Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

MSSM Higgs boson decays to bottom quark pairs reexamined

We present an update of neutral Higgs boson decays into bottom quark pairs in the minimal supersymmetric extension of the standard model. In particular the resummation of potentially large higher-order corrections due to the soft supersymmetry (SUSY) breaking parameters Ab and is extended. The remaining theoretical uncertainties due to unknown higher-order SUSY-QCD corrections are analyzed quantitatively.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

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Minimal truncations of supersingular p-divisible groups

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Catalan's intervals and realizers of triangulations

The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice which is an extension of the Kreweras lattice. The Stanley order can be defined on the set of Dyck paths of size n as the relation of being above. Hence, intervals in the Stanley lattice are pairs of non-crossing Dyck paths. In a former article, the second author defined a bijection Φ between pairs of non-crossing Dyck paths and the realizers of triangulations (or Schnyder woods). We give a simpler description of the bijection Φ. Then, we study the restriction of Φ to Tamari’s and Kreweras’ intervals. We prove that Φ induces a bijection between Tamari intervals and minimal realizers. This gives a bijection between Tamari intervals and triangulations. We also prove that Φ induces a bijection between Kreweras intervals and the (unique) realizers of stack triangulations. Thus, Φ induces a bijection between Kreweras intervals and stacktriangulations which are known to be in bijection with ternary trees.

El desastre quotidià i la disciplina repressora, respostes a la geometria minimal

La proposta de tesi pren com a punt de partida les respostes artístiques i teòriques dutes a terme a partir dels anys seixanta contra un context de coneixement tradicional fonamentalment racionalista, que segueix la tradició lògica de la modernitat i que troba el seu reflex i aplicació social en l’ordre espaial i per extensió, en la geometria. Un cop descrites les nocions que d’aquesta modernitat han estat aplicades a l’art dels anys 50 i 60, es mostra com les crítiques de determinats filòsofs i artistes han anat conformant un corpus teòric i artístic que ha implicat un intent d’enderrocament d’aquest sistema tradicional de coneixement, interpretació, lectura i atorgament de sentit a les obres artístiques. Aquests són: M.Foucault, J.Derrida, R. Smithson, R. Serra, R. Morris, Mona Hatoum, Imi Knoebel o Tacita Dean, entre d’altres. Seguidament es presenta un anàlisi més profund i detallat d’aquelles respostes artístiques més paradigmàtiques, tant al sistema de pensament tradicional com a l’ordre espaial que aquest conseqüentment implica. Aquestes crítiques s’organitzen en dues parts antagòniques: l’una és “L’adveniment del caos”, i l’altra és la “Crítica de l’ordre”. Els artistes són: L. Bourgeois, E.Hesse, A.Mendieta i P.Halley. En una tercera part, es descriu com aquest inici deconstructor del paradigma de coneixement tradicional iniciat als anys seixanta es desenvolupa durant els següents vint anys tenint en aquest cas com a fonament teòric les crítiques de R.Krauss, J. Baudrillard, P.Virilio, i com artistes els arquitectes P. Eienmann i F. Gehri, entre d’altres. La conclusió fonamental d’aquests apartats intenta posar de manifest la subversió o infracció de la geometria com a contenidora dels conceptes de la modernitat: raó i ordre moral. Finalment, en una quarta part s’inclou el propi projecte artístic que representa l’experimentació i praxi de les conclusions teòriques d’aquesta tesi.

Green vs. Lempert functions: a minimal example

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.

A note on Luttens’ Minimal rights based solidarity

Following the approach developed by Luttens (2010), we consider a model where individuals with di fferent levels of skills exert di fferent levels of e ffor. Speci fically, we propose a redistribution mechanism based on a lower bound on what every individual deserves: the so-called minimal rights (O'Neill (1982)). Our re finement of Luttens' mechanism ensures at the same time minimal rights based solidarity, participation (non-negativity) and claims feasibility. Keywords: Redistribution mechanism, Minimal rights, Solidarity, Participation, Claims feasibility. JEL classi fication: C71, D63, D71.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Bootstrapping pairs in Distance-Based Regression

La regressió basada en distàncies és un mètode de predicció que consisteix en dos passos: a partir de les distàncies entre observacions obtenim les variables latents, les quals passen a ser els regressors en un model lineal de mínims quadrats ordinaris. Les distàncies les calculem a partir dels predictors originals fent us d'una funció de dissimilaritats adequada. Donat que, en general, els regressors estan relacionats de manera no lineal amb la resposta, la seva selecció amb el test F usual no és possible. En aquest treball proposem una solució a aquest problema de selecció de predictors definint tests estadístics generalitzats i adaptant un mètode de bootstrap no paramètric per a l'estimació dels p-valors. Incluim un exemple numèric amb dades de l'assegurança d'automòbils.

Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number N of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N = 7 and verify that they are minimal up to N = 5.