an efficient strategy for generating all descendant subtree patterns from phylogenetic trees with its implementation abstract phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we efficiently solve two subtree comparison problems on a set of phylogenetic trees which have practical applications to analyze the evolution and co evolution genes clustering of genomic sequences let t 1 t 2 t k be a set of k phylogenetic trees such that the leaves of each tree are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same where n is the maximum number of the leaves among the k trees we present a linear time algorithm to find all the leaf agreement descendant subtrees by further extending this result we present a linear time algorithm to find all the leaf agreement isomorphic descendant subtrees based on our algorithms a web based system using input tree files from treebase is also implemented

fast comparison of evolutionary trees abstract constructing evolutionary trees for species sets is a fundamental problem in biology unfortunately there is no single agreed upon method for this task and many methods are in use current practice dictates that trees be constructed using different methods and that the resulting trees then be compared for consensus it has become necessary to automate this process as the number of species under consideration has grown we study the unrooted maximum agreement subtree problem umast and its rooted variant rmast the umast problem is as follows given a set a and two trees t 0 and t 1 leaf labeled by the elements of a find a maximum cardinality subset b of a such that the restrictions of t 0 and t 1 to b are topologically isomorphic our main result is an o n 2 o 1 time algorithm for the umast problem we also derive an o n 2 time algorithm for the rmast problem the previous best algorithm for both these problems has running time o n 4 5 o 1

the matrix stick breaking process flexible bayes meta analysis in analyzing data from multiple related studies it often is of interest to borrow information across studies and to cluster similar studies although parametric hierarchical models are commonly used of concern is sensitivity to the form chosen for the random effects distribution a dirichlet process dp prior can allow the distribution to be unknown while clustering studies however the dp does not allow local clustering of studies with respect to a subset of the coefficients without making independence assumptions motivated by this problem we propose a matrix stick breaking process msbp as a prior for a matrix of random probability measures properties of the msbp are considered and methods are developed for posterior computation using markov chain monte carlo using the msbp as a prior for a matrix of study specific regression coefficients we demonstrate advantages over parametric modeling in simulated examples the methods are further illustrated using a multinational uterotrophic bioassay s

on inconsistent bayes estimates of location on montre que dans certaines situations relativement naturelles les estimateurs de position bayesiens sont inconsistants

bayesian semiparametric median regression modeling median regression models become an attractive alternative to mean regression models when employing flexible families of distributions for the errors classical approaches are typically algorithmic with desirable properties emerging asymptotically however nonparametric error models may be most attractive in the case of smaller sample sizes where parametric specifications are difficult to justify hence a bayesian approach enabling exact inference given the observed data may be appealing in this context there is little bayesian work we develop two fully bayesian modeling approaches employing mixture models for the errors in a median regression model the associated families of error distributions allow for increased variability skewness and flexible tail behavior the first family is semiparametric with extra variability captured nonparametrically through mixing and skewness handled parametrically the second family a fully nonparametric one includes all unimodal densities on the real line with

algebraic cycles and infinite loop spaces in this paper we use recent results about the topology of chow varieties to answer an open question in infinite loop space theory that is we construct an infinite loop space structure on a certain product of eilenberg maclane spaces so that the total chern map is an infinite loop map an analogous result for the total stiefel whitney map is also proved further results on the structure of stabilized spaces of alebraic cycles are obtained and computational consequences are also outlined

the stable topology of self dual moduli spaces soit m une 4 variete de riemann compacte connexe orientee et soit g un groupe de lie connexe simple on fixe un entier q m q alors l application inclusion i induit un epimorphisme sur les groupes respectifs d homologie et d homotopie a toutes les dimensions inferieures ou egales a q

