International Nuclear Information System (INIS)
Garnier, Robert; Chevalier, Marcel
2000-01-01
Studying large and complex industrial sites, requires more and more accuracy in modeling. In particular, when considering Spares, Maintenance and Repair / Replacement processes, determining optimal Integrated Logistic Support policies requires a high level modeling formalism, in order to make the model as close as possible to the real considered processes. Generally, numerical methods are used to process this kind of study. In this paper, we propose an alternate way to process optimal Integrated Logistic Support policy determination when dealing with large, complex and distributed multi-policies industrial sites. This method is based on the use of behavioral Monte Carlo simulation, supported by Generalized Stochastic Petri Nets. (author)
History-dependent stochastic Petri nets
Schonenberg, H.; Sidorova, N.; Aalst, van der W.M.P.; Hee, van K.M.; Pnueli, A.; Virbitskaite, I.; Voronkov, A.
2010-01-01
Stochastic Petri Nets are a useful and well-known tool for performance analysis. However, an implicit assumption in the different types of Stochastic Petri Nets is the Markov property. It is assumed that a choice in the Petri net only depends on the current state and not on earlier choices. For many
Distributed evaluation of stochastic Petri nets
Bell, A.; Buchholz, Peter; Lehnert, Ralf; Pioro, Micha
2004-01-01
In this paper we present on the distributed performance evaluation and model checking of systems specified by stochastic Petri nets. The approaches discussed rely on an explicit state-space generation and target at the usage of clusters of workstations. We present results for systems with several
Stochastic petri nets for wireless networks
Lei, Lei; Zhong, Zhangdui
2015-01-01
This SpringerBrief presents research in the application of Stochastic Petri Nets (SPN) to the performance evaluation of wireless networks under bursty traffic. It covers typical Quality-of-Service performance metrics such as mean throughput, average delay and packet dropping probability. Along with an introduction of SPN basics, the authors introduce the key motivation and challenges of using SPN to analyze the resource sharing performance in wireless networks. The authors explain two powerful modeling techniques that treat the well-known state space explosion problem: model decomposition and
CSL model checking of deterministic and stochastic Petri nets
Martinez Verdugo, J.M.; Haverkort, Boudewijn R.H.M.; German, R.; Heindl, A.
2006-01-01
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under
Complex accident scenarios modelled and analysed by Stochastic Petri Nets
International Nuclear Information System (INIS)
Nývlt, Ondřej; Haugen, Stein; Ferkl, Lukáš
2015-01-01
This paper is focused on the usage of Petri nets for an effective modelling and simulation of complicated accident scenarios, where an order of events can vary and some events may occur anywhere in an event chain. These cases are hardly manageable by traditional methods as event trees – e.g. one pivotal event must be often inserted several times into one branch of the tree. Our approach is based on Stochastic Petri Nets with Predicates and Assertions and on an idea, which comes from the area of Programmable Logic Controllers: an accidental scenario is described as a net of interconnected blocks, which represent parts of the scenario. So the scenario is firstly divided into parts, which are then modelled by Petri nets. Every block can be easily interconnected with other blocks by input/output variables to create complex ones. In the presented approach, every event or a part of a scenario is modelled only once, independently on a number of its occurrences in the scenario. The final model is much more transparent then the corresponding event tree. The method is shown in two case studies, where the advanced one contains a dynamic behavior. - Highlights: • Event & Fault trees have problems with scenarios where an order of events can vary. • Paper presents a method for modelling and analysis of dynamic accident scenarios. • The presented method is based on Petri nets. • The proposed method solves mentioned problems of traditional approaches. • The method is shown in two case studies: simple and advanced (with dynamic behavior)
Stochastic Petri net analysis of a replicated file system
Bechta Dugan, Joanne; Ciardo, Gianfranco
1989-01-01
A stochastic Petri-net model of a replicated file system is presented for a distributed environment where replicated files reside on different hosts and a voting algorithm is used to maintain consistency. Witnesses, which simply record the status of the file but contain no data, can be used in addition to or in place of files to reduce overhead. A model sufficiently detailed to include file status (current or out-of-date), as well as failure and repair of hosts where copies or witnesses reside, is presented. The number of copies and witnesses is a parameter of the model. Two different majority protocols are examined, one where a majority of all copies and witnesses is necessary to form a quorum, and the other where only a majority of the copies and witnesses on operational hosts is needed. The latter, known as adaptive voting, is shown to increase file availability in most cases.
Modelling the protocol stack in NCS with deterministic and stochastic petri net
Hui, Chen; Chunjie, Zhou; Weifeng, Zhu
2011-06-01
Protocol stack is the basis of the networked control systems (NCS). Full or partial reconfiguration of protocol stack offers both optimised communication service and system performance. Nowadays, field testing is unrealistic to determine the performance of reconfigurable protocol stack; and the Petri net formal description technique offers the best combination of intuitive representation, tool support and analytical capabilities. Traditionally, separation between the different layers of the OSI model has been a common practice. Nevertheless, such a layered modelling analysis framework of protocol stack leads to the lack of global optimisation for protocol reconfiguration. In this article, we proposed a general modelling analysis framework for NCS based on the cross-layer concept, which is to establish an efficiency system scheduling model through abstracting the time constraint, the task interrelation, the processor and the bus sub-models from upper and lower layers (application, data link and physical layer). Cross-layer design can help to overcome the inadequacy of global optimisation based on information sharing between protocol layers. To illustrate the framework, we take controller area network (CAN) as a case study. The simulation results of deterministic and stochastic Petri-net (DSPN) model can help us adjust the message scheduling scheme and obtain better system performance.
Modeling and Simulation of Multi-scale Environmental Systems with Generalized Hybrid Petri Nets
Directory of Open Access Journals (Sweden)
Mostafa eHerajy
2015-07-01
Full Text Available Predicting and studying the dynamics and properties of environmental systems necessitates the construction and simulation of mathematical models entailing different levels of complexities. Such type of computational experiments often require the combination of discrete and continuous variables as well as processes operating at different time scales. Furthermore, the iterative steps of constructing and analyzing environmental models might involve researchers with different background. Hybrid Petri nets may contribute in overcoming such challenges as they facilitate the implementation of systems integrating discrete and continuous dynamics. Additionally, the visual depiction of model components will inevitably help to bridge the gap between scientists with distinct expertise working on the same problem. Thus, modeling environmental systems with hybrid Petri nets enables the construction of complex processes while keeping the models comprehensible for researchers working on the same project with significantly divergent education path. In this paper we propose the utilization of a special class of hybrid Petri nets, Generalized Hybrid Petri Nets (GHPN, to model and simulate environmental systems exposing processes interacting at different time-scales. GHPN integrate stochastic and deterministic semantics as well as other types of special basic events. Moreover, a case study is presented to illustrate the use of GHPN in constructing and simulating multi-timescale environmental scenarios.
Research on user behavior authentication model based on stochastic Petri nets
Zhang, Chengyuan; Xu, Haishui
2017-08-01
A behavioural authentication model based on stochastic Petri net is proposed to meet the randomness, uncertainty and concurrency characteristics of user behaviour. The use of random models in the location, changes, arc and logo to describe the characteristics of a variety of authentication and game relationships, so as to effectively implement the graphical user behaviour authentication model analysis method, according to the corresponding proof to verify the model is valuable.
Modelling M/G/1 queueing systems with server vacations using stochastic Petri nets
Directory of Open Access Journals (Sweden)
K Ramanath
2006-12-01
Full Text Available The theory of non-Markovian stochastic Petri nets is employed in this paper to derive an alternative method for studying the steady state behaviour of the M/G/1 vacation queueing system with a limited service discipline. Three types of vacation schemes are considered, and sytems with both a finite population and those with an infinite population (but finite capacity are considered. Simple numerical examples are also provided to illustrate the functionality of the methods and some useful performance measures for the system are obtained.
International Nuclear Information System (INIS)
Balakrishnan, Meera; Trivedi, Kishor S.
1996-01-01
In this paper, we present a comparative reliability analysis of an application on a corporate B-ISDN network under various alternate-routing protocols. For simple cases, the reliability problem can be cast into fault-tree models and solved rapidly by means of known methods. For more complex scenarios, state space (Markov) models are required. However, generation of large state space models can get very labor intensive and error prone. We advocate the use of stochastic reward nets (a variant of stochastic Petri nets) for the concise specification, automated generation and solution of alternate-routing protocols in networks. This paper is written in a tutorial style so as to make it accessible to a large audience
International Nuclear Information System (INIS)
Labadi, Karim; Saggadi, Samira; Amodeo, Lionel
2009-01-01
The dynamic behavior of a discrete event dynamic system can be significantly affected for some uncertain changes in its decision parameters. So, parameter sensitivity analysis would be a useful way in studying the effects of these changes on the system performance. In the past, the sensitivity analysis approaches are frequently based on simulation models. In recent years, formal methods based on stochastic process including Markov process are proposed in the literature. In this paper, we are interested in the parameter sensitivity analysis of discrete event dynamic systems by using stochastic Petri nets models as a tool for modelling and performance evaluation. A sensitivity analysis approach based on stochastic Petri nets, called PSA-SPN method, will be proposed with an application to a production line system.
Sociophysics of sexism: normal and anomalous petrie multipliers
Eliazar, Iddo
2015-07-01
A recent mathematical model by Karen Petrie explains how sexism towards women can arise in organizations where male and female are equally sexist. Indeed, the Petrie model predicts that such sexism will emerge whenever there is a male majority, and quantifies this majority bias by the ‘Petrie multiplier’: the square of the male/female ratio. In this paper—emulating the shift from ‘normal’ to ‘anomalous’ diffusion—we generalize the Petrie model to a stochastic Poisson model that accommodates heterogeneously sexist men and woman, and that extends the ‘normal’ quadratic Petrie multiplier to ‘anomalous’ non-quadratic multipliers. The Petrie multipliers span a full spectrum of behaviors which we classify into four universal types. A variation of the stochastic Poisson model and its Petrie multipliers is further applied to the context of cyber warfare.
