a good estimate is found from a single image. Most implementations of POSIT only work on non-coplanar points (in other words, it won't work with flat objects or planes). Another approach is to register a 3D CAD model over the photograph of a known object by optimizing a suitable distance measure with respect to the pose parameters.
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Evaluation using the monomial form of a degree-n polynomial requires at most n additions and (n2 + n)/2 multiplications, if powers are calculated by repeated multiplication and each monomial is evaluated individually. (This can be reduced to n additions and 2n − 1 multiplications by evaluating the powers of x iteratively.) If numerical data are represented in terms of digits (or bits), then the naive algorithm also entails storing approximately 2n times the number of bits of x (the evaluated polynomial has approximate magnitude xn, and one must also store xn itself). By contrast, Horner's method requires only n additions and n multiplications, and its storage requirements are only n times the number of bits of x. Alternatively, Horner's method can be computed with n fused multiply–adds.
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Animated creation of a Sierpinski triangle using a chaos game method The way the "chaos game" works is illustrated well when every path is accounted for. In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fraction of the distance between the previous point and one of the vertices of the polygon; the vertex is chosen at random in each iteration. Repeating this iterative process a large number of times, selecting the vertex at random on each iteration, and throwing out the first few points in the sequence, will often (but not always) produce a fractal shape.
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According to the submission document, the name "Grøstl" is a multilingual play-on-words, referring to an Austrian dish that is very similar to hash (food). Like other hash functions in the MD5/SHA family, Grøstl divides the input into blocks and iteratively computes hi = f(hi−1, mi). However, Grøstl maintains a hash state at least twice the size of the final output (512 or 1024 bits), which is only truncated at the end of hash computation. The compression function f is based on a pair of 256- or 512-bit permutation functions P and Q, and is defined as: : f(h, m) = P(h ⊕ m) ⊕ Q(m) ⊕ h The permutation functions P and Q are heavily based on the Rijndael (AES) block cipher, but operate on 8×8 or 8×16 arrays of bytes, rather than 4×4.
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The decomposition of a permutation into a product of transpositions is obtained for example by writing the permutation as a product of disjoint cycles, and then splitting iteratively each of the cycles of length 3 and longer into a product of a transposition and a cycle of length one less: :(a~b~c~d~\ldots~y~z) = (a~b)\cdot (b~c~d~\ldots~y~z). This means the initial request is to move a to b, b to c, y to z, and finally z to a. Instead one may roll the elements keeping a where it is by executing the right factor first (as usual in operator notation, and following the convention in the article on Permutations). This has moved z to the position of b, so after the first permutation, the elements a and z are not yet at their final positions.
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Perturbation theory develops an expression for the desired solution in terms of a formal power series in some "small" parameter – known as a perturbation series – that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the deviation in the solution, due to the deviation from the initial problem. Formally, we have for the approximation to the full solution , a series in the small parameter (here called ), like the following: : A= A_0 + \varepsilon^1 A_1 + \varepsilon^2 A_2 + \cdots In this example, would be the known solution to the exactly solvable initial problem and represent the first-order, second- order and higher-order terms, which may be found iteratively by a mechanistic procedure. For small these higher-order terms in the series generally (but not always!) become successively smaller.
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Iteratively, the probabilistic application of variation operators on selected individuals guides the population to tentative solutions of higher quality. The most well-known metaheuristic families based on the manipulation of a population of solutions are evolutionary algorithms (EAs), ant colony optimization (ACO), particle swarm optimization (PSO), scatter search (SS), differential evolution (DE), and estimation distribution algorithms (EDA). Algorithm: Sequential population-based metaheuristic pseudo- code Generate(P(0)); // Initial population t := 0; // Numerical step while not Termination Criterion(P(t)) do ...Evaluate(P(t)); // Evaluation of the population ...P′′(t) := Apply Variation Operators(P′(t)); // Generation of new solutions ...P(t + 1) := Replace(P(t), P′′(t)); // Building the next population ...t := t + 1; endwhile For non-trivial problems, executing the reproductive cycle of a simple population-based method on long individuals and/or large populations usually requires high computational resources. In general, evaluating a fitness function for every individual is frequently the most costly operation of this algorithm.