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

bounded hairpin completion hairpin completion is a formal operation inspired from biochemistry here we consider a restricted variant of hairpin completion called bounded hairpin completion applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x hairpin completion produces a new word z which is a prolongation of x to the right or to the left by annealing although this operation is a purely mathematical one and the biological reality is just a source of inspiration it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion the restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion they cannot be longer than a given constant closure properties of some classes of formal languages under the non iterated and iterated bounded hairpin completion are investigated we consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them finally also the inverse operation namely bounded hairpin reduction as well as the set of all primitive bounded hairpin roots of a regular language are considered

from gene trees to species trees this paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model this is a fundamental problem in computational molecular biology our main results are as follows a linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree this answers a problem raised recently by eulenstein mirkin and vingron j comput bio 5 1998 pp 135 148 the complexity of finding an optimal species tree from gene trees is studied the problem is proved to be np hard for the duplication cost and for the mutation cost further the concept of reconciled trees was introduced by goodman et al and formalized by page for visualizing the relationship between gene and species trees we show that constructing an optimal reconciled tree for gene trees is also np hard finally we consider a general reconstruction problem and show it to be np hard even for the well known nearest neighbor interchange distance a new and efficiently computable metric is defined based on the duplication cost we show that the problem of finding an optimal species tree from gene trees is np hard under this new metric but it can be approximated within factor 2 in polynomial time using this approximation result we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other our heuristic method is significantly better than the existing program in page s genetree 1 0 that starts the search from a random tree

the topology of instanton moduli spaces i the atiyah jones conjecture in this paper we study the global geometry and topology of the moduli spaces of based su 2 instantons over the 4 sphere s4 these instanton moduli spaces have a rich history and have been analyzed from many points of view originally these spaces which we denote by mk were defined as solution spaces modulo gauge equivalence to certain partial differential equations namely the self duality equations associated to the yang mills functional in su 2 gauge theory they have been successfully studied from this point of view by taubes t1 t2 uhlenbeck u and others an important alternative approach was initiated by ward w who related instantons to certain holomorphic bundles on cp3 and was continued by atiyah and ward in aw this allowed the classification of instantons on 4 in terms of quaternionic linear algebra by atiyah drinfeld hitchin and manin adhm this holomorphic approach was further extended by donaldson d who showed that these bundles were determined by their restriction to a cp2 and that the restricted bundles only had to satisfy the constraint of being trivial on a fixed line in c2r2 hurtubise hul then exploited this fact to study the moduli spaces mk as did atiyah a to show that mk arise naturally in the theory of holomorphic maps into loop groups this latter approach was continued by gravesen g atiyah and jones aj obtained the first results and formulated the foundational questions on the global topology of these moduli spaces recall that an element of mk is a based gauge equivalence class of a connection on the principal su 2 bundle over 4 denoted by pk with second chern class k satisfying the self duality equations there is a natural forgetful map to the based equivalence classes of all connections in pk atiyah and jones aj showed that this target space which we denote by bk is homotopy equivalent

on finding the adams consensus tree abstract this article presents a fast algorithm for finding the adams consensus tree of a set of conflicting phylogenetic trees with identical leaf labels its worst case running time is o k n log n where k is the number of input trees and n is the size of the leaf label set in comparison the original algorithm of adams has a worst case running time of o k n 2 to achieve subquadratic running time the centroid path decomposition technique is applied in a novel way that traverses the input trees by following a centroid path in each of them in unison for k 2 an even faster algorithm running in o n log n log log n time is provided which relies on an extension of the wavelet tree based technique of bose et al for orthogonal range counting on a grid our extended wavelet tree data structure also supports truncated range maximum minimum queries efficiently

inferring a tree from lowest common ancestors with an application to the optimization of relational expressions we present an algorithm for constructing a tree to satisfy a set of lineage constraints on common ancestors we then apply this algorithm to synthesize a relational algebra expression from a simple tableau a problem arising in the theory of relational databases

finding maximal leaf agreement isomorphic descendent subtrees from phylogenetic trees with different species phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we consider two descendent subtree comparison problems on phylogenetic trees given a set of k phylogenetic trees whose leaves are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same we first present a linear time algorithm to final all the maximal leaf agreement descendent subtrees based on this result we also present a linear time algorithm to find all the maximal leaf agreement isomorphic descendent subtrees

