stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

multicommodity max flow min cut theorems and their use in designing approximation algorithms in this paper we establish max flow min cut theorems for several important classes of multicommodity flow problems in particular we show that for any n node multicommodity flow problem with uniform demands the max flow for the problem is within an o log n factor of the upper bound implied by the min cut the result which is existentially optimal establishes an important analogue of the famous 1 commodity max flow min cut theorem for problems with multiple commodities the result also has substantial applications to the field of approximation algorithms for example we use the flow result to design the first polynomial time polylog n times optimal approximation algorithms for well known np hard optimization problems such as graph partitioning min cut linear arrangement crossing number vlsi layout and minimum feedback arc set applications of the flow results to path routing problems network reconfiguration communication in distributed networks scientific computing and rapidly mixing markov chains are also described in the paper categories and subject descriptors f 2 2 analysis of algorithms and problem complexity

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

minimal multicut and maximal integer multiflow a survey we present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems such as the multiterminal cut and the unsplittable flow problems we consider neither continuous multiflow nor minimum cost multiflow most of the results are very recent and some are new we recall the dual relationship between both problems give complexity results and algorithms firstly in unrestricted graphs and secondly in several special graphs trees bipartite or planar graphs a table summarizes the most important results

deterministic pivoting algorithms for constrained ranking and clustering problems we consider ranking and clustering problems related to the aggregation of inconsistent information in particular rank aggregation weighted feedback arc set in tournaments consensus and correlation clustering and hierarchical clustering ailon et al ailon n m charikar a newman 2005 aggregating inconsistent information ranking and clustering proc 37th annual acm sympos theory comput stoc 05 684 693 ailon and charikar ailon n m charikar 2005 fitting tree metrics hierarchical clustering and phylogeny proc 46th annual ieee sympos foundations comput sci focs 05 73 82 and ailon ailon n 2007 aggregation of partial rankings p ratings and top m lists proc 18th annual acm siam sympos discrete algorithms soda 07 415 424 proposed randomized constant factor approximation algorithms for these problems which recursively generate a solution by choosing a random vertex as pivot and dividing the remaining vertices into two groups based on the pivot vertex in this paper we answer an open question in these works by giving deterministic approximation algorithms for these problems the analysis of our algorithms is simpler than the analysis of the randomized algorithms in addition we consider the problem of finding minimum cost rankings and clusterings that must obey certain constraints e g an input partial order in the case of ranking problems which were introduced by hegde and jain hegde r k jain 2006 personal communication we show that the first type of algorithms we propose can also handle these constrained problems in addition we show that in the case of a rank aggregation or consensus clustering problem if the input rankings or clusterings obey the constraints then we can always ensure that the output of any algorithm obeys the constraints without increasing the objective value of the solution

approximate max flow min multi cut theorems and their applications consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed we prove the following approximate max flow min multicut theorem dst frac mbox rm min multicut o log k leq mbox rm max flow leq mbox rm min multicut noindent where k is the number of commodities our proof is constructive it enables us to find a multicut within o log k of the max flow and hence also the optimal multicut in addition the proof technique provides a unified framework in which one can also analyse the case of flows with specified demands of leighton and rao and klein et al and thereby obtain an improved bound for the latter problem

perturbed optimization in banach spaces iii semi infinite optimization this paper is devoted to the study of perturbed semi infinite optimization problems i e minimization over er n with an infinite number of inequality constraints we obtain the second order expansion of the optimal value function and the first order expansion of approximate optimal solutions in two cases i when the number of binding constraints is finite and ii when the inequality constraints are parametrized by a real scalar these results are partly obtained by specializing the sensitivity theory for perturbed optimization developed in part i cf siam j control optim 34 1996 pp 1151 1171 and deriving specific sharp lower estimates for the optimal value function which take into account the curvature of the positive cone in the space c omega of continuous real valued functions

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

second order derivatives of extremal value functions and optimality conditions for semi infinite programs second order differential properties of an extremal value function v are studied it is shown that under certain assumptions in particular the strong second order sufficiency conditions v is locally expressible as the maximum of a finite number of c2 functions after removing the assumption of strong sufficiency lower and upper bounds on the second order local behaviour of v are proposed the obtained results are applied to give second order optimally conditions for a semi infinite program

