Extreme values for Benedicks-Carleson quadratic maps

We consider the quadratic family of maps given by $f_{a}(x)=1-a x^2$ with $x\in [-1,1]$, where $a$ is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes $X_0,X_1,...$, given by $X_{n}=f_a^n$, for every integer $n\geq0$, where each random variable $X_n$ is distributed according to the unique absolutely continuous, invariant probability of $f_a$. Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of $M_n=\max\{X_0,...,X_{n-1}\}$ is the same as that which would apply if the sequence $X_0,X_1,...$ was independent and identically distributed. This result allows us to conclude that the asymptotic distribution of $M_n$ is of Type III (Weibull).Comment: 18 page

Extreme Value Laws in Dynamical Systems for Non-smooth Observations

We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a counterpart to the result of the authors in the absolutely continuous case. Moreover, we prove an equivalent result for returns to dynamically defined cylinders. This allows us to show that we have Extreme Value Laws for various dynamical systems with equilibrium states with good mixing properties. In order to achieve these goals we tailor our observables to the form of the measure at hand

Extreme Value Laws for sequences of intermittent maps

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16}, where we generalised the theory of extreme values for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. The present work is an extension of our previous results for concatenations of uniformly expanding maps obtained in \cite{FFV16}.Comment: To appear in Proceedings of the American Mathematical Society. arXiv admin note: substantial text overlap with arXiv:1510.0435

Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical systems, in particular to {\em sequential dynamical systems}, given by uniformly expanding maps, and to a few classes of random dynamical systems. Some examples are presented and worked out in detail

Speed of convergence for laws of rare events and escape rates

We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems

Complete convergence and records for dynamically generated stochastic processes

We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given potential along its orbits. This is done both in the absence and presence of clustering. A new formula for the piling of points on the vertical direction of bi-dimensional limiting point processes, in the presence of clustering, is given, which is then generalised for higher dimensions. The limiting multi-dimensional processes are computed for systems with sufficiently fast decay of correlations. The complete convergence results are used to study the effect of clustering on the convergence of extremal processes, record time and record values point processes. An example where the clustering prevents the convergence of the record times point process is given

Rare Events for the Manneville-Pomeau map

We prove a dichotomy for Manneville-Pomeau maps $f:[0,1]\to [0, 1]$: given any point $\zeta\in [0,1]$, either the Rare Events Point Processes (REPP), counting the number of exceedances, which correspond to entrances in balls around $\zeta$, converge in distribution to a Poisson process; or the point $\zeta$ is periodic and the REPP converge in distribution to a compound Poisson process. Our method is to use inducing techniques for all points except 0 and its preimages, extending a recent result by Haydn, Winterberg and Zweim\"uller, and then to deal with the remaining points separately. The preimages of 0 are dealt with applying recent results by Ayta\c{c}, Freitas and Vaienti. The point $\zeta=0$ is studied separately because the tangency with the identity map at this point creates too much dependence, which causes severe clustering of exceedances. The Extremal Index, which measures the intensity of clustering, is equal to 0 at $\zeta=0$, which ultimately leads to a degenerate limit distribution for the partial maxima of stochastic processes arising from the dynamics and for the usual normalising sequences. We prove that using adapted normalising sequences we can still obtain non-degenerate limit distributions at $\zeta=0$

A configuração de comunidades de aprendizagem em blended learning no ensino superior

VII Conferência Internacional de TIC na Educação, realizada em BragaEm tempos de profundas transformações sociais, económicas e culturais e vertiginosa evolução das tecnologias de informação e da comunicação deparamo-nos com a necessidade de redefinir pedagogia, também, no Ensino Superior. O enfoque nas competências e o apelo à mobilidade pelo Processo de Bolonha convidam a um paradigma educacional que privilegie novas formas de pensar, desenvolver e avaliar os processos de formação centrados no estudante e nas suas estratégias de autorregulação e domínio de ferramentas mediatizadas pelas oportunidades tecnológicas e reflexividade em parceria, sob supervisão dos professores facilitadores da aprendizagem. Este trabalho visa, pois, ilustrar a operatividade de modelos em blended learning, analisando o impacto de novos cenários de aprendizagem na criação de comunidades, de aprendizagem baseada em problemas. Para tal, exploramos relações possíveis entre modalidades de ensino presencial e online, em que a relação pedagógica estabelecida face-a-face é confrontada com a criação de comunidades virtuais de aprendizagem e de investigação.When there are profound social, economic and cultural changes and rapid evolution of information and communication technologies we are faced with the need to redefine pedagogy in higher education. The focus on skills and appeal to mobility subscribed by the ways of thinking, develop and evaluate training processes, student-centred and fostering its self-regulation and mastery of tools influenced by technological opportunities and refection in partnership, under the supervision of teachers and facilitators of learning. This work aims illustrate the operativity of models in blended learning, analyzing the impact of new scenarios in creating learning communities, problem-based. To this end, we explore possible relations between modalities of presencial and on-line teaching, in which the pedagogical relationship established face-to-face is compared with the generation of virtual communities of learning and inquiry

Self-concept of competence of higher education students learning in virtual environments

Assuming that academic success is influenced not only by the power of learning but also by the way students perceive themselves, we have relied on national studies concerning self-concept of competence of students. The main issue was to situate the self-concept of competence of university students into new virtual learning environments. We aim validate the instrument for collecting empirical data adapted to virtual learning environments, identify the degree of selfconcept of competence, when learning in such an approach, and estimate whether students perceive themselves as much or more competent than in real environments with face-to-face interaction. This research involved 280 higher education students in Social Sciences, who appraised perception and self-concept of competence. The main findings indicate favorable self-concept of competence. Also, the results suggest that the application of online pedagogical models may have a very positive impact on self-concept of competence of students in higher education, even in social dimensions and in the perception of a careful coaching.Fundação para a Ciência e a Tecnologi

Education and learning in higher education in Portugal: evaluation of the self concept of competence in online environments

Conferência internacional realizada de 10-11 de Novembro de 2011 no "Palazzo Medici Riccardi", em FlorençaStudies focused on learning experiences have clarified the concept of education in higher education, particularly in Portugal, but few have elucidated about virtual environments on academic achievement and feelings of competence of students as they learn. On the assumption that academic success is influenced not only by the power of learning but also the way students perceive themselves, and that these factors predict their subsequent success, we've relied on national studies concerning self- concept of competence of students. The main issue was to situate the self-concept of competence of university students into new virtual learning environments through online methods of teaching.This research involved 278 higher education students enrolled in classes for courses in Social Sciences which was introduced a novel approach, with education mediated by web tools, and then appraised on their perception and self-concept of competence. We rely on the Self-Concept of Competence Scale, having adapted all 31 items to online environments. The main findings indicate that the students had high perceptions of their self-concept level of competence. The results suggest therefore that the application of online pedagogical models, may have a very positive impact on self-concept of competence of students in higher education, even in social dimensions