Subgroups of small index in Aut(Fn) and Kazhdan's property (T)

We give a series of interesting subgroups of finite index in Aut(Fn). One of them has index 42 in Aut(F3) and infinite abelianization. This implies that Aut(F3) does not have Kazhdan’s property (T) (see [3] and [6] for another proofs). We proved also that every subgroup of finite index in Aut(Fn), n &= 3, which contains the subgroup of IA-automorphisms, has a finite abelianization.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

Explaining High Economic Growth in Small Tourism Countries with a Dynamic General Equilibrium Model

This paper shows that tourism specialisation can help to explain the observed high growth rates of small countries. For this purpose, two models of growth and trade are constructed to represent the trade relations between two countries. One of the countries is large, rich, has an own source of sustained growth and produces a tradable capital good. The other is a small poor economy, which does not have an own engine of growth and produces tradable tourism services. The poor country exports tourism services to and imports capital goods from the rich economy. In one model tourism is a luxury good, while in the other the expenditure elasticity of tourism imports is unitary. Two main results are obtained. In the long run, the tourism country overcomes decreasing returns and permanently grows because its terms of trade continuously improve. Since the tourism sector is relatively less productive than the capital good sector, tourism services become relatively scarcer and hence more expensive than the capital good. Moreover, along the transition the growth rate of the tourism economy holds well above the one of the rich country for a long time. The growth rate differential between countries is particularly high when tourism is a luxury good. In this case, there is a faster increase in the tourism demand. As a result, investment of the small economy is boosted and its terms of trade highly improve.

A Thomason model structure on the category of small n-fold categories

We construct a cofibrantly generated Thomason model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences.

Organització nuclear dels gens que codifiquen per a les proteïnes làcties en cèlules epitelials mamàries en diferents estadis de desenvolupament

Estudi realitzat a partir d’una estada al Institut National de la Recherche Agronomique (INRA), a França, entre 2006 i 2008. En el ultims anys, estudis realitzats en diferents tipus cel•lulars han pogut determinar l’importància de l’organització nuclear en el control i regulació gènica. S’han realizat diferents experiments per tal de determinar si la posició dels gens de les proteïnes làcties en el nucli interfàsic de cel•lules epitelials mamaries és important per regular la seva expressió. Els gens de les proteïnes de la llet s’expressen a la glàndula mamaria durant la lactació en resposta a les hormones lactogèniques (majoritàriament prolactina i glucocorticoids). Mitjançant la tècnica de FISH (fluorescent in situ hibridization) en 3D s’ha caracteritzat la localització nuclear del gens WAP (whey acidic protein) i les caseïnes en cèl•lules epitelials mamaries de ratolí (HC11) cultivades en l’absència i presencia d’hormones lactogèniques. En absència d’hormones, els dos gens estan distribuïts dins del nucli de forma no aleatòria, el gen WAP es troba localitzat en l’interior del nucli, mentre que les caseïnes es troben localitzades prop de la perifèria nuclear. L’estimulació hormonal indueix un canvi significatiu en la distància dels dos gens a la perifèria nuclear. Així mateix, la posició del locus de la caseïna en relació al seu territori cromosòmic (CT) 5 està correlacionada amb la inducció hormonal i per tant amb la seva activació transcripcional, mentre que la posició del gen WAP amb relació al seu CT11 sembla més determinada pel context cromosòmic del gen. Per últim, no s’han trobat diferencies en la localització dels gens en relació a l'heterocromatina del centròmer, descrit com a compartiment repressiu, entre les cèl•lules estimulades amb hormones i les que no. En els dos casos s’ha trobat un gran percentatge de gens que no estan associats als centròmers.

On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Small firms, growth and financial constraints

This paper analyses the impact of different sources of finance on the growth of firms. Using panel data from Spanish manufacturing firms for the period 2000-2006, we investigate the effects of internal and external finances on firm growth. In particular, we examine three dimensions of these financial sources: a) the performance of the firms’ capital structure in accordance with firm size; b) the effects of internal and external financial sources on growth performance; c) the combined effect of equity, external debt and cash flow on firm growth. We find that low-growth firms are sensitive to cash flow and short-term bank debt, while high-growth firms are more sensitive to long-term debt. Furthermore, equity capital seems to reduce barriers to external finance. Our main conclusion is that during the start-up phase, firms are unable to increase their financial leverage and so their capital structure fails to promote correct investment strategies. However, as their equity capital increases, alternative financial mechanisms, in particular long-term debt, become available, which have a positive impact on firm growth.

