autocorrelation based fuzzy clustering of time series the traditional approaches to clustering a set of time series are generally applicable if there is a fixed underlying structure to the time series so that each will belong to one cluster or the other however time series often display dynamic behaviour in their evolution over time this dynamic behaviour should be taken into account when attempting to cluster time series for instance during a certain period a time series might belong to a certain cluster afterwards its dynamics might be closer to that of another cluster in this case the traditional clustering approaches are unlikely to find and represent the underlying structure in the given time series this switch from one time state to another which is typically vague can be naturally treated following a fuzzy approach this paper proposes a fuzzy clustering approach based on the autocorrelation functions of time series in which each time series is not assigned exclusively to only one cluster but it is allowed to belong to different clusters with various membership degrees

fast algorithms for computing tree lcs the lcs of two rooted ordered and labeled trees f and g is the largest forest that can be obtained from both trees by deleting nodes we present algorithms for computing tree lcs which exploit the sparsity inherent to the tree lcs problem assuming g is smaller than f our first algorithm runs in time o email protected height f height g lglg g where r is the number of pairs email protected f email protected g such that v and w have the same label our second algorithm runs in time o email protected lglg g where l is the size of the lcs of f and g for this algorithm we present a novel three dimensional alignment graph our third algorithm is intended for the constrained variant of the problem in which only nodes with zero or one children can be deleted for this case we obtain an o rhlglg g time algorithm where h height f height g

on the approximation of largest common subtrees and largest common point sets this paper considers the approximability of the largest common subtree and the largest common subgraph problems which have applications in molecular biology it is shown that approximating the problems within a factor of ne is np complete while a general search algorithm which approximates both problems within a factor of o n log n is presented moreover several variants of the largest common subtree problem are studied

consistent classification of nonstationary time series using stochastic wavelet representations consider the situation when we have training data containing many time series having known group membership and testing data with unknown group membership the goals are to find timescale features using training data that can best separate the groups and to use these highly discriminant features to classify test data we propose a method for classification using a bias corrected nondecimated wavelet transform wavelets are ideal for identifying highly discriminant local time and scale features the observed signals will be treated as realizations of locally stationary wavelet processes under which we define and rigorously estimate the evolutionary wavelet spectrum timescale decomposition of variance the evolutionary wavelet spectrum which contains the second moment information on the signals is used as the classification signature for each test time series we compute the empirical wavelet spectrum and its divergence from the wavelet spectrum of each group the test time series is then assigned

kernelization and parameterized algorithms for covering a tree by a set of stars or paths two restricted versions of the subforest isomorphism problem the covering a tree by a set of stars ctss and the covering a tree by a set of paths ctsp problems are studied both problems are np complete the problems are closely related to a number of well studied problems including the problems subgraph isomorphism tree editing and graph packing it is shown that the problems ctss and ctsp are fixed parameter tractable thorough development of parameterized algorithms and kernelization algorithms for these problems are presented

learning high dimensional markov forest distributions analysis of error rates the problem of learning forest structured discrete graphical models from i i d samples is considered an algorithm based on pruning of the chow liu tree through adaptive thresholding is proposed it is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size for the high dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n sufficient conditions on n d k are given for the algorithm to satisfy structural and risk consistencies in addition the extremal structures for learning are identified we prove that the independent resp tree model is the hardest resp easiest to learn using the proposed algorithm in terms of error rates for structure learning

robust reconstruction on trees is determined by the second eigenvalue consider a markov chain on an infinite tree t v e rooted at in such a chain once the initial root state is chosen each vertex iteratively chooses its state from the one of its parent by an application of a markov transition rule and all such applications are independent let j denote the resulting measure for j j is defined on configurations x x2v 2 a v where a is some finite set let n denote the restriction of to the sigma algebra generated by the variables x where x is at distance exactly n from letting n maxi j2a dtv n n where dtv denotes total variation distance we say that the reconstruction problem is solvable if liminfn 1 n 0 reconstruction solvability roughly means that the n th level of the tree contains a non vanishing amount of information on the root of the tree as n 1 in this paper we study the problem of robust reconstruction let be a non degenerate distribution on a and 0 let be chosen according to n and 0 be obtained from by letting for each node independently v 0 v with probability 1 and 0 v to be an independent sample from otherwise we denote by n the resulting measure on 0 the measure n is a perturbation of the measure n letting n maxi j2a dtv n n we say that the reconstruction problem is robust solvable if liminfn 1 n 0 for all 0 1 where 2 m is the second largest eigenvalue of m in absolute value then for all non degenerate the reconstruction problem is robust solvable we prove a converse and show that the reconstruction problem is not robust solvable if b 2 m 2 1 this proves a conjecture by the second author and peres we also consider other models of noise and general trees

