Jak se čtou genomy: bioinformatika jakožto obor na pomezí biologie a exaktních věd
K otázke fyzikálneho významu Hodgkin-Huxleyho empirických rovníc pre iónové vodivosti počas vzruchu
Když se matematika potká s biologií: matematická ekologie
Článek se zabývá některými aplikacemi matematiky v ekologii. V historickém kontextu ukazuje, že jednak teoretické základy populační a evoluční ekologie využívají matematické metodologie založené na diferenciálních či diferenčních rovnicích, jednak ekologické problémy motivují vznik nových matematických disciplín, jako je např. evoluční teorie her.
Když se matematika potká s biologií: matematická epidemiologie
Středověká morová epidemie způsobila smrt asi 17-22 % světové populace, z toho asi 30-60 % evropské populace, a trvalo zhruba 200 let, než se světová populace vrátila na svou původní úroveň. Epidemie dnes často zmiňované španělské chřipky v letech 1918-1920 vedla ke smrti přibližně 3-5 % světové populace. Svědky méně závažných, avšak stále dramatických epidemií jsme i v současnosti. Pandemie těžkého akutního respiračního syndromu (SARS) mezi roky 2002 a 2004, pandemie prasečí chřipky způsobené kmenem...
Kendall's tau-type rank statistics in genome data
High-dimensional data models abound in genomics studies, where often inadequately small sample sizes create impasses for incorporation of standard statistical tools. Conventional assumptions of linearity of regression, homoscedasticity and (multi-) normality of errors may not be tenable in many such interdisciplinary setups. In this study, Kendall's tau-type rank statistics are employed for statistical inference, avoiding most of parametric assumptions to a greater extent. The proposed procedures...
Kermack-McKendrick epidemic model revisited
This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size . Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer...
Kermack-McKendrick epidemics vaccinated
This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack–McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are...
Kinetical systems
The aim of the paper is to give some preliminary information concerning a class of nonlinear differential equations often used in physical chemistry and biology. Such systems are often very large and it is well known that where studying properties of such systems difficulties rapidly increase with their dimension. One way how to get over the difficulties is to use special forms of such systems.
KIS: An automated attribute induction method for classification of DNA sequences
This paper presents an application of methods from the machine learning domain to solving the task of DNA sequence recognition. We present an algorithm that learns to recognize groups of DNA sequences sharing common features such as sequence functionality. We demonstrate application of the algorithm to find splice sites, i.e., to properly detect donor and acceptor sequences. We compare the results with those of reference methods that have been designed and tuned to detect splice sites. We also show...
La docencia de la bioestadística: un cambio de perspectiva.
Hace apenas seis años, aparecieron dos números de la revista Estadística Española dedicados a la docencia de la estadística. Releyendo el artículo del profesor C. M. Cuadras y los amplios comentarios de un buen número de profesores del área sobre la docencia de la bioestadística en España, he tenido la impresión de que, a pesar de mantener su validez en líneas generales, la perspectiva ha cambiado radicalmente. En el cambio han intervenido, a mi parecer, dos hechos fundamentales: la irrupción de...
La procédure de vote de Simon Lhuilier
La statistica nelle prove cliniche
Si descrivono le attività e le responsabilità dello statistico professionale nella conduzione di una prova clinica in una industria farmaceutica o in un ente di ricerca.
Laplace Adomian decomposition method for solving a fish farm model
In this work, a combined form of the Laplace transform method and the Adomian decomposition method is implemented to give an approximate solution of nonlinear systems of differential equations such as fish farm model with three components nutrient, fish and mussel. The technique is described and illustrated with a numerical example.
Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences
To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov...
Large deviations and quasi-potential of a Fleming-Viot process.
Large deviations for Dirichlet processes and Poisson-Dirichlet distribution with two parameters.
Large population limit and time behaviour of a stochastic particle model describing an age-structured population
We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...
Large scale behaviour of the spatial -Fleming–Viot process
We consider the spatial -Fleming–Viot process model (Electron. J. Probab.15(2010) 162–216) for frequencies of genetic types in a population living in , in the special case in which there are just two types of individuals, labelled and . At time zero, everyone in a given half-space has type 1, whereas everyone in the complementary half-space has type . We are concerned with patterns of frequencies of the two types at large space and time scales. We consider two cases, one in which the dynamics...
Large time behavior in a density-dependent population dynamics problem with age structure and child care
Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the environmental...
Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system
This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.