robust spatially constrained fuzzy c means algorithm for brain mr image segmentation abstract objective accurate brain tissue segmentation from magnetic resonance mr images is an essential step in quantitative brain image analysis and hence has attracted extensive research attention however due to the existence of noise and intensity inhomogeneity in brain mr images many segmentation algorithms suffer from limited robustness to outliers over smoothness for segmentations and limited segmentation accuracy for image details to further improve the accuracy for brain mr image segmentation a robust spatially constrained fuzzy c means rscfcm algorithm is proposed in this paper method firstly a novel spatial factor is proposed to overcome the impact of noise in the images by incorporating the spatial information amongst neighborhood pixels the proposed spatial factor is constructed based on the posterior probabilities and prior probabilities and takes the spatial direction into account it plays a role as linear filters for smoothing and restoring images corrupted by noise therefore the proposed spatial factor is fast and easy to implement and can preserve more details secondly the negative log posterior is utilized as dissimilarity function by taking the prior probabilities into account which can further improve the ability to identify the class for each pixel finally to overcome the impact of intensity inhomogeneity we approximate the bias field at the pixel by pixel level by using a linear combination of orthogonal polynomials the fuzzy objective function is then integrated with the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain mr images simultaneously results to demonstrate the performances of the proposed algorithm for the images with without skull stripping the first group of experiments is carried out in clinical 3t weighted brain mr images which contain quite serious intensity inhomogeneity and noise then we quantitatively compare our algorithm to state of the art segmentation approaches by using jaccard similarity on benchmark images obtained from ibsr and brainweb with different level of noise and intensity inhomogeneity the comparison results demonstrate that the proposed algorithm can produce higher accuracy segmentation and has stronger ability of denoising especially in the area with abundant textures and details conclusion in this paper the rscfcm algorithm is proposed by utilizing the negative log posterior as the dissimilarity function introducing a novel factor and integrating the bias field estimation model into the fuzzy objective function this algorithm successfully overcomes the drawbacks of existing fcm type clustering schemes and em type mixture models our statistical results mean and standard deviation of jaccard similarity for each tissue on both synthetic and clinical images show that the proposed algorithm can overcome the difficulties caused by noise and bias fields and is capable of improving over 5 segmentation accuracy comparing with several state of the art algorithms

using dual approximation algorithms for scheduling problems theoretical and practical results the problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is perhaps the most well studied problem in the theory of approximation algorithms for np hard optimization problems in this paper the strongest possible type of result for this problem a polynomial approximation scheme is presented more precisely for each e an algorithm that runs in time o n e 1 e 2 and has relative error at most e is given in addition more practical algorithms for e 1 5 2 k and e 1 6 2 k which have running times o n k log n and o n km 4 log n are presented the techniques of analysis used in proving these results are extremely simple especially in comparison with the baroque weighting techniques used previously the scheme is based on a new approach to constructing approximation algorithms which is called dual approximation algorithms where the aim is to find superoptimal but infeasible solutions and the performance is measured by the degree of infeasibility allowed this notion should find wide applicability in its own right and should be considered for any optimization problem where traditional approximation algorithms have been particularly elusive

convex separable optimization is not much harder than linear optimization the polynomiality of nonlinear separable convex concave optimization problems on linear constraints with a matrix with small subdeterminants and the polynomiality of such integer problems provided the inteter linear version of such problems ins polynomial is proven this paper presents a general purpose algorithm for converting procedures that solves linear programming problems the conversion is polynomial for constraint matrices with polynomially bounded subdeterminants among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix to integer separable convex programming an algorithm for finding a e accurate optimal continuous solution to the nonlinear problem that is polynomial in log 1 e and the input size and the largest subdeterminant of the constraint matrix is also presented these developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function the practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function only a polynomial number of function evaluations on a prespecified grid

cross domain soft partition clustering with diversity measure and knowledge reference conventional soft partition clustering approaches such as fuzzy c means fcm maximum entropy clustering mec and fuzzy clustering by quadratic regularization fc qr are usually incompetent in those situations where the data are quite insufficient or much polluted by underlying noise or outliers in order to address this challenge the quadratic weights and gini simpson diversity based fuzzy clustering model qwgsd fc is first proposed as a basis of our work based on qwgsd fc and inspired by transfer learning two types of cross domain soft partition clustering frameworks and their corresponding algorithms referred to as type i type ii knowledge transfer oriented c means ti kt cm and tii kt cm are subsequently presented respectively the primary contributions of our work are four fold 1 the delicate qwgsd fc model inherits the most merits of fcm mec and fc qr with the weight factors in the form of quadratic memberships similar to fcm it can more effectively calculate the total intra cluster deviation than the linear form recruited in mec and fc qr meanwhile via gini simpson diversity index like shannon entropy in mec and equivalent to the quadratic regularization in fc qr qwgsd fc is prone to achieving the unbiased probability assignments 2 owing to the reference knowledge from the source domain both ti kt cm and tii kt cm demonstrate high clustering effectiveness as well as strong parameter robustness in the target domain 3 ti kt cm refers merely to the historical cluster centroids whereas tii kt cm simultaneously uses the historical cluster centroids and their associated fuzzy memberships as the reference this indicates that tii kt cm features more comprehensive knowledge learning capability than ti kt cm and tii kt cm consequently exhibits more perfect cross domain clustering performance and 4 neither the historical cluster centroids nor the historical cluster centroid based fuzzy memberships involved in ti kt cm or tii kt cm can be inversely mapped into the raw data this means that both ti kt cm and tii kt cm can work without disclosing the original data in the source domain i e they are of good privacy protection for the source domain in addition the convergence analyses regarding both ti kt cm and tii kt cm are conducted in our research the experimental studies thoroughly evaluated and demonstrated our contributions on both synthetic and real life data scenarios the novel qwgsd fc model is designed for soft partition clustering two cross domain clustering methods ti tii kt cm are subsequently proposed ti tii kt cm are superior to or competitive with other existing methods the convergences of both ti kt cm and tii kt cm are proved