Indian Academy of Sciences (India)
GENERAL I ARTICLE ... In Part 1 of this two-part article, we have seen im- ..... mable logic controller and VLSI arrays, office automation systems, workflow management systems, ... complex discrete event and real-time systems; and Petri nets.
Stochastic quantization of general relativity
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
Following an elementary exposition of the basic mathematical concepts used in the theory of stochastic relaxation processes the stochastic quantization method of Parisi and Wu is briefly reviewed. The method is applied to Einstein's theory of gravitation using a formalism that is manifestly covariant with respect to field redefinitions. This requires the adoption of Ito's calculus and the introduction of a metric in field configuration space, for which there is a unique candidate. Due to the indefiniteness of the Euclidean Einstein-Hilbert action stochastic quantization is generalized to the pseudo-Riemannian case. It is formally shown to imply the DeWitt path integral measure. Finally a new type of perturbation theory is developed. (Author)
Stochastic Generalized Method of Moments
Yin, Guosheng; Ma, Yanyuan; Liang, Faming; Yuan, Ying
2011-01-01
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Stochastic Generalized Method of Moments
Yin, Guosheng
2011-08-16
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 9. Petri Nets - Applications. Y Narahari. General Article Volume 4 Issue 9 September 1999 pp 44-52 ... Author Affiliations. Y Narahari1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560 012, India.
Discrete, continuous, and hybrid petri nets
David, René
2004-01-01
Petri nets do not designate a single modeling formalism. In fact, newcomers to the field confess sometimes to be a little puzzled by the diversity of formalisms that are recognized under this "umbrella". Disregarding some extensions to the theoretical modeling capabilities, and looking at the level of abstraction of the formalisms, Condition/Event, Elementary, Place/Transition, Predicate/Transition, Colored, Object Oriented... net systems are frequently encountered in the literature. On the other side, provided with appropriate interpretative extensions, Controled Net Systems, Marking Diagrams (the Petri net generalization of State Diagrams), or the many-many variants in which time can be explicitly incorporated -Time(d), Deterministic, (Generalized) Stochastic, Fuzzy...- are defined. This represents another way to define practical formalisms that can be obtained by the "cro- product" of the two mentioned dimensions. Thus Petri nets constitute a modeling paradigm, understandable in a broad sense as "the total...
Indian Academy of Sciences (India)
In a computer system, for example, typical discrete events ... This project brought out a series of influential reports on Petri net theory in the mid and late ... Technology became a leading centre for Petri net research and from then on, Petri nets ...
Generalization of stochastic visuomotor rotations.
Directory of Open Access Journals (Sweden)
Hugo L Fernandes
Full Text Available Generalization studies examine the influence of perturbations imposed on one movement onto other movements. The strength of generalization is traditionally interpreted as a reflection of the similarity of the underlying neural representations. Uncertainty fundamentally affects both sensory integration and learning and is at the heart of many theories of neural representation. However, little is known about how uncertainty, resulting from variability in the environment, affects generalization curves. Here we extend standard movement generalization experiments to ask how uncertainty affects the generalization of visuomotor rotations. We find that although uncertainty affects how fast subjects learn, the perturbation generalizes independently of uncertainty.
Fluid Survival Tool: A Model Checker for Hybrid Petri Nets
Postema, Björn Frits; Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Ghasemieh, Hamed
2014-01-01
Recently, algorithms for model checking Stochastic Time Logic (STL) on Hybrid Petri nets with a single general one-shot transition (HPNG) have been introduced. This paper presents a tool for model checking HPNG models against STL formulas. A graphical user interface (GUI) not only helps to
Algorithm for the Stochastic Generalized Transportation Problem
Directory of Open Access Journals (Sweden)
Marcin Anholcer
2012-01-01
Full Text Available The equalization method for the stochastic generalized transportation problem has been presented. The algorithm allows us to find the optimal solution to the problem of minimizing the expected total cost in the generalized transportation problem with random demand. After a short introduction and literature review, the algorithm is presented. It is a version of the method proposed by the author for the nonlinear generalized transportation problem. It is shown that this version of the method generates a sequence of solutions convergent to the KKT point. This guarantees the global optimality of the obtained solution, as the expected cost functions are convex and twice differentiable. The computational experiments performed for test problems of reasonable size show that the method is fast. (original abstract
Coloured Petri Nets and the Invariant Method
DEFF Research Database (Denmark)
Jensen, Kurt
1981-01-01
processes to be described by a common subnet, without losing the ability to distinguish between them. Our generalization, called coloured Petri nets, is heavily influenced by predicate transition-nets introduced by H.J. Genrich and K. Lautenbach. Moreover our paper shows how the invariant-method, introduced...... for Petri nets by K. Lautenbach, can be generalized to coloured Petri nets....
Expansions of general stationary stochastic optical fields: general formalism
International Nuclear Information System (INIS)
Martinez-Herrero, R.; Mejias, P.M.
1985-01-01
A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed
Towards a Standard for Modular Petri Nets
DEFF Research Database (Denmark)
Kindler, Ekkart; Petrucci, Laure
2009-01-01
concepts could or should be subject to import and export in high-level Petri nets. In this paper, we formalise a minimal version of modular high-level Petri nets, which is based on the concepts of modular PNML. This shows that modular PNML can be formalised once a specific version of Petri net is fixed....... Moreover, we present and discuss some more advanced features of modular Petri nets that could be included in the standard. This way, we provide a formal foundation and a basis for a discussion of features to be included in the upcoming standard of a module concept for Petri nets in general and for high-level...
Directory of Open Access Journals (Sweden)
C.Q. Hou
2014-12-01
Full Text Available Livelocks, like deadlocks, can result in the serious problems in running process of flexible manufacturing systems (FMSs as well. Current deadlock control policies based on the approaches of siphon detection and control, cannot cope with livelocks in a system of sequential systems with shared resources (S4R, a typical subclass of Petri nets that can model FMSs. On the basis of the mixed integer programming method, this study proposes a livelock control policy (LCP that can not only solve the new smart siphons (NSSs associated with livelocks or deadlocks in an S4R system directly, but also make the solved NSSs max′-controlled by adding the corresponding control places (CPs. As a result, an original S4R system with livelocks or deadlocks can be turned into the live controlled one in which no NSSs can be found. The related theoretical analysis and several examples are given to demonstrate the proposed LCP. Compared with the existing methods in the literature, the proposed one is more general and powerful.
Generalization of uncertainty relation for quantum and stochastic systems
Koide, T.; Kodama, T.
2018-06-01
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.
A general comparison theorem for backward stochastic differential equations
Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.
2010-01-01
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...
Generalized bounds for convex multistage stochastic programs
Künzi, H; Fandel, G; Trockel, W; Basile, A; Drexl, A; Dawid, H; Inderfurth, K; Kürsten, W; Schittko, U
2005-01-01
This work was completed during my tenure as a scientific assistant and d- toral student at the Institute for Operations Research at the University of St. Gallen. During that time, I was involved in several industry projects in the field of power management, on the occasion of which I was repeatedly c- fronted with complex decision problems under uncertainty. Although usually hard to solve, I quickly learned to appreciate the benefit of stochastic progr- ming models and developed a strong interest in their theoretical properties. Motivated both by practical questions and theoretical concerns, I became p- ticularly interested in the art of finding tight bounds on the optimal value of a given model. The present work attempts to make a contribution to this important branch of stochastic optimization theory. In particular, it aims at extending some classical bounding methods to broader problem classes of practical relevance. This book was accepted as a doctoral thesis by the University of St. Gallen in June 2004.1...
Global synchronization of general delayed complex networks with stochastic disturbances
International Nuclear Information System (INIS)
Tu Li-Lan
2011-01-01
In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito's differential rule and the linear matrix inequality (LMI) optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions. (general)
Diagnostic system based on condition turbogenerator Petri nets
International Nuclear Information System (INIS)
Kachur, S.A.; Shakhova, N.V.
2016-01-01
A stochastic model of the automated monitoring systems and process control turbine generator based on Petri nets, allowing to detect local changes in the state of the stator windings of turbogenerator, is presented in the paper [ru
Pricing decisions in an experimental dynamic stochastic general equilibrium economy
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian dynamic stochastic general equilibrium (DSGE) model. We analyze the behavior of firms’ pricing decisions in four different experimental economies. We consider how
A Stochastic Maximum Principle for General Mean-Field Systems
International Nuclear Information System (INIS)
Buckdahn, Rainer; Li, Juan; Ma, Jin
2016-01-01
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
A Stochastic Maximum Principle for General Mean-Field Systems
Energy Technology Data Exchange (ETDEWEB)
Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)
2016-12-15
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Learning Theory Estimates with Observations from General Stationary Stochastic Processes.
Hang, Hanyuan; Feng, Yunlong; Steinwart, Ingo; Suykens, Johan A K
2016-12-01
This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using gaussian kernels for both least squares and quantile regression. It turns out that for independent and identically distributed (i.i.d.) processes, our learning rates for ERM recover the optimal rates. For non-i.i.d. processes, including geometrically [Formula: see text]-mixing Markov processes, geometrically [Formula: see text]-mixing processes with restricted decay, [Formula: see text]-mixing processes, and (time-reversed) geometrically [Formula: see text]-mixing processes, our learning rates for SVMs with gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called effective number of observations for various mixing processes.
Stochastic abstract policies: generalizing knowledge to improve reinforcement learning.