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

computational results of an interior point algorithm for large scale linear programming this paper gives computational results for an efficient implementation of a variant of dual projective algorithm for linear programming the implementation uses the preconditioned conjugate gradient method for computing projections our computational experience reported in this paper indicates that this algorithm has potential as an alternative for solving very large lps in which the direct methods fail due to memory and cpu time requirements the conjugate gradient algorithm was able to find very accurate directions even when the system was ill conditioned the paper also discusses a new mathematical technique called the reciprocal estimates for estimating the primal variables we have conducted extensive computational experiments on problems representative of large classes of applications of current interest we have also chosen instances of the problems of future potential interest which could not be solved in the past due to the weakness of the prior solution methods but which represent a large class of new applications the hypergraph model is such an example comparison of our implementation with minos 5 1 shows that our implementation is orders of magnitude faster than minos 5 1 for these problems

aggregating inconsistent information ranking and clustering we address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs specifically the problems we address are rank aggregation the feedback arc set problem on tournaments and correlation and consensus clustering we show that for all these problems and various weighted versions of them we can obtain improved approximation factors using essentially the same remarkably simple algorithm additionally we almost settle a long standing conjecture of bang jensen and thomassen and show that unless np bpp there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments

perturbed optimization in banach spaces i a general theory based on a weak directional constraint qualification using a directional form of constraint qualification weaker than robinson s we derive an implicit function theorem for inclusions and use it for first and second order sensitivity analyses of the value function in perturbed constrained optimization we obtain holder and lipschitz properties and under a no gap condition first order expansions for exact and approximate solutions as an application differentiability properties of metric projections in hilbert spaces are obtained using a condition generalizing polyhedricity we also present in the appendix a short proof of a generalization of the convex duality theorem in banach spaces

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

on sensitivity analysis of nonlinear programs in banach spaces the approach via composite unconstrained optimization this article studies local sensitivity analysis of nonlinear programming problems in banach spaces with arbitrary sets of solutions and no a priori regularity properties this is done by first developing a corresponding theory for unconstrained optimization involving simple composite functions and then applying this theory to general nonlinear programs by way of certain reduction principles

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

spectral measures of bipartivity in complex networks we introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity it is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks trophic interactions in food webs construction principles in metabolic networks or communities in social networks

on network bipartivity systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite we propose two measures quantifying the notion of bipartivity the two measures one well known and natural but computationally intractable one computationally less complex but also less intuitive are examined on model networks that continuously interpolates between bipartite graphs and graphs with many odd circuits we find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity and thus conclude that the measures are quite relevant we also measure and discuss the values of our bipartivity measures for empirical social networks constructed from professional collaborations internet communities and field surveys here we find as expected that networks arising from romantic online interaction have high and professional collaboration networks have low bipartivity values in some other cases probably due to low average degree of the network the bipartivity measures cannot distinguish between romantic and friendship oriented interaction

robust stochastic dominance and its application to risk averse optimization we introduce a new preference relation in the space of random variables which we call robust stochastic dominance we consider stochastic optimization problems where risk aversion is expressed by a robust stochastic dominance constraint these are composite semi infinite optimization problems with constraints on compositions of measures of risk and utility functions we develop necessary and sufficient conditions of optimality for such optimization problems in the convex case in the nonconvex case we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem

sorting of permutations by cost constrained transpositions the problem of finding a minimum decomposition of a permutation in terms of transpositions with predetermined non uniform and non negative costs is addressed alternatively computing the transposition distance between two permutations where transpositions are endowed with arbitrary non negative costs is studied for such cost functions polynomial time constant approximation decomposition algorithms are described for metric path costs exact polynomial time decomposition algorithms are presented the algorithms in this paper represent a combination of viterbi type algorithms and graph search techniques for minimizing the cost of individual transpositions and dynamic programing algorithms for finding minimum cost decompositions of cycles the presented algorithms have a myriad of applications in information theory bioinformatics and algebra

correlation clustering in general weighted graphs we consider the following general correlation clustering problem n bansal a blum s chawla correlation clustering in proc 43rd annu ieee symp on foundations of computer science vancouver canada november 2002 pp 238 250 given a graph with real nonnegative edge weights and a edge labelling partition the vertices into clusters to minimize the total weight of cut edges and uncut edges thus edges with large weights representing strong correlations between endpoints encourage those endpoints to belong to a common cluster while edges with large weights encourage the endpoints to belong to different clusters in contrast to most clustering problems correlation clustering specifies neither the desired number of clusters nor a distance threshold for clustering both of these parameters are effectively chosen to be best possible by the problem definition correlation clustering was introduced by bansal et al correlation clustering in proc 43rd annu ieee syrup on foundations of computer science vancouver canada november 2002 pp 238 250 motivated by both document clustering and agnostic learning they proved np hardness and gave constant factor approximation algorithms for the special case in which the graph is complete full information and every edge has the same weight we give an o log n approximation algorithm for the general case based on a linear programming rounding and the region growing technique we also prove that this linear program has a gap of log n and therefore our approximation is tight under this approach we also give an o r3 approximation algorithm for kr r minor free graphs on the other hand we show that the problem is equivalent to minimum multicut and therefore apx hard and difficult to approximate better than log n