the price of anarchy of affine congestion games with similar strategies abstract affine congestion games are a well studied model for selfish behavior in distributed systems such as transportation and communication networks seminal influential papers in algorithmic game theory have bounded the worst case inefficiency of nash equilibria termed as price of anarchy in several variants of these games in this work we investigate to what extent these bounds depend on the similarities among the players strategies our notion of similarity is modeled by assuming that given a parameter 1 the costs of any two strategies available to a same player when evaluated in absence of congestion are within a factor one from the other it turns out that for the non atomic case better bounds can always be obtained for any finite value of for the atomic case instead 3 2 and 2 are necessary and sufficient conditions to obtain better bounds in games played on general graph topologies and on parallel link graphs respectively it is worth noticing that small values of model the behavioral attitude of players who are partially oblivious to congestion and are not willing to significantly deviate from what is their best strategy in absence of congestion

information cascade with marginal stability in a network of chaotic elements abstract a newly discovered cascade process of clusters is studied in a network of chaotic elements it is shown that the splitting of clusters and the synchronization of elements are balanced in a class of partially ordered states where marginal stability is sustained over an interval of the bifurcation parameters the partition information creation in bit space shows an avalanche process of information which leads to the anomalous behavior of power spectra roughly fitted by a power law form of the wavenumber lyapunov spectra have accumulation at null exponents analogous with those studied in fluid turbulence models

genetic based stereo algorithm and disparity map evaluation in this paper a new genetic based stereo algorithm is presented our motivation is to improve the accuracy of the disparity map by removing the mismatches caused by both occlusions and false targets in our approach the stereo matching problem is considered as an optimization problem the algorithm first takes advantage of multi view stereo images to detect occlusions and therefore removes mismatches caused by visibility problems by optimizing the compatibility between corresponding points and the continuity of the disparity map using a genetic algorithm mismatches caused by false targets are removed the quadtree structure is used to implement the multi resolution framework since nodes at different level of the quadtree cover different number of pixels selecting nodes at different levels gives a similar effect as adjusting the window size at different locations of the image the experimental results show that our approach can generate more accurate disparity maps than two existing approaches in addition we introduce a new disparity map evaluation technique which is developed based on a similar technique employed in the image segmentation area comparing with two existing evaluation approaches the new technique can evaluate the disparity maps generated without additional knowledge of the scene such as the correct depth information or novel views

cost sharing scheduling games on restricted unrelated machines we study a very general cost sharing scheduling game an instance consists of k jobs and m machines and an arbitrary weighted bipartite graph denoting the jobs strategies an edge connecting a job and a machine specifies that the job may choose the machine edge weights correspond to processing times each machine has an activation cost that needs to be covered by the jobs assigned to it jobs assigned to a particular machine share its cost proportionally to the load they generate our game generalizes singleton cost sharing games with weighted players we provide a complete analysis of the game with respect to equilibrium existence computation convergence and quality with respect to the total cost and the maximal cost we study both unilateral and coordinated deviations we show that the main factor in determining the stability of an instance and the quality of a stable assignment is the machines activation cost games with unit cost machines are generalized ordinal potential games and every instance has an optimal solution which is also a pure nash equilibrium pne on the other hand with arbitrary cost machines a pne is guaranteed to exist only for very limited instances and the price of stability is linear in the number of players also the problem of deciding whether a given game instance has a pne is np complete in our analysis of coordinated deviations we characterize instances for which a strong equilibrium exists and can be calculated efficiently and show tight bounds for the strong price of anarchy and the price of stability

a new evolutionary search strategy for global optimization of high dimensional problems global optimization of high dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation the weakness of randomization based evolutionary algorithms in searching high dimensional spaces is demonstrated in this paper a new strategy sp uci is developed to treat complexity caused by high dimensionalities this strategy features a slope based searching kernel and a scheme of maintaining the particle population s capability of searching over the full search space examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that sp uci surpasses two popular algorithms particle swarm optimizer pso and differential evolution de on high dimensional problems experimental results also corroborate the argument that in high dimensional optimization only problems with well formative fitness landscapes are solvable and slope based schemes are preferable to randomization based ones

the structure and complexity of nash equilibria for a selfish routing game in this work we study the combinatorial structure and the computational complexity of nash equilibria for a certain game that models selfish routing over a network consisting of m parallel links we assume a collection of n users each employing a mixed strategy which is a probability distribution over links to control the routing of her own traffic in a nash equilibrium each user selfishly routes her traffic on those links that minimize her expected latency cost given the network congestion caused by the other users the social cost of a nash equilibrium is the expectation over all random choices of the users of the maximum over all links latency through a link we embark on a systematic study of several algorithmic problems related to the computation of nash equilibria for the selfish routing game we consider in a nutshell these problems relate to deciding the existence of a pure nash equilibrium constructing a nash equilibrium constructing the pure nash equilibria of minimum and maximum social cost and computing the social cost of a given mixed nash equilibrium our work provides a comprehensive collection of efficient algorithms hardness results and structural results for these algorithmic problems our results span and contrast a wide range of assumptions on the syntax of the nash equilibria and on the parameters of the system

relative complexity changes in time series using information measures abstract estimation of complexity is of great interest in nonlinear signal and system analysis several complexity measures have been proposed lyapunov exponents lempel and ziv approximate entropy in the present study complexity measures derived from shannon entropy harvda charvat darovczy tsallis q entropies and their corresponding relative information measures are presented and evaluated in the context of nonlinear systems presenting abrupt complexity changes the performance of the proposed measures in the presence of controlled complexity is evaluated through numerical experiments using nonlinear models an example with heart rate variability signals is presented the results obtained show that the entropic and the relative complexity measures approach allow to discern complexity changes in a similar qualitative way compared against classical techniques but with much less computational cost and less amount of data in the presence of noise the relative complexity measures behave as robust tools for relative complexity changes detection time scale complexity analyses are presented using the continuous multiresolution entropies the assessment of time scale complexity changes is also discussed

