on the integral cohomology of wreath products we use the techniques pioneered by nakaoka to study the integral cohomology of wreath products the situation is considerably more complicated than for field coefficients we describe the cohomology of h wr c for c cyclic of prime order and any h whose cohomology is finitely generated in each degree we discuss various related results and conjectures concerning the exponent of integral cohomology of finite groups these include a conjecture of a adem recently solved by j pakianathan conjectures of j carlson one solved in this work and some of our own one example given is a 2 group whose index four subgroups have non trivial intersection but whose integral cohomology has exponent four answering a question posed in 8

cohomology of infinitesimal and discrete groups an infinitesimal algebraic group over a field k is a connected algebraic group scheme whose coordinate ring is a finite dimension al k algebra if one begins with a reductive algebraic group g defined over fp then one has a close relationship between the representation theory of g that of its infinitesimal subgroups g defined as the kernels of the frobenius endomorphisms rr g g and that of its finite chevalley subgroups g fq of fq rational points q pd a basic theorem of cline et al i 9 theorem 6 6 relates the cohomology of g in a rational representation to that of the finite groups g fq related work of cline et al 6 and of the authors 1 16 relates the cohomology of g to that of its infinitesimal subgroups a determination of the cohomology of the first infinitesimal subgroup g 1 of g with trivial coefficients has enabled the authors in 14 to make certain explicit cohomology calculations for the finite groups g fq with certain nontrivial coefficients in this paper we continue our study of infinitesimal subgroups of simple algebraic groups by proving various qualitative properties of their cohomology and by extending our computational knowledge in particular we provide a computation which applies in a range of degrees to chevalley groups over the prime field we also investigate the cohomology of infinitesimal subgroups of nilpotent groups enabling us for example to determine the cohomology of their lie algebras in certain cases we apply this lie algebra cohomology computation to determine the integral cohomology of various torsion free nilpotent groups modulo small prime torsion thereby extending a theorem of dwyer 12 in more detail the paper begins in sect 1 with a spectral sequence converging to the cohomology of the first infinitesimal subgroup g which was previously studied in 14 from this spectral sequence it easily follows that h g1 m is a noetherian h g1 k module for each finite dimensional rational gl module m we then apply the work of andersen and jantzen 1 on the gl cohomology of induced modules to obtain the analogous result for the second infinitesimal subgroup gz our analysis also permits a determination of the generic

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

cyclicity and invariant subspaces in dirichlet spaces let be a positive finite measure on the unit circle and d the associated dirichlet space the generalized brown shields conjecture asserts that an outer function f d is cyclic if and only if c z f 0 where c is the capacity associated with d and z f is the zero set of f in this paper we prove that this conjecture is true for measures with countable support we also give in this case a complete and explicit characterization of invariant subspaces

experiments in quadratic 0 1 programming we present computational experience with a cutting plane algorithm for 0 1 quadratic programming without constraints our approach is based on a reduction of this problem to a max cut problem in a graph and on a partial linear description of the cut polytope

the cohomology of the integer heisenberg groups abstract we give a closed formula for the cohomology groups of the standard integer lattice in the simply connected heisenberg lie group of dimension 2 n 1 n z we also provide a recursion relation involving n for these cohomology groups

derivations the lawrence sullivan interval and the fiorenza manetti mapping cone we describe the rational homotopy type of any component of the based mapping space map x y as an explicit l algebra defined on the desuspended and positive derivations between quillen models of x and y when considering the lawrence sullivan model of the interval we obtain an l model of the contractible path space of y we then relate this in a geometrical and natural manner to the l structure on the fiorenza manetti mapping cone of any differential graded lie algebra morphism two in principal different algebraic objects in which bernoulli numbers appear

on fox and augmentation quotients of semidirect products let g be a group which is the semidirect product of a normal subgroup n and some subgroup t let in g n 1 denote the powers of the augmentation ideal i g of the group ring z g using homological methods the groups qn g h in 1 g i h in g i h h g n t are functorially expressed in terms of enveloping algebras of certain lie rings associated with n and t in the following cases for n 4 and arbitrary g n t except from one direct summand of q4 g n and for all n 2 if certain filtration quotients of n and t are torsion free

cohomology of nilpotent groups of class 2 abstract we compute the cohomology rings of a number of nilpotent groups of class 2 for appropriate coefficients and we do some more sample calculations of various cohomology groups the basic tool is a suitable small free resolution for an arbitrary nilpotent group of class 2 constructed in a previous paper

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

facets of the clique partitioning polytope a subseta of the edge set of a graphg v e is called a clique partitioning ofg is there is a partition of the node setv into disjoint setsw 1 w k such that eachw i induces a clique i e a complete but not necessarily maximal subgraph ofg and such thata 1 uv u v w i u v given weightsw e for alle e the clique partitioning problem is to find a clique partitioninga ofg such that e a w e is as small as possible this problem known to be hard see wakabayashi 1986 comes up for instance in data analysis and here the underlying graphg is typically a complete graph in this paper we study the clique partitioning polytope of the complete graphk n i e is the convex hull of the incidence vectors of the clique partitionings ofk n we show that triangles 2 chorded odd cycles 2 chorded even wheels and other subgraphs ofk n induce facets of the theoretical results described here have been used to design an empirically efficient cutting plane algorithm with which large real world instances of the clique partitioning problem could be solved these computational results can be found in grotschel and wakabayashi 1989

extended formulations for the a cut problem letg v e be an undirected graph anda v we consider the problem of finding a minimum cost set of edges whose deletion separates every pair of nodes ina we consider two extended formulations using both node and edge variables an edge variable formulation has previously been considered for this problem chopra and rao 1991 cunningham 1991 we show that the lp relaxations of the extended formulations are stronger than the lp relaxation of the edge variable formulation even with an extra class of valid inequalities added this is interesting because while the lp relaxations of the extended formulations can be solved in polynomial time the lp relaxation of the edge variable formulation cannot we also give a class of valid inequalities for one of the extended formulations computational results using the extended formulations are performed

on the length of the conjugacy classes of finite groups abstract let g be a finite group the question of how certain arithmetical conditions on the degrees of the irreducible characters of g influence the group structure was studied by several authors our purpose here is to impose analogous conditions on the lengths of the conjugacy classes of g and to describe the group structure under these conditions

cluster analysis and mathematical programming given a set of entities cluster analysis aims at finding subsets called clusters which are homogeneous and or well separated as many types of clustering and criteria for homogeneity or separation are of interest this is a vast field a survey is given from a mathematical programming viewpoint steps of a clustering study types of clustering and criteria are discussed then algorithms for hierarchical partitioning sequential and additive clustering are studied emphasis is on solution methods i e dynamic programming graph theoretical algorithms branch and bound cutting planes column generation and heuristics

fedosov dg manifolds associated with lie pairs given any pair l a of lie algebroids we construct a differential graded manifold l 1 oplus l a q which we call fedosov dg manifold we prove that the homological vector field q constructed on l 1 oplus l a by the fedosov iteration method arises as a byproduct of the poincare birkhoff witt map established in 18 finally using the homological perturbation lemma we establish a quasi isomorphism of dolgushev fedosov type the differential graded algebras of functions on the dg manifolds a 1 d a and l 1 oplus l a q are homotopy equivalent

