Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations

This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable, respectively. The well-known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here. The class of nonlocal nonlinear wave equations also covers a variety of well-known wave equations such as various forms of the Boussinesq equation. Local existence of solutions of the Cauchy problem with initial data in suitable Sobolev spaces is proven and the conditions for global existence and finite-time blow-up of solutions are established.Comment: 17 page

Caracterización socioeconómica de las personas con privaciones habitacionales : un abordaje de los usuarios de la red de refugios de Montevideo

The aim of this research is to assess the homeless’ characteristics in Montevideo, pointing out in their capacity to link with the community. Given the capabilities and functioning framework developed by Amartya Sen, we analyze the multidimensionality poverty and the social exclusion. Even if these individuals share the fact that they have slept at least one night during the winter in a homeless’ shelter, there are many differences in their functionings. We carried out a survey in a representative day in the winter of 2005, with socio economic questions, and also we implement a Rorschach’s test. The main results are: even if their income is below to the poverty line, they do not present high levels of extreme poverty respect to their income. They have extremely weak primary affective links and many difficulties to have a job. Finally, there are differences between males and females respect to their labor market performance and their homelessness’ path.socioeconomic characteristics, homeless, Capability approach, Rorschach’s test.

Random orthogonal additive filters: a solution to the vanishing/exploding gradient of deep neural networks

Since the recognition in the early nineties of the vanishing/exploding (V/E) gradient issue plaguing the training of neural networks (NNs), significant efforts have been exerted to overcome this obstacle. However, a clear solution to the V/E issue remained elusive so far. In this manuscript a new architecture of NN is proposed, designed to mathematically prevent the V/E issue to occur. The pursuit of approximate dynamical isometry, i.e. parameter configurations where the singular values of the input-output Jacobian are tightly distributed around 1, leads to the derivation of a NN's architecture that shares common traits with the popular Residual Network model. Instead of skipping connections between layers, the idea is to filter the previous activations orthogonally and add them to the nonlinear activations of the next layer, realising a convex combination between them. Remarkably, the impossibility for the gradient updates to either vanish or explode is demonstrated with analytical bounds that hold even in the infinite depth case. The effectiveness of this method is empirically proved by means of training via backpropagation an extremely deep multilayer perceptron of 50k layers, and an Elman NN to learn long-term dependencies in the input of 10k time steps in the past. Compared with other architectures specifically devised to deal with the V/E problem, e.g. LSTMs for recurrent NNs, the proposed model is way simpler yet more effective. Surprisingly, a single layer vanilla RNN can be enhanced to reach state of the art performance, while converging super fast; for instance on the psMNIST task, it is possible to get test accuracy of over 94% in the first epoch, and over 98% after just 10 epochs

Interpreting multi-stable behaviour in input-driven recurrent neural networks

Recurrent neural networks (RNNs) are computational models inspired by the brain. Although RNNs stand out as state-of-the-art machine learning models to solve challenging tasks as speech recognition, handwriting recognition, language translation, and others, they are plagued by the so-called vanishing/exploding gradient issue. This prevents us from training RNNs with the aim of learning long term dependencies in sequential data. Moreover, a problem of interpretability affects these models, known as the ``black-box issue'' of RNNs. We attempt to open the black box by developing a mechanistic interpretation of errors occurring during the computation. We do this from a dynamical system theory perspective, specifically building on the notion of Excitable Network Attractors. Our methodology is effective at least for those tasks where a number of attractors and a switching pattern between them must be learned. RNNs can be seen as massively large nonlinear dynamical systems driven by external inputs. When it comes to analytically investigate RNNs, often in the literature the input-driven property is neglected or dropped in favour of tight constraints on the input driving the dynamics, which do not match the reality of RNN applications. Trying to bridge this gap, we framed RNNs dynamics driven by generic input sequences in the context of nonautonomous dynamical system theory. This brought us to enquire deeply into a fundamental principle established for RNNs known as the echo state property (ESP). In particular, we argue that input-driven RNNs can be reliable computational models even without satisfying the classical ESP formulation. We prove a sort of input-driven fixed point theorem and exploit it to (i) demonstrate the existence and uniqueness of a global attracting solution for strongly (in amplitude) input-driven RNNs, (ii) deduce the existence of multiple responses for certain input signals which can be reliably exploited for computational purposes, and (iii) study the stability of attracting solutions w.r.t. input sequences. Finally, we highlight the active role of the input in determining qualitative changes in the RNN dynamics, e.g. the number of stable responses, in contrast to commonly known qualitative changes due to variations of model parameters

"Queimaduras em regiões articulares: condutas na prevenção de sequelas".