unsupervised hierarchical image segmentation through fuzzy entropy maximization we present an unsupervised multilevel segmentation scheme for automatically segmenting grayscale and color images fuzzy 2 partition entropy is combined with graph cut to form a bi level segmentation operator that splits a given region into 2 parts based on both global optimal threshold and local spatial coherence a multilevel segmentation scheme iteratively performs on selected regions and color channels producing a coarse to fine hierarchy of segments the presented algorithm is evaluated using the berkeley segmentation database and achieves competitive results compared with the state of the art methods the fuzzy c partition entropy has been widely adopted as a global optimization technique for finding the optimal thresholds when performing multilevel gray image segmentation nevertheless existing fuzzy c partition entropy approaches generally have two limitations i e partition number cneeds to be manually tuned for different input and the methods can process grayscale images only to address these two limitations an unsupervised multilevel segmentation algorithm is presented in this paper the core step of our algorithm is a bi level segmentation operator which uses binary graph cuts to maximize both fuzzy 2 partition entropy and segmentation smoothness by iteratively performing this bi level segmentation operator multilevel image segmentation is achieved in a hierarchical manner starting from the input color image our algorithm first picks the color channel that can best segment the image into two labels and then iteratively selects channels to further split each labels until convergence the experimental results demonstrate the presented hierarchical segmentation scheme can efficiently segment both grayscale and color images quantitative evaluations over classic gray images and the berkeley segmentation database show that our method is comparable to the state of the art multi scale segmentation methods yet has the advantage of being unsupervised efficient and easy to implement

intrinsic robustness of the price of anarchy the price of anarchy defined as the ratio of the worst case objective function value of a nash equilibrium of a game and that of an optimal outcome quantifies the inefficiency of selfish behavior remarkably good bounds on this measure are known for a wide range of application domains however such bounds are meaningful only if a game s participants successfully reach a nash equilibrium this drawback motivates inefficiency bounds that apply more generally to weaker notions of equilibria such as mixed nash equilibria and correlated equilibria and to sequences of outcomes generated by natural experimentation strategies such as successive best responses and simultaneous regret minimization we establish a general and fundamental connection between the price of anarchy and its seemingly more general relatives first we identify a canonical sufficient condition for an upper bound on the price of anarchy of pure nash equilibria which we call a smoothness argument second we prove an extension theorem every bound on the price of anarchy that is derived via a smoothness argument extends automatically with no quantitative degradation in the bound to mixed nash equilibria correlated equilibria and the average objective function value of every outcome sequence generated by no regret learners smoothness arguments also have automatic implications for the inefficiency of approximate equilibria for bicriteria bounds and under additional assumptions for polynomial length best response sequences third we prove that in congestion games smoothness arguments are complete in a proof theoretic sense despite their automatic generality they are guaranteed to produce optimal worst case upper bounds on the price of anarchy

designing network protocols for good equilibria designing and deploying a network protocol determines the rules by which end users interact with each other and with the network we consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users we consider network cost sharing games where the set of nash equilibria depends fundamentally on the choice of an edge cost sharing protocol previous research focused on the shapley protocol in which the cost of each edge is shared equally among its users we systematically study the design of optimal cost sharing protocols for undirected and directed graphs single sink and multicommodity networks and different measures of the inefficiency of equilibria our primary technical tool is a precise characterization of the cost sharing protocols that induce only network games with pure strategy nash equilibria we use this characterization to prove among other results that the shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs

threshold selection using renyi s entropy image segmentation is an important and fundamental task in many digital image processing systems image segmentation by thresholding is the simplest technique and involves the basic assumption that objects and background in the digital image have distinct gray level distributions in this paper we present a general technique for thresholding of digital images based on renyi s entropy our method includes two of the previously proposed well known global thresholding methods the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

the price of anarchy under nonlinear and asymmetric costs in this paper we characterize the price of anarchy i e the inefficiency between user and system optimal solutions when costs are nonseparable asymmetric and nonlinear generalizing earlier work that has addressed the price of anarchy under separable costs the results in this paper apply primarily to nonatomic games such as the traffic equilibrium problem but also in competitive multiperiod pricing and competitive supply chain settings the bounds established in this paper are tight and explicitly account for the degree of asymmetry and nonlinearity of the cost function we first provide a proof method for problems with a positive definite jacobian matrix subsequently we use ideas from semidefinite optimization in order to account for problems with a positive semidefinite jacobian matrix where the first approach does not apply this latter connection also provides a different application of semidefinite optimization

a simple adaptive procedure leading to correlated equilibrium we propose a new and simple adaptive procedure for playing a game regret matching in this procedure players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past it is shown that our adaptive procedure guarantees that with probability one the empirical distributions of play converge to the set of correlated equilibria of the game

convergence and approximation in potential games we study the speed of convergence to approximately optimal states in two classes of potential games we provide bounds in terms of the number of rounds where a round consists of a sequence of movements with each player appearing at least once in each round we model the sequential interaction between players by a best response walk in the state graph where every transition in the walk corresponds to a best response of a player our goal is to bound the social value of the states at the end of such walks in this paper we focus on two classes of potential games selfish routing games and cut games or party affiliation games fabrikant et al 2004 12 other than bounding the price of anarchy of selfish routing games roughgarden and tardos 2002 25 awerbuch et al 2005 2 christodoulou and koutsoupias 2005 9 there are many interesting problems about game dynamics in these games it is known that exponentially long best response walks may exist to pure nash equilibria fabrikant et al 2004 12 and random best response walks converge to solutions with good approximation guarantees after polynomially many best responses goemans et al 2005 17 in this paper we study the speed of convergence on deterministic best response walks in these games and prove that starting from an arbitrary configuration after one round of best responses of players the resulting configuration is a q n approximate solution furthermore we show that starting from an empty configuration the solution after any round of best responses is a constant factor approximation we also provide a lower bound for the multi round case where we show that for any constant number of rounds t the approximation guarantee cannot be better than n e t for some e t 0 we also study cut games that provide an illustrative example of potential games the convergence of potential games to locally optimum solutions has been studied in the context of local search algorithms johnson et al 1988 19 schaffer and yannakakis 1991 28 in these games we consider two social functions the cut defined as the weight of the edges in the cut and the total happiness defined as the weight of the edges in the cut minus the weight of the remaining edges for the cut social function we prove that the expected social value after one round of a random best response walk is at least a constant factor approximation to the optimal social value we also exhibit exponentially long best response walks with poor social value for the unweighted version of this cut game we prove w n and o n lower and upper bounds on the number of rounds of best responses to converge to a constant factor cut in addition we suggest a way to modify the game to enforce a fast convergence in any fair best response walk for the total happiness social function we show that for unweighted graphs of sufficiently large girth starting from a random configuration greedy behavior of players in a random order converges to an approximate solution after one round

