Dimension and product structure of hyperbolic measures

We prove that every hyperbolic measure invariant under a C^{1+\alpha} diffeomorphism of a smooth Riemannian manifold possesses asymptotically ``almost'' local product structure, i.e., its density can be approximated by the product of the densities on stable and unstable manifolds up to small exponentials. This has not been known even for measures supported on locally maximal hyperbolic sets. Using this property of hyperbolic measures we prove the long-standing Eckmann-Ruelle conjecture in dimension theory of smooth dynamical systems: the pointwise dimension of every hyperbolic measure invariant under a C^{1+\alpha} diffeomorphism exists almost everywhere. This implies the crucial fact that virtually all the characteristics of dimension type of the measure (including the Hausdorff dimension, box dimension, and information dimension) coincide. This provides the rigorous mathematical justification of the concept of fractal dimension for hyperbolic measures.Comment: 29 pages, published versio

An Evolutionary Game Approach to the Issues of Migration, Nationalism, Assimilation and Enclaves

I use evolutionary game theory to address the relation between nationalism and immigration, studying how two different populations in a country, one composed of national citizens and the other of immigrants, evolve over time. Both populations depart from some polymorphic initial state. A national citizen may behave either nationalistically or may welcome immigrants. Immigrants may have an interest in learning the host country language or not. I also account for the presence of enclaves, which make the immigrants� own population effects important. The results show that six types of evolutionary equilibria are possible, although they never co-exist in the state space. A low cost of learning the host country language leads to complete assimilation of immigrants over time. Enclaves make assimilation a less competitive strategy. A high cost of learning may lead to peaceful multiculturalism or to political instability depending on the ability of policy makers to prevent nationalistic attitudes.

Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion

This article presents stability analytical results of a two component reaction-diffusion system with linear cross-diffusion posed on continuously evolving domains. First the model system is mapped from a continuously evolving domain to a reference stationary frame resulting in a system of partial differential equations with time-dependent coefficients. Second, by employing appropriately asymptotic theory, we derive and prove cross-diffusion-driven instability conditions for the model system for the case of slow, isotropic domain growth. Our analytical results reveal that unlike the restrictive diffusion-driven instability conditions on stationary domains, in the presence of cross-diffusion coupled with domain evolution, it is no longer necessary to enforce cross nor pure kinetic conditions. The restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Reaction-cross-diffusion models with equal diffusion coefficients in the principal components as well as those of the short-range inhibition, long-range activation and activator-activator form can generate patterns only in the presence of cross-diffusion coupled with domain evolution. To confirm our theoretical findings, detailed parameter spaces are exhibited for the special cases of isotropic exponential, linear and logistic growth profiles. In support of our theoretical predictions, we present evolving or moving finite element solutions exhibiting patterns generated by a short-range inhibition, long-range activation reaction-diffusion model with linear cross-diffusion in the presence of domain evolution

Elections and the public expenditure mix

The paper presents an intertemporal utility model that determines the effects of elections on the public expenditure composition. Conventional political budget cycle models describe incumbents as concerned only with the conditions that guarantee re-appointment. Aiming at achieving re-election, incumbents behave opportunistically in order to seduce voters about their political performance. The paper introduces another motivation for the manipulation of the public expenditure mix near elections: the incumbent’s concern with her future utility in the case of defeat. We provide data to suggest that both central and local governments in the European Union do manipulate the budget composition around election moments. In order to rationalise this observation, the paper proposes a model where voters and incumbent are rational, have complete information and no bias towards any category of public expenditure, namely consumption expenditure or investment expenditure. The paper shows that even under these extreme conditions, an electorally induced cycle on public expenditure mix is still expected, one where consumption expenditure raises relative to investment expenditure in pre-election periods. This opportunistic budget manipulation follows from two facts. First, any decision an incumbent makes on consumption expenditure pays back political dividends during the same period the expenditure is incurred, while any investment expenditure only becomes visible to voters with a one-period delay. Second, re-election is an uncertain event, which makes the second state of nature valuable. Outside politics, the incumbents’ pay back is a direct function of the voters’ assessment of the incumbents’ job while in office. The model is then extended to accommodate the scenario where voters and society at large do not share preferences. When voters or society evidence a preference prone to one of the public expenditure categories, a bias towards such category emerges in post-election periods. In pre-election periods two cases are found. Consumption expenditures exceed investment expenditures if either voters or society prefer the former category at the margin. The cycle’s nature is ambiguous if the marginal preferences of voters or society are biased towards investment expenditures. JEL classification: H50, E62. Keywords: Political Budget Cycles, Public Expenditure, Elections.

Anthropic versus cosmological solutions to the coincidence problem

In this paper we investigate possible solutions to the coincidence problem in flat phantom dark energy models with a constant dark energy equation of state and quintessence models with a linear scalar field potential. These models are representative of a broader class of cosmological scenarios in which the universe has a finite lifetime. We show that, in the absence of anthropic constraints, including a prior probability for the models inversely proportional to the total lifetime of the universe excludes models very close to the $\Lambda {\rm CDM}$ model. This relates a cosmological solution to the coincidence problem with a dynamical dark energy component having an equation of state parameter not too close to -1 at the present time. We further show, that anthropic constraints, if they are sufficiently stringent, may solve the coincidence problem without the need for dynamical dark energy.Comment: 7 pages, 7 figure

On the topological pressure of random bundle transformations in sub-additive case

In this paper, we define the topological pressure for sub-additive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.Comment: 16page

A PRACTICAL APPROACH TO MODEL BANKING RISKS USING LOSS DISTRIBUTION APPROACH (LDA) IN BASEL II FRAMEWORK

In Basel II Capital Accord, the Advanced Measurement Approaches (AMA) is stated as one of the pillar stone methods for calculating corporate risk reserves. One of the common yet cumbersome methods is the one known as loss distribution approach (cf. [Chernobai A S, Rachev S T and Fabozzi F J, (2007)]. In this article, we present an easy to implement scheme through electronic means and discuss some of the mathematical problems we encountered in the process together with proposed solution methods and further sought on the issues.loss distribution approach, corporate risk, Basel II principles

Is Ambient Intelligence a truly Human-Centric Paradigm in Industry? Current Research and Application Scenario

The use of pervasive networked devices is nowadays a reality in the service sector. It impacts almost all aspects of our daily lives, although most times we are not aware of its influence. This is a fundamental characteristic of the concept of Ambient Intelligence (AmI). Ambient Intelligence aims to change the form of human-computer interaction, focusing on the user needs so they can interact in a more seamless way, with emphasis on greater user-friendliness. The idea of recognizing people and their context situation is not new and has been successfully applied with limitations, for instance, in the health and military sectors. However its appearance in the manufacturing industry has been elusive. Could the concept of AmI turn the current shop floor into a truly human centric environment enabling comprehensive reaction to human presence and action? In this article an AmI scenario is presented and detailed with applications in human’s integrity and safety.Ambient Intelligence, networks, human-computer interaction