Koga, Marcelo L; Freire, Valdinei; Costa, Anna H R
2015-01-01
Reinforcement learning (RL) enables an agent to learn behavior by acquiring experience through trial-and-error interactions with a dynamic environment. However, knowledge is usually built from scratch and learning to behave may take a long time. Here, we improve the learning performance by leveraging prior knowledge; that is, the learner shows proper behavior from the beginning of a target task, using the knowledge from a set of known, previously solved, source tasks. In this paper, we argue that building stochastic abstract policies that generalize over past experiences is an effective way to provide such improvement and this generalization outperforms the current practice of using a library of policies. We achieve that contributing with a new algorithm, AbsProb-PI-multiple and a framework for transferring knowledge represented as a stochastic abstract policy in new RL tasks. Stochastic abstract policies offer an effective way to encode knowledge because the abstraction they provide not only generalizes solutions but also facilitates extracting the similarities among tasks. We perform experiments in a robotic navigation environment and analyze the agent's behavior throughout the learning process and also assess the transfer ratio for different amounts of source tasks. We compare our method with the transfer of a library of policies, and experiments show that the use of a generalized policy produces better results by more effectively guiding the agent when learning a target task.
DEFF Research Database (Denmark)
Jensen, Kurt
1987-01-01
The author describes a Petri net model, called coloured Petri nets (CP-nets), by means of which it is possible to describe large systems without having to cope with unnecessary details. The author introduces CP-nets and provide a first impression of their modeling power and the suitability...
Stochastic programming problems with generalized integrated chance constraints
Czech Academy of Sciences Publication Activity Database
Branda, Martin
2012-01-01
Roč. 61, č. 8 (2012), s. 949-968 ISSN 0233-1934 R&D Projects: GA ČR GAP402/10/1610 Grant - others:SVV(CZ) 261315/2010 Institutional support: RVO:67985556 Keywords : chance constraints * integrated chance constraints * penalty functions * sample approximations * blending problem Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.707, year: 2012 http://library.utia.cas.cz/separaty/2012/E/branda-stochastic programming problems with generalized integrated.pdf
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
Directory of Open Access Journals (Sweden)
Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
DEFF Research Database (Denmark)
Westergaard, Michael
2006-01-01
This paper introduces the notion of game coloured Petri nets. This allows the modeler to explicitly model what parts of the model comprise the modeled system and what parts are the environment of the modeled system. We give the formal definition of game coloured Petri nets, a means of reachability...... analysis of this net class, and an application of game coloured Petri nets to automatically generate easy-to-understand visualizations of the model by exploiting the knowledge that some parts of the model are not interesting from a visualization perspective (i.e. they are part of the environment...
Spreading dynamics on complex networks: a general stochastic approach.
Noël, Pierre-André; Allard, Antoine; Hébert-Dufresne, Laurent; Marceau, Vincent; Dubé, Louis J
2014-12-01
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.
Kolmogorov's refined similarity hypotheses for turbulence and general stochastic processes
International Nuclear Information System (INIS)
Stolovitzky, G.; Sreenivasan, K.R.
1994-01-01
Kolmogorov's refined similarity hypotheses are shown to hold true for a variety of stochastic processes besides high-Reynolds-number turbulent flows, for which they were originally proposed. In particular, just as hypothesized for turbulence, there exists a variable V whose probability density function attains a universal form. Analytical expressions for the probability density function of V are obtained for Brownian motion as well as for the general case of fractional Brownian motion---the latter under some mild assumptions justified a posteriori. The properties of V for the case of antipersistent fractional Brownian motion with the Hurst exponent of 1/3 are similar in many details to those of high-Reynolds-number turbulence in atmospheric boundary layers a few meters above the ground. The one conspicuous difference between turbulence and the antipersistent fractional Brownian motion is that the latter does not possess the required skewness. Broad implications of these results are discussed
Wingender, E
2011-01-01
It was suggested some years ago that Petri nets might be well suited to modeling metabolic networks, overcoming some of the limitations encountered by the use of systems employing ODEs (ordinary differential equations). Much work has been done since then which confirms this and demonstrates the usefulness of this concept for systems biology. Petri net technology is not only intuitively understood by scientists trained in the life sciences, it also has a robust mathematical foundation and provides the required degree of flexibility. As a result it appears to be a very promising approach to mode
Davidson's generalization of the Fenyes-Nelson stochastic model of quantum mechanics
International Nuclear Information System (INIS)
Shucker, D.S.
1980-01-01
Davidson's generalization of the Fenyes-Nelson stochastic model of quantum mechanics is discussed. It is shown that this author's previous results concerning the Fenyes-Nelson process extend to the more general theory of Davidson. (orig.)
The ePNK: An Extensible Petri Net Tool for PNML
DEFF Research Database (Denmark)
Kindler, Ekkart
2011-01-01
The Petri Net Markup Language (PNML) is an XML-based interchange format for all kinds of Petri nets, which is an ISO/IEC International Standard 15909-2 now. The focus of this standard is on PNML as an interchange format for high-level Petri nets. PNML, however, is more general and allows exchanging...
DEFF Research Database (Denmark)
Jensen, Kurt
1991-01-01
This paper describes how Coloured Petri Nets (CP-nets) have been developed — from being a promising theoretical model to being a full-fledged language for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and...
Jensen, Kurt
2009-01-01
Coloured Petri Nets (CPN) is a graphical language for modelling and validating concurrent and distributed systems, and other systems in which concurrency plays a major role. This book introduces the constructs of the CPN modelling language and presents the related analysis methods. It provides a comprehensive road map for the practical use of CPN.
DEFF Research Database (Denmark)
Jensen, Kurt; Kristensen, Lars Michael
Coloured Petri Nets (CPN) is a graphical language for modelling and validating concurrent and distributed systems, and other systems in which concurrency plays a major role. The development of such systems is particularly challenging because of inherent intricacies like possible nondeterminism an...
Semi-analytical stochastic analysis of the generalized van der Pol system
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
(2018) ISSN 1802-680X R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : stochastic stability * generalized van der Pol system * stochastic averaging * limit cycles Subject RIV: JM - Building Engineering OBOR OECD: Construction engineering, Municipal and structural engineering https://www.kme.zcu.cz/acm/acm/article/view/407
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
Linearly convergent stochastic heavy ball method for minimizing generalization error
Loizou, Nicolas; Richtarik, Peter
2017-01-01
In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss
Stochastic resonance in a generalized Von Foerster population growth model
Energy Technology Data Exchange (ETDEWEB)
Lumi, N.; Mankin, R. [Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn (Estonia)
2014-11-12
The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.
Linearly convergent stochastic heavy ball method for minimizing generalization error
Loizou, Nicolas
2017-10-30
In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder problem. While in the analysis we constrain ourselves to quadratic loss, the overall objective is not necessarily strongly convex.
General no-go condition for stochastic pumping
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel; Thomas, S.R.
2010-01-01
Roč. 132, č. 23 (2010), 234116/1-234116/6 ISSN 0021-9606 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520 Keywords : stochastic pumps * molecular motors * non-Markov dynamics Subject RIV: BE - Theoretical Physics Impact factor: 2.920, year: 2010 http://jcp.aip.org/jcpsa6/v132/i23/p234116_s1
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
International Nuclear Information System (INIS)
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-01-01
This article introduces the notion of generalized Poisson–Kac (GPK) processes which generalize the class of ‘telegrapher’s noise dynamics’ introduced by Kac (1974 Rocky Mount. J. Math . 4 497) in 1974, using Poissonian stochastic perturbations. In GPK processes the stochastic perturbation acts as a switching amongst a set of stochastic velocity vectors controlled by a Markov-chain dynamics. GPK processes possess trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the convergence towards Brownian motion (and to stochastic dynamics driven by Wiener perturbations), which characterizes also the long-term/long-distance properties of these processes. In this article we introduce the structural properties of GPK processes, leaving all the physical implications to part II and part III (Giona et al 2016a J. Phys. A: Math. Theor ., 2016b J. Phys. A: Math. Theor .). (paper)
DEFF Research Database (Denmark)
Engberg, Uffe Henrik; Winskel, Glynn
This article shows how individual Petri nets form models of Girard's intuitionistic linear logic. It explores questions of expressiveness and completeness of linear logic with respect to this interpretation. An aim is to use Petri nets to give an understanding of linear logic and give some apprai...
Determinization of timed Petri nets behaviors
Czech Academy of Sciences Publication Activity Database
Komenda, Jan; Lahaye, S.; Boimond, J.-L.
2016-01-01
Roč. 26, č. 3 (2016), s. 413-437 ISSN 0924-6703 R&D Projects: GA MŠk LH13012; GA ČR GA15-02532S Institutional support: RVO:67985840 Keywords : timed Petri nets * (max,+) automata * determinization Subject RIV: BA - General Mathematics Impact factor: 1.660, year: 2016 http://link.springer.com/article/10.1007%2Fs10626-015-0214-1
Control of Petri Nets by finite automata
Energy Technology Data Exchange (ETDEWEB)
Burkhard, H D
1983-01-01
Petri Nets are considered where the firings are controlled by finite automata. The control may be distributed to various automata working over disjoint sets of transitions. To avoid deadlocks and conflicts for the whole system the distribution of control must be organised in an appropriate manner. The existence of deadlocks and conflicts is shown to be undecidable in general, but conflict resolving and deadlock free controls can be constructed for given nets. 10 references.