polynomiality properties of group extensions with a torsion free abelian kernel abstract in studying torsion free nilpotent groups of class 2 it is a key fact that each central group extension z n e z mis representable by abilinearcocycle so for investigating nilpotent groups of higher class it is natural to ask for a generalization of this fact namely when z mis replaced by sometorsion free nilpotentgroupgand z nby sometorsion free abeliangroupbwithnilpotent g action in this paper we study a suitable notion of bi polynomialcocycles in the strong sense of polynomiality introduced by passi and prove the desiredrepresentability theorem 4 3 this was known before only forcentralextensions withdivisiblekernel and with kernel z ifgis abelian nilpotent of class 2 or if the quotients of the lower central series ofgare torsion free our representability result implies aconvergence theoremfor an approximation ofh2 g b bypolynomial cohomology groups 4 4 since the latter ones are well accessible to computation one obtains a formula forh2 g b in terms of a presentation ofgwhich can be evaluated by integral matrix calculus more precisely a given presentation ofgamounts to a three term cochain complex consisting offinitely generated free z modulesif the groupsgandbare finitely generated the cohomology of this complex is identified withh2 g b in such a way that representing 2 cocycles are explicitly given in terms of integer valued rational polynomial functions 6 4 as an application we establish an explicitbijectionbetween torsion free nilpotentgroupsand z torsion free nilpotentlie ringsboth finitely generated and nilpotent ofclass 3 7 2 in case a given group extension is representable by a polynomial cocycle we also determine theminimal degreeof polynomiality for which this holds indeed dropping the assumption thatgis torsion free nilpotent we give anintrinsic characterizationof all group extensions with torsion free abelian kernel which are representable by a polynomial cocycle of degree n provided that the cokernel is finitely generated and acts nilpotently on the kernel 4 2 thus a polynomiality theory for group extensions as asked for by passi is now achieved in case the kernel istorsion free a motivation for this apart from calculatingh2 g b explicitly comes from a question posed by j milnor in 1977 namely whether all finitely generated torsion free virtually polycyclic groups arise as fundamental groups of compact complete affinely flat manifolds even the case of torsion free nilpotent groups is interesting but far from being understood notably since counterexamples of this type have recently been discovered a connection of milnor s question for nilpotent groups with polynomial constructions was first indicated in the work of p igodt and k b lee recently a very close connection of this type was established and anobstruction theorydeveloped for the problem in terms of polynomial cohomology on the other hand polynomiality properties of extensions with atorsionkernel are closely related todimension subgroups as was observed by passi in the case ofcentralextensions an extension of this idea to thenoncentralcase is provided by theorem 3 4 below this might be of interest in connection with the recent discovery of gupta and kuz min that the quotient groupdn g n g is an abelian normal but in general noncentral subgroup ofg n g moreover we obtain afunctorial equivalencebetween extensions oftorsion free nilpotent groupsand of z torsion free nilpotent modules 5 1 this improves a general result of reiner and roggenkamp in the special situation of torsion free nilpotent groups as applications it yields an inductive cohomological description ofautomorphism groupsof torsion free nilpotent groups 9 and a generalization of the classicaldold kan equivalence between simplicial abelian groups and chain complexes of abelian groups to simplicial groups of class 2 applications in localization theory are also to be expected namely to questions concerning the genus of torsion free nilpotent groups all the above mentioned results are based on the more technical work of the first section there also generalizations of theorems of witt and quillen are obtained concerning certain lie algebras associated with groups these results might be of independent interest

a least squares algorithm for fitting additive trees to proximity data a least squares algorithm for fitting additive trees to proximity data is described the algorithm uses a penalty function to enforce the four point condition on the estimated path length distances the algorithm is evaluated in a small monte carlo study finally an illustrative application is presented

on the perturbation algebra we introduce a certain differential graded bialgebra neither commutative nor cocommutative that governs perturbations of a differential on complexes supplied with an abstract hodge decomposition this leads to a conceptual treatment of the homological perturbation lemma and its multiplicative version as an application we give an explicit form of the decomposition theorem for a algebras and a modules and more generally for twisted objects in differential graded categories

cohomology of metacyclic groups group n by a finite cyclic group k using homological perturbation theory we introduce the beginning of a free resolution of the integers z over the group ring zg of g in such a way that the resolution reflects the structure of g as an extension of n by k and we use this resolution to compute the additive structure of the integral cohomology of g in many cases we proceed by first establishing a number of special cases thereafter constructing suitable cohomology classes thereby obtaining a lower bound then computing characteristic classes introduced in an earlier paper and finally exploiting these classes obtaining upper bounds for the cohomology via the integral cohomology spectral sequence of the extension e the calculation is then completed by comparing the two bounds

a simulated annealing algorithm for the clustering problem abstract in this paper we discuss the solution of the clustering problem usually solved by the k means algorithm the problem is known to have local minimum solutions which are usually what the k means algorithm obtains the simulated annealing approach for solving optimization problems is described and is proposed for solving the clustering problem the parameters of the algorithm are discussed in detail and it is shown that the algorithm converges to a global solution of the clustering problem we also find optimal parameters values for a specific class of data sets and give recommendations on the choice of parameters for general data sets finally advantages and disadvantages of the approach are presented

experiments in projection and clustering by simulated annealing simulated annealing is a stochastic relaxation algorithm which has been used successfully to optimize functions of many variables this paper analyzes the simulated annealing algorithm when applied to the minimization of functions from two common problems encountered in exploratory pattern analysis projection and clustering the projection is a nonlinear mapping of patterns in high dimension to two dimensions the simulated annealing mapping is compared to gradient descent minimization of the same objective function as well as eigenvector projection the simulated annealing clustering is compared to a k means algorithm empirical results show that simulated annealing can produce results as good as those obtained by conventional methods but are impractical for small data sets because of the high computational cost simulated annealing does in the case of the mapping problem yield a better optimization and better retained structure for large data sets containing tight gaussian clusters

on the cohomology of the holomorph of a finite cyclic group abstract we determine the mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2

quadratic maps between modules we introduce a notion of r quadratic maps between modules over a commutative ring r which generalizes several classical notions arising in linear algebra and group theory on a given module m such maps are represented by r linear maps on a certain module pr2 m the structure of this module is described in term of the symmetric tensor square symr2 m the degree 2 component r2 m of the divided power algebra over m and the ideal i2 of r generated by the elements r2 r r r the latter is shown to represent quadratic derivations on r which arise in the theory of modules over square rings this allows to extend the classical notion of nilpotent r group of class 2 with coefficients in a 2 binomial ring r to any ring r we provide a functorial presentation of i2 and several exact sequences embedding the modules pr2 m and r2 m

formulations and valid inequalities for the node capacitated graph partitioning problem we investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition the objective is to minimize the sum of the costs of the edges between the subsets of the partition this problem has a variety of applications for instance in the design of electronic circuits and devices we present alternative integer programming formulations for this problem and discuss the links between these formulations having chosen to work in the space of edges of the multicut we investigate the convex hull of incidence vectors of feasible multicuts in particular several classes of inequalities are introduced and their strength and robustness are analyzed as various problem parameters change

open closed homotopy algebra in mathematical physics in this paper we discuss various aspects of open closed homotopy algebras ochas presented in our previous paper inspired by zwiebach s open closed string field theory but that first paper concentrated on the mathematical aspects here we show how an ocha is obtained by extracting the tree part of zwiebach s quantum open closed string field theory we clarify the explicit relation of an ocha with kontsevich s deformation quantization and with the b models of homological mirror symmetry an explicit form of the minimal model for an ocha is given as well as its relation to the perturbative expansion of open closed string field theory we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

computational study of large scale p median problems given a directed graph g v a the p median problem consists of determining p nodes the median nodes minimizing the total distance from the other nodes of the graph we present a branch and cut and price algorithm yielding provably good solutions for instances with v 3795 key ingredients of the algorithm are a delayed column and row generation technique exploiting the special structure of the formulation to solve the lp relaxation and cutting planes to strengthen the formulation and limit the size of the enumeration tree

algebraic models of non connected spaces and homotopy theory of l algebras we develop a homotopy theory of l algebras based on the lawrence sullivan construction a complete differential graded lie algebra which as we show satisfies the necessary properties to become the right cylinder in this category as a result we obtain a general procedure to algebraically model the rational homotopy type of non connected spaces 2012 elsevier ltd

