Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

Production externalities : cooperative and non-cooperative approaches

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Exposants géométriques des modèles de boucles dilués et idempotents des TL-modules de la chaîne de spins XXZ

Cette thèse porte sur les phénomènes critiques survenant dans les modèles bidimensionnels sur réseau. Les résultats sont l'objet de deux articles : le premier porte sur la mesure d'exposants critiques décrivant des objets géométriques du réseau et, le second, sur la construction d'idempotents projetant sur des modules indécomposables de l'algèbre de Temperley-Lieb pour la chaîne de spins XXZ. Le premier article présente des expériences numériques Monte Carlo effectuées pour une famille de modèles de boucles en phase diluée. Baptisés "dilute loop models (DLM)", ceux-ci sont inspirés du modèle O(n) introduit par Nienhuis (1990). La famille est étiquetée par les entiers relativement premiers p et p' ainsi que par un paramètre d'anisotropie. Dans la limite thermodynamique, il est pressenti que le modèle DLM(p,p') soit décrit par une théorie logarithmique des champs conformes de charge centrale c(\kappa)=13-6(\kappa+1/\kappa), où \kappa=p/p' est lié à la fugacité du gaz de boucles \beta=-2\cos\pi/\kappa, pour toute valeur du paramètre d'anisotropie. Les mesures portent sur les exposants critiques représentant la loi d'échelle des objets géométriques suivants : l'interface, le périmètre externe et les liens rouges. L'algorithme Metropolis-Hastings employé, pour lequel nous avons introduit de nombreuses améliorations spécifiques aux modèles dilués, est détaillé. Un traitement statistique rigoureux des données permet des extrapolations coïncidant avec les prédictions théoriques à trois ou quatre chiffres significatifs, malgré des courbes d'extrapolation aux pentes abruptes. Le deuxième article porte sur la décomposition de l'espace de Hilbert \otimes^nC^2 sur lequel la chaîne XXZ de n spins 1/2 agit. La version étudiée ici (Pasquier et Saleur (1990)) est décrite par un hamiltonien H_{XXZ}(q) dépendant d'un paramètre q\in C^\times et s'exprimant comme une somme d'éléments de l'algèbre de Temperley-Lieb TL_n(q). Comme pour les modèles dilués, le spectre de la limite continue de H_{XXZ}(q) semble relié aux théories des champs conformes, le paramètre q déterminant la charge centrale. Les idempotents primitifs de End_{TL_n}\otimes^nC^2 sont obtenus, pour tout q, en termes d'éléments de l'algèbre quantique U_qsl_2 (ou d'une extension) par la dualité de Schur-Weyl quantique. Ces idempotents permettent de construire explicitement les TL_n-modules indécomposables de \otimes^nC^2. Ceux-ci sont tous irréductibles, sauf si q est une racine de l'unité. Cette exception est traitée séparément du cas où q est générique. Les problèmes résolus par ces articles nécessitent une grande variété de résultats et d'outils. Pour cette raison, la thèse comporte plusieurs chapitres préparatoires. Sa structure est la suivante. Le premier chapitre introduit certains concepts communs aux deux articles, notamment une description des phénomènes critiques et de la théorie des champs conformes. Le deuxième chapitre aborde brièvement la question des champs logarithmiques, l'évolution de Schramm-Loewner ainsi que l'algorithme de Metropolis-Hastings. Ces sujets sont nécessaires à la lecture de l'article "Geometric Exponents of Dilute Loop Models" au chapitre 3. Le quatrième chapitre présente les outils algébriques utilisés dans le deuxième article, "The idempotents of the TL_n-module \otimes^nC^2 in terms of elements of U_qsl_2", constituant le chapitre 5. La thèse conclut par un résumé des résultats importants et la proposition d'avenues de recherche qui en découlent.

An approximation to the standard of living index: the Colombian case

El documento busca mostrar las principales propiedades de un indicador de estándar de vida dentro del enfoque teórico de Amartya Sen. Establecemos un puente entre conceptos tales como: bienestar económico, bienestar, logro de agencia y estándar de vida. La metodología del Optimal scaling fue usada para probar las propiedades de Monotonicidad, No independencia de alternativas irrelevantes, Concavidad, informatividad y sustituibilidad.

A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

How is the balance of a forecast ensemble affected by adaptive and non-adaptive localization schemes?

This paper investigates the effect on balance of a number of Schur product-type localization schemes which have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a non-adaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes, namely a simplified version of SENCORP (Smoothed ENsemble COrrelations Raised to a Power) and ECO-RAP (Ensemble COrrelations Raised to A Power). The paper shows, we believe for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately but also minimizes disruption of balance (where the 'correct' degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g. the degree of truncation in the schemes that use the spectral basis, the 'order' of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to our diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.

