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Detailed balance : For any reaction mechanism and a given positive equilibrium a cone of possible velocities for the systems with detailed balance is defined for any non-equilibrium state N Q D B ( N ) = c o n e , _(N)=\(w_^(N)-w_^(N))\ |\ r=1,\ldots ,m\, where cone stands for the conical hull and the piecewise-const... |
Detailed balance : Detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process and requires reversibility of all elementary processes. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc.... |
Detailed balance : T-symmetry Microscopic reversibility Master equation Balance equation Gibbs sampling Metropolis–Hastings algorithm Atomic spectral line (deduction of the Einstein coefficients) Random walks on graphs == References == |
Diffusion model : In machine learning, diffusion models, also known as diffusion probabilistic models or score-based generative models, are a class of latent variable generative models. A diffusion model consists of three major components: the forward process, the reverse process, and the sampling procedure. The goal o... |
Diffusion model : Score-based generative model is another formulation of diffusion modelling. They are also called noise conditional score network (NCSN) or score-matching with Langevin dynamics (SMLD). |
Diffusion model : DDPM and score-based generative models are equivalent. This means that a network trained using DDPM can be used as a NCSN, and vice versa. We know that x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) |x_\sim N\left(_x_,\sigma _^I\right) , so by Tweedie's formula, we have ∇ x t ln q ( x t ) = 1 σ t 2 ( − x t +... |
Diffusion model : Abstractly speaking, the idea of diffusion model is to take an unknown probability distribution (the distribution of natural-looking images), then progressively convert it to a known probability distribution (standard gaussian distribution), by building an absolutely continuous probability path connec... |
Diffusion model : This section collects some notable diffusion models, and briefly describes their architecture. |
Diffusion model : Diffusion process Markov chain Variational inference Variational autoencoder |
Diffusion model : Review papers Yang, Ling (2024-09-06), YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy, retrieved 2024-09-06 Yang, Ling; Zhang, Zhilong; Song, Yang; Hong, Shenda; Xu, Runsheng; Zhao, Yue; Zhang, Wentao; Cui, Bin; Yang, Ming-Hsuan (2023-11-09). "Diffusion Models: A Comprehensive Survey of Methods ... |
Discrete phase-type distribution : The discrete phase-type distribution is a probability distribution that results from a system of one or more inter-related geometric distributions occurring in sequence, or phases. The sequence in which each of the phases occur may itself be a stochastic process. The distribution can ... |
Discrete phase-type distribution : A terminating Markov chain is a Markov chain where all states are transient, except one which is absorbing. Reordering the states, the transition probability matrix of a terminating Markov chain with m transient states is P = [ T T 0 0 T 1 ] , =\left[&\mathbf ^\\\mathbf ^&1\end\rig... |
Discrete phase-type distribution : Fix a terminating Markov chain. Denote T the upper-left block of its transition matrix and τ the initial distribution. The distribution of the first time to the absorbing state is denoted P H d ( τ , T ) _(,) or D P H ( τ , T ) (,) . Its cumulative distribution function is F ( k )... |
Discrete phase-type distribution : Just as the continuous time distribution is a generalisation of the exponential distribution, the discrete time distribution is a generalisation of the geometric distribution, for example: Degenerate distribution, point mass at zero or the empty phase-type distribution – 0 phases. Geo... |
Discrete phase-type distribution : Phase-type distribution Queueing model Queueing theory |
Discrete phase-type distribution : M. F. Neuts. Matrix-Geometric Solutions in Stochastic Models: an Algorithmic Approach, Chapter 2: Probability Distributions of Phase Type; Dover Publications Inc., 1981. G. Latouche, V. Ramaswami. Introduction to Matrix Analytic Methods in Stochastic Modelling, 1st edition. Chapter 2:... |
Dynamic Markov compression : Dynamic Markov compression (DMC) is a lossless data compression algorithm developed by Gordon Cormack and Nigel Horspool. It uses predictive arithmetic coding similar to prediction by partial matching (PPM), except that the input is predicted one bit at a time (rather than one byte at a tim... |
Dynamic Markov compression : DMC predicts and codes one bit at a time. It differs from PPM in that it codes bits rather than bytes, and from context mixing algorithms such as PAQ in that there is only one context per prediction. The predicted bit is then coded using arithmetic coding. |
Dynamic Markov compression : Data Compression Using Dynamic Markov Modelling Google Developers YouTube channel: Compressor Head Episode 3 (Markov Chain Compression) ( Page will play audio when loaded) |
