violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

critical exponents from power spectra we have simulated the two and three dimensional ising models at their respective critical points with a conventional monte carlo algorithm from the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz 2 16 2 19 andz 2 05 in agreement with the results quoted in the literature we have also studied the power spectrum for the kardar parisi zhang and sun guo grant equations describing interface dynamics arguments similar to what was recently used to conclude thatz 4 for model b in critical dynamics were applied to the sun guo grant growth model and the known exact values for the roughening and dynamic exponents were obtained from an analysis of the corresponding power spectrum in self organized critical sand models one obtains a recently proposed hyperscaling relation

sharing the cost of multicast transmissions in wireless networks a crucial issue in non cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network each station acts as a selfish agent that may misreport its utility i e the maximum cost it is willing to incur to receive the service in terms of power consumption in order to maximize its individual welfare defined as the difference between its true utility and its charged cost a provider can discourage such deceptions by using a strategyproof cost sharing mechanism that is a particular public algorithm that by forcing the agents to truthfully reveal their utility starting from the reported utilities decides who gets the service the receivers and at what price a mechanism is said budget balanced bb if the receivers pay exactly the possibly minimum cost of the transmission and approximate budget balanced bb if the total cost charged to the receivers covers the overall cost and is at most times the optimal one while it is efficient if it maximizes the sum of the receivers utilities minus the total cost over all receivers sets in this paper we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or bb when the power assignments are induced by a fixed universal spanning tree or 3 ln k 1 bb k is the number of receivers otherwise then we consider the case in which the stations lay in a d dimensional euclidean space and the powers fall as 1 d and provide strategyproof mechanisms that are either 1 bb or efficient for 1 or d 1 finally we show the existence of 2 3d 1 bb strategyproof mechanisms in any d dimensional space for every d for the special case of d 2 such a result can be improved to achieve 12 bb mechanisms

minimum cost spanning tree games we consider the problem of cost allocation among users of a minimum cost spanning tree network it is formulated as a cooperative game in characteristic function form referred to as a minimum cost spanning tree m c s t game we show that the core of a m c s t game is never empty in fact a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem for m c s t games with efficient coalition structures we define and construct m c s t games on the components of the structure we show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli respectively of the induced games on the components of the efficient coalition structure

cooperative interval games mountain situations with interval data in this paper we extend mountain situations by using interval calculus we define the interval bird allocation and show that this allocation is a special core element of the interval cost game corresponding to an interval mountain situation we deal with the interval cost sharing problem by introducing the cooperative interval cost game further we consider a subset of the interval core of the related interval cost game each element of this set is extendable to a population monotonic interval allocation scheme or shortly pmias finally we show that each interval core element of an interval connection game is extendable to bi monotonic interval allocation scheme or shortly bi mias

on the concavity of delivery games abstract delivery games introduced by hamers borm van de leensel and tijs in 1994 are combinatorial optimization games that arise from delivery problems closely related to the chinese postman problem cpp they showed that delivery games are not necessarily balanced for delivery problems corresponding to the class of bridge connected euler graphs they showed that the related games are balanced this paper focuses on the concavity property for delivery games a delivery game arising from a delivery model corresponding to a bridge connected euler graph need not be concave the main result will be that for delivery problems corresponding to the class of bridge connected cyclic graphs which is a subclass of the class of bridge connected euler graphs the related delivery games are concave further we discuss some extreme points of the core and the value for this class of concave delivery games

universality along the critical line of the ising cellular automata the author checks the hypothesis of universality along the critical line of the ising cellular automata ica by measuring critical exponents of damage propagation at the transition temperature tk in zero field and at higher temperatures in nonzero field and at the kauffman limit t infinity numerical results support the claim of universality

a new look at the role of players weights in the weighted shapley value abstract everal new families of semivalues for weighted n person transferable utility games are axiomatically constructed and discussed under increasing collections of axioms where the weighted shapley value arises as the resulting one member family a more general approach to such weighted games defined in the form of two components a weight vector and a classical tu game v is provided the proposed axiomatizations are done both in terms of and v several new axioms related to the weight vector are discussed including the so called amalgamating payoffs axiom which characterizes the value of a weighted game in terms of another game with a smaller number of players they allow for a new look at the role of players weights in the context of the weighted shapley value for the model of weighted games giving new properties of it besides another simple formula for the weighted shapley value is found and examples illustrating some surprising behavior of it in the context of players weights are given the paper contains a wide discussion of the results obtained

population monotonic allocation schemes for vertex cover games abstract for vertex cover games introduced by deng et al 1999 2 we investigate population monotonic allocation schemes introduced by sprumont 1990 11 we show that the existence of a population monotonic allocation scheme pmas for short for vertex cover games can be determined efficiently and that a pmas if exists can be constructed accordingly we also show that integral pmas es for vertex cover games can be characterized with stable matchings and be enumerated by employing gale shapley algorithm introduced by gale and shapley 1962 4