globally coupled circle maps abstract a network of circle maps is investigated successive transitions are found among coherent ordered partially ordered po and turbulent phases in the ordered phase two cluster attractors with similarity have a large basin volume which are reduced to a unique circle map through a scaling transformation with two parameters the po phase is characterized by the increase of partition complexity in the phase chaotic itinerancy is observed whose dynamics consists of quasistationary high dimensional chaotic motion low dimensional attractor ruins and switching among them dependence of the diffusion constant on the size and the nonlinearity clearly deviates from that by a random phase approximation suggesting remaining correlation among elements even in the turbulent phase

chaotic itinerancy and power law residence time distribution in stochastic dynamical systems chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy the model consists of a random walk on a half line and a markov chain with a transition probability matrix the stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins it is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of truncated power law distributions if the basin of attraction for each attractor ruin has a zero measure this result is confirmed by simulation of models exhibiting chaotic itinerancy chaotic itinerancy is also shown to be absent in coupled milnor attractor systems if the transition probability among attractor ruins can be represented as a markov chain

selfish routing in capacitated networks according to wardrop s first principle agents in a congested network choose their routes selfishly a behavior that is captured by the nash equilibrium of the underlying noncooperative game a nash equilibrium does not optimize any global criterion per se and so there is no apparent reason why it should be close to a solution of minimal total travel time i e the system optimum in this paper we offer positive results on the efficiency of nash equilibria in traffic networks in contrast to prior work we present results for networks with capacities and for latency functions that are nonconvex nondifferentiable and even discontinuous the inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows in this more general model multiple nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient nonetheless our main result shows that the best equilibrium is as efficient as in the model without capacities moreover this holds true for broader classes of travel cost functions than considered hitherto

recursive algorithm based on fuzzy 2 partition entropy for 2 level image thresholding the fuzzy c partition entropy approach for threshold selection behaves well in segmenting images but the size of search space increases very rapidly when the number of parameters needed to determine the membership function increases the computation complexity of the fuzzy 2 partition entropy approach is bounded by o l 3 in this paper a recursive scheme which decreases the computation complexity of the basic algorithm to o l 2 is proposed the approach does not need the calculation of the membership function the processing time of each image is reduced from more than 5min to less than 20s

integral decomposition in polyhedra we say that a polyhedronp satisfies weak integral decomposition if whenever an integral vector is the sum ofk vectors inp it is also the sum ofk integral vectors inp this property is related to rounding results for packing and covering problems we study the property and two related properties and give results concerning integral polymatroids totally unimodular matrices and network flows pairs of strongly base orderable matroids and branchings in directed graphs

partition complexity in a network of chaotic elements a network of chaotic elements is investigated with the use of globally coupled maps elements can split into clusters with synchronized oscillation in a partially ordered phase the clustering has an inhomogeneous tree structure like replica symmetry breaking in spin glass the clustering has large variety by attractors and strongly depends on initial conditions the variety of clusterings is characterized by the distribution of partitions originated in spin glass theory the qualitative similarity and quantitative disagreement of the given attractors with a spin glass are clarified

on the existence of pure nash equilibria in weighted congestion games we study the existence of pure nash equilibria in weighted congestion games let c denote a set of cost functions we say that c is consistent if every weighted congestion game with cost functions in c possesses a pure nash equilibrium our main contribution is a complete characterization of consistency of continuous cost functions we prove that a set c of continuous functions is consistent for two player games if and only if c contains only monotonic functions and for all nonconstant functions c1 c2 c there are constants a b r such that c1 x a c2 x b for all x r 0 for games with at least three players we prove that c is consistent if and only if exactly one of the following cases holds a c contains only affine functions b c contains only exponential functions such that c x ac e x bc for some ac bc r where ac and bc may depend on c while must be equal for every c c the latter characterization is even valid for three player games finally we derive several characterizations of consistency of cost functions for games with restricted strategy spaces such as weighted network congestion games or weighted congestion games with singleton strategies

a novel automatic microcalcification detection technique using tsallis entropy a type ii fuzzy index this article investigates a novel automatic microcalcification detection method using a type ii fuzzy index the thresholding is performed using the tsallis entropy characterized by another parameter q which depends on the non extensiveness of a mammogram in previous studies q was calculated using the histogram distribution which can lead to erroneous results when pectoral muscles are included in this study we have used a type ii fuzzy index to find the optimal value of q the proposed approach has been tested on several mammograms the results suggest that the proposed tsallis entropy approach outperforms the two dimensional non fuzzy approach and the conventional shannon entropy partition approach moreover our thresholding technique is completely automatic unlike the methods of previous related works without tsallis entropy enhancement detection of microcalcifications is meager 80 21 tps true positives with 8 1 fps false positives whereas upon introduction of the tsallis entropy the results surge to 96 55 tps with 0 4 fps

design of price mechanisms for network resource allocation via price of anarchy we study the design of price mechanisms for communication network problems in which a user s utility depends on the amount of flow she sends through the network and the congestion on each link depends on the total traffic flows over it the price mechanisms are characterized by a set of axioms that have been adopted in the cost sharing games and we search for the price mechanisms that provide the minimum price of anarchy we show that given the non decreasing and concave utilities of users and the convex quadratic congestion costs in each link if the price mechanism cannot depend on utility functions the best achievable price of anarchy is 4 3 2 sqrt 2 approx 31 4 thus the popular marginal cost pricing with price of anarchy less than 1 3 33 3 is nearly optimal we also investigate the scenario in which the price mechanisms can be made contingent on the users preference profile while such information is available

