Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Processus de reconnaissance et d'identification de personnes décédées

Recognition and identification processes for deceased persons. Determining the identity of deceased persons is a routine task performed essentially by police departments and forensic experts. This thesis highlights the processes necessary for the proper and transparent determination of the civil identities of deceased persons. The identity of a person is defined as the establishment of a link between that person ("the source") and information pertaining to the same individual ("identifiers"). Various identity forms could emerge, depending on the nature of the identifiers. There are two distinct types of identity, namely civil identity and biological identity. The paper examines four processes: identification by witnesses (the recognition process) and comparisons of fingerprints, dental data and DNA profiles (the identification processes). During the recognition process, the memory function is examined and helps to clarify circumstances that may give rise to errors. To make the process more rigorous, a body presentation procedure is proposed to investigators. Before examining the other processes, three general concepts specific to forensic science are considered with regard to the identification of a deceased person, namely, matter divisibility (Inman and Rudin), transfer (Locard) and uniqueness (Kirk). These concepts can be applied to the task at hand, although some require a slightly broader scope of application. A cross comparison of common forensic fields and the identification of deceased persons reveals certain differences, including 1 - reverse positioning of the source (i.e. the source is not sought from traces, but rather the identifiers are obtained from the source); 2 - the need for civil identity determination in addition to the individualisation stage; and 3 - a more restricted population (closed set), rather than an open one. For fingerprints, dental and DNA data, intravariability and intervariability are examined, as well as changes in these post mortem (PM) identifiers. Ante-mortem identifiers (AM) are located and AM-PM comparisons made. For DNA, it has been shown that direct identifiers (taken from a person whose civil identity has been alleged) tend to lead to determining civil identity whereas indirect identifiers (obtained from a close relative) direct towards a determination of biological identity. For each process, a Bayesian model is presented which includes sources of uncertainty deemed to be relevant. The results of the different processes combine to structure and summarise an overall outcome and a methodology. The modelling of dental data presents a specific difficulty with respect to intravariability, which in itself is not quantifiable. The concept of "validity" is, therefore, suggested as a possible solution to the problem. Validity uses various parameters that have an acknowledged impact on teeth intravariability. In cases where identifying deceased persons proves to be extremely difficult due to the limited discrimination of certain procedures, the use of a Bayesian approach is of great value in bringing a transparent and synthetic value. RESUME : Titre: Processus de reconnaissance et d'identification de personnes décédées. L'individualisation de personnes décédées est une tâche courante partagée principalement par des services de police, des odontologues et des laboratoires de génétique. L'objectif de cette recherche est de présenter des processus pour déterminer valablement, avec une incertitude maîtrisée, les identités civiles de personnes décédées. La notion d'identité est examinée en premier lieu. L'identité d'une personne est définie comme l'établissement d'un lien entre cette personne et des informations la concernant. Les informations en question sont désignées par le terme d'identifiants. Deux formes distinctes d'identité sont retenues: l'identité civile et l'identité biologique. Quatre processus principaux sont examinés: celui du témoignage et ceux impliquant les comparaisons d'empreintes digitales, de données dentaires et de profils d'ADN. Concernant le processus de reconnaissance, le mode de fonctionnement de la mémoire est examiné, démarche qui permet de désigner les paramètres pouvant conduire à des erreurs. Dans le but d'apporter un cadre rigoureux à ce processus, une procédure de présentation d'un corps est proposée à l'intention des enquêteurs. Avant d'entreprendre l'examen des autres processus, les concepts généraux propres aux domaines forensiques sont examinés sous l'angle particulier de l'identification de personnes décédées: la divisibilité de la matière (Inman et Rudin), le transfert (Locard) et l'unicité (Kirk). Il est constaté que ces concepts peuvent être appliqués, certains nécessitant toutefois un léger élargissement de leurs principes. Une comparaison croisée entre les domaines forensiques habituels et l'identification de personnes décédées montre des différences telles qu'un positionnement inversé de la source (la source n'est plus à rechercher en partant de traces, mais ce sont des identifiants qui sont recherchés en partant de la source), la nécessité de devoir déterminer une identité civile en plus de procéder à une individualisation ou encore une population d'intérêt limitée plutôt qu'ouverte. Pour les empreintes digitales, les dents et l'ADN, l'intra puis l'inter-variabilité sont examinées, de même que leurs modifications post-mortem (PM), la localisation des identifiants ante-mortem (AM) et les comparaisons AM-PM. Pour l'ADN, il est démontré que les identifiants directs (provenant de la personne dont l'identité civile est supposée) tendent à déterminer une identité civile alors que les identifiants indirects (provenant d'un proche parent) tendent à déterminer une identité biologique. Puis une synthèse des résultats provenant des différents processus est réalisée grâce à des modélisations bayesiennes. Pour chaque processus, une modélisation est présentée, modélisation intégrant les paramètres reconnus comme pertinents. À ce stade, une difficulté apparaît: celle de quantifier l'intra-variabilité dentaire pour laquelle il n'existe pas de règle précise. La solution préconisée est celle d'intégrer un concept de validité qui intègre divers paramètres ayant un impact connu sur l'intra-variabilité. La possibilité de formuler une valeur de synthèse par l'approche bayesienne s'avère d'une aide précieuse dans des cas très difficiles pour lesquels chacun des processus est limité en termes de potentiel discriminant.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Las secuencias didácticas de lengua: una encrucijada entre teoría y metodología

