Seminarios

Eventos Pasados

2019-01-14
16:30hrs.
Seminario de Sistemas Dinámicos
Alberto Pinto. Faculty of Sciences, University of Porto
Piecewice chaotic maps
Abstract:
We will consider the class of Cr unidimensional piecewise maps with a transitive attractor. These maps can have simultaneously discontinuities, criticalities and singularities. We will show that topological chaos is equivalent to metric chaos. We recall that this result is known in several classes strictly contained in the general class that we are presenting.
Sala 2
2019-01-11
12:00 hrs.
Seminario de Estadística
David Dahl. Department of Statistics, Brigham Young University
Summarizing Distributions of Latent Structure
Abstract:
In a typical Bayesian analysis, consider effort is placed on "fitting the model" (e.g., obtaining samples from the posterior distribution) but this is only half of the inference problem.  Meaningful inference usually requires summarizing the posterior distribution of the parameters of interest.  Posterior summaries can be especially important in communicating the results and conclusions from a Bayesian analysis to a diverse audience.  If the parameters of interest live in R^n, common posterior summaries are means, medians, and modes.  Summarizing posterior distributions of parameters with complicated structure is a more difficult problem.  For example, the "average" network in the posterior distribution on a network is not easily defined. This paper reviews methods for summarizing distributions of latent structure and then proposes a novel search algorithm for posterior summaries.  We apply our method to distributions on variable selection indicators, partitions, feature allocations, and networks.  We illustrate our approach in a variety of models for both simulated and real datasets.

Seminario organizado por el Centro para el Descubrimiento de Estructuras en Datos Complejos - MiDaS.
Sala 5, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chilehttp://midas.mat.uc.cl
2019-01-10
16:30hrs.
Seminario de Sistemas Dinámicos
Alberto Pinto. Faculty of Sciences, University of Porto
Pseudo-Anosov diffeomorphisms
Abstract:
We will introduce pseudo Cr smooth structures on surfaces that will have the following property; the Pseudo-Anosov diffeomorphisms are uniformly Cr hyperbolic. We will conjecture that the Bochi-Mane theorem will extend to such pesudo C1 smooth structures recovering the duality of the result for all surfaces.
Sala 2
2019-01-10
12:00 hrs.
Seminario de Estadística
Dae-Jin Lee. Bcam - Basque Center for Applied Mathematics
Hierarchical modelling of patient-reported outcomes data based on the beta-binomial distribution
Abstract:
The beta-binomial distribution does not belong to the exponential family and, hence classical regression techniques cannot be used when dealing with outcomes following the mentioned distribution. In this talk, we propose and develop regression models based on the beta-binomial distribution for the analysis of U, J or inverse J-shaped discrete and bounded outcomes. In fact, although this work is focused on the analysis of patient-reported outcomes (PROs), which usually follow the mentioned distributional shapes, proposed models can also be extended to several fields. First of all, we make a review and comparison of existing beta-binomial regression approaches in independent data context, concluding that the marginal approach is the most adequate. However, PRO studies are usually carried out in a longitudinal framework, where patients' responses are measured over time. This leads to a multilevel or correlated data structure and consequently, we extend the marginal beta-binomial regression approach to the inclusion of random effects to accommodate the hierarchical structure of the data. We develop the estimation and inference procedure for the model proposal. Furthermore, we compare the performance of our proposal with similar approaches in the literature, showing that it gets better results in terms of reducing the bias of the estimates. We apply the model to a longitudinal Chronic Obstructive Pulmonary Disease study carried out at Galdakao Hospital in Biscay, Spain, reaching clinically and statistically relevant results about the evolution of the patients over time. PROs are usually obtained using rating scale questionnaires consisting of questions or items, grouped into one or more subscales, often called dimensions or domains. Therefore, we also propose a multivariate regression model based on the beta-binomial distribution for the joint analysis of all the longitudinal dimensions provided by different questionnaires. Finally, it is worth mentioning that we have implemented all the proposed regression models in the PROreg R- package which is available at CRAN.
Sala 1, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chile
2019-01-04
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Yuri Bilu. Université de Bordeaux
Singular units do not exist
Abstract:
In the first part, I will revise the classical theory of complex multiplication of elliptic curves (or C-lattices); in particular, I will define the notion of a singular modulus, the j-invariant of an elliptic curve (or a C-lattice) with complex multiplication.  According to the old result of Weber, a singular modulus is an algebraic integer. In the second part, I will briefly describe the recent work of Habegger, Kühne and myself proving that a singular modulus cannot be algebraic unit.
Sala 2
2019-01-03
16:00hrs.
Seminario de Análisis y Geometría
Armin Schikorra . University of Pittsburgh
Self-repulsive curvature energies for curves and surfaces: regularity theory and relation to harmonic maps
Abstract:
I will talk about a class of curvature energies for curves, the O'Hara energies, that are nonlocal in nature. In particular, I will present an approach for regularity theory of minimizers and critical points for these curves which is based on a relation to (fractional) harmonic maps. Then I will present some results towards attempts of generalizing this idea to surfaces.
Sala 2