Dynamics of Markovian particles : Dynamics of Markovian particles (DMP) is the basis of a theory for kinetics of particles in open heterogeneous systems. It can be looked upon as an application of the notion of stochastic process conceived as a physical entity; e.g. the particle moves because there is a transition prob... |
Dynamics of Markovian particles : Bergner—DMP, a kinetics of macroscopic particles in open heterogeneous systems |
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).... |
Entropy rate : In the mathematical theory of probability, the entropy rate or source information rate is a function assigning an entropy to a stochastic process. For a strongly stationary process, the conditional entropy for latest random variable eventually tend towards this rate value. |
Entropy rate : A process X with a countable index gives rise to the sequence of its joint entropies H n ( X 1 , X 2 , … X n ) (X_,X_,\dots X_) . If the limit exists, the entropy rate is defined as H ( X ) := lim n → ∞ 1 n H n . H_. Note that given any sequence ( a n ) n )_ with a 0 = 0 =0 and letting Δ a k := a k − a ... |
Entropy rate : While X may be understood as a sequence of random variables, the entropy rate H ( X ) represents the average entropy change per one random variable, in the long term. It can be thought of as a general property of stochastic sources - this is the subject of the asymptotic equipartition property. |
Entropy rate : The entropy rate may be used to estimate the complexity of stochastic processes. It is used in diverse applications ranging from characterizing the complexity of languages, blind source separation, through to optimizing quantizers and data compression algorithms. For example, a maximum entropy rate crite... |
Entropy rate : Information source (mathematics) Markov information source Asymptotic equipartition property Maximal entropy random walk - chosen to maximize entropy rate |
Entropy rate : Cover, T. and Thomas, J. (1991) Elements of Information Theory, John Wiley and Sons, Inc., ISBN 0-471-06259-6 [1] |
Examples of Markov chains : This article contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general state space, see Markov chains on a measurable state space. |
Examples of Markov chains : Mark V. Shaney Interacting particle system Stochastic cellular automata |
Examples of Markov chains : Monopoly as a Markov chain |
Forward algorithm : The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterb... |
Forward algorithm : The forward and backward algorithms should be placed within the context of probability as they appear to simply be names given to a set of standard mathematical procedures within a few fields. For example, neither "forward algorithm" nor "Viterbi" appear in the Cambridge encyclopedia of mathematics.... |
Forward algorithm : The goal of the forward algorithm is to compute the joint probability p ( x t , y 1 : t ) ,y_) , where for notational convenience we have abbreviated x ( t ) as x t and ( y ( 1 ) , y ( 2 ) , . . . , y ( t ) ) as y 1 : t . Once the joint probability p ( x t , y 1 : t ) ,y_) is computed, the other... |
Forward algorithm : This example on observing possible states of weather from the observed condition of seaweed. We have observations of seaweed for three consecutive days as dry, damp, and soggy in order. The possible states of weather can be sunny, cloudy, or rainy. In total, there can be 3 3 = 27 =27 such weather se... |
Forward algorithm : Complexity of Forward Algorithm is Θ ( n m 2 ) ) , where m is the number of hidden or latent variables, like weather in the example above, and n is the length of the sequence of the observed variable. This is clear reduction from the adhoc method of exploring all the possible states with a complex... |
Forward algorithm : Hybrid Forward Algorithm: A variant of the Forward Algorithm called Hybrid Forward Algorithm (HFA) can be used for the construction of radial basis function (RBF) neural networks with tunable nodes. The RBF neural network is constructed by the conventional subset selection algorithms. The network st... |
Forward algorithm : The forward algorithm is one of the algorithms used to solve the decoding problem. Since the development of speech recognition and pattern recognition and related fields like computational biology which use HMMs, the forward algorithm has gained popularity. |
Forward algorithm : The forward algorithm is mostly used in applications that need us to determine the probability of being in a specific state when we know about the sequence of observations. The algorithm can be applied wherever we can train a model as we receive data using Baum-Welch or any general EM algorithm. The... |
Forward algorithm : Viterbi algorithm Forward-backward algorithm Baum–Welch algorithm |
Forward algorithm : Russell and Norvig's Artificial Intelligence, a Modern Approach, starting on page 570 of the 2010 edition, provides a succinct exposition of this and related topics Smyth, Padhraic, David Heckerman, and Michael I. Jordan. "Probabilistic independence networks for hidden Markov probability models." Ne... |
