theories of learning in games and heterogeneity bias work begins with pooled estimation of the model s under scrutiny i show that in the presence of parameter heterogeneity pooled estimation can produce a severe bias that tends to unduly favor reinforcement learning relative to belief learning this occurs when comparisons are based on goodness of fit and when comparisons are based on the relative importance of the two kinds of learning in hybrid structural models even misspecified random parameter estimators can greatly reduce the bias relative to pooled estimation

hidden integrable hierarchies of akns type a method for constructing integrable hierarchies by restricting akns flows on manifolds of finite codimension in the space of independent parameters is provided two particular types of hierachies are characterized one is given by nonlinear differential equations with coordinate dependent coefficients and the other is related to schrodinger spectral problems with energy dependent potentials of even degree

zero sets of functions and hidden hierarchies of kdv type the zero sets of kdv functions are characterized in terms of the stratification of the infinite grassmannian it is shown that these sets are related to integrable hierarchies arising from schrodinger equations with energy dependent potentials

an evaluation of econometric models of adaptive learning this paper evaluates the effectiveness of four econometric approaches intended to identify the learning rules being used by subjects in experiments with normal form games this is done by simulating experimental data and then estimating the econometric models on the simulated data to determine if they can correctly identify the rule that was used to generate the data the results show that all of the models examined possess difficulties in accurately distinguishing between the data generating processes

computation tree logic model checking based on possibility measures in order to deal with the systematic verification with uncertain information in possibility theory li and li 2013 introduced model checking of linear time properties in which the uncertainty is modeled by possibility measures xue lei and li 2011 defined computation tree logic ctl based on possibility measures which is called possibilistic ctl poctl this paper is a continuation of the above work first we study the expressiveness of poctl unlike probabilistic ctl it is shown that poctl in particular qualitative poctl is more powerful than ctl with respect to their expressiveness the equivalent expressions of basic ctl formulae using qualitative poctl formulae are presented in detail some poctl formulae that cannot be expressed by any ctl formulae are presented in particular some qualitative properties of repeated reachability and persistence are expressed using poctl formulae next adapting ctl model checking algorithm a method to solve the poctl model checking problem and its time complexity are discussed in detail finally an example is given to illustrate the poctl model checking method

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

the evolution of conventions the author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality the game is repeated many times by different players each player chooses an optimal reply based on incomplete information about what other players have done in the past occasionally they make mistakes when the likelihood of mistakes is very small typically one coordination equilibrium will be played almost all of the time over the long run this stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed markov processes copyright 1993 by the econometric society

singular sector of the kadomtsev petviashvili hierarchy operators of nonzero index and associated integrable systems integrable hierarchies associated with the singular sector of the kadomtsev petviashvili kp hierarchy or equivalently with operators of nonzero index are studied they arise as the restriction of the standard kp hierarchy to submanifolds of finite codimension in the space of independent variables for higher index these hierarchies represent themselves as families of multidimensional equations with multidimensional constraints the dressing method is used to construct these hierarchies hidden korteweg de vries boussinesq and hidden gelfand dikii hierarchies are considered too

the approach to the dispersionless kp hierarchy the dispersionless limit of the scalar nonlocal problem is derived it is given by a special class of nonlinear first order equations a quasiclassical version of the dressing method is presented it is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of beltrami type equations the universal whitham hierarchy and in particular the dispersionless kp hierarchy turn out to be rings of symmetries for the quasiclassical problem pacs number 02 30 uk

topological landau ginzburg theory with a rational potential and the dispersionless kp hierarchy based on the dispersionless kp dkp theory we study a topological landau ginzburg lg theory characterized by a rational potential writing the dkp hierarchy in a general form treating all the primaries in an equal basis we find that the hierarchy naturally includes the dispersionless continuous limit of toda hierarchy and its generalizations having a finite number of primaries several flat solutions of the topological lg theory are obtained in this formulation and are identified with those discussed by dubrovin we explicitly construct gravitational descendants for all the primary fields giving a residue formulae for the 3 point functions of the fields we show that these 3 point functions satisfy the topological recursion relation the string equation is obtained as the generalized hodograph solutions of the dkp hierarchy which show that all the gravitational effects to the constitutive equations 2 point functions can be renormalized into the coupling constants in the small phase space