Annotating Coloured Petri Nets
DEFF Research Database (Denmark)
Lindstrøm, Bo; Wells, Lisa Marie
2002-01-01
Coloured Petri nets (CP-nets) can be used for several fundamentally different purposes like functional analysis, performance analysis, and visualisation. To be able to use the corresponding tool extensions and libraries it is sometimes necessary to include extra auxiliary information in the CP......-net. An example of such auxiliary information is a counter which is associated with a token to be able to do performance analysis. Modifying colour sets and arc inscriptions in a CP-net to support a specific use may lead to creation of several slightly different CP-nets – only to support the different uses...... of the same basic CP-net. One solution to this problem is that the auxiliary information is not integrated into colour sets and arc inscriptions of a CP-net, but is kept separately. This makes it easy to disable this auxiliary information if a CP-net is to be used for another purpose. This paper proposes...
The response analysis of fractional-order stochastic system via generalized cell mapping method.
Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei
2018-01-01
This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.
DEFF Research Database (Denmark)
various journals and collections. As a result, much of this knowledge is not readily available to people who may be interested in using high-level nets. Within the Petri net community this problem has been discussed many times, and as an outcome this book has been compiled. The book contains reprints...... of some of the most important papers on the application and theory of high-level Petri nets. In this way it makes the relevant literature more available. It is our hope that the book will be a useful source of information and that, e.g., it can be used in the organization of Petri net courses. To make......High-level Petri nets are now widely used in both theoretical analysis and practical modelling of concurrent systems. The main reason for the success of this class of net models is that they make it possible to obtain much more succinct and manageable descriptions than can be obtained by means...
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
2011-01-01
New Keynesian dynamic stochastic general equilibrium models are the principal paradigm currently employed for central bank policymaking. In this paper, we construct experimental economies, populated with human subjects, with the structure of a New Keynesian DSGE model. We give individuals monetary
Barbagallo, Annamaria; Di Meglio, Guglielmo; Mauro, Paolo
2017-07-01
The aim of the paper is to study, in a Hilbert space setting, a general random oligopolistic market equilibrium problem in presence of both production and demand excesses and to characterize the random Cournot-Nash equilibrium principle by means of a stochastic variational inequality. Some existence results are presented.
A generalization of Fenyes-Nelson stochastic model of quantum mechanics
International Nuclear Information System (INIS)
Davidson, M.
1979-01-01
It is shown that the stochastic model of Fenyes and Nelson can be generalized in such a way that the diffusion constant of the Markov theory becomes a free parameter. This extra freedom allows one to identify quantum mechanics with a class of Markov processes with diffusion constants varying from 0 to infinity. (Auth.)
Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience
Directory of Open Access Journals (Sweden)
Yan Chen
2017-01-01
Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.
Han, Qun; Xu, Wei; Sun, Jian-Qiao
2016-09-01
The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.
A General Stochastic Maximum Principle for SDEs of Mean-field Type
International Nuclear Information System (INIS)
Buckdahn, Rainer; Djehiche, Boualem; Li Juan
2011-01-01
We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng’s-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966–979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng’s stochastic maximum principle.
Tamellini, L.; Le Maî tre, O.; Nouy, A.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
The propagation of travelling waves for stochastic generalized KPP equations
International Nuclear Information System (INIS)
Elworthy, K.D.; Zhao, H.Z.
1993-09-01
We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, milk, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the appendix J.G. Gaines illustrates these different regimes by computer simulations. (author). 27 refs, 13 figs
Energy Technology Data Exchange (ETDEWEB)
Harko, Tiberiu [University College London, Department of Mathematics, London (United Kingdom); Leung, Chun Sing [Polytechnic University, Department of Applied Mathematics, Hong Kong (China); Mocanu, Gabriela [Babes-Bolyai University, Faculty of Physics, Cluj-Napoca (Romania)
2014-05-15
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)
International Nuclear Information System (INIS)
Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela
2014-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)
Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela
2014-05-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.
Special Section on Coloured Petri Nets
DEFF Research Database (Denmark)
1998-01-01
Special section on coloured Petri nets, their basic concepts, analysis methods, tool support and industrial applications.......Special section on coloured Petri nets, their basic concepts, analysis methods, tool support and industrial applications....
Simulation of the chemical stage in water radiolysis with the help of Continuous Petri nets
International Nuclear Information System (INIS)
Barilla, J.; Lokajíček, M.V.; Pisaková, H.; Simr, P.
2014-01-01
The final biological effect of ionizing particles may be influenced often strongly by some chemical substances present in cells during irradiation by low-LET radiation. It may occur during the chemical stage of the given process, due to chemical reactions of radicals running in the given process. However, the whole chemical process may be hardly described sufficiently with the help of the usual approach based on the deterministic diffusion-kinetic computations and the stochastic Monte-Carlo simulations. We have proposed already earlier a model describing the processes (i.e., the combined effect of cluster diffusion and chemical reactions) running in individual radical clusters that might be responsible for corresponding damages of DNA molecules (i.e., formation of DSBs). Now a further generalization of the given model (using Continuous Petri nets) will be presented that makes it possible to characterize more detailed behavior of individual radicals in corresponding clusters, which might be useful especially for low-LET radiation when individual radical clusters meet a DNA molecule at different time intervals after their formation; the decreasing presence of individual radicals in corresponding clusters being established. In this paper we shall focus on the design of the corresponding mathematical model and its application; the comparison of corresponding results with experimental data obtained in the case of deoxygenated system will be presented. - Highlights: • Creation of the mathematical model. • Realization of the model with the help of Continuous Petri nets. • Obtain the time dependence of changes in the concentration of radicals
Reachability Trees for High-level Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt; Jensen, Arne M.; Jepsen, Leif Obel
1986-01-01
the necessary analysis methods. In other papers it is shown how to generalize the concept of place- and transition invariants from place/transition nets to high-level Petri nets. Our present paper contributes to this with a generalization of reachability trees, which is one of the other important analysis...
Putting Petri nets to work in Industry
Aalst, van der W.M.P.
1994-01-01
Petri nets exist for over 30 years. Especially in the last decade Petri nets have been put into practive extensively. Thanks to several useful extensions and the availability of computer tools, Petri nets have become a mature tool for modelling and analysing industrial systems. This paper describes
Delta Semantics Defined By Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt; Kyng, Morten; Madsen, Ole Lehrmann
and the possibility of using predicates to specify state changes. In this paper a formal semantics for Delta is defined and analysed using Petri nets. Petri nets was chosen because the ideas behind Petri nets and Delta concide on several points. A number of proposals for changes in Delta, which resulted from...
Petri Nets in Cryptographic Protocols
DEFF Research Database (Denmark)
Crazzolara, Federico; Winskel, Glynn
2001-01-01
A process language for security protocols is presented together with a semantics in terms of sets of events. The denotation of process is a set of events, and as each event specifies a set of pre and postconditions, this denotation can be viewed as a Petri net. By means of an example we illustrate...
Non-cooperative stochastic differential game theory of generalized Markov jump linear systems
Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning
2017-01-01
This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...
Pecevski, Dejan; Buesing, Lars; Maass, Wolfgang
2011-12-01
An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows ("explaining away") and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.
Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang
2017-09-01
A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 extinct with probability one, whereas if R0 > 1, then the system remains permanent in the mean.
Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states
International Nuclear Information System (INIS)
Moodley, Mervlyn; Nsio Nzundu, T; Paul, S
2012-01-01
We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)
The Petri Net Markup Language : concepts, technology, and tools
Billington, J.; Christensen, S.; Hee, van K.M.; Kindler, E.; Kummer, O.; Petrucci, L.; Post, R.D.J.; Stehno, C.; Weber, M.; Aalst, van der W.M.P.; Best, E.
2003-01-01
The Petri Net Markup Language (PNML) is an XML-based interchange format for Petri nets. In order to support different versions of Petri nets and, in particular, future versions of Petri nets, PNML allows the definition of Petri net types.Due to this flexibility, PNML is a starting point for a
Application and Theory of Petri Nets
DEFF Research Database (Denmark)
This volume contains the proceedings of the 13th International Conference onApplication and Theory of Petri Nets, held in Sheffield, England, in June 1992. The aim of the Petri net conferences is to create a forum for discussing progress in the application and theory of Petri nets. Typically....... Balbo and W. Reisig, 18 submitted papers, and seven project papers. The submitted papers and project presentations were selectedby the programme committee and a panel of referees from a large number of submissions....
Modeling integrated cellular machinery using hybrid Petri-Boolean networks.
Directory of Open Access Journals (Sweden)
Natalie Berestovsky
Full Text Available The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them
Multi-choice stochastic transportation problem involving general form of distributions.
Quddoos, Abdul; Ull Hasan, Md Gulzar; Khalid, Mohammad Masood
2014-01-01
Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.
Ren, Jiagang; Wu, Jing; Zhang, Hua
2015-01-01
In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.
Dependencies in event trees analyzed by Petri nets
International Nuclear Information System (INIS)
Nývlt, Ondřej; Rausand, Marvin
2012-01-01
This paper discusses how non-marked Petri nets can be used to model and analyze event trees where the pivotal (branching) events are dependent and modeled by fault trees. The dependencies may, for example, be caused by shared utilities, shared components, or general common cause failures that are modeled by beta-factor models. These dependencies are cumbersome to take into account when using standard event-/fault tree modeling techniques, and may lead to significant errors in the calculated end-state probabilities of the event tree if they are not properly analyzed. A new approach is proposed in this paper, where the whole event tree is modeled by a non-marked Petri net and where P-invariants, representing the structural properties of the Petri net, are used to obtain the frequency of each end-state of the event tree with dependencies. The new approach is applied to a real example of an event tree analysis of the Strahov highway tunnel in Prague, Czech Republic, including two types of dependencies (shared Programmable Logic Controllers and Common Cause Failures). - Highlights: ► In this paper, we model and analyze event trees (ET) using Petri nets. ► The pivotal events of the modeled event trees are dependent (e.g., shared PLCs, CCF). ► A new method based on P-invariants to obtain probabilities of end states is proposed. ► Method is shown in the case study of the Stahov tunnel in the Czech Republic.