Forward algorithm : Hidden Markov Model R-Package contains functionality for computing and retrieving forward procedure momentuHMM R-Package provides tools for using and inferring HMMs. GHMM Library for Python The hmm package Haskell library for HMMS, implements Forward algorithm. Library for Java contains Machine Lear... |
Forward–backward algorithm : The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions o 1 : T := o 1 , … , o T :=o_,\dots ,o_ , i.e. it computes, for all hidden state variables X t ∈ ... |
Forward–backward algorithm : In the first pass, the forward–backward algorithm computes a set of forward probabilities which provide, for all t ∈ , the probability of ending up in any particular state given the first t observations in the sequence, i.e. P ( X t | o 1 : t ) \ |\ o_) . In the second pass, the algorith... |
Forward–backward algorithm : The following description will use matrices of probability values rather than probability distributions, although in general the forward-backward algorithm can be applied to continuous as well as discrete probability models. We transform the probability distributions related to a given hidd... |
Forward–backward algorithm : A similar procedure can be constructed to find backward probabilities. These intend to provide the probabilities: b t : T ( i ) = P ( o t + 1 , o t + 2 , … , o T | X t = x i ) (i)=\mathbf (o_,o_,\dots ,o_|X_=x_) That is, we now want to assume that we start in a particular state ( X t = x ... |
Forward–backward algorithm : This example takes as its basis the umbrella world in Russell & Norvig 2010 Chapter 15 pp. 567 in which we would like to infer the weather given observation of another person either carrying or not carrying an umbrella. We assume two possible states for the weather: state 1 = rain, state 2 ... |
Forward–backward algorithm : The forward–backward algorithm runs with time complexity O ( S 2 T ) T) in space O ( S T ) , where T is the length of the time sequence and S is the number of symbols in the state alphabet. The algorithm can also run in constant space with time complexity O ( S 2 T 2 ) T^) by recomputing... |
Forward–backward algorithm : algorithm forward_backward is input: guessState int sequenceIndex output: result if sequenceIndex is past the end of the sequence then return 1 if (guessState, sequenceIndex) has been seen before then return saved result result := 0 for each neighboring state n: result := result + (transiti... |
Forward–backward algorithm : Given HMM (just like in Viterbi algorithm) represented in the Python programming language: We can write the implementation of the forward-backward algorithm like this: The function fwd_bkw takes the following arguments: x is the sequence of observations, e.g. ['normal', 'cold', 'dizzy']; st... |
Forward–backward algorithm : Baum–Welch algorithm Viterbi algorithm BCJR algorithm |
Forward–backward algorithm : Lawrence R. Rabiner, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE, 77 (2), p. 257–286, February 1989. 10.1109/5.18626 Lawrence R. Rabiner, B. H. Juang (January 1986). "An introduction to hidden Markov models". IEEE ASSP Magazine... |
Forward–backward algorithm : An interactive spreadsheet for teaching the forward–backward algorithm (spreadsheet and article with step-by-step walk-through) Tutorial of hidden Markov models including the forward–backward algorithm Collection of AI algorithms implemented in Java (including HMM and the forward–backward a... |
Gene prediction : In computational biology, gene prediction or gene finding refers to the process of identifying the regions of genomic DNA that encode genes. This includes protein-coding genes as well as RNA genes, but may also include prediction of other functional elements such as regulatory regions. Gene finding is... |
Gene prediction : In empirical (similarity, homology or evidence-based) gene finding systems, the target genome is searched for sequences that are similar to extrinsic evidence in the form of the known expressed sequence tags, messenger RNA (mRNA), protein products, and homologous or orthologous sequences. Given an mRN... |
Gene prediction : Ab Initio gene prediction is an intrinsic method based on gene content and signal detection. Because of the inherent expense and difficulty in obtaining extrinsic evidence for many genes, it is also necessary to resort to ab initio gene finding, in which the genomic DNA sequence alone is systematicall... |
Gene prediction : Programs such as Maker combine extrinsic and ab initio approaches by mapping protein and EST data to the genome to validate ab initio predictions. Augustus, which may be used as part of the Maker pipeline, can also incorporate hints in the form of EST alignments or protein profiles to increase the acc... |
Gene prediction : As the entire genomes of many different species are sequenced, a promising direction in current research on gene finding is a comparative genomics approach. This is based on the principle that the forces of natural selection cause genes and other functional elements to undergo mutation at a slower rat... |