bounds for permutation rate distortion we study the rate distortion relationship in the set of permutations endowed with the kendall tau metric and the chebyshev metric the ell infty metric this paper is motivated by the application of permutation rate distortion to the average case and worst case distortion analysis of algorithms for ranking with incomplete information and approximate sorting algorithms for the kendall tau metric we provide bounds for various distortion regimes while for the chebyshev metric we present bounds that are valid for all distortions and are especially accurate for small distortions in addition for the chebyshev metric we provide a construction for covering codes

complexity of the cluster deletion problem on subclasses of chordal graphs we consider the following vertex partition problem on graphs given a graph with real nonnegative edge weights partition the vertices into clusters in this case cliques to minimize the total weight of edges out of the clusters this optimization problem is known to be an np complete problem even for unweighted graphs and has been studied extensively in the scope of fixed parameter tractability fpt where it is commonly known as the cluster deletion problem many of the recently developed fpt algorithms rely on being able to solve cluster deletion in polynomial time on restricted graph structures in this paper the complexity of the cluster deletion problem is investigated for the family of chordal graphs it is shown that this problem is np complete for edge weighted split graphs edge weighted interval graphs and edge unweighted chordal graphs we also prove that the cluster deletion is an np complete problem for edge weighted cographs some polynomial time solvable cases are also identified in particular cluster deletion for unweighted split graphs unweighted proper interval graphs and weighted block graphs

on the hardness of labeled correlation clustering problem motivated by practical applications the labeled correlation clustering problem a variant of correlation clustering problem is formally defined and studied in this paper since the problem is np complete we consider the parameterized complexities three different parameterizations are considered and the corresponding parameterized complexities are studied for the two parameterized problems which are fixed parameter tractable the lower bounds of them are analyzed under seth strong exponential time hypothesis

constructions of rank modulation codes rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines modeling rank modulation involves construction of packings of the space of permutations equipped with the kendall tau distance as our main set of results we present several general constructions of codes in permutations that cover a broad range of code parameters in particular we show a number of ways in which conventional error correcting codes can be modified to correct errors in the kendall space our constructions are nonasymptotic and afford simple encoding and decoding algorithms of essentially the same complexity as required to correct errors in the hamming metric as an example from binary bose chaudhuri hocquenghem codes we obtain codes correcting t kendall errors in n memory cells that support the order of n log2n t messages for any constant t 1 2 we give many examples of rank modulation codes with specific parameters turning to asymptotic analysis we construct families of rank modulation codes that correct a number of errors that grows with n at varying rates from n to n2 one of our constructions gives rise to a family of rank modulation codes for which the tradeoff between the number of messages and the number of correctable kendall errors approaches the optimal scaling rate

a parametric view on the mangasarian fromovitz constraint qualification in this paper we consider the behaviour of the multipliers for one parametric semi infinite programs near critical parameters where the mangasarian fromovitz constraint qualification can be violated the growth of the multipliers when the parameter approaches such a critical parameter is characterized by a parametric constraint qualification which is introduced here it is equivalent to a bound on the growth of the multipliers

stabilization of regime switching processes by feedback control based on discrete time observations this work aims to extend x r mao s work automatica j ifac 49 2013 pp 3677 3681 on stabilization of hybrid stochastic differential equations by discrete time feedback control in x r mao s work the feedback control depends on discrete time observation of the state process but on continuous time observation of the switching process while in this work we study the feedback control depending on discrete time observations of the state process and the switching process our criteria depend explicitly on the regular conditions of the coefficients of the stochastic differential equation and on the stationary distribution of the switching process the sharpness of our criteria is shown through studying the stability of linear systems which also shows explicitly that the stability of hybrid stochastic differential equations depends essentially on the long time behavior of the switching process