classification trees for time series this paper proposes an extension of classification trees to time series input variables a new split criterion based on time series proximities is introduced first the criterion relies on an adaptive i e parameterized time series metric to cover both behaviors and values proximities the metrics parameters may change from one internal node to another to achieve the best bisection of the set of time series second the criterion involves the automatic extraction of the most discriminating subsequences the proposed time series classification tree is applied to a wide range of datasets public and new real and synthetic univariate and multivariate data we show through the experiments performed in this study that the proposed tree outperforms temporal trees using standard time series distances and performs well compared to other competitive time series classifiers

a generalized kernel approach to dissimilarity based classification usually objects to be classified are represented by features in this paper we discuss an alternative object representation based on dissimilarity values if such distances separate the classes well the nearest neighbor method offers a good solution however dissimilarities used in practice are usually far from ideal and the performance of the nearest neighbor rule suffers from its sensitivity to noisy examples we show that other more global classification techniques are preferable to the nearest neighbor rule in such cases for classification purposes two different ways of using generalized dissimilarity kernels are considered in the first one distances are isometrically embedded in a pseudo euclidean space and the classification task is performed there in the second approach classifiers are built directly on distance kernels both approaches are described theoretically and then compared using experiments with different dissimilarity measures and datasets including degraded data simulating the problem of missing values

ordered and unordered tree inclusion the following tree matching problem is considered given labeled trees p and t can p be obtained from t by deleting nodes deleting a node u entails removing all edges incident to u and if u has a parent v replacing the edge from v to u by edges from v to the children of u the problem is motivated by the study of query languages for structured text databases simple solutions to this problem require exponential time for ordered trees an algorithm is presented that requires o p t time and space the corresponding problem for unordered trees is also considered and a proof of its np completeness is given an algorithm is presented for the unordered problem this algorithm works in o p t time if the out degrees of the nodes in p are bounded by a constant and in polynomial time if they are o log t

evolutionary trees and the ising model on the bethe lattice a proof of steel s conjecture a major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data the evolutionary model is given by a markov chain on a tree given samples from the leaves of the markov chain the goal is to reconstruct the leaf labelled tree it is well known that in order to reconstruct a tree onn leaves sample sequences of length log n are needed it was conjectured by m steel that for the cfn ising evolutionary model if the mutation probability on all edges of the tree is less thanp p 2 1 2 3 2 then the tree can be recovered from sequences of length o logn the value p is given by the transition point for the extremality of the free gibbs measure for the ising model on the binary tree steel s conjecture was proven by the second author in the special case where the tree is balanced the second author also proved that if all edges have mutation probability larger thanp then the length needed isn 1 here we show that steel s conjecture holds true for general trees by giving a reconstruction algorithm that recovers the tree from o logn length sequences when the mutation probabilities are discretized and less than p our proof and results demonstrate that extremality of the free gibbs measure on the infinite binary tree which has been studied before in probability statistical physics and computer science determines how distinguishable are gibbs measures on finite binary trees

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

exact algorithms for computing the tree edit distance between unordered trees this paper presents a fixed parameter algorithm for the tree edit distance problem for unordered trees under the unit cost model that works in o 2 62 email protected poly n time and o n 2 space where the parameter k is the maximum bound of the edit distance and n is the maximum size of input trees this paper also presents polynomial time algorithms for the case where the maximum degree of the largest common subtree is bounded by a constant

two particle cluster integral in the expansion of the dielectric constant we study in detail the two particle cluster integral in the cluster expansion for the effective dielectric constant of a suspension of spherically symmetric polarizable inclusions embedded in a uniform medium although our form for the integrand differs from that derived earlier by finkel berg and by jeffrey we show that the integral is equivalent the two body dielectric problem for particles with an arbitrary radial dependence of the dielectric constant is solved by an expansion in spherical harmonics numerical results for some special models illustrate the importance of multipole contributions to the effective dielectric constant

phase transitions in phylogeny we apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies we consider the cavender farris neyman model of evolution on trees where all the inner nodes have degree at least 3 and the net transition on each edge is bounded by e motivated by a conjecture by m steel we show that if 2 1 2 2 1 then for balanced trees the topology of the underlying tree having n leaves can be reconstructed from o logn samples characters at the leaves on the other hand we show that if 2 1 2 2 1 then there exist topologies which require at least n 1 samples for reconstruction our results are the first rigorous results to establish the role of phase transitions for markov random fields on trees as studied in probability statistical physics and information theory for the study of phylogenies in mathematical biology

