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SNP sites are generally discovered by sequencing regions of the human genome in a limited number of individuals. This may leave SNP sites present in the region, but containing rare mutant nucleotides, undetected. Consequently, estimates of nucleotide diversity obtained from assays of detected SNP sites are biased. In this research we present a statistical model of the SNP discovery process, which is used to evaluate the extent of this bias. This model involves the symmetric Beta distribution of...
In this paper we analyze the stochastic version of a minimalistic multi-strain model,
which captures essential differences between primary and secondary infections in dengue
fever epidemiology, and investigate the interplay between stochasticity, seasonality and
import. The introduction of stochasticity is needed to explain the fluctuations observed
in some of the available data sets, revealing a scenario where noise and complex
deterministic skeleton...
This paper describes three cytological image segmentation methods. The analysis includes the watershed algorithm, active contouring and a cellular automata GrowCut method. One can also find here a description of image pre-processing, Hough transform based pre-segmentation and an automatic nuclei localization mechanism used in our approach. Preliminary experimental results collected on a benchmark database present the quality of the methods in the analyzed issue. The discussion of common errors and...
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
Blood rheology is completely determined by its major corpuscles which are erythrocytes,
or red blood cells (RBCs). That is why understanding and correct mathematical description
of RBCs behavior in blood is a critical step in modelling the blood dynamics. Various
phenomena provided by RBCs such as aggregation, deformation, shear-induced diffusion and
non-uniform radial distribution affect the passage of blood through the vessels. Hence,
they have...
DNA microarrays provide a new technique of measuring gene expression, which has attracted a lot of research interest in recent years. It was suggested that gene expression data from microarrays (biochips) can be employed in many biomedical areas, e.g., in cancer classification. Although several, new and existing, methods of classification were tested, a selection of proper (optimal) set of genes, the expressions of which can serve during classification, is still an open problem. Recently we have...
An analysis of all possible icosahedral viral capsids is proposed. It takes into account
the diversity of coat proteins and their positioning in elementary pentagonal and
hexagonal configurations, leading to definite capsid size. We show that the
self-organization of observed capsids during their production implies a definite
composition and configuration of elementary building blocks. The exact number of different
protein dimers is related to the...
We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.
We have developed a chemical kinetics simulation that can be used as both an educational
and research tool. The simulator is designed as an accessible, open-source project that
can be run on a laptop with a student-friendly interface. The application can potentially
be scaled to run in parallel for large simulations. The simulation has been successfully
used in a classroom setting for teaching basic electrochemical properties. We have shown
that...
Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.
Bidomain models are commonly used for studying and simulating
electrophysiological waves in the cardiac tissue. Most of the
time, the associated PDEs are solved using explicit finite
difference methods on structured grids. We propose an implicit
finite element method using unstructured grids for an anisotropic
bidomain model. The impact and numerical requirements of
unstructured grid methods is investigated using a test case
with re-entrant waves.
We investigate the structure of
travelling waves for a model of a fungal disease propagating over
a vineyard. This model is based on a set of ODEs of the SIR-type
coupled with two reaction-diffusion equations describing the
dispersal of the spores produced by the fungus inside and over the
vineyard. An estimate of the biological parameters in the model
suggests to use a singular perturbation analysis. It allows us to
compute the speed and the profile of the travelling waves. The
analytical results...
In this note we give a result of convergence when time goes to infinity for a
quasi static linear elastic model, the elastic tensor of which vanishes at
infinity. This method is applied to segmentation of medical images, and improves
the 'elastic deformable template' model introduced previously.
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