the connected p center problem on block graphs with forbidden vertices let g v e w l denote an n vertex and m edge graph in which w is a function mapping each vertex v to a positive weight w v and l is a function mapping each edge e to a positive length l e given a positive integer p the p center problem involves finding a set q with p vertices of g to be the locations for building facilities the objective is to minimize the maximum weighted distance from each vertex in v q to its nearest vertex in q this paper considers a practical restriction the induced subgraph of the selected p vertices must be connected the new variant is called the connected p center problem the cpc problem for each fixed integer t 1 on block graphs with exactly t blocks we first show that the cpc problem is np hard when 1 w v 1 for all vertices v and l e 1 2 for all edges e and 2 w v 1 2 for all vertices v and l e 1 for all edges e respectively second an o n m time algorithm for solving the cpc problem on block graphs with unit vertex weights and unit edge lengths is proposed then the algorithmic result is extended to handle the situation in which some vertices in g cannot be included to form feasible solutions the complexity of the extended algorithm is also o n m

multiplicative noise induced coherence resonance via two different mechanisms in bistable neural models the bistable fitzhugh nagumo fhn neural model driven by two multiplicative noises and one additive noise is investigated two different potential mechanisms for enhancing coherence of bistable fhn model are presented that is the first multiplicative noise changes the system from the bistable to the oscillatory regime and the second multiplicative noise can enhance the symmetry of two stable states of the system the two mechanisms are analytically or numerically explained at any level of the second multiplicative noise a maximal coherence have been found at some intermediate noise intensity of the first multiplicative noise only when the first multiplicative noise intensity is less than 0 0001 can a maximal coherence be obtained at some intermediate noise intensity of the second multiplicative noise these coherence resonance phenomena have been understood in terms of the presented mechanisms

primal dual algorithms for deterministic inventory problems we consider several classical models in deterministic inventory theory the single item lot sizing problem the joint replenishment problem and the multistage assembly problem these inventory models have been studied extensively and play a fundamental role in broader planning issues such as the management of supply chains for each of these problems we wish to balance the cost of maintaining surplus inventory for future demand against the cost of replenishing inventory more frequently for example in the joint replenishment problem demand for several commodities is specified over a discrete finite planning horizon the cost of maintaining inventory is linear in the number of units held but the cost incurred for ordering a commodity is independent of the size of the order furthermore there is an additional fixed cost incurred each time a nonempty subset of commodities is ordered the goal is to find a policy that satisfies all demands on time and minimizes the overall holding and ordering cost we shall give a novel primal dual framework for designing algorithms for these models that significantly improve known results in several ways the performance guarantees for the quality of the solutions improve on or match previously known results the performance guarantees hold under much more general assumptions about the structure of the costs and the algorithms and their analysis are significantly simpler than previous known results finally our primal dual framework departs from the structure of previously studied primal dual approximation algorithms in significant ways and we believe that our approach may find applications in other settings more specifically we provide 2 approximation algorithms for the joint replenishment problem and for the assembly problem and solve the single item lot sizing problem to optimality the results for the joint replenishment and the lot sizing problems also hold for their generalizations with back orders allowed as a byproduct of our work we prove known and new upper bounds on the integrality gap of some linear programming lp relaxations of the abovementioned problems

compact location problems we consider the problem of placing a specified number p of facilities on the nodes of a network so as to minimize some measure of the distances between facilities this formulation models a number of problems arising in facility location statistical clustering pattern recognition and also a processor allocation problem in multiprocessor systems

equivariant stable homotopy and segal s burnside ring conjecture analogous results were proved later for ko in the generality of compact lie groups by atiyah and segal 8 and for kfq the algebraic k theory spectrum associated to the finite field fq by rector 29 using quillen s 26 computation of it kfq in each case the answer involves an appropriate completed representation ring of g and the cohomology theory in question is constructed from the permutative category of finite dimensional vector spaces over a field see 31 if one considers cohomology theories constructed from other permutative categories one expects to find analogous computations in terms of a completed representation ring of g in the given category appropriately defined in particular stable cohomotopy ts is constructed from the category of finite sets 31 and for this category the analogue of the representation ring is a well known object the burnside ring a g 13 a g is a commutative ring with augmentation so one may speak of a g the completed burnside ring moreover there is

small approximate pareto sets for biobjective shortest paths and other problems we investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy epsilon the pareto curve of a multiobjective optimization problem we show that for a broad class of biobjective problems containing many important widely studied problems such as shortest paths spanning tree matching and many others we can compute in polynomial time an epsilon pareto set that contains at most twice as many solutions as the minimum set furthermore we show that the factor of 2 is tight for these problems i e it is np hard to do better we present upper and lower bounds for three or more objectives as well as for the dual problem of computing a specified number k of solutions which provide a good approximation to the pareto curve

proof verification and the hardness of approximation problems we show that every language in np has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof if a string is in the language then there exists a proof such that the verifier accepts with probability 1 i e for every choice of its random string for strings not in the language the verifier rejects every provided proof with probability at least 1 2 our result builds upon and improves a recent result of arora and safra 1998 whose verifiers examine a nonconstant number of bits in the proof though this number is a very slowly growing function of the input length as a consequence we prove that no max snp hard problem has a polynomial time approximation scheme unless np p the class max snp was defined by papadimitriou and yannakakis 1991 and hard problems for this class include vertex cover maximum satisfiability maximum cut metric tsp steiner trees and shortest superstring we also improve upon the clique hardness results of feige et al 1996 and arora and safra 1998 and show that there exists a positive e such that approximating the maximum clique size in an n vertex graph to within a factor of n e is np hard

