Grothendieck topologies from unique factorisation systems

This article presents a way to associate a Grothendieck site structure to a category endowed with a unique factorisation system of its arrows. In particular this recovers the Zariski and Etale topologies and others related to Voevodsky's cd-structures. As unique factorisation systems are also frequent outside algebraic geometry, the same construction applies to some new contexts, where it is related with known structures dened otherwise. The paper details algebraic geometrical situations and sketches only the other contexts.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Monopolistic competition and different wage setting systems

In this paper we match the static disequilibrium unemployment model without frictions in the labor market and monopolistic competition with an infinite horizon model of growth. We compare the wages set at the firm, sector and national (centralized) levels, their unemployment rates and growth of the economic variables, for the Cobb-Douglas production function, in order to see under wich conditions the inverse U hypothesis between unemployment and centralization of wage bargain is confirmed. We also analyze, in the three wage setting systems, the effect of an increase in the monopoly power on employment and growth.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

On stability of solutions to systems of convex inequalities

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Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

On p-optimal proof systems and logics for PTIME

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On slicewise monotone parameterized problems and optimal proof systems for TAUT

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Hard instances of algorithms and proof systems

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Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Biophysical requirements of power-supply systems: nuclear energy and fossil energy

The report presents a grammar capable of analyzing the process of production of electricity in modular elements for different power-supply systems, defined using semantic and formal categories. In this way it becomes possible to individuate similarities and differences in the process of production of electricity, and then measure and compare “apples” with “apples” and “oranges” with “oranges”. For instance, when comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. As a matter of facts, the performance of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. By adopting this approach, it becomes possible to compare the performance of the two power-supply systems by comparing their relative biophysical requirements for the phases that both nuclear energy power plants and fossil energy power plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. This report presents the evaluation of the biophysical requirements for the two powersupply systems: nuclear energy and fossil energy. In particular, the report focuses on the following requirements: (i) electricity; (ii) fossil-fuels, (iii) labor; and (iv) materials.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Information systems for water resources management improvement in developing countries

Water resources management, as also water service provision projects in developing countries have difficulties to take adequate decisions due to scarce reliable information, and a lack of proper information managing. Some appropriate tools need to be developed in order to improve decision making to improve water management and access of the poorest, through the design of Decision Support Systems (DSS). On the one side, a DSS for developing co-operation projects on water access improvement has been developed. Such a tool has specific context constrains (structure of the system, software requirements) and needs (Logical Framework Approach monitoring, organizational-learning, accountability and evaluation) that shall be considered for its design. Key aspects for its successful implementation have appeared to be a participatory design of the system and support of the managerial positions at the inception phase. A case study in Tanzania was conducted, together with the Spanish NGO ONGAWA – Ingeniería para el Desarrollo. On the other side, DSS are required also to improve decision making on water management resources in order to achieve a sustainable development that not only improves the living conditions of the population in developing countries, but that also does not hinder opportunities of the poorest on those context. A DSS made to fulfil these requirements shall be using information from water resources modelling, as also on the environment and the social context. Through the research, a case study has been conducted in the Central Rift Valley of Ethiopia, an endhorreic basin 160 km south of Addis Ababa. There, water has been modelled using ArcSWAT, a physically based model which can assess the impact of land management practices on large complex watersheds with varying soils, land use and management conditions over long periods of time. Moreover, governance on water and environment as also the socioeconomic context have been studied.