Gene prediction : Pseudogenes are close relatives of genes, sharing very high sequence homology, but being unable to code for the same protein product. Whilst once relegated as byproducts of gene sequencing, increasingly, as regulatory roles are being uncovered, they are becoming predictive targets in their own right. ... |
Gene prediction : Metagenomics is the study of genetic material recovered from the environment, resulting in sequence information from a pool of organisms. Predicting genes is useful for comparative metagenomics. Metagenomics tools also fall into the basic categories of using either sequence similarity approaches (MEGA... |
Gene prediction : List of gene prediction software Phylogenetic footprinting Protein function prediction Protein structure prediction Protein–protein interaction prediction Pseudogene (database) Sequence mining Sequence similarity (homology) |
Gene prediction : Augustus FGENESH Archived 2013-01-04 at archive.today GeMoMa - Homology-based gene prediction based on amino acid and intron position conservation as well as RNA-Seq data geneid, SGP2 Glimmer Archived 2011-08-26 at the Wayback Machine, GlimmerHMM Archived 2011-08-18 at the Wayback Machine GenomeThread... |
Generalized filtering : Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action, formulated in generalized coordinates of motion. Note that "generalized coordinates of motion" are related to—but distinct from—generalized coord... |
Generalized filtering : Definition: Generalized filtering rests on the tuple ( Ω , U , X , S , p , q ) : A sample space Ω from which random fluctuations ω ∈ Ω are drawn Control states U ∈ R – that act as external causes, input or forcing terms Hidden states X : X × U × Ω → R – that cause sensory states and depen... |
Generalized filtering : Usually, the generative density or model is specified in terms of a nonlinear input-state-output model with continuous nonlinear functions: s = g ( x , u ) + ω s x ˙ = f ( x , u ) + ω x s&=g(x,u)+\omega _\\&=f(x,u)+\omega _\end The corresponding generalized model (under local linearity assumptio... |
Generalized filtering : Generalized filtering has been primarily applied to biological timeseries—in particular functional magnetic resonance imaging and electrophysiological data. This is usually in the context of dynamic causal modelling to make inferences about the underlying architectures of (neuronal) systems gene... |
Generalized filtering : Dynamic Bayesian network Kalman filter Linear predictive coding Optimal control Particle filter Recursive Bayesian estimation System identification Variational Bayesian methods |
Generalized filtering : software demonstrations and applications are available as academic freeware (as Matlab code) in the DEM toolbox of SPM papers collection of technical and application papers |
GLIMMER : In bioinformatics, GLIMMER (Gene Locator and Interpolated Markov ModelER) is used to find genes in prokaryotic DNA. "It is effective at finding genes in bacteria, archea, viruses, typically finding 98-99% of all relatively long protein coding genes". GLIMMER was the first system that used the interpolated Mar... |
GLIMMER : GLIMMER can be downloaded from The Glimmer home page (requires a C++ compiler). Alternatively, an online version is hosted by NCBI [1]. |
GLIMMER : GLIMMER primarily searches for long-ORFS. An open reading frame might overlap with any other open reading frame which will be resolved using the technique described in the sub section. Using these long-ORFS and following certain amino acid distribution GLIMMER generates training set data. Using these training... |
GLIMMER : Glimmer supports genome annotation efforts on a wide range of bacterial, archaeal, and viral species. In a large-scale reannotation effort at the DNA Data Bank of Japan (DDBJ, which mirrors Genbank). Kosuge et al. (2006) examined the gene finding methods used for 183 genomes. They reported that of these proje... |
GLIMMER : The Glimmer home page at CCB, Johns Hopkins University, from which the software can be downloaded. |
Google matrix : A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages. The PageRank of each page can then be generated iteratively from the Google matrix using the power method. However, in order for the p... |
Google matrix : In order to generate the Google matrix G, we must first generate an adjacency matrix A which represents the relations between pages or nodes. Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j is filled with 1 if node j has a link to node i , and 0 otherwis... |
Google matrix : Then the final Google matrix G can be expressed via S as: G i j = α S i j + ( 1 − α ) 1 N ( 1 ) =\alpha S_+(1-\alpha )\;\;\;\;\;\;\;\;\;\;\;(1) By the construction the sum of all non-negative elements inside each matrix column is equal to unity. The numerical coefficient α is known as a damping factor.... |
Google matrix : An example of the matrix S construction via Eq.(1) within a simple network is given in the article CheiRank. For the actual matrix, Google uses a damping factor α around 0.85. The term ( 1 − α ) gives a surfer probability to jump randomly on any page. The matrix G belongs to the class of Perron-Frob... |