Pecevski, Dejan; Buesing, Lars; Maass, Wolfgang
2011-01-01
An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows (“explaining away”) and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons. PMID:22219717
Directory of Open Access Journals (Sweden)
Dejan Pecevski
2011-12-01
Full Text Available An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows ("explaining away" and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.
Extinction time of a stochastic predator-prey model by the generalized cell mapping method
Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao
2018-03-01
The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.
Gasevic, Dragan; Devedzic, Vladan
2004-01-01
This paper presents Petri net software tool P3 that is developed for training purposes of the Architecture and organization of computers (AOC) course. The P3 has the following features: graphical modeling interface, interactive simulation by single and parallel (with previous conflict resolution) transition firing, two well-known Petri net…
Flinders Petrie and Eugenics at UCL
Directory of Open Access Journals (Sweden)
Kathleen L. Sheppard
2010-05-01
Full Text Available William Matthew Flinders Petrie is considered the father of scientific archaeology and is credited with developing a chronology of Ancient Egypt using the nondescript artefacts that other archaeologists had ignored. He occupied the first chair of Egyptology in England, and was also well-known for the museum built around his personal collection of Egyptian artifacts at University College London. Petrie's archaeological work has been studied by scholars, from various disciplines, for its scholarly, cultural, and historical value, while Petrie's life and career outside of archaeology have been the subject of relatively little study. Petrie himself wrote two life stories: the first, 'Ten Years Digging in Egypt, 1881–1891' (1892, detailed the years before his professorship at UCL; in 1932 he published his second, more complete autobiography, 'Seventy Years in Archaeology'. After he died in 1942 there were various obituaries and memorials that outlined his life and major achievements in archaeology. There was very little written about Petrie the man until 1985, when Margaret Drower's 'Flinders Petrie: A Life in Archaeology' was published; it remains the most comprehensive work on Petrie's life. A thin volume of the correspondence of Hilda and Flinders Petrie also allows a glimpse into life on excavation. In short, much of what is known about Petrie focuses on his excavations in Egypt, his time as Professor of Egyptology at University College London, or the museum that bears his name. Subsequently, as a historical matter, Petrie's work in the discipline of eugenics has rarely been discussed as part of his career.
Threat driven modeling framework using petri nets for e-learning system.
Khamparia, Aditya; Pandey, Babita
2016-01-01
Vulnerabilities at various levels are main cause of security risks in e-learning system. This paper presents a modified threat driven modeling framework, to identify the threats after risk assessment which requires mitigation and how to mitigate those threats. To model those threat mitigations aspects oriented stochastic petri nets are used. This paper included security metrics based on vulnerabilities present in e-learning system. The Common Vulnerability Scoring System designed to provide a normalized method for rating vulnerabilities which will be used as basis in metric definitions and calculations. A case study has been also proposed which shows the need and feasibility of using aspect oriented stochastic petri net models for threat modeling which improves reliability, consistency and robustness of the e-learning system.
Symmetric Cryptosystem Based on Petri Net
Directory of Open Access Journals (Sweden)
Hussein A. Lafta
2017-12-01
Full Text Available In this wok, a novel approach based on ordinary Petri net is used to generate private key . The reachability marking of petri net is used as encryption/decryption key to provide more complex key . The same ordinary Petri Nets models are used for the sender(encryption and the receiver(decryption.The plaintext has been permutated using look-up table ,and XOR-ed with key to generate cipher text
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-08-01
In this second part, we analyze the dissipation properties of generalized Poisson-Kac (GPK) processes, considering the decay of suitable L 2-norms and the definition of entropy functions. In both cases, consistent energy dissipation and entropy functions depend on the whole system of primitive statistical variables, the partial probability density functions \\{ p_α({x}, t) \\}α=1N , while the corresponding energy dissipation and entropy functions based on the overall probability density p({x}, t) do not satisfy monotonicity requirements as a function of time. These results provide new insights on the theory of Markov operators associated with irreversible stochastic dynamics. Examples from chaotic advection (standard map coupled to stochastic GPK processes) illustrate this phenomenon. Some complementary physical issues are also addressed: the ergodicity breaking in the presence of attractive potentials, and the use of GPK perturbations to mollify stochastic field equations.
Modeling of system reliability Petri nets with aging tokens
International Nuclear Information System (INIS)
Volovoi, V.
2004-01-01
The paper addresses the dynamic modeling of degrading and repairable complex systems. Emphasis is placed on the convenience of modeling for the end user, with special attention being paid to the modeling part of a problem, which is considered to be decoupled from the choice of solution algorithms. Depending on the nature of the problem, these solution algorithms can include discrete event simulation or numerical solution of the differential equations that govern underlying stochastic processes. Such modularity allows a focus on the needs of system reliability modeling and tailoring of the modeling formalism accordingly. To this end, several salient features are chosen from the multitude of existing extensions of Petri nets, and a new concept of aging tokens (tokens with memory) is introduced. The resulting framework provides for flexible and transparent graphical modeling with excellent representational power that is particularly suited for system reliability modeling with non-exponentially distributed firing times. The new framework is compared with existing Petri-net approaches and other system reliability modeling techniques such as reliability block diagrams and fault trees. The relative differences are emphasized and illustrated with several examples, including modeling of load sharing, imperfect repair of pooled items, multiphase missions, and damage-tolerant maintenance. Finally, a simple implementation of the framework using discrete event simulation is described
Directory of Open Access Journals (Sweden)
Ivo Martiník
2015-01-01
Full Text Available Rich-media describes a broad range of digital interactive media that is increasingly used in the Internet and also in the support of education. Last year, a special pilot audiovisual lecture room was built as a part of the MERLINGO (MEdia-rich Repository of LearnING Objects project solution. It contains all the elements of the modern lecture room determined for the implementation of presentation recordings based on the rich-media technologies and their publication online or on-demand featuring the access of all its elements in the automated mode including automatic editing. Property-preserving Petri net process algebras (PPPA were designed for the specification and verification of the Petri net processes. PPPA does not need to verify the composition of the Petri net processes because all their algebraic operators preserve the specified set of the properties. These original PPPA are significantly generalized for the newly introduced class of the SNT Petri process and agent nets in this paper. The PLACE-SUBST and ASYNC-PROC algebraic operators are defined for this class of Petri nets and their chosen properties are proved. The SNT Petri process and agent nets theory were significantly applied at the design, verification, and implementation of the programming system ensuring the pilot audiovisual lecture room functionality.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-08-01
This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.
International Nuclear Information System (INIS)
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-01-01
This third part extends the theory of Generalized Poisson–Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker–Planck–Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed. (paper)
Bouchard , Bruno; Dang , Ngoc Minh
2013-01-01
International audience; We consider a singular with state constraints version of the stochastic target problems studied in Soner and Touzi (2002) and more recently Bouchard, Elie and Touzi (2008), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly suits to market models with proportional transaction costs and to order book liquidation issues. Our main result is a PDE characterization of the associated pri...
International Nuclear Information System (INIS)
Nemnes, G A; Anghel, D V
2010-01-01
We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of canonical ensembles. This approach introduces a tool for describing interacting fermionic and bosonic systems in non-equilibrium as ideal FES systems, in a computationally efficient manner. The two types of statistics are analyzed comparatively, indicating their intrinsic thermodynamic differences and revealing key aspects related to the species size
Stochastic Petri Net Modeling of Wave Sequences in Cardiac Arrhythmias.
1987-11-01
Wolff - Parkinson - White syndrome . The ventricles are divided into two parts. One of these is excited normally and produces R...example, in a condition called the Wolff - Parkinson - White syn- drome the ECG displays an abnormally early onset of the ventricular activity. It also...8217. , ’ ", -’ , .’ %,,? .’ ,; ’ .- ’ ’ -’ € ’ , . ’ - I. 32 Wolfe- Parkinson - White Syndrome (Fig. 8c) This model uses "basic" elements for the
Flache, A.
2002-01-01
Concerns about models of cultural adaptation as analogs of genetic selection have led cognitive game theorists to explore learning-theoretic specifications. Two prominent examples, the Bush-Mosteller stochastic learning model and the Roth-Erev payoff-matching model, are aligned and integrated as
International Nuclear Information System (INIS)
Menezes, G.; Svaiter, N.F.
2006-04-01
We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)
International Nuclear Information System (INIS)
Pham, Nhu Viet Ha
2011-02-01
To predict the space-time dependent behavior of a nuclear reactor, the conventional space-dependent kinetics equations are widely used for treating the spatial variables. However, the solutions of such deterministic space-dependent kinetics equations, which give only the mean values of the neutron population and the delayed neutron precursor concentrations, do not offer sufficient insight into the actual dynamic processes within a reactor, where the interacting populations vary randomly with space and time. It is also noted that at high power levels, the random behavior of a reactor is negligible but at low power levels, such as at start-up, random fluctuations in population dynamics can be significant. To mathematically describe the evolution of the state of a nuclear reactor using a set of stochastic kinetics equations, the forward stochastic model (FSM) in stochastic kinetics theory is devised through the concept of reactor transition probability and its probability generating function as the spatial domain of a reactor is partitioned into a number of space cells. Nevertheless, the FSM equations for the mean value of neutron and precursor distribution are deterministic-like. Furthermore, the numerical treatment of the FSM equations for the means, variances, and covariances is quite complicated and time-consuming. In the present study, a generalized stochastic model (called the stochastic space-dependent kinetics model or SSKM) based on the FSM and the Its stochastic differential equations was newly developed for the analysis of monoenergetic spacetime nuclear reactor kinetics in one dimension. First, the FSM equations for determining the mean values of neutron and delayed-neutron precursor populations were considered as the deterministic ones without taking into account their variances and covariances. Second, the system of interest was randomized again in the light of the Its stochastic differential equations in order to derive the SSKM. The proposed model
State Space Methods for Timed Petri Nets
DEFF Research Database (Denmark)
Christensen, Søren; Jensen, Kurt; Mailund, Thomas
2001-01-01
it possible to condense the usually infinite state space of a timed Petri net into a finite condensed state space without loosing analysis power. The second method supports on-the-fly verification of certain safety properties of timed systems. We discuss the application of the two methods in a number......We present two recently developed state space methods for timed Petri nets. The two methods reconciles state space methods and time concepts based on the introduction of a global clock and associating time stamps to tokens. The first method is based on an equivalence relation on states which makes...
