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

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

Minimal truncations of supersingular p-divisible groups

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

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.

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.

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.

A minimal i-motif stabilized by minor groove G:T:G:T tetrads

The repetitive DNA sequences found at telomeres and centromeres play a crucial role in the structure and function of eukaryotic chromosomes. This role may be related to the tendency observed in many repetitive DNAs to adopt non-canonical structures. Although there is an increasing recognition of the importance of DNA quadruplexes in chromosome biology, the co-existence of different quadruplex-forming elements in the same DNA structure is still a matter of debate. Here we report the structural study of the oligonucleotide d(TCGTTTCGT) and its cyclic analog d. Both sequences form dimeric quadruplex structures consisting of a minimal i-motif capped, at both ends, by a slipped minor groove-aligned G:T:G:T tetrad. These mini i-motifs, which do not exhibit the characteristic CD spectra of other i-motif structures, can be observed at neutral pH, although they are more stable under acidic conditions. This finding is particularly relevant since these oligonucleotide sequences do not contain contiguous cytosines. Importantly, these structures resemble the loop moiety adopted by an 11-nucleotide fragment of the conserved centromeric protein B (CENP-B) box motif, which is the binding site for the CENP-B.

A minimal i-motif stabilized by minor groove G:T:G:T tetrads

The repetitive DNA sequences found at telomeres and centromeres play a crucial role in the structure and function of eukaryotic chromosomes. This role may be related to the tendency observed in many repetitive DNAs to adopt non-canonical structures. Although there is an increasing recognition of the importance of DNA quadruplexes in chromosome biology, the co-existence of different quadruplex-forming elements in the same DNA structure is still a matter of debate. Here we report the structural study of the oligonucleotide d(TCGTTTCGT) and its cyclic analog d. Both sequences form dimeric quadruplex structures consisting of a minimal i-motif capped, at both ends, by a slipped minor groove-aligned G:T:G:T tetrad. These mini i-motifs, which do not exhibit the characteristic CD spectra of other i-motif structures, can be observed at neutral pH, although they are more stable under acidic conditions. This finding is particularly relevant since these oligonucleotide sequences do not contain contiguous cytosines. Importantly, these structures resemble the loop moiety adopted by an 11-nucleotide fragment of the conserved centromeric protein B (CENP-B) box motif, which is the binding site for the CENP-B.

Minimal requirements for parameters to be used for the development of predictive models for microbial source tracking. The example of the pair somatic coliphages and phages infecting Bacteroides

Several methods and approaches for measuring parameters to determine fecal sources of pollution in water have been developed in recent years. No single microbial or chemical parameter has proved sufficient to determine the source of fecal pollution. Combinations of parameters involving at least one discriminating indicator and one universal fecal indicator offer the most promising solutions for qualitative and quantitative analyses. The universal (nondiscriminating) fecal indicator provides quantitative information regarding the fecal load. The discriminating indicator contributes to the identification of a specific source. The relative values of the parameters derived from both kinds of indicators could provide information regarding the contribution to the total fecal load from each origin. It is also essential that both parameters characteristically persist in the environment for similar periods. Numerical analysis, such as inductive learning methods, could be used to select the most suitable and the lowest number of parameters to develop predictive models. These combinations of parameters provide information on factors affecting the models, such as dilution, specific types of animal source, persistence of microbial tracers, and complex mixtures from different sources. The combined use of the enumeration of somatic coliphages and the enumeration of Bacteroides-phages using different host specific strains (one from humans and another from pigs), both selected using the suggested approach, provides a feasible model for quantitative and qualitative analyses of fecal source identification.

Minimal requirements for parameters to be used for the development of predictive models for microbial source tracking. The example of the pair somatic coliphages and phages infecting Bacteroides

Several methods and approaches for measuring parameters to determine fecal sources of pollution in water have been developed in recent years. No single microbial or chemical parameter has proved sufficient to determine the source of fecal pollution. Combinations of parameters involving at least one discriminating indicator and one universal fecal indicator offer the most promising solutions for qualitative and quantitative analyses. The universal (nondiscriminating) fecal indicator provides quantitative information regarding the fecal load. The discriminating indicator contributes to the identification of a specific source. The relative values of the parameters derived from both kinds of indicators could provide information regarding the contribution to the total fecal load from each origin. It is also essential that both parameters characteristically persist in the environment for similar periods. Numerical analysis, such as inductive learning methods, could be used to select the most suitable and the lowest number of parameters to develop predictive models. These combinations of parameters provide information on factors affecting the models, such as dilution, specific types of animal source, persistence of microbial tracers, and complex mixtures from different sources. The combined use of the enumeration of somatic coliphages and the enumeration of Bacteroides-phages using different host specific strains (one from humans and another from pigs), both selected using the suggested approach, provides a feasible model for quantitative and qualitative analyses of fecal source identification.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

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.