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Displaying 381 –
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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...
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...
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...
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...
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...
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...
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...
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...
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...
It is well established that resource variability generated by spatial patchiness and turbulence is an important
influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations
indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can
be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...
Whether the size of an animal population is environmentally limited or regulated
by density dependent negative feedback mechanisms is of ecological interest. Proponents of
limitation theory have issued a set of specific challenges which are addressed in this paper
using field data for the insect Tipula paludosa. This species is known to be subject to population crashes caused by adverse environmental conditions and assumed to be limited.
We re-examine published data in support of this hypothesis...
Population geneticists study the variability of gene sequences within a species, whereas phylogeneticists compare gene sequences between species and usually have only one representative sequence per species. Stochastic models in population genetics are used to determine probability distributions for gene frequencies and to predict the probability that a new mutation will become fixed in a population. Stochastic models in phylogenetics describe the substitution process in the single sequence that...
Relaxation oscillations are limit cycles with two clearly different
time scales. In this article the spatio-temporal dynamics of a
standard prey-predator system in the parameter region of relaxation
oscillation is investigated. Both prey and predator population are
distributed irregularly at a relatively high average level between a
maximal and a minimal value. However, the slowly developing complex
pattern exhibits a feature of “inverse excitability”: Both
populations show collapses which occur...
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