Incentives and promotion in wage hierarchies

Most of the large firms organization schemes consist in hierarchical structures of tiers with different wage levels. Traditionally the existence of this kind of organizations has been associated to the separation of productive and managerial or supervision tasks and to differences in the skills of the workers. However, many firms now employ workers with similar skills, and then the hierarchical structure can be related to an incentive scheme to ensure that workers supply effort. The model we present investigates how firm owners should determine the optimal wage distribution in order to maximize profits.

Incentives and promotion in wage hierarchies

Most of the large firms organization schemes consist in hierarchical structures of tiers with different wage levels. Traditionally the existence of this kind of organizations has been associated to the separation of productive and managerial or supervision tasks and to differences in the skills of the workers. However, many firms now employ workers with similar skills, and then the hierarchical structure can be related to an incentive scheme to ensure that workers supply effort. The model we present investigates how firm owners should determine the optimal wage distribution in order to maximize profits.

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

The Cost of ownership in the governance of interfirm collaborations

This paper investigates the selection of governance forms in interfirm collaborations taking into account the predictions from transaction costs and property rights theories. Transaction costs arguments are often used to justify the introduction of hierarchical controls in collaborations, but the ownership dimension of going from “contracts” to “hierarchies” has been ignored in the past and with it the so called “costs of ownership”. The theoretical results, tested with a sample of collaborations in which participate Spanish firms, indicate that the cost of ownership may offset the benefits of hierarchical controls and therefore limit their diffusion. Evidence is also reported of possible complementarities between reputation effects and forms of ownership that go together with hierarchical controls (i.e. joint ventures), in contrast with the generally assumed substitutability between the two.

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.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Bioinformàtica: add-in d'anàlisi i manipulació de seqüències per Microsoft Word

L'objectiu del projecte consisteix en el desenvolupament d'un add-in d'anàlisi i manipulació de seqüències, senzill i de fàcil ús, integrable en l'entorn Microsoft Word per permetre la manipulació de seqüències genètiques directament des de Microsoft Word, estalviant temps, en evitar haver de canviar constantment de programa i format per treballar amb elles; i, també, complicacions a l'usuari final. L'add-in ha estat desenvolupat en Visual Basic + VSTO i ofereix diverses funcionalitats d'edició i anàlisi de seqüències, com ara el complement, la recerca de motius o l'alineament.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.