We discuss the Minority Game, a model of heterogeneous, indictive rational agents inspired by the El Farol Bar problem. We derive the exact solution of the model in the limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the collective behavior plays a key role: even though for each agent this effect is very sma...

The Time-Domain Vector Fitting (TD-VF) algorithm for macromodeling of linear multiport systems is presented. A rational approximation for the system matrix transfer function is easily derived from transient input/output port responses. Several validations illustrate the high accuracy of the method.

Given an open bounded set G in the complex plane and a weight function W (z) which is analytic and di erent from zero in G, we consider the problem of locally uniform rational approximation of any function f(z), which is analytic in G, by particular ray sequences of weighted rational functions of the form Wm+n(z)Rm;n(z), where Rm;n(z) = Pm(z)=Qn(z); with deg Pm m and degQn n: The main result of...

The need to evaluate expressions of the form f(A) or f(A)b, where f is a nonlinear function, A is a large sparse n × n matrix, and b is an n-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of A can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of ...

We propose a constructive solution to the problem of finding a cubic parametric curve in a plane if the tangent vectors (derivatives with respect to the parameter) and signed curvatures are given at its end-points but the end-points themselves are unknown. We also show how these curves can be applied to construct blending curves subject to curvature, arc length, inflection and area constraints.

There is abundant evidence that many individuals violate the rationality assumptions routinely made in economics. However, powerful evidence also indicates that violations of individual rationality do not necessarily refute the aggregate predictions of standard economic models that assume full rationality of all agents. Thus, a key question is how the interactions between rational and irrationa...

An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve self-sustainability. Our work is in two parts. First, we characterize iterated learnability in geometric terms and show how a slight, steady increase in the...

Many game theorists are turning to evolutionary simulations to model the behavior of boundedly rational agents. This new methodology allows researchers to observe purely adaptive behaviors in games, to observe differences of behavior due to changes in the games’ parameters, to discover equilibria in games that are too complex to calculate analytically, and to discover new strategies for playing...

In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the inclusion may exhibit inelastic material behavior. In this paper only plane stress/strain problems are considered. In our approach the geometry of the inclusion i...

We explicitly compute some double Dirichlet series constructed from n order Gauss sums over rational function fields. These turn out to be rational functions in q−s1 and q−s2 , where q is the size of the constant field. Key use is made of the group of 6 functional equations satisfied by these series.