Última atualização: 01/06/16
Encontros de pesquisa em
BIOMATEMÁTICA
Palestrante |
Título |
Resumo |
Prof Marcelo Sobottka MTM/UFSC |
Statistical test for a hidden Markov model for nucleotide distribution in bacterial DNA |
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. [1]
M. Sobottka and A. G. Hart. A model capturing novel
strand symmetries in
bacterial DNA. Biochemical and
Biophysical Research Communications 410, 4,
823--828 (2011). Note: This is a joint work with A. G. Hart (Centro de Modelamiento Matemático (Univ. de Chile) and M. W. Mendonça (UFSC). |
Prof. Erwan Hingant Universidade Estadual de Rio de Janeiro |
Stochastic model of aggregation-fragmentation |
In this presentation we will introduce a stochastic version of the Becker-Döring equations. This concerns aggregation and fragmentation of clusters as it arises in fibrils/polymer formation. Such phenomena occurs in Alzheimer's disease, Prion, etc. We will show how we can approach such system by a deterministic equation (scaling limit) and we may interest to first passage time and large deviation linking these phenomenon to biological interrogations. |
Prof. Erwan Hingant Universidade Estadual de Rio de Janeiro |
|
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, namely 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. |
| Profa Flávia MTM/UFSC |
TBA |
TBA |
Atualização: 01/06/16