Cohomology of classes of symbols and classi cation of traces on corresponding classes of operators with non positive order

This thesis is devoted to the classification issue of traces on classical pseudo-differential operators with fixed non positive order on closed manifolds of dimension $n>1$. We describe the space of homogeneous functions on a symplectic cone in terms of Poisson brackets of appropriate homogeneous functions, and we use it to find a representation of a pseudo-differential operator as a sum of commutators. We compute the cohomology groups of certain spaces of classical symbols on the $n$--dimensional Euclidean space with constant coefficients, and we show that any closed linear form on the space of symbols of fixed order can be written either in terms of a leading symbol linear form and the noncommutative residue, or in terms of a leading symbol linear form and the cut-off regularized integral. On the operator level, we infer that any trace on the algebra of classical pseudo-differential operators of order $a\in\Z$ can be written either as a linear combination of a generalized leading symbol trace and the residual trace when $-n+1\leq2a\leq0$, or as a linear combination of a generalized leading symbol trace and any linear map that extends the $L^2$--trace when $2a\leq-n\leq a$. In contrast, for odd class pseudo-differential operators in odd dimensions, any trace can be written as a linear combination of a generalized leading symbol trace and the canonical trace. We derive from these results the classification of determinants on the Fr\'echet Lie group associated to the algebras of classical pseudo-differential operators with non positive integer order

Constructive approximations to the q=1/2 maximum entropy distribution from redundant and noisy data

An approach adopted to consider the problem of constructing the q=1/2 maximum entropy distribution from redundant and noisy data was discussed. The advantage of this generalized approach, when dealing with very noisy data was illustrated by a numerical simulation. A strategy was proposed that evolved through different steps such as independent constraints were first preselected by recourse to a data independent technique. A backward approach was also proposed for reducing the parameters of such distributions. It was found that the sub-optimal strategies could be utilized in a broad range of situations

Multi-person Spatial Interaction in a Large Immersive Display Using Smartphones as Touchpads

In this paper, we present a multi-user interaction interface for a large immersive space that supports simultaneous screen interactions by combining (1) user input via personal smartphones and Bluetooth microphones, (2) spatial tracking via an overhead array of Kinect sensors, and (3) WebSocket interfaces to a webpage running on the large screen. Users are automatically, dynamically assigned personal and shared screen sub-spaces based on their tracked location with respect to the screen, and use a webpage on their personal smartphone for touchpad-type input. We report user experiments using our interaction framework that involve image selection and placement tasks, with the ultimate goal of realizing display-wall environments as viable, interactive workspaces with natural multimodal interfaces.Comment: 8 pages with reference

Control of the chemical composition and thickness of deposited coatings over carbon nanotubes using acrylic acid plasma

In this study, it is demonstrated that the surface of carbonnanotubes can be coated with a polymer nanometer size film (nanocoating) with tailored surface polar behavior when treated with acrylic acid plasma. The polar behavior of the polymer nanocoating can be hydrophilic or hydrophobic depending deposition and erosion processes caused by ionized species in the plasma. In turn, deposition and erosion can be controlled by plasma power. Deposition dominates at 20 W power, where a significant amount of polymer nanocoating is produced with carboxylic acid functional groups in the surface thus having an hydrophilic behavior. On the contrary, a smaller amount of polymer nanocoating with hydrophobic behavior (i.e. without any functional groups on its surface) suggests that erosion isthe dominant process when 40 W power is used. Finally, a competition between deposition and erosion processes results in different polar behavior and amount of polymer nanocoating depending of the treatment time

Residual contamination detection and serovar distribution of Listeria monocytogenes isolates in pork slaughterhouse and cutting facilities in province of Quebec

L. monocytogenes (L. mono) is recognised as a zoonotic foodborne pathogen. Its control is focused on the “Readyto Eat” food production level. Recently, Health Canada had reinforced its “Policy on L. mono in Ready-to-Eat Foods”, highlighting environmental surveillance and control of meat processing facilities as important risk reduction tools. The industry wants to improve its management of L. mono risk, taking into account previous steps of meat production. Nowadays, few information are available on the presence, distribution and types of strains in the environments concerning this pathogen in pork slaughterhouses and cutting facilities in Canada. Our objective was to detect and described residual L. mono contamination and analyse serovars distribution in different areas in the pork production continuum in and between slaughterhouses and cutting facilities in province of Quebec, during a one year period. Such data are a pre-requisite to achieve the optimization of the management measures by the industrials

