Congruences on Menger algebras

We discuss some types of congruences on Menger algebras of rank $n$, which are generalizations of the principal left and right congruences on semigroups. We also study congruences admitting various types of cancellations and describe their relationship with strong subsets

Actions and Events in Concurrent Systems Design

In this work, having in mind the construction of concurrent systems from components, we discuss the difference between actions and events. For this discussion, we propose an(other) architecture description language in which actions and events are made explicit in the description of a component and a system. Our work builds from the ideas set forth by the categorical approach to the construction of software based systems from components advocated by Goguen and Burstall, in the context of institutions, and by Fiadeiro and Maibaum, in the context of temporal logic. In this context, we formalize a notion of a component as an element of an indexed category and we elicit a notion of a morphism between components as morphisms of this category. Moreover, we elaborate on how this formalization captures, in a convenient manner, the underlying structure of a component and the basic interaction mechanisms for putting components together. Further, we advance some ideas on how certain matters related to the openness and the compositionality of a component/system may be described in terms of classes of morphisms, thus potentially supporting a compositional rely/guarantee reasoning.Comment: In Proceedings LAFM 2013, arXiv:1401.056

Market Power and Efficiency in a Computational Electricity Market with Discriminatory Double-Auction Pricing

This study reports experimental market power and efficiency outcomes for a computational wholesale electricity market operating in the short run under systematically varied concentration and capacity conditions. The pricing of electricity is determined by means of a clearinghouse double auction with discriminatory midpoint pricing. Buyers and sellers use a modifed Roth-Erev individual reinforcement learning algorithm to determine their price and quantity offers in each auction round. It is shown that high market efficiency is generally attained, and that market microstructure is strongly predictive for the relative market power of buyers and sellers independently of the values set for the reinforcement learning parameters. Results are briefly compared against results from an earlier electricity study in which buyers and sellers instead engage in social mimicry learning via genetic algorithms. Related work can be accessed at: http://www.econ.iastate.edu/tesfatsi/AMESMarketHome.htmagent-based computational economics; Wholesale electricity market; restructuring; repeated double auction; market power; efficiency; concentration; capacity; individual reinforcement learning; genetic algorithm social learning

Transient cognitive dynamics, metastability, and decision making

Transient Cognitive Dynamics, Metastability, and Decision Making. Rabinovich et al. PLoS Computational Biology. 2008. 4(5) doi:10.1371/journal.pcbi.1000072The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. The main problem faced when using dynamical theory to describe transient cognitive processes is the fundamental contradiction between reproducibility and flexibility of transient behavior. In this paper, we propose a theoretical description of transient cognitive dynamics based on the interaction of functionally dependent metastable cognitive states. The mathematical image of such transient activity is a stable heteroclinic channel, i.e., a set of trajectories in the vicinity of a heteroclinic skeleton that consists of saddles and unstable separatrices that connect their surroundings. We suggest a basic mathematical model, a strongly dissipative dynamical system, and formulate the conditions for the robustness and reproducibility of cognitive transients that satisfy the competing requirements for stability and flexibility. Based on this approach, we describe here an effective solution for the problem of sequential decision making, represented as a fixed time game: a player takes sequential actions in a changing noisy environment so as to maximize a cumulative reward. As we predict and verify in computer simulations, noise plays an important role in optimizing the gain.This work was supported by ONR N00014-07-1-0741. PV acknowledges support from Spanish BFU2006-07902/BFI and CAM S-SEM-0255-2006