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Kalman filter : In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those bas... |
Kalman filter : The filtering method is named for Hungarian émigré Rudolf E. Kálmán, although Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. Richard S. Bucy of the Johns Hopkins Applied Physics Laboratory contributed to the theory, causing it to be known sometimes as Kalman–Bucy filte... |
Kalman filter : Kalman filtering uses a system's dynamic model (e.g., physical laws of motion), known control inputs to that system, and multiple sequential measurements (such as from sensors) to form an estimate of the system's varying quantities (its state) that is better than the estimate obtained by using only one ... |
Kalman filter : As an example application, consider the problem of determining the precise location of a truck. The truck can be equipped with a GPS unit that provides an estimate of the position within a few meters. The GPS estimate is likely to be noisy; readings 'jump around' rapidly, though remaining within a few m... |
Kalman filter : The Kalman filter is an efficient recursive filter estimating the internal state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering and econometric applications from radar and computer vision to estimation of structural macroeconomic models, and is ... |
Kalman filter : Kalman filtering is based on linear dynamic systems discretized in the time domain. They are modeled on a Markov chain built on linear operators perturbed by errors that may include Gaussian noise. The state of the target system refers to the ground truth (yet hidden) system configuration of interest, w... |
Kalman filter : The Kalman filter is a recursive estimator. This means that only the estimated state from the previous time step and the current measurement are needed to compute the estimate for the current state. In contrast to batch estimation techniques, no history of observations and/or estimates is required. In w... |
Kalman filter : Consider a truck on frictionless, straight rails. Initially, the truck is stationary at position 0, but it is buffeted this way and that by random uncontrolled forces. We measure the position of the truck every Δt seconds, but these measurements are imprecise; we want to maintain a model of the truck's ... |
Kalman filter : For simplicity, assume that the control input u k = 0 _=\mathbf . Then the Kalman filter may be written: x ^ k ∣ k = F k x ^ k − 1 ∣ k − 1 + K k [ z k − H k F k x ^ k − 1 ∣ k − 1 ] . _=\mathbf _ _+\mathbf _[\mathbf _-\mathbf _\mathbf _ _]. A similar equation holds if we include a non-zero contr... |
Kalman filter : The Kalman filter can be derived as a generalized least squares method operating on previous data. |
Kalman filter : The Kalman filtering equations provide an estimate of the state x ^ k ∣ k _ and its error covariance P k ∣ k _ recursively. The estimate and its quality depend on the system parameters and the noise statistics fed as inputs to the estimator. This section analyzes the effect of uncertainties in the sta... |
Kalman filter : One problem with the Kalman filter is its numerical stability. If the process noise covariance Qk is small, round-off error often causes a small positive eigenvalue of the state covariance matrix P to be computed as a negative number. This renders the numerical representation of P indefinite, while its ... |
Kalman filter : The Kalman filter is efficient for sequential data processing on central processing units (CPUs), but in its original form it is inefficient on parallel architectures such as graphics processing units (GPUs). It is however possible to express the filter-update routine in terms of an associative operator... |
Kalman filter : The Kalman filter can be presented as one of the simplest dynamic Bayesian networks. The Kalman filter calculates estimates of the true values of states recursively over time using incoming measurements and a mathematical process model. Similarly, recursive Bayesian estimation calculates estimates of an... |
Kalman filter : Related to the recursive Bayesian interpretation described above, the Kalman filter can be viewed as a generative model, i.e., a process for generating a stream of random observations z = (z0, z1, z2, ...). Specifically, the process is Sample a hidden state x 0 _ from the Gaussian prior distribution p ... |
