coreness of cooperative games with truncated submodular profit functions coreness represents solution concepts related to core in cooperative games which captures the stability of players motivated by the scale effect in social networks economics and other scenario we study the coreness of cooperative game with truncated submodular profit functions specifically the profit function f cdot is defined by a truncation of a submodular function sigma cdot f cdot sigma cdot if sigma cdot ge eta and f cdot 0 otherwise where eta is a given threshold in this paper we study the core and three core related concepts of truncated submodular profit cooperative game we first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty when core is empty we show hardness results and approximation algorithms for computing other core related concepts including relative least core value absolute least core value and least average dissatisfaction value

exact approaches for testing hypotheses based on the intra class kappa coefficient testing involving the intra class kappa coefficient is commonly performed in order to assess agreement involving categorical ratings a number of procedures have been proposed which make use of the limiting null distribution as the sample size goes to infinity in order to compute the observed significance as with many tests based on asymptotic null distributions these tests are associated with problematic type i error control for selected sample sizes and points in the parameter space we propose and study a collection of exact testing approaches for both the one sample and k sample scenarios for the one sample case p values are obtained using the exact distribution of the test statistic conditional on a sufficient statistic in addition unconditional approaches are considered on the basis of maximization across the nuisance parameter space numerical evaluation reveals advantages with the exact unconditional procedures copyright 2014 john wiley sons ltd

random walks on graphs electric networks and fractals this paper is devoted to the problem of the nearest neighbour random walk on infinite graphs we investigate the rw x n started from a fixed vertex x0 x v of the graph g v e and the expected value of the first exit time t n from the n ball b n in g it will be shown that if g is sufficiently regular then d underset raise0 3em hbox smash scriptscriptstyle geqslant d omega d r underset raise0 3em hbox smash scriptscriptstyle geqslant 2 and d r d 2 d omega where d r is the rw dimension d is the fractal dimension and d is the exponent of the growth of the resistance of b n though the method of the paper was developed for the case when x0 x is a fixed vertex of the graph we hope that the result can be generalized

complementary cooperation minimal winning coalitions and power indices we introduce a new simple game which is referred to as the complementary weighted multiple majority game c wmmg for short c wmmg models a basic cooperation rule the complementary cooperation rule and can be taken as a sister model of the famous weighted majority game wmg for short in c wmmg each player is characterized by a nonnegative vector with a fixed dimension and players in the same coalition cooperate by producing a characteristic vector for this coalition each dimension of this vector equals the maximum of the corresponding dimensions of its members the value of a coalition is 1 if and only if the sum of its characteristic vector is larger than that of its complementary coalition in which case the coalition is called winning otherwise the coalitional value is 0 in this paper we concentrate on the two dimensional c wmmg an interesting property of this case is that there are at most n 1 minimal winning coalitions mwcs for short and they can be enumerated in time o nlogn where n is the number of players this property guarantees that the two dimensional c wmmg is more handleable than wmg in particular we prove that the main power indices i e the shapley shubik index the penrose banzhaf index the holler packel index and the deegan packel index are all polynomially computable to make a comparison with wmg we know that it may have exponentially many mwcs and none of the four power indices is polynomially computable unless p np still for the two dimensional case we show that local monotonicity holds for all of the four power indices in wmg this property is possessed by the shapley shubik index and the penrose banzhaf index but not by the holler packel index or the deegan packel index since our model fits very well the cooperation and competition in team sports we hope that it can be potentially applied in measuring the values of players in team sports say help people give more objective ranking of nba players and select mvps and consequently bring new insights into contest theory and the more general field of sports economics it may also provide some interesting enlightenments into the design of non additive voting mechanisms last but not least the threshold version of c wmmg is a generalization of wmg and natural variants of it are closely related with the famous airport game and the stable marriage roommates problem

a goodness of fit approach to inference procedures for the kappa statistic confidence interval construction significance testing and sample size estimation we propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome the procedure is based on a chi square goodness of fit test as applied to a model frequently used for clustered binary data the procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures the procedure also has use for significance testing and the planning of corresponding sample size requirements