computing maximally separated sets in the plane let s be a set of n points in reals 2 given an integer 1 le k le n we wish to find a maximally separated subset i subseteq s of size k this is a subset for which the minimum among the k choose 2 pairwise distances between its points is as large as possible the decision problem associated with this problem is to determine whether there exists i subseteq s i k so that all k choose 2 pairwise distances in i are at least 2 this problem can also be formulated in terms of disk intersection graphs let d be the set of unit disks centered at the points of s the disk intersection graph g of d has as edges all pairs of disks with nonempty intersection any set i with the above properties is then the set of centers of disks that form an independent set in the graph g this problem is known to be np complete if k is part of the input in this paper we first present a linear time eps approximation algorithm for any constant k next we give exact algorithms for the cases k 3 and k 4 that run in time o n 4 3 polylog n we also present a simpler n o sqrt k time exact algorithm as compared with the recent algorithm in j alber and j fiala j algorithms 52 2004 pp 134 151 for arbitrary values of k

covering moving points with anchored disks consider a set of mobile clients represented by n points in the plane moving at constant speed along n different straight lines we study the problem of covering all mobile clients using a set of k disks centered at k fixed centers each disk exists only at one instant and while it does covers any client within its coverage radius the task is to select an activation time and a radius for each disk such that every mobile client is covered by at least one disk in particular we study the optimization problem of minimizing the maximum coverage radius first we prove that although the static version of the problem is polynomial the kinetic version is np hard moreover we show that the problem is not approximable by a constant factor unless p np we then present a generic framework to solve it for fixed values of k which in turn allows us to solve more general optimization problems our algorithms are efficient for constant values of k

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

information based objective functions for active data selection learning can be made more efficient if we can actively select particularly salient data points within a bayesian learning framework objective functions are discussed that measure the expected informativeness of candidate measurements three alternative specifications of what we want to gain information about lead to three different criteria for data selection all these criteria depend on the assumption that the hypothesis space is correct which may prove to be their main weakness

robust optimization of contaminant sensor placement for community water systems we present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected we formulate sensor placement problems as mixed integer programs for which the objective coefficients are not known with certainty we consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data and we define three robust optimization models that differ in how the coefficients in the objective vary under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients under other assumptions we can apply sorting to solve each worst case realization efficiently or we can apply duality to integrate the worst case outcome and have one integer program the most difficult case is where the objective parameters are bilinear and we prove its complexity is np hard even under simplifying assumptions we consider a relaxation that provides an approximation giving an overall guarantee of near optimality when used with branch and bound search we present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications

probabilistic checking of proofs a new characterization of np we give a new characterization of np the class np contains exactly those languages l for which membership proofs a proof that an input x is in l can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof we discuss implications of this characterization specifically we show that approximating clique and independent set even in a very weak sense is np hard

fcm based model selection algorithms for determining the number of clusters clustering is an important research topic that has practical applications in many fields it has been demonstrated that fuzzy clustering using algorithms such as the fuzzy c means fcm has clear advantages over crisp and probabilistic clustering methods like most clustering algorithms however fcm and its derivatives need the number of clusters in the given data set as one of their initializing parameters the main goal of this paper is to develop an effective fuzzy algorithm for automatically determining the number of clusters after a brief review of the relevant literature we present a new algorithm for determining the number of clusters in a given data set and a new validity index for measuring the goodness of clustering experimental results and comparisons are given to illustrate the performance of the new algorithm

light noise induced suprathreshold circadian oscillations and coherent resonance in drosophila based on a reduced circadian oscillator model in drosophila smolen biophys j 83 2349 2002 the effects of light noise and time delay on a circadian oscillator near a hopf bifurcation are studied by using numerical computation when the light controlled parameter is suprathreshold it was found that the circadian oscillations can be induced by light fluctuation there is an optimal light noise intensity at which a remarkable coherent circadian oscillation is observed which implies a significant resonance phenomenon in the sense of preferred biological circadian oscillations time delay can control the coherence of noise induced circadian oscillations and the strength of coherent resonance achieves a maximum under a moderate time delay

a best possible heuristic for the k center problem in this paper we present a 2 approximation algorithm for the k center problem with triangle inequality this result is best possible since for any 2 the existence of approximation algorithm would imply that p np it should be noted that no approximation algorithm for any constant has been reported to date linear programming duality theory provides interesting insight to the problem and enables us to derive in o e log e time a solution with value no more than twice the k center optimal value a by product of the analysis is an o e algorithm that identifies a dominating set in g2 the square of a graph g the size of which is no larger than the size of the minimum dominating set in the graph g the key combinatorial object used is called a strong stable set and we prove the np completeness of the corresponding decision problem

stable splittings of the dual spectrum of the classifying space of a compact lie group for a compact lie group g there is a map from the g equivariant fixed point spectrum of the zero sphere to the dual spectrum of the classifying space of g dbg when g is finite the affirmative solution to segal s conjecture states that this map is an equivalence upon appropriate completion of the source in the case of a compact lie group we obtain splitting results of dbg via this map upon taking p adic completions

