Noticimat 15

Título: A Boltzmann-based EDA via information geometry

Ponente: Dr. Ignacio Segovia Domínguez (University of Texas at Dallas)

Hora: 12:30 pm

(Trasmisión por el sistema bluejeans: https://bluejeans.com/690410873).

Resumen: The relevance of sampling densities in Evolutionary Algorithms (EA) is due to the crucial role in simulating individuals in promising regions. Although most of Estimation of Distribution Algorithms (EDA) use their global density (or search distribution) as the sampling density, it would be interesting to manage both functions as separated models. However, which parameters should have the sampling density? In this talk we introduce formulae for updating parameters of a sampling density function via the natural gradient technique. A density constructed in this way is a predictive model in the sense that such model is adapted according to an expected improvement of the fitness function. We guide the parameter updating via the Kullback-Leibler divergence between the multivariate normal and the Boltzmann densities. Since we take into account the model's parameter structure via information geometry, we avoid the usual perspective of updating the density function on the Euclidean space. It allows us to create an efficient algorithm named Natural Gradient based Estimation of Distribution Algorithm (NAGEDA). Finally, statistical results support that NAGEDA is in close competition with state of the art algorithms, mainly because the proposed natural gradient allows for the control of the exploration and exploitation phases.

 

Título: ¿Qué geometría describen los nodos de una curva plana irreducible?

Ponente: César Adrián Lozano Huerta (Instituto de Matemáticas/UNAM)

Hora: 15:30 pm

(Trasmisión por el sistema bluejeans: https://bluejeans.com/170548655).

Resumen: La variedad de Severi parametriza curvas planas irreducibles de grado d con k nodos. En algunos casos, dichos nodos son puntos del plano que están en posición general. Sin embargo en la gran mayoría de casos, los nodos están en posición especial. Un objetivo de esta charla es reportar investigación sobre la geometría de los nodos cuando éstos están en posición especial.

Durante la charla discutiremos también que conocer la geometría de los nodos, cuando éstos están en posición especial, nos permitiría escribir ecuaciones (y sus sizigias) que definen curvas canónicas de género mayor que 10.

Este trabajo es conjunto con Tim Ryan (Universidad de Michigan, Ann-Arbor).

 

Título: Estimates for strongly singular operators

Ponente: Ricardo Sáenz (Universidad de Colima)

Hora: 4:00 pm

(Trasmisión por el sistema bluejeans: https://bluejeans.com/148242916).

Resumen: In this talk we discuss 1-dimensional oscillatory integrals with strongly singular kernels whose singularity is worse than 1/t. Oscillatory integrals with kernels with a singularity of the form 1/t^a with a>1 have been studied widely in recent decades, and it is known that they require oscillatory factors of the form t^b with a and b satisfying a proper condition. In this talk we discuss oscillatory integrals with kernels whose singularity is much worse than a power of t, say, of exponential type, as in e^{k/t} with k>0. In this case one needs oscillatory factors also of exponential type, and we give sufficient conditions to guarantee that such operators are bounded 

in L^p for p>1 and of weak type 1-1. We also discuss some recent results for strongly singular operators along curves.

 

Título: Computational homology in statistical genetics: applications to cancer genomic data

Ponente: Dr. Javier Arsuaga, UC Davis

Hora: 10:00 am

(Trasmisión por el sistema bluejeans, ID por confirmar).

Resumen: Genomic technologies have revolutionized the field of genetics. In particular, the identification of genetic elements has greatly benefited from statistical genetics tools that, through association studies, test thousands of genetic elements for a given phenotype.

In this talk I will present a methodology that combines topological data analysis with statistical genetics to identify genetic signatures (in the form of copy number aberrations) in breast cancer. The proposed topological encoding of these chromosome aberrations allows to: (1) map chromosome aberrations across the cancer genome using the zero homology group (2) build predictive models using machine learning techniques (3) identify some co-amplifications of the genome using the first homology group (4) identify cancer driving genes when incorporating a fiber bundle-like structure to the data.