on finding common subtrees abstract let t and r be two arbitrary ordered trees t r whose nodes are labelled over an alphabet a we devise a simple solution for detecting all the common subtrees in o t time and space if the size of a is finite and o t log min a t time otherwise we solve the problem of finding in t and r all occurrences if any of any given tree b in either o t b or o b t b time this requires to set up a simple data structure in o t time that allows to find all maximal subtrees of b in o b time and to solve other related problems

bayesian semiparametric analysis of structural equation models with mixed continuous and unordered categorical variables recently structural equation models sems have been applied for analyzing interrelationships among observed and latent variables in biological and medical research latent variables in these models are typically assumed to have a normal distribution this article considers a bayesian semparametric sem with covariates and mixed continuous and unordered categorical variables in which the explanatory latent variables in the structural equation are modeled via an appropriate truncated dirichlet process with a stick breaking procedure results obtained from a simulation study and an analysis of a real medical data set are presented to illustrate the methodology

monopoles non linear σ models and two fold loop spaces in this paper we study the topology of hat m k the moduli spaces ofsu 2 monopoles associated with the yang mills higgs and bogomol nyi equations and m k non linear models from quantum field theory beautiful work of donaldson 18 19 hitchin 24 25 and taubes 37 39 40 shows that gauge equivalence classes of monopoles correspond to based rational self maps of the riemann sphere similarly the non linear models we consider here are based harmonic maps from the riemann sphere to complex projectivem space in seminal work segal 35 studied m k the space of based rational maps from the riemann sphere to complex projectivem space of a fixed degreek any element of m k is clearly an element of k2cp m the space of all based continuous maps from the riemann sphere to complex projectivem space of a fixed degreek and this assignment gives rise to the natural inclusion of m k in k2cp m segal showed that these natural inclusions are homotopy equivalences through dimensionk 2m 1 as the topology of the two fold loop space 2cp m is well understood segal s result gives a very efficient way to explicitly determine the low dimensional topology of m k thus iterated loop spaces have much to say about the topology of monopoles and non linear models

algebraic cycles and homotopy theory examine its homotopy groups which after a certain idealization of the space turn out to be astonishingly simple in fact for complex projective space pn the structure can be understood completely this yields new information about the topology of the classical chow varieties and establishes an explicit relationship with universal cohomology operations in the general case complete computations are difficult but we shall establish a complex suspension theorem and lay the foundations for a theory based on the homotopy groups of chow varieties to state the results we must give precise meaning to the space of subvarieties we begin with the fundamental case of subvarieties in complex projective n space pln for each pair of integers p and d with d 1 and 0 p n consider the set wp d pn of all finite formal sums

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

bayesian nonparametric estimation of the median part i computation of the estimates let x i i 1 ldots n be i i d sim f theta where f theta x f x theta for some f that has median equal to 0 f is assumed unknown or only partially known and the problem is to estimate theta priors are put on the pair f theta the priors on f concentrate all their mass on c d f s with median equal to 0 these priors include dirichlet type priors the marginal posterior distribution of theta given x 1 ldots x n is computed the mean of the posterior is taken as the estimate of theta

resultants and the algebraicity of the join pairing on chow varieties the chow van der waerden approach to algebraic cycles via resultants is used to give a purely algebraic proof for the algebraicity of the complex suspension the algebraicity of the join pairing on chow varieties then follows the approach implies a more algebraic proof of lawson s complex suspension theorem in characteristic 0 the continuity of the action of the linear isometries operad on the group completion of the stable chow variety is a consequence

on the complexity of finding a largest common subtree of bounded degree the largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship the problem is known to be np hard for unordered trees in this paper we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant d we present an o nd time algorithm where n is the maximum size of two input trees which improves a previous o n2d time algorithm we also present an o h222h1d2h d1poly n time algorithm where h is the maximum height of two input trees

an algebraic view of the relation between largest common subtrees and smallest common supertrees the relationship between two important problems in tree pattern matching the largest common subtree and the smallest common supertree problems is established by means of simple constructions which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them and vice versa these constructions are the same for isomorphic homeomorphic topological and minor embeddings they take only time linear in the size of the trees and they turn out to have a clear algebraic meaning

