Stratifications and foliations in phase portraits of gene network models

Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ensembles of trajectories of the corresponding dynamical systems, in particular, to estimate the highest likelihood domain of the initial data, to solve inverse problems of parameter identification, to list the equilibrium points and their characteristics, to localize cycles in the phase portraits, to construct stratification of the phase portraits to subdomains with different qualities of trajectory behavior, etc. Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section “Investigation of functions and plot of their graphs” of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. In the present paper, we construct ensembles of trajectories in phase portraits of some dynamical systems. These ensembles are 2-dimensional surfaces invariant with respect to shifts along the trajectories. This is analogous to classical construction in analytic mechanics, i. e. the level surfaces of motion integrals (energy, kinetic moment, etc.). Such surfaces compose foliations in phase portraits of dynamical systems of Hamiltonian mechanics. In contrast with this classical mechanical case, the foliations considered in this paper have singularities: all their leaves have a non-empty intersection, they contain limit cycles on their boundaries. Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations

Non-invasive optical method for evaluating the oxygen status in breast neoplasms

The paper presents the results from a study of the breast oxygen status by diffuse optical tomography (DOT). Detection of breast tissue at wavelengths of 684, 794, and 850 nm could provide information on the distribution of basic tissue chromophores: oxygenized and deoxygenized hemoglobin. Normal breast tissue was characterized by the even distribution of these compounds and stabilization of their level. In breast cancer, the distribution of oxy- and deoxyhemoglobin was noted for uneven distribution and blood oxygen saturation was lower in the projection of a tumor nodule. The blood oxygen saturation data obtained by DOT demonstrate physiological differ- ences between normal and tumor tissues in different tumor areas

Methodology for Selecting the Configuration of Ground Base Stations of a Local Navigation System to Provide the Lowest Errors of Navigation Definitions

В данной статье приведена методика выбора наилучшей конфигурации наземных базовых станций локальной навигационной системы. Локальные навигационные системы активно применяются для навигационно-временного обеспечения наземных и воздушных объектов, точность определения координат которых зависит от значения геометрического фактора. Взаимное расположение наземных базовых станций напрямую влияет на значение геометрического фактора, а следовательно, на точность определения координат в навигационной аппаратуре потребителей. Однако необходимо учитывать, что на выбор взаимного расположения (конфигурации) наземных базовых станций влияют энергетическая доступность сигналов от наземных базовых станций в зоне навигации, особенности рельефа местности на трассах «наземная базовая станция – навигационная аппаратура потребителей», требуемый размер зоны действия локальной системы навигации, размеры зоны, в которой возможно размещение базовых станций, наличие прямой радиовидимости от базовых станций до потребителя, ослабление сигналов на трассе распространения радиоволн. Данная методика учитывает приведенные выше факторы и в качестве показателя эффективности предлагает использовать среднее арифметическое значение геометрического фактора в зоне навигацииIn this article presents a methodology for choosing the best configuration of ground base stations of a local navigation system. Local navigation systems are actively used for navigation and time support of ground and air objects, the accuracy of determining the coordinates of which depends on the magnitude of the geometric factor – a measure of the deterioration of accuracy in the navigation receiver. The relative location of ground base stations directly affects the value of the geometric factor, and, consequently, the accuracy of determining the coordinates in the navigation equipment of consumers. However, it should be taken into account that the choice of the relative location (configuration) of ground base stations is influenced by the energy availability of signals from ground base stations in the navigation zone, the terrain features on the routes “ground base station – navigation equipment of consumers “, the required size of the area of operation of the local navigation system, the size of the zone in which it is possible to place a ground base station, the presence of direct radio visibility from the ground base station to the navigation equipment of the carriers, attenuation of the signals of the local positioning system on the route of propagation of radio waves “ground base station – navigation equipment of consumers”. This technique takes into account the above limitations and suggests using the arithmetic mean of the geometric factor in the navigation zone as an indicator of efficienc

