Glassy states in the stochastic Potts model

We have studied by numerical simulations the relaxation of the stochastic seven-state Potts model after a quench from a high temperature down to a temperature below the first-order transition. For quench temperatures just below the transition temperature the phase ordering occurs by simple coarsening under the action of surface tension. For sufficient low temperatures however the straightening of the interface between domains drives the system toward a metastable disordered state, identified as a glassy state. Escaping from this state occurs, if the quench temperature is nonzero, by a thermal activated dynamics that eventually drives the system toward the equilibrium state. (C) 2009 Elsevier B.V. All rights reserved.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

On the efficiency of data representation on the modeling and characterization of complex networks

Specific choices about how to represent complex networks can have a substantial impact on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically by adjacency matrices or dynamically by adjacency lists. Three theoretical models of complex networks are considered: two types of Erdos-Renyi as well as the Barabasi-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance. (C) 2011 Elsevier B.V. All rights reserved.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Landskommunens beslutsfattande kvinnor : Om kvinnors representation i kommunalfullmäktige ochförekomst i fullmäktigeprotokoll i Kalmar länslandskommuner 1939-1951

Syftet med denna uppsats är att undersöka den kvinnliga representationen i Kalmar läns landskommuners kommunalfullmäktige från 1938 till kommunsammanslagningen 1951. Detta innefattar att söka en översikt över i vilken grad kvinnor är representerade i länets kommunalfullmäktigeförsamlingaroch att undersöka hur dessa kvinnliga ledamöter syns i protokollsmaterial i ett par kommuners fullmäktigeprotokoll. Södra Möckelby och Vickleby kommuner med relativt hög andel kvinnliga ledamöter har valts som exempel.Undersökningen av valstatistiken visar en ökning i både antal kvinnor och antal kommunalfullmäktige med kvinnlig representation under perioden. Länet ligger under riksgenomsnittet, men ökningen är ungefär densamma i relativa termer. Närläsningen av protokoll visar att kvinnor främst omnämns vid frånvaro, vid val till olika uppdrag eller vid uppföljning av dessa val. I den kommun som har en längre tradition av relativt hög kvinnlig representation märks kvinnor i fler sammanhang som förutsätter att man tar ett större utrymme på mötena. Dessa tillfällen sammanfaller med en speciell kvinnas aktiva period i fullmäktige och försvinner när den kvinnliga representationen minskar till en ensam kvinna.

Environmental Objectives, Cost Efficiency, and Multivariate Stochastic Control

This paper is concerned with the cost efficiency in achieving the Swedish national air quality objectives under uncertainty. To realize an ecologically sustainable society, the parliament has approved a set of interim and long-term pollution reduction targets. However, there are considerable quantification uncertainties on the effectiveness of the proposed pollution reduction measures. In this paper, we develop a multivariate stochastic control framework to deal with the cost efficiency problem with multiple pollutants. Based on the cost and technological data collected by several national authorities, we explore the implications of alternative probabilistic constraints. It is found that a composite probabilistic constraint induces considerably lower abatement cost than separable probabilistic restrictions. The trend is reinforced by the presence of positive correlations between reductions in the multiple pollutants.

La confrontation de la laideur avec la beauté dans lesromans Mercure et Attentat. Une étude sur lareprésentation de la dualité thématique laideur-beautéchez Amélie Nothomb. : "Where there is Quasimodo, there is also Esmeralda." The confrontationbetween ugliness and beauty in the novels Mercure and Attentat. Astudy on the representation of the duality beauty-ugliness in the worksof Amélie Nothomb.

This paper studies one of the recurrent topics of writing found in Amélie Nothomb’snovels: beauty and ugliness. The novels Mercure and Attentat are analyzed in detail,with respect to figures of speech used to describe the extreme physical appearance ofthe protagonists and the role of the duality beauty-ugliness in the advancement of theplot.

Representation and interpretation : textbooks, teachers, and historical culture

This article presents a study of how contemporary Swedish lower secondary school textbooks present the emergence of the Cold War and how 10 active lower secondary school history teachers interpreted a quotation that was ambiguous in relation to the general narrative in the studied Swedish textbooks, seeking to analyse textbooks both from the perspectives of content and reception. Applying a theoretical framework of uses of history, the study finds that the narratives presented in the studied textbooks are what could be called traditional in the sense that they do not acknowledge perspective and representation in history. While the interviewed teachers generally acknowledged that textbook narratives are representations of history and contingent on perspective, few teachers extended this to include how their own views affect their interpretations, suggesting an intermediary appreciation of the contextual contingency of historical narratives.