Google matrix : For 0 < α < 1 there is only one maximal eigenvalue λ = 1 with the corresponding right eigenvector which has non-negative elements P i which can be viewed as stationary probability distribution. These probabilities ordered by their decreasing values give the PageRank vector P i with the PageRank K i ... |
Google matrix : The Google matrix with damping factor was described by Sergey Brin and Larry Page in 1998 [22], see also articles on PageRank history [23],[24]. |
Google matrix : CheiRank Arnoldi iteration Markov chain Transfer operator Perron–Frobenius theorem Web search engines |
Google matrix : Google matrix at Scholarpedia Google PR Shut Down Video lectures at IHES Workshop "Google matrix: fundamental, applications and beyond", Oct 2018 |
Hidden Markov model : A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred to as X ). An HMM requires that there be an observable process Y whose outcomes depend on the outcomes of X in a known way. Since X cannot be observed directly... |
Hidden Markov model : Let X n and Y n be discrete-time stochastic processes and n ≥ 1 . The pair ( X n , Y n ) ,Y_) is a hidden Markov model if X n is a Markov process whose behavior is not directly observable ("hidden"); P ( Y n ∈ A | X 1 = x 1 , … , X n = x n ) = P ( Y n ∈ A | X n = x n ) Y_\in A\ \ X_=x_,\... |
Hidden Markov model : The diagram below shows the general architecture of an instantiated HMM. Each oval shape represents a random variable that can adopt any of a number of values. The random variable x(t) is the hidden state at time t (with the model from the above diagram, x(t) ∈ ). The random variable y(t) is the o... |
Hidden Markov model : Several inference problems are associated with hidden Markov models, as outlined below. |
Hidden Markov model : The parameter learning task in HMMs is to find, given an output sequence or a set of such sequences, the best set of state transition and emission probabilities. The task is usually to derive the maximum likelihood estimate of the parameters of the HMM given the set of output sequences. No tractab... |
Hidden Markov model : HMMs can be applied in many fields where the goal is to recover a data sequence that is not immediately observable (but other data that depend on the sequence are). Applications include: Computational finance Single-molecule kinetic analysis Neuroscience Cryptanalysis Speech recognition, including... |
Hidden Markov model : Hidden Markov models were described in a series of statistical papers by Leonard E. Baum and other authors in the second half of the 1960s. One of the first applications of HMMs was speech recognition, starting in the mid-1970s. From the linguistics point of view, hidden Markov models are equivale... |
Hidden Markov model : Given a Markov transition matrix and an invariant distribution on the states, a probability measure can be imposed on the set of subshifts. For example, consider the Markov chain given on the left on the states A , B 1 , B 2 ,B_ , with invariant distribution π = ( 2 / 7 , 4 / 7 , 1 / 7 ) . By ign... |
Interacting particle system : In probability theory, an interacting particle system (IPS) is a stochastic process ( X ( t ) ) t ∈ R + ^ on some configuration space Ω = S G given by a site space, a countably-infinite-order graph G and a local state space, a compact metric space S . More precisely IPS are continuous-... |
Interacting particle system : The voter model (usually in continuous time, but there are discrete versions as well) is a process similar to the contact process. In this process η ( x ) is taken to represent a voter's attitude on a particular topic. Voters reconsider their opinions at times distributed according to ind... |
Interacting particle system : Clifford, Peter; Aidan Sudbury (1973). "A Model for Spatial Conflict". Biometrika. 60 (3): 581–588. doi:10.1093/biomet/60.3.581. Durrett, Richard; Jeffrey E. Steif (1993). "Fixation Results for Threshold Voter Systems". The Annals of Probability. 21 (1): 232–247. doi:10.1214/aop/1176989403... |
Iterative Viterbi decoding : Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algori... |
Iterative Viterbi decoding : A basic (non-optimized) version, finding the sequence s with the smallest normalized distance from some subsequence of t is: // input is placed in observation s[1..n], template t[1..m], // and [[distance matrix]] d[1..n,1..m] // remaining elements in matrices are solely for internal computa... |
Iterative Viterbi decoding : Silaghi, M., "Spotting Subsequences matching a HMM using the Average Observation Probability Criteria with application to Keyword Spotting", AAAI, 2005. Rozenknop, Antoine, and Silaghi, Marius; "Algorithme de décodage de treillis selon le critère de coût moyen pour la reconnaissance de la p... |
Iterative Viterbi decoding : Li, Huan-Bang; Kohno, Ryuji (2006). An Efficient Code Structure of Block Coded Modulations with Iterative Viterbi Decoding Algorithm. 3rd International Symposium on Wireless Communication Systems. Valencia, Spain: IEEE. doi:10.1109/ISWCS.2006.4362391. ISBN 978-1-4244-0397-4. Wang, Qi; Wei, ... |
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