bayesian inference for kappa from single and multiple studies summary cohen s kappa coefficient is a widely popular measure for chance corrected nominal scale agreement between two raters this article describes bayesian analysis for kappa that can be routinely implemented using markov chain monte carlo mcmc methodology we consider the case of m 2 independent samples of measured agreement where in each sample a given subject is rated by two rating protocols on a binary scale a major focus here is on testing the homogeneity of the kappa coefficient across the different samples the existing frequentist tests for this case assume exchangeability of rating protocols whereas our proposed bayesian test does not make any such assumption extensive simulation is carried out to compare the performances of the bayesian and the frequentist tests the developed methodology is illustrated using data from a clinical trial in ophthalmology

constrained coalition formation on valuation structures coalition structure generation is the problem of partitioning the agents of a given environment into disjoint and exhaustive coalitions so that the whole available worth is maximized while this problem has been classically studied in settings where all coalitions are allowed to form it has been recently reconsidered in the literature moving from the observation that environments often forbid the formation of certain coalitions by following this latter perspective a model for coalition structure generation is proposed where constraints of two different kinds can be expressed simultaneously indeed the model is based on the concept of valuation structure which consists of a set of pivotal agents that are pairwise incompatible plus an interaction graph prescribing that a coalition c can form only if the subgraph induced over the nodes agents in c is connected it is shown that valuation structures can be used to model a number of relevant problems arising in real world application domains then the complexity of coalition structure generation over valuation structures is studied by assuming that the functions associating each coalition with its worth are given as input according to some compact encodingrather than explicitly listing all exponentially many associations in particular islands of tractability are identified based on the topological properties of the underlying interaction graphs and on suitable algebraic properties of the given worth functions finally stability issues over valuation structures are studied too by considering the core as the prototypical solution concept

maximum likelihood estimation of the kappa coefficient from models of matched binary responses we present an estimate of the kappa coefficient of agreement between two methods of rating based on matched pairs of binary responses and show that the estimate depends on the common intraclass correlation coefficient between the pairs via monte carlo simulation we investigate power of the test of significance on kappa and the large sample bias and variance of its maximum likelihood estimator

assessment on homogeneity tests for kappa statistics under equal prevalence across studies in reliability in this paper we assess the performance of homogeneity tests for two or more kappa statistics when prevalence rates across reliability studies are assumed to be equal the likelihood score method and the chi square goodness of fit gof test provide type 1 error rates that are satisfactorily close to the nominal level but a fleiss like test is not satisfactory for small or moderate sample sizes simulations show that the score test is more powerful than the chi square gof test and the approximate sample size required for a specific power of the former is substantially smaller than the latter in addition the score test is robust to deviations from the equal prevalence assumption while the gof test is highly sensitive and it may give a grossly misleading type 1 error rate when the assumption of equal prevalence is violated we conclude that the homogeneity score test is the preferred method

the cg position value for games on fuzzy communication structures abstract a cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation the best known of these allocations is the shapley value a communication structure defines the feasible bilateral communication relationships among the agents in a cooperative situation some solutions incorporating this information have been defined from the shapley value the myerson value the position value etc later fuzzy communication structures were introduced in a fuzzy communication structure the membership of the players and the relations among them are leveled several ways of defining the myerson value for games on fuzzy communication structure were proposed one of them is the choquet by graphs cg version now we study in this work the cg position value and its calculation the cg position value is defined as a solution for games with fuzzy communication structure which considers the bilateral communications as players so the shapley value is applied for a new game the link game over the fuzzy sets of links in the fuzzy communication structure and the profit obtained for each link is allocated between both players in the link as we see in our examples and results the cg position value is more concerned with the graphical position of the players and their communications than the other cg values in this paper we also introduce a procedure to compute exactly the position value avoiding to calculate the characteristic function of the link game for all coalitions this procedure is used to determine the cg position value finally we compare the new value with other cg values in an applied example about the power of the groups in the european parliament

