Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Hybrid heuristic-waterfilling game theory approach in MC-CDMA resource allocation

This paper discusses the power allocation with fixed rate constraint problem in multi-carrier code division multiple access (MC-CDMA) networks, that has been solved through game theoretic perspective by the use of an iterative water-filling algorithm (IWFA). The problem is analyzed under various interference density configurations, and its reliability is studied in terms of solution existence and uniqueness. Moreover, numerical results reveal the approach shortcoming, thus a new method combining swarm intelligence and IWFA is proposed to make practicable the use of game theoretic approaches in realistic MC-CDMA systems scenarios. The contribution of this paper is twofold: (i) provide a complete analysis for the existence and uniqueness of the game solution, from simple to more realist and complex interference scenarios; (ii) propose a hybrid power allocation optimization method combining swarm intelligence, game theory and IWFA. To corroborate the effectiveness of the proposed method, an outage probability analysis in realistic interference scenarios, and a complexity comparison with the classical IWFA are presented. (C) 2011 Elsevier B.V. All rights reserved.

Measure functional differential equations and functional dynamic equations on time scales

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti-Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. (C) 2012 Elsevier Inc. All rights reserved.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Liberalism, Marxism and Democratic Theory Revisited: Proposal of a Joint Index of Political and Economic Democracy

Liberalism and Marxism are two schools of thought which have left deep imprints in sociological, political and economic theory. They are usually perceived as opposite, rival approaches. In the field of democracy there is a seemingly insurmountable rift around the question of political versus economic democracy. Liberals emphasize the former, Marxists the latter. Liberals say that economic democracy is too abstract and fuzzy a concept, therefore one should concentrate on the workings of an objective political democracy. Marxists insist that political democracy without economic democracy is insufficient. The article argues that both propositions are valid and not mutually exclusive. It proposes the creation of an operational, quantifiable index of economic democracy that can be used alongside the already existing indexes of political democracy. By using these two indexes jointly, political and economic democracy can be objectively evaluated. Thus, the requirements of both camps are met and maybe a more dialogical approach to democracy can be reached in the debate between liberals and Marxists. The joint index is used to evaluate the levels of economic and political democracy in the transition countries of Eastern Europe.

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.