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The homology modeling procedure can be broken down into four sequential steps: template selection, target-template alignment, model construction, and model assessment. The first two steps are often essentially performed together, as the most common methods of identifying templates rely on the production of sequence alignments; however, these alignments may not be of sufficient quality because database search techniques prioritize speed over alignment quality. These processes can be performed iteratively to improve the quality of the final model, although quality assessments that are not dependent on the true target structure are still under development. Optimizing the speed and accuracy of these steps for use in large-scale automated structure prediction is a key component of structural genomics initiatives, partly because the resulting volume of data will be too large to process manually and partly because the goal of structural genomics requires providing models of reasonable quality to researchers who are not themselves structure prediction experts.
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In general, greedy algorithms have five components: # A candidate set, from which a solution is created # A selection function, which chooses the best candidate to be added to the solution # A feasibility function, that is used to determine if a candidate can be used to contribute to a solution # An objective function, which assigns a value to a solution, or a partial solution, and # A solution function, which will indicate when we have discovered a complete solution Greedy algorithms produce good solutions on some mathematical problems, but not on others. Most problems for which they work will have two properties: ; Greedy choice property: We can make whatever choice seems best at the moment and then solve the subproblems that arise later. The choice made by a greedy algorithm may depend on choices made so far, but not on future choices or all the solutions to the subproblem. It iteratively makes one greedy choice after another, reducing each given problem into a smaller one.
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An algorithm for the direct solution is: // dominator of the start node is the start itself Dom(n0) = {n0} // for all other nodes, set all nodes as the dominators for each n in N - {n0} Dom(n) = N; // iteratively eliminate nodes that are not dominators while changes in any Dom(n) for each n in N - {n0}: Dom(n) = {n} union with intersection over Dom(p) for all p in pred(n) The direct solution is quadratic in the number of nodes, or O(n2). Lengauer and Tarjan developed an algorithm which is almost linear, and in practice, except for a few artificial graphs, the algorithm and a simplified version of it are as fast or faster than any other known algorithm for graphs of all sizes and its advantage increases with graph size. Keith D. Cooper, Timothy J. Harvey, and Ken Kennedy of Rice University describe an algorithm that essentially solves the above data flow equations but uses well engineered data structures to improve performance.
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The simplest training algorithm for vector quantization is: # Pick a sample point at random # Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance # Repeat A more sophisticated algorithm reduces the bias in the density matching estimation, and ensures that all points are used, by including an extra sensitivity parameter : # Increase each centroid's sensitivity s_i by a small amount # Pick a sample point P at random # For each quantization vector centroid c_i, let d(P, c_i) denote the distance of P and c_i # Find the centroid c_i for which d(P, c_i) - s_i is the smallest # Move c_i towards P by a small fraction of the distance # Set s_i to zero # Repeat It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another (simpler) method is LBG which is based on K-Means. The algorithm can be iteratively updated with 'live' data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples.
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The second-order QSS method, QSS2, follows the same principle as QSS1, except that it defines q(t) as a piecewise linear approximation of the trajectory x(t) that updates its trajectory as soon as the two differ from each other by one quantum. The pattern continues for higher-order approximations, which define the quantized state q(t) as successively higher-order polynomial approximations of the system's state. It is important to note that, while in principle a QSS method of arbitrary order can be used to model a continuous-time system, it is seldom desirable to use methods of order higher than four, as the Abel–Ruffini theorem implies that the time of the next quantization, t, cannot (in general) be explicitly solved for algebraically when the polynomial approximation is of degree greater than four, and hence must be approximated iteratively using a root-finding algorithm. In practice, QSS2 or QSS3 proves sufficient for many problems and the use of higher-order methods results in little, if any, additional benefit.