modelling patterns of agreement for nominal scales the measurement of agreement of repeat rating is the usual method of assessing the reliability of categorical scales measurement of agreement is also important in genetic twin studies based on categorical scales one of the most commonly used methods of analysis for both types of study is the kappa coefficient for scales with more than two categories one approach is to use a single summary kappa coefficient while this may be sufficient for many studies in some instances investigation of heterogeneity in the pattern of agreement may give additional insights as there may be greater agreement for some pairs of categories than for others in this paper kappa type coefficients are used to model heterogeneity in the pattern of agreement constraints are added to the heterogeneous model to obtain simplified models procedures for estimation confidence intervals and inference for these coefficients are described for the case of two ratings per subject for a single sample and for the comparison of two independent samples formulae for sample size and power calculation are derived using the non central chi squared distribution two simulation studies are carried out to check the empirical test size and power methods are illustrated by two examples involving nominal scales with three categories

matching games the least core and the nucleolus a matching game is a cooperative game defined by a graph g n e the player set is n and the value of a coalition s n is defined as the size of a maximum matching in the subgraph induced by s we show that the nucleolus of such games can be computed efficiently the result is based on an alternative characterization of the least core which may be of independent interest the general case of weighted matching games remains unsolved

kappa statistic for clustered matched pair data kappa statistic is widely used to assess the agreement between two procedures in the independent matched pair data for matched pair data collected in clusters on the basis of the delta method and sampling techniques we propose a nonparametric variance estimator for the kappa statistic without within cluster correlation structure or distributional assumptions the results of an extensive monte carlo simulation study demonstrate that the proposed kappa statistic provides consistent estimation and the proposed variance estimator behaves reasonably well for at least a moderately large number of clusters e g k 50 compared with the variance estimator ignoring dependence within a cluster the proposed variance estimator performs better in maintaining the nominal coverage probability when the intra cluster correlation is fair 0 3 with more pronounced improvement when is further increased to illustrate the practical application of the proposed estimator we analyze two real data examples of clustered matched pair data copyright 2014 john wiley sons ltd

the quasi assouad dimension of stochastically self similar sets the class of stochastically self similar sets contains many famous examples of random sets for example mandelbrot percolation and general fractal percolation under the assumption of the uniform open set condition and some mild assumptions on the iterated function systems used we show that the quasi assouad dimension of self similar random recursive sets is almost surely equal to the almost sure hausdorff dimension of the set we further comment on random homogeneous and v variable sets and the removal of overlap conditions

interval estimation for a difference between intraclass kappa statistics summary model based inference procedures for the kappa statistic have developed rapidly over the last decade however no method has yet been developed for constructing a confidence interval about a difference between independent kappa statistics that is valid in samples of small to moderate size in this article we propose and evaluate two such methods based on an idea proposed by newcombe 1998 statistics in medicine 17 873 890 for constructing a confidence interval for a difference between independent proportions the methods are shown to provide very satisfactory results in sample sizes as small as 25 subjects per group sample size requirements that achieve a prespecified expected width for a confidence interval about a difference of kappa statistic are also presented

kappa coefficients in medical research kappa coefficients are measures of correlation between categorical variables often used as reliability or validity coefficients we recapitulate development and definitions of the k categories by m ratings kappas k x m discuss what they are well or ill designed to do and summarize where kappas now stand with regard to their application in medical research the 2 x m m 2 intraclass kappa seems the ideal measure of binary reliability a 2 x 2 weighted kappa is an excellent choice though not a unique one as a validity measure for both the intraclass and weighted kappas we address continuing problems with kappas there are serious problems with using the k x m intraclass k 2 or the various k x m weighted kappas for k 2 or m 2 in any context either because they convey incomplete and possibly misleading information or because other approaches are preferable to their use we illustrate the use of the recommended kappas with applications in medical research