algebraic cycles on real varieties and z 2 equivariant homotopy theory in this paper the spaces of algebraic cycles on a real projective variety x are studied as z 2 spaces under the action of the galois group gal c r in particular the equivariant homotopy type of the group of algebraic p cycles zp pc is computed a version of lawson homology for real varieties is proposed the real lawson homology groups are computed for a class of real varieties

computing the maximum agreement of phylogenetic networks we introduce the maximum agreement phylogenetic subnetwork problem masn for finding branching structure shared by a set of phylogenetic networks we prove that the problem is np hard even if restricted to three phylogenetic networks and give an o n2 time algorithm for the special case of two level 1 phylogenetic networks where n is the number of leaves in the input networks and where n is called a level f phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of n containing at most f nodes with indegree 2 we also show how to extend our technique to yield a polynomial time algorithm for any two level f phylogenetic networks n1 n2 satisfying f o log n more precisely its running time is o v n1 v n2 2f1 f2 where v ni and fi denote the set of nodes in ni and the level of ni respectively for i 1 2

sparse dynamic programming for evolutionary tree comparison constructing evolutionary trees for species sets is a fundamental problem in biology unfortunately there is no single agreed upon method for this task and many methods are in use current practice dictates that trees be constructed using different methods and that the resulting trees should be compared for consensus it has become necessary to automate this process as the number of species under consideration has grown we study one formalization of the problem the maximum agreement subtree mast problem the mast problem is as follows given a set a and two rooted trees ct 0 and ct 1 leaf labeled by the elements of a find a maximum cardinality subset b of a such that the topological restrictions of ct 0 and ct 1 to b are isomorphic in this paper we will show that this problem reduces to unary weighted bipartite matching uwbm with an o n 1 o 1 additive overhead we also show that uwbm reduces linearly to mast thus our algorithm is optimal unless uwbm can be solved in near linear time the overall running time of our algorithm is o n 1 5 log n improving on the previous best algorithm which runs in o n 2 we also derive an o n c sqrt log n time algorithm for the case of bounded degrees whereas the previously best algorithm runs in o n 2 as in the unbounded case

enumeration of bc subtrees of trees a bc tree block cutpoint tree is a tree with at least two vertices where the distance between any two leaves is even motivated from the study of the core of a graph bc trees form an interes

tree contractions and evolutionary trees an evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species evolutionary trees are useful for modeling the evolutionary history of species an agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees we give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees t1 and t2 with n leaves each if the maximum degree d of these trees is bounded by a constant the time complexity is o n log2n and is within a log n factor of optimal for general d this algorithm runs in o nd2 log d log2 n time or alternatively in o nd sqrt d log 3 n time

novel transformation techniques using q heaps with applications to computational geometry using the notions of q heaps and fusion trees developed by fredman and willard we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces in particular we develop a fast fractional cascading technique which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by o log epsilon n for some constant epsilon 0 where n is the total size of all the lists stored in the tree we apply the fast fractional cascading technique in combination with the other techniques to derive the first linear space sublogarithmic time algorithms for two fundamental geometric retrieval problems orthogonal segment intersection and rectangular point enclosure

an o n log n algorithm for the maximum agreement subtree problem for binary trees the maximum agreement subtree problem is the following given two rooted trees whose leaves are drawn from the same set of items e g species find the largest subset of these items so that the portions of the two trees restricted to these items are isomorphic we consider the case which occurs frequently in practice i e the case when the trees are binary and give an o nlog n time algorithm for this problem

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

algebraic cycles representing cohomology operations in this paper we will show that certain universal homology classes which are fundamental in topology are algebraic to be specific the products of eilenberg maclane spaces mathcal k 2q equiv k mathbf z 2 times k mathbf z 4 times cdots times k mathbf z 2q have models which are limits of complex projective varieties precisely we have mathcal k 2q varinjlim nolimits d rightarrow infty mathcal c q d mathbf p n where mathcal c q d mathbf p n denotes the chow variety of effective cycles of codimension q and degree d on mathbf p mathbf c n it is natural to ask which elements in the homology of mathcal k 2q are represented by algebraic cycles in these approximations in this paper we find such representations for the even dimensional classes which are known as steenrod squares as well as their pontrjagin and join products these classes are dual to the cohomology classes which correspond to the basic cohomology operations also known as the steenrod squares