The problem of identification of upper respiratory tract infectious diseases

Основными возбудителями воспалительного процесса верхних дыхательных путей являются S. pyogenes и S. aureus, на долю которых приходится от 25 до 60 % выделенных возбудителей. Сравнение пейзажа выделенных культур показало их количественную и качественную идентичность у взрослого и детского населения.The main causative agents of inflammation of upper respiratory tract are the S. pyogenes and S. aureus, which accounted for 25 to 60 % of the isolated pathogens. Comparing of isolated culture pictures showed their qualitative and quantitative identity in the adult and child population

Normative productivity of the global vegetation

<p>Abstract</p> <p>Background</p> <p>The biosphere models of terrestrial productivity are essential for projecting climate change and assessing mitigation and adaptation options. Many of them have been developed in connection to the International Geosphere-Biosphere Program (IGBP) that backs the work of the Intergovernmental Panel on Climate Change (IPCC). In the end of 1990s, IGBP sponsored release of a data set summarizing the model outputs and setting certain norms for estimates of terrestrial productivity. Since a number of new models and new versions of old models were developed during the past decade, these normative data require updating.</p> <p>Results</p> <p>Here, we provide the series of updates that reflects evolution of biosphere models and demonstrates evolutional stability of the global and regional estimates of terrestrial productivity. Most of them fit well the long-living Miami model. At the same time we call attention to the emerging alternative: the global potential for net primary production of biomass may be as high as 70 PgC y^-1, the productivity of larch forest zone may be comparable to the productivity of taiga zone, and the productivity of rain-green forest zone may be comparable to the productivity of tropical rainforest zone.</p> <p>Conclusion</p> <p>The departure from Miami model's worldview mentioned above cannot be simply ignored. It requires thorough examination using modern observational tools and techniques for model-data fusion. Stability of normative knowledge is not its ultimate goal – the norms for estimates of terrestrial productivity must be evidence-based.</p

Современные этиологические и эпидемиологические особенности острых вирусных поражений печени

Проведено порівняльне вивчення епідеміологічних особливостей вражень печінки вірусного характеру серед населення Миколаївської, Одеської та Херсонської областей протягом 2010-2017 рр. Встановлено, що на території південних областей України рівень захворюваності на гострі враження печінки (ГА, ГВ, ГС) був вірогідно нижчим, ніж по країні, випадки захворювань мали постійний цілорічний характер реєстрації. При розрахунку тенденції епідемічного процесу встановлено помірний спад рівня захворюваності на гострі гепатити серед населення всіх південних областей України, має місце недореєстрація гепатитів з контактним механізмом передачі.A comparative study of the epidemiological features of viral liver impressions among the population of Mykolaiv, Odesa and Kherson regions during 2010-2017 was conducted. It was established that in the territory of southern oblasts of Ukraine, the incidence rate for acute liver impressions (НA, НВ, HС) was significantly lower than in country, cases of diseases had a permanent year-round registration. In calculating the tendency of the epidemic process, a moderate decline in the incidence of acute hepatitis among the population of all southern regions of Ukraine is established, there is a lack of registration of hepatitis with a contact mechanism of transmission.Проведено сравнительное изучение эпидемиологических особенностей поражений печени вирусного характера среди населения Николаевской, Одесской и Херсонской областей в течение 2010-2017 гг. Установлено, что на территории южных областей Украины уровень заболеваемости острыми гепатитами (ГА, ГВ, ГС) был достоверно ниже, чем по стране, случаи заболеваний имели постоянный круглогодичный характер регистрации. При расчете тенденции эпидемического процесса установлено умеренный спад уровня заболеваемости острыми гепатитами среди населения всех южных областей Украины, имеет место недорегистрация гепатитов с контактным механизмом передачи

Research of accuracy characteristics of measurement of coordinates in the ground-based radionavigation system based on pseudosatellites

The issues of measurement accuracy of coordinates in the short-range navigation system based on pseudosatellites are considered in the article. The analysis of the errors components the of measurement of radio-navigation parameters is given, the values of the geometrical factor are calculated for various options of system constructin