a general goodness of fit approach for inference procedures concerning the kappa statistic the kappa statistic is frequently used as a measure of agreement among two or more raters although considerable research on statistical inferences for this statistic has been published for the case of two raters and a binary outcome relatively little work has appeared on inference problems for the case of multiple raters and or polytomous nominal outcome categories in this paper we propose a new procedure for constructing inferences for the kappa statistic that may be applied to this general case the procedure is based on a chi square goodness of fit test as applied to the dirichlet multinomial model and is a natural extension of previously proposed procedures that apply to more restricted cases a simulation study shows that the new procedure provides confidence interval coverage levels and type i error rates close to nominal over a wide range of parameter combinations we also present a sample size formula which may be used to determine the required number of subjects and raters for a given number of outcome categories

characteristic function games with restricted agent interactions in many real world settings the structure of the environment constrains the formation of coalitions among agents these settings can be represented by characteristic function games also known as coalitional games equipped with interaction graphs an interaction graph determines the set of all feasible coalitions in that a coalition c can form only if the subgraph induced over the nodes agents in c is connected our work analyzes stability issues arising in such environments by focusing on the core as a solution concept and by considering the coalition structure viewpoint that is without assuming that the grand coalition necessarily forms the complexity of the coalition structure core is studied over a variety of interaction graph structures of interest including complete graphs lines cycles trees and nearly acyclic graphs formally having bounded treewidth the related stability concepts of the least core and the cost of stability are also studied results are derived for the setting of compact coalitional games i e for games that are implicitly described via a compact encoding and where simple calculations on this encoding are to be performed in order to compute the payoff associated with any coalition moreover specific results are provided for compact games defined via marginal contribution networks an expressive encoding mechanism that received considerable attention in the last few years

core stability of minimum coloring games in cooperative game theory a characterization of games with stable cores is known as one of the most notorious open problems we study this problem for a special case of the minimum coloring games introduced by deng et al 1999 which arise from a cost allocation problem when the players are involved in conflict in this paper we show that the minimum coloring game on a perfect graph has a stable core if and only if every vertex of the graph belongs to a maximum clique we also consider the problem on the core largeness the extendability and the exactness of minimum coloring games as a consequence we show that it is conp complete to decide whether a given game has a large core is extendable or is exact

brownian motion on a homogeneous random fractal we introduce a simple random fractal based on the sierpinski gasket and construct a brownian motion upon the fractal the properties of the process on the sierpinski gasket are modified by the random environment a sample path construction of the process via time truncation is used which is a direct construction of the process on the fractal from the associated dirichlet forms we obtain estimates on the resolvent and transition density for the process and hence a value for the spectral dimension which satisfiesd s 2d f dw a branching process in a random environment can be used to deduce some of the sample path properties of the process

brownian motion on the sierpinski gasket we construct a brownian motion taking values in the sierpinski gasket a fractal subset of 2 and study its properties this is a diffusion process characterized by local isotropy and homogeneity properties we show for example that the process has a continuous symmetric transition density p t x y with respect to an appropriate hausdorff measure and obtain estimates on p t x y

interval estimation under two study designs for kappa with binary classifications cornfield s test based method of setting a confidence interval on a parameter associated with a two by two contingency table is adapted for use with the measure of agreement kappa one sided confidence intervals derived in this way are compared to other intervals proposed for kappa under two study designs both designs involve two ratings per subject on a dichotomous scale in one design the same two raters make all evaluations in the other possibly different pairs of raters evaluate different subjects or the same rater carries out a pair of independent assessments for each subject it is shown through simulation that lower bounds based on cornfield s test based method attain the nominal coverage probability more often than other intervals proposed in the literature