[ES] El objetivo de este trabajo es analizar secuencias didácticas(SD) para enseñar lengua/s diseñadas por profesores de educación primaria y proponer algunos indicadores que guíen a los enseñantes en la confección y validación (o autoevaluación) de las mismas. Entendemos la secuencia didáctica en el sentido de sus creadores ginebrinos, es decir, como una herramienta para la enseñanza del género textual como unidad comunicativa. El diseño de las secuencias estudiadas en este artículo se realiza a lo largo de unas sesiones de formación de profesorado; a la vista de los obstáculos que se observan en su elaboración (dificultades para explicitar la consigna, noción difusa del género textual, etc.), decidimos analizarlas a partir de unos ítems o criterios extraídos básicamente de los principios que rigen las secuencias didácticas. Pensamos que las principales dificultades derivarán de las concepciones teóricas y metodológicas previas que tienen los profesores y de una concepción disociada de la SD y del género textual. Los resultados ponen de relieve cuáles son algunos de los aspectos que merecen especial atención a la hora de diseñar secuencias didácticas y sugieren el interés de contar con unos indicadores que guíen al docente en la confección de las mismas. Eso no significa, sin embargo, que deba tratarse de una lista cerrada y, evidentemente, futuros trabajos habrán de modificarla y completarla. Hasta el momento, estos criterios nos permiten confirmar la importancia de insistir en las bases teóricas y metodológicas de las secuencias didácticas en el marco de las sesiones formativas.

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

Stability of nonlinear system using takagi-sugeno fuzzy models and hyper-rectangle of LMIs

This paper presents a theorem based on the hyper-rectangle defined by the closed set of the time derivatives of the membership functions of Takagi-Sugeno fuzzy systems. This result is also based on Linear Matrix Inequalities and allows the reduction of the conservatism of the stability analysis in the sense of Lyapunov. The theorem generalizes previous results available in the literature. © 2013 Brazilian Society for Automatics - SBA.

