A special family of Galton-Watson processes with explosions

The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer four-parameter family of reproduction laws. The corresponding Galton-Watson processes also allow for explicit calculations, now with possibility for infinite mean, or even infinite number of offspring. We study the properties of this special family of branching processes, and show, in particular, that in some explosive cases the time to explosion can be approximated by the Gumbel distribution

Sample genealogies and genetic variation in populations of variable size

We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression, Eq. (27), for the moments of these distributions for an arbitrary smooth dependence of the population size on time. We investigate how the frequency of population-size variations alters the distributions. This allows us to discuss their influence on the distribution of the number of mutations, and on the population homozygosity in populations with variable size.Comment: 19 pages, 8 figures, 1 tabl

An accurate model for genetic hitch-hiking

We suggest a simple deterministic approximation for the growth of the favoured-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitch-hiking. Only when Ns < 10 (N is the population size and s denotes the selection coefficient), are discrepancies between our approximation and direct numerical simulations of a Moran model noticeable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.Comment: 12 pages, 10 figure

Linkage disequilibrium under recurrent bottlenecks

Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus, but additional insights can be gained by investigating genetic variation at multiple loci. The corresponding patterns of variation reflect linkage disequilibrium and provide information about the underlying multi-locus gene genealogies. The statistical properties of two-locus genealogies have been intensively studied for populations of constant census size, as well as for simple demographic histories such as exponential population growth, and single bottlenecks. By contrast, the combined effect of recombination and sustained demographic fluctuations is poorly understood. Addressing this issue, we study a two-locus Wright-Fisher model of a population subject to recurrent bottlenecks. We derive coalescent approximations for the covariance of the times to the most recent common ancestor at two loci. We find, first, that an effective population-size approximation describes the numerically observed linkage disequilibrium provided that recombination occurs either much faster or much more slowly than the population size changes. Second, when recombination occurs frequently between bottlenecks but rarely within bottlenecks, we observe long-range linkage disequilibrium. Third, we show that in the latter case, a commonly used measure of linkage disequilibrium, sigma_d^2 (closely related to r^2), fails to capture long-range linkage disequilibrium because constituent terms, each reflecting long-range linkage disequilibrium, cancel. Fourth, we analyse a limiting case in which long-range linkage disequilibrium can be described in terms of a Xi-coalescent process allowing for simultaneous multiple mergers of ancestral lines.Comment: 34 pages, 7 figure

Optimal scheduling of the next preventive maintenance activity for a wind farm

A large part of the operational cost for a wind farm is due to the cost of equipment maintenance, especially for offshore wind farms. How to reduce the maintenance cost, and hence increase profitability, is this article's focus. It presents a binary linear optimization model whose solution may inform the wind turbine owners about which components, and when, should undergo the next preventive maintenance (PM) replacements. The suggested short-term scheduling strategy takes into account eventual failure events of the multi-component system – in that after the failed system is repaired, the previously scheduled PM plan should be updated, assuming that the restored components are as good as new. The optimization algorithm of this paper, NextPM, is tested through numerical case studies applied to a four-component model of a wind turbine. The first study addresses the important case of a single component system, used for parameter calibration purposes. The second study analyses the case of seasonal variations of mobilization costs, as compared to the constant mobilization cost setting. Among other things, this analysis reveals a 35 % cost reduction achieved by the NextPM model, as compared to the pure corrective maintenance (CM) strategy. The third case study compares the NextPM model with another optimization model – the preventive maintenance scheduling problem with interval costs (PMSPIC), which was the major source of inspiration for this article. This comparison demonstrates that the NextPM model is accurate and much faster in terms of computational time.</p

Evolutionary branching in a stochastic population model with discrete mutational steps

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.Comment: 12 pages, 8 figures. Revised versio

Evaluation of the effect of locally produced biological pesticide (AқKөbelek ™) on biodiversity and abundance of beneficial insects in four forage crops in the Almaty region of Kazakhstan

Using a non-replicated plot design, we experimentally assessed the effects of a locally produced biological pesticide on the abundance, species richness and Shannon diversity of beneficial insects in four forage crops (alfalfa, soybeans, corn, and triticale) in southeastern Kazakhstan. 2-way ANOV tests detected no effect of the biological pesticide treatment on the abundance (N) of either predators or pollinators. However, there were significant differences in pollinator and predator abundances among crops. Pairwise t-tests between the experiment and control plots for each crop detected no significant differences in predator or pollinator Shannon diversity index values (H). Paired t-tests revealed significant differences in diversity index values for both predator and pollinator functional groups among crops within each treatment (experiment, control). Corn and triticale plots had notably similar predator abundance (N), species richness (S) and Shannon diversity index (H) values. Corn, alfalfa and soy-triticale differed in pollinator Shannon H, N and S values, suggesting each contained a distinct pollinator assemblage. A trial rapid assessment for differences using a point-based system for indicator species showed only small difference among crops and between treatment and control plots. This method may be more applicable in situations sampling disturbance needs to be minimized and a rapid but less thorough assessment is required

Synthesis of Carboxymethyl Starch for increasing drilling mud quality in drilling oil and gas wells

This paper describes the impact of carboxymethyl starch preparation conditions on physicochemical properties of polysaccharide reagent, widely used as fluid loss reducing agent in drilling mud. Variation of the main parameters of carboxymethylation is researched in the experiment. The following conditions such as temperature and reaction time, amount of water, as well as ratio of NaOH to monochloracetic acid define the characteristics of carboxymethyl starch. The degree of substitution is defined for polysaccharides, as well as the characteristics of samples have been studied by infrared spectroscopy. Rheological characteristics and fluid loss indicator have been investigated to study the impact of the reagents on drilling mud quality

ВЫЯВЛЕНИЕ НЕБЛАГОПРИЯТНЫХ ФАКТОРОВ, СПОСОБСТВУЮЩИХ РАЗВИТИЮ МИОПИИ У СТУДЕНТОВ МЕДИЦИНСКИХ КОЛЛЕДЖЕЙ

To define the risk factors of myopia development among the students the authors got acquainted with spreading of the pathology among the students and their parents. 313 students of Tuimaizy medical college (at the age of 16 to 22 ys) and their parents (n = 579) participated in the study. Attention was paid to the internal factors (heredity, family atmosphere, quality of life) and to the external factors (the life, intensity in studying) -the factors promoting development of myopia. Special psychomedico-pedagogical commission has been organized for better health protection of the organ of vision in teenagers in Tuimaizy medical college.С целью определения факторов риска развития миопии среди студентов была изучена распространенность данного заболевания у студентов и их родителей. Проведено исследование студентов Туймазинского медицинского колледжа в возрасте от 16 до 22 лет, всего 313 человек, и их кровных родителей - 579 человек. В процессе исследования были выявлены следующие факторы: внутренние (наследственно-семейная среда, качество жизни) и внешние (образ жизни, интенсивность учебного процесса), способствующие возникновению или дальнейшему развитию миопии. Для укрепления здоровья органа зрения подростков на базе Туймазинского медицинского колледжа организована психолого-медико-педагогическая комиссия. Ведется комплексная работа, в которой участвуют психолог, преподаватели колледжа, фельдшер, офтальмолог, что обеспечивает массовую профилактику близорукости среди студентов

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure