one and a half quantum de finetti theorems when n k systems of an n partite permutation invariant state are traced out the resulting state can be approximated by a convex combination of tensor product states this is the quantum de finetti theorem in this paper we show that an upper bound on the trace distance of this approximation is given by 2 frac kd 2 n where d is the dimension of the individual system thereby improving previously known bounds our result follows from a more general approximation theorem for representations of the unitary group consider a pure state that lies in the irreducible representation u mu nu subset u mu otimes u nu of the unitary group u d for highest weights and let be the state obtained by tracing out u then is close to a convex combination of the coherent states u mu g v mu rangle where g in u d and v mu rangle is the highest weight vector in u

existence of equilibrium for generalized abstract fuzzy economies in this paper we introduce and study a new class of generalized abstract fuzzy economies we prove some new existence theorems of equilibrium and maximal element for generalized abstract fuzzy economies with uncountable number of agents and qualitative fuzzy games respectively

the existence of nash equilibrium in n person games with c concavity abstract the purpose of this paper is to introduce the c concavity condition and next prove a new existence theorem of nash equilibrium in n person games with c concavity and as an application we shall prove a minimax theorem finally we shall give some examples of a two person game where the c concavity can be applied but the previous general concavity conditions cannot be applied our results generalize the corresponding results due to nash and forgo in several ways

acyclic fuzzy preferences and the orlovsky choice function a note abstract this note corrects and extends a recent axiomatic characterization of the orlovsky choice function for a particular class of transitive fuzzy relations the interest of characterizing choice functions for well behaved fuzzy relations is then discussed

a continuous version of de finetti s theorem a continuous version of de finetti s theorem is proved in which the role of the homogeneous product states is played by the independent increment stationary processes on the real line the proof is based on a conditional finite de finetti s theorem i e a result involving only a finite number of random variables and exchangeable conditional expectations rather than exchangeable probabilities our technique of proof improves and simplifies a result of freedman and includes a generalization of the quantum de finetti s theorem as well as some more recent variants of it the last section of the paper is an attempt to answer a question of diaconis and freedman

a most compendious and facile quantum de finetti theorem in its most basic form the finite quantum de finetti theorem states that the reduced k partite density operator of an n partite symmetric state can be approximated by a convex combination of k fold product states variations of this result include renner s exponential approximation by almost product states a theorem which deals with certain triples of representations of the unitary group and the result of d cruz et al e print quant ph 0606139 phys rev lett 98 160406 2007 for infinite dimensional systems we show how these theorems follow from a single general de finetti theorem for representations of symmetry groups each instance corresponding to a particular choice of symmetry group and representation of that group this gives some insight into the nature of the set of approximating states and leads to some new results including an exponential theorem for infinite dimensional systems

a noncommutative de finetti theorem for boolean independence abstract we introduce a family of quantum semigroups and its natural coactions on noncommutative polynomials we define three invariance conditions for the joint distribution of sequences of selfadjoint noncommutative random variables associated with these coactions for one of the invariance conditions we show that the joint distribution of an infinite sequence of noncommutative random variables satisfy it is equivalent to the fact that the sequence of the random variables is identically distributed and boolean independent with respect to the conditional expectation onto its tail algebra this is a boolean analogue of de finetti theorem on exchangeable sequences in the end of the paper we also discuss the other two invariance conditions which lead to some trivial results

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

on structural stability and robustness to bounded rationality in this paper we study the model m a parameterized class of general games together with an associated abstract rationality function we prove that model m is structurally stable and robust to equilibria for almost all parameter values

sensitivity and specificity of a monitoring test summary the usefulness of a diagnostic test is generally assessed by calculating the sensitivity and specificity or the predictive value positive and predictive value negative of the test when subjects are monitored periodically for evidence of disease these calculations must incorporate the varying amounts of information per individual if in addition the test results lie on a continuous scale these quantities vary with the cutoff value cutpoint used to define a positive test they are usually calculated for a spectrum of potential cutpoints in order to produce receiver operator characteristic curves in this paper we use a partial likelihood solution to the discrete logistic model in order to obtain estimates of the diagnostic test indices and to provide a significance test when the diagnostic test is administered repeatedly to individuals