completions and fibrations for topological monoids we show that for a certain class of topological monoids there is a homotopy equivalence between the homotopy theoretic group completion m of a monoid m in that class and the topologized grothendieck group m associated to m the class under study is broad enough to include the chow monoids effective cycles associated to a projective algebraic variety and also the infinite symmetric products of finite cw complexes we associate principal fibrations to the completions of pairs of monoids showing the existence of long exact sequences for the naive approach to lawson homology fri91 lf91 a another proof of the eilenberg steenrod axioms for the functors x sp x in the category of finite cw complexes dold thom theorem dt56 is obtained

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3

bayesian inference for semiparametric binary regression abstract we propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale predictors enter linearly we demonstrate bayesian inference calculations in this model by modifying the dirichlet process we obtain a natural prior measure over this semiparametric model and we use polya sequence theory to formulate this measure in terms of a finite number of unobserved variables we design a markov chain monte carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer

a bayesian semiparametric model for random effects meta analysis in meta analysis there is an increasing trend to explicitly acknowledge the presence of study variability through random effects models that is one assumes that for each study there is a study specific effect and one is observing an estimate of this latent variable in a random effects model one assumes that these study specific effects come from some distribution and one can estimate the parameters of this distribution as well as the study specific effects themselves this distribution is most often modeled through a parametric family usually a family of normal distributions the advantage of using a normal distribution is that the mean parameter plays an important role and much of the focus is on determining whether or not this mean is 0 for example it may be easier to justify funding further studies if it is determined that this mean is not 0 typically this normality assumption is made for the sake of convenience rather than from some theoretical justification and may not actually hold w

delaunay triangulations in o sort n time and more we present several results about delaunay triangulations dts and convex hulls in transdichotomous and hereditary settings i the dt of a planar point set can be computed in expected time o sort n on a word ram where sort n is the time to sort n numbers we assume that the word ram supports the shuffle operation in constant time ii if we know the ordering of a planar point set in x and in y direction its dt can be found by a randomized algebraic computation tree of expected linear depth iii given a universe u of points in the plane we construct a data structure d for delaunay queries for any p s u d can find the dt of p in expected time o vpv log log vuv iv given a universe u of points in 3 space in general convex position there is a data structure d for convex hull queries for any p s u d can find the convex hull of p in expected time o vpv log log vuv 2 v given a convex polytope in 3 space with n vertices which are colored with g 2 colors we can split it into the convex hulls of the individual color classes in expected time o n log log n 2 the results i iii generalize to higher dimensions where the expected running time now also depends on the complexity of the resulting dt we need a wide range of techniques most prominently we describe a reduction from dts to nearest neighbor graphs that relies on a new variant of randomized incremental constructions using dependent sampling

maximum agreement subtree in a set of evolutionary trees metrics and efficient algorithms the maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species an agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent under a suitable definition in all given evolutionary trees recently dynamic programming ideas were used to provide polynomial time algorithms for finding a maximum homeomorphic agreement subtree of two trees generalizing these methods to sets of more than two trees yields algorithms that are exponential in the number of trees unfortunately it turns out that in reality one is usually presented with more than two trees sometimes as many as thousands of trees in this paper we prove that the maximum homeomorphic agreement subtree problem is cal np complete for three trees with unbounded degrees we then show an approximation algorithm of time o kn5 for choosing the species that are not in a maximum agreement subtree of a set of k trees our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution while the set of evolutionary trees may be large in practice the trees usually have very small degrees typically no larger than three we develop a new method for finding a maximum agreement subtree of k trees of which one has degree bounded by d this new method enables us to find a maximum agreement subtree in time o knd 1 n2d