optimistic weighted shapley rules in minimum cost spanning tree problems abstract we introduce optimistic weighted shapley rules in minimum cost spanning tree problems we define them as the weighted shapley values of the optimistic game v introduced in bergantinos and vidal puga bergantinos g vidal puga j j forthcoming the optimistic tu game in minimum cost spanning tree problems international journal of game theory available from we prove that they are obligation rules tijs s branzei r moretti s norde h 2006 obligation rules for minimum cost spanning tree situations and their monotonicity properties european journal of operational research 175 121 134

kinetics of domain growth in systems with local barriers we study domain growth in spin 1 lattice models having nonconserved spin flip kinetics with local barriers our primary motivation is to model the relaxational behavior of physical systems in which molecular motion is impeded by local kinetic barriers the kinetic constraint is such that a spin from an up down state can flip to a down up state only via the zero state which has a higher energy we examine how the usual curvature driven domain growth is affected by these local barriers and whether the single spin barriers have a collective effect this paper presents comprehensive numerical results for phase ordering dynamics in this model using monte carlo simulations we demonstrate dynamical scaling for domain size distribution functions and spatial correlation functions we also present results for the time dependence of characteristic length scales and autocorrelation functions the length scale behavior is interpreted in terms of the random walk of steps on domain boundaries furthermore we present a simple stochastic model to derive an analytic expression for the autocorrelation function which exhibits a stretched exponential behavior over an extended regime in agreement with our numerical simulations

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

parameterized learnability of juntas we study the parameterized complexity of learning k juntas and some variations of juntas we show the hardness of learning k juntas and subclasses of k juntas in the pac model by reductions from a w 2 complete problem on the other hand as a consequence of a more general result we show that k juntas are exactly learnable with improper equivalence queries and access to a w p oracle

on the dynamic exponent of the two dimensional ising model the authors use the method of damage spreading to measure the time taken for the equilibrium damage the magnetization to disappear in finite systems 10 or 2 27

the description identification problem abstract in this note we introduce a notion of description identification which generalises both concept learning as conceptualised by winston young et al and mitchell and also incremental description refinement as described by bobrow and webber assuming certain properties of the description space involved there is an algorithm for solving the more general description identification problem which extends the version space strategy of mitchell and we present this the work described here can be regarded as a further formalisation and development of the work of mitchell on version space representation and the work of young et al and plotkin on description spaces plotkin s unpublished work presented a similar though slightly more restricted approach to the concept learning part of our subject and gave examples of types of description spaces that connect the work with the earlier work of winston

how bad may learning curves be in this paper we motivate the need for estimating bounds on learning curves of average case learning algorithms when they perform the worst on training samples we then apply the method of reducing learning problems to hypothesis testing ones to investigate the learning curves of a so called ill disposed learning algorithm in terms of a system complexity the boolean interpolation dimension since the ill disposed algorithm behaves worse than ordinal ones and the boolean interpolation dimension is generally bounded by the number of system weights the results can apply to interpreting or to bounding the worst case learning curve in real learning situations this study leads to a new understanding of the worst case generalization in real learning situations which differs significantly from that in the uniform learnable setting via vapnik chervonenkis vc dimension analysis we illustrate the results with some numerical simulations

computing the nucleolus of some combinatorially structured games in this paper we introduce the prenucleolus for a transferable utility game n v where 2 n the prenucleolus is a straightforward generalization of the ordinary prenucleolus where only the coalitions in determine the outcome we impose a combinatorial structure on the collection which enables us to compute the prenucleolus in n 3 time the algorithm can be used for computing the nucleolus of several classes of games among which is the class of minimum cost spanning tree games

damage spreading in the kawasaki ising model abstract we observe no phase transition in the damage spreading probability at the curie point of the 2d ising model with nearest neighbor spin exchange dynamics furthermore we report values of the growth exponent z close to unity implying speed of light transmission of information and values of the exponents describing the scaling behavior of the damage mass with time and distance close to two finally we discuss the spreading of damage in a one dimensional system

multi criteria minimum cost spanning tree games abstract the minimum cost spanning tree game mcst game is a well known model within operations research games that has been widely studied in the literature in this paper we introduce the multi criteria version of the mcst game as a set valued tu game we prove that the extension of bird s cost allocation rule provides dominance core elements in this game we also give a family of core solutions that are different from the previous one these solutions are based on proportional allocations obtained using scalar solutions of the multi criteria spanning tree problem besides we prove necessary and sufficient conditions ensuring that the preference core of this game is not empty