The identity of Mygale brunnipes CL Koch 1842 (Araneae, Theraphosidae), with a redescription of the species and the description of a new genus

We describe Kochiana new genus to accommodate a small Brazilian theraphosine species described originally as Mygale brunnipes by Koch (1842), resulting in Kochiana brunnipes new combination. Recently, specimens were rediscovered in northeastern Brazilian Atlantic rainforest. A preliminary cladistic analysis using equal weights parsimony and implied weights, was carried out to examine its phylogenetic placement. Kochiana new genus was monophyletic in all trees regardless of weighting scheme or concavity used. There is preliminary evidence for Kochiana new genus monophyly and weak evidence for its placement as sister group of Plesiopelma. Kochiana new genus can be characterized by the presence of a hornshaped spermatheca in females and males with a palpal bulb having prolateral accessory keels and a well developed medial crest on the embolus apex.

Revalidation of Pterinopelma Pocock 1901 with description of a new species and the female of Pterinopelma vitiosum (Keyserling 1891) (Araneae: Theraphosidae: Theraphosinae)

We revalidate the theraphosid genus Pterinopelma Pocock 1901, describe the female of P. vitiosum for first time and Pterinopelma sazimai sp. nov. from Brazil. These two species were included in a matrix with 35 characters and 32 taxa and were analyzed both with all characters having same weight and with implied weights. Searches considering all characters non-additive or some additive were also carried out. The preferred tree, obtained with implied weights, concavity 6 and all characters non-additive shows that Pterinopelma is a monophyletic genus sister to the clade Lasiodora (Vitalius + Nhandu). The presence of denticles on the prolateral inferior male palpal bulb keel is a synapomorphy of the genus.

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Zipf`s law strikes again : the case of tourism

This paper examines the applicability of Zipf's law to tourism. It is established that a variation of this law holds in this case - a rank-size rule with concavity. Due to this non-linearity, it is shown that a spline regression provides an extremely convenient tool for predicting tourist arrivals in a country. The concavity is explained by appealing to random growth theory (lognormal distribution; Gibrat's law) and locational fundamentals.

Robust strictly positive real synthesis of polynomial segments for discrete time systems

By using the result of robust strictly positive real synthesis of polynomial segments for continuous time systems, it is proved that, for any two n-th order polynomials a(z) and b(z), the Schur stability of their convex combination is necessary and sufficient for the existence of an n-th order polynomial c(z) such that c(z)/a(z) and c(z)/b(z) are both strictly positive real. We also provide the construction method of c(z). Illustrative examples are provided to show the effectiveness of this method.

Photoaffinity labeling of the N-methyltransferase domains of cyclosporin synthetase

The multifunctional polypeptide cyclosporin synthetase (CySyn) remains one of the most complex nonribosomal peptide synthetase described. In this study we used a highly specific photoaffinity labeling procedure with the natural cofactor S-adenosyl-l-methionine (AdoMet), 14C-isotopically labeled at the Sδ methyl group to probe the concerted AdoMet-binding interaction of the N-methyltransferase (N-MTase) centers of CySyn. The binding stoichiometry for the enzyme–AdoMet complex was determined to be 1:7, which is in agreement with inferences made from analysis of the complementary DNA sequence of the simA gene encoding the CySyn polypeptide. The photolabeling of the AdoMet-binding sites displayed homotropic negative cooperativity, characterized by a curvilinear Scatchard plot with upward concavity. Although, the process of N-methyl transfer is not a critical event for peptide elongation, the destabilizing homotropic interactions between N-MTase centers that were observed may represent a mechanism whereby the enzyme preserves the proficiency of the substrate-channeling process of cyclosporin peptide assembly over a broad range of cofactor concentrations. Furthermore, we demonstrated the utility of the photolabeling procedure for tracking the enzyme during purification.

Relative responsiveness of bargaining solutions to changes in status-quo payoffs

It is a well-known fact that several prominent bargaining solutions are responsive to changes in status-quo (i.e., disagreement or fallback) payoffs. When an agent’s status-quo payoff increases, his solution payoff either stays the same or increases. A fully general result for these solutions’ status-quo point ranking is impossible to establish. In this paper, using an important class of bargaining problems, a ranking of the relative status-quo point responsiveness of prominent bargaining solutions is obtained. Using the Constant Elasticity of Substitution class of bargaining problems, regardless of the concavity of the Pareto frontier and the level of increase in one’s status-quo payoff, we find the equal gains solution is the most responsive with respect to changes in status-quo payoffs, followed by the Nash solution. The equal sacrifice solutions is the least responsive, followed by the Kalai/Smorodinsky solution.

Vehicle detection and classification by measuring and processing magnetic signal

This paper presents novel vehicle detection and classification method by measuring and processing magnetic signal based on single micro-electro- mechanical system (MEMS) magnetic sensor. When a vehicle moves over the ground, it generates a succession of impacts on the earth's magnetic field, which can be detected by single magnetic sensor. The magnetic signal measured by the magnetic sensor is related to the moving direction and the type of the vehicle. Generally, the recognition rate using single sensor detector is not high. In order to improve the recognition rate, a novel feature extraction algorithm and a novel vehicle classification and recognition algorithm are presented. The concavity and convexity areas, and the angles of concave and convex parts of the waveform are extracted. An improved support vector machine (ISVM) classifier is developed to perform vehicle classification and recognition. The effectiveness of the proposed approach is verified by outdoor experiments.