spectral functions for two dimensional random conductors abstract we collect together a number of results for the spectral function for two dimensional random conductors exact solutions are available for the conductivity of sheets containing a few elliptical inclusions we show that exact results can also be obtained for polygonal holes using conformal mapping techniques for polygonal inclusions with arbitrary conductivity the conductivity can be expressed in terms of a spectral function which we have obtained numerically using a boundary element method in this method the singularities associated with the sharp corners are explicitly taken care of spectral functions can also be used to obtain an exact solution for the conductivity when the effect of pairs of circular inclusions is also included throughout this paper we express the conductivity of the composite in terms of the total induced dipole moment and exploit the simplifications due to the reciprocity theorem in two dimensions

three body problem in the theory of the dielectric constant we study the corrections to the clausius mossotti formula for the dielectric constant of a disordered system of polarizable spherical particles previously we have derived an exact cluster expansion for the correction terms here we study the three body correction in detail we derive an explicit expression for the integrand of the three body cluster integral for a system of polarizable point dipoles

a tree matching algorithm based on node splitting and merging an algorithm that computes the best matching of two trees is described the degree of mismatch i e the distance is measured in terms of the number of node splitting and merging operations required the proposed tree distance is a more appropriate measurement of structural defonnation than the tree distance measure in terms of the number of insertions deletions and substitutions of tree nodes as defined in previous studies an algorithm that uses a divide and conquer strategy is presented the analysis shows that the time complexity is o nm2 where n and al are the number of nodes of the two trees respectively the algorithm has been implemented on a vax 11 780

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

analytical study of performance of linear discriminant analysis in stochastic settings this paper provides exact analytical expressions for the first and second moments of the true error for linear discriminant analysis lda when the data are univariate and taken from two stochastic gaussian processes the key point is that we assume a general setting in which the sample data from each class do not need to be identically distributed or independent within or between classes we compare the true errors of designed classifiers under the typical i i d model and when the data are correlated providing exact expressions and demonstrating that depending on the covariance structure correlated data can result in classifiers with either greater error or less error than when training with uncorrelated data the general theory is applied to autoregressive and moving average models of the first order and it is demonstrated using real genomic data

dielectric function for a material containing hyperspherical inclusions to o c 2 i multipole expansions by averaging over pairs of hyperspheres we have obtained the dielectric function for a binary mixture containing hyperspherical inclusions up to order c 2 where c is the volume fraction of inclusions the method used is based on multipole expansions for the potential of two spheres in a uniform eld and is a generalization of the method of jerey to d dimensional space numerical results are presented for the second order coecient in the low c expansion of the dielectric constant for arbitrary d these verify earlier known results as well as showing the dependence of on dimensionality which is particularly simple as d 1 and as d 1 ever since the time of maxwell 1873 the study of the properties of random mix tures or suspensions containing a low volume fraction of inclusions has been of much interest the problems concerned are applicable to the study of electrical conduc tion thermal conduction electric permittivity magnetic permeability and others by virtue of the universality of laplace s equation in this paper we will concentrate on the case of dielectric inclusions other cases being easily obtainable by renaming the symbols maxwell 1873 provided the exact rst order coecient to o c for a system of spherical inclusions other similar problems too c not within the univer sal class have also attracted much interest for example the o c coecient for the viscosity of a suspension containing a system of hard spheres was found by einstein 1906 more recent exact results for the o c coecient of electrical conductivity for inclusions of other shapes in two dimensions were obtained by thorpe 1992 using conformal mapping a method favoured by maxwell it took nearly 100 years before any serious quantitative studies were made of the second order o c 2 coecient the original work being done by batchelor 1972 and batchelor green 1972 who unfortunately undertook initially to study the more complex fluid suspensions problem to this day few exact results are known batchelor 1974 1977 we remark here that the second order coecient we are interested in is related to the so called huggins coecient h for fluid suspensions i e the expansion of the viscosity is given by 0 1 c h c 2

thick pen transformation for time series traditional visualisation of time series data often consists of plotting the time series values against time and connecting the dots we propose an alternative multiscale visualisation technique motivated by the scale space approach in computer vision in brief our method also connects the dots but uses a range of pens of varying thicknesses for this purpose the resulting multiscale map termed the thick pen transform tpt corresponds to viewing the time series from a range of distances we formally prove that the tpt is a discriminatory statistic for two gaussian time series with distinct correlation structures further we show interesting possible applications of the tpt to measuring cross dependence in multivariate time series classifying time series and testing for stationarity in particular we derive the asymptotic distribution of our test statistic and argue that the test is applicable to both linear and nonlinear processes under low moment assumptions various other aspects of the methodology including other possible applications are also discussed