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

clustering partially observed graphs via convex optimization this paper considers the problem of clustering a partially observed unweighted graph i e one where for some node pairs we know there is an edge between them for some others we know there is no edge and for the remaining we do not know whether or not there is an edge we want to organize the nodes into disjoint clusters so that there is relatively dense observed connectivity within clusters and sparse across clusters we take a novel yet natural approach to this problem by focusing on finding the clustering that minimizes the number of disagreements i e the sum of the number of observed missing edges within clusters and observed present edges across clusters our algorithm uses convex optimization its basis is a reduction of disagreement minimization to the problem of recovering an unknown low rank matrix and an unknown sparse matrix from their partially observed sum we evaluate the performance of our algorithm on the classical planted partition stochastic block model our main theorem provides sufficient conditions for the success of our algorithm as a function of the minimum cluster size edge density and observation probability in particular the results characterize the tradeoff between the observation probability and the edge density gap when there are a constant number of clusters of equal size our results are optimal up to logarithmic factors

detecting communities in large networks we develop an algorithm to detect community structure in complex networks the algorithm is based on spectral methods and takes into account weights and link orientation since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned it turns to be specially suitable for the analysis of social and information networks we test the algorithm on a large scale data set from a psychological experiment of word association in this case it proves to be successful both in clustering words and in uncovering mental association patterns

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

towards parameter independent data clustering and image segmentation while there are a large amount of clustering algorithms proposed in the literature the clustering results of existing algorithms usually depend on user specified parameters heavily and it is usually difficult to determine the optimal parameters with the pairwise data similarity matrix as the input dominant sets clustering has been shown to be an effective data clustering and image segmentation approach partly due to its ability to find out the underlying data structure and determine the number of clusters automatically however we find that the original dominant sets algorithm is sensitive to the similarity measures used in building the similarity matrix this means that parameter tuning is required to generate satisfactory clustering results and dominant sets clustering results are also parameter dependent in order to remove the dependence on the user specified parameter we study how the similarity measures influence the dominant sets clustering results as a result we propose to transform similarity matrices by histogram equalization before clustering while this transformation is shown to remove the sensitiveness to similarity measures effectively it also results in over segmentation therefore in the next step we present a cluster extension method to overcome the over segmentation effect and generate more reasonable clustering results we test the enhanced clustering algorithm in both data clustering and image segmentation experiments and comparisons with the state of the art algorithms validate the effectiveness of our algorithm highlightswe study how similarity measures influence the dominant sets clustering results we use histogram equalization to remove the dependence on similarity parameters we present a density based cluster extension method to overcome over segmentation experiments validate the effectiveness of our algorithm

cost optimal constrained correlation clustering via weighted partial maximum satisfiability abstract integration of the fields of constraint solving and data mining and machine learning has recently been identified within the ai community as an important research direction with high potential this work contributes to this direction by providing a first study on the applicability of state of the art boolean optimization procedures to cost optimal correlation clustering under constraints in a general similarity based setting we develop exact formulations of the correlation clustering task as maximum satisfiability maxsat the optimization version of the boolean satisfiability sat problem for obtaining cost optimal clusterings we apply a state of the art maxsat solver for solving the resulting maxsat instances optimally resulting in cost optimal clusterings we experimentally evaluate the maxsat based approaches to cost optimal correlation clustering both on the scalability of our method and the quality of the clusterings obtained furthermore we show how the approach extends to constrained correlation clustering where additional user knowledge is imposed as constraints on the optimal clusterings of interest we show experimentally that added user knowledge allows clustering larger datasets and at the same time tends to decrease the running time of our approach we also investigate the effects of maxsat level preprocessing symmetry breaking and the choice of the maxsat solver on the efficiency of the approach

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

stabilization of hybrid systems by feedback control based on discrete time state observations recently mao automatica j ifac 49 2013 pp 3677 3681 initiated the study the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations in the same paper mao also obtains an upper bound on the duration tau between two consecutive state observations however it is due to the general technique used there that the bound on tau is not very sharp in this paper we will be able to establish a better bound on tau making use of lyapunov functionals we will discuss the stabilization not only in the sense of exponential stability as mao does in automatica j ifac 49 2013 pp 3677 3681 but also in other sense that of h infty stability or asymptotic stability we will consider not only the mean square stability but also the almost sure stability

community detection as an inference problem we express community detection as an inference problem of determining the most likely arrangement of communities we then apply belief propagation and mean field theory to this problem and show that this leads to fast accurate algorithms for community detection

sensitivity analysis of optimization problems under second order regular constraints we present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition this is a technical condition that is always satisfied in the case of semi definite optimization we derive lipschitz and holder expansions of approximate optimal solutions under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem we show how the theory applies to semi infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds and discuss the differentiability of metric projections as well as the moreau yosida regularization finally we show how the theory applies to semi definite optimization