kinetic clustering of points on the line the problem of clustering a set of points moving on the line consists of the following given positive integers n and k the initial position and the velocity of n points find an optimal k clustering of the points we consider two classical quality measures for the clustering minimizing the sum of the clusters diameters and minimizing the maximum diameter of a cluster for the former we present polynomial time algorithms under some assumptions and for the latter a 2 71 e approximation

saturated fusion systems over a class of finite p groups abstract let p be an odd prime and f be a saturated fusion system over a finite p group s with derived subgroup of prime order excepting the case when s p a where p is a minimal nonabelian p group with p 1 p 1 1 p is cyclic and a is a finite abelian p group in this paper we prove that s f that is s is resistant this generalizes a result of stancu in the odd prime case

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

combination can be hard approximability of the unique coverage problem we prove semilogarithmic inapproximability for a maximization problem called unique coverage given a collection of sets find a subcollection that maximizes the number of elements covered exactly once specifically assuming that mathrm np not subseteq operatorname bptime 2 n varepsilon for an arbitrary varepsilon 0 we prove o 1 log sigma n inapproximability for some constant sigma sigma varepsilon we also prove o 1 log 1 3 varepsilon n inapproximability for any varepsilon 0 assuming that refuting random instances of 3sat is hard on average and we prove o 1 log n inapproximability under a plausible hypothesis concerning the hardness of another problem balanced bipartite independent set we establish an omega 1 log n approximation algorithm even for a more general budgeted setting and obtain an omega 1 log b approximation algorithm when every set has at most b elements we also show that our inapproximability results extend to envy free pricing an important problem in computational economics we describe how the budgeted unique coverage problem motivated by real world applications has close connections to other theoretical problems including max cut maximum coverage and radio broadcasting

nonlinear dimensionality reduction by locally linear inlaying high dimensional data is involved in many fields of information processing however sometimes the intrinsic structures of these data can be described by a few degrees of freedom to discover these degrees of freedom or the low dimensional nonlinear manifold underlying a high dimensional space many manifold learning algorithms have been proposed here we describe a novel algorithm locally linear inlaying lli which combines simple geometric intuitions and rigorously established optimality to compute the global embedding of a nonlinear manifold using a divide and conquer strategy lli gains some advantages in itself first its time complexity is linear in the number of data points and hence lli can be implemented efficiently second lli overcomes problems caused by the nonuniform sample distribution third unlike existing algorithms such as isometric feature mapping isomap local tangent space alignment ltsa and locally linear coordination llc lli is robust to noise in addition to evaluate the embedding results quantitatively two criteria based on information theory and kolmogorov complexity theory respectively are proposed furthermore we demonstrated the efficiency and effectiveness of our proposal by synthetic and real world data sets

all p local finite groups of rank two for odd prime p in this paper we give a classification of the rank two p local finite groups for odd p this study requires the analysis of the possible saturated fusion systems in terms of the outer automorphism group of the possible f radical subgroups also for each case in the classification either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p local finite group getting some new examples of these for p 3

general bounds for incremental maximization we propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems the defining characteristic of our framework is that the cardinality support of the solution is bounded by a value k in mathbb n that grows over time and we allow the solution to be extended one element at a time we investigate the best possible competitive ratio of such an incremental solution i e the worst ratio over all k between the incremental solution after k steps and an optimum solution of cardinality k we consider a large class of problems that contains many important cardinality constrained maximization problems like maximum matching knapsack and packing covering problems we provide a general 2 618 competitive incremental algorithm for this class of problems and we show that no algorithm can have competitive ratio below 2 18 in general in the second part of the paper we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step this algorithm is known to be 1 58 competitive for submodular objective functions but it has unbounded competitive ratio for the class of incremental problems mentioned above we define a relaxed submodularity condition for the objective function capturing problems like maximum weighted d dimensional matching maximum weighted b matching and a variant of the maximum flow problem we show a general bound for the competitive ratio of the greedy algorithm on the class of problems that satisfy this relaxed submodularity condition our bound generalizes the tight bound of 1 58 slightly beyond sub modular functions and yields a tight bound of 2 313 for maximum weighted b matching our bound is also tight for a more general class of functions as the relevant parameter goes to infinity note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems and our bounds for the greedy algorithm carry over both

robust submodular observation selection in many applications one has to actively select among a set of expensive observations before making an informed decision for example in environmental monitoring we want to select locations to measure in order to most effectively predict spatial phenomena often we want to select observations which are robust against a number of possible objective functions examples include minimizing the maximum posterior variance in gaussian process regression robust experimental design and sensor placement for outbreak detection in this paper we present the submodular saturation algorithm a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity an intuitive diminishing returns property moreover we prove that better approximation algorithms do not exist unless np complete problems admit efficient algorithms we show how our algorithm can be extended to handle complex cost functions incorporating non unit observation cost or communication and path costs we also show how the algorithm can be used to near optimally trade off expected case e g the mean square prediction error in gaussian process regression and worst case e g maximum predictive variance performance we show that many important machine learning problems fit our robust submodular observation selection formalism and provide extensive empirical evaluation on several real world problems for gaussian process regression our algorithm compares favorably with state of the art heuristics described in the geostatistics literature while being simpler faster and providing theoretical guarantees for robust experimental design our algorithm performs favorably compared to sdp based algorithms c 2008 andreas krause h brendan mcmahan carlos guestrin and anupam gupta krause mcmahan guestrin and gupta

