Restricted walks in regular trees

Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must follow a number of predetermined steps. We give formulas for the number of such walks by expressing the problem in terms of equations in F and solving the corresponding equations.

New FFT/IFFT Factorizations with Regular Interconnection Pattern Stage-to-Stage Subblocks

Les factoritzacions de la FFT (Fast Fourier Transform) que presenten un patró d’interconnexió regular entre factors o etapes son conegudes com algorismes paral·lels, o algorismes de Pease, ja que foren originalment proposats per Pease. En aquesta contribució s’han desenvolupat noves factoritzacions amb blocs que presenten el patró d’interconnexió regular de Pease. S’ha mostrat com aquests blocs poden ser obtinguts a una escala prèviament seleccionada. Les noves factoritzacions per ambdues FFT i IFFT (Inverse FFT) tenen dues classes de factors: uns pocs factors del tipus Cooley-Tukey i els nous factors que proporcionen la mateix patró d’interconnexió de Pease en blocs. Per a una factorització donada, els blocs comparteixen dimensions, el patró d’interconnexió etapa a etapa i a més cada un d’ells pot ser calculat independentment dels altres.

On the growth rate of minor-closed classes of graphs

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Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

Level-wise node size distribution of randomly generated regular trees

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On a family of strongly regular graphs with λ = 1

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Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Irregular to regular sampling, denoising and deconvolution

We propose a restoration algorithm for band limited images that considers irregular(perturbed) sampling, denoising, and deconvolution. We explore the application of a family ofregularizers that allow to control the spectral behavior of the solution combined with the irregular toregular sampling algorithms proposed by H.G. Feichtinger, K. Gr¨ochenig, M. Rauth and T. Strohmer.Moreover, the constraints given by the image acquisition model are incorporated as a set of localconstraints. And the analysis of such constraints leads to an early stopping rule meant to improvethe speed of the algorithm. Finally we present experiments focused on the restoration of satellite images, where the micro-vibrations are responsible of the type of distortions we are considering here. We will compare results of the proposed method with previous methods and show an extension tozoom.

On the closed-form approximation of short-time random strike options

In this paper we propose a general technique to develop first and second order closed-form approximation formulas for short-time options withrandom strikes. Our method is based on Malliavin calculus techniques andallows us to obtain simple closed-form approximation formulas dependingon the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches ontwo-assets and three-assets spread options as Kirk's formula or the decomposition mehod presented in Alòs, Eydeland and Laurence (2011).

Realització d'una aplicació de gestió de xarxes per a la xarxa sensefils de Manresa GuifiBages

En els últims anys, la popularitat de les xarxes sensefils (WIFI) ha anat en augment a un ritme incansable. Des de petits aparells instal•lats a les cases amb aquesta tecnologia com a complement dels routers d’accés a internet instal•lats per diverses companyies, fins a empreses fent petits desplegaments per comunicar entre si les seves seus. Al marge d’aquests escenaris, s’ha produït un fenomen social d’acolliment d’aquesta tecnologia a nivell mundial, en forma del que coneixem com a xarxes ciutadanes / xarxes lliures / xarxes socials. Aquestes xarxes han estat possibles gràcies a diverses raons que han fet assequible a col•lectius de persones, tant els aparells com els coneixements necessaris per dur a terme aquestes actuacions. Dintre d’aquest marc, al Bages, concretament a Manresa, es va començar a desenvolupar una d’aquestes xarxes. Les decisions d’aquesta xarxa d’utilitzar exclusivament hardware i software de codi obert, i determinats aspectes tècnics de la xarxa, ha comportat que la xarxa fos incompatible amb algunes de les aplicacions de gestió de xarxes existents desenvolupades per comunicats com gufi.net a Osona. És per això que per garantir el creixement, la supervivència i l’èxit d’aquesta xarxa en el temps, és indispensable poder comptar amb una eina de gestió que s’adigui a les característiques de GuifiBages. L’objectiu principal d’aquest treball és dotar a la xarxa GuifiBages de les eines necessàries per poder gestionar tota la informació referent a l’estructura de la seva xarxa, tant per facilitar l’accés a nous usuaris sense molts coneixements tècnics, com per facilitar nous desplegaments / reparacions / modificacions de la xarxa d’una manera automàtica. Com a conclusió d’aquest treball, podem afirmar que les avantatges que proporciones tecnologies com Plone, faciliten enormement la creació d’aplicacions de gestió de continguts en entorn web. Alhora, l’ús de noves tècniques de programació com AJAX o recursos com els que ofereix Google, permeten desenvolupar aplicacions web que no tenen res a envejar al software tradicional. D’altra banda, voldríem destacar l’ús exclusiu de programari lliure tant en els paquets de software necessaris pel desenvolupament, com en el sistema operatiu i programes dels ordinadors on s’ha dut a terme, demostrant que es poden desenvolupar sistemes de qualitat sense dependre de programari privatiu.

Regular population monotonic allocation schemes and the core

A subclass of games with population monotonic allocation schemes is studied, namelygames with regular population monotonic allocation schemes (rpmas). We focus on theproperties of these games and we prove the coincidence between the core and both theDavis-Maschler bargaining set and the Mas-Colell bargaining set

Sedimentological and palaeohydrological responses to tectonics and climate in a small, closed lacustrine system: Oligocene As Pontes Basin (Spain)

A small, closed, lacustrine system developed during the restraining overstep stages of the Oligocene As Pontes strike-slip basin (Spain). The increase in basin accommodation and the headward spread of the drainage, which increased the water input, triggered a change from shallow, holomictic to deeper, meromictic conditions.

Derivation of the gauge-invariant action for open and closed free bosonic string field theories

The gauge-invariant actions for open and closed free bosonic string field theories are obtained from the string field equations in the conformal gauge using the cohomology operations of Banks and Peskin. For the closed-string theory no restrictions are imposed on the gauge parameters.