Trabalho de Conclusão de Curso - Universidade Federal de Santa Catarina, Centro de Ciências da Saúde, Departamento de Pediatria, Curso de Medicina, Florianópolis, 197

Policy implications of suboptimal choice: theory and evidence: misperceptions about tax audits

For some entities, such as self-employed individuals reporting income taxes or firms reporting value-added taxes, the optimal evasion rate depends substantially on audit features like audit probabilities and penalty rates (Allingham and Sandmo 1972). Whereas it is easy for firms to find other important information such as inflation rates or exchange rates, it is difficult to find information about the probability of being audited and penalty rates. Indeed, Bérgolo et al. (2017) show evidence that firms have large misperceptions about these audit features.1 In this paper, we expand their analysis to explore the sources of these misperceptions.Fil: Bérgolo, Marcelo. Universidad de la República; UruguayFil: Ceni, Rodrigo. Universidad de la República; UruguayFil: Cruces, Guillermo Antonio. Universidad Nacional de La Plata. Facultad de Ciencias Económicas. Departamento de Ciencias Económicas. Centro de Estudios Distributivos Laborales y Sociales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Giaccobasso, Matias. University of California at Los Angeles; Estados UnidosFil: Perez Truglia, Ricardo. University of California at Los Angeles; Estados Unido

Transitions in echo index and dependence on input repetitions

The echo index counts the number of simultaneously stable asymptotic responses of a nonautonomous (i.e. input-driven) dynamical system. It generalizes the well-known echo state property for recurrent neural networks - this corresponds to the echo index being equal to one. In this paper, we investigate how the echo index depends on parameters that govern typical responses to a finite-state ergodic external input that forces the dynamics. We consider the echo index for a nonautonomous system that switches between a finite set of maps, where we assume that each map possesses a finite set of hyperbolic equilibrium attractors. We find the minimum and maximum repetitions of each map are crucial for the resulting echo index. Casting our theoretical findings in the RNN computing framework, we obtain that for small amplitude forcing the echo index corresponds to the number of attractors for the input-free system, while for large amplitude forcing, the echo index reduces to one. The intermediate regime is the most interesting; in this region the echo index depends not just on the amplitude of forcing but also on more subtle properties of the input

Flying together towards EFL teacher development as language learners and professionals through genre writing

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Comunicação e Expressão, Programa de Pós-Graduação em Letras/Inglês e Literatura Correspondente, Florianópolis, 2009This qualitative study on the inter-relation between English as a Foreign Language Teacher Education (EFLTE) and the teaching of writing follows, mainly, the theoretical-methodological approach of Socio-discursive Interactionism (Bronckart, 2003, 2006, 2008a and his followers). Its general objective is to investigate in what aspects and to what extent an interventionist practice concerning the teaching of writing can contribute to EFL teachers development as language learners and professionals. Specifically, the aims of this study are: a) to identify which elements related to the language capacities of action, discursive and linguistic-discursive can be taught for the writing of an academic summary (AS); b) to investigate in what aspects and to what extent the process of writing an AS by means of a didactic sequence (DS) can contribute to teachers development; c) to investigate in what aspects and to what extent the process of planning a DS to the teaching of writing of specific genres can contribute to the teachers' development; and d) to investigate which individual representations were constructed during the processes of writing an AS and planning DS for the teaching of writing specific genres. Four main sets of data are analyzed: a corpus of ten ASs produced by the participant-teachers of an EFLTE course, participant-teachers DS plans, and participant-teachers direct self-confrontation texts. The results of the analysis of each set of data reveals that: 1) the elements related to the three language capacities to be studied for writing an AS should be: the thematic content and context of production of the academic article, descriptive type of sequence and theoretical type of discourse, affirmative sentences, present simple tense and present passive, nominal group, nominal and pronominal anaphora, logic modalization, connectors and reporting verbs; 2) the participants substantially developed as language learners, since they made considerable progress in the three language capacities from the first to the last AS versions; 3) the participants knowledge development related to the three language capacities in the task of planning DSs was partially adequate. Crossing the results from the second and third sets of data with the teaching knowledge base dimensions (Richards, 1998), named Theories of Teaching, Teaching Skills, Communication Skills, Pedagogical Knowledge Skills and Decision Making and Contextual Knowledge reveals that the participants developed in the six dimensions; 4) the participants also developed in the reflective dimensions named Epistemological, Ontological, Pedagogical, Linguistic and Axiological. The overall findings, therefore, reveal that a genre-based perspective for the teaching of writing through the use of the procedure of DS can be seen as an adequate theoretical, methodological and reflexive mechanism for EFLTE.Este estudo qualitativo sobre a inter-relação entre formação de professores de inglês como língua estrangeira e ensino de escrita segue, principalmente, a abordagem teórico-metodológica do Interacionismo Sociodiscursivo (Bronckart, 2003; 2006; 2008a e seus seguidores). Seu objetivo geral é investigar em que aspectos e até que ponto uma prática intervencionista relacionada ao ensino de escrita pode contribuir no desenvolvimento de professores de Inglês como língua estrangeira como aprendizes e profissionais. Especificamente, este estudo objetiva: a) identificar quais elementos relacionados às capacidades de linguagem de ação, discursiva e lingüístico-discursiva podem ser ensinados na escrita de um resumo acadêmico (RA); b) investigar de que forma e até que ponto o processo de escrita de um RA através do procedimento de sequência didática (SD) pode contribuir para o desenvolvimento de professores; c) investigar de que forma e até que ponto o processo de planejamento de uma SD para o ensino de escrita pode contribuir para o desenvolvimento de professores; e d) investigar que representações individuais foram construídas durante o processo de escrita de um RA e planejamento de uma SD para ensino de escrita de gêneros específicos. Quatro conjuntos de dados são analisados: um corpus de dez RAs, resumos acadêmicos produzidos por professores de inglês participantes de um curso de formação continuada, planos de SD dos professores participantes, e textos de auto-confrontação simples dos participantes. Os resultados da análise de cada conjunto de dados mostram que: 1) os elementos, relacionados às três capacidades de linguagem, a serem estudados na escrita de RAs devem ser: o conteúdo temático e o contexto de produção do artigo acadêmico, tipo de sequência descritiva e tipo de discurso teórico, orações afirmativas, presente simples e voz passiva no presente, grupo nominal e anáfora nominal e pronominal, modalização lógica, conectores e verbos de dizer; 2) os participantes se desenvolveram substancialmente como aprendizes da língua inglesa, pois progrediram consideravelmente nas três capacidades de linguagem da primeira à última versão dos RAs; 3) o desenvolvimento dos participantes com relação às três capacidades de linguagem na tarefa de planejamento de SDs foi parcialmente adequado. O cruzamento dos dados do segundo e terceiro conjuntos com as seis dimensões básicas de conhecimento de ensino (Richards, 1998), nomeadamente, Teorias de Ensino, Habilidades de Ensino, Habilidades de Comunicação, Habilidades Pedagógicas e Poder de Decisão e Conhecimento do Contexto revela que os participantes se desenvolveram nas seis dimensões; 4) os participantes também se desenvolveram nas dimensões reflexivas Epistemológica, Ontológica, Pedagógica, Linguística e Axiológica. Os resultados gerais deste estudo revelam que uma perspectiva de ensino de escrita baseada em gêneros textuais através do procedimento de SD pode ser um mecanismo teórico, metodológico e reflexivo adequado para o desenvolvimento de professores de inglês como língua estrangeira