cost allocation for a tree network with heterogeneous customers we analyze a cost allocation problem which could naturally arise from a situation wherein a tree networkt n 0 e serving heterogeneous customers has to be constructed the customers located atn require some service from a central supplier located at vertex 0 the customers have heterogeneous preferences for the level or quality of service received from the central supplier we formulate the above cost allocation problem as a cooperative game referred to as anextended tree game the extended tree game is a proper extension of megiddo s 1978 tree game wherein all the customers have identical preferences regarding the level of service received we prove that an extended tree game is convex and we show that its shapley value can be computed in p n time wherep is the number of distinct preference levels we further provide a complete facial description of the core polytope of an extended tree game and demonstrate that even when there are only two classes of customers the number of nonredundant core constraints could be exponential in n nevertheless we are able to construct an p n algorithm to check the core membership of an arbitrary cost allocation which can be used to construct an p n 3 combinatorial algorithm to compute the nucleolus of an extended tree game finally we show that the complements of the facet defining coalitions for the core are all connected in an auxiliary tree graph with node setn

effective analysis of damage spreading in ising models using large lattices and different methods of simulation and analysis the kinetic critical exponent z for damage spreading is shown to be consistent with z 2 in two to five dimensions without the logarithmic problems seen in some earlier work

new techniques for cost sharing in combinatorial optimization games combinatorial optimization games form an important subclass of cooperative games in recent years increased attention has been given to the issue of finding good cost shares for such games in this paper we define a very general class of games called integer minimization games which includes the combinatorial optimization games in the literature as special cases we then present new techniques based on row and column generation for computing good cost shares for these games to illustrate the power of these techniques we apply them to traveling salesman and vehicle routing games our results generalize and unify several results in the literature the main underlying idea is that suitable valid inequalities for the associated combinatorial optimization problems can be used to derive improved cost shares

congestion network problems and related games this paper analyzes network problems with congestion effects from a cooperative game theoretic perspective it is shown that for network problems with convex congestion costs the corresponding games have a non empty core if congestion costs are concave then the corresponding game has not necessarily core elements but it is derived that contrary to the convex congestion situation there always exist optimal tree networks extensions of these results to a class of relaxed network problems and associated games are derived

interactive learning of monotone boolean functions this paper presents some optimal interactive algorithms for some problems related to learning of monotone boolean functions these algorithms are based on the fundamental hansel theorem the advantage of the algorithms is that they are not heuristics as is often the case of many known algorithms for general boolean functions but they are optimal in the sense of the shannon function this paper also formulates a new problem for the joint restoration of two nested monotone boolean functions f1 and f2 this formulation allows one to further decrease the dialogue with an expert and restore nonmonotone functions of the form f2 f1 the effectiveness of the proposed approaches is demonstrated by some illustrative computational experiments

the role of droplet fluctuations in kinetic ising models the authors examine by monte carlo simulation and the damage algorithm the late time behaviour of fluctuations in the low temperature ordered phase of the two dimensional kinetic ising model it has been suggested that at late times correlations could be dominated by long lived droplet fluctuations of the other ordered phase giving rise to stretched exponential decays of the spin auto correlation function over the time regimes they have studied they see no evidence for anomalous long lived droplets and find that the probability distribution for droplet lifetimes decays by an ordinary exponential

critical dynamics of the three dimensional ising model a monte carlo study extensive monte carlo simulations have been performed to analyze the dynamical behavior of the three dimensional ising model with local dynamics we have studied the equilibrium correlation functions and the power spectral densities of odd and even observables the exponential relaxation times have been calculated in the asymptotic one exponential time region we find that the critical exponentz 2 09 0 02 characterizes the algebraic divergence with lattice size for all observables the influence of scaling corrections has been analyzed we have determined integrated relaxation times as well their dynamical exponentzint agrees withz for correlations of the magnetization and its absolute value but it is different for energy correlations we have applied a scaling method to analyze the behavior of the correlation functions this method verifies excellent scaling behavior and yields a dynamical exponentzscal which perfectly agrees withz

a fuzzy inductive learning strategy for modular rules abstract in real applications data provided to a learning system usually contain linguistic information which greatly influences concept descriptions derived by conventional inductive learning methods the design of learning methods to learn concept descriptions in working with vague data is thus very important in this paper we apply fuzzy set concepts to machine learning to solve this problem a fuzzy learning algorithm based on the maximum information gain is proposed to manage linguistic information the proposed learning algorithm generates fuzzy rules from soft instances which differ from conventional instances in that they have class membership values experiments on the sports and the iris flower classification problems are presented to compare the accuracy of the proposed algorithm with those of some other learning algorithms experimental results show that the rules derived from our approach are simpler and yield higher accuracy than those from some other learning algorithms

learning by canonical smooth estimation ii learning and choice of model complexity this paper analyzes the properties of a procedure for learning from examples this canonical learner is based on a canonical error estimator developed in part i in learning problems one can observe data that consists of labeled sample points and the goal is to find a model or hypothesis from a set of candidates that will accurately predict the labels of new sample points the expected mismatch between a hypothesis prediction and the actual label of a new sample point is called the hypothesis generalization error we compare the canonical learner with the traditional technique of finding hypotheses that minimize the relative frequency based empirical error estimate it is shown that for a broad class of learning problems the set of cases for which such empirical error minimization works is a proper subset of the cases for which the canonical learner works we derive bounds to show that the number of samples required by these two methods is comparable we also address the issue of how to determine the appropriate complexity for the class of candidate hypotheses