Kalman filter : In cases where the dimension of the observation vector y is bigger than the dimension of the state space vector x, the information filter can avoid the inversion of a bigger matrix in the Kalman gain calculation at the price of inverting a smaller matrix in the prediction step, thus saving computing tim... |
Kalman filter : The optimal fixed-lag smoother provides the optimal estimate of x ^ k − N ∣ k _ for a given fixed-lag N using the measurements from z 1 _ to z k _ . It can be derived using the previous theory via an augmented state, and the main equation of the filter is the following: [ x ^ t ∣ t x ^ t − 1 ∣ t ⋮ x... |
Kalman filter : The optimal fixed-interval smoother provides the optimal estimate of x ^ k ∣ n _ ( k < n ) using the measurements from a fixed interval z 1 _ to z n _ . This is also called "Kalman Smoothing". There are several smoothing algorithms in common use. |
Kalman filter : Pioneering research on the perception of sounds at different frequencies was conducted by Fletcher and Munson in the 1930s. Their work led to a standard way of weighting measured sound levels within investigations of industrial noise and hearing loss. Frequency weightings have since been used within fil... |
Kalman filter : The basic Kalman filter is limited to a linear assumption. More complex systems, however, can be nonlinear. The nonlinearity can be associated either with the process model or with the observation model or with both. The most common variants of Kalman filters for non-linear systems are the Extended Kalm... |
Kalman filter : Adaptive Kalman filters allow to adapt for process dynamics which are not modeled in the process model F ( t ) (t) , which happens for example in the context of a maneuvering target when a constant velocity (reduced order) Kalman filter is employed for tracking. |
Kalman filter : Kalman–Bucy filtering (named for Richard Snowden Bucy) is a continuous time version of Kalman filtering. It is based on the state space model d d t x ( t ) = F ( t ) x ( t ) + B ( t ) u ( t ) + w ( t ) z ( t ) = H ( t ) x ( t ) + v ( t ) \mathbf (t)&=\mathbf (t)\mathbf (t)+\mathbf (t)\mathbf (t)+\m... |
Kalman filter : Most physical systems are represented as continuous-time models while discrete-time measurements are made frequently for state estimation via a digital processor. Therefore, the system model and measurement model are given by x ˙ ( t ) = F ( t ) x ( t ) + B ( t ) u ( t ) + w ( t ) , w ( t ) ∼ N ( 0 , Q ... |
Kalman filter : The traditional Kalman filter has also been employed for the recovery of sparse, possibly dynamic, signals from noisy observations. Recent works utilize notions from the theory of compressed sensing/sampling, such as the restricted isometry property and related probabilistic recovery arguments, for sequ... |
Kalman filter : Since linear Gaussian state-space models lead to Gaussian processes, Kalman filters can be viewed as sequential solvers for Gaussian process regression. |
Kalman filter : A New Approach to Linear Filtering and Prediction Problems, by R. E. Kalman, 1960 Kalman and Bayesian Filters in Python. Open source Kalman filtering textbook. How a Kalman filter works, in pictures. Illuminates the Kalman filter with pictures and colors Kalman–Bucy Filter, a derivation of the Kalman–Bu... |
Kruskal count : The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift coupling) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coup... |
Kruskal count : The trick is performed with cards, but is more a magical-looking effect than a conventional magic trick. The magician has no access to the cards, which are manipulated by members of the audience. Thus sleight of hand is not possible. Rather the effect is based on the mathematical fact that the output of... |
Kruskal count : Coupling (probability) Discrete logarithm Equifinality Ergodic theory Geometric distribution Overlapping instructions Pollard's kangaroo algorithm Random walk Self-synchronizing code |
Kruskal count : Dynkin [Ды́нкин], Evgenii Borisovich [Евге́ний Бори́сович]; Uspenskii [Успе́нский], Vladimir Andreyevich [Влади́мир Андре́евич] (1963). Written at University of Moscow, Moscow, Russia. Putnam, Alfred L.; Wirszup, Izaak (eds.). Random Walks (Mathematical Conversations Part 3). Survey of Recent East Europ... |
