Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.Comment: 17 pages, RevTeX LATeX file, to appear in Journal of Mathematical Physic

Bogoliubov Renormalization Group and Symmetry of Solution in Mathematical Physics

Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparameterisation one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of new approach to solution for a problem of self-focusing laser beam in a non-linear medium.Comment: Contribution to the proceedings of conference "RG 2000" (Taxco, Mexico, Jan. 1999). To be published in Physics Report

Discrete Symmetry and Stability in Hamiltonian Dynamics

In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear normal modes (NNMs), i.e periodic solutions which represent continuations of the system's linear normal modes in the nonlinear regime. We examine the existence of such solutions and discuss different methods for constructing them and studying their stability under fixed and periodic boundary conditions. In the periodic case, we employ group theoretical concepts to identify a special type of NNMs called one-dimensional "bushes". We describe how to use linear combinations such NNMs to construct s(>1)-dimensional bushes of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit the symmetries of the linearized equations to simplify the study of their destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we review a number of interesting results, which have appeared in the recent literature. We then turn to an analytical and numerical construction of quasiperiodic orbits, which does not depend on the symmetries or boundary conditions. We demonstrate that the well-known "paradox" of FPU recurrences may be explained in terms of the exponential localization of the energies Eq of NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,.... Thus, we show that the stability of these low-dimensional manifolds called q-tori is related to the persistence or FPU recurrences at low energies. Finally, we discuss a novel approach to the stability of orbits of conservative systems, the GALIk, k=2,...,2N, by means of which one can determine accurately and efficiently the destabilization of q-tori, leading to the breakdown of recurrences and the equipartition of energy, at high values of the total energy E.Comment: 50 pages, 13 figure

Rational dimension of a basis of a regression model for adaptive short-term forecasting the state of a discrete nonstationary dynamic system

Relevance. Today, there are many methodologies for predicting power consumption of various objects. However, there is no a general methodology that is suitable for all types of energy systems, including the sectoral characteristics of small northern settlements and other objects with the stochastic nature of electricity consumption schedules. At the same time, during the development of problem-oriented forecasting methods, it is necessary to take into account computational and statistical features of forecasted time series to the maximum and apply them adequately. The mentioned circumstance prompts the creation of criteria-indicators that allow evaluating the quality of the applied model for solving the forecasting problem, correctness of its construction and correctness of applying a priori information about the object and its physical properties.Aim. Develop and apply the criteria-indicators, which allow evaluating the quality of the forecast regression model and the influence of the dimensionality of such model base on a forecasting error. Methods. The choice of rational dimensionality of the regression model basis for the adaptive forecasting problem is based on the known and developed criteria-indicators. The main provisions of such criteria-indicators were formulated, which provide an assessment of the quality of conditioning of an equivalent square matrix, the presence of uninformative elements of the matrix, and linear dependence of the columns. Results. Based on the analysis of criteria-indicators, the authors selected a rational dimension of the regression model basis for the problem of adaptive short-term forecasting of the state of discrete non-stationary dynamic systems. Conclusions. The authors have previously selected the most promising criteria-indicators and developed a normalized difference factor of diagonal predominance. This allows us to evaluate the influence of the basis size change on the regression model quality when building an approach of adaptive short-term forecasting of electricity consumption by autonomous power systems of small northern settlements on the basis of regression analysis methods. Based on the analysis of criteria-indicators the authors obtained information about the influence of the regression model basis dimension on the forecasting problem solution error. The authors stated the further stages of research to reduce this error. The paper introduces and describes one of the ways to improve the forecasting model quality. The dependence of the forecasting error on the size of the regression model basis were revealed; the criteria-indicators considered in the article were successfully applied. It is confirmed that the pre-selected and developed criteria-indicators make it possible, at the stage of compiling an equivalent square matrix and performing preliminary actions on it, to track changes within the matrix. The changes will lead to improvement in the solution of the problem of adaptive short-term forecasting

Commercial articulated collaborative in situ 3D bioprinter for skin wound healing

In situ bioprinting is one of the most clinically relevant techniques in the emerging bioprinting technology because it could be performed directly on the human body in the operating room and it does not require bioreactors for post-printing tissue maturation. However, commercial in situ bioprinters are still not available on the market. In this study, we demonstrated the benefit of the originally developed first commercial articulated collaborative in situ bioprinter for the treatment of full-thickness wounds in rat and porcine models. We used an articulated and collaborative robotic arm from company KUKA and developed original printhead and correspondence software enabling in situ bioprinting on curve and moving surfaces. The results of in vitro and in vivo experiments show that in situ bioprinting of bioink induces a strong hydrogel adhesion and enables printing on curved surfaces of wet tissues with a high level of fidelity. The in situ bioprinter was convenient to use in the operating room. Additional in vitro experiments (in vitro collagen contraction assay and in vitro 3D angiogenesis assay) and histological analyses demonstrated that in situ bioprinting improves the quality of wound healing in rat and porcine skin wounds. The absence of interference with the normal process of wound healing and even certain improvement in the dynamics of this process strongly suggests that in situ bioprinting could be used as a novel therapeutic modality in wound healing.publishersversionPeer reviewe