domain growth kinetics and symmetry breaking in a thermally quenched system the authors simulate thermal quenches on a two dimensional hard core model with symmetry breaking phase transition by dividing large configurations into many small sub squares lack of self averaging is avoided and statistics are improved dynamic scaling is observed during more than two decades

a general lower bound on the number of examples needed for learning abstract we prove a lower bound of 1 ln 1 vcdim c on the number of random examples required for distribution free learning of a concept class c where vcdim c is the vapnik chervonenkis dimension and and are the accuracy and confidence parameters this improves the previous best lower bound of 1 ln 1 vcdim c and comes close to the known general upper bound of o 1 ln 1 vcdim c ln 1 for consistent algorithms we show that for many interesting concept classes including k cnf and k dnf our bound is actually tight to within a constant factor

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

cost allocation in the chinese postman problem this paper considers a cost allocation problem that arises from a delivery problem associated with the chinese postman problem cpp a delivery problem is described by a connected undirected graph in which each edge belongs to a different player a cost function on the edges of this graph and a fixed vertex which is referred to as the post office assume that the post office is providing some service to the players the nature of this service which can be thought of as mail delivery requires that a server will travel along the edges of the graph and returns to the post office the cost allocation problem is concerned with the cost of providing the service to all players a specific cost allocation rule is introduced and characterized further the class of delivery problems gives rise to a new class of cooperative combinatorial optimization games called delivery games it is shown that the outcome of the allocation rule with respect to a bridge connected euler graph is a core element of the corresponding delivery game

generalization as search abstract the problem of concept learning or forming a general description of a class of objects given a set of examples and non examples is viewed here as a search problem existing programs that generalize from examples are characterized in terms of the classes of search strategies that they employ several classes of search strategies are then analyzed and compared in terms of their relative capabilities and computational complexities

investigation on irreducible cost vectors in minimum cost arborescence problems abstract we study cost allocation rules in minimum cost arborescence problems where agents need to build a network to a source in order to obtain some resource provided a vector of costs of edges agent source pairs the agents cooperate to construct a minimum cost arborescence rooted at the source in order to reduce the total building cost minimum cost arborescence problems are extensions of well studied minimum cost spanning tree problems to deal with asymmetric edge costs regarding cost allocation rules in minimum cost arborescence problems dutta and mishra 2012 extended the folk rule which is one of the most important rules in minimum cost spanning tree problems based on the problem with the vector of the most reduced costs called irreducible form in minimum cost spanning tree problems several axiomatic characterizations of the folk rule have been proposed however it is difficult to extend them in minimum cost arborescence problems one of the reasons is that strong and reasonable axioms in minimum cost spanning tree problems which imply irreducible form dependence of cost allocation rules are not satisfied by the folk rule in minimum cost arborescence problems hence we search for other axioms which imply irreducible form dependence for this purpose we investigate irreducible cost vectors in minimum cost arborescence problems and characterize the irreducible form

iterative version spaces an incremental depth first algorithm for computing the s and set of mitchell s candidate elimination and mellish s description identification algorithm is presented as in mellish s approach lowerbounds examples as well as upperbounds can be handled instead of storing the complete s and sets only one element s s and g is stored together with backtrack information the worst case space complexity of our algorithm is linear in the number of lower and upperbounds for the candidate elimination algorithm this can be exponential we introduce a test for membership of s and with a number of coverage tests linear in the number of examples consequently the worst case time complexity to compute s and for each example is only a linear factor worse than the candidate elimination algorithm s

autocorrelation functions for phase separation in ternary mixtures we present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures the numerical results are obtained from monte carlo simulations of the spin 1 blume emery griffiths model with spin exchange kinetics further we model the autocorrelation functions using an approach based on the continuous time random walk formalism the aging property of these functions is related to the time dependence of the domain size distribution our analytical results are found to be in good agreement with the numerical data

highway games on weakly cyclic graphs a highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices a cost function on the edges of the graph and a set of players each in need of constructing a connection between a specific entry and exit vertex mosquera 2007 introduce highway problems and the corresponding cooperative cost games called highway games to address the problem of fair allocation of the construction costs in case the underlying graph is a tree in this paper we study the concavity and the balancedness of highway games on weakly cyclic graphs a graph g is called highway game concave if for each highway problem in which g is the underlying graph the corresponding highway game is concave we show that a graph is highway game concave if and only if it is weakly triangular moreover we prove that highway games on weakly cyclic graphs are balanced