Transactions on Petri Nets and Other Models of Concurrency VII
DEFF Research Database (Denmark)
The first section is concerned with the creation of Petri net models and their validation The second section addresses semantic issues and analysis methods The third section is devoted to the automatic synthesis of Petri nets These Transactions publish archival papers in the broad area of Petri n...
Transactions on Petri Nets and Other Models of Concurrency V
DEFF Research Database (Denmark)
submission track of ToPNoC. The 12 papers cover a diverse range of topics including model checking and system verification, synthesis, foundational work on specific classes of Petri nets, and innovative applications of Petri nets and other models of concurrency. Thus, this volume gives a good view of ongoing...... concurrent systems and Petri nets research...
Chai, Bian-fang; Yu, Jian; Jia, Cai-Yan; Yang, Tian-bao; Jiang, Ya-wen
2013-07-01
Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.
Robust modelling and simulation integration of SIMIO with coloured petri nets
De La Mota, Idalia Flores; Mujica Mota, Miguel; Angel Piera, Miquel
2017-01-01
This book presents for the first time a methodology that combines the power of a modelling formalism such as colored petri nets with the flexibility of a discrete event program such as SIMIO. Industrial practitioners have seen the growth of simulation as a methodology for tacking problems in which variability is the common denominator. Practically all industrial systems, from manufacturing to aviation are considered stochastic systems. Different modelling techniques have been developed as well as mathematical techniques for formalizing the cause-effect relationships in industrial and complex systems. The methodology in this book illustrates how complexity in modelling can be tackled by the use of coloured petri nets, while at the same time the variability present in systems is integrated in a robust fashion. The book can be used as a concise guide for developing robust models, which are able to efficiently simulate the cause-effect relationships present in complex industrial systems without losing the simulat...
Macian-Sorribes, Hector; Pulido-Velazquez, Manuel; Tilmant, Amaury
2015-04-01
Stochastic programming methods are better suited to deal with the inherent uncertainty of inflow time series in water resource management. However, one of the most important hurdles in their use in practical implementations is the lack of generalized Decision Support System (DSS) shells, usually based on a deterministic approach. The purpose of this contribution is to present a general-purpose DSS shell, named Explicit Stochastic Programming Advanced Tool (ESPAT), able to build and solve stochastic programming problems for most water resource systems. It implements a hydro-economic approach, optimizing the total system benefits as the sum of the benefits obtained by each user. It has been coded using GAMS, and implements a Microsoft Excel interface with a GAMS-Excel link that allows the user to introduce the required data and recover the results. Therefore, no GAMS skills are required to run the program. The tool is divided into four modules according to its capabilities: 1) the ESPATR module, which performs stochastic optimization procedures in surface water systems using a Stochastic Dual Dynamic Programming (SDDP) approach; 2) the ESPAT_RA module, which optimizes coupled surface-groundwater systems using a modified SDDP approach; 3) the ESPAT_SDP module, capable of performing stochastic optimization procedures in small-size surface systems using a standard SDP approach; and 4) the ESPAT_DET module, which implements a deterministic programming procedure using non-linear programming, able to solve deterministic optimization problems in complex surface-groundwater river basins. The case study of the Mijares river basin (Spain) is used to illustrate the method. It consists in two reservoirs in series, one aquifer and four agricultural demand sites currently managed using historical (XIV century) rights, which give priority to the most traditional irrigation district over the XX century agricultural developments. Its size makes it possible to use either the SDP or
Yin, Fancheng; Yu, Xiaoyan
2015-01-01
This paper is concerned with the existence of stationary distribution and extinction for multispecies stochastic Lotka-Volterra predator-prey system. The contributions of this paper are as follows. (a) By using Lyapunov methods, the sufficient conditions on existence of stationary distribution and extinction are established. (b) By using the space decomposition technique and the continuity of probability, weaker conditions on extinction of the system are obtained. Finally, a numer...
Petri Nets as Models of Linear Logic
DEFF Research Database (Denmark)
Engberg, Uffe Henrik; Winskel, Glynn
1990-01-01
The chief purpose of this paper is to appraise the feasibility of Girad's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic...
A Brief Introduction to Coloured Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1997-01-01
Coloured Petri Nets (CP-nets or CPN) is a graphical oriented language for design, specification, simulation and verification of systems. It is in particular well- suited for systems in which communication, synchronisation and resource sharing are important. Typical examples of application areas a...
Verification of Timed-Arc Petri Nets
DEFF Research Database (Denmark)
Jacobsen, Lasse; Jacobsen, Morten; Møller, Mikael Harkjær
2011-01-01
of interesting theoretical properties distinguishing them from other time extensions of Petri nets. We shall give an overview of the recent theory developed in the verification of TAPN extended with features like read/transport arcs, timed inhibitor arcs and age invariants. We will examine in detail...
Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel
2012-06-01
We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.
DEA models equivalent to general Nth order stochastic dominance efficiency tests
Czech Academy of Sciences Publication Activity Database
Branda, Martin; Kopa, Miloš
2016-01-01
Roč. 44, č. 2 (2016), s. 285-289 ISSN 0167-6377 R&D Projects: GA ČR GA13-25911S; GA ČR GA15-00735S Grant - others:GA ČR(CZ) GA15-02938S Institutional support: RVO:67985556 Keywords : Nth order stochastic dominance efficiency * Data envelopment analysis * Convex NSD efficiency * NSD portfolio efficiency Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.657, year: 2016 http://library.utia.cas.cz/separaty/2016/E/branda-0458120.pdf
International Nuclear Information System (INIS)
Krommes, J.A.; Kleva, R.G.; Oberman, C.
1978-05-01
A systematic theory is developed for the computation of electron transport in stochastic magnetic fields. Small scale magnetic perturbations arising, for example, from finite-β micro-instabilities are assumed to destroy the flux surfaces of a standard tokamak equilibrium. Because the magnetic lines then wander in a volume, electron radial flux is enhanced due to the rapid particle transport along as well as across the lines. By treating the magnetic lines as random variables, it is possible to develop a kinetic equation for the electron distribution function. This is solved approximately to yield the diffusion coefficient
Energy Technology Data Exchange (ETDEWEB)
Krommes, J.A.; Kleva, R.G.; Oberman, C.
1978-05-01
A systematic theory is developed for the computation of electron transport in stochastic magnetic fields. Small scale magnetic perturbations arising, for example, from finite-..beta.. micro-instabilities are assumed to destroy the flux surfaces of a standard tokamak equilibrium. Because the magnetic lines then wander in a volume, electron radial flux is enhanced due to the rapid particle transport along as well as across the lines. By treating the magnetic lines as random variables, it is possible to develop a kinetic equation for the electron distribution function. This is solved approximately to yield the diffusion coefficient.
Directory of Open Access Journals (Sweden)
Wang Yajun
2008-12-01
Full Text Available In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method (SFEM based on the harmonious finite element (HFE technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.
Directory of Open Access Journals (Sweden)
Dan Ye
2013-01-01
Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.
Automatic pipeline operation using Petri Nets
Energy Technology Data Exchange (ETDEWEB)
Moreira, Guilherme O. [PETROBRAS TRANSPORTE S.A., Rio de Janeiro, RJ (Brazil)
2009-07-01
A pipeline operation requires several actions, attention and time from the control room operator in each of its operating phases. This article proposition is to use automation as something more than a remote control, drastically reducing the number of repetitive and routine actions needed from the operator to start and stop the system, granting more time for system supervision, decision making during critical conditions and avoiding errors caused due to the need of several actions being executed in a short period of time. To achieve these objectives the pipeline operation will be modeled as a Petri Net consisting of states, event and actions. A methodology for converting this Petri Net into a Ladder controller code will also be proposed. (author)
Towards Self-Managed Executable Petri Nets
DEFF Research Database (Denmark)
Hansen, Klaus Marius; Zhang, Weishan; Ingstrup, Mads
2008-01-01
An issue in self-managed systems is that different abstractions and programming models are used on different architectural layers, leading to systems that are harder to build and understand. To alleviate this, we introduce a self-management approach which combines high-level Petri nets...... with the capability of distributed communication among nets. Organized in a three-layer goal management, change management, and component control architecture this allows for self-management in distributed systems. We validate the approach through the Flamenco/CPN middleware that allows for self-management of service......-oriented pervasive computing systems through the runtime interpretation of colored Petri nets. The current work focuses on the change management and component control layers....
Performance Analysis using Coloured Petri Nets
DEFF Research Database (Denmark)
Wells, Lisa Marie
Performance is often a central issue in the design, development, and configuration of systems. It is not always enough to know that systems work properly, they must also work effectively. There are numerous studies, e.g. in the areas of computer and telecommunication systems, manufacturing......, military, health care, and transportation, that have shown that time, money, and even lives can be saved if the performance of a system is improved. Performance analysis studies are conducted to evaluate existing or planned systems, to compare alternative configurations, or to find an optimal configuration...... of a system. There are three alternative techniques for analysing the performance of a system: measurement, analytical models, and simulation models. This dissertation focuses on the the use of coloured Petri nets for simulationbased performance analysis of industrial-sized systems. Coloured Petri nets...