cumulants in noncommutative probability theory iv noncrossing cumulants de finetti s theorem and lp inequalities abstract de finetti s theorem states that any exchangeable sequence of classical random variables is conditionally i i d with respect to some algebra in this paper we prove a free noncommutative analog of this theorem namely we show that any noncrossing exchangeability system with a faithful state which satisfies a so called weak singleton condition can be embedded into an free product with amalgamation over a certain subalgebra such that the interchangeable algebras remain interchangeable with respect to the operator valued expectation vanishing of crossing cumulants can be verified by checking a certain weak freeness condition and the weak singleton condition is satisfied e g when the state is tracial the proof follows the classical proof of de finetti s theorem the main technical tool being a noncommutative l p inequality for i i d sums of centered noncommutative random variables in noncrossing exchangeability systems

a fermionic de finetti theorem quantum versions of de finetti s theorem are powerful tools yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean field approaches such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles in this work we derive a de finetti theorem for finite sized majorana fermionic systems it is shown much reflecting the spirit of other quantum de finetti theorems that a state which is invariant under certain permutations of modes loses most of its anti symmetric character and is locally well described by a mode separable state we discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the hartree fock approximation of quantum systems we hint at a link to generalized pauli principles fo

inequalities and nash equilibria abstract this paper concentrates on the problem of the existence of equilibrium points for non cooperative generalized n person games n person games of normal form and their related inequalities we utilize the k k m lemma to obtain a theorem and then use it to obtain a new fan type inequality and minimax theorems various new equilibrium point theorems are derived with the necessary and sufficient conditions and with strategy spaces with no fixed point property examples are given to demonstrate that these existence theorems cover areas where other existence theorems break down

existence of best proximity pairs and equilibrium pairs in this paper using the fixed point theorem for kakutani factorizable multifunctions we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies which include the previous fixed point theorems and equilibrium existence theorems

a noncommutative de finetti theorem invariance under quantum permutations is equivalent to freeness with amalgamation we show that the classical de finetti theorem has a canonical noncommutative counterpart if we strengthen exchangeability i e invariance of the joint distribution of the random variables under the action of the permutation group to invariance under the action of the quantum permutation group more precisely for an infinite sequence of noncommutative random variables x i i in mathbb n we prove that invariance of the joint distribution of the xi s under quantum permutations is equivalent to the fact that the xi s are identically distributed and free with respect to the conditional expectation onto the tail algebra of the xi s

existence of nash equilibria with c convexity abstract the purpose of this paper is to introduce general c convex and c concave conditions and then to prove two existence theorems of nash equilibria in generalized games with c concavity our results generalize the corresponding results due to nash forgo takahashi and kim lee in several ways

estimates of sensitivity and specificity in a multistage screen for medical diagnosis a multistage screen is used when k different medical tests are available to the physician and a patient is subjected to test j only if test j1 yielded a positive result 2 j k in observational studies a multivariate random vector x j of frequencies results from stage j this random vector also contains information from patient dropouts i e those patients who discontinue even though they had positive test results at all stages through stage j for j 2 the conditional distribution of x y is the product of two multinomial distributions it is conditional because the sample sizes of the two multinomial distributions depend on the outcomes of the previous stage a certain subset of x 1 x k has an unconditional distribution which is multinomial and the estimation of sensitivity and specificity is formulated from this subset a numerical example for the diagnosis of open spina bifida in human fetuses is provided

bounded rationality in multiobjective games abstract in this paper we will establish the connections between bounded rationality and multiobjective games we obtain some new results for robustness to equilibria and structural stability of multiobjective games and generalized multiobjective games

finite de finetti theorem for conditional probability distributions describing physical theories we work in a general framework where the state of a physical system is defined by its behavior under measurement and the global state is constrained by no signaling conditions we show that the marginals of symmetric states in such theories can be approximated by convex combinations of independent and identical conditional probability distributions generalizing the classical finite de finetti theorem of diaconis and freedman our results apply to correlations obtained from quantum states even when there is no bound on the local dimension so that known quantum de finetti theorems cannot be used

ground states of fermions on lattices we consider fermion systems on integer lattices we establish the existence of dynamics for a class of long range interactions the infinite volume ground states are considered the equivalence of the variational principle and ground state conditions is proved for long range interactions we also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full car algebra for the hamiltonian with a chemical potential equivalence of ensemble for canonical and ground canonical states at the zero temperature

a new class of generalized multiobjective games in bounded rationality with fuzzy mappings structural λ e stability and λ e robustness to e equilibria abstract in this paper we introduce a new class of generalized multiobjective games with fuzzy mappings and study the solution existence for this class of games the model of bounded rationality proposed by anderlini and canning 2001 and miyazaki and azuma 2013 is applied to a new class of generalized multiobjective games with fuzzy mappings in infinite dimensional spaces we introduce a related abstract rationality function for this model using the nonlinear scalarization method and we show that the structural stability i e e stability of this model implies its robustness i e e robustness to e equilibria