precoder design for physical layer multicasting this paper studies the instantaneous rate maximization and the weighted sum delay minimization problems over a k user multicast channel where multiple antennas are available at the transmitter as well as at all the receivers motivated by the degree of freedom optimality and the simplicity offered by linear precoding schemes we consider the design of linear precoders using the aforementioned two criteria we first consider the scenario wherein the linear precoder can be any complex valued matrix subject to rank and power constraints we propose cyclic alternating ascent based precoder design algorithms and establish their convergence to respective stationary points simulation results reveal that our proposed algorithms considerably outperform known competing solutions we then consider a scenario in which the linear precoder can be formed by selecting and concatenating precoders from a given finite codebook of precoding matrices subject to rank and power constraints we show that under this scenario the instantaneous rate maximization problem is equivalent to a robust submodular maximization problem which is strongly np hard we propose a deterministic approximation algorithm and show that it yields a bicriteria approximation for the weighted sum delay minimization problem we propose a simple deterministic greedy algorithm which at each step entails approximately maximizing a submodular set function subject to multiple knapsack constraints and establish its performance guarantee

on the peterson hit problem let pk f2 x1 x2 xk pk f2 x1 x2 xk be the polynomial algebra over the prime field of two elements f2f2 in k variables x1 x2 xkx1 x2 xk each of degree 1 we study the hit problem set up by f peterson of finding a minimal set of generators for pkpk as a module over the mod 2 steenrod algebra aa in this paper we study a minimal set of generators for aa module pkpk in some so called generic degrees and apply these results to explicitly determine the hit problem for k 4k 4

robust monotone submodular function maximization we consider a robust formulation introduced by krause et al j artif intell res 42 427 486 2011 of the classical cardinality constrained monotone submodular function maximization problem and give the first constant factor approximation results the robustness considered is w r t adversarial removal of up to tau elements from the chosen set for the fundamental case of tau 1 we give a deterministic 1 1 e 1 vartheta m approximation algorithm where m is an input parameter and number of queries scale as o n m 1 in the process we develop a deterministic 1 1 e 1 vartheta m approximate greedy algorithm for bi objective maximization of two monotone submodular functions generalizing the ideas and using a result from chekuri et al in focs 10 ieee pp 575 584 2010 we show a randomized 1 1 e epsilon approximation for constant tau and epsilon le frac 1 tilde varomega tau making o n 1 epsilon 3 queries further for tau ll sqrt k we give a fast and practical 0 387 algorithm finally we also give a black box result result for the much more general setting of robust maximization subject to an independence system

on stably decomposing products of classifying spaces john martino1 stewart priddy2 jason douma3 1 department of mathematics and statistics western michigan university kalamazoo mi 49008 usa e mail martino math stat wmich edu 2 department of mathematics northwestern university evanston il 60208 usa e mail priddy math nwu edu 3 department of mathematics university of sioux falls sioux falls sd 57105 usa e mail jason douma thecoo edu

the groups of order 256 abstract building on earlier work a new method for generating descriptions of p groups is developed the theory and implementation of this method are described and its application in determining the 56 092 groups of order 256 is outlined

a bad instance for k means k means is a seeding technique for the k means method with an expected approximation ratio of o logk where k denotes the number of clusters examples are known on which the expected approximation ratio of k means is w logk showing that the upper bound is asymptotically tight however it remained open whether k means yields a constant approximation with probability 1 poly k or even with constant probability we settle this question and present instances on which k means achieves an approximation ratio no better than 2 email protected logk with probability exponentially close to 1

robust discrete optimization and network flows we propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution and is computationally tractable both practically and theoretically in particular when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation when only the cost coefficients are subject to uncertainty and the problem is a 0 1 discrete optimization problem on n variables then we solve the robust counterpart by solving at most n 1 instances of the original problem thus the robust counterpart of a polynomially solvable 0 1 discrete optimization problem remains polynomially solvable in particular robust matching spanning tree shortest path matroid intersection etc are polynomially solvable we also show that the robust counterpart of an np hard approximable 0 1 discrete optimization problem remains approximable finally we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network

hecke algebras and cohomotopical mackey functors in this paper we define the concept of the cohomotopical mackey functor which is more general than the usual cohomological mackey functor and show that hecke algebra techniques are applicable to cohomotopical mackey functors our theory is valid for any possibly infinite discrete group some applications to topology are also given

nonlinear dimensionality reduction by topologically constrained isometric embedding many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space the embedding process usually relies on distances between neighboring features mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non convexity distortions resulting from using long geodesics indiscriminately lead to a known limitation of the isomap algorithm when used to map non convex manifolds presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries the resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold thus avoiding an inherent limitation of the isomap algorithm since the proposed algorithm matches non local structures it is robust to strong noise we show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques both global and local in nature