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

complexity of the minimum base game on matroids this paper studies the complexity of computing solution concepts for a cooperative game called the minimum base game mbg e c where its characteristic function c 2e is defined as c s the weight w b of a minimum weighted base b s for a given matroid m e and a weight function w e the minimum base game contains as a special case the minimum spanning tree game mstg in an edge weighted graph in which players are located on the edges by interpreting solution concepts of games such as core value and shapley value in terms of matroid theory we obtain the core of mbg is nonempty if and only if the matroid m has no circuit consisting only of edges with negative weights checking the concavity and subadditivity of an mbg can be done in oracle polynomial time the value of an mbg exists if and only if the core is not empty the value of mstg can be computed in polynomial time while there is no oracle polynomial algorithm for a general mbg computing the shapley value

on the core and nucleolus of directed acyclic graph games we introduce directed acyclic graph dag games a generalization of standard tree games to study cost sharing on networks this structure has not been previously analyzed from a cooperative game theoretic perspective every monotonic and subadditive cost game including monotonic minimum cost spanning tree games can be modeled as a dag game we provide an efficiently verifiable condition satisfied by a large class of directed acyclic graphs that is sufficient for the balancedness of the associated dag game we introduce a network canonization process and prove various structural results for the core of canonized dag games in particular we characterize classes of coalitions that have a constant payoff in the core in addition we identify a subset of the coalitions that is sufficient to determine the core this result also guarantees that the nucleolus can be found in polynomial time for a large class of dag games

dynamical properties of the two and three dimensional ising models by damage spreading the method of damage spreading is used to measure the dynamic exponent z for both the two and three dimensional ising models with heat bath dynamics the authors also measure a new exponent alpha describing the rate at which a damage cloud grows they report values of z 2 24 or 0 04 and alpha 0 77 or 0 11 in two dimensions and z 2 202 or 0 03 and alpha 0 92 or 0 10 in three dimensions

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

on knapsacks partitions and a new dynamic programming technique for trees let g be an acyclic directed graph with weights and values assigned to its vertices in the partially ordered knapsack problem we wish to find a maximum valued subset of vertices whose total weight does not exceed a given knapsack capacity and which contains every predecessor of a vertex if it contains the vertex itself we consider the special case where g is an out tree even though this special case is still np complete we observe how dynamic programming techniques can be used to construct pseudopolynomial time optimization algorithms and fully polynomial time approximation schemes for it in particular we show that a nonstandard approach we call left right dynamic programming is better suited for this problem than the standard bottom up approach and we show how this left right approach can also be adapted to the case of in trees and to a related tree partitioning problem arising in integrated circuit design we conclude by presenting complexity results which indicate that similar success cannot be expected with either problem when the restriction to trees is lifted

near optimal sample compression for nearest neighbors we present the first sample compression algorithm for nearest neighbors with non trivial performance guarantees we complement these guarantees by demonstrating almost matching hardness lower bounds which show that our performance bound is nearly optimal our result yields new insight into margin based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds some encouraging empirical results are also presented

on the core of network synthesis games we use polynomial formulations to show that several rational and discrete network synthesis games including the minimum cost spanning tree game satisfy the assumptions of owen s linear production game model we also discuss computational issues related to finding and recognizing core points for these classes of 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

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

a cooperative location game based on the 1 center location problem abstract in this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces the players are the customers demand points in the location problem and the characteristic value of a coalition is the cost of serving its members specifically the cost in our games is the service radius of the coalition we call these games the minimum radius location games mrlg we study the existence of core allocations and the existence of polynomial representations of the cores of these games focusing on network spaces i e finite metric spaces induced by undirected graphs and positive edge lengths and on the lp metric spaces defined over r d

dynamic exponent for 2d ising model by power spectra method we consider power spectra for fluctuating quantities at a critical point p omega varies as omega phi where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered from the magnetization spectra obtained with simulations z is found to be 2 13 or 0 03 for the two dimensional glauber kinetic ising model hence in accord with recent monte carlo relaxational studies but at odds with those obtained by series expansion and damage spreading methods excellent dynamic finite size scaling for system sizes l 10 to 128 supports our estimate

solving the multiple instance problem with axis parallel rectangles the multiple instance problem arises in tasks where the training examples are ambiguous a single example object may have many alternative feature vectors instances that describe it and yet only one of those feature vectors may be responsible for the observed classification of the object this paper describes and compares three kinds of algorithms that learn axis parallel rectangles to solve the multiple instance problem algorithms that ignore the multiple instance problem perform very poorly an algorithm that directly confronts the multiple instance problem by attempting to identify which feature vectors are responsible for the observed classifications performs best giving 89 correct predictions on a musk odor prediction task the paper also illustrates the use of artificial data to debug and compare these algorithms

