Consider n+m non-intersecting Brownian bridges, with n of them leaving from 0 at time t = −1 and returning to 0 at time t = 1, while the m remaining ones (wanderers) go from m points ai to m points bi. First we keep m fixed and we scale ai, bi appropriately with n. In the large-n limit we obtain a new Airy process with wanderers, in the neighborhood of √ 2n, the approximate location of the righ...

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex optimization. Algorithms for convex optimization benefitted from many pre-established ideas from classical mathematics, but nonconvex problems require new concepts...

It seems easy to accept that rationality involves many features that cannot be summarized in terms of some straightforward formula, such as binary consistency.  However, this recognition does not immediately lead to alternative characterizations that might be regarded as satisfactory, even though the inadequacies of the traditional assumptions of rational behavior standard used in economic theo...

Bi-intuitionistic propositional logic (also known as Heyting-Brouwer logic, subtractive logic) extends intuitionistic propositional logic with a connective that is dual to implication, called coimplication. It is the logic of bi-[Cartesian closed] categories and it also has a Kripke semantics. It first got the attention of C. Rauszer who studied it in a number of papers. Later, it has been inve...

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

this paper seeks to trace some of the roots and problems of the rational view of innovation. concentrating primarily upon product innovation, we point out that the eighteenth century notion of social progress in the light of reason has gradually given an enormous impetus to a rational view of product innovation in modern organizations. we summarize several decades of research into management of...

This paper aims to explore the role of questions in communication in a group of cooperative rational agents. Using epistemic representation of questions proposed in [6] we employ the framework of public announcement logic to explore the flow of information in the process of asking and replying questions in a group. We show that some of the erotetic notions we introduce nicely correspond to the ...

We show through a number of examples how it is possible to express beliefs of agents and communication among agents by employing a rst-order logic language with metalogical facilities. We argue that (i) such a language is suitable to characterise rational agents in diierent application areas, and (ii) the interplay between metalogical reasoning and diierent modalities of communications allows u...