Integral inequalities for algebraic and trigonometric polynomials

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Tecla d'Iconi, més enllà de la llegenda : estudi del paper desenvolupat per la dona en el cristianisme primitiu a través de la protagonista dels Actes de Pau i Tecla

El cristianisme, en els seus inicis, significà per la dona la possibilitat de triar un destí diferent al del matrimoni i la maternitat que li deparava la societat greco-romana. Tanmateix, en el procés d'institucionalització de la nova religió (s. I-IV), la dona, que en les primitives comunitats cristianes havia ocupat llocs de responsabilitats al costat dels seus companys masculins, va quedar relegada al desenvolupament de tasques assistencials. Els canvis experimentats pel rol femení durant aquest període es manifestaran en les transformacions operades a través de la literatura en la figura de Tecla d'Iconi (santa Tecla), un personatge intemporal, tan capaç de representar els diferents arquetips de dona ideal que ha creat l'Església cristiana, com les ànsies emancipadores d'alguns col·lectius feministes.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Neogene antecedents of the modern human hand and its relation to bipedalism

El present projecte s'ha dut a terme a l'American Museum of Natural History (AMNH, New York) entre el 31 de Desembre de 2010 i el 30 de Desembre de 2012. L'objectiu del projecte era elucidar la història evolutiva de la mà humana: traçar els canvis evolutius en la seva forma i proporcions que van propiciar la seva estructura moderna que permet als humans manipular amb precisió. El treball realitzat ha inclòs recol•lecció de dades i anàlisis, redacció de resultats i formació en mètodes analítics específics. Durant aquest temps, l'autor a completat la seva de base de dades existent en mesures lineals de la mà a hominoides. També s'han agafat dades del peu; d'aquesta forma ara mateix es compta amb una base de dades amb més de 500 individus, amb més de 200 mesures per cada un. També s'han agafat dades en tres imensions utilitzant un làser escàner. S'han après tècniques de morfometria geomètrica 3D directament dels pioners al camp a l'AMNH. Com a resultat d'aquesta feina s'han produït 10 resums (publicats a congressos internacionals) i 9 manuscrits (molts d'ells ja publicats a revistes internacionals) amb resultats de gran rellevància: La mà humana posseeix unes proporcions relativament primitives, que són més similars a les proporciones que tenien els hominoides fòssils del Miocè que no pas a la dels grans antropomorfs actuals. Els darrers tenen unes mans allargades amb un polzes molt curts que reflexen l'ús de la mà com a eina de suspensió sota les branques. En canvi, els hominoides del Miocè tenien unes mans relativament curtes amb un polze llarg que feien servir per estabilitzar el seu pes quan caminaven per sobre de les branques. Una vegada els primers homínids van aparèixer al final del Miocè (fa uns 6 Ma) i van començar a fer servir el bipedisme com a mitjà més comú de locomoció, les seves mans van ser "alliberades" de les seves funcions locomotores. La selecció natural—ara només treballant en la manipulació—va convertir les proporcions ja existents de la mà d'aquests primats en l'òrgan manipulatori que representa la mà humana avui dia.

Economic rationality and ethical behavior

This paper argues that economic rationality and ethical behavior cannotbe reduced one to the other, casting doubts on the validity of formulaslike 'profit is ethical' or 'ethics pays'. In order to express ethicaldilemmas as opposing economic interest with ethical concerns, we proposea model of rational behavior that combines these two irreducible dimensions in an open but not arbitrary manner. Behaviors that are neither ethicalnor profitable are considered irrational (non-arbitrariness). However,behaviors that are profitable but unethical, and behaviors that are ethicalbut not profitable, are all treated as rational (openness). Combiningethical concerns with economic interest, ethical business is in turn anoptimal form of rationality between venality and sacrifice.Because every one prefers to communicate that he acts ethically, ethicalbusiness remains ambiguous until some economic interest is actuallysacrificed. We argue however that ethical business has an interest indemonstrating its consistency between communication and behavior by atransparent attitude. On the other hand, venal behaviors must remainconfidential to hide the corresponding lack of consistency. Thisdiscursive approach based on transparency and confidentiality helpsto further distinguish between ethical and unethical business behaviors.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Chemical defenses in Sacoglossan Opisthobranchs: Taxonomic trends and evolutionary implications

Sacoglossan sea slugs (Mollusca: Opisthobranchia) are one of the few groups of specialist herbivores in the marine environment. Sacoglossans feed suctorially on the cell sap of macroalgae, from which they 'steal' chloroplasts (kleptoplasty) and deterrent substances (kleptochemistry), retaining intracellularly both host plastids and chemicals. The ingested chloroplasts continue to photosynthesize for periods ranging from a few hours or days up to 3 months in some species. Shelled, more primitive sacoglossans feed only on the siphonalean green algal genus Caulerpa, and they do not have functional kleptoplasty. The diet of sacoglossans has radiated out from this ancestral food. Among the shell-less Plakobranchidae (=Elysiidae), the more primitive species feed on other siphonales (families Derbesiaceae, Caulerpaceae, Bryopsidaceae and Codiaceae) and fix carbon, while the more 'advanced' species within the Plakobranchidae and Limapontioidae have a more broad dietary range. Most of these 'advanced' species are unable to fix carbon because the chloroplasts of their food algae are mechanically disrupted during ingestion. Mesoherbivores are likely to be eaten if they live on palatable seaweeds, their cryptic coloration and form not always keeping them safe from predators. Sacoglossans prefer to live on and eat chemically defended seaweeds, and they use ingested algal chemicals as deterrents of potential predators. The most ancestral shelled sacoglossans (Oxynoidae) and some Plakobranchidae such as Elysia translucens, Thuridilla hopei and Bosellia mimetica have developed a diet-derived chemical defense mechanism. Oxynoids and Thuridilla hopei are able to biomodify the algal metabolites. However, the Plakobranchidae Elysia timida and E. viridis, together with Limapontioidea species, are characterized by their ability to de novo synthesize polypropionate metabolites. A whole analysis of kleptoplasty and chemical defenses in sacoglossans may offer a better understanding of the ecology and evolution of these specialized opisthobranchs. In this paper we summarize some of the latest findings, related mainly to Mediterranean species, and offer a plausible evolutionary scenario based on the biological and chemical trends we can distinguish in them.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.