Edge of stability echo state networks

Echo State Networks (ESNs) are time-series processing models working under the Echo State Property (ESP) principle. The ESP is a notion of stability that imposes an asymptotic fading of the memory of the input. On the other hand, the resulting inherent architectural bias of ESNs may lead to an excessive loss of information, which in turn harms the performance in certain tasks with long short-term memory requirements. With the goal of bringing together the fading memory property and the ability to retain as much memory as possible, in this paper we introduce a new ESN architecture, called the Edge of Stability Echo State Network (ES$^2$N). The introduced ES$^2$N model is based on defining the reservoir layer as a convex combination of a nonlinear reservoir (as in the standard ESN), and a linear reservoir that implements an orthogonal transformation. We provide a thorough mathematical analysis of the introduced model, proving that the whole eigenspectrum of the Jacobian of the ES$^2$N map can be contained in an annular neighbourhood of a complex circle of controllable radius, and exploit this property to demonstrate that the ES$^2$N's forward dynamics evolves close to the edge-of-chaos regime by design. Remarkably, our experimental analysis shows that the newly introduced reservoir model is able to reach the theoretical maximum short-term memory capacity. At the same time, in comparison to standard ESN, ES$^2$N is shown to offer an excellent trade-off between memory and nonlinearity, as well as a significant improvement of performance in autoregressive nonlinear modeling

PARETO DIAGRAMS STUDY OF GROSS REGIONAL DOMESTIC PRODUCT EXPOSURE IN CERTAIN SECTORS IN A REGION

Study is learning scientific study. A Pareto chart is a diagram consisting of a bar graph and a line graph that illustrates a comparison of each type of problem data with its overall causes. Gross Regional Domestic Product (PDRB) is the total gross added value arising from all economic sectors in a particular area. Which is usually a Pareto Diagram made to describe the PDRB of a particular area which aims to help make regional policies or planning, evaluate development results, provide information that can describe the regional economic performance. In terms of the topic of this pareto diagram study, the author takes the exposure of rock mining in Manokwari Regency. The mining of these rocks is a source of income in the Manokwari Regency area which can support the economy in the Manokwari Regency area. Where mining activity or mining activity is a process or activity of taking material that can be extracted from the earth to the utilization of minerals, both for the benefit of the company, the surrounding community, as well as local and central government