on the complexity of nash equilibria and other fixed points we reexamine what it means to compute nash equilibria and more generally what it means to compute a fixed point of a given brouwer function and we investigate the complexity of the associated problems specifically we study the complexity of the following problem given a finite game gamma with 3 or more players and given epsilon 0 compute an approximation within epsilon of some actual nash equilibrium we show that approximation of an actual nash equilibrium even to within any nontrivial constant additive factor epsilon 1 2 in just one desired coordinate is at least as hard as the long standing square root sum problem as well as a more general arithmetic circuit decision problem that characterizes p time in a unit cost model of computation with arbitrary precision rational arithmetic thus placing the approximation problem in p or even np would resolve major open problems in the complexity of numerical computation we show similar results for market equilibria it is hard to estimate with any nontrivial accuracy the equilibrium prices in an exchange economy with a unique equilibrium where the economy is given by explicit algebraic formulas for the excess demand functions we define a class fixp which captures search problems that can be cast as fixed point computation problems for functions represented by algebraic circuits straight line programs over basis max min with rational constants we show that the exact or approximate computation of nash equilibria for 3 or more players is complete for fixp the price equilibrium problem for exchange economies with algebraic demand functions is another fixp complete problem we show that the piecewise linear fragment of fixp equals ppad many other problems in game theory economics and probability theory can be cast as fixed point problems for such algebraic functions we discuss several important such problems computing the value of shapley s stochastic games and the simpler games of condon extinction probabilities of branching processes probabilities of stochastic context free grammars and termination probabilities of recursive markov chains we show that for some of them the approximation or even exact computation problem can be placed in ppad while for others they are at least as hard as the square root sum and arithmetic circuit decision problems

pure nash equilibria in player specific and weighted congestion games unlike standard congestion games weighted congestion games and congestion games with player specific delay functions do not necessarily possess pure nash equilibria it is known however that there exist pure equilibria for both of these variants in the case of singleton congestion games i e if the players strategy spaces contain only sets of cardinality one in this paper we investigate how far such a property on the players strategy spaces guaranteeing the existence of pure equilibria can be extended we show that both weighted and player specific congestion games admit pure equilibria in the case of matroid congestion games i e if the strategy space of each player consists of the bases of a matroid on the set of resources we also show that the matroid property is the maximal property that guarantees pure equilibria without taking into account how the strategy spaces of different players are interweaved additionally our analysis of player specific matroid congestion games yields a polynomial time algorithm for computing pure equilibria we also address questions related to the convergence time of such games for player specific matroid congestion games in which the best response dynamics may cycle we show that from every state there exists a short sequences of better responses to an equilibrium for weighted matroid congestion games we present a superpolynomial lower bound on the convergence time of the best response dynamics showing that players do not even converge in pseudopolynomial time

two algorithms for maximizing a separable concave function over a polymatroid feasible region abstract in this paper we present two new algorithms for maximizing a separable concave function on a polymatroid both algorithms apply to the discrete as well as the continuous version of the problem the application of these algorithms to several types of polymatroids is discussed and we show that the decomposition algorithm runs in polynomial time in the discrete version for network and generalized symmetric polymatroids and the bottom up algorithm in the discrete version runs in polynomial time when the polymatroid is given as an explicit list of constraints

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

dynamical complexity detection in pre seismic emissions using nonadditive tsallis entropy abstract we investigate within the framework of nonextensive tsallis entropy particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system the focal area of an impending earthquake the tsallis like time dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence

non atomic one round walks in congestion games abstract in this paper we study the approximation ratio of the solutions achieved after an approximate one round walk in non atomic congestion games prior to this work the solution concept of one round walks had been studied for atomic congestion games with linear latency functions only christodoulou et al 1 bilo et al 2 we give an explicit formula to determine the approximation ratio for non atomic congestion games having general latency functions in particular we focus on polynomial latency functions and we prove that the approximation ratio is exactly 1 p 1 p 1 for every polynomial of degree p then we show that by resorting to static resp dynamic resource taxation the approximation ratio can be lowered to 1 p 1 p 1 p resp 1 p 1 p 1

potential games are necessary to ensure pure nash equilibria in cost sharing games we consider the problem of designing distribution rules to share welfare cost or revenue among individually strategic agents there are many known distribution rules that guarantee the existence of a pure nash equilibrium in this setting e g the shapley value and its weighted variants however a characterization of the space of distribution rules that guarantees the existence of a nash equilibrium is unknown our work provides an exact characterization of this space for a specific class of scalable and separable games that includes a variety of applications such as facility location routing network formation and coverage games given arbitrary local welfare functions x1d568 we prove that a distribution rule guarantees equilibrium existence for all games i e all possible sets of resources agent action sets etc if and only if it is equivalent to a generalized weighted shapley value on some ground welfare functions x1d568 which can be distinct from x1d568 however if budget balance is required in

computation and efficiency of potential function minimizers of combinatorial congestion games we study the computation and efficiency of pure nash equilibria in combinatorial congestion games where the strategies of each player i are given by the binary vectors of a polytope p i our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure nash equilibria with attractive social cost approximation guarantees to this aim we identify two general properties of the underlying aggregation polytope p n sum i p i which are sufficient for our results to go through namely the integer decomposition property idp and the box totally dual integrality property box tdi our main results for polytopal congestion games satisfying idp and box tdi are as follows i we show that pure nash equilibria can be computed in polynomial time in fact we obtain this result through a general framework for separable convex function minimization which might be of independent interest ii we bound the inefficiency of these equilibria and show that this provides a tight bound on the price of stability iii we also prove that these results extend to strong equilibria for the bottleneck variant of polytopal congestion games examples of polytopal congestion games satisfying idp and box tdi include common source network congestion games symmetric totally unimodular congestion games non symmetric matroid congestion games and symmetric matroid intersection congestion games in particular r arborescences and strongly base orderable matroids

buy at bulk network design with protection we consider approximation algorithms for buy at bulk network design with the additional constraint that demand pairs be protected against a single edge or node failure in the network in practice the most popular model used in high speed telecommunication networks for protection against failures is the so called 1 1 model in this model two edge or node disjoint paths are provisioned for each demand pair we obtain the first nontrivial approximation algorithms for buy at bulk network design in the 1 1 model for both edge and node disjoint protection requirements our results are for the single cable cost model which is prevalent in optical networks more specifically we present a constant factor approximation for the single sink case and a polylogarithmic factor approximation for the multicommodity case these results are of interest for practical applications and also suggest several new challenging theoretical problems