on the core and nucleolus of minimum cost spanning tree games we develop two efficient procedures for generating cost allocation vectors in the core of a minimum cost spanning tree m c s t game the first procedure requires o n 2 elementary operations to obtain each additional point in the core wheren is the number of users the efficiency of the second procedure which is a natural strengthening of the first procedure stems from the special structure of minimum excess coalitions in the core of an m c s t game this special structure is later used i to ease the computational difficulty in computing the nucleolus of an m c s t game and ii to provide a geometric characterization for the nucleolus of an m c s t game this geometric characterization implies that in an m c s t game the nucleolus is the unique point in the intersection of the core and the kernel we further develop an efficient procedure for generating fair cost allocations which in some instances coincide with the nucleolus finally we show that by employing sterns transfer scheme we can generate a sequence of cost vectors which converges to the nucleolus

on some network flow games we analyze three subclasses of cooperative games arising from network optimization problems in which the resources such as arcs or nodes in the network are controlled by individuals who have conflicting objectives the first subclass of cooperative games is induced by network optimization problems over directed augmented trees we show that for this subclass of games the kernel coincides with the nucleolus and that the nucleolus can be characterized as the unique revenue allocation vector in which every pair of arc owners who are adjacent in the tree are located symmetrically with respect to their bargaining range we further give a linear characterization of the core of this subclass of games which is then used to provide a more explicit representation of the nucleolus and to construct a strongly polynomial algorithm for generating it the second subclass of cooperative games is induced by maximum flow problems in simple undirected networks we provide a useful parametric representation of the core of this subclass of games which is used to characterize the nucleolus and the intersection of the core and the kernel explicitly we show that the intersection of the core and the kernel consists of all revenue allocations in the core which assign equal payoffs to any pair of unseparated arc owners we further demonstrate that among the core vectors the nucleolus is the unique revenue allocation vector in which the smallest allocations are maximized in a lexicographical sense the third cooperative game that we study is the assignment game introduced by shapley and shubik 1972 this game is induced by the assignment problem which can be cast as a network optimization problem we investigate the relationship between the kernel and the core of the assignment game and provide a necessary and sufficient condition for the core to be contained in the kernel we further show that in general the intersection of the kernel and the core is not a convex set we also exhibit that under certain conditions the nucleolus has a simple characterization as the unique vector in the core in which the smallest revenue allocations are maximized in a lexicographical sense finally we consider the horse market example of bohm bawerk 1923 for which it is shown that the core is contained in the kernel and that the nucleolus is the midpoint of the core

simulation of time exponent in 2d glauber kinetic ising model abstract simulations of the magnetization relaxation of large square lattices at the curie point give a dynamical exponent near 2 2 somewhat higher than expected

minimum cost spanning tree games and population monotonic allocation schemes in this paper we present the subtraction algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme as a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegative combination of minimum cost spanning tree games corresponding to 0 1 cost functions it turns out that the subtraction algorithm is closely related to the famous algorithm of kruskal for the determination of minimum cost spanning trees for variants of the classical minimum cost spanning tree games we show that population monotonic allocation schemes do not necessarily exist

learning decision trees with taxonomy of propositionalized attributes we consider the problem of exploiting a taxonomy of propositionalized attributes in order to learn compact and robust classifiers we introduce propositionalized attribute taxonomy guided decision tree learner pat dtl an inductive learning algorithm that exploits a taxonomy of propositionalized attributes as prior knowledge to generate compact decision trees since taxonomies are unavailable in most domains we also introduce propositionalized attribute taxonomy learner pat learner that automatically constructs taxonomy from data pat dtl uses top down and bottom up search to find a locally optimal cut that corresponds to the literals of decision rules from data and propositionalized attribute taxonomy pat learner propositionalizes attributes and hierarchically clusters the propositionalized attributes based on the distribution of class labels that co occur with them to generate a taxonomy our experimental results on uci repository data sets show that the proposed algorithms can generate a decision tree that is generally more compact than and is sometimes comparably accurate to those produced by standard decision tree learners

learning boolean formulas efficient distribution free learning of boolean formulas from positive and negative examples is considered it is shown that classes of formulas that are efficiently learnable from only positive examples or only negative examples have certain closure properties a new substitution technique is used to show that in the distribution free case learning dnf disjunctive normal form formulas is no harder than learning monotone dnf we prove that monomials cannot be efficiently learned from negative examples alone even if the negative examples are uniformly distributed it is also shown that if the examples are drawn from uniform distributions then the class of dnf in which each variable occurs at most once is efficiently weakly learnable i e individual examples are correctly classified with a probability larger than 1 2 1 p where p is a polynomial in the relevant parameters of the learning problem we then show an equivalence between the notion of weak learning and the notion of group learning where a group of examples of polynomial size either all positive or all negative must be correctly classified with high probability

shortest path games abstract we study cooperative games that arise from the problem of finding shortest paths from a specified source to all other nodes in a network such networks model among other things efficient development of a commuter rail system for a growing metropolitan area we motivate and define these games and provide reasonable conditions for the corresponding rail application we show that the core of a shortest path game is nonempty and satisfies the given conditions but that the shapley value for these games may lie outside the core however we show that the shortest path game is convex for the special case of tree networks and we provide a simple polynomial time formula for the shapley value in this case in addition we extend our tree results to the case where users of the network travel to nodes other than the source finally we provide a necessary and sufficient condition for shortest paths to remain optimal in dynamic shortest path games where nodes are added to the network sequentially over time