A Petri Nets Model for Blockchain Analysis
Pinna, Andrea; Tonelli, Roberto; Orrú, Matteo; Marchesi, Michele
2017-01-01
A Blockchain is a global shared infrastructure where cryptocurrency transactions among addresses are recorded, validated and made publicly available in a peer- to-peer network. To date the best known and important cryptocurrency is the bitcoin. In this paper we focus on this cryptocurrency and in particular on the modeling of the Bitcoin Blockchain by using the Petri Nets formalism. The proposed model allows us to quickly collect information about identities owning Bitcoin addresses and to re...
Modeling of Biometric Identification System Using the Colored Petri Nets
Petrosyan, G. R.; Ter-Vardanyan, L. A.; Gaboutchian, A. V.
2015-05-01
In this paper we present a model of biometric identification system transformed into Petri Nets. Petri Nets, as a graphical and mathematical tool, provide a uniform environment for modelling, formal analysis, and design of discrete event systems. The main objective of this paper is to introduce the fundamental concepts of Petri Nets to the researchers and practitioners, both from identification systems, who are involved in the work in the areas of modelling and analysis of biometric identification types of systems, as well as those who may potentially be involved in these areas. In addition, the paper introduces high-level Petri Nets, as Colored Petri Nets (CPN). In this paper the model of Colored Petri Net describes the identification process much simpler.
International Nuclear Information System (INIS)
Mechitoua, Boukhmes
2001-01-01
This paper shows what can be the stochastic neutronic contribution for the interpretation of criticality accidents. Stochastic neutronic comprehensive texts may be found in refs.1 through 4. We limit our study to the use of initiation probability, which is an important stochastic neutronic tally. Initiation probability P may be defined as the probability for one neutron to initiate an infinite neutron fission chain. The complement probability of P is the extinction probability Q. The probability that the neutron fission chain produced by one neutron will quench is equal to the multiplication of the probability of production of i neutrons g i by the probability of extinction of these i neutrons. We can estimate P by a Newton or by a dichotomic method. We suppose that P S (t) is the probability that an infinite neutron fission chain has been initiated before time t by a neutron produced by the source S(t). P S (t + dt) is the sum of two probabilities: 1. the probability that an infinite neutron fission chain has been initiated before time t by a neutron produced by the source S(t): P S (t); 2. The second probability is a multiplication of two probabilities: the probability that there was no initiation before t that is 1-P S (t), and the probability that a neutron emitted by the source with the probability S dt initiates an infinite neutron fission chain with the probability P(t). This last relation gives the link between P and the source density. The aim of this paper is to show how one can apply the foregoing derivations. We have simplified the Tokaimura criticality accident for this application. We have mono-energetic neutrons with infinite and homogeneous media; we have two reactions: capture and fission. In this section, we show how one can estimate the initiation probability with a source density as a function of time. This estimation makes use of three steps: 1. Reactivity insertion: Estimation of the multiplication coefficient as a function of time K(t). This
STOCHASTIC PRICING MODEL FOR THE REAL ESTATE MARKET: FORMATION OF LOG-NORMAL GENERAL POPULATION
Directory of Open Access Journals (Sweden)
Oleg V. Rusakov
2015-01-01
Full Text Available We construct a stochastic model of real estate pricing. The method of the pricing construction is based on a sequential comparison of the supply prices. We proof that under standard assumptions imposed upon the comparison coefficients there exists an unique non-degenerated limit in distribution and this limit has the lognormal law of distribution. The accordance of empirical distributions of prices to thetheoretically obtained log-normal distribution we verify by numerous statistical data of real estate prices from Saint-Petersburg (Russia. For establishing this accordance we essentially apply the efficient and sensitive test of fit of Kolmogorov-Smirnov. Basing on “The Russian Federal Estimation Standard N2”, we conclude that the most probable price, i.e. mode of distribution, is correctly and uniquely defined under the log-normal approximation. Since the mean value of log-normal distribution exceeds the mode - most probable value, it follows that the prices valued by the mathematical expectation are systematically overstated.
Gower, Robert M.
2018-02-12
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices in such a way that all iterates (approximate solutions) generated by the algorithm are positive definite matrices themselves. This opens the way for many applications in the field of optimization and machine learning. As an application of our general theory, we develop the {\\\\em first accelerated (deterministic and stochastic) quasi-Newton updates}. Our updates lead to provably more aggressive approximations of the inverse Hessian, and lead to speed-ups over classical non-accelerated rules in numerical experiments. Experiments with empirical risk minimization show that our rules can accelerate training of machine learning models.
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
Necessary and sufficient liveness condition of GS3PR Petri nets
Liu, GaiYun; Barkaoui, Kamel
2015-05-01
Structural analysis is one of the most important and efficient methods to investigate the behaviour of Petri nets. Liveness is a significant behavioural property of Petri nets. Siphons, as structural objects of a Petri net, are closely related to its liveness. Many deadlock control policies for flexible manufacturing systems (FMS) modelled by Petri nets are implemented via siphon control. Most of the existing methods design liveness-enforcing supervisors by adding control places for siphons based on their controllability conditions. To compute a liveness-enforcing supervisor with as much as permissive behaviour, it is both theoretically and practically significant to find an exact controllability condition for siphons. However, the existing conditions, max, max‧, and max″-controllability of siphons are all overly restrictive and generally sufficient only. This paper develops a new condition called max*-controllability of the siphons in generalised systems of simple sequential processes with resources (GS3PR), which are a net subclass that can model many real-world automated manufacturing systems. We show that a GS3PR is live if all its strict minimal siphons (SMS) are max*-controlled. Compared with the existing conditions, i.e., max-, max‧-, and max″-controllability of siphons, max*-controllability of the SMS is not only sufficient but also necessary. An example is used to illustrate the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre ' Kurchatov Institute,' (Russian Federation)
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
International Nuclear Information System (INIS)
Basharov, A. M.
2012-01-01
It is shown that the effective Hamiltonian representation, as it is formulated in author’s papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are “locked” inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Condensed State Spaces for Symmetrical Coloured Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1996-01-01
equivalence classes of states and equivalence classes of state changes. It is then possible to construct a condensed state space where each node represents an equivalence class of states while each arc represents an equivalence class of state changes. Such a condensed state space is often much smaller than...... the full state space and it is also much faster to construct. Nevertheless, it is possible to use the condensed state space to verify the same kind of behavioural properties as the full state space. Hence, we do not lose analytic power. We define state spaces and condensed state spaces for a language......-nets (or Petri nets in general) - although such knowledge will, of course, be a help. The first four sections of the paper introduce the basic concepts of CP-nets. The next three sections deal with state spaces, condensed state spaces and computer tools for state space analysis. Finally, there is a short...
Characterizing behavioural congruences for Petri nets
DEFF Research Database (Denmark)
Nielsen, Mogens; Priese, Lutz; Sassone, Vladimiro
1995-01-01
We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding...... four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers....
Directory of Open Access Journals (Sweden)
Maxim Ioan
2009-05-01
Full Text Available In our paper we build a reccurence from generalized Garman equation and discretization of 3-dimensional domain. From reccurence we build an algorithm for computing values of an option based on time, momentan volatility of support and value of support on a
Requirements and Evaluation of tool papers for PETRI NETS
DEFF Research Database (Denmark)
Franceschinis, Giuliana; van Hee, Kees; Kindler, Ekkart
2008-01-01
This paper gives guidelines for the publication of papers on software tools, in particular for Petri net tools. The guidelines are illustrated by an example.......This paper gives guidelines for the publication of papers on software tools, in particular for Petri net tools. The guidelines are illustrated by an example....
Modeling of water treatment plant using timed continuous Petri nets
Nurul Fuady Adhalia, H.; Subiono, Adzkiya, Dieky
2017-08-01
Petri nets represent graphically certain conditions and rules. In this paper, we construct a model of the Water Treatment Plant (WTP) using timed continuous Petri nets. Specifically, we consider that (1) the water pump always active and (2) the water source is always available. After obtaining the model, the flow through the transitions and token conservation laws are calculated.
Petri Net Modeling of Computer Virus Life Cycle | Ikekonwu ...
African Journals Online (AJOL)
Virus life cycle, which refers to the stages of development of a computer virus, is presented as a suitable area for the application of Petri nets. Petri nets a powerful modeling tool in the field of dynamic system analysis is applied to model the virus life cycle. Simulation of the derived model is also presented. The intention of ...
Computer Tools for Construction, Modification and Analysis of Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1987-01-01
The practical use of Petri nets is — just as any other description technique — very dependent on the existence of adequate computer tools, which may assist the user to cope with the many details of a large description. For Petri nets there is a need for tools supporting construction of nets...