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

quantitative computation tree logic model checking based on generalized possibility measures we study generalized possibilistic computation tree logic gpoctl model checking in this paper which is an extension of possibilistic computation logic model checking introduced by li et al 2014 the system is modeled by generalized possibilistic kripke structures and the verifying property is specified by a gpoctl formula based on generalized possibility measures and generalized necessity measures the method of gpoctl model checking is discussed and the corresponding algorithm and its complexity are shown in detail furthermore the comparison between possibilistic computation tree logic and gpoctl is given finally a thermostat example is given to illustrate the gpoctl model checking method

fuzzy logic and meteorological variables a case study of solar irradiance solar irradiance is an extreme case of an uncertain variable when measured on an hourly or shorter time interval in this paper solar irradiance has been considered as a case study for physical fuzzy modelling of a climate variable the uncertainty of the solar irradiance is treated as a fuzzy uncertainty whilst other variables are considered crisp the approach is robust as it does not rely on statistical assumptions and it is a possible alternative to modelling complex systems to our knowledge this is the first time that a physical model of a meteorological variable based on fuzzy numbers has been proposed previous rule based fuzzy meteorological models are only descriptive and cannot be extrapolated to non measured cases when compared with previous non fuzzy models of solar irradiance the fuzzy model shows an improved performance and when compared with experimental data the performance can be evaluated by fuzzy indices that take into account the uncertainty of the data and the model output

limit matrices for the toda flow and periodic flags for loop groups sato s theory of infinite dimensional grassmannians has been applied to explain the geometry of the k p equation s djkm it has been used as a tool to study blow up behaviors and to regularize the solutions near the blow up a vm2 the point is that realizing the k p flow as a holomorphic flow of planes enables one to follow what happens to the limiting planes as the equation in the original bad coordinates blows up the blow up behaviors are characterized by the various strata the orbit of planes visits in the grassmannian in this paper such ideas are applied to the n periodic toda flow on periodic jacobi matrices which translates into a flow on the space of n periodic flags of planes in the grassmannians indeed here the n periodic toda flow amounts to n coupled kp equations with special interactions between time flows u t how such matrices blow up has been studied in fi f1 ha a vm1 for arbitrary lie algebras and kac moody lie algebras whereas this paper focusses on regularizing the flow near the blow up locus that is on finding the boundary of isospectral sets if n periodic jacobi matrices

probabilities possibilities and fuzzy sets a formal analysis of probabilities possibilities and fuzzy sets is presented in this paper a number of theorems proved show the above measures have equal representational power when their domains are infinite however for finite domains it is proved that probabilities have a higher representational power than both possibilities and fuzzy sets the cost of this increased power is high computational complexity and reduced computational efficiency the resulting trade off of high complexity and representational power versus computational efficiency is discussed under the spectrum of experimental systems and applications

quasiclassical limit of coupled kdv equations riemann invariants and multi hamiltonian structure abstract we consider the quasiclassical limit of the first nontrivial flow in coupled kdv hierarchy written down in riemann invariants it assumes the extremely simple form r i k 1 n r k 2r i r x i i 1 n up to certain natural equivalence this turns out to be the only hydrodynamic system with n 1 compatible purely local hamiltonian structures

model checking of linear time properties based on possibility measure using possibility measure we study model checking of linear time properties in possibilistic kripke structures first the notion of possibilistic kripke structures and the related possibility measure are introduced and then model checking of reachability and repeated reachability linear time properties in finite possibilistic kripke structures are studied standard safety properties and regular properties in possibilistic kripke structures are introduced the verification of regular safety properties and regular properties using finite automata are thoroughly studied it has been shown that the verification of regular safety properties and regular properties in a finite possibilistic kripke structure can be transformed into the verification of reachability properties and repeated reachability properties in the product possibilistic kripke structure that is introduced in this paper several examples are given to illustrate the methods that are presented in this paper