solving coalitional resource games coalitional resource games crgs are a form of non transferable utility ntu game which provide a natural formal framework for modelling scenarios in which agents must pool scarce resources in order to achieve mutually satisfying sets of goals although a number of computational questions surrounding crgs have been studied there has to date been no attempt to develop solution concepts for crgs or techniques for constructing solutions in this paper we rectify this omission following a review of the crg framework and a discussion of related work we formalise notions of coalition structures and the core for crgs and investigate the complexity of questions such as determining nonemptiness of the core we show that while such questions are in general computationally hard it is possible to check the stability of a coalition structure in time exponential in the number of goals in the system but polynomial in the number of agents and resources as a consequence checking stability is feasible for systems with small or bounded numbers of goals we then consider constructive approaches to generating coalition structures we present a negotiation protocol for crgs give an associated negotiation strategy and prove that this strategy forms a subgame perfect equilibrium we then show that coalition structures produced by the protocol satisfy several desirable properties pareto optimality dummy player and pseudo symmetry

computing the least core and nucleolus for threshold cardinality matching games cooperative games provide a framework for fair and stable profit allocation in multi agent systems core least core and nucleolus are such solution concepts that characterize stability of cooperation in this paper we study the algorithmic issues of the least core and nucleolus of threshold cardinality matching games tcmg a tcmg is defined on a graph g v e and a threshold t in which the player set is v and the profit of a coalition s v is 1 if the size of a maximum matching in g s meets or exceeds t and 0 otherwise we first show that for a tcmg the problems of computing least core value finding and verifying least core payoff are all polynomial time solvable we also provide a general characterization of the least core for a large class of tcmg cf theorem 2 next based on gallai edmonds decomposition in matching theory we establish a concise formulation of the nucleolus for a special case of tcmg when the threshold t equals 1 for arbitrary t we prove that the nucleolus of tcmg can be obtained in polynomial time for bipartite graphs and graphs with a perfect matching for a tcmg the problems of computing least core value finding and verifying least core payoff are polynomial time solvable we provide a general characterization of the least core for a large class of tcmg we establish a concise formulation of the nucleolus for a typical case of tcmg when the threshold t equals 1 for an arbitrary threshold t the nucleolus of tcmg can be obtained in polynomial time for graphs with a perfect matching for an arbitrary threshold t the nucleolus of tcmg can be obtained in polynomial time for bipartite graphs

testing the equality of two dependent kappa statistics procedures are developed and compared for testing the equality of two dependent kappa statistics in the case of two raters and a dichotomous outcome variable such problems may arise when each of a sample of subjects are rated under two distinct settings and it is of interest to compare the observed levels of inter observer and intra observer agreement the procedures compared are extensions of previously developed procedures for comparing kappa statistics computed from independent samples the results of a monte carlo simulation show that adjusting for the dependency between samples tends to be worthwhile only if the between setting correlation is comparable in magnitude to the within setting correlations in this case a goodness of fit procedure that takes into account the dependency between samples is recommended

harmonic analysis for resistance forms abstract in this paper we define the green functions for a resistance form by using effective resistance and harmonic functions then the green functions and harmonic functions are shown to be uniformly lipschitz continuous with respect to the resistance metric making use of this fact we construct the green operator and the measure valued laplacian the domain of the laplacian is shown to be a subset of uniformly lipschitz continuous functions while the domain of the resistance form in general consists of uniformly 1 2 holder continuous functions

cooperation through social influence abstract we consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents we model this scenario by an influence game a cooperative simple game in which a team or coalition of players succeeds if it is able to convince enough agents to participate in the task to vote in favor of a decision we take the linear threshold model as the influence model we show first the expressiveness of influence games showing that they capture the class of simple games then we characterize the computational complexity of various problems on influence games including measures length and width values shapley shubik and banzhaf and properties of teams and players finally we analyze those problems for some particular extremal cases with respect to the propagation of influence showing tighter complexity characterizations