depth first iterative deepening an optimal admissible tree search abstract the complexities of various search algorithms are considered in terms of time space and cost of solution path it is known that breadth first search requires too much space and depth first search can use too much time and doesn t always find a cheapest path a depth first iterative deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches the algorithm has been used successfully in chess programs has been effectively combined with bi directional search and has been applied to best first heuristic search as well this heuristic depth first iterative deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the fifteen puzzle within practical resource limits

decision theoretic generalizations of the pac model for neural net and other learning applications we describe a generalization of the pac learning model that is based on statistical decision theory in this model the learner receives randomly drawn examples each example consisting of an instance x in x and an outcome y in y and tries to find a hypothesis h x a where h in h that specifies the appropriate action a in a to take for each instance x in order to minimize the expectation of a loss l y a here x y and a are arbitrary sets l is a real valued function and examples are generated according to an arbitrary joint distribution on x times y special cases include the problem of learning a function from x into y the problem of learning the conditional probability distribution on y given x regression and the problem of learning a distribution on x density estimation we give theorems on the uniform convergence of empirical loss estimates to true expected loss rates for certain hypothesis spaces h and show how this implies learnability with bounded sample size disregarding computational complexity as an application we give distribution independent upper bounds on the sample size needed for learning with feedforward neural networks our theorems use a generalized notion of vc dimension that applies to classes of real valued functions adapted from pollard s work and a notion of capacity and metric dimension for classes of functions that map into a bounded metric space supersedes 89 30 and 90 52 also in information and computation vol 100 no 1 september 1992

a new rule for source connection problems abstract in this paper we study situations where a group of agents require a service that can only be provided from a source the so called source connection problems these problems contain the standard fixed tree the classical minimum spanning tree and some other related problems such as the k hop the degree constrained and the generalized minimum spanning tree problems among others our goal is to divide the cost of a network among the agents to this end we introduce a rule which will be referred to as a painting rule because it can be interpreted by means of a story about painting some meaningful properties in this context and a characterization of the rule are provided

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

dynamic linear programming games with risk averse players motivated by situations in which independent agents wish to cooperate in some uncertain endeavor over time we study dynamic linear programming games which generalize classical linear production games to multi period settings under uncertainty we specifically consider that players may have risk averse attitudes towards uncertainty and model this risk aversion using coherent conditional risk measures for this setting we study the strong sequential core a natural extension of the core to dynamic settings we characterize the strong sequential core as the set of allocations that satisfy a particular finite set of inequalities that depend on an auxiliary optimization model and then leverage this characterization to establish sufficient conditions for emptiness and non emptiness qualitatively whereas the strong sequential core is always non empty when players are risk neutral our results indicate that cooperation in the presence of risk aversion is much more difficult we illustrate this with an application to cooperative newsvendor games where we find that cooperation is possible when it least benefits players and may be impossible when it offers more benefit

traveling salesman games in this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited we introduce two types of cooperative games fixed route traveling salesman games and traveling salesman games as a tool to attack this problem under very mild conditions we prove that fixed route traveling salesman games have non empty cores if the fixed route is a solution of the classical traveling salesman problem core elements provide us with fair cost allocations a traveling salesman game may have an empty core even if the cost matrix satisfies the triangle inequality in this paper we introduce a class of matrices defining ts games with non empty cores

sharing supermodular costs we study cooperative games with supermodular costs we show that supermodular costs arise in a variety of situations in particular we show that the problem of minimizing a linear function over a supermodular polyhedron a problem that often arises in combinatorial optimization has supermodular optimal costs in addition we examine the computational complexity of the least core and least core value of supermodular cost cooperative games we show that the problem of computing the least core value of these games is strongly np hard and in fact is inapproximable within a factor strictly less than 17 16 unless p np for a particular class of supermodular cost cooperative games that arises from a scheduling problem we show that the shapley value which in this case is computable in polynomial time is in the least core while computing the least core value is np hard

the dynamic critical exponent of the three dimensional ising model we measure the dynamic exponent of the three dimensional ising model using a damage spreading monte carlo approach as described by macisaac and jan we simulate systems froml 5 tol 60 at the critical temperature tc 4 5115 we report a dynamic exponent z 2 35 0 05 a value much larger than the consensus value of 2 02 whereas if we assume logarithmic corrections we find thatz 2 05 0 05