experience weighted attraction learning in normal form games in experience weighted attraction ewa learning strategies have attractions that reflect initial predispositions are updated based on payoff experience and determine choice probabilities according to some rule e g logit a key feature is a parameter that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded relative to reinforcement of chosen strategies according to received payoffs the other key features are two discount rates and which separately discount previous attractions and an experience weight ewa includes reinforcement learning and weighted fictitious play belief learning as special cases and hybridizes their key elements when 0 and 0 cumulative choice reinforcement results when 1 and levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs using three sets of experimental data parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample estimates of are generally around 50 around 8 1 and varies from 0 to reinforcement and belief learning special cases are generally rejected in favor of ewa though belief models do better in some constant sum games ewa is able to combine the best features of previous approaches allowing attractions to begin and grow flexibly as choice reinforcement does but reinforcing unchosen strategies substantially as belief based models implicitly do

quantitative model checking of linear time properties based on generalized possibility measures abstract model checking of linear time properties based on possibility measures was studied in previous work li and li 2013 however the linear time properties considered in the previous work was qualitative and was based on boolean logic the linear time properties containing possibility information we call it fuzzy linear time properties here which is based on fuzzy logic of system could not be represented and tackled using the previous methods we shall study quantitative model checking of fuzzy linear time properties based on generalized possibility measures in the paper both the model of the system as well as the properties the system needs to adhere to are described using possibility information to identify the uncertainty in the model properties the systems are modeled by generalized possibilistic kripke structures gpks in short and the properties are described by fuzzy linear time properties concretely fuzzy linear time properties about reachability always reachability constrain reachability repeated reachability and persistence in gpkss are introduced and studied fuzzy regular safety properties and fuzzy regular properties in gpkss are introduced the verification of fuzzy regular safety properties and fuzzy regular properties using fuzzy finite automata are thoroughly studied it has been shown that the verification of fuzzy regular safety properties and fuzzy regular properties in a finite gpks can be transformed into the verification of always reachability properties and repeated reachability persistence properties in the product gpks introduced in this paper several examples are given to illustrate the methods presented in the paper

the toda lattice dynkin diagrams singularities and abelian varieties the periodic l 1 particle toda lattices coresponding to extended dynkin diagrams have l 1 polynomial constants of the motion namely as many as there are dots in the dynkin diagram for most values of the constants their intersection defines as l dimensional affine invariant manifold which completes into a complex algebraic torus abelian variety by glueing on a divisor entirely specified by the extended dynkin diagram therefore the global geometry of the complex invariant tori such as polarization dimension of certain linear systems divisor equivalences etc is entirely given by the extended dynkin diagram in particular an explicit geometric description for the case of three particle toda lattices is given which describes the divisors their singularities and how the various divisors intersect

singular sector of the burgers hopf hierarchy and deformations of hyperelliptic curves we discuss the structure of shock singularities of the burgers hopf hierarchy it is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy the stratification is associated with the birkhoff decomposition of the grassmannian given by the set of linear spaces spanned by the hierarchy we then construct integrable hierarchy on each stratum and demonstrate that it describes a deformation of a hyperelliptic curve parametrizing the stratum the hierarchy is called the hidden burgers hopf hierarchy and we found the riemann invariant form and the hodograph solution

application of fuzzy naive bayes and a real valued genetic algorithm in identification of fuzzy model we present a method to identify a fuzzy model from data by using the fuzzy naive bayes and a real valued genetic algorithm the identification of a fuzzy model is comprised of the extraction of if then rules that is followed by the estimation of their parameters the involved parameters include those which determine the membership function of fuzzy sets and the certainty factors of fuzzy if then rules in our method as long as the fuzzy partition in the input output space is given the certainty factor of each rule is computed with the fuzzy conditional probability of the consequent conditioned on the antecedent by using the fuzzy naive bayes which is a generalization of naive bayes the fuzzy model involves the rules characterized by the highest values of certainty factors the certainty factor of each rule is the fuzzy conditional probability and it reflects the inner relationship between the antecedent and the consequent in order to improve the accuracy of the fuzzy model the real valued genetic algorithm is incorporated into our identification process this process concerns the optimization of the membership functions occurring in the rules we just involve the parameters of membership function of the fuzzy sets into the real valued genetic algorithm since the certainty factor of each rule can be computed automatically the performance of the model is shown for the backing truck problem and the prediction of mackey glass time series