Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

General equilibrium with asymmetric information: a dual approach

We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive transactions, the environment is described as a continuum economy with indivisible commodities. We characterize incentive efficient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external effects in these markets. Because under certain conditions such effects may generate non-convexities, randomization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external effects may have critical implications for market efficiency. With adverse selection, in fact, cross-subsidization across agents with different private information may be necessary for optimality, and so, the market need not even achieve an incentive efficient allocation. In contrast, for the case of a single commodity, we find that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external effects are fully internalized at a market equilibrium.

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Generic object classification for autonomous robots

Un dels principals problemes de la interacció dels robots autònoms és el coneixement de l'escena. El reconeixement és fonamental per a solucionar aquest problema i permetre als robots interactuar en un escenari no controlat. En aquest document presentem una aplicació pràctica de la captura d'objectes, de la normalització i de la classificació de senyals triangulars i circulars. El sistema s'introdueix en el robot Aibo de Sony per a millorar-ne la interacció. La metodologia presentada s'ha comprobat en simulacions i problemes de categorització reals, com ara la classificació de senyals de trànsit, amb resultats molt prometedors.

A public-key cryptosystem based on second order linear sequences

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

The generic Hanna Neumann conjecture and post correspondence problem

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A theoretical and practical study on linear reforms of dual taxes

We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Quasiconformal maps, analytic capacity, and non linear potentials

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