Dynamical robustness of biological networks with hierarchical distribution of time scales

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First, we obtain the following result for linear networks: for large multiscale systems with hierarchical distribution of time scales the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. We argue that similar phenomena are valid in the nonlinear case as well. As a numerical illustration we use a model of signalling network that can be applied to important transcription factors such as NFkB

Asymptotology of Chemical Reaction Networks

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.Comment: 23 pages, 8 figures, 84 refs, Corrected Journal Versio

Report in Documentary Communication in Southern Region of Russia during First Half of 18th Century

This article examines the report as a new type of document in the business writing system of the first half of the 18th century. The aim is to identify common and distinctive features of reports from various institutions in the southern region of Russia. The materials used for this study are documents from the Don Army (State Archive of the Volgograd Region) and the Astrakhan Province (National Archive of the Republic of Kalmykia). Through a comparative analysis of their content, functions, and speech organization, it is revealed that all reports were submitted from subordinate subjects to superiors, served informative purposes, and occasionally served as accompanying documents. They shared a similar form (addressee, addresser, title, main text, date, place of creation), although there were variations in the placement of requisites, document titles, and addresser formulas. Differences were also identified, such as the larger number of reports in the documentation of the Don Army and their frequent use as accompanying documents, while Astrakhan reports often contained financial reports. In Don reports, the addresser was referred to in the final formula as “about this report,” while Astrakhan reports only included their name (or signature). It can be concluded that reports were increasingly integrated into official communication, becoming firmly established in the military sphere, and their form became more standardized, reflecting the development of common rules for document management

Registration Documents of the Don Army in the 18th Century: Content and Structure of Texts

The article is devoted to the analysis of the content and speech organization of the texts of accounting and reporting documents of the 18th century of the Chanceries of the Don Fund Troops of the Mikhailovsky stanitsa ataman of the State Archives of the Volgograd Region. The relevance of the research is determined by solving the problems of creating an annotated linguistic corpus of documents. Lists, catalogues, registers, inventories, statements, notes are considered from the point of view of such genre parameters as name, addressee, addressee, date and place of creation of the document. Highlighted speech markers, explicating these parameters and organizing the text. The similarities and differences of documents of different genres are revealed. It is shown that the composition of texts has a two — or three-part structure; in some documents it varies, in others it is constant; the availability of the date, the indication of the addressee also varies. Information about the enumerated objects in documents of one genre is conveyed in more or less detail, systematized or not, in text or tabular form. With the variability of texts, a tendency towards standardization of texts of one genre and differentiation of different genres was noted. The considered parameters allow to establish the genre of documents without self-naming and can be used for automated meta-tagging of texts

Influence of the thermal factor on the composition of electron-beam high-entropy ALTiVCrNbMo coatings

This paper reports results of studying the element and phase compositions of electron-beam coatings based on the high-entropy alloy AlTiVCrNbMo, depending on the deposition temperature (in the range of 300...700 °С). The high-entropy alloys were melted in an arc furnace in an atmosphere of high-purity argon. Vacuum condensates of the high-entropy alloy (AlTiVCrNbMo) with a thickness of 3–5 µm were obtained in the vacuum setup UVN-2M-1 at a working vacuum of 5·10-5 mТоrr. The alloy evaporation was performed from the water-cooled ingot mold using an electron-beam gun with a power of 5 kW. Condensation of vapors of all the elements of the alloy was performed onto copper substrates at temperatures of 300, 500, 700 °C. Based on analysis of the element composition of materials of the target made of the high-entropy six-element alloy AlTiVCrNbMo and electron-beam coatings, based on it, we established the critical parameter (specific heat of vaporization of an element) that defined a selective change in the element composition. In accordance with a characteristic change in the composition of coatings of the multi-element high-entropy alloy, 3 groups of elements were distinguished: with a specific heat of evaporation of 280...350 kJ/mol (group 1), 420…460 kJ/mol (group 2), and 590…680 kJ/mol (group 3). It was shown that the formation of a single-phase coating of the high-entropy alloy (based on BCC of the crystalline lattice) occurs at the higher deposition temperature of 500...700 °C when the coating consists of not less than 5 elements. It was established that based on the conditions for an electron-beam process of materials formation, the results obtained can be divided into two types: those determined by the condition of evaporation of the target and those determined by the conditions of coating deposition. The density of flows of elements, evaporated from the target, is determined by their specific heat of evaporation. However, the ratio of atoms in the flow, derived in this way, may not be retained in the formed coating due to the secondary evaporation of elements from the growth surface. The obtained results allow us to substantiate principles for the selection of components for achieving the optimal element and phase compositions of high-entropy alloys.На основі аналізу елементного складу матеріалів мішені з високоентропійного шестиелементного сплаву AlTiVCrNbMo і електронно-променевих покриттів на його основі встановлено критичний параметр (питома теплота випаровування елемента), який визначає селективну зміну елементного складу. Показано, що формування однофазного покриття високоентропійного сплаву відбувається, коли до складу покриття входить не менше 5 елементів. Отримані результати дозволяють обґрунтувати принципи підбору компонент для досягнення оптимальних елементного та фазового складу високоентропійних сплавів

