Suppression of growth by multiplicative white noise in a parametric resonant system

The author studied the growth of the amplitude in a Mathieu-like equation with multiplicative white noise. The approximate value of the exponent at the extremum on parametric resonance regions was obtained theoretically by introducing the width of time interval, and the exponents were calculated numerically by solving the stochastic differential equations by a symplectic numerical method. The Mathieu-like equation contains a parameter $\alpha$ that is determined by the intensity of noise and the strength of the coupling between the variable and the noise. The value of $\alpha$ was restricted not to be negative without loss of generality. It was shown that the exponent decreases with $\alpha$, reaches a minimum and increases after that. It was also found that the exponent as a function of $\alpha$ has only one minimum at $\alpha \neq 0$ on parametric resonance regions of $\alpha = 0$. This minimum value is obtained theoretically and numerically. The existence of the minimum at $\alpha \neq 0$ indicates the suppression of the growth by multiplicative white noise.Comment: The title and the description in the manuscript are change

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

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Notes on the Zbigniew Herbert’s Poem «Chess» [Szachy]

The article is devoted to the motive of playing chess in the poetry of Z. Herbert (“Mr. Сogito’s Game” (from the book “Pan Сogito”, 1974) and “Chess” (from the book “Epilogue of the Storm”, 1998). The poem “Mr. Сogito’s Game” describes the escape of the Russian revolutionary Kropotkin from the conclusion, moreover, the description is given in terms of the intellectual game. The poem emphasizes the function of the intellect – “mediation” in obtaining freedom. Otherwise, the theme of the chess game in the “Сhess.” The poem is associated with the 1996 chess duel of Garry Kasparov and the IBM Deep Blue computer. The confrontation of the players is reduced to the opposition «man-machine» and more broadly to the opposition «nature-culture». Both opponents get ambivalent characteristics in the poem. A computer is a «monster» and a «dragon», but at the same time its attribute is the “Olympic world.” Attributing the properties of a deity to a computer is equivalent to including it in a series of phenomena divorced from life and, therefore, dead. The attribute of a person is “a knife in the teeth” (primitivism and wildness), but at the same time it indicates the activity and vitality of a person. The last stanzas indicate that imagination is the deliverance of enslavement and short circuits in schemes.Статья посвящена мотиву игры в шахматы в поэзии З. Герберта («Игра Господина Когито» (из книги «Господин Когито», 1974) и «Шахматы» (из книги «Эпилог Бури», 1998). В стихотворении «Игра Господина Когито» описывается побег русского революционера Петра Кропоткина из заключения, причем описание дано в терминах интеллектуальной игры. В стихотворении подчеркивается функция интеллекта – «посредничество» в получении свободы. Иным образом раскрывается тема шахматной игры в «Шахматах». Стихотворение связано с шахматной дуэлью 1996 года Гарри Каспарова и компьютера IBM Deep Blue. Противостояние игроков сводится к оппозиции «человек-машина» и в более широком плане к оппозиции «природа-культура». Оба противника получают в стихотворении амбивалентные характеристики. Компьютер – это «монстр» и «дракон», но в то же время его атрибутом является «олимпийский мир». Приписывание свойств божества компьютеру равносильно включению его в ряд явлений, оторванных от жизни и потому мертвых. Атрибут человека – «нож в зубах» (примитивизм и дикость), но в то же время это указывает на активность и жизнеспособность человека. Последние строфы указывают на то, что воображение – это избавление порабощения и замыкания в схемах

Notes on the Zbigniew Herbert’s Poem «Chess» [Szachy]

The article is devoted to the motive of playing chess in the poetry of Z. Herbert (“Mr. Сogito’s Game” (from the book “Pan Сogito”, 1974) and “Chess” (from the book “Epilogue of the Storm”, 1998). The poem “Mr. Сogito’s Game” describes the escape of the Russian revolutionary Kropotkin from the conclusion, moreover, the description is given in terms of the intellectual game. The poem emphasizes the function of the intellect – “mediation” in obtaining freedom. Otherwise, the theme of the chess game in the “Сhess.” The poem is associated with the 1996 chess duel of Garry Kasparov and the IBM Deep Blue computer. The confrontation of the players is reduced to the opposition «man-machine» and more broadly to the opposition «nature-culture». Both opponents get ambivalent characteristics in the poem. A computer is a «monster» and a «dragon», but at the same time its attribute is the “Olympic world.” Attributing the properties of a deity to a computer is equivalent to including it in a series of phenomena divorced from life and, therefore, dead. The attribute of a person is “a knife in the teeth” (primitivism and wildness), but at the same time it indicates the activity and vitality of a person. The last stanzas indicate that imagination is the deliverance of enslavement and short circuits in schemes.Статья посвящена мотиву игры в шахматы в поэзии З. Герберта («Игра Господина Когито» (из книги «Господин Когито», 1974) и «Шахматы» (из книги «Эпилог Бури», 1998). В стихотворении «Игра Господина Когито» описывается побег русского революционера Петра Кропоткина из заключения, причем описание дано в терминах интеллектуальной игры. В стихотворении подчеркивается функция интеллекта – «посредничество» в получении свободы. Иным образом раскрывается тема шахматной игры в «Шахматах». Стихотворение связано с шахматной дуэлью 1996 года Гарри Каспарова и компьютера IBM Deep Blue. Противостояние игроков сводится к оппозиции «человек-машина» и в более широком плане к оппозиции «природа-культура». Оба противника получают в стихотворении амбивалентные характеристики. Компьютер – это «монстр» и «дракон», но в то же время его атрибутом является «олимпийский мир». Приписывание свойств божества компьютеру равносильно включению его в ряд явлений, оторванных от жизни и потому мертвых. Атрибут человека – «нож в зубах» (примитивизм и дикость), но в то же время это указывает на активность и жизнеспособность человека. Последние строфы указывают на то, что воображение – это избавление порабощения и замыкания в схемах

Parametric resonance in coupled oscillators driven by colored noise

The parametric resonance in two coupled oscillators driven by a Gaussian colored parametric noise is investigated. It is shown that the resonance depends essentially on the form of coupling. The phenomenon is illustrated by stability diagrams, which are obtained numerically

Beneficial effect of noise in suppression of self-excited vibrations

We discuss the possibility of full suppressions of self-excited vibrations by noise. Recently, periodic excitations have been intensively studied for this aim. We compare the used periodic and random noise excitations in the case of a two-mass system. It is shown that the random noise excitations can be more efficient under certain conditions. The telegraphic process is used as the source of noise. The mean-square (energetic) asymptotic stability of the system is a tool in study of the suppression. The stability charts are presented for different values of the transition rate of the telegraphic noise. </jats:p