the hit problem for the modular invariants of linear groups abstract let the mod 2 steenrod algebra a and the general linear group glk gl k f 2 act on pk f 2 x1 xk with deg xi 1 in the usual manner we prove that for a family of some rather small subgroups g of glk every element of positive degree in the invariant algebra pkg is hit by a in pk in other words pkg a pk where pkg and a denote respectively the submodules of pkg and a consisting of all elements of positive degree this family contains most of the parabolic subgroups of glk it should be noted that the smaller the group g is the harder the problem turns out to be remarkably when g is the smallest group of the family the invariant algebra pkg is a polynomial algebra in k variables whose degrees are 8 and fixed while k increases it has been shown by hu ng trans amer math soc 349 1997 3893 3910 that for g glk the inclusion pkglk a pk is equivalent to a weak algebraic version of the long standing conjecture stating that the only spherical classes in q0s0 are the elements of hopf invariant 1 and those of kervaire invariant 1

a parallel repetition theorem we show that a parallel repetition of any two prover one round proof system mip 2 1 decreases the probability of error at an exponential rate no constructive bound was previously known the constant in the exponent in our analysis depends only on the original probability of error and on the total number of possible answers of the two provers the dependency on the total number of possible answers is logarithmic which was recently proved to be almost the best possible u feige and o verbitsky proc 11th annual ieee conference on computational complexity ieee computer society press los alamitos ca 1996 pp 70 76

stochastic resonance in an autonomous system with a nonuniform limit cycle in a recent numerical study gang et al phys rev lett 71 807 1993 presented the first example of stochastic resonance in an autonomous system they considered a two variable model in which a limit cycle is born as some parameter is varied their numerical experiments revealed various noise induced effects including a noise induced shift in the frequency of the limit cycle oscillations and noise induced oscillations in the absence of a deterministic limit cycle we show that both of these effects are simple consequences of the nonuniformity of the motion along the limit cycle

effects of colored noise and noise delay on a calcium oscillation system abstract as a calcium oscillations system is in steady state the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods the results indicate that 1 the colored noise can induce coherence bi resonance phenomenon 2 there exist three peaks in the r 0 r is the reciprocal coefficient of variance and 0 is the self correlation time of the colored noise curves for the same noise intensity q 1 the gaussian colored noise can induce calcium spikes but the white noise cannot do this 3 the delay time can improve noise induced spikes regularity as 0 is small and r has a significant minimum with increasing as 0 is large 4 large values of reduce noise induced spikes regularity

clustering to minimize the maximum intercluster distance the problem of clustering a set of points so as to minimize the maximum intercluster distance is studied an o kn approximation algorithm where n is the number of points and k is the number of clusters that guarantees solutions with an objective function value within two times the optimal solution value is presented this approximation algorithm succeeds as long as the set of points satisfies the triangular inequality we also show that our approximation algorithm is best possible with respect to the approximation bound if pz np

near optimal sensor placements in gaussian processes theory efficient algorithms and empirical studies when monitoring spatial phenomena which can often be modeled as gaussian processes gps choosing sensor locations is a fundamental task there are several common strategies to address this task for example geometry or disk models placing sensors at the points of highest entropy variance in the gp model and a d or e optimal design in this paper we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected we prove that the problem of finding the configuration that maximizes mutual information is np complete to address this issue we describe a polynomial time approximation that is within 1 1 e of the optimum by exploiting the submodularity of mutual information we also show how submodularity can be used to obtain online bounds and design branch and bound search procedures we then extend our algorithm to exploit lazy evaluations and local structure in the gp yielding significant speedups we also extend our approach to find placements which are robust against node failures and uncertainties in the model these extensions are again associated with rigorous theoretical approximation guarantees exploiting the submodularity of the objective function we demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real world data sets

the complex bordism of groups with periodic cohomology is is proved that if bg is the classifying space of a group g with periodic cohomology then the complex bordism groups mu bg are obtained from the connective k theory groups ku bg by just tensoring up with the generators of mu as a polynomial algebra over ku the explicit abelian group structure is also given the bulk of the work is the verification when g is a generalized quaternionic group 1 statement of results it is well known ce that a finite group has periodic cohomology if and only if its sylow subgroups are all cyclic or generalized quaternionic another characterization sw is that these are precisely the finite groups which can act freely on a finite simplicial homotopy sphere in wo it was shown exactly which of these the spherical space form groups admit a free orthogonal action on a standard sphere let mu denote reduced complex bordism and bu connective ktheory homology it is well known cf1 that if bg denotes the classifying space of a finite group g then mun bg is isomorphic to the group of bordism classes of stably almost complex n manifolds with free g action here and elsewhere x is the space obtained from x by adjoining a disjoint basepoint the coefficient rings are mu mu s z x2 i 1 and bu bu s0 z x2 where x21 is a generator of degree 2i in a polynomial algebra our main result proves an extension of a conjecture of gilkey g bd theorem 1 1 if g is any finite group with periodic cohomology then there is an isomorphism of graded abelian groups mu bg bu bg 0 z x2i i 2 received by the editors may 1 1988 1980 mathematics subject classification 1985 revision primary 57r85 secondary 55r35 55n22