from collective oscillations to collective chaos in a globally coupled oscillator system abstract various types of collective behaviors are discovered in globally coupled ginzburg landau oscillators when the coupling is sufficiently weak the oscillators are either in complete synchrony or their phases are scattered completely randomly for finite coupling new collective behaviors emerge such as splitting of the population into a small number of clusters or their fusion into a continuous stringlike distribution in the phase plane low dimensional chaotic dynamics arises from the coupled motion of 3 point clusters chaotic motion is also exhibited by fused clusters which is of extremely high dimension possibly proportional to the system size as is implied from its lyapunov analysis in the latter type of chaos the motion of the string is in some cases characterized by repeated stretching and foldings it is argued how this kind of coherent behavior seen on a collective level does not contradict the high dimensionality of the corresponding chaotic attractor

a new model for selfish routing in this work we introduce and study a new potentially rich model for selfish routing over non cooperative networks as an interesting hybridization of the two prevailing such models namely the kpmodel e koutsoupias c h papadimitriou worst case equilibria in g meinel s tison eds proceedings of the 16th annual symposium on theoretical aspects of computer science in lecture notes in computer science vol 1563 springer verlag 1999 pp 404 413 and the wmodel j g wardrop some theoretical aspects of road traffic research proceedings of the of the institute of civil engineers 1 pt ii 1952 325 378 in the hybrid model each of nusers is using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links in a nash equilibrium no user can unilaterally improve its expected individual cost to evaluate nash equilibria we introduce quadratic social cost as the sum of the expectations of the latencies incurred by the squares of the accumulated traffic this modeling is unlike the kp model where social cost e koutsoupias c h papadimitriou worst case equilibria in g meinel s tison eds proceedings of the 16th annual symposium on theoretical aspects of computer science in lecture notes in computer science vol 1563 springer verlag 1999 pp 404 413 is the expectation of the maximum latency incurred by the accumulated traffic but it is like the w model since the quadratic social cost can be expressed as a weighted sum of expected individual costs we use the quadratic social cost to define quadratic coordination ratio here are our main findings quadratic social cost can be computed in polynomial time this is unlike the p completeness d fotakis s kontogiannis e koutsoupias m mavronicolas p spirakis the structure and complexity of nash equilibria for a selfish routing game in p widmayer f triguero r morales m hennessy s eidenbenz r conejo eds proceedings of the 29th international colloquium on automata languages and programming in lecture notes in computer science vol 2380 springer verlag 2002 pp 123 134 of computing social cost for the kp model for the case of identical users and identical links the fully mixed nash equilibrium m mavronicolas p spirakis the price of selfish routing algorithmica 48 1 2007 91 126 where each user assigns positive probability to every link maximizes quadratic social cost as our main result we present a comprehensive collection of tight constant that is independent of m and n strictly less than 2 lower and upper bounds on the quadratic coordination ratio for several interesting special cases some of the bounds stand in contrast to corresponding super constant bounds on the coordination ratio previously shown in a czumaj b vocking tight bounds for worst case equilibria acm transactions on algorithms 3 1 2007 e koutsoupias m mavronicolas p spirakis approximate equilibria and ball fusion theory of computing systems 36 6 2003 683 693 e koutsoupias c h papadimitriou worst case equilibria in g meinel s tison eds proceedings of the 16th annual symposium on theoretical aspects of computer science in lecture notes in computer science vol 1563 springer verlag 1999 pp 404 413 m mavronicolas p spirakis the price of selfish routing algorithmica 48 1 2007 91 126 for the kp model

optimal cost sharing for resource selection games joint use of resources with usage dependent cost raises the question who pays how much we study cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources our goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability we investigate three classes of protocols basic protocols guarantee the existence of at least one pure nash equilibrium separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource uniform protocols are separable and require that the cost shares on a resource may not depend on the instance that is they remain the same even if new resources are added to or removed from the instance we find optimal basic and separable protocols that guarantee the price of stability and price of anarchy to grow logarithmically in the number of players except for the case of matroid games induced by separable protocols where the price of anarchy grows linearly with the number of players for uniform protocols we show that the price of anarchy is unbounded even for singleton games

sharing the cost of a capacity network we consider a communication network where each pair of users requests a connection guaranteeing a certain capacity the cost of building capacity is identical across pairs efficiency is achieved by any maximal cost spanning tree we construct cost sharing methods ensuring standalone core stability monotonicity of one s cost share in one s capacity requests and continuity in everyone s requests we define a solution for simple problems where each pairwise request is zero or one and extend it piecewise linearly to all problems the uniform solution obtains if we require one s cost share to be weakly increasing in everyone s capacity request in the solution we propose on the contrary one s cost share is weakly decreasing in other agents requests the computational complexity of both solutions is polynomial in the number of users the uniform solution admits a closed form expression and is the analog of a popular solution for the minimal cost spanning tree problem

threshold selection based on fuzzy c partition entropy approach abstract thresholding is an important topic for image processing pattern recognition and computer vision selecting thresholds is a critical issue for many applications the fuzzy set theory has been successfully applied to many areas such as control image processing pattern recognition computer vision medicine social science etc it is generally believed that image processing bears some fuzziness in nature in this paper we use the concept of fuzzy c partition and the maximum fuzzy entropy principle to select threshold values for gray level images we have conducted experiments on many images the experimental results demonstrate that the proposed approach can select the thresholds automatically and effectively and the resulting images can preserve the main features of the components of the original images very well

forecasting exchange rate using variational mode decomposition and entropy theory abstract in this paper we propose a new exchange rate forecasting model using variational mode decomposition vmd with parameter optimization by the combined mean square error mse and error entropy ee criterion exchange rate is decomposed into a series of underlying data components in the transformed multiscale domain using the vmd model a new mse ee criterion is proposed to determine the scale for transient factors among different extracted data components the proposed model extracts the transient factor more accurately and produces more accurate forecasts empirical studies using extensive exchange rates confirmed that the multiscale data structure can be identified more effectively in the decomposed multiscale domain using the proposed methodology the proposed model demonstrates the superior performance compared to the benchmark models

efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization the fuzzy c partition entropy has been widely adopted as a global optimization technique for finding the optimized thresholds for multilevel image segmentation however it involves expensive computation as the number of thresholds increases and often yields noisy segmentation results since spatial coherence is not enforced in this paper an iterative calculation scheme is presented for reducing redundant computations in entropy evaluation the efficiency of threshold selection is further improved through utilizing the artificial bee colony algorithm as the optimization technique finally instead of performing thresholding for each pixel independently the presented algorithm oversegments the input image into small regions and uses the probabilities of fuzzy events to define the costs of different label assignments for each region the final segmentation results is computed using graph cut which produces smooth segmentation results the experimental results demonstrate the presented iterative calculation scheme can greatly reduce the running time and keep it stable as the number of required thresholds increases quantitative evaluations over 20 classic images also show that the presented algorithm outperforms existing multilevel segmentation approaches