System GMM estimation with a small sample

Properties of GMM estimators for panel data, which have become very popular in the empirical economic growth literature, are not well known when the number of individuals is small. This paper analyses through Monte Carlo simulations the properties of various GMM and other estimators when the number of individuals is the one typically available in country growth studies. It is found that, provided that some persistency is present in the series, the system GMM estimator has a lower bias and higher efficiency than all the other estimators analysed, including the standard first-differences GMM estimator.

A three dimensional signed small ball inequality

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

Are small firms more sensitive to financial variables?

This paper analyses the impact of different sources of finance on the growth of firms. sing panel data from Spanish manufacturing firms for the period 2000-2006, we investigate the effects of internal and external finances on firm growth. In particular, we examine wo dimensions of these financial sources: a) the performance of the firms' capital structure n accordance with firm size; b) the combined effect of equity, external debt and cash low n firm growth. We find that low-growth firms are sensitive to cash low and short-term ank debt, while high-growth firms are more sensitive to long-term debt. Furthermore, ur results show that low-growth firms are more sensitive to short-term financial variables, hile fast growth firms are more sensitive to long-term financial variables. EL codes: L25, R12. eywords: Finance, Firm growth, Quantile regressions, Small firms

The problem of the competitiveness of nuclear energy: a biophysical explanation

In this study I try to explain the systemic problem of the low economic competitiveness of nuclear energy for the production of electricity by carrying out a biophysical analysis of its production process. Given the fact that neither econometric approaches nor onedimensional methods of energy analyses are effective, I introduce the concept of biophysical explanation as a quantitative analysis capable of handling the inherent ambiguity associated with the concept of energy. In particular, the quantities of energy, considered as relevant for the assessment, can only be measured and aggregated after having agreed on a pre-analytical definition of a grammar characterizing a given set of finite transformations. Using this grammar it becomes possible to provide a biophysical explanation for the low economic competitiveness of nuclear energy in the production of electricity. 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. Since the cost of production of fossil energy provides the base line of economic competitiveness of electricity, the (lack of) economic competitiveness 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. In particular, the analysis focuses on fossil-fuel requirements and labor requirements for those phases that both nuclear plants and fossil energy plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. By adopting this approach, it becomes possible to explain the systemic low economic competitiveness of nuclear energy in the production of electricity, because of: (i) its dependence on oil, limiting its possible role as a carbon-free alternative; (ii) the choices made in relation to its fuel cycle, especially whether it includes reprocessing operations or not; (iii) the unavoidable uncertainty in the definition of the characteristics of its process; (iv) its large inertia (lack of flexibility) due to issues of time scale; and (v) its low power level.

Interpolation and sampling in small Bergman spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Uranium reserve, nuclear fuel cycle delusion, CO2 emission from the sea, and electricity supply: reflections after the fuel meltdown of Fukushima nuclear power units

The Great Tohoku-Kanto earthquake and resulting tsunami has brought considerable attention to the issue of the construction of new power plants. We argue in this paper, nuclear power is not a sustainable solution to energy problems. First, we explore the stock of uranium-235 and the different schemes developed by the nuclear power industry to exploit this resource. Second, we show that these methods, fast breeder and MOX fuel reactors, are not feasible. Third, we show that the argument that nuclear energy can be used to reduce CO2 emissions is false: the emissions from the increased water evaporation from nuclear power generation must be accounted for. In the case of Japan, water from nuclear power plants is drained into the surrounding sea, raising the water temperature which has an adverse affect on the immediate ecosystem, as well as increasing CO2 emissions from increased water evaporation from the sea. Next, a short exercise is used to show that nuclear power is not even needed to meet consumer demand in Japan. Such an exercise should be performed for any country considering the construction of additional nuclear power plants. Lastly, the paper is concluded with a discussion of the implications of our findings.