Kruskal count : Humble, Steve "Dr. Maths" (2010). "Dr. Maths Randomness Show". YouTube (Video). Alchemist Cafe, Dublin, Ireland. Retrieved 2023-09-05. [23:40] "Mathematical Card Trick Source". Close-Up Magic. GeniiForum. 2015–2017. Archived from the original on 2023-09-04. Retrieved 2023-09-05. Behr, Denis, ed. (2023).... |
Mark V. Shaney : Mark V. Shaney is a synthetic Usenet user whose postings in the net.singles newsgroups were generated by Markov chain techniques, based on text from other postings. The username is a play on the words "Markov chain". Many readers were fooled into thinking that the quirky, sometimes uncannily topical po... |
Mark V. Shaney : A classic example, from 1984, originally sent as a mail message, later posted to net.singles is reproduced here: >From mvs Fri Nov 16 17:11 EST 1984 remote from alice It looks like Reagan is going to say? Ummm... Oh yes, I was looking for. I'm so glad I remembered it. Yeah, what I have wondered if I ha... |
Mark V. Shaney : In The Usenet Handbook Mark Harrison writes that after September 1981, students joined Usenet en masse, "creating the USENET we know today: endless dumb questions, endless idiots posing as savants, and (of course) endless victims for practical jokes." In December, Rob Pike created the netnews group net... |
Mark V. Shaney : The program was discussed by A. K. Dewdney in the Scientific American "Computer Recreations" column in 1989, by Penn Jillette in his PC Computing column in 1991, and in several books, including the Usenet Handbook, Bots: the Origin of New Species, Hippo Eats Dwarf: A Field Guide to Hoaxes and Other B.S... |
Mark V. Shaney : Turing test Dissociated press On the Internet, nobody knows you're a dog Parody generator |
Mark V. Shaney : FAQ for the Plan 9 operating system by Mark V. Shaney Unofficial biography "Mark V. Shaney at Your Service" online version by Yisong Yue. "Mark V. Shaney in Common Lisp" at Racine Systems. Every Mark V. Shaney post at Google Groups Usenet archive. "Sable Debutante's Journal", a Mark V. Shaney clone at ... |
Markov chain : In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only o... |
Markov chain : Andrey Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Markov Processes in continuous time were discovered long before his work in the early 20th century in the form of the Poisson process. Markov was interested in studying an extension of indep... |
Markov chain : Mark V. Shaney is a third-order Markov chain program, and a Markov text generator. It ingests the sample text (the Tao Te Ching, or the posts of a Usenet group) and creates a massive list of every sequence of three successive words (triplet) which occurs in the text. It then chooses two words at random, ... |
Markov chain : Two states are said to communicate with each other if both are reachable from one another by a sequence of transitions that have positive probability. This is an equivalence relation which yields a set of communicating classes. A class is closed if the probability of leaving the class is zero. A Markov c... |
Markov chain : Markov chains have been employed in a wide range of topics across the natural and social sciences, and in technological applications. They have been used for forecasting in several areas: for example, price trends, wind power, stochastic terrorism, and solar irradiance. The Markov chain forecasting model... |
Markov chain : == External links == |
Markov chain central limit theorem : In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more... |
Markov chain central limit theorem : Suppose that: the sequence X 1 , X 2 , X 3 , … ,X_,X_,\ldots of random elements of some set is a Markov chain that has a stationary probability distribution; and the initial distribution of the process, i.e. the distribution of X 1 , is the stationary distribution, so that X 1 , X... |
Markov chain central limit theorem : The Markov chain central limit theorem can be guaranteed for functionals of general state space Markov chains under certain conditions. In particular, this can be done with a focus on Monte Carlo settings. An example of the application in a MCMC (Markov Chain Monte Carlo) setting is... |
Markov chain central limit theorem : Not taking into account the additional terms in the variance which stem from correlations (e.g. serial correlations in markov chain monte carlo simulations) can result in the problem of pseudoreplication when computing e.g. the confidence intervals for the sample mean. |