version spaces and the consistency problem a version space is a collection of concepts consistent with a given set of positive and negative examples mitchell artificial intelligence 18 1982 203 226 proposed representing a version space by its boundary sets the maximally general g and maximally specific consistent concepts s for many simple concept classes the size of g and s is known to grow exponentially in the number of positive and negative examples this paper argues that previous work on alternative representations of version spaces has disguised the real question underlying version space reasoning we instead show that tractable reasoning with version spaces turns out to depend on the consistency problem i e determining if there is any concept consistent with a set of positive and negative examples indeed we show that tractable version space reasoning is possible if and only if there is an efficient algorithm for the consistency problem our observations give rise to new concept classes for which tractable version space reasoning is now possible e g 1 decision lists monotone depth two formulas and halfspaces

a generalization of obligation rules for minimum cost spanning tree problems tijs et al 23 introduce the family of obligation rules for minimum cost spanning tree problems we give a generalization of such family we prove that our family coincides with the set of rules satisfying an additivity property and a cost monotonicity property we also provide two new characterizations for the family of obligation rules using the previous properties in the first one we add a property of separability and in the second one we add core selection

fractal dimensions in three dimensional kauffman cellular automata the kauffman random networks of automata are studied on a simple cubic lattice by computer simulations each automaton follows random rules depending on its six neighbours and fixed in time a transition between the frozen and the chaotic phase is observed and the fractal dimension of the asymptotic actual damage at the phase transition is measured

learning decision trees from random examples needed for learning abstract we define the rank of a decision tree and show that for any fixed r the class of all decision trees of rank at most r on n boolean variables is learnable from random examples in time polynomial in n and linear in 1 and log 1 where is the accuracy parameter and is the confidence parameter using a suitable encoding of variables rivest s polynomial learnability result for decision lists can be interpreted as a special case of this result for rank 1 as another corollary we show that decision trees on n boolean variables of size polynomial in n are learnable from random examples in time linear in n o log n 1 and log 1 as a third corollary we show that boolean functions that have polynomial size dnf expressions for both their positive and their negative instances are learnable from random examples in time linear in n o log n 2 1 and log 1

bayes point machines kernel classifiers comprise a powerful class of non linear decision functions for binary classification the support vector machine is an example of a learning algorithm for kernel classifiers that singles out the consistent classifier with the largest margin i e minimal real valued output on the training sample within the set of consistent hypotheses the so called version space we suggest the bayes point machine as a well founded improvement which approximates the bayes optimal decision by the centre of mass of version space we present two algorithms to stochastically approximate the centre of mass of version space a billiard sampling algorithm and a sampling algorithm based on the well known perceptron algorithm it is shown how both algorithms can be extended to allow for soft boundaries in order to admit training errors experimentally we find that for the zero training error case bayes point machines consistently outperform support vector machines on both surrogate data and real world benchmark data sets in the soft boundary soft margin case the improvement over support vector machines is shown to be reduced finally we demonstrate that the real valued output of single bayes points on novel test points is a valid confidence measure and leads to a steady decrease in generalisation error when used as a rejection criterion

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics

quantifying inductive bias ai learning algorithms and valiant s learning framework abstract we show that the notion of inductive bias in concept learning can be quantified in a way that directly relates to learning performance in the framework recently introduced by valiant our measure of bias is based on the growth function introduced by vapnik and chervonenkis and on the vapnik chervonenkis dimension we measure some common language biases including restriction to conjunctive concepts conjunctive concepts with internal disjunction k dnf and k cnf concepts we also measure certain types of bias that result from a preference for simpler hypotheses using these bias measurements we analyze the performance of the classical learning algorithm for conjunctive concepts from the perspective of valiant s learning framework we then augment this algorithm with a hypothesis simplification routine that uses a greedy heuristic and show how this improves learning performance on simpler target concepts improved learning algorithms are also developed for conjunctive concepts with internal disjunction k dnf and k cnf concepts we show that all our algorithms are within a logarithmic factor of optimal in terms of the number of examples they require to achieve a given level of learning performance in the valiant framework our results hold for arbitrary attribute based instance spaces defined by either tree structured or linear attributes

computational limitations on learning from examples the computational complexity of learning boolean concepts from examples is investigated it is shown for various classes of concept representations that these cannot be learned feasibly in a distribution free sense unless r np these classes include a disjunctions of two monomials b boolean threshold functions and c boolean formulas in which each variable occurs at most once relationships between learning of heuristics and finding approximate solutions to np hard optimization problems are given

probabilistic inductive inference inductive inference machines construct programs for total recursive functions given only example values of the functions probabilistic inductive inference machines are defined and for various criteria of successful inference it is asked whether a probabilistic inductive inference machine can infer larger classes of functions if the inference criterion is relaxed to allow inference with probability at least p 0 p ex and bc it is shown that any class of functions that can be inferred from examples with probability exceeding 1 2 can be inferred deterministically and that for probabilities p 1 2 there is a discrete hierarchy of inferability parameterized by p the power of probabilistic inference strategies is characterized by equating the classes of probabilistically inferable functions with those classes that can be inferred by teams of inductive inference machines a parallel model of inference or by a third model called frequency inference