effective elasticity of a solid suspension of spheres i stress strain constitutive relation abstract we consider the problem of the elastic behaviour of a random medium composed of identical spherically symmetric inclusions each made of a linear elastic material with varying shear and bulk moduli distributed randomly in a uniform matrix made of a linear elastic material with moduli 0 k 0 we consider the response of a finite sample to an externally imposed incident displacement field and by eliminating the external field obtain a linear constitutive relation between mean stress and mean strain in the material using the cluster expansion method of felderhof ford and cohen we show that in the thermodynamic limit of an infinite system there is a well defined effective elasticity operator for the medium expressible as a sum of terms which involve successively the problem of 1 2 p inclusions in an infinite matrix the elasticity operator is given in detail through second order terms in the number density of inclusions by passing to a long wavelength limit we show how the constitutive relation reduces to a local relation expressible in terms of effective moduli eff k eff

the conductivity of a sheet containing inclusions with sharp corners we have written down an integral equation for the surface charge on the interface between an n sided regular polygonal inclusion with conductivity o 1 and a host with conductivity 0 the conductivity of a sheet with few inclusions can be determined from the induced dipole associated with this charge distribution the integral equation is solved numerically and detailed results are given for n 3 4 and 6 the circle limit is approached for large n we show that our results are consistent with the reciprocity theorem for two dimensional conducting media and we reproduce the known analytic results in the limits when the inclusion is either a hole or a superconducting region we also find the conductivity of a sheet containing a general n pointed star analytic fits to our numerical results are given which are used as input for effective medium theories the results given in this paper for the electrical conductivity apply also to the thermal conductivity and to dielectric media

cluster expansion for the dielectric constant of a polarizable suspension we derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background this also leads to a cluster expansion for the effective dielectric constant it is shown that the cluster integrals of any order are absolutely convergent so that the dielectric constant is well defined and independent of the shape of the sample in the limit of a large system we compare with virial expansions derived earlier in statistical mechanics for the dielectric constant of a nonpolar gas in these expansions the virial coefficients are given by integrals which are only conditionally convergent

a few logs suffice to build almost all trees part ii abstract inferring evolutionary trees is an interesting and important problem in biology but one that is computationally difficult as most associated optimization problems are np hard although many methods are provably statistically consistent i e the probability of recovering the correct tree converges to 1 as the sequence length increases the actual rate of convergence for different methods has not been well understood in a recent paper we introduced a new method for reconstructing evolutionary trees called the dyadic closure method dcm and we showed that dcm has a very fast convergence rate dcm runs in o n 5 log n time where n is the number of sequences and so although polynomial the computational requirements are potentially too large to be of use in practice in this paper we present another tree reconstruction method the witness antiwitness method wam wam is faster than dcm especially on random trees and converges to the true tree topology at the same rate as dcm we also compare wam to other methods used to reconstruct trees including neighbor joining possibly the most popular method among molecular biologists and new methods introduced in the computer science literature

evolutionary trees can be learned in polynomial time in the two state general markov model the j state general markov model of evolution due to steel is a stochastic model concerned with the evolution of strings over an alphabet of size j in particular the two state general markov model of evolution generalizes the well known cavender farris neyman model of evolution by removing the symmetry restriction which requires that the probability that a 0 turns into a 1 along an edge is the same as the probability that a 1 turns into a 0 along the edge farach and kannan showed how to probably approximately correct pac learn markov evolutionary trees in the cavender farris neyman model provided that the target tree satisfies the additional restriction that all pairs of leaves have a sufficiently high probability of being the same we show how to remove both restrictions and thereby obtain the first polynomial time pac learning algorithm in the sense of kearns et al proceedings of the 26th annual acm symposium on the theory of computing 1994 pp 273 282 for the general class of two state markov evolutionary trees

cavities vis a vis rigid inclusions elastic moduli of materials with polygonal inclusions in this paper we explore the correspondence between rigid inclusions and cavities dundurs 1989 j appl mech 56 786 790 as applied to the effective elastic moduli of materials with polygonal rigid inclusions and cavities in the analysis we use a complex variable method of elasticity and a conformal transformation to solve for the stress field due to a single rigid inclusion then we use a far field approach to obtain the effective elastic constants of composites with a dilute concentration of rigid polygonal inclusions by employing the dundurs correspondence we can automatically obtain the result for the effective elastic moduli of materials with cavities finally we use effective medium theories to predict the elastic moduli of materials containing a finite concentration of inclusions

nonlinear pattern matching in trees tree pattern matching is a fundamental operation that is used in a number of programming tasks such as mechanical theorem proving term rewriting symbolic computation and nonprocedural programming languages in this paper we present new sequential algorithms for nonlinear pattern matching in trees our algorithm improves upon know tree pattern matching algorithms in important aspects such as time performance ease of integration with several reduction strategies and ability to avoid unnecessary computation steps on match attempts that fail the expected time complexity of our algorithm is linear in the sum of the sizes of the two trees