asymmetric k center is log n hard to approximate in the asymmetric k center problem the input is an integer k and a complete digraph over n points together with a distance function obeying the directed triangle inequality the goal is to choose a set of k points to serve as centers and to assign all the points to the centers so that the maximum distance of any point from its center is as small as possible we show that the asymmetric k center problem is hard to approximate up to a factor of log n o 1 unless np dtime nlog log n since an o log n approximation algorithm is known for this problem this resolves the asymptotic approximability of asymmetric k center this is the first natural problem whose approximability threshold does not polynomially relate to the known approximation classes we also resolve the approximability threshold of the metric symmetric k center problem with costs

learning from minimum entropy queries in a large committee machine in supervised learning the redundancy contained in random examples can be avoided by learning from queries using statistical mechanics we study learning from minimum entropy queries in a large tree committee machine the generalization error decreases exponentially with the number of training examples providing a significant improvement over the algebraic decay for random examples the connection between entropy and generalization error in multi layer networks is discussed and a computationally cheap algorithm for constructing queries is suggested and analysed

the relative burnside module and the stable maps between classifying spaces of compact lie groups tom dieck s burnside ring of compact lie groups is generalized to the relative case for any g d n a compact lie group and its normal subgroup a g n is defined to be an appropriate set of the equivalence classes of compact g enr s with free n action in such a way that i a g d n 7g n so b n g where b n g is the classifying space of principal n g bundle under the product situation i e g f x k n k a f x k d k is also denoted by a f k as it turns out to be the usual a f k when both f and k are finite then a couple of applications are given to the study of stable maps between classifying spaces of compact lie groups a conceptual proof of feshbach s double coset formula and a density theorem on the map ap a l h a a bl bh p for any compact lie groups l k when p is odd some restriction is applied to l when p 2 this latter result may be regarded as the pushout of feshbach s density theorem and the theorem of may snaith zelewski over the celebrated carlsson solution of segal s burnside ring conjecture 0 introduction even before the arrival of carlsson s celebrated paper c the segal conjecture for finite groups was known to imply the complete calculation of the stable maps between classifying spaces of finite groups agm lmm more recently snaith s2 got interested in the stable maps between classifying spaces of compact lie groups while studying his explicit brauer induction problem see s2 which is a nice reference on this topic snaith s research led to the further generalization of the segal conjecture by msz theorem a msz let f and j be finite groups and let k be a compact lie group then a induces the isomorphism a a f x j k a j fxj bfj bfk f where a f x j k is the grothendieck a f x j module of principal f x j k bundles over finite f x j sets and aj fxj is the completion of received by the editors june 23 1993 1991 mathematics subject classification primary 55p42 55r35 57s15 secondary 55q91 55r9 1

loop structures on homotopy fibers of self maps of spheres let s 2 n 1 k denote the fiber of the degree k map on the sphere s 2 n 1 if k p r where p is an odd prime and n divides p 1 then s 2 n 1 k is known to be a loop space it is also known that s 3 2 r is a loop space for r 3 in this paper we study the possible loop structures on this family of spaces for all primes p in particular we show that s 3 4 is not a loop space our main result is that whenever s 2 n 1 p r is a loop space the loop structure is unique up to homotopy

generalized p center problems complexity results and approximation algorithms abstract in an earlier paper two alternative p center problems where the centers serving costumers must be chosen so that exactly one node from each of p prespecified disjoint pairs of nodes is selected were shown to be np complete this paper considers a generalized version of these problems in which the nodes from which the p servers are to be selected are partitioned into k sets and the number of servers selected from each set must be within a prespecified range we refer to these problems as the set p center problems we establish that the triangle inequality inequality versions of these problems in which the edge weights are assumed to satisfy the triangle inequality are also np complete we also provide a polynomial time approximation algorithm for the two inequality set p center problems that is optimal for one of the problems in the sense that no algorithm with polynomial running time can provide a better constant factor performance guarantee unless p np for the special case alternative p center problems which we refer to as the pair p center problems we extend the previous results in several ways for example the results mentioned above for the set p center problems also apply to the pair p center problems furthermore we establish and exploit a correspondence between satisfiability and the dominating set type of problems that naturally arise when considering the decision versions of the pair p center problems

fault tolerant k center problems the basic k center problem is a fundamental facility location problem where we are asked to locate k facilities in a graph and to assign vertices to facilities so as to minimize the maximum distance from a vertex to the facility to which it is assigned this problem is known to be np hard and several optimal approximation algorithms that achieve an approximation factor of 2 have been developed for it we focus our attention on a generalization of this problem where each vertex is required to have a set of k centers close to it in particular we study two different versions of this problem in the first version each vertex is required to have at least centers close to it in the second version each vertex that does not have a center placed on it is required to have at least centers close to it for both these versions we are able to provide polynomial time approximation algorithms that achieve constant approximation factors for any for the first version we give an algorithm that achieves an approximation factor of 3 for any and achieves an approximation factor of 2 for 4 for the second version we provide algorithms with approximation factors of 2 for any the best possible approximation factor for even the basic k center problem is 2 assuming p np in addition we give a polynomial time approximation algorithm for a generalization of the k supplier problem where a subset of at most k supplier nodes must be selected as centers so that every demand node has at least centers close to it for this version our approximation factor is 3 the best possible approximation factor for even the basic k supplier problem is 3 assuming p np