best proximity pairs and equilibrium pairs for kakutani multimaps new existence theorems of best proximity pairs for a finite family of kakutani multimaps are proved in a normed space setting as applications new existence theorems of equilibrium pairs for free n person and 1 person games are obtained our results generalize and improve several well known results 2008 elsevier ltd all rights reserved

on the existence of maximal elements fixed points and equilibria of generalized games in a fuzzy environment we give new sufficient conditions for the existence of fuzzy maximal elements fuzzy fixed points and equilibria of generalized fuzzy games in our results a key role is played by the existence of upper semicontinuous selection maps of set valued functions that we obtain for the class of generalized transfer open lower sections maps

de finetti representation theorem for infinite dimensional quantum systems and applications to quantum cryptography we show that the quantum de finetti theorem holds for states on infinite dimensional systems provided they satisfy certain experimentally verifiable conditions this result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks

de finetti theorems for braided parafermions the classical de finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables this result has application in quantum information here we study states that are invariant with respect to a natural action of the braid group and we emphasize the pictorial formulation and interpretation of our results we prove a new type of de finetti theorem for the four string double braid group acting on the parafermion algebra to braid qudits a natural symmetry in the quon language for quantum information we prove that a braid invariant state is extremal if and only if it is a product state furthermore we provide an explicit characterization of braid invariant states on the parafermion algebra including finding a distinction that depends on whether the order of the parafermion algebra is square free we characterize the extremal nature of product states an inverse de finetti theorem

existence and stability of the α core for fuzzy games abstract in this study we establish the existence of the core in fuzzy games using the existence results we identify a class of fuzzy games comprising a dense residual subset of fuzzy games such that every point of the core is essential we also show that every fuzzy game in this class has an essential component of its core

de finetti theorem on the car algebra the symmetric states on a quasi local c algebra on the infinite set of indices j are those invariant under the action of the group of the permutations moving only a finite but arbitrary number of elements of j the celebrated de finetti theorem describes the structure of the symmetric states i e exchangeable probability measures in classical probability in the present paper we extend the de finetti theorem to the case of the car algebra that is for physical systems describing fermions namely after showing that a symmetric state is automatically even under the natural action of the parity automorphism we prove that the compact convex set of such states is a choquet simplex whose extremal i e ergodic w r t the action of the group of permutations previously described are precisely the product states in the sense of araki moriya in order to do that we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self containing interest

cumulants in noncommutative probability theory ii we continue the investigation of noncommutative cumulants in this paper various characterizations of generalized gaussian random variables are proved

a further study on rationality conditions of fuzzy choice functions the investigation of rationality plays a central role in the study of fuzzy choice functions in this paper we deal with some important rationality conditions of fuzzy choice functions including weak strong fuzzy congruence axiom weak strong axiom of fuzzy revealed preference fuzzy versions of famous crisp conditions a b c and d etc in the framework of the banerjee choice function we systematically investigate the relationships between these conditions under the assumption that every involved choice set is normal and verify some equivalence results for arbitrary t norms as a result a fuzzy version of the arrow sen theorem is presented the research makes a significant difference compared with the current investigation in the framework of the georgescu choice function

joint extension of states of subsystems for a car system the problem of existence and uniqueness of a state of a joint system with given restrictions to subsystems is studied for a fermion system where a novel feature is non commutativity between algebras of subsystems for an arbitrary finite or infinite number of given subsystems a product state extension is shown to exist if and only if all states of subsystems except at most one are even with respect to the fermion number if the states of all subsystems are pure then the same condition is shown to be necessary and sufficient for the existence of any joint extension if the condition holds the unique product state extension is the only joint extension for a pair of subsystems with one of the given subsystem states pure a necessary and sufficient condition for the existence of a joint extension and the form of all joint extensions unique for almost all cases are given for a pair of subsystems with non pure subsystem states some classes of examples of joint extensions are given where non uniqueness of joint extensions prevails

nash equilibrium and minimax theorem with c concavity the purpose of this paper is to introduce a generalized c concave condition and by using himmelberg s fixed point theorem to prove a new existence theorem of nash equilibrium in non compact generalized game with c concavity as applications we shall prove a minimax theorem in non compact settings and prove a minimax inequality in compact settings