finding a maximum likelihood tree is hard maximum likelihood ml is an increasingly popular optimality criterion for selecting evolutionary trees felsenstein 1981 finding optimal ml trees appears to be a very hard computational task but for tractable cases ml is the method of choice in particular algorithms and heuristics for ml take longer to run than algorithms and heuristics for the second major character based criterion maximum parsimony mp however while mp has been known to be np complete for over 20 years foulds and graham 1982 day et al 1986 such a hardness result for ml has so far eluded researchers in the field an important work by tuffley and steel 1997 proves quantitative relations between the parsimony values of given sequences and the corresponding log likelihood values however a direct application of their work would only give an exponential time reduction from mp to ml another step in this direction has recently been made by addario berry et al 2004 who proved that ancestral maximum likelihood aml is np complete aml lies in between the two problems having some properties of mp and some properties of ml still the aml proof is not directly applicable to the ml problem we resolve the question showing that regular ml on phylogenetic trees is indeed intractable our reduction follows the vertex cover reductions for mp day et al 1986 and aml addario berry et al 2004 but its starting point is an approximation version of vertex cover known as gap vc the crux of our work is not the reduction but its correctness proof the proof goes through a series of tree modifications while controlling the likelihood losses at each step using the bounds of tuffley and steel 1997 the proof can be viewed as correlating the value of any ml solution to an arbitrarily close approximation to vertex cover

tree structure for contractible regions in r 3 for contractible regions in 3 with generic smooth boundary we determine the global structure of the blum medial axis m we give an algorithm for decomposing m into irreducible components which are attached to each other along fin curves the attaching cannot be described by a tree structure as in the 2d case however a simplified but topologically equivalent medial structure m with the same irreducible components can be described by a two level tree structure the top level describes the simplified form of the attaching and the second level tree structure for each irreducible component specifies how to construct the component by attaching smooth medial sheets to the network of y branch curves the conditions for these structures are complete in the sense that any region whose blum medial axis satisfies the conditions is contractible

on the factorial functional series and their application to random media functional series with a pointwise random input the density field of a random set of points bf x j are considered the series are rearranged so as the so called factorial fields of the set bf x j appear the obtained series are called factorial the basic result of the paper states that the factorial series possess virial property this means that if a random field u bf x is expanded as a factorial series the truncation u p bf x of the latter after the p tuple term coincides in the statistical sense with u bf x to the order n p where n is the number density of the set bf x j p 1 2 cdots the performance of the factorial series in random media problems is illustrated on the example of steady state diffusion in a random dispersion of spheres whose sink strength differs from that of the matrix the full statistical solution of this problem correct to the order c 2 is obtained in particular the effective sink strength of the dispersion i

discrimination and clustering for multivariate time series abstract minimum discrimination information provides a useful generalization of likelihood methodology for classification and clustering of multivariate time series discrimination between different classes of multivariate time series that can be characterized by differing covariance or spectral structures is of importance in applications occurring in the analysis of geophysical and medical time series data for discrimination between such multivariate series kullback leibler discrimination information and the chernoff information measure are developed for the multivariate non gaussian case asymptotic error rates and limiting distributions are given for a generalized spectral disparity measure that includes the foregoing criteria as special cases applications to problems of clustering and classifying earthquakes and mining explosions are given

effective elasticity of a solid suspension of spheres ii effective moduli in lowest multipole approximation abstract we evaluate explicitly through terms of second order in volume fraction the effective elastic moduli derived formally in a preceeding article for a random suspension of spherically symmetric inclusions in a background matrix by interpreting the earlier formulae in terms of induced stresses on an inclusion we reduce the calculation to the treatment of a one inclusion and a two inclusion problem only to treat the one inclusion problem we derive a faxen type theorem for the total stress induced on the inclusion by an incident displacement field for the two inclusion problem we use a method of reflections whereby we obtain the contribution of lowest order in the separation of inclusion centres by introducing a point stress model of the inclusions we sum a subset of reflections to all orders in inclusion separation we find that in the point stress model the effective moduli are given in terms of only two of the scattering coefficients introduced elsewhere for the one inclusion problem for the special case of uniform inclusions we give numerical results for the effective moduli which are compared with exact upper and lower bounds

multi modal and multi scale temporal metric learning for a robust time series nearest neighbors classification abstract the definition of a metric between time series is inherent to several data analysis and mining tasks including clustering classification or forecasting time series data present naturally several modalities covering their amplitude behavior or frequential spectrum that may be expressed with varying delays and at multiple temporal scales exhibited globally or locally combining several modalities at multiple temporal scales to learn a holistic metric is a key challenge for many real temporal data applications this paper proposes a multi modal and multi scale temporal metric learning m 2 tml approach for a robust time series nearest neighbors classification the solution lies in embedding time series into a dissimilarity space where a pairwise svm is used to learn both linear and non linear combined metric a sparse and interpretable variant of the solution shows the ability of the learned temporal metric to localize accurately discriminative modalities as well as their temporal scales a wide range of 30 public and challenging datasets encompassing images traces and ecg data are used to show the efficiency and the potential of m 2 tml for an effective time series nearest neighbors classification