automorphisms of p groups given as cyclic by elementary abelian central extensions abstract we determine the structure of aut g and its relation to symplectic groups when g is a non abelian p group given by a central extension of the form 1 z p g z p z p 1

asymmetry in k center variants this paper explores three concepts the k center problem some of its variants and asymmetry the k center problem is fundamental in location theory variants of k center may more accurately model real life problems than the original formulation asymmetry is a significant impediment to approximation in many graph problems such as k center facility location k median and the tsp we give an o log n approximation algorithm for the asymmetric weighted k center problem here the vertices have weights and we are given a total budget for opening centers in the p neighbor variant each vertex must have p unweighted centers nearby we give an o log k bicriteria algorithm using 2k centers for small p finally we show the following three versions of the asymmetric k center problem to be inapproximable priority k center k supplier and outliers with forbidden centers

hybrid manifold embedding in this brief we present a novel supervised manifold learning framework dubbed hybrid manifold embedding hyme unlike most of the existing supervised manifold learning algorithms that give linear explicit mapping functions the hyme aims to provide a more general nonlinear explicit mapping function by performing a two layer learning procedure in the first layer a new clustering strategy called geodesic clustering is proposed to divide the original data set into several subsets with minimum nonlinearity in the second layer a supervised dimensionality reduction scheme called locally conjugate discriminant projection is performed on each subset for maximizing the discriminant information and minimizing the dimension redundancy simultaneously in the reduced low dimensional space by integrating these two layers in a unified mapping function a supervised manifold embedding framework is established to describe both global and local manifold structure as well as to preserve the discriminative ability in the learned subspace experiments on various data sets validate the effectiveness of the proposed method

a combinatorial strongly polynomial algorithm for minimizing submodular functions this paper presents a combinatorial polynomial time algorithm for minimizing submodular functions answering an open question posed in 1981 by grotschel lovasz and schrijver the algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter the resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value the paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set independent of the function values

a general framework of hierarchical clustering and its applications hierarchical clustering problem is a traditional topic in computer science which aims to discover a consistent hierarchy of clusters with different granularities one of the most important open questions on hierarchical clustering is the identification of the meaningful clustering levels in the hierarchical structure in this paper we answer this question from algorithmic point of view in particular we derive a quantitative analysis on the impact of the low level clustering costs on high level clusters when agglomerative algorithms are run to construct the hierarchy this analysis enables us to find meaningful clustering levels which are independent of the clusters hierarchically beneath it we thus propose a general agglomerative hierarchical clustering framework which automatically constructs meaningful clustering levels this framework is proven to be generally applicable to any k clustering problem in any relaxed metric space in which strict triangle inequality is relaxed within some constant factor to fully utilize the hierarchical clustering framework we conduct some case studies on k median and k means clustering problems in both of which our framework achieves better approximation factor than the state of the art methods we also extend our framework to handle the data stream clustering problem which allows only one scan on the whole data set by incorporating our framework into guha s data stream clustering algorithm the clustering quality is greatly enhanced with only small extra computation cost incurred the extensive experiments show that our proposal is superior to the distance based agglomerative hierarchical clustering and data stream clustering algorithms on a variety of data sets

generalized submodular cover problems and applications the greedy approach has been successfully applied in the past to produce logarithmic ratio approximations to np hard problems under certain conditions the problems for which these conditions hold are known as submodular cover problems the current paper3extends the applicability of the greedy approach to wider classes of problems the usefulness of our extensions is illustrated by giving new approximate solutions for two different types of problems the first problem is that of finding the spanning tree of minimum weight among those whose diameter is bounded by d a logarithmic ratio approximation algorithm is given for the cases of d 4 and 5 this approximation ratio is also proved to be the best possible unless p np the second type involves some known and new center selection problems for which new logarithmic ratio approximation algorithms are given again it is shown that the ratio must be at least logarithmic unless p np

the negative answer to kameko s conjecture on the hit problem abstract the goal of this paper is to give a negative answer to kameko s conjecture on the hit problem stating that the cardinal of a minimal set of generators for the polynomial algebra p k considered as a module over the steenrod algebra a is dominated by an explicit quantity depending on the number of the polynomial algebra s variables k the conjecture was shown by kameko himself for k 3 in his phd thesis in the johns hopkins university in 1990 and recently proved by us and kameko for k 4 however we claim that it turns out to be wrong for any k 4 in order to deny kameko s conjecture we study a minimal set of generators for a module p k in some so call generic degrees what we mean by generic degrees is a bit different from that of other authors in the fields such as crabb hubbuck nam repka selick wood we prove an inductive formula for the cardinal of the minimal set of generators in these generic degrees when the number of the variables k increases as an immediate consequence of this inductive formula we recognize that kameko s conjecture is no longer true for any k 4

almost all generalized extraspecial p groups are resistant a p group p is called resistant if for any finite group g having p as a sylow p subgroup the normalizer ng p controls p fusion in g the aim of this paper is to prove that any generalized extraspecial p group p is resistant excepting the case when p e a where a is elementary abelian and e is dihedral of order 8 when p 2 or extraspecial of order p3 and exponent p when p is odd this generalizes a result of green and minh

the weak conjecture on spherical classes let mathcal a be the mod 2 steenrod algebra we construct a chain level representation of the dual of singer s algebraic transfer which maps singer s invariant theoretic model of the dual of the lambda algebra gamma k wedge to bf f 2 x 1 pm 1 ldots x k pm 1 and is the inclusion of the dickson algebra d k subset gamma k wedge into bf f 2 x 1 ldots x k this chain level representation allows us to confirm the weak conjecture on spherical classes see 9 assuming the truth of 1 either the conjecture that the dickson invariants of at least k 3 variables are homologically zero in tor k mathcal a bf f 2 bf f 2 2 or a conjecture on mathcal a decomposability of the dickson algebra in gamma k wedge we prove the conjecture in item 1 for k 3 and also show a weak form of the conjecture in item 2