Optimal Distributed Globally Bounded Control for Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions and a Linear Quality Criterion

For the problem of optimal control of a parabolic-hyperbolic process with nonlocal point boundary conditions, an explicit form of the solution is obtained in the form of formal series according to the system of eigenfunctions, which are generated by the spatial differential operator and boundary conditions. At the same time, the unequivocal solvability of the intermediate problems is established for each iteration. In addition, sufficient conditions for the convergence of the series are established, which determine the obtained formal solution of the optimal control problem, which justifies its correctness system of differential equations; Lyapunov exponents; fractal dimensio

Теоретические модели управления пристеночными потоками в гидродинамических системах

Розвинено нелінійний алгоритм керування пристінковим потоком, який використовує спіймані вихори в поперечних канавках, а також ежекцію рідини. Побудований контролер ґрунтується на моделі точкових вихорів з одним ступенем свободи і складається з рівняння рівноваги вихору та умови Кутта-Жуковського в гострих крайках канавки. Розраховано параметри керуючої системи для канавок різної глибини в стаціонарному потоці. Одержано, що в мілких канавках область стійкості вихорів є ширшою, ніж в глибоких, тому вони є більш перспективними для керування. Ці результати використано для розрахунку параметрів активної керуючої схеми зі зворотним зв’язком у нестаціонарному потоці, коли система оперативно реагує на зовнішні збурення. Наведено приклади реалізації цієї схеми, коли швидкість течії змінюється періодично або за лінійним законом.We present a non-linear near-wall flows control algorithm. This algorithm uses captured vortices in the cross grooves and fluid ejection. The controller is based on a model of point vortices with one degree of freedom and consists of the equation of vortex equilibrium and the Kutta condition in the groove edges. Parameters of a control system for grooves of different depths in a stationary stream are calculated. We determined that in shallow grooves, the region of stability of vortices is wider, than in deep grooves, so they are more promising for control. These results are used to estimate the parameters of the active control scheme with a feedback in a nonstationary flow when the system is responsive to external perturbations. Examples of an implementation of such a scheme are presented for the case when the flow velocity changes periodically or linearly.Развит нелинейный алгоритм управления пристеночным потоком, который использует пойманные вихри в поперечных канавках и эжекцию жидкости. Построенный контроллер основывается на модели точечных вихрей с одной степенью свободы и состоит из уравнения равновесия вихря и условия Кутта-Жуковского в острых кромках канавки. Рассчитаны параметры управляющей системы для канавок различной глубины в стационарном потоке. Получено, что в мелких канавках область устойчивости вихрей шире, чем в глубоких, поэтому они являются более перспективными для управления. Эти результаты использованы для расчета параметров активной управляющей схемы с обратной связью в нестационарном потоке, когда система оперативно реагирует на внешние возмущения. Приведены примеры реализации этой схемы, когда скорость течения меняется периодически или по линейному закону

Long-time Behavior of State Functions for Badyko Models

In this note we examine the long-time behavior of state functions for a climate energy balance model (Budyko Model) in the strongest topologies of the phase and the extended phase spaces. Strongest convergence results for all weak solutions are obtained. New structure and regularity properties for global and trajectory attractors are justified