second order interactions in a medium containing perfect conducting hyperspherical inclusions we consider the interaction between two hyperspherical inclusions surrounded by a medium experiencing an e field in the perfect conducting limit by the use of d dimensional dipole moments we show that the dielectric function of the medium can be calculated to any order n in particular d n the coefficient of o c 2 in the series expansion for the dielectric function is determined in terms of a dimensional dependence which even though it is mathematically complex proves to be superior in convergence to other methods we calculate the potential difference between the two hyperspheres for various limits including the all important closely packed limit using the theory of continued fractions we investigate the convergence of the interaction terms between the two inclusions and obtain results that reduce the enormous number of calculations that need to be computed as n the latter may be useful in the pursuit of a theory that resums the complicated interaction terms present in the two body medium problem with a view towards an improved effective medium theory

simulation relations for pattern matching in directed graphs we consider the problem of finding the occurrences of a pattern tree t in a directed graph g and propose two algorithms one for preprocessing and one for searching for t in g it is assumed that

approximation and parameterized algorithms for common subtrees and edit distance between unordered trees given two rooted labeled unordered trees the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship the tree edit distance problem is to determine the least cost sequence of insertions deletions and substitutions that converts a tree into another given tree both problems are known to be hard to approximate within some constant factor in general we tackle these problems from two perspectives giving exact algorithms either for special cases or in terms of some parameters and approximation algorithms and hardness of approximation we present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees this is complemented with a tighter apx hardness proof that holds when the trees are of height one and two respectively furthermore we present the first approximation algorithms for both problems in particular for the common subtree problem for t trees we present an algorithm achieving a tlog 2 b o p t 1 ratio where b o p t is the number of branching nodes in the optimal solution we also present constant factor approximation algorithms for both problems in the case of bounded height trees

a large deviation analysis of the maximum likelihood learning of markov tree structures the problem of maximum likelihood ml estimation of discrete tree structured distributions is considered chow and liu established that ml estimation reduces to the construction of a maximum weight spanning tree using the empirical mutual information quantities as the edge weights using the theory of large deviations we analyze the exponent associated with the error probability of the event that the ml estimate of the markov tree structure differs from the true tree structure given a set of independently drawn samples by exploiting the fact that the output of ml estimation is a tree we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event we prove that in this dominant crossover event a non neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non neighbor pair using ideas from euclidean information theory we then analyze the scenario of ml estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio which is interpreted as the signal to noise ratio snr for learning tree distributions we show via numerical experiments that in this regime our snr approximation is accurate

weighted dynamic time warping for time series classification dynamic time warping dtw which finds the minimum path by providing non linear alignments between two time series has been widely used as a distance measure for time series classification and clustering however dtw does not account for the relative importance regarding the phase difference between a reference point and a testing point this may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition therefore we propose a novel distance measure called a weighted dtw wdtw which is a penalty based dtw our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers the rationale underlying the proposed distance measure is demonstrated with some illustrative examples a new weight function called the modified logistic weight function mlwf is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point by applying different weights to adjacent points the proposed algorithm can enhance the detection of similarity between two time series we show that some popular distance measures such as dtw and euclidean distance are special cases of our proposed wdtw measure we extend the proposed idea to other variants of dtw such as derivative dynamic time warping ddtw and propose the weighted version of ddtw we have compared the performances of our proposed procedures with other popular approaches using public data sets available through the ucr time series data mining archive for both time series classification and clustering problems the experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems

a metric for rooted trees with unlabeled vertices based on nested parentheses in this paper we propose a new metric for rooted trees with unlabeled vertices based on alignments of nested parenthesis strings we prove that the time complexity for computing this metric is np hard and present a 1 5 approximation algorithm for it

learning latent tree graphical models we study the problem of learning a latent tree graphical model where samples are available only from a subset of variables we propose two consistent and computationally efficient algorithms for learning minimal latent trees that is trees without any redundant hidden nodes unlike many existing methods the observed nodes or variables are not constrained to be leaf nodes our algorithms can be applied to both discrete and gaussian random variables and our learned models are such that all the observed and latent variables have the same domain state space our first algorithm recursive grouping builds the latent tree recursively by identifying sibling groups using so called information distances one of the main contributions of this work is our second algorithm which we refer to as clgrouping clgrouping starts with a pre processing procedure in which a tree over the observed variables is constructed this global step groups the observed nodes that are likely to be close to each other in the true latent tree thereby guiding subsequent recursive grouping or equivalent procedures such as neighbor joining on much smaller subsets of variables this results in more accurate and efficient learning of latent trees we also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions we compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden markov models and star graphs in addition we demonstrate the applicability of our methods on real world data sets by modeling the dependency structure of monthly stock returns in the s p index and of the words in the 20 newsgroups data set

