Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

On the choice of an exchange rate regime: target zones revisited

From the classical gold standard up to the current ERM2 arrangement of the European Union, target zones have been a widely used exchange regime in contemporary history. This paper presents a benchmark model that rationalizes the choice of target zones over the rest of regimes: the fixed rate, the free float and the managed float. It is shown that the monetary authority may gain efficiency by reducing volatility of both the exchange rate and the interest rate at the same time. Furthermore, the model is consistent with some known stylized facts in the empirical literature that previous models were not able to produce, namely, the positive relation between the exchange rate and the interest rate differential, the degree of non-linearity of the function linking the exchage rate to fundamentals and the shape of the exchange rate stochastic distribution.

Free triples, large indifference classes and the majority rule

We present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

The density of injective endomorphisms of a free group

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

Avaluació de l'aprofitament energètic de la biomassa forestal del Parc de Collserola

En aquest treball se sintetitzen els resultats més destacats del projecte de final de carrera de la llicenciatura de Ciències Ambientals sobre l’aprofitament de la biomassa forestal al Parc de Collserola (PCo), realitzat a la Universitat Autònoma de Barcelona (UAB). L’objectiu principal és determinar la disponibilitat de biomassa forestal susceptible a ser extreta del PCo a fi d’aprofitar-la per a l’obtenció d’energia. Els principals factors analitzats són: la producció anual per cada espècie, les limitacions que marquen l’explotació i la tecnologia aplicable per a l’aprofitament en tres possibles escenaris. La proposta d’explotació sostenible dels boscos del PCo s’efectua sobre les espècies de Pinus halepensis, Quercus ilex i Quercus cerrioides, que presenten una producció major de biomassa susceptible a ser aprofitada, 5.500, 4.000 i 300 t psa1/any, respectivament. Per tant, la biomassa extraïble de forma sostenible al PCo s’estima en aproximadament 9.700 tones/any. L’estudi de l’aprofitament forestal està marcat per limitacions d’extracció, tals com les limitacions silvícoles (zones amb una cobertura arbòria igual o superior al 70% i un pendent igual o inferior al 60%) i d’accessibilitat (franges de 25 metres a banda i banda de les vies forestals). Amb la quantitat de biomassa extraïble es poden establir diferents escenaris d’aplicació energètica, mitjançant la seva combustió en calderes amb diverses potències de funcionament. Des del nivell domèstic (calderes domèstiques) fins al d’una gran planta (cogeneració), passant per l’aplicació en un barri residencial (District Heating). D’aquesta manera s’obté energia tèrmica, per calefacció, o elèctrica, aplicable a residències individuals, a barris residencials o a polígons industrials. S’ha escollit l’escenari de District Heating com el més viable, ja que és el que més avantatges presenta dintre del context del parc i un ventall de possibilitats d’aplicació més elevat. Per determinar-ne la viabilitat, s’han integrat diversos aspectes: tecnològics (eficiència, producció energètica, tipus de combustible i requeriment de biomassa), ambientals (impactes generats), socials (percepció dels usuaris) i econòmics (llocs de treball generats i viabilitat econòmica).

Zones lliures de transgènics a Europa : origen, desenvolupament i implantació a l'Estat Espanyol i a Catalunya

El nou moviment de les Zones Lliures de Transgènics (ZLT) sorgeix dels moviments d’oposició als OMGAs, paral·lement al debat que està tenint lloc en el sí de la UE, entorn la viabilitat de la coexistència entre l’agricultura transgènica i la convencional o ecològica. Aquest moviment que s’articula des de la dimensió local però amb un marcat simbolisme i rellevància en l’àmbit global, constitueix una important eina de desobediència civil dins el marc regulatori de la UE. Actualment, dins el context europeu, és a l’Estat Espanyol on es concentra la major superfície de blat de moro MG a escala comercial, cosa que dificulta l’establiment de ZLT. Aquest moviment, que reivindica la sobirania de les regions dins el gegant europeu, constitueix una alternativa real al model de producció, consum i dedesenvolupament actuals.

Nous actors, noves cultures? : evolució de les polítiques ambientals a Catalunya : els casos de l'aigua i l'energia

Les polítiques ambientals són el resultat d’un gran nombre de factors: el context social, el moment polític, el marc internacional, etc. En l’àmbit català s’ha demostrat que un factor que pot impactar de manera rellevant és l’aflorament de moviments ciutadans que reclamen canvis en les formes de fer política, encaminant-les cap a models més sostenibles. Malgrat sembli complicat que en el cas de l’energia es donin les condicions que van permetre el pas a la Nova Cultura de l’Aigua, no es descarta la possibilitat que s’arribi per altres mitjans a un canvi del paradigma energètic, ja que no tots els canvis són sempre apreciables des dels seus inicis.

L'Avion, L'Avion

Combined media on photographic paper. 56" x 84" Yarema Family Foundation