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

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

the topology of rational functions and divisors of surfaces segal studied the homotopy types of the spaces of holomorphic functions of the 2 sphere s 2 of closed surfaces of higher genus and of the spaces of divisors of these surfaces we continue segal s program by describing the entire stable homotopy types of these spaces in terms of the homotopy types of more familiar spaces

quaternionic algebraic cycles and reality in this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real brauer severi varieties under the action of the galois group gal c r appropriate stabilizations of these spaces yield two equivariant spectra the first one classifies dupont seymour s quaternionic k theory and the other one classifies an equivariant cohomology theory 3 which is a natural recipient of characteristic classes kh x 3 x for quaternionic bundles over real spaces x

efficient seed computation revisited the notion of the cover is a generalization of a period of a string and there are linear time algorithms for finding the shortest cover the seed is a more complicated generalization of periodicity it is a cover of a superstring of a given string and the shortest seed problem is of much higher algorithmic difficulty the problem is not well understood no linear time algorithm is known in the paper we give linear time algorithms for some of its versions computing shortest left seed array longest left seed array and checking for seeds of a given length the algorithm for the last problem is used to compute the seed array of a string i e the shortest seeds for all the prefixes of the string in o n 2 time we describe also a simpler alternative algorithm computing efficiently the shortest seeds as a by product we obtain an o nlog n m time algorithm checking if the shortest seed has length at least m and finding the corresponding seed we also correct some important details missing in the previously known shortest seed algorithm iliopoulos et al 1996 14

inferring evolutionary trees with strong combinatorial evidence we consider the problem of inferring the evolutionary tree of a set of n species we propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence let q be a set of resolved quartets defined on the studied species the method computes the unique maximum subset q of q which is equivalent to a tree and outputs the corresponding tree as an estimate of the species phylogeny we use a characterization of the subset q due to bandelt and dress adv appl math 7 1986 309 343 to provide an o n4 incremental algorithm for this variant of the np hard quartet consistency problem moreover when chosing the resolution of the quartets by the four point method fpm and considering the cavender farris model of evolution we show that the convergence rate of the q method is at worst polynomial when the maximum evolutive distance between two species is bounded we complete these theoretical results by an experimental study on real and simulated data sets the results show that i as expected the strong combinatorial constraints it imposes on each edge leads the q method to propose very few incorrect edges ii more surprisingly the method infers trees with a relatively high degree of resolution

bayesian estimation in the symmetric location problem let x i i for i 1 n where the i s are i i d f and f is symmetric about 0 f is assumed unknown or only partially known and the problem is to estimate priors are put on the pair f the priors on f are obtained from doksum s neutral to the right priors and include symmetrized dirichlet priors the marginal posterior distribution of given x1 xnis computed and its general properties studied it is found that for certain classes of distributions of the i s the posterior distribution of is for all large n a point mass at the true value of if the distribution of the i s is not exactly symmetric the bayes estimates can behave very poorly

bayesian nonparametric estimation of the median part ii asymptotic properties of the estimates for data theta varepsilon i i 1 ldots n where varepsilon i are i i d sim f with the median of f equal to 0 but f otherwise unknown it is desired to estimate theta in doss 1985 priors are put on the pair f theta the marginal posterior distribution of theta is computed and the mean of the posterior is taken as the estimate of theta in the present paper a frequentist point of view is adopted the consistency properties of the bayes estimates computed in doss 1985 are investigated when the prior on f is of the dirichlet type any f whose median is 0 is in the support of these priors it is shown that if the varepsilon i are i i d from a discrete distribution then the bayes estimates are consistent however if the distribution of the varepsilon is is continuous the bayes estimates can be inconsistent

efficient algorithms for shortest partial seeds in words abstract a factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w a factor u is a seed of w if it is a cover of a superstring of w covers and seeds extend the classical notions of periodicity we introduce a new notion of partial seed that is a factor covering as a seed at least positions in a given word we use the cover suffix tree recently introduced in the context of partial covers kociumaka et al 2015 13 an o n log n time algorithm constructing such a tree is known however it appears that partial seeds are more complicated than partial covers our algorithms require algebraic manipulations of special functions related to edges of the modified cover suffix tree and the border array we present a procedure for computing shortest partial seeds that works in o n time if the cover suffix tree is already given this is a full version which includes all the proofs of a paper that appeared at cpm 2014 1