density expansion of transport properties on 2d site disordered lattices i general theory a systematic kinetic theory is developed for calculating transport properties on 2d lattices with random site impurities in concentration c which can be modelled by hopping models the authors main results are expressions in terms of lattice sums for the static and frequency dependent conductivity and for the velocity autocorrelation function

phase transition in the sample complexity of likelihood based phylogeny inference reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods here we study maximum likelihood a classical statistical technique which is perhaps the most widely used in phylogenetic practice because of its superior empirical accuracy at the theoretical level except for its consistency that is the guarantee of eventual correct reconstruction as the size of the input data grows much remains to be understood about the statistical properties of maximum likelihood in this context in particular the best bounds on the sample complexity or sequence length requirement of maximum likelihood that is the amount of data required for correct reconstruction are exponential in the number n of tips far from known lower bounds based on information theoretic arguments here we close the gap by proving a new upper bound on the sequence length requirement of maximum likelihood that matches up to constants the known lower bound for some standard models of evolution more specifically for the r state symmetric model of sequence evolution on a binary phylogeny with bounded edge lengths we show that the sequence length requirement behaves logarithmically in n when the expected amount of mutation per edge is below what is known as the kesten stigum threshold in general the sequence length requirement is polynomial in n our results imply moreover that the maximum likelihood estimator can be computed efficiently on randomly generated data provided sequences are as above our main technical contribution which may be of independent interest relates the total variation distance between the leaf state distributions of two trees with a notion of combinatorial distance between the trees in words we show in a precise quantitative manner that the more different two evolutionary trees are the easier it is to distinguish their output

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

alignment of trees an alternative to tree edit abstract in this paper we propose the alignment of trees as a measure of the similarity between two labeled trees both ordered and unordered trees are considered an algorithm is designed for ordered trees the time complexity of this algorithm is o t 1 t 2 deg t 1 deg t 2 2 where t 1 is the number of nodes in t 1 and deg t 1 is the degree of t 1 i 1 2 the algorithm is faster than the best known algorithm for tree edit when deg t 1 and deg t 2 are smaller than the depths of t 1 and t 2 for unordered trees we show that the alignment problem can be solved in polynomial time if the trees have a bounded degree and becomes max snp hard if one of the trees is allowed to have an arbitrary degree in contrast the edit problem for unordered trees is max snp hard even if both trees have a bounded degree zhang and jiang 1994 finally multiple alignment of trees is discussed

effective conductivity of a two dimensional medium containing elliptical inhomogeneities two effective medium theories the maxwell method and the differential method are used to estimate the effective conductivity of a two dimensional medium consisting of a random distribution of elliptical inclusions in an otherwise homogeneous matrix results are found for arbitrary values of the matrix inclusion conductivity ratio and arbitrary values of the inclusion aspect ratio both predictions are shown to satisfy keller s reciprocity relation the differential prediction is found always to lie within the hashin shtrikman bounds whereas the maxwell prediction typically violates the bounds for sufficiently large inclusion concentrations comparison with three sets of experimental numerical data shows that both theories offer an improvement over the first order dilute concentration results however it does not seem that either method is superior to the other in general furthermore neither method is reliable near the percolation limit

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

simple fast algorithms for the editing distance between trees and related problems ordered labeled trees are trees in which the left to right order among siblings is significant the distance between two ordered trees is considered to be the weighted number of edit operations insert delete and modify to transform one tree to another the problem of approximate tree matching is also considered specifically algorithms are designed to answer the following kinds of questions 1 what is the distance between two trees 2 what is the minimum distance between t 1 and t 2 when zero or more subtrees can be removed from t 2 3 let the pruning of a tree at node n mean removing all the descendants of node n the analogous question for prunings as for subtrees is answered a dynamic programming algorithm is presented to solve the three questions in sequential time o t 1 times t 2 times min textit depth t 1 textit leaves t 1 times min textit depth t 2 textit leaves t 2 and space o t 1 times t 2 compared with o t 1 times t 2 t

a clustering procedure for exploratory mining of vector time series a two step procedure is developed for the exploratory mining of real valued vector multivariate time series using partition based clustering methods the proposed procedure was tested with model generated data multiple sensor based process data as well as simulation data the test results indicate that the proposed procedure is quite effective in producing better clustering results than a hidden markov model hmm based clustering method if there is a priori knowledge about the number of clusters in the data two existing validity indices were tested and found ineffective in determining the actual number of clusters determining the appropriate number of clusters in the case that there is no a priori knowledge is a known unresolved research issue not only for our proposed procedure but also for the hmm based clustering method and further development is necessary

