Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

On the relation between tax rates and evasion in a multi-period economy

We extend the basic tax evasion model to a multi-period economy exhibiting sustained growth. When individuals conceal part of their true income from the tax authority, they face the risk of being audited and hence of paying the corresponding fine. Both taxes and fines determine individual saving and the rate of capital accumulation. In this context we show that the sign of the relation between the level of the tax rate and the amount of evaded income is the same as that obtained in static setups. Moreover, high tax rates on income are typically associated with low growth rates as occurs in standard growth models that disregard the tax evasion phenomenon.

Limit Cycles for a class of three dimensional polynomial differential systems

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Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

MB-MDR: Model-Based Multifactor Dimensionality Reduction for detecting interactions in high-dimensional genomic data

L’anàlisi de l’efecte dels gens i els factors ambientals en el desenvolupament de malalties complexes és un gran repte estadístic i computacional. Entre les diverses metodologies de mineria de dades que s’han proposat per a l’anàlisi d’interaccions una de les més populars és el mètode Multifactor Dimensionality Reduction, MDR, (Ritchie i al. 2001). L’estratègia d’aquest mètode és reduir la dimensió multifactorial a u mitjançant l’agrupació dels diferents genotips en dos grups de risc: alt i baix. Tot i la seva utilitat demostrada, el mètode MDR té alguns inconvenients entre els quals l’agrupació excessiva de genotips pot fer que algunes interaccions importants no siguin detectades i que no permet ajustar per efectes principals ni per variables confusores. En aquest article il•lustrem les limitacions de l’estratègia MDR i d’altres aproximacions no paramètriques i demostrem la conveniència d’utilitzar metodologies parametriques per analitzar interaccions en estudis cas-control on es requereix l’ajust per variables confusores i per efectes principals. Proposem una nova metodologia, una versió paramètrica del mètode MDR, que anomenem Model-Based Multifactor Dimensionality Reduction (MB-MDR). La metodologia proposada té com a objectiu la identificació de genotips específics que estiguin associats a la malaltia i permet ajustar per efectes marginals i variables confusores. La nova metodologia s’il•lustra amb dades de l’Estudi Espanyol de Cancer de Bufeta.

Multi-Scale Integrated Analysis of Societal and Ecosystem Metabolism (MUSIASEM): an outline of rationale and theory

This paper presents an outline of rationale and theory of the MuSIASEM scheme (Multi-Scale Integrated Analysis of Societal and Ecosystem Metabolism). First, three points of the rationale behind our MuSIASEM scheme are discussed: (i) endosomatic and exosomatic metabolism in relation to Georgescu-Roegen’s flow-fund scheme; (2) the bioeconomic analogy of hypercycle and dissipative parts in ecosystems; (3) the dramatic reallocation of human time and land use patterns in various sectors of modern economy. Next, a flow-fund representation of the MUSIASEM scheme on three levels (the whole national level, the paid work sectors level, and the agricultural sector level) is illustrated to look at the structure of the human economy in relation to two primary factors: (i) human time - a fund; and (ii) exosomatic energy - a flow. The three levels representation uses extensive and intensive variables simultaneously. Key conceptual tools of the MuSIASEM scheme - mosaic effects and impredicative loop analysis - are explained using the three level flow-fund representation. Finally, we claim that the MuSIASEM scheme can be seen as a multi-purpose grammar useful to deal with sustainability issues.

Multi-product firms and product variety

The goal of this paper is to study the role of multi-product firms in the market provision of product variety. The analysis is conducted using the spokes model of non-localized competition proposed by Chen and Riordan (2007). Firstly, we show that multi-product firms are at a competitive disadvantage vis-a-vis single-product firms and can only emerge if economies of scope are sufficiently strong. Secondly, under duopoly product variety may be higher or lower with respect to both the first best and the monopolistically competitive equilibrium. However, within a relevant range of parameter values duopolists drastically restrict their product range in order to relax price competition, and as a result product variety is far below the efficient level.

Multi-phase post-mortem CT angiography: development of a standardized protocol.

The objective of this work was to develop an easily applicable technique and a standardized protocol for high-quality post-mortem angiography. This protocol should (1) increase the radiological interpretation by decreasing artifacts due to the perfusion and by reaching a complete filling of the vascular system and (2) ease and standardize the execution of the examination. To this aim, 45 human corpses were investigated by post-mortem computed tomography (CT) angiography using different perfusion protocols, a modified heart-lung machine and a new contrast agent mixture, specifically developed for post-mortem investigations. The quality of the CT angiographies was evaluated radiologically by observing the filling of the vascular system and assessing the interpretability of the resulting images and by comparing radiological diagnoses to conventional autopsy conclusions. Post-mortem angiography yielded satisfactory results provided that the volumes of the injected contrast agent mixture were high enough to completely fill the vascular system. In order to avoid artifacts due to the post-mortem perfusion, a minimum of three angiographic phases and one native scan had to be performed. These findings were taken into account to develop a protocol for quality post-mortem CT angiography that minimizes the risk of radiological misinterpretation. The proposed protocol is easy applicable in a standardized way and yields high-quality radiologically interpretable visualization of the vascular system in post-mortem investigations.

The Measurement of social polarization in a multi-group context

Polarization indices presented up to now have only focused their attention on the distribution of income/wealth. However, in many circumstances income is not the only relevant dimension that might be the cause of social conflict, so it is very important to have a social polarization index able to cope with alternative dimensions. In this paper we present an axiomatic characterization of one of such indices: it has been obtained as an extension of the (income) polarization measure introduced in Duclos, Esteban and Ray (2004) to a wider domain. It turns out that the axiomatic structure introduced in that paper alone is not appropriate to obtain a fully satisfactory characterization of our measure, so additional axioms are proposed. As a byproduct, we present an alternative axiomatization of the aforementioned income polarization measure.

Hopf bifurcation in higher dimensional differential systems via the averaging method

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