multiresolution color image segmentation image segmentation is the process by which an original image is partitioned into some homogeneous regions in this paper a novel multiresolution color image segmentation mcis algorithm which uses markov random fields mrf s is proposed the proposed approach is a relaxation process that converges to the map maximum a posteriori estimate of the segmentation the quadtree structure is used to implement the multiresolution framework and the simulated annealing technique is employed to control the splitting and merging of nodes so as to minimize an energy function and therefore maximize the map estimate the multiresolution scheme enables the use of different dissimilarity measures at different resolution levels consequently the proposed algorithm is noise resistant since the global clustering information of the image is required in the proposed approach the scale space filter ssf is employed as the first step the multiresolution approach is used to refine the segmentation experimental results of both the synthesized and real images are very encouraging in order to evaluate experimental results of both synthesized images and real images quantitatively a new evaluation criterion is proposed and developed

exact price of anarchy for polynomial congestion games we show exact values for the worst case price of anarchy in weighted and unweighted atomic unsplittable congestion games provided that all cost functions are bounded degree polynomials with nonnegative coefficients the given values also hold for weighted and unweighted network congestion games

image segmentation by iterated region merging with localized graph cuts this paper presents an iterated region merging based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions however the extraction of objects in a complex background often requires a lot of user interaction the proposed algorithm starts from the user labeled sub graph and works iteratively to label the surrounding un segmented regions in each iteration only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced meanwhile the data models of the object and background are updated iteratively based on high confident labeled regions the sub graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the grabcut methods in either qualitative or quantitative evaluation

on the value of coordination in network design we study network design games where n self interested agents have to form a network by purchasing links from a given set of edges we consider shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge it is well known that the price of anarchy of these games is as high as n another line of research has focused on evaluating the price of stability i e the cost of the best nash equilibrium relative to the social optimum in this paper we investigate to which extent coordination among agents can improve the quality of solutions we resort to the concept of strong nash equilibria which were introduced by aumann and are resilient to deviations by coalitions of agents we analyze the price of anarchy of strong nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs these bounds are tight or nearly tight for many scenarios it shows that by using coordination the price of anarchy drops from linear to logarithmic bounds we complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria without coordination in undirected graphs more specifically we show a lower bound of omega log w log log w for weighted games where w is the total weight of all the agents this almost matches the known upper bound of o log w our results imply that for most settings the worst case performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination these settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs

how fast elements can affect slow dynamics a chain of coupled chaotic elements with different time scales is studied in contrast with the adiabatic approximation we find that correlations between elements are transferred from faster to slower elements when the differences in the time scales of the elements lie within a certain range for such correlations to occur three features are essential strong correlations among the elements a bifurcation in the dynamics of the fastest element by changing its control parameter and cascade propagation of the bifurcation by studying coupled rossler equations we demonstrate that fast elements can affect the dynamics of slow elements when these conditions are satisfied the relevance of our results to biological memory is briefly discussed

on the impact of combinatorial structure on congestion games we study the impact of combinatorial structure in congestion games on the complexity of computing pure nash equilibria and the convergence time of best response sequences in particular we investigate which properties of the strategy spaces of individual players ensure a polynomial convergence time we show that if the strategy space of each player consists of the bases of a matroid over the set of resources then the lengths of all best response sequences are polynomially bounded in the number of players and resources we also prove that this result is tight that is the matroid property is a necessary and sufficient condition on the players strategy spaces for guaranteeing polynomial time convergence to a nash equilibrium in addition we present an approach that enables us to devise hardness proofs for various kinds of combinatorial games including first results about the hardness of market sharing games and congestion games for overlay network design our approach also yields a short proof for the pls completeness of network congestion games in particular we show that network congestion games are pls complete for directed and undirected networks even in case of linear latency functions

the complexity of computing a nash equilibrium in 1951 john f nash proved that every game has a nash equilibrium ann of math 2 54 1951 pp 286 295 his proof is nonconstructive relying on brouwer s fixed point theorem thus leaving open the questions is there a polynomial time algorithm for computing nash equilibria and is this reliance on brouwer inherent many algorithms have since been proposed for finding nash equilibria but none known to run in polynomial time in 1991 the complexity class ppad polynomial parity arguments on directed graphs for which brouwer s problem is complete was introduced c papadimitriou j comput system sci 48 1994 pp 489 532 motivated largely by the classification problem for nash equilibria but whether the nash problem is complete for this class remained open in this paper we resolve these questions we show that finding a nash equilibrium in three player games is indeed ppad complete and we do so by a reduction from brouwer s problem thus establishing that the two problems are computationally equivalent our reduction simulates a stylized brouwer function by a graphical game m kearns m littman and s singh graphical model for game theory in 17th conference in uncertainty in artificial intelligence uai 2001 relying on gadgets graphical games performing various arithmetic and logical operations we then show how to simulate this graphical game by a three player game where each of the three players is essentially a color class in a coloring of the underlying graph subsequent work x chen and x deng setting the complexity of 2 player nash equilibrium in 47th annual ieee symposium on foundations of computer science focs 2006 established by improving our construction that even two player games are ppad complete here we show that this result follows easily from our proof

mean field fluctuation of a network of chaotic elements remaining fluctuation and correlation in the large size limit fluctuation of the mean field is studied for a network of chaotic elements with the use of globally coupled maps as the size n is increased the variance of the mean field decreases up to a crossover size nc but then stays constant where the remaining variance is roughly proportional to 1nc the distribution of the mean field approaches a gaussian form up to nc but keeps some deviation for n nc the breakdown of the law of large numbers implies some hidden coherence among elements confirmed by finite mutual information and lyapunov spectra the breakdown is also supported by the instability of the self consistent solution for the perron frobenius operator the anomalous effect of additional noise to our system is also reported results from other globally coupled maps suggest that the law of large numbers is generally broken in a turbulent phase with local stretching and contraction but is satisfied for a map with stretching only