Markov chain central limit theorem : Gordin, M. I. and Lifšic, B. A. (1978). "Central limit theorem for stationary Markov processes." Soviet Mathematics, Doklady, 19, 392–394. (English translation of Russian original). Geyer, Charles J. (2011). "Introduction to MCMC." In Handbook of Markov Chain Monte Carlo, edited by ... |
Markov chain geostatistics : Markov chain geostatistics uses Markov chain spatial models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical mode... |
Markov chain geostatistics : Li, W. 2007. Markov chain random fields for estimation of categorical variables. Math. Geol., 39(3): 321–335. Li, W. et al. 2015. Bayesian Markov chain random field cosimulation for improving land cover classification accuracy. Math. Geosci., 47(2): 123–148. Li, W., and C. Zhang. 2019. Mark... |
Markov chain Monte Carlo : In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution ... |
Markov chain Monte Carlo : MCMC methods are primarily used for calculating numerical approximations of multi-dimensional integrals, for example in Bayesian statistics, computational physics, computational biology and computational linguistics. In Bayesian statistics, Markov chain Monte Carlo methods are typically used ... |
Markov chain Monte Carlo : Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to evaluate an integral over that variable, as its expected value or variance. Practically, an ensemble of chains is generall... |
Markov chain Monte Carlo : While MCMC methods were created to address multi-dimensional problems better than generic Monte Carlo algorithms, when the number of dimensions rises they too tend to suffer the curse of dimensionality: regions of higher probability tend to stretch and get lost in an increasing volume of spac... |
Markov chain Monte Carlo : Usually it is not hard to construct a Markov chain with the desired properties. The more difficult problem is to determine how many steps are needed to converge to the stationary distribution within an acceptable error. A good chain will have rapid mixing: the stationary distribution is reach... |
Markov chain Monte Carlo : Several software programs provide MCMC sampling capabilities, for example: ParaMonte parallel Monte Carlo software available in multiple programming languages including C, C++, Fortran, MATLAB, and Python. Packages that use dialects of the BUGS model language: WinBUGS / OpenBUGS/ MultiBUGS JA... |
Markov chain Monte Carlo : Coupling from the past Integrated nested Laplace approximations Markov chain central limit theorem Metropolis-adjusted Langevin algorithm |
Markov partition : A Markov partition in mathematics is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic dynamics. By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical chara... |
Markov partition : Let ( M , φ ) be a discrete dynamical system. A basic method of studying its dynamics is to find a symbolic representation: a faithful encoding of the points of M by sequences of symbols such that the map φ becomes the shift map. Suppose that M has been divided into a number of pieces E 1 , E 2 ,... |
Markov partition : A Markov partition is a finite cover of the invariant set of the manifold by a set of curvilinear rectangles ,E_,\ldots ,E_\ such that For any pair of points x , y ∈ E i , that W s ( x ) ∩ W u ( y ) ∈ E i (x)\cap W_(y)\in E_ Int E i ∩ Int E j = ∅ E_\cap \operatorname E_=\emptyset for i ≠ j ... |
Markov partition : Markov partitions have been constructed in several situations. Anosov diffeomorphisms of the torus. Dynamical billiards, in which case the covering is countable. Markov partitions make homoclinic and heteroclinic orbits particularly easy to describe. The system ( [ 0 , 1 ) , x ↦ 2 x m o d 1 ) has th... |
Markov partition : Lind, Douglas; Marcus, Brian (1995). An introduction to symbolic dynamics and coding. Cambridge University Press. ISBN 978-0-521-55124-3. Zbl 1106.37301. Pytheas Fogg, N. (2002). Berthé, Valérie; Ferenczi, Sébastien; Mauduit, Christian; Siegel, Anne (eds.). Substitutions in dynamics, arithmetics and ... |
Markov property : In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its future evolution is independent of its history. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Ma... |
