{"title":"A Simple Stochastic Differential Equation with Discontinuous Drift","authors":"Maria Simonsen, J. Leth, H. Schiøler, H. Cornean","doi":"10.4204/EPTCS.124.11","DOIUrl":"https://doi.org/10.4204/EPTCS.124.11","url":null,"abstract":"In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function which approximates the discontinuous drift and apply the Euler-Maruyama method and the Fokker-Planck equation with this input. The point of departure for this work is a particular SDE with discontinuous drift.","PeriodicalId":360438,"journal":{"name":"HAS","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131172917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A stochastic hybrid model of a biological filter","authors":"Andrea Ocone, G. Sanguinetti","doi":"10.4204/EPTCS.124.10","DOIUrl":"https://doi.org/10.4204/EPTCS.124.10","url":null,"abstract":"We present a hybrid model of a biological filter, a genetic circuit which removes fast fluctuations in the cell's internal representation of the extra cellular environment. The model takes the classic feed-forward loop (FFL) motif and represents it as a network of continuous protein concentrations and binary, unobserved gene promoter states. We address the problem of statistical inference and parameter learning for this class of models from partial, discrete time observations. We show that the hybrid representation leads to an efficient algorithm for approximate statistical inference in this circuit, and show its effectiveness on a simulated data set.","PeriodicalId":360438,"journal":{"name":"HAS","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122916359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"HyLTL: a temporal logic for model checking hybrid systems","authors":"Davide Bresolin","doi":"10.4204/EPTCS.124.8","DOIUrl":"https://doi.org/10.4204/EPTCS.124.8","url":null,"abstract":"The model-checking problem for hybrid systems is a well known challenge in the scientific community. Most of the existing approaches and tools are limited to safety properties only, or operates by transforming the hybrid system to be verified into a discrete one, thus loosing information on the continuous dynamics of the system. In this paper we present a logic for specifying complex properties of hybrid systems called HyLTL, and we show how it is possible to solve the model checking problem by translating the formula into an equivalent hybrid automaton. In this way the problem is reduced to a reachability problem on hybrid automata that can be solved by using existing tools.","PeriodicalId":360438,"journal":{"name":"HAS","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115226281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Integrated Framework for Diagnosis and Prognosis of Hybrid Systems","authors":"E. Chanthery, P. Ribot","doi":"10.4204/EPTCS.124.4","DOIUrl":"https://doi.org/10.4204/EPTCS.124.4","url":null,"abstract":"Complex systems are naturally hybrid: their dynamic behavior is both continuous and discrete. For these systems, maintenance and repair are an increasing part of the total cost of final product. Efficient diagnosis and prognosis techniques have to be adopted to detect, isolate and anticipate faults. This paper presents an original integrated theoretical framework for diagnosis and prognosis of hybrid systems. The formalism used for hybrid diagnosis is enriched in order to be able to follow the evolution of an aging law for each fault of the system. The paper presents a methodology for interleaving diagnosis and prognosis in a hybrid framework.","PeriodicalId":360438,"journal":{"name":"HAS","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132841682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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