Modelling human factor with Petri nets
International Nuclear Information System (INIS)
Bedreaga, Luminita; Constantinescu, Cristina; Guzun, Basarab
2007-01-01
The human contribution to risk and safety of nuclear power plant operation can be best understood, assessed and quantified using tools to evaluate human reliability. Human reliability analysis becomes an important part of every probabilistic safety assessment and it is used to demonstrate that nuclear power plants designed with different safety levels are prepared to cope with severe accidents. Human reliability analysis in context of probabilistic safety assessment consists in: identifying human-system interactions important to safety; quantifying probabilities appropriate with these interactions. Nowadays, the complex system functions can be modelled using special techniques centred either on states space adequate to system or on events appropriate to the system. Knowing that complex system model consists in evaluating the likelihood of success, in other words, in evaluating the possible value for that system being in some state, the inductive methods which are based on the system states can be applied also for human reliability modelling. Thus, switching to the system states taking into account the human interactions, the underlying basis of the Petri nets can be successfully applied and the likelihoods appropriate to these states can also derived. The paper presents the manner to assess the human reliability quantification using Petri nets approach. The example processed in the paper is from human reliability documentation without a detailed human factor analysis (qualitative). The obtained results by these two kinds of methods are in good agreement. (authors)
Bouchaud, Jean-Philippe; Sornette, Didier
1994-06-01
The ability to price risks and devise optimal investment strategies in thé présence of an uncertain "random" market is thé cornerstone of modern finance theory. We first consider thé simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize thé analysis to a large class of stochastic processes, such as ARCH, jump or Lévy processes. We also address thé case of correlated Gaussian processes, which is shown to be a good description of three différent market indices (MATIF, CAC40, FTSE100). Our main result is thé introduction of thé concept of an optimal strategy in the sense of (functional) minimization of the risk with respect to the portfolio. If the risk may be made to vanish for particular continuous uncorrelated 'quasiGaussian' stochastic processes (including Black and Scholes model), this is no longer the case for more general stochastic processes. The value of the residual risk is obtained and suggests the concept of risk-corrected option prices. In the presence of very large deviations such as in Lévy processes, new criteria for rational fixing of the option prices are discussed. We also apply our method to other types of options, `Asian', `American', and discuss new possibilities (`doubledecker'...). The inclusion of transaction costs leads to the appearance of a natural characteristic trading time scale. L'aptitude à quantifier le coût du risque et à définir une stratégie optimale de gestion de portefeuille dans un marché aléatoire constitue la base de la théorie moderne de la finance. Nous considérons d'abord le problème le plus simple de ce type, à savoir celui de l'option d'achat `européenne', qui a été résolu par Black et Scholes à l'aide du calcul stochastique d'Ito appliqué aux marchés modélisés par un processus Log
Wen, Xing-Chun; He, Ling-Yun
2015-08-01
There is a bitter controversy over what drives the housing price in China in the existing literature. In this paper, we investigate the underlying driving force behind housing price fluctuations in China, especially focusing on the role of housing demand shock with that of money supply shock in explaining housing price movements, by a new Keynesian dynamic stochastic general equilibrium model. Empirical results suggest that it is housing demand, instead of money supply, that mainly drives China's housing price movements. Relevant policy implication is further discussed, namely, whether to consider the housing price fluctuations in the conduct of monetary policy. By means of the policy simulations, we find that a real house price-augmented money supply rule is a better monetary policy for China's economy stabilization. 1. Investment refers to fixed capital investment. 2. Housing price refers to national average housing price. Quarterly data on housing price during the period of our work are not directly available. However, monthly data of the value of sales on housing and sale volume on housing can be directly obtained from National Bureau of Statistics of China. We add up the monthly data and calculate one quarter's housing price by dividing the value of housing sales by its sale volume in one quarter. 3. M2 means the broad money supply in China.
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Séquentialisation du comportement des réseaux de Petri temporisés
Czech Academy of Sciences Publication Activity Database
Boimond, J.-L.; Komenda, Jan; Lahaye, S.
2013-01-01
Roč. 47, 1-3 (2013), s. 139-154 ISSN 1269-6935. [Modélisation des Systèmes Réactifs (MSR) 2013. Rennes, 13.11.2013-15.11.2013] R&D Projects: GA ČR(CZ) GAP103/11/0517 Institutional support: RVO:67985840 Keywords : timed Petri nets * (max,+) automata * race policy Subject RIV: BA - General Mathematics http://jesa.revuesonline.com/article.jsp?articleId=18769
Pragmatics Annotated Coloured Petri Nets for Protocol Software Generation and Verification
DEFF Research Database (Denmark)
Fagerland Simonsen, Kent Inge; Kristensen, Lars Michael; Kindler, Ekkart
2015-01-01
PetriCode is a tool that supports automated generation of protocol software from a restricted class of Coloured Petri Nets (CPNs) called Pragmatics Annotated Coloured Petri Nets (PA-CPNs). Petri-Code and PA-CPNs have been designed with five main requirements in mind, which include the same model...
PNet: A Python Library for Petri Net Modeling and Simulation
Zhu En Chay; Bing Feng Goh; Maurice HT Ling
2016-01-01
Petri Net is a formalism to describe changes between 2 or more states across discrete time and has been used to model many systems. We present PNet – a pure Python library for Petri Net modeling and simulation in Python programming language. The design of PNet focuses on reducing the learning curve needed to define a Petri Net by using a text-based language rather than programming constructs to define transition rules. Complex transition rules can be refined as regular Python functions. To de...
Petri nets SM-cover-based on heuristic coloring algorithm
Tkacz, Jacek; Doligalski, Michał
2015-09-01
In the paper, coloring heuristic algorithm of interpreted Petri nets is presented. Coloring is used to determine the State Machines (SM) subnets. The present algorithm reduces the Petri net in order to reduce the computational complexity and finds one of its possible State Machines cover. The proposed algorithm uses elements of interpretation of Petri nets. The obtained result may not be the best, but it is sufficient for use in rapid prototyping of logic controllers. Found SM-cover will be also used in the development of algorithms for decomposition, and modular synthesis and implementation of parallel logic controllers. Correctness developed heuristic algorithm was verified using Gentzen formal reasoning system.
The application of Petri nets to failure analysis
International Nuclear Information System (INIS)
Liu, T.S.; Chiou, S.B.
1997-01-01
Unlike the technique of fault tree analysis that has been widely applied to system failure analysis in reliability engineering, this study presents a Petri net approach to failure analysis. It is essentially a graphical method for describing relations between conditions and events. The use of Petri nets in failure analysis enables to replace logic gate functions in fault trees, efficiently obtain minimal cut sets, and absorb models. It is demonstrated that for failure analysis Petri nets are more efficient than fault trees. In addition, this study devises an alternative; namely, a trapezoidal graph method in order to account for failure scenarios. Examples validate this novel method in dealing with failure analysis
Czech Academy of Sciences Publication Activity Database
Komenda, Jan; Zerhouni, N.; El Moudni, A.
2001-01-01
Roč. 11, 1/2 (2001), s. 59-76 ISSN 0924-6703 R&D Projects: GA AV ČR IAC1019007 Keywords : hybrid Petri nets%dioid algebra%modelling Subject RIV: BA - General Mathematics Impact factor: 0.552, year: 2001
XML as a format of expression of Object-Oriented Petri Nets
Directory of Open Access Journals (Sweden)
Petr Jedlička
2004-01-01
Full Text Available A number of object-oriented (OO variants have so far been devised for Petri Nets (PN. However, none of these variants has ever been described using an open, independent format – such as XML. This article suggests several possibilities and advantages of such a description. The outlined XML language definition for the description of object-oriented Petri Nets (OOPN is based on XMI (description of UML object-oriented models, SOX (simple description of general OO systems and PNML (an XML-based language used for the description of structured and modular PN. For OOPN, the XML form of description represents a standard format for storing as well as for transfer between various OOPN-processing (analysis, simulation, ... tools.
Software Design Modelling with Functional Petri Nets | Bakpo ...
African Journals Online (AJOL)
Software Design Modelling with Functional Petri Nets. ... of structured programs and a FPN Software prototype proposed for the conventional programming construct: if-then-else statement. ... EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT
How to Find Invariants for Coloured Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1981-01-01
This paper shows how invariants can be found for coloured Petri Nets. We define a set of transformation rules, which can be used to transform the incidence matrix, without changing the set of invariants....
PETRI NET MODELING OF COMPUTER VIRUS LIFE CYCLE
African Journals Online (AJOL)
Dr Obe
dynamic system analysis is applied to model the virus life cycle. Simulation of the derived model ... Keywords: Virus lifecycle, Petri nets, modeling. simulation. .... complex process. Figure 2 .... by creating Matlab files for five different computer ...
Petri nets - part 1: concepts and application areas
International Nuclear Information System (INIS)
Sivertsen, Terje
2004-03-01
There exist a number of models, languages, methods, and tools that support the specification and analysis of system requirements. One important class comprises graphical methods based on the concept of Petri nets. Due to the wide variety of applications, these methods are relevant also in research and applications outside the digital systems safety domain. The present report constitutes the first of three parts of a unified exposition of graphical methods based on the concept of Petri nets. The report provides an introduction to basic concepts of Petri nets and an overview of a wide variety of application areas. The second part of the trilogy will present a number of techniques and tools. The third part will focus on analysis. Petri nets have been proposed for a wide variety of applications, and new areas are considered as new challenges emerge from scientific, technological, and social developments. The wide variety of application areas reflects a broad interest in Petri nets, coming from diverse directions. Empirically, as well as theoretically, there are good reasons to claim that Petri nets are applicable for many different kinds of problems. What is common to the different applications and problems addressed is the need for a formalism that allows adequate representation of important system characteristics like concurrency, asyncronicity, distribution, parallelism, and non-determinism. Several of the references in the report discuss NPP-related applications, or applications with great potentials for technology transfer from other areas to the nuclear domain. (Author)
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Fluid Petri Nets and hybrid model-checking: a comparative case study
International Nuclear Information System (INIS)
Gribaudo, M.; Horvath, A.; Bobbio, A.; Tronci, E.; Ciancamerla, E.; Minichino, M.
2003-01-01
The modeling and analysis of hybrid systems is a recent and challenging research area which is actually dominated by two main lines: a functional analysis based on the description of the system in terms of discrete state (hybrid) automata (whose goal is to ascertain conformity and reachability properties), and a stochastic analysis (whose aim is