brownian motion on a random recursive sierpinski gasket we introduce a random recursive fractal based on the sierpinski gasket and construct a diffusion upon the fractal via a dirichlet form this form and its symmetrizing measure are determined by the electrical resistance of the fractal the effective resistance provides a metric with which to discuss the properties of the fractal and the diffusion the main result is to obtain uniform upper and lower bounds for the transition density of the brownian motion on the fractal in terms of this metric the bounds are not tight as there are logarithmic corrections due to the randomness in the environment and the behavior of the shortest paths in the effective resistance metric is not well understood the results are deduced from the study of a suitable general branching process

homogeneity score test for the intraclass version of the kappa statistics and sample size determination in multiple or stratified studies quand le coefficient de correlation intra classe ou sa version equivalente du coefficient d agrement kappa ont ete estimes a partir de plusieurs etudes independantes ou d une etude avec stratification nous nous trouvons devant le probleme de la comparaison de statistiques kappa et de la combinaison d information sur ces statistiques en un kappa commun quand leur supposition d homogeneite est satisfaite dans cet article en utilisant la theorie de vraisemblance du score etendue aux parametres de nuisance tarone 1988 nous presentons un test d homogeneite efficace pour comparer plusieurs statistiques kappa independantes et de surcroit nous donnons une methode du score d homogeneite modifiee en employant comme alternative un estimateur non iteratif et consistant nous fournissons la taille d echantillon en employant la methode du score d homogeneite modifiee et nous la comparons a celle de la qualite d ajustement gof donner eliasziw et klar 1996 une etude de simulation pour des tailles d echantillon faibles et moderes a montre que le niveau actuel du test du score d homogeneite employant les estimateurs du maximum de vraisemblance mles des parametres est de maniere satisfaisante proche du nominal et qu il est plus faible que ceux du score d homogeneite mortifiee et des tests de la qualite d ajustement nous etudions les proprietes statistiques de plusieurs estimateurs non iteratifs d un kappa commun l estimateur donner eliasziw et klar 1996 est essentiellement efficace et peut etre employe comme une alternative au mle iteratif nous presentons une estimation par intervalle efficace d un kappa commun en employant la methode de vraisemblance du score

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 complexity of cooperative solution concepts we study from a complexity theoretic standpoint the various solution concepts arising in cooperative game theory we use as a vehicle for this study a game in which the players are nodes of a graph with weights on the edges and the value of a coalition is determined by the total weight of the edges contained in it the shapley value is always easy to compute the core is easy to characterize when the game is convex and is intractable np complete otherwise similar results are shown for the kernel the nucleolus the e core and the bargaining set as for the von neumann morgenstern solution we point out that its existence may not even be decidable many of these results generalize to the case in which the game is presented by a hypergraph with edges of size k 2

testing the homogeneity of kappa statistics procedures are compared for testing the homogeneity of k or 2 independent kappa statistics in the case of two raters and a dichotomous outcome one of the procedures is based on the estimated large sample variance derived under a model frequently adopted for inferences concerning interobserver agreement the other is based on a goodness of fit approach to this model the results of a monte carlo simulation show that the two approaches have similar properties if the number of subjects in each sample is large 100 and the prevalence of the underlying trait of interest is not extreme while the goodness of fit approach is recommended for comparisons involving smaller numbers of subjects or in which the prevalence of the underlying trait is small 0 3

note the complexity of power index comparison abstract we study the complexity of the following problem given two weighted voting games g and g that each contain a player p in which of these games is p s power index value higher we study this problem with respect to both the shapley shubik power index and the banzhaf power index our main result is that for both of these power indices the problem is complete for probabilistic polynomial time i e is pp complete we apply our results to partially resolve some recently proposed problems regarding the complexity of weighted voting games we also study the complexity of the raw shapley shubik power index deng and papadimitriou showed that the raw shapley shubik power index is p metric complete we strengthen this by showing that the raw shapley shubik power index is many one complete for p and our strengthening cannot possibly be further improved to parsimonious completeness since we observe that in contrast with the raw banzhaf power index the raw shapley shubik power index is not p parsimonious complete