a necessary and sufficient condition for the existence of orlovsky s choice set abstract in a previous paper 2 the authors proved that a property of acyclity in fuzzy preference relations was a necessary and sufficient condition for the existence of unfuzzy nondominated alternatives when such a set of alternatives is finite in this paper a general property of foundation is proved to be a necessary and sufficient condition without requiring finiteness on the set of alternatives both concepts are based on classical results in crisp binary relations

a coalitional extension of generalized fuzzy games abstract in this paper we give a coalitional extension of generalized fuzzy games and introduce the notion of coalitional fuzzy equilibria we first prove the existence of coalitional fuzzy equilibria in our model as an application we further show the existence theorem of strong fuzzy equilibria for fuzzy games

fuzzy preference and orlovsky choice procedure abstract this paper provides an axiomatic characterization of the orlovsky choice procedure for a decision maker whose preference are fuzzy in contrast to the result in banerjee 1993 our characterization does not require that in a pairwise choice the choice coincides with the orlovsky set moreover our characterization result holds for a larger domain of preferences than that in banerjee 1993

measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups this article studies the problem of measuring and estimating the diagnostic accuracy when there are three ordinal diagnostic groups we use a receiver operating characteristic roc surface to describe the probabilities of correct classifications into three diagnostic groups based on various sets of diagnostic thresholds of a test and propose to use the entire and the partial volume under the surface to measure the diagnostic accuracy mathematical properties and probabilistic interpretations of the proposed measure of diagnostic accuracy are discussed under the assumption of normal distributions of the diagnostic test from three diagnostic groups we present the maximum likelihood estimate to the volume under the roc surface and give the asymptotic variance to the estimate we further propose several asymptotic confidence interval estimates to the volume under the roc surface the performance of these confidence interval estimates is evaluated in terms of attaining the nominal coverage probability based on a simulation study in addition we develop a method of sample size determination to achieve an adequate accuracy of the confidence interval estimate finally we demonstrate the proposed methodology by applying it to the clinical diagnosis of early stage alzheimer s disease based on the neuropsychological database of the washington university alzheimer s disease research center

the general prenucleolus of n person cooperative fuzzy games abstract in this paper we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions for the general prenucleolus we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess sakawa and nishizaki 1994 15 as a result we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions such as the equalizer solution molina and tejada 2002 5 and shapley function etc we prove that the least square general prenucleolus minimizing the variance of the resulting player complaints is the general prenucleolus thus an optimal solution considered from two aspects of the lexicographic order and the least square criterion is obtained in addition several general prenucleoli are proposed in terms of specific situations

roc curves with multiple marker measurements summary properties of receiver operating characteristic roc curves are explored for markers that are measured repeatedly through space or time for each subject the true underlying response positive or negative of each subject is assumed to be constant across marker measurements and is determined from assessment of some gold standard a marker based test is considered positive when at least one of a subject s marker values exceeds a designated cutoff if subjects with positive and negative underlying responses differ in the number of marker measurements per subject the roc curve for a noninformative marker is bowed above or below the diagonal line representing the null curve for a marker that is measured just once per subject if subjects with negative responses tend to have more measurements than those with positive responses the roc curve for even an informative marker may lie beneath the curve for the same marker measured once per subject the form of the roc curve for a marker used in this way is strongly influenced by the strength of the correlation of measurements within subjects

variational relation problem without the kkm property with applications abstract in this paper we will study variational relation problems without the kkm property whose proof techniques differ between luc 2008 1 and pu and yang 2012 9 as applications some existence theorems of solution for the generalized kkm theorem variational inclusion problem generalized vector ky fan minimax inequality generalized ky fan section theorem n person noncooperative generalized game and n person noncooperative multi objective generalized game are obtained

a note on congruence conditions of fuzzy choice functions in order to reflect the fuzziness existing in a choice problem banerjee introduces the concept of fuzzy choice function meanwhile banerjee proposes three congruence conditions in assessing the rationality of a fuzzy choice function in this paper we prove some dependencies among these conditions although banerjee asserts that they are independent

a noncommutative extended de finetti theorem abstract the extended de finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i i d and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability our main result is a noncommutative version of this theorem in contrast to the classical result of ryll nardzewski exchangeability turns out to be stronger than spreadability for infinite sequences of noncommutative random variables out of our investigations emerges noncommutative conditional independence in terms of a von neumann algebraic structure closely related to popa s notion of commuting squares and kummerer s generalized bernoulli shifts our main result is applicable to classical probability quantum probability in particular free probability braid group representations and jones subfactors