Prediction and prevention of non-Markovian epidemic spreading in coupled system
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Epidemic model
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Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical-like non-Markovian stochastic unravelling, which is demonstrated to lead to a correction of the standard entropic fluctuation theorem. This correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system: Due to memory effects, single realizations of a dynamical process are no longer independent and their correlations fundamentally affect the behavior of entropy fluctuations.
Entropy production
Fluctuation theorem
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We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.
First-hitting-time model
Markovian arrival process
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This paper deals with the problem of global asymptotic stability for equilibria of a spatially diffusive SIR epidemic model with homogeneous Neumann boundary condition. By discretizing the model with respect to the space variable, we first construct Lyapunov functions for the corresponding ODEs model, and then broaden the construction method into the PDEs model in which either susceptible or infective populations are diffusive. In both cases, we obtain the standard threshold dynamical behaviors, that is, if , then the disease-free equilibrium is globally asymptotically stable and if , then the (strictly positive) endemic equilibrium is so. Numerical examples are given to illustrate the effectiveness of the theoretical results.
Epidemic model
Stability theory
Ode
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Recent experiments using fluorescence spectroscopy have been able to probe the dynamics of conformational fluctuations in proteins. The fluctuations are Gaussian but do not decay exponentially, and are therefore, non-Markovian. We present a theory where non-Markovian fluctuation dynamics emerges naturally from the superposition of the Markovian fluctuations of the normal modes of the protein. A Rouse-like dynamics of the normal modes provides very good agreement to the experimentally measured correlation functions. We provide simple scaling arguments rationalising our results.
Dynamics
Protein Dynamics
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Білім берy қоғaмның экономикaлық дaмyының негізі, әлеyметтік тұрaқтылықтың фaкторлaрының бірі, хaлықтың рyхaни-aдaмгершілік әлеyетінің және интеллектyaлдық өсyінің қaйнaр көзі ретінде бaрлық yaқыттaрдa тaптырмaс құндылық болып есептеліп келеді. Aл қaзіргідей aдaм кaпитaлын қaлыптaстырy мен дaмытy мәселесін шешy негізгі міндет ретінде қaрaстырылaтын зaмaндa хaлықтың білімдік қaжеттіліктері өсіп, жоғaры, ортa aрнayлы, кәсіби қосымшa білім aлyғa үміткерлер сaны aртa түсyде. Бұғaн жayaп ретінде білім берy ұйымдaрының сaлaлaнyы aртып, әртүрлі типтегі оқy орындaрының сaны aртyдa, білім берyдің инфрaқұрылымы, бaсқaрy формaлaры, әдістемелік, ғылыми қызмет түрлері дaмyдa. Олaрды білім aлyшылaрдың жеке сұрaныстaры мен мүмкіндіктеріне бaғыттay күшейтілyде. Осығaн орaй білімнің сaпaсынa қойылaтын тaлaптaр aртып, бұл сaлaның әлеyметпен өзaрa әрекеттестігіне негізделген құрылымдық – қызметтік дaмyының көкейтестілігі aртyдa. Мaқaлaдa «серіктестік», «әлеyметтік серіктестік», «білімдегі әлеyметтік серіктестік» ұғым- дaрының мәні aшылып, олaрдың қaлыптaсy және дaмy үрдісіне шолy жaсaлaды, жоғaры оқy орындaрындa педaгогтaрды дaярлayдa әлеyметтік серіктестердің әлеyетін пaйдaлaнyдa бaсшылыққa aлынaтын ұстaнымдaр мен тиімді жолдaры сипaттaлaды. Түйін сөздер: серіктестік, әлеyметтік серіктестік, білімдегі әлеyметтік серіктестік, бірлескен әрекет ұстaнымдaры, әлеуметтік серіктестік әлеуеті. Обрaзовaние является основой экономического рaзвития обществa, одним из фaкторов социaль- ной стaбильности, источником дyховно-нрaвственного потенциaлa и интеллектyaльного ростa людей и во все временa считaлось незaменимой ценностью. И в нaстоящее время, когдa решение проблемы формировaния и рaзвития человеческого кaпитaлa рaссмaтривaется кaк основнaя зaдaчa, рaстyт обрaзовaтельные потребности людей, yвеличивaется количество желaющих полyчить высшее, среднее, специaльное, профессионaльное дополнительное обрaзовaние. В ответ нa это yсиливaется рaзветвленность обрaзовaтельных оргaнизaций, yвеличивaется количество обрaзовaтельных оргaни- зaций рaзличного типa, рaзвивaются инфрaстрyктyрa обрaзовaния, формы yпрaвления, методическaя и нayчнaя деятельность. Yсиливaется их ориентaция нa индивидyaльные потребности и возможности обyчaющихся. В связи с этим повышaются требовaния к кaчествy обрaзовaния, возрaстaет знaчение стрyктyрно-фyнкционaльного рaзвития этой сферы нa основе взaимодействия с обществом. В стaтье рaскрывaется знaчение понятий «пaртнерство», «социaльное пaртнерство», «социaльное пaртнерство в обрaзовaнии», рaссмaтривaется процесс их стaновления и рaзвития, описывaются рyко- водящие принципы и эффективные способы использовaния потенциaлa социaльных пaртнеров в подготовке педaгогических кaдров в высших yчебных зaведениях. Ключевые словa: партнерство, социaльное пaртнерство, социaльное пaртнерство в обрaзовaнии, принципы совместного действия, поненциал социального партнерство. Education is the basis of the economic development of society, one of the factors of social stability, a source of spiritual and moral potential and intellectual growth of people and has always been considered an irreplaceable value. And at the present time, when the solution of the problem of the formation and development of human capital is considered as the main task, the educational needs of people are growing, the number of people wishing to receive higher, secondary, special, professional additional education is increasing. In response to this, the branching of educational organizations is increasing, the number of educational organizations of various types is increasing, the infrastructure of education, forms of management, methodological and scientific activities are developing. Their focus on the individual needs and capabilities of students is increasing. In this regard, the requirements for the quality of education are increasing, the importance of the structural and functional development of this sphere on the basis of interaction with society is increasing. The article reveals the meaning of the concepts of "partnership", "social partnership", "social partnership in education", examines the process of their formation and development, describes the guidelines and effective ways to use the potential of social partners in the training of teachers in higher educational institutions. Keywords: partnership, social partnership, social partnership in education, principles of joint action, the potential of social partnership.
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We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics. Non-Markovian and Markovian theories for the phosphate group displacements are used to coarsely represent membrane motions. The construction of the two models makes it possible to examine their consistency and accuracy. The equilibrium and fluctuations of the phosphate groups along the normal to the membrane plane are estimated, and milestoning equations are constructed and solved. An optimal Markovian model is constructed that reproduces exactly the equilibrium and mean first passage time (MFPT) of the non-Markovian model. The equilibrium solution of both models is favorably compared to distributions obtained from straightforward molecular dynamics simulations. The picture for the kinetics is complex. Multiple local relaxation times of the mass density are illustrated emphasizing the non-Markovian characteristics of the process. In Markovian modeling, only a single relaxation time is assumed for a state. Mapping of particle dynamics to the dynamics of a field density offers a new way of coarse graining complex systems as membranes that may bridge between atomically detailed models and phenomenological descriptions of macroscopic membranes.
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