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

structure of finite groups under certain arithmetical conditions on class sizes abstract let g be a finite solvable group we assume that the set of conjugacy class sizes of g is 1 m n m k with m and n coprime positive integers greater than 1 and k a divisor of n then we obtain several properties on the structure of g

a recursive lagrangian method for clustering problems abstract the problem of partitioning a finite set of objects into subsets or clusters so as to optimize an objective function is treated it is shown that for the particular case where all the objects lie upon a line the clustering problem may be solved exactly by an algorithm utilizing only lagrangian relaxation and dynamic programming by exploiting the approximately unimodal shape of the envelope of optimal objective values a search procedure in the space is devised and this allows the solution in reasonable computation time of the combinatorially large problem several examples are presented and the method is applied to one set of noncollinear data which is first transformed so as to become collinear further promising directions for computational enhancement are noted the important aspects of computer implementation are given

multi derivation maurer cartan algebras and sh lie rinehart algebras abstract we extend the classical characterization of a finite dimensional lie algebra g in terms of its maurer cartan algebra the familiar differential graded algebra of alternating forms on g with values in the ground field endowed with the standard lie algebra cohomology operator to sh lie rinehart algebras to this end we first develop a characterization of sh lie rinehart algebras in terms of differential graded cocommutative coalgebras and lie algebra twisting cochains that extends the nowadays standard characterization of an ordinary sh lie algebra equivalently l algebra in terms of its associated generalized cartan chevalley eilenberg coalgebra our approach avoids any higher brackets but reproduces these brackets in a conceptual manner the new technical tool we develop is a notion of filtered multi derivation chain algebra somewhat more general than the standard concept of a multicomplex endowed with a compatible algebra structure the crucial observation just as for ordinary lie rinehart algebras is this for a general sh lie rinehart algebra the generalized cartan chevalley eilenberg operator on the corresponding graded algebra involves two operators one coming from the sh lie algebra structure and the other one from the generalized action on the corresponding algebra the sum of the two operators is defined on the algebra while the operators are individually defined only on a larger ambient algebra we illustrate the structure with quasi lie rinehart algebras

variations on a theorem by alan camina on conjugacy class sizes let g be a finite group we extend alan camina s theorem on conjugacy class sizes which asserts that if the conjugacy class sizes of g are exactly 1 p a q b p a q b for two primes p and q t heng is nilpotent if we assume that g is solvable we show that when the set of conjugacy class sizes of g is 1 m n mn with m and n arbitrary positive integers such that m n 1 then g is nilpotent and m p a and n q b for two primes p and q

a tabu search based heuristic for clustering abstract this paper considers a clustering problem where a given data set is partitioned into a certain number of natural and homogeneous subsets such that each subset is composed of elements similar to one another but different from those of any other subset for the clustering problem a heuristic algorithm is exploited by combining the tabu search heuristic with two complementary functional procedures called packing and releasing procedures the algorithm is numerically tested for its effectiveness in comparison with reference works including the tabu search algorithm the k means algorithm and the simulated annealing algorithm

min cut clustering we describe a decomposition framework and a column generation scheme for solving a min cut clustering problem the subproblem to generate additional columns is itself an np hard mixed integer programming problem we discuss strong valid inequalities for the subproblem and describe some efficient solution strategies computational results on compiler construction problems are reported

homotopy algebras inspired by classical open closed string field theory we define a homotopy algebra associated to classical open closed strings we call it an open closed homotopy algebra ocha it is inspired by zwiebach s open closed string field theory and also is related to the situation of kontsevich s deformation quantization we show that it is actually a homotopy invariant notion for instance the minimal model theorem holds also we show that our open closed homotopy algebra gives us a general scheme for deformation of open string structures a algebras by closed strings l algebras