the price of routing unsplittable flow in this paper we study the price of anarchy for the general class of weighted and unweighted atomic congestion games with the sum of players costs as the objective function we show that for linear resource cost functions the price of anarchy is exactly frac 3 sqrt 5 2 approx 2 618 for weighted congestion games and exactly 2 5 for unweighted congestion games we show that for resource cost functions that are polynomials of degree d the price of anarchy is d theta d our results also hold for mixed strategies in particular these results apply to atomic routing games where the traffic demand from a source to a destination must be satisfied by choosing a single path between source and destination

on the strength of attractors in a high dimensional system milnor attractor network robust global attraction and noise induced selection abstract strength of attractor is studied by the return rate to itself after perturbations for a multi attractor state of a globally coupled map it is found that fragile milnor attractors have a large basin volume at the partially ordered phase such dominance of fragile attractors is understood by robustness of global attraction in the phase space change of the attractor strength and basin volume against the parameter and size are studied in the partially ordered phase the dynamics is often described as milnor attractor network which leads to a new interpretation of chaotic itinerancy noise induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude relevance of the observed results to neural dynamics and cell differentiation is also discussed

computing pure nash and strong equilibria in bottleneck congestion games bottleneck congestion games properly model the properties of many real world network routing applications they are known to possess strong equilibria a strengthening of nash equilibrium to resilience against coalitional deviations in this paper we study the computational complexity of pure nash and strong equilibria in these games we provide a generic centralized algorithm to compute strong equilibria which has polynomial running time for many interesting classes of games such as e g matroid or single commodity bottleneck congestion games in addition we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics using unilateral improvement dynamics in matroid games pure nash equilibria can be reached efficiently in contrast computing even a single coalitional improvement move in matroid and single commodity games is strongly np hard in addition we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics they continue to hold even for convergence to approximate equilibria

efficiency of scalar parameterized mechanisms we consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing fully rational users we study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks in particular we restrict attention to mechanisms where users are restricted to one dimensional strategy spaces we first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate we study the worst case efficiency loss ratio of the utility associated with a nash equilibrium to the maximum possible utility and show that kelly s proportional allocation mechanism minimizes the efficiency loss when users are price anticipating we then turn our attention to mechanisms where price differentiation is permitted using an adaptation of the vickrey clarke groves class of mechanisms we construct a class of mechanisms with one dimensional strategy spaces where nash equilibria are fully efficient these mechanisms are shown to be fully efficient even in general convex environments under reasonable assumptions our results highlight a fundamental insight in mechanism design when the pricing flexibility available to the mechanism designer is limited restricting the strategic flexibility of bidders may actually improve the efficiency guarantee

study of a high dimensional chaotic attractor the nature of a very high dimensional chaotic attractor in an infinite dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high dimensional attractor in the phase space we introduce two complementary bases from which the attractor is observed one the lyapunov basis composed of the lyapunov vectors and the another the fourier basis composed of the fourier modes we introduce the exterior subspaces on the basis of the lyapunov vectors and observe the chaotic motion projected onto these exteriors it is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor the origin of such a phenomenon is attributed to more fundamental features of our attractor which become manifest when the attractor is observed from the lyapunov basis a counterpart of the phenomenon can be observed also on the fourier basis because there is a statistical one to one correspondence between the lyapunov vectors and the fourier modes in particular a statistical property of the high pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

wavelet based seismic signal de noising using shannon and tsallis entropy seismograms are the vital sources of information in seismic engineering but these records are always contaminated with noise which has to be removed before using them in seismic applications recently wavelet based techniques proved to be very effective in de noising by achieving high snr however selection of the correct threshold plays a crucial role in deciding the snr value it is strange that only very few thresholders exist in seismic and non seismic studies in this paper we have proposed a set of novel entropy based thresholders through 2 experiments in experiment 1 we have proposed a shannon entropy based algorithm which has produced 11 205 snr in experiment 2 we used tsallis entropy which has moderately improved the result by providing 12 23 snr existing thresholders like visu and normal shrink have managed to produce 10 19 and 10 07 snr respectively through our experiments we observed that for low frequency problems s 0 27 the performance of both entropies matched appreciably however for high frequency s 2 7 tsallis produced slightly better snr and is more feasible in detecting the occurrence of p and s waves by smoothing the accelerograms

mammographic mass segmentation embedding multiple features in vector valued level set in ambiguous regions mammographic mass segmentation plays an important role in computer aided diagnosis systems it is very challenging because masses are always of low contrast with ambiguous margins connected with the normal tissues and of various scales and complex shapes to effectively detect true boundaries of mass regions we propose a feature embedded vector valued contour based level set method with relaxed shape constraint in particular we initially use the contour based level set method to obtain the initial boundaries on the smoothed mammogram as the shape constraint to prevent the contour leaking and meanwhile preserve the radiative characteristics of specific malignant masses afterward we relax the obtained shape constraint by analyzing possible valid regions around the initial boundaries the relaxed shape constraint is then used to design a novel stopping function for subsequent vector valued level set method since texture maps gradient maps and the original intensity map can reflect different characteristics of the mammogram we integrate them together to obtain more accurate segmentation by incorporating the new stopping function into the newly proposed feature embedded vector valued contour based level set method the experimental results suggest that the proposed feature embedded vector valued contour based level set method with relaxed shape constraint can effectively find ambiguous margins of the mass regions comparing against existing active contours methods the new scheme is more effective and robust in detecting complex masses

settling the complexity of computing two player nash equilibria we prove that bimatrix the problem of finding a nash equilibrium in a two player game is complete for the complexity class ppad polynomial parity argument directed version introduced by papadimitriou in 1991 our result building upon the work of daskalakis et al 2006a on the complexity of four player nash equilibria settles a long standing open problem in algorithmic game theory it also serves as a starting point for a series of results concerning the complexity of two player nash equilibria in particular we prove the following theorems bimatrix does not have a fully polynomial time approximation scheme unless every problem in ppad is solvable in polynomial time the smoothed complexity of the classic lemke howson algorithm and in fact of any algorithm for bimatrix is not polynomial unless every problem in ppad is solvable in randomized polynomial time our results also have a complexity implication in mathematical economics arrow debreu market equilibria are ppad hard to compute