Markov property : A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past. A process with this property i... |
Markov property : Let ( Ω , F , P ) ,P) be a probability space with a filtration ( F s , s ∈ I ) _,\ s\in I) , for some (totally ordered) index set I ; and let ( S , S ) ) be a measurable space. A ( S , S ) ) -valued stochastic process X = t ∈ I :\Omega \to S\_ adapted to the filtration is said to possess the Markov ... |
Markov property : Alternatively, the Markov property can be formulated as follows. E [ f ( X t ) ∣ F s ] = E [ f ( X t ) ∣ σ ( X s ) ] [f(X_)\mid _]=\operatorname [f(X_)\mid \sigma (X_)] for all t ≥ s ≥ 0 and f : S → R bounded and measurable. |
Markov property : Suppose that X = ( X t : t ≥ 0 ) :t\geq 0) is a stochastic process on a probability space ( Ω , F , P ) ,P) with natural filtration t ≥ 0 _\_ . Then for any stopping time τ on Ω , we can define F τ = ∩ A ∈ F t _=\:\forall t\geq 0,\\cap A\in _\ . Then X is said to have the strong Markov property ... |
Markov property : In the fields of predictive modelling and probabilistic forecasting, the Markov property is considered desirable since it may enable the reasoning and resolution of the problem that otherwise would not be possible to be resolved because of its intractability. Such a model is known as a Markov model. |
Markov property : Assume that an urn contains two red balls and one green ball. One ball was drawn yesterday, one ball was drawn today, and the final ball will be drawn tomorrow. All of the draws are "without replacement". Suppose you know that today's ball was red, but you have no information about yesterday's ball. T... |
Markov property : Causal Markov condition Chapman–Kolmogorov equation Hysteresis Markov blanket Markov chain Markov decision process Markov model == References == |
Markov switching multifractal : In financial econometrics (the application of statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fisher that incorporates stochastic volatility components of heterogeneous durations. MSM c... |
Markov switching multifractal : The MSM model can be specified in both discrete time and continuous time. |
Markov switching multifractal : When M has a discrete distribution, the Markov state vector M t takes finitely many values m 1 , . . . , m d ∈ R + k ¯ ,...,m^\in R_^ . For instance, there are d = 2 k ¯ possible states in binomial MSM. The Markov dynamics are characterized by the transition matrix A = ( a i , j ) 1 ≤... |
Markov switching multifractal : Given r 1 , … , r t ,\dots ,r_ , the conditional distribution of the latent state vector at date t + n is given by: Π ^ t , n = Π t A n . _=\Pi _A^.\, MSM often provides better volatility forecasts than some of the best traditional models both in and out of sample. Calvet and Fisher rep... |
Markov switching multifractal : MSM is a stochastic volatility model with arbitrarily many frequencies. MSM builds on the convenience of regime-switching models, which were advanced in economics and finance by James D. Hamilton. MSM is closely related to the Multifractal Model of Asset Returns. MSM improves on the MMAR... |
Markov switching multifractal : Brownian motion Rogemar Mamon Markov chain Multifractal model of asset returns Multifractal Stochastic volatility |
Markov switching multifractal : Financial Time Series, Multifractals and Hidden Markov Models |
MegaHAL : MegaHAL is a computer conversation simulator, or "chatterbot", created by Jason Hutchens. |
MegaHAL : In 1996, Jason Hutchens entered the Loebner Prize Contest with HeX, a chatterbot based on ELIZA. HeX won the competition that year and took the $2000 prize for having the highest overall score. In 1998, Hutchens again entered the Loebner Prize Contest with his new program, MegaHAL. MegaHAL made its debut in t... |
MegaHAL : MegaHal is based at least in part on a so-called "hidden Markov Model", so that the first thing that Megahal does when it "trains" on a script or text is to build a database of text fragments encompassing every possible subset of perhaps 4, 5, or even 6 consecutive words, so that for example - if MegaHal trai... |
MegaHAL : There are some sentences that MegaHAL generated: CHESS IS A FUN SPORT, WHEN PLAYED WITH SHOT GUNS. and COWS FLY LIKE CLOUDS BUT THEY ARE NEVER COMPLETELY SUCCESSFUL. |
MegaHAL : MegaHAL is distributed under the Unlicense. Its source code can be downloaded from the Github repository. |