the nonabelian tensor square and schur multiplicator of nilpotent groups of class 2 abstract the nonabelian tensor square and the schur multiplicator are determined for arbitrary groups of class 2 in a closed form a functorial description is given in terms of a polynomial quotient of the integral group ring as well as a more explicit formula for finite groups which can be evaluated by matrix calculus this is carried out for 2 generator groups also some homotopical data of the suspended classifying space of class 2 groups are derived the approach is based on the use of polynomial maps and constructions in the sense of passi

on the heegaard floer homology of a surface times a circle we make a detailed study of the heegaard floer homology of the product of a closed surface sg of genus g with s1 we determine completely in the case which for g3 was previously unknown we show that in this case hf8 is closely related to the cohomology of the total space of a certain circle bundle over the jacobian torus of sg and furthermore that contains nontrivial 2 torsion whenever g3 and this is the first example known to the authors of torsion in coefficient heegaard floer homology our methods also give new information on the action of h1 sg s1 on when is nonzero

perturbation theory and free resolutions for nilpotent groups of class 2 abstract using homological perturbation theory we construct a small free resolution for any nilpotent group g of class 2 which reflects the structure of g as a central extension of an abelian group by an abelian group

a tabu search approach for the minimum sum of squares clustering problem in this paper a tabu search based clustering approach called ts clustering is proposed to deal with the minimum sum of squares clustering problem in the ts clustering algorithm five improvement operations and three neighborhood modes are given the improvement operation is used to enhance the clustering solution obtained in the process of iterations and the neighborhood mode is used to create the neighborhood of tabu search the superiority of the proposed method over some known clustering techniques is demonstrated for artificial and real life data sets

a comparison of heuristic procedures for minimum within cluster sums of squares partitioning perhaps the most common criterion for partitioning a data set is the minimization of the within cluster sums of squared deviation from cluster centroids although optimal solution procedures for within cluster sums of squares wcss partitioning are computationally feasible for small data sets heuristic procedures are required for most practical applications in the behavioral sciences we compared the performances of nine prominent heuristic procedures for wcss partitioning across 324 simulated data sets representative of a broad spectrum of test conditions performance comparisons focused on both percentage deviation from the best found wcss values as well as recovery of true cluster structure a real coded genetic algorithm and variable neighborhood search heuristic were the most effective methods however a straightforward two stage heuristic algorithm hk means also yielded exceptional performance a follow up experiment using 13 empirical data sets from the clustering literature generally supported the results of the experiment using simulated data our findings have important implications for behavioral science researchers whose theoretical conclusions could be adversely affected by poor algorithmic performances

an exact solution procedure for a cluster hub location problem abstract this paper proposes a new mip model formulation and a new solution procedure for the hub network design problem under a non restrictive policy introduced by sung and jin sung c s jin h w 2001 dual based approach for a hub network design problem under non restrictive policy european journal of operational research 132 1 88 105 the model formulation contains significantly fewer variables so that optimal solutions for the lp relaxation of the model can be determined for large instances using standard procedures for lp models furthermore the lp relaxation provides very tight lower bounds computational results are given which demonstrate that the new model formulation allows for solving much larger instances it turned out that the new exact solution procedure which utilises the new model formulation is faster than the heuristic proposed by sung and jin 2001 it is also shown that the problem is np hard

a tabu search approach to the clustering problem in this paper we consider the problem of clustering m objects into c clusters the objects are represented by points in an n dimensional euclidean space and the objective is to classify these m points into c clusters such that the distance between points within a cluster and its center which is to be found is minimized the problem is a nonconvex program that has many local minima it has been studied by many researchers and the most well known algorithm for solving it is the k means algorithm in this paper we develop a new algorithm for solving this problem based on a tabu search technique preliminary computational experience on the developed algorithm are encouraging and compare favorably with both the k means and the simulated annealing algorithms

a tabu search heuristic procedure in markov chain bootstrapping abstract markov chain theory is proving to be a powerful approach to bootstrap finite states processes especially where time dependence is non linear in this work we extend such approach to bootstrap discrete time continuous valued processes to this purpose we solve a minimization problem to partition the state space of a continuous valued process into a finite number of intervals or unions of intervals i e its states and identify the time lags which provide memory to the process a distance is used as objective function to stimulate the clustering of the states having similar transition probabilities the problem of the exploding number of alternative partitions in the solution space which grows with the number of states and the order of the markov chain is addressed through a tabu search algorithm the method is applied to bootstrap the series of the german and spanish electricity prices the analysis of the results confirms the good consistency properties of the method we propose

application of honey bee mating optimization algorithm on clustering cluster analysis is one of attractive data mining technique that use in many fields one popular class of data clustering algorithms is the center based clustering algorithm k means used as a popular clustering method due to its simplicity and high speed in clustering large datasets however k means has two shortcomings dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort in order to overcome local optima problem lots of studies done in clustering over the last decade modeling the behavior of social insects such as ants and bees for the purpose of search and problem solving has been the context of the emerging area of swarm intelligence honey bees are among the most closely studied social insects honey bee mating may also be considered as a typical swarm based approach to optimization in which the search algorithm is inspired by the process of marriage in real honey bee honey bee has been used to model agent based systems in this paper we proposed application of honeybee mating optimization in clustering hbmk means we compared hbmk means with other heuristics algorithm in clustering such as ga sa ts and aco by implementing them on several well known datasets our finding shows that the proposed algorithm works than the best one

a cutting plane algorithm for a clustering problem in this paper we consider a clustering problem that arises in qualitative data analysis this problem can be transformed to a combinatorial optimization problem the clique partitioning problem we have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope these theoretical results are utilized in this paper we describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before we discuss some details of the implementation of our code and present our computational results we mention applications from e g zoology economics and the political sciences

higher order whitehead products and l structures on the homology of a dgl abstract we detect higher order whitehead products on the homology h of a differential graded lie algebra l in terms of higher brackets in the transferred l structure on h via a given homotopy retraction of l onto h

k harmonic means data clustering with simulated annealing heuristic abstract clustering procedures partition a set of objects into clusters such that objects in the same cluster are more similar to each other than objects in different clusters according to some predefined criteria clustering is a popular data analysis and data mining technique since clustering problem have np complete nature the larger the size of the problem the harder to find the optimal solution and furthermore the longer to reach a reasonable results one of the most used techniques for clustering is based on k means such that the data is partitioned into k clusters although k means algorithm is easy to implement and works fast in most situations it suffers from two major drawbacks one is sensitivity to initialization and the other is convergence to local optima it is seen from the studies k harmonic means clustering solves the problem of initialization but since its greedy search nature the second problem convergence to local optima still remains in this paper we develop a new algorithm for solving this problem based on a simulated annealing technique simulated annealing k harmonic means clustering sakhmc the experiment results on the iris and the other well known data illustrate the robustness of the sakhmc clustering algorithm

dg resolutions of nc smooth thickenings and nc fourier mukai transforms we give a construction of nc smooth thickenings a notion defined by kapranov j reine angew math 505 73 118 1998 of a smooth variety equipped with a torsion free connection we show that a twisted version of this construction realizes all nc smooth thickenings as 0 th cohomology of a differential graded sheaf of algebras similarly to fedosov s construction in j differ geom 40 213 238 1994 we use this dg resolution to construct and study sheaves on nc smooth thickenings in particular we construct an nc version of the fourier mukai transform from coherent sheaves on a commutative curve to perfect complexes on the canonical nc smooth thickening of its jacobian we also define and study analytic nc manifolds we prove nc versions of some of gaga theorems and give a c infty construction of analytic nc thickenings that can be used in particular for kahler manifolds with constant holomorphic sectional curvature finally we describe an analytic nc thickening of the poincare line bundle for the jacobian of a curve and the corresponding fourier mukai functor in terms of a infty structures