DEPARTAMENTO DE MATEMÁTICA – CFM / UFSC

Encontros de Biomatemática

Statistical test for a hidden Markov model for nucleotide distribution in bacterial DNA

Prof. Dr. Marcelo Sobottka MTM/UFSC

Resumo:

In this work, we present parameter estimators for a hidden-Markov based model for the distributional structure of nucleotides in bacterial DNA sequences. Such model supposes that the gross structure of bacterial DNA sequences can be derived from uniformly distributed mutations of some primitive genome which is constructed following a ten-parameter Markov process [1].
The proposed estimators can be used to construct a statistical test which indicates if a given DNA sequence can be simulated by the model.

This is a joint work with A. G. Hart (Centro de Modelamiento Matemático, Universidad de Chile) and M. Weber Mendonça (Universidade Federal de Santa Catarina). M. Sobottka was supported by CNPq-Brazil grant 455399/2011-5 and by CAPES-Brazil Fellowship.

Dia – Hora:  9/06/2016 – 15:30h

Local: sala 302 do Departamento de Matemática UFSC

Ciclo de Palestras em Biomatemática

Becker-Doring equations and its Lifschitz Slyozov limit, the entrant case

Professor Erwan Hingant da UERJ

Segunda Palestra

Resumo: Becker-Doring equations is a phase transition model that describes aggregation and fragmentation of clusters by capturing or shedding monomers one-by-one. It consists in an infinite set of ordinary equation over each size $i\geq 1$ of clusters. We are interesting to link such system with a continuous model with continuous size $x>0$. Such limit model arise after scaling consideration and named Lifschitz-Slyozov. This consits in a non-linear transport equation. This equation is well-known when the flux at the boundary $x=0$ is negative, mnamely small clusters tends to fragment. In this presentation we are concerned with the opposite case, when small clusters tends to aggregate. We show our we can derive a boundary condition for the limit problem departing from the discrete version.
We would emphasis on 3 points: How a scaling procedure works; How can we prove a limit theorem; and introduce the notion of quasy steady state approximation for fast varying variable.

Dia – Horário: 17/06/2016 – 14:00-15:00
Local: Auditório do Departamento de Matemática (LAED), sala 007