MegaHAL : Loebner prize ELIZA |
MegaHAL : Hutchens, Jason L.; Alder, Michael D. (1998), "Introducing MegaHAL" (PDF), NeMLaP3 / CoNLL98 Workshop on Human-Computer Conversation, ACL (271): 274 |
MegaHAL : Github repository |
Models of DNA evolution : A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyse... |
Models of DNA evolution : These models are phenomenological descriptions of the evolution of DNA as a string of four discrete states. These Markov models do not explicitly depict the mechanism of mutation nor the action of natural selection. Rather they describe the relative rates of different changes. For example, mut... |
Models of DNA evolution : Molecular evolution Molecular clock UPGMA |
Models of DNA evolution : DAWG: DNA Assembly With Gaps — free software for simulating sequence evolution |
MRF optimization via dual decomposition : In dual decomposition a problem is broken into smaller subproblems and a solution to the relaxed problem is found. This method can be employed for MRF optimization. Dual decomposition is applied to markov logic programs as an inference technique. |
MRF optimization via dual decomposition : Discrete MRF Optimization (inference) is very important in Machine Learning and Computer vision, which is realized on CUDA graphical processing units. Consider a graph G = ( V , E ) with nodes V and Edges E . The goal is to assign a label l p to each p ∈ V so that the MRF ... |
MRF optimization via dual decomposition : The main idea behind decomposition is surprisingly simple: decompose your original complex problem into smaller solvable subproblems, extract a solution by cleverly combining the solutions from these subproblems. A sample problem to decompose: min x Σ i f i ( x ) \Sigma _f^(x) ... |
MRF optimization via dual decomposition : The original MRF optimization problem is NP-hard and we need to transform it into something easier. τ is a set of sub-trees of graph G where its trees cover all nodes and edges of the main graph. And MRFs defined for every tree T in τ will be smaller. The vector of MRF para... |
MRF optimization via dual decomposition : Theorem 1. Lagrangian relaxation (9) is equivalent to the LP relaxation of (2). min , x \,x\^=s_,x^\in (\chi ^)\ Theorem 2. If the sequence of multipliers \ satisfies α t ≥ 0 , lim t → ∞ α t = 0 , ∑ t = 0 ∞ α t = ∞ \geq 0,\lim _\alpha _=0,\sum _^\alpha _=\infty then the alg... |
Multiple sequence alignment : Multiple sequence alignment (MSA) is the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. These alignments are used to infer evolutionary relationships via phylogenetic analysis and can highlight homologous features between ... |
Multiple sequence alignment : Given m sequences S i , i = 1 , ⋯ , m similar to the form below: S := S_=(S_,S_,\ldots ,S_)\\S_=(S_,S_,\cdots ,S_)\\\,\,\,\,\,\,\,\,\,\,\vdots \\S_=(S_,S_,\ldots ,S_)\end A multiple sequence alignment is taken of this set of sequences S by inserting any amount of gaps needed into each ... |
Multiple sequence alignment : A general approach when calculating multiple sequence alignments is to use graphs to identify all of the different alignments. When finding alignments via graph, a complete alignment is created in a weighted graph that contains a set of vertices and a set of edges. Each of the graph edges ... |
Multiple sequence alignment : There are various alignment methods used within multiple sequence to maximize scores and correctness of alignments. Each is usually based on a certain heuristic with an insight into the evolutionary process. Most try to replicate evolution to get the most realistic alignment possible to be... |
Multiple sequence alignment : The necessary use of heuristics for multiple alignment means that for an arbitrary set of proteins, there is always a good chance that an alignment will contain errors. For example, an evaluation of several leading alignment programs using the BAliBase benchmark found that at least 24% of ... |
Multiple sequence alignment : Multiple sequence alignments can be used to create a phylogenetic tree. This is made possible by two reasons. The first is because functional domains that are known in annotated sequences can be used for alignment in non-annotated sequences. The other is that conserved regions known to be ... |
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