an axiomatic approach to constructing distances for rank comparison and aggregation we propose a new family of distance measures on rankings derived through an axiomatic approach that consider the nonuniform relevance of the top and bottom of ordered lists and similarities between candidates the proposed distance functions include specialized weighted versions of the kendall distance and the cayley distance and are suitable for comparing rankings in a number of applications including information retrieval and rank aggregation in addition to proposing the distance measures and providing the theoretical underpinnings for their applications we also analyze algorithmic and computational aspects of weighted distance based rank aggregation we present an aggregation method based on approximating weighted distance measures by a generalized version of spearman s footrule distance as well as a markov chain method inspired by pagerank where transition probabilities of the markov chain reflect the chosen weighted distances

correlation clustering with constrained cluster sizes and extended weights bounds we consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges our contributions are twofold first we introduce the problem of correlation clustering with bounded cluster sizes second we extend the regime of weight values for which the clustering may be performed with constant approximation guarantees in polynomial time and apply the results to the bounded cluster size problem

on lipschitzian stability of optimal solutions of parametrized semi infinite programs we study continuity properties of optimal solutions of parametrized semi infinite programming problems the involved constraints are formulated in a form of cone constraints and then a slightly modified general result of shapiro and bonnans 1992 on lipschitzian stability of optimal solutions is applied it is shown that under certain second order sufficient conditions optimal solutions of the semi infinite programs are lipschitzian stable provided a regularity assumption related to a linearization of the considered programs is satisfied

clustering and outlier detection using isoperimetric number of trees we propose a graph based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria we show that our basic clustering algorithm runs in o nlogn and with post processing in almost o nlogn average case and o n 2 worst case time where n is the size of the data set it is also shown that our generalized graph model which also allows the use of potentials at vertices can be used to extract an extra piece of information related to anomalous data patterns and outliers in this regard we propose an algorithm that extracts outliers in parallel to data clustering we also provide a comparative performance analysis of our algorithms with other related ones and we show that they behave quite effectively on hard synthetic data sets as well as real world benchmarks

error correction in flash memories via codes in the ulam metric we consider rank modulation codes for flash memories that allow for handling arbitrary charge drop errors unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements the proposed translocation rank codes account for more general forms of errors that arise in storage systems translocations represent a natural extension of the notion of adjacent transpositions and as such may be analyzed using related concepts in combinatorics and rank modulation coding our results include derivation of the asymptotic capacity of translocation rank codes construction techniques for asymptotically good codes as well as simple decoding methods for one class of constructed codes as part of our exposition we also highlight the close connections between the new code family and permutations with short common subsequences deletion and insertion error correcting codes for permutations and permutation codes in the hamming distance

stabilization of stochastic differential equations driven by g brownian motion with feedback control based on discrete time state observation abstract this paper mainly concerns the stability of the solutions for stochastic differential equations driven by g brownian motion g sdes via feedback control based on discrete time state observation more precisely the discrete time state feedback control is included in the drift coefficient of the g sdes by constructing an appropriate g lyapunov function a set of conditions is obtained for the h stability asymptotic stability and mean square exponential stability of the controlled systems finally an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique

the complexity of multiterminal cuts in the multiterminal cut problem one is given an edge weighted graph and a subset of the vertices called terminals and is asked for a minimum weight set of edges that separates each terminal from all the others when the number k of terminals is two this is simply the mincut max flow problem and can be solved in polynomial time it is shown that the problem becomes np hard as soon as k 3 but can be solved in polynomial time for planar graphs for any fixed k the planar problem is np hard however if k is not fixed a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 2 k of the optimal cut weight is also described

method to find community structures based on information centrality community structures are an important feature of many social biological and technological networks here we study a variation on the method for detecting such communities proposed by girvan and newman and based on the idea of using centrality measures to define the community boundaries m girvan and m e j newman proc natl acad sci u s a 99 7821 2002 we develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality we test the algorithm on computer generated and real world networks whose community structure is already known or has been studied by means of other methods we show that our algorithm although it runs to completion in a time o n4 is very effective especially when the communities are very mixed and hardly detectable by the other methods

a unified approach to approximation algorithms for bottleneck problems in this paper a powerful and yet simple technique for devising approximation algorithms for a wide variety of np complete problems in routing location and communication network design is investigated each of the algorithms presented here delivers an approximate solution guaranteed to be within a constant factor of the optimal solution in addition for several of these problems we can show that unless p np there does not exist a polynomial time algorithm that has a better performance guarantee

