http://www.recercat.cat:80/handle/2072/1176 www.crm.es 2012-02-11T21:31:12Z http://www.recercat.cat:80/handle/2072/179356 On Lundh's percolation diffusion Carroll, T.; O'Donovan, Julie; Ortega Cerdà, Joaquim A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/179300 The β-Meixner model Ferreiro Castilla, Albert We propose to approximate the Meixner model by a member of the B-family introduced in [Kuz10a]. The advantage of such approximations are the semi-explicit formulas for the running extrema under the B-family processes which enables us to produce more efficient algorithms for certain path dependent options. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/179281 Deux extensions de Théorèmes de Hamburger (portant sur l'équation fonctionnelle de la fonction dzêta) Burnol, J.-F. We propose two types of extensions to Hamburger’s theorems on the Dirichlet series with functional equation like the one of the Riemann zeta function, under weaker hypotheses. This builds upon the dictionary betweeen the moderate meromorphic functions with functional equation and the tempered distributions with extended S-support condition.; Nous proposons deux types d’extensions aux théorèmes de Hamburger sur les séries de Dirichlet avec équation fonctionnelle comme celle de la fonction zêta de Riemann, sous des hypothèses plus faibles. Ceci repose sur le dictionnaire entre les fonctions méromorphes modérées avec cette équation fonctionnelle et les distributions tempérées avec la condition de support S-étendue. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/179280 Extensional flow of nematic liquid crystal under electric field gradient Cummings, L. J.; Myers, T.G.; Low, J. Systematic asymptotic methods are used to formulate a model for the extensional flow of a thin sheet of nematic liquid crystal. With no external body forces applied, the model is found to be equivalent to the so-called Trouton model for Newtonian sheets (and fi bers), albeit with a modi fied "Trouton ratio". However, with a symmetry-breaking electric field gradient applied, behavior deviates from the Newtonian case, and the sheet can undergo fi nite-time breakup if a suitable destabilizing field is applied. Some simple exact solutions are presented to illustrate the results in certain idealized limits, as well as sample numerical results to the full model equations. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/179279 Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation Ortiz-Gracia, Luís; Masdemont Soler, Josep To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/179278 Decomposable approximations of nuclear C*-algebras Hirshberg, I.; White, Stuart; Kirchberg, E. We show that nuclear C*-algebras have a re ned version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171421 Equivalence relations in set theory, computation theory, model theory and complexity theory Friedman, Sy D. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171420 Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs Sinclair, Alistair; Srivastava, Piyush; Thurley, Marc 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. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171360 C*-algebras nearly contained in type I algebras Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.; White, Stuart "Vegeu el resum a l'inici del document del fitxer adjunt" 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171359 An approximation algorithm for #k-SAT Thurley, Marc "Vegeu el resum a l'inici del document del fitxer adjunt" 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171358 A lower bound in Nehari's theorem on the polydisc Ortega Cerdà, Joaquim; Seip, Kristian "Vegeu el resum a l'inici del document del fitxer adjunt" 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171357 Computing hypergraph width measures exactly Moll, Lukas; Tazari, Siamak; Thurley, Marc Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171355 On the system of the functions x (s) / (s-r)k Burnol, J.-F. "Vegeu el resum a l'inici del document del fitxer adjunt." 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171354 The β-Meixner model Ferreiro Castilla, Albert; Schoutens, Wim We propose to approximate the Meixner model by a member of the B–family introduced in [Kuz10a]. The advantage of such approximations are the semi–explicit formulas for the running extrema under the B–family processes which enables us to produce more efficient algorithms for certain path dependent options. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171353 An approximate solution method for boundary layer flow of a power law fluid over a flat plate Myers, T.G. The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/171352 Green vs. Lempert functions: a minimal example Thomas, Pascal J. The Lempert function for a set of poles in a domain of Cn at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, and majorizes the corresponding multi-pole pluricomplex Green function. Coman proved that both coincide in the case of sets of two poles in the unit ball. We give an example of a set of three poles in the unit ball where this equality fails. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169952 Interpolation and sampling in small Bergman spaces Seip, Kristian "Vegeu el resum a l'inici del document del fitxer adjunt." 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169951 On Lundh's percolation diffusion Carroll, T.; O'Donovan, Julie; Ortega Cerdà, Joaquim A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169774 On Borel equivalence relations in generalized Baire space Friedman, Sy D.; Hyttinen, Tapani "Vegeu el resum a l'inici del document del fitxer adjunt." 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169740 Hard instances of algorithms and proof systems Chen, Yijia; Flum, Jörg; Müller, Moritz "Vegeu el resum a l'inici del document del fitxer adjunt." 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169739 Non-characteristic half-lives in radioactive decay Corral, Álvaro; Font Martinez, Francesc; Camacho Castro, Juan Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that explore a method for fitting power-laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169738 Contact melting of a three-dimensional phase change material on a flat substrate De Decker, Michelle M.; Myers, T.G. In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169737 The non-absoluteness of model existence in uncountable cardinals for Lw1,w Friedman, Sy D.; Hyttinen, Tapani; Koerwien, Martin "Vegeu el resum a l'inici del document del fitxer adjunt" 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169736 Consistency and optimality Chen, Yijia; Flum, Jörg; Müller, Moritz Assume that the problem Qo is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T U {ConT} as the minimal extension of T proving for some algorithm that it decides Qo as fast as any algorithm B with the property that T proves that B decides Qo. Here, ConT claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169508 On the stability of the optimal value and the optimal set in optimization problems Dinh, N.; Goberna, M. A.; López, M.A. The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property). 2010-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169477 Strong isomorphism reductions in complexity theory Buss, Samuel R.; Chen, Yijia; Flum, Jörg; Friedman, Sy D.; Müller, Moritz We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees. 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169476 Potential isomorphism of elementary substructures of a strictly stable homogeneous model Friedman, Sy D.; Hyttinen, Tapani; Walczak-Typke, Agatha C. "Vegeu el resum a l'inici del document del fitxer adjunt." 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169475 Generalized descriptive set theory and classification theory Friedman, Sy D.; Hyttinen, Tapani; Kulikov, Vadim Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations. 2010-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169474 Double adjunctions Fiore, Thomas M.; Gambino, Nicola; Kock, Joachim We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg-Moore objects in double categories. We improve upon an earlier result of Fiore-Gambino-Kock in [7] to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category horizontally and vertically, and also in its vertical 2-category. We also prove that a double category admits Eilenberg-Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double Yoneda Lemma. 2010-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/169473 Sur les symboles modulaires de Manin-Teitelbaum pour Fq(T) Armana, Cécile "Vegeu el resum a l'inici del document del fitxer adjunt" 2010-12-01T00:00:00Z