asymptotic form of the spectral dimension at the fractal to lattice crossover the authors study the spectral dimension of the sierpinski gasket family of fractals each member of the family is labelled by an integer b 2 or b infinity so that when b to infinity both the fractal and spectral dimension approach the euclidean value 2 the asymptotic law for the spectral dimension was recently suggested to be ds approximately 2 b 1nb beta with b and beta being some constants here the authors demonstrate that this form should be replaced by the asymptotic law ds approximately 2 1n 1nb constant 1nb their analysis is based on the exact calculation of the electric resistances rb for all members of the family up to b 650

harmonic calculus on p c f self similar sets the main object of this paper is the laplace operator on a class of fractals first we establish the concept of the renormalization of difference operators on post critically finite p c f for short self similar sets which are large enough to include finitely ramified self similar sets and extend the results for sierpinski gasket given in 10 to this class under each invariant operator for renormalization the laplace operator green function dirichlet form and neumann derivatives are explicitly constructed as the natural limits of those on finite pre self similar sets which approximate the p c f self similar sets also harmonic functions are shown to be finite dimensional and they are characterized by the solution of an infinite system of finite difference equations

2 x 2 kappa coefficients measures of agreement or association summary two general but different contexts in which kappa might be used are defined agreement and association two models one for agreement and one for utility of association are defined yielding different kappa coefficients and different sampling theory asymptotic results are derived for both models small sample evaluations are presented for the model for agreement

finite rationality and interpersonal complexity in repeated games a measure of complexity for repeated game strategies is studied this measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting specifically the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set i e the number of distinct strategies induced by the original strategy in all possible subgames we observe that this cardinality is equal to the size cardinality of the state set of the smallest automaton which can implement the strategy thus in a sense complexity is measured on the basis of the amount of computing power inherent in the strategy a measure of strategic memory is also studied the following results are obtained 1 combining two notions of bounded rationality epsilon equilibrium and finite complexity we find that every subgame perfect equilibrium of the repeated game can be approximated with regard to payoffs by a subgame perfect epsilon equilibrium of finite complexity 2 for a generic class of normal form stage games at every discount robust subgame perfect drsp equilibrium there are necessary relationships among the complexities and memories of the players strategies in the two player case strategies must be equally complex and must have equal memories 3 for a second class of two pla yer stage games we show that the payoff vectors for all drsp equilibria are obtainable via equilibria in which the players strategies are equally complex and have equal memoiies

parabolic type equations associated with the dirichlet form on the sierpinski gasket by using analytic tools from stochastic analysis we initiate a study of some non linear parabolic equations on sierpinski gasket motivated by modellings of fluid flows along fractals which can be considered as models of simplified rough porous media unlike the regular space case such parabolic type equations involving non linear convection terms must take a different form due to the fact that convection terms must be singular to the linear part which defines the heat semigroup in order to study these parabolic type equations a new kind of sobolev inequalities for the dirichlet form on the gasket will be established these sobolev inequalities which are interesting on their own and in contrast to the case of euclidean spaces involve two l p norms with respect to two mutually singular measures by examining properties of singular convolutions of the associated heat semigroup we derive the space time regularity of solutions to these parabolic equations under a few technical conditions the burgers equations on the sierpinski gasket are also studied for which a maximum principle for solutions is derived using techniques from backward stochastic differential equations and the existence uniqueness and regularity of its solutions are obtained

v variable fractals fractals with partial self similarity we establish properties of a new type of fractal which has partial self similarity at all scales for any collection of iterated functions systems with an associated probability distribution and any positive integer v there is a corresponding class of v variable fractal sets or measures these v variable fractals can also be obtained from the points on the attractor of a single deterministic iterated function system existence uniqueness and approximation results are established under average contractive assumptions we also obtain extensions of some basic results concerning iterated function systems

