Localization of response functions of spiral waves in the FitzHugh-Nagumo system

Dynamics of spiral waves in perturbed, e. g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spiral's Response Functions, which are eigenfunctions of the adjoint linearised problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh-Nagumo model, and show that they are effectively localised in the vicinity of the spiral core.Comment: 11 pages, 2 figure

Gendarmes and the modernization of local rule in Russia (research experience and prospects)

The article was submitted on 06.04.2015.The article explores the historiography of the secret police in the Russian Empire. Revealing the approaches of historians to this subject, the methods and manner of their work with historical sources, the author demonstrates the negative consequences that were a result of political topicality and the concealing of information about the state. A review of historiographic heritage enables the author to cleanse the perception of the topic from a number of “quasi-evident facts” created at various times and under different circumstances. Additionally, she pays attention to the existence of a vast number of documents of the police department which can still be found in state archives. Special attention needs to be paid to those ones that contain the reflections of gendarme officers on professional ethics and duties. The author reveals documental evidence of conflicts of interest between the local administration and the police officers controlling its activity. The approach used by the author bears a non-conventional character which consists in the study of creation of these documents and their functions in the police department. Preliminary results enable the author to claim that these certificates can provide information not only about the sphere of impact and peculiarities of the secret police, but also about the ways of implementation of the political concept of a regular, well-organized state in 19th century-Russia and the ways of self-improvement of government.Статья содержит анализ историографии тайной полиции в Российской империи. Выявляя подходы историков к данной теме и способы их работы с историческими свидетельствами, автор показывает негативные следствия политической актуальности и процесса герметизации знаний о государстве. Ревизия историографического наследия позволяет автору освободить восприятие темы от созданных в разные времена и в разных условиях «квазиочевидностей». Одновременно обращается внимание на наличие богатого комплекса делопроизводственных документов полицейского ведомства, сохранившихся в государственном архиве. Предлагая неоинституциональный подход к их анализу, автор показывает очевидные и латентные информационные возможности обнаруженных документов. Среди них особенный интерес представляют тексты, в которых зафиксировалась рефлексия жандармских офицеров о профессиональной этике и служебном долге, а также находятся свидетельства конфликтов интересов местной администрации и контролирующей ее деятельность полиции. Оригинальность предлагаемого подхода состоит в том, чтобы исследовать логику создания этих документов, их назначение в полицейском управлении. Предварительные результаты позволяют автору утверждать, что данные свидетельства могут рассказать не только о сфере полномочий и характере работы тайной полиции, но и о способах реализации политической концепции «регулярного, хорошо организованного» государства в России XIX в., о путях самоусовершенствования государственного аппарата.Исследование осуществлено в рамках программы «Научный фонд НИУ ВШЭ» в 2013–2014 гг. (проект № 12-01-0123)

Filament tension and phase-locked drift of meandering scroll waves

Rotating scroll waves are self-organising patterns which are found in many oscillating or excitable systems. Here we show that quasi-periodic (meandering) scroll waves, which include the rotors that organise cardiac arrhythmias, exhibit filament tension when averaged over the meander cycle. With strong filament curvature or medium thickness gradients, however, scroll wave dynamics are governed by phase-locked drift instead of filament tension. Our results are validated in computational models of cycloidal meander and a cardiac tissue model with linear core.Comment: accepted for publication in Physical Review Letters (December 2017

Localization of response functions of spiral waves in the FitzHugh-Nagumo system

Preprint of an article submitted for consideration and subsequently published in International Journal of Bifurcation and Chaos © 2005 copyright World Scientific Publishing Company. http://www.worldscientific.com/worldscinet/ijbcDynamics of spiral waves in perturbed, e. g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spiral's Response Functions, which are eigenfunctions of the adjoint linearised problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh-Nagumo model, and show that they are effectively localised in the vicinity of the spiral core

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.Comment: 26 pages, 13 figures, appendix and 2 movies, as accepted to PLoS ONE 2011/08/0

Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

Toxic properties of potential hepatic protectors study of new pyrimidine derivatives class

© 2014 AENSI Publisher All rights reserved. The basic toxic properties of the potential hepatic protectors of the pyrimidine derivatives class were studied on the basis of Daphnia culture experiments. These protectors are the new analogues of the domestic drug Xymedon. The doses of acute toxicity, the chronic toxicity and embryotoxicity values are determined. It was revealed that according to all the studied toxicometry parameters the 29-R compound has the least levels of toxicity

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.Comment: 22 pages, 3 figures, 2 table

Fungal and bacterial successions in the process of co-composting of organic wastes as revealed by 454 pyrosequencing

© 2017 Galitskaya et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Composting is viewed as one of the primary methods to treat organic wastes. Co-composting may improve the efficiency of this treatment by establishing the most suitable conditions for decomposers than those present in the individual wastes. Given that bacteria and fungi are the driving agents of composting, information about the composition of their communities and dynamics during composting may improve reproducibility, performance and quality of the final compost as well as help to evaluate the potential human health risk and the choice of the most appropriate application procedure. In this study, the co-composting of mixtures containing two similar components (organic fraction of municipal solid waste and sawdust polluted by oil) and one discriminate component (sewage sludges of different origin) were investigated. Bacterial and fungal community successions in the two mixtures were analyzed during the composting process by determining the change in their structural dynamics using qPCR and 454 pyrosequencing methods in a lab experiment for a period of 270 days. During the initial composting stage, the number of 16S bacterial copies was (3.0 ±0.2) × 10 6 and (0.4±0.0) × 10 7 g -1 , and the Rhodospiralles and Lactobacialles orders dominated. Fungal communities had (2.9±0.0) ×10 5 and (6.1±0.2) ×10 5 ITS copies g -1 , and the Saccharomycetales order dominated. At the end of the thermophilic stage on the 30 th day of composting, bacterial and fungal communities underwent significant changes: dominants changed and their relative abundance decreased. Typical compost residents included Flavobacteriales, Chitinophagaceae and Bacterioidetes for bacteria and Microascaceae, Dothideomycetes, Eurotiomycetes, Sordariomycetes, and Agaricomycetes for fungi. During the later composting stages, the dominating taxa of both bacterial and fungal communities remained, while their relative abundance decreased. In accordance with the change in the dominating OTUs, it was concluded that the dynamics of the bacterial and fungal communities were not similar. Analysis by non-metric multidimensional scaling (NMDS) revealed that the bacterial communities of the two composts became progressively more similar; a similar trend was followed by the fungal community