time warp edit distance with stiffness adjustment for time series matching in a way similar to the string to string correction problem we address discrete time series similarity in light of a time series to time series correction problem for which the similarity between two time series is measured as the minimum cost sequence of edit operations needed to transform one time series into another to define the edit operations we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call time warp edit distance twed twed is slightly different in form from dynamic time warping dtw longest common subsequence lcss or edit distance with real penalty erp algorithms in particular it highlights a parameter that controls a kind of stiffness of the elastic measure along the time axis we show that the similarity provided by twed is a potentially useful metric in time series retrieval applications since it could benefit from the triangular inequality property to speed up the retrieval process while tuning the parameters of the elastic measure in that context a lower bound is derived to link the matching of time series into down sampled representation spaces to the matching into the original space the empiric quality of the twed distance is evaluated on a simple classification task compared to edit distance dtw lcss and erp twed has proved to be quite effective on the considered experimental task

algorithms for the constrained editing distance between ordered labeled trees and related problems abstract this paper considers the problem of computing a constrained editing distance between ordered labeled trees this distance metric can be applied to pattern recognition syntactic tree comparison classification tree comparison and other applications the problem of approximate ordered tree matching is also considered we present optimal algorithms for solving these problems in sequential time o t1 t2

generalized lcs the longest common subsequence lcs is a well studied problem having a wide range of implementations its motivation is in comparing strings it has long been of interest to devise a similar measure for comparing higher dimensional objects and more complex structures in this paper we study the longest common substructure of two matrices and show that this problem is np hard we also study the longest common subforest problem for multiple trees including a constrained version as well we show np hardness for k 2 unordered trees in the constrained lcs we also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees

on the parameterized complexity of associative and commutative unification this article studies the parameterized complexity of the unification problem with associative commutative or associative commutative functions with respect to the parameter number of variables it is shown that if every variable occurs only once then both of the associative and associative commutative unification problems can be solved in polynomial time but that in the general case both problems are w 1 hard even when one of the two input terms is variable free for commutative unification an algorithm whose time complexity depends exponentially on the number of variables is presented moreover if a certain conjecture is true then the special case where one input term is variable free belongs to fpt some related results are also derived for a natural generalization of the classic string and tree edit distance problems that allows variables

the conductivity of a sheet containing a few polygonal holes and or superconducting inclusions i use conformal mapping techniques to determine the change in the conductivity of a sheet containing a few well separated holes the hole shapes studied are the equilateral triangle square pentagon and regular n gons i show that the conductivity can be written as sigma sigma 0 1 alpha n f o f 2 where f is the area fraction of the inclusions and the coefficient alpha n frac tan pi n 2 pi n gamma 4 left frac 1 n right gamma 2 left frac 2 n right which is 2 5811 2 1884 2 0878 for triangles squares and pentagons and tends to the circle limit of 2 as n rightarrow infty the coefficient alpha n is proportional to the induced dipole moment around the polygonal hole which can be found using an appropriate conformal mapping i have also examined and compared the results for long thin needle like holes in the shape of diamonds rectangles and ellipses in all cases the conductivity parallel to the needles has the limiting form sigma sigma 0 1 f while for the perpendicular conductivity i find that sigma sigma 0 1 n pi a 2 where 2a is the length of the needle and n is the number of needles per unit area for thicker needles the shape becomes important and i compare the results with recent analog experiments and computer simulations because of the reciprocity theorem all the results found here apply equally well to superconducting inclusions

time series characterization poisson integral and robust divergence measures new functions are proposed for time series characterization based on a relationship between the poisson integral and spectral analysis these functions are shown to completely specify the correlation structure of a time series and can be estimated consistently and uniformly even if the time series has a mixed spectrum they are also shown to be equipped with flexible parameters that can be used to achieve desired frequency selectability using these characterization functions a new divergence measure is proposed for time series discrimination and change detection sensitivity of the new divergence is investigated under the additive and multiplicative spectral departure models the divergence is shown to be more robust than some spectral density based divergence measures in fighting against narrow band spectral contamination and distortion a change detection example in speech processing is given to demonstrate the effectiveness of the new method

dielectric function for a material containing hyperspherical inclusions to o c2 ii method of images we have developed the method of images for the solution of two hyperspheres in d dimensions in a uniform field in order to study the o c 2 coefficient in the dielectric constant of the medium the method employs extensions of image theory for classical charges and dipoles for dielectric spheres which produce novel line charge and line dipole densities numerical results for with arbitrary integer d are consistent with our previous paper i this issue and demonstrate that the image method shows superior convergence properties although computationally less convenient the procedure is in principle calculable term by term and leads to useful analytic results in the weak scattering limit this work also produces a simple algebraic approximation that is useful everywhere