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 nonparametric statistical approach to clustering via mode identification a new clustering approach based on mode identification is developed by applying new optimization techniques to a nonparametric density estimator a cluster is formed by those sample points that ascend to the same local maximum mode of the density function the path from a point to its associated mode is efficiently solved by an em style algorithm namely the modal em mem this method is then extended for hierarchical clustering by recursively locating modes of kernel density estimators with increasing bandwidths without model fitting the mode based clustering yields a density description for every cluster a major advantage of mixture model based clustering moreover it ensures that every cluster corresponds to a bump of the density the issue of diagnosing clustering results is also investigated specifically a pairwise separability measure for clusters is defined using the ridgeline between the density bumps of two clusters the ridgeline is solved for by the ridgeline em rem algorithm an extension of mem based upon this new measure a cluster merging procedure is created to enforce strong separation experiments on simulated and real data demonstrate that the mode based clustering approach tends to combine the strengths of linkage and mixture model based clustering in addition the approach is robust in high dimensions and when clusters deviate substantially from gaussian distributions both of these cases pose difficulty for parametric mixture modeling a c package on the new algorithms is developed for public access at http www stat psu edu jiali hmac

spectral multidimensional scaling an important tool in information analysis is dimensionality reduction there are various approaches for large data simplification by scaling its dimensions down that play a significant role in recognition and classification tasks the efficiency of dimension reduction tools is measured in terms of memory and computational complexity which are usually a function of the number of the given data points sparse local operators that involve substantially less than quadratic complexity at one end and faithful multiscale models with quadratic cost at the other end make the design of dimension reduction procedure a delicate balance between modeling accuracy and efficiency here we combine the benefits of both and propose a low dimensional multiscale modeling of the data at a modest computational cost the idea is to project the classical multidimensional scaling problem into the data spectral domain extracted from its laplace beltrami operator there embedding into a small dimensional euclidean space is accomplished while optimizing for a small number of coefficients we provide a theoretical support and demonstrate that working in the natural eigenspace of the data one could reduce the process complexity while maintaining the model fidelity as examples we efficiently canonize nonrigid shapes by embedding their intrinsic metric into a method often used for matching and classifying almost isometric articulated objects finally we demonstrate the method by exposing the style in which handwritten digits appear in a large collection of images we also visualize clustering of digits by treating images as feature points that we map to a plane

the cohomology of the steenrod algebra and representations of the general linear groups let tr k be the algebraic transfer that maps from the coinvariants of certain gl k representations to the cohomology of the steenrod algebra this transfer was defined by w singer as an algebraic version of the geometrical transfer tr k s bv k s s 0 it has been shown that the algebraic transfer is highly nontrivial more precisely that tr k is an isomorphism for k 1 2 3 and that tr k tr k is a homomorphism of algebras in this paper we first recognize the phenomenon that if we start from any degree d and apply sq repeatedly at most k 2 times then we get into the region in which all the iterated squaring operations are isomorphisms on the coinvariants of the gl k representations as a consequence every finite sq 0 family in the coinvariants has at most k 2 nonzero elements two applications are exploited the first main theorem is that tr k is not a n isomorphism for k 5 furthermore for every k 5 there are infinitely many degrees in which tr k is not an isomorphism we also show that if tr detects a nonzero element in certain degrees of ker sq 0 then it is not a monomorphism and further for each k tr k is not a monomorphism in infinitely many degrees the second main theorem is that the elements of any sq 0 family in the cohomology of the steenrod algebra except at most its first k 2 elements are either all detected or all not detected by tr k for every k applications of this study to the cases k 4 and 5 show that tr 4 does not detect the three families g d 3 and p and that tr 5 does not detect the family h n 1g n n 1

on the complexity of a class of combinatorial optimization problems with uncertainty we consider a robust minmax regret version of the problem of selecting p elements of minimum total weight out of a set of m elements with uncertainty in weights of the elements we present a polynomial algorithm with the order of complexity o min p m p 2m for the case where uncertainty is represented by means of interval estimates for the weights we show that the problem is np hard in the case of an arbitrary finite set of possible scenarios even if there are only two possible scenarios this is the first known example of a robust combinatorial optimization problem that is np hard in the case of scenario represented uncertainty but is polynomially solvable in the case of the interval representation of uncertainty

robust experimental design for multivariate generalized linear models a simple heuristic is proposed for constructing robust experimental designs for multivariate generalized linear models the method is based on clustering a set of local optimal designs a method for finding local d optimal designs using available resources is also introduced clustering with its simplicity and minimal computation needs is demonstrated to outperform more complex and sophisticated methods