Influence of Maturity and Vineyard Location on Free and Bound Aroma Compounds of Grapes from the País Cultivar

Some of the volatile compounds present in grapes give wine is its unique and genuine characteristics.  “Terroir” and berry maturity are considered to be the main influences on the expression of these characteristics. This work was undertaken to establish the specific characteristics that define Vitis vinifera cv. País, based on its aromatic profile and free and bound compounds (glycosides), and to assess the effects of location and maturity. Free and bound volatile compounds presented significant differences in the three locations studied. The total amount of free alcohols, acids and ketones depended on the location. During ripening, the amount of aroma precursors increased in all chemical groups in every location studied, and they were found mainly in the skins. With reference to free volatile compounds, it was found that cis-2-hexenol could be a good candidate to assess maturity, and that terpene content seemed to be strongly related to the vineyard location and cultivar conditions. Also, data analysis showed that the free aroma profile seemed to be influenced more by the maturity of the grapes and the bound aroma fraction more by the location

A dedicated greedy pursuit algorithm for sparse spectral representation of music sound

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal as a linear superposition of as few spectral components as possible, without affecting the quality of the reproduction. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the fast Fourier transform. The achieved sparsity is theoretically equivalent to that rendered by the orthogonal matching pursuit (OMP) method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard OMP algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral representation is illustrated by comparison with the traditional method, in the line of the short time Fourier transform, involving only the corresponding orthonormal trigonometric basis

La reducción del resarcimiento por culpa de la víctima. Reflexiones a la luz del análisis de algunas fuentes romanas

The paper discusses which criteria should be applied to calculate damages in cases of contributory negligence. It analyzes the meaning and scope of the so called comparative negligence doctrine in Roman law and how it was later abandoned after Christian Wolff’s work. The paper shows that, contrary to current teachings, Roman jurists allowed the possibility of dividing the damages between the victim and the tortfeasor. These jurists identified objective criteria which served as a nexus between the behavior of the victim and the portion of¡ risk that it had to assume.Este artículo se inserta en la discusión en torno a los criterios que deberían emplearse para efectuar la reducción del resarcimiento en caso de culpa concurrente de la víctima. Con el fin de contribuir a dicha discusión, el trabajo presenta un análisis sobre el sentido y alcance de la llamada compensación de culpas en derecho romano y su superación por obra de Christian Wolff. El trabajo pone de manifiesto que –al contrario de lo que generalmente se enseña– los juristas romanos contemplaron la posibilidad de repartir el daño entre víctima y agente, para lo cual se ocuparon de identificar criterios objetivos que permitieran una conexión entre la conducta de la víctima y la porción de riesgo que debía soportar

La cláusula ‘ex fide bona’ y su influencia en el ‘quantum respondeatur’ como herramienta para recuperar el equilibrio patrimonial en derecho romano

This article refers the relationship between the ex bona fide clause and the amount of the condemnation in Roman law. Through the analysis of two passages of the Justinian Digest, it reveals that, thanks to the elasticity of the clause ex fide bona, Roman jurists used quantum respondeatur as a mechanism to restore the equity balance, excluding some amounts that, at first, would have been included into the Summa condemnationis. Thus in Rome the good faith was not only a mechanism of integration of the contract through the extensión of their obligations, but also a mechanism for attenuation of these obligations, when its demand in literal terms was contrary to the equity balance in good faith’s contracts.Este artículo se refiere a la relación existente entre la cláusula ex fide bona y la cuantía de la condena en derecho romano. Mediante la exégesis de dos pasajes del Digesto se pone en evidencia que, gracias a la elasticidad de la cláusula ex fide bona, los juristas romanos utilizaron el quantum respondeatur como un mecanismo para restablecer el equilibrio patrimonial, excluyendo de la summa condemnationis cantidades que en principio habrían debido incluirse. En consecuencia, en Roma la buena fe no era solo un mecanismo de integración del contrato mediante la ampliación de las obligaciones contraídas por las partes, sino también un mecanismo de atenuación de dichas obligaciones, cuando su exigencia en términos literales resultaba contraria al equilibrio propio de los contratos de buena fe