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Exam 1984

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Exam 1983

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Exam 1984 pdf

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Exam 1983 pdf

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Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Degenerative process and cell death in salivary glands of Rhipicephalus sanguineus (Latreille, 1806) (Acari: Ixodidae) semi-engorged female exposed to the acaricide permethrin

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Features of autophagic cell death in Plasmodium liver-stage parasites

Analyzing molecular determinants of Plasmodium parasite cell death is a promising approach for exploring new avenues in the fight against malaria. Three major forms of cell death (apoptosis, necrosis and autophagic cell death) have been described in multicellular organisms but which cell death processes exist in protozoa is still a matter of debate. Here we suggest that all three types of cell death occur in Plasmodium liver-stage parasites. Whereas typical molecular markers for apoptosis and necrosis have not been found in the genome of Plasmodium parasites, we identified genes coding for putative autophagy-marker proteins and thus concentrated on autophagic cell death. We characterized the Plasmodium berghei homolog of the prominent autophagy marker protein Atg8/LC3 and found that it localized to the apicoplast. A relocalization of PbAtg8 to autophagosome-like vesicles or vacuoles that appear in dying parasites was not, however, observed. This strongly suggests that the function of this protein in liver-stage parasites is restricted to apicoplast biology.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

Weak Ergodicity of Mt /Mt /N /N + R Queue

2000 Mathematics Subject Classification: 60J27, 60K25.