Structural insights into thrombolytic activity of destabilase from medicinal leech

Destabilase from the medical leech Hirudo medicinalis belongs to the family of i-type lysozymes. It has two different enzymatic activities: microbial cell walls destruction (muramidase activity), and dissolution of the stabilized fibrin (isopeptidase activity). Both activities are known to be inhibited by sodium chloride at near physiological concentrations, but the structural basis remains unknown. Here we present two crystal structures of destabilase, including a 1.1 Å-resolution structure in complex with sodium ion. Our structures reveal the location of sodium ion between Glu34/Asp46 residues, which were previously recognized as a glycosidase active site. While sodium coordination with these amino acids may explain inhibition of the muramidase activity, its influence on previously suggested Ser49/Lys58 isopeptidase activity dyad is unclear. We revise the Ser49/Lys58 hypothesis and compare sequences of i-type lysozymes with confirmed destabilase activity. We suggest that the general base for the isopeptidase activity is His112 rather than Lys58. pKa calculations of these amino acids, assessed through the 1 μs molecular dynamics simulation, confirm the hypothesis. Our findings highlight the ambiguity of destabilase catalytic residues identification and build foundations for further research of structure–activity relationship of isopeptidase activity as well as structure-based protein design for potential anticoagulant drug development.</p

Стехиометрическая модель метаболизма человека

The present study deals with the “Human” component of the bioregenerative life support system. Here we develop a model that allows calculating metabolic mass flow rates of the “Human” component and monitoring the production of toxic substances – ammonia, hydrogen sulfide, and methanethiol. The model is designed as an Excel-VBA interactive program. The “Human” component is considered as an object with incoming and outgoing flows of matter. Food ingredients, water, and oxygen constitute the input flows, and the outgoing flows consist of metabolic products. The input flows are distributed along metabolic channels. To specify the characteristics of the “Human” component, a calorie counter and a space diet planner are connected to the model. The calorie counter is designed to determine a crewman’s daily energy requirements depending on age, weight, height, gender, and level of physical activity. In turn, the numerical energy value is transmitted to the diet planner, which determines the food set. To more accurately present the metabolism of phosphorus, nucleic acids and phospholipids are included in the food composition. Each substance in the model is assigned a stoichiometric formula. The core of the model consists of seven stoichiometric equations and the water exchange unit, which are the link between the incoming and outgoing flows of matter. The solution of stoichiometric equations and balancing the water exchange unit are carried out using the Solver Add-in for Excel, which is embedded in the metabolic circuit. To show the validity of the model, a calculation of the human metabolism depending on calorie counter and diet planner is presentedОбъектом исследования является компонент «Человек», находящийся в биорегенеративной системе жизнеобеспечения. В данной работе разрабатывается модель, позволяющая рассчитывать метаболические массовые потоки компонента «Человек» и контролировать выработку токсичных веществ – аммиака, сероводорода и метантиола. Модель выполнена в виде интерактивной программы Excel-VBA. Компонент «Человек» рассматривается как объект с входящими и исходящими потоками вещества. Входные потоки составляют пищевые ингредиенты, вода и кислород, а исходящие – продукты метаболизма. Входные потоки распределяются по метаболическим каналам. Для задания характеристик компонента «Человек» к модели подключены счетчик калорий и космический планировщик диеты. Счетчик калорий предназначен для определения суточной потребности человека в энергии в зависимости от возраста, веса, роста, пола и уровня физической активности. В свою очередь, численное значение энергии передается в планировщик диеты, который определяет пищевой набор. Для более точного представления метаболизма фосфора в состав пищи включены нуклеиновые кислоты и фосфолипиды. Каждому веществу в модели присвоена стехиометрическая формула. Ядро модели составляют семь стехиометрических уравнений и блок водного обмена, которые являются связующим звеном между входящими и исходящими потоками вещества. Решение стехиометрических уравнений и балансировка блока водного обмена осуществляются с помощью надстройки Solver для Excel, которая встроена в метаболический контур. Для демонстрации обоснованности модели представлен расчет метаболизма человека в зависимости от счетчика калорий и планировщика диет