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Several methods have been developed that make use of the estimated (via 1H or 13C shifts) or predicted (via sequence) secondary structure content of the protein being analyzed. These programs include PSSI, CheckShift, LACS, and PANAV. Both PANAV <> and CheckShift are also available as web servers. The PSSI and PANAV programs use the secondary structure determined by 1H shifts (which are almost never mis-referenced) to adjust the target protein’s 13C and 15N shifts to match the 1H-derived secondary structure. LACS uses the difference between secondary 13Cα and 13Cβ shifts plotted against secondary 13Cα shifts or secondary 13Cβ shifts to determine reference offsets. A more recent version of LACS has been adapted to identify 15N chemical shift mis-referencing. This new version of LACS exploits the well-known relationship between secondary 15N shifts and the secondary 13Cα and 13Cβ shifts of the preceding residue. In contrast to LACS and PANAV/PSSI, CheckShift uses secondary structure predicted from high- performance secondary structure prediction programs such as PSIPRED to iteratively adjust 13C and 15N chemical shifts so that their secondary shifts match the predicted secondary structure.
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Like dead-end elimination, the SCMF method explores conformational space by discretizing the dihedral angles of each side chain into a set of rotamers for each position in the protein sequence. The method iteratively develops a probabilistic description of the relative population of each possible rotamer at each position, and the probability of a given structure is defined as a function of the probabilities of its individual rotamer components. The basic requirements for an effective SCMF implementation are: # A well-defined finite set of discrete independent variables # A precomputed numerical value (considered the "energy") associated with each element in the set of variables, and associated with each binary element pair # An initial probability distribution describing the starting population of each individual rotamer # A way of updating rotamer energies and probabilities as a function of the mean-field energy The process is generally initialized with a uniform probability distribution over the rotamers — that is, if there are p rotamers at the kth position in the protein, then the probability of any individual rotamer r_{k}^{A} is 1/p. The conversion between energies and probabilities is generally accomplished via the Boltzmann distribution, which introduces a temperature factor (thus making the method amenable to simulated annealing).
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As long as the math is programmed correctly using Barnsley's matrix of constants, the same fern shape will be produced. The first point drawn is at the origin (x0 = 0, y0 = 0) and then the new points are iteratively computed by randomly applying one of the following four coordinate transformations: ƒ1 :xn + 1 = 0 :yn + 1 = 0.16 yn. This coordinate transformation is chosen 1% of the time and just maps any point to a point in the first line segment at the base of the stem. This part of the figure is the first to be completed during the course of iterations. ƒ2 :xn + 1 = 0.85 xn \+ 0.04 yn :yn + 1 = −0.04 xn \+ 0.85 yn \+ 1.6. This coordinate transformation is chosen 85% of the time and maps any point inside the leaflet represented by the red triangle to a point inside the opposite, smaller leaflet represented by the blue triangle in the figure. ƒ3 :xn + 1 = 0.2 xn − 0.26 yn :yn + 1 = 0.23 xn + 0.22 yn + 1.6. This coordinate transformation is chosen 7% of the time and maps any point inside the leaflet (or pinna) represented by the blue triangle to a point inside the alternating corresponding triangle across the stem (it flips it).
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Early examples of these algorithms are primarily decrease and conquer – the original problem is successively broken down into single subproblems, and indeed can be solved iteratively. Binary search, a decrease-and-conquer algorithm where the subproblems are of roughly half the original size, has a long history. While a clear description of the algorithm on computers appeared in 1946 in an article by John Mauchly, the idea of using a sorted list of items to facilitate searching dates back at least as far as Babylonia in 200 BC. Another ancient decrease-and-conquer algorithm is the Euclidean algorithm to compute the greatest common divisor of two numbers by reducing the numbers to smaller and smaller equivalent subproblems, which dates to several centuries BC. An early example of a divide-and-conquer algorithm with multiple subproblems is Gauss's 1805 description of what is now called the Cooley–Tukey fast Fourier transform (FFT) algorithm,Heideman, M. T., D. H. Johnson, and C. S. Burrus, "Gauss and the history of the fast Fourier transform", IEEE ASSP Magazine, 1, (4), 14–21 (1984). although he did not analyze its operation count quantitatively, and FFTs did not become widespread until they were rediscovered over a century later.
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