Novas condições de estabilidade de sistemas não lineares utilizando funções de Lyapunov fuzzy

Pós-graduação em Engenharia Elétrica - FEIS

More maximal arcs in Desarguesian projective planes and their geometric structure

In a previous paper R. Mathon gave a new construction method for maximal arcs in finite Desarguesian projective planes via closed sets of conics, as well as giving many new examples of maximal arcs. In the current paper, new classes of maximal arcs are constructed, and it is shown that every maximal arc so constructed gives rise to an infinite class of maximal arcs. Apart from when they are of Denniston type or dual hyperovals, closed sets of conics are shown to give maximal arcs that are not isomorphic to the known constructions. An easy characterisation of when a closed set of conics is of Denniston type is given. Results on the geometric structure of the maximal arcs and their duals are proved, as well as on elements of their collineation stabilisers.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

On-line learning of unrealizable tasks

The dynamics of on-line learning is investigated for structurally unrealizable tasks in the context of two-layer neural networks with an arbitrary number of hidden neurons. Within a statistical mechanics framework, a closed set of differential equations describing the learning dynamics can be derived, for the general case of unrealizable isotropic tasks. In the asymptotic regime one can solve the dynamics analytically in the limit of large number of hidden neurons, providing an analytical expression for the residual generalization error, the optimal and critical asymptotic training parameters, and the corresponding prefactor of the generalization error decay.

Noise, regularizers, and unrealizable scenarios in online learning from restricted training sets

We study the dynamics of on-line learning in multilayer neural networks where training examples are sampled with repetition and where the number of examples scales with the number of network weights. The analysis is carried out using the dynamical replica method aimed at obtaining a closed set of coupled equations for a set of macroscopic variables from which both training and generalization errors can be calculated. We focus on scenarios whereby training examples are corrupted by additive Gaussian output noise and regularizers are introduced to improve the network performance. The dependence of the dynamics on the noise level, with and without regularizers, is examined, as well as that of the asymptotic values obtained for both training and generalization errors. We also demonstrate the ability of the method to approximate the learning dynamics in structurally unrealizable scenarios. The theoretical results show good agreement with those obtained by computer simulations.

The theory of on-line learning: a statistical physics approach

In this paper we review recent theoretical approaches for analysing the dynamics of on-line learning in multilayer neural networks using methods adopted from statistical physics. The analysis is based on monitoring a set of macroscopic variables from which the generalisation error can be calculated. A closed set of dynamical equations for the macroscopic variables is derived analytically and solved numerically. The theoretical framework is then employed for defining optimal learning parameters and for analysing the incorporation of second order information into the learning process using natural gradient descent and matrix-momentum based methods. We will also briefly explain an extension of the original framework for analysing the case where training examples are sampled with repetition.

Young toddlers' word comprehension is flexible and efficient.

Much of what is known about word recognition in toddlers comes from eyetracking studies. Here we show that the speed and facility with which children recognize words, as revealed in such studies, cannot be attributed to a task-specific, closed-set strategy; rather, children's gaze to referents of spoken nouns reflects successful search of the lexicon. Toddlers' spoken word comprehension was examined in the context of pictures that had two possible names (such as a cup of juice which could be called "cup" or "juice") and pictures that had only one likely name for toddlers (such as "apple"), using a visual world eye-tracking task and a picture-labeling task (n = 77, mean age, 21 months). Toddlers were just as fast and accurate in fixating named pictures with two likely names as pictures with one. If toddlers do name pictures to themselves, the name provides no apparent benefit in word recognition, because there is no cost to understanding an alternative lexical construal of the picture. In toddlers, as in adults, spoken words rapidly evoke their referents.

Closed-loop model re-identification of processes under MPC with zone control

This work deals with a procedure for model re-identification of a process in closed loop with ail already existing commercial MPC. The controller considered here has a two-layer structure where the upper layer performs a target calculation based on a simplified steady-state optimization of the process. Here, it is proposed a methodology where a test signal is introduced in a tuning parameter of the target calculation layer. When the outputs are controlled by zones instead of at fixed set points, the approach allows the continuous operation of the process without an excessive disruption of the operating objectives as process constraints and product specifications remain satisfied during the identification test. The application of the method is illustrated through the simulation of two processes of the oil refining industry. (c) 2008 Elsevier Ltd. All rights reserved.