a comparison of methods for calculating a stratified kappa investigators use the kappa coefficient to measure chance corrected agreement among observers in the classification of subjects into nominal categories the marginal probability of classification may depend however on one or more confounding variables we consider assessment of interrater agreement with subjects grouped into strata on the basis of these confounders we assume overall agreement across strata is constant and consider a stratified index of agreement or stratified kappa based on weighted summations of the individual kappas we use three weighting schemes 1 equal weighting 2 weighting by the size of the table and 3 weighting by the inverse of the variance in a simulation study we compare these methods under differing probability structures and differing sample sizes for the tables we find weighting by sample size moderately efficient under most conditions we illustrate the techniques by assessing agreement between surgeons and graders of fundus photographs with respect to retinal characteristics with stratification by initial severity of the disease

on the computational complexity of coalitional resource games we study coalitional resource games crgs a variation of qualitative coalitional games qcgs in which each agent is endowed with a set of resources and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources we investigate and classify the computational complexity of a number of natural decision problems for crgs over and above those previously investigated for qcgs in general for example we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound i e a limit value for every resource is co np complete we then investigate the relationship between crgs and qcgs and in particular the extent to which it is possible to translate between the two models we first characterise the complexity of determining equivalence between crgs and qcgs we then show that it is always possible to translate any given crg into a succinct equivalent qcg and that it is not always possible to translate a qcg into an equivalent crg we establish some necessary and some sufficient conditions for a translation from qcgs to crgs to be possible and show that even where an equivalent crg exists it may have size exponential in the number of goals and agents of its source qcg

transition densities for brownian motion on the sierpinski carpet upper and lower bounds are obtained for the transition densitiesp t x y of brownian motion on the sierpinski carpet these are of the same form as those which hold for the sierpinski gasket in addition the joint continuity ofp t x y is proved the existence of the spectral dimension is established and the einstein relation connecting the spectral dimension the hausdorff dimension and the resistance exponent is shown to hold

reasoning about coalitional games we develop investigate and compare two logic based knowledge representation formalisms for reasoning about coalitional games the main constructs of coalitional game logic cgl are expressions for representing the ability of coalitions which may be combined with expressions for representing the preferences that agents have over outcomes modal coalitional game logic mcgl is a normal modal logic in which the main construct is a modality for expressing the preferences of groups of agents for both frameworks we give complete axiomatisations and show how they can be used to characterise solution concepts for coalitional games we show that while cgl is more expressive than mcgl the former can only be used to reason about coalitional games with finitely many outcomes while mcgl can be used to reason also about games with infinitely many outcomes and is in addition more succinct we characterise the computational complexity of satisfiability for cgl and give a tableaux based decision procedure

derivations and dirichlet forms on fractals abstract we study derivations and fredholm modules on metric spaces with a local regular conservative dirichlet form in particular on finitely ramified fractals we show that there is a non trivial fredholm module if and only if the fractal is not a tree i e not simply connected this result relates fredholm modules and topology refines and improves known results on p c f fractals we also discuss weakly summable fredholm modules and the dixmier trace in the cases of some finitely and infinitely ramified fractals including non self similar fractals if the so called spectral dimension is less than 2 in the finitely ramified self similar case we relate the p summability question with estimates of the lyapunov exponents for harmonic functions and the behavior of the pressure function

on the asymptotics of the eigenvalue counting function for random recursive sierpinski gaskets we consider natural laplace operators on random recursive affine nested fractals based on the sierpinski gasket and prove an analogue of weyl s classical result on their eigenvalue asymptotics the eigenvalue counting function n is shown to be of order ds 2 as where we can explicitly compute the spectral dimension d s moreover the limit n ds 2 will typically exist and can be expressed as a deterministic constant multiplied by a random variable this random variable is a power of the limiting random variable in a suitable general branching process and has an interpretation as the volume of the fractal

brownian motion on the continuum tree we construct brownian motion on a continuum tree a structure introduced as an asymptotic limit to certain families of finite trees we approximate the dirichlet form of brownian motion on the continuum tree by adjoining one dimensional brownian excursions we study the local times of the resulting diffusion using time change methods we find explicit expressions for certain hitting probabilities and the mean occupation density of the process