tight bounds on the solutions of multidimensional divide and conquer maximin recurrences abstract in this paper upper bounds are presented for the solution of the following multidimensional divide and conquer maximin recurrence g n max n 1 n 2 n p n n 1 n 2 n p 1 i 1 p g n i smin 1 i p k f n i where p 2 1 k f is an arbitrary nondecreasing function and smin 1 i p k f n i denotes the sum of the smallest k numbers among f n 1 f n 2 and f n p all the presented upper bounds are at most log 2 k p times the exact solution of g n the derivation of the upper bounds is based on properties of partition trees for k 1 and k p 1 we obtain respectively two of the recurrences previously studied by alonso et al siam j discrete math 8 1995 428 447 in both of these two cases our results improve theirs

homology operations on a new infinite loop space boyer et al 1 defined a new infinite loop space structure on the space mo hrni k z 2n such that the total chern class map bu mo is an infinite loop map this is a sort of riemann roch theorem without denominators for example it implies fulton macpherson s theorem that the chern classes of the direct image of a vector bundle e under a given finite covering map are determined by the rank and chern classes of e we compute the dyer lashof operations on the homology of mo they provide a new explanation for kochman s calculation of the operations on the homology of bu and they suggest a possible characterization of the infinite loop structure on mo the total chern class of the direct sum of two vector bundles c e g f is not the sum but rather the product of the total chern classes c e e f c e c f in other words for a topological space x the total chern class map c k x fnl h2n x z is not a homomorphism of abelian groups for the obvious additive group structure on the set ln 1 h2n x z but only for a multiplicative abelian group structure on it let m x 1 hn 1 h2n x z with the appropriate multiplicative group structure since the group kox is the 0th term of a cohomology theory k x 0 connective k theory it is natural to expect that m x is also the 0th term of a cohomology theory m x with the property that the map c k x kox m x extends to a map of cohomology theories k x m x recently boyer lawson lima filho mann and michelsohn 1 defined a cohomology theory m with this property if mo denotes the infinite loop space such that x mo m x then mo fl 1 k z 2n as a space and we know the h space structure on mo it is not the usual h space structure on a product of eilenberg mac lane spaces in this paper we continue the analysis of the infinite loop space mo by computing the araki kudo dyer lashof operations on h mo z p the computation starts with kochman s calculation of these operations on h bu 4 but there is a pleasant side effect to our analysis we only need kochman s calculation in the lowest nontrivial dimension and with that as input the rich structure of mo it is the multiplicative e space which underlies one component of an e ring space allows us to find all the operations on h mo and hence on h bu in particular one could say that the existence of bllmm s theory gives a conceptual explanation for the simplicity of kochman s formulas received by the editors august 20 1993 1991 mathematics subject classification primary 55s12 secondary 55p47 this paper was supported by an nsf postdoctoral fellowship 1995 american mathematical society

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors

verification and sensitivity analysis of minimum spanning trees in linear time komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree the total computational work required by his method is much larger than linear however this paper describes a linear time algorithm for verifying a minimum spanning tree this algorithm combines the result of komlos with a preprocessing and table look up method for small subproblems and with a previously known almost linear time algorithm additionally an optimal deterministic algorithm and a linear time randomized algorithm for sensitivity analysis of minimum spanning trees are presented

algorithms for finding the weight constrained k longest paths in a tree and the length constrained k maximum sum segments of a sequence in this work we obtain the following new results given a tree t v e with a length function e r and a weight function w e r a positive integer k and an interval l u the weight constrainedklongest paths problem is to find the k longest paths among all paths in t with weights in the interval l u we show that the weight constrainedklongest paths problem has a lower bound w vlogv k in the algebraic computation tree model and give an o vlogv k time algorithm for it given a sequence a a 1 a 2 a n of numbers and an interval l u we define the sum and length of a segment a i j to be a i a i 1 a j and j i 1 respectively the length constrainedkmaximum sum segments problem is to find the k maximum sum segments among all segments of a with lengths in the interval l u we show that the length constrainedkmaximum sum segments problem can be solved in o n k time