a new correlation coefficient for comparing and aggregating non strict and incomplete rankings abstract we introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non strict i e with ties and incomplete i e unknown preferences the correlation coefficient is designed to enforce a neutral treatment of incompleteness whereby no assumptions are made about individual preferences involving unranked objects the new measure which can be regarded as a generalization of the seminal kendall tau correlation coefficient is proven to satisfy a set of metric like axioms and to be equivalent to a recently developed ranking distance function associated with kemeny aggregation in an effort to further unify and enhance both robust ranking methodologies this work proves the equivalence of an additional distance and correlation coefficient pairing in the space of non strict incomplete rankings these connections induce new exact optimization methodologies a specialized branch and bound algorithm and an exact integer programming formulation moreover the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem the latter premise is bolstered by an accompanying set of experiments on random instances which are generated via a herein developed sampling technique connected with the classic mallows distribution of ranking data associated experiments with the branch and bound algorithm demonstrate that as data becomes noisier the featured correlation coefficient yields relatively fewer alternative optimal solutions and that the aggregate rankings tend to be closer to an underlying ground truth shared by a majority

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

prediction and clustering in signed networks a local to global perspective the study of social networks is a burgeoning research area however most existing work is on networks that simply encode whether relationships exist or not in contrast relationships in signed networks can be positive like trust or negative dislike distrust the theory of social balance shows that signed networks tend to conform to some local patterns that in turn induce certain global characteristics in this paper we exploit both local as well as global aspects of social balance theory for two fundamental problems in the analysis of signed networks sign prediction and clustering local patterns of social balance have been used in the past for sign prediction we define more general measures of social imbalance mois based on l cycles in the network and give a simple sign prediction rule interestingly by examining measures of social imbalance we show that the classic katz measure which is used widely in unsigned link prediction also has a balance theoretic interpretation when applied to signed networks motivated by the global structure of balanced networks we propose an effective low rank modeling approach for both sign prediction and clustering we provide theoretical performance guarantees for our low rank matrix completion approach via convex relaxations scale it up to large problem sizes using a matrix factorization based algorithm and provide extensive experimental validation including comparisons with local approaches our experimental results indicate that by adopting a more global viewpoint of social balance we get significant performance and computational gains in prediction and clustering tasks on signed networks our work therefore highlights the usefulness of the global aspect of balance theory for the analysis of signed networks

linear programming based approximation algorithms for feedback set problems in bipartite tournaments we consider the feedback vertex set and feedback arc set problems on bipartite tournaments we improve on recent results by giving a 2 approximation algorithm for the feedback vertex set problem we show that this result is the best that we can attain when using optimal solutions to a certain linear program as a lower bound on the optimal value for the feedback arc set problem on bipartite tournaments we show that a recent 4 approximation algorithm proposed by gupta 2008 8 is incorrect we give an alternative 4 approximation algorithm based on an algorithm for the feedback arc set on non bipartite tournaments given by van zuylen and williamson 2009 14

density peak clustering based on relative density relationship abstract the density peak clustering algorithm treats local density peaks as cluster centers and groups non center data points by assuming that one data point and its nearest higher density neighbor are in the same cluster while this algorithm is shown to be promising in some applications its clustering results are found to be sensitive to density kernels and large density differences across clusters tend to result in wrong cluster centers in this paper we attribute these problems to the inconsistency between the assumption and implementation adopted in this algorithm while the assumption is based totally on relative density relationship this algorithm adopts absolute density as one criterion to identify cluster centers this observation prompts us to present a cluster center identification criterion based only on relative density relationship specifically we define the concept of subordinate to describe the relative density relationship and use the number of subordinates as a criterion to identify cluster centers our approach makes use of only relative density relationship and is less influenced by density kernels and density differences across clusters in addition we discuss the problems of two existing density kernels and present an average distance based kernel in data clustering experiments we validate the new criterion and density kernel respectively and then test the whole algorithm and compare with some other clustering algorithms

correlation clustering with noisy partial information in this paper we propose and study a semi random model for the correlation clustering problem on arbitrary graphs g we give two approximation algorithms for correlation clustering instances from this model the first algorithm finds a solution of value 1 opt cost o nlog 3 n with high probability where opt cost is the value of the optimal solution for every 0 the second algorithm finds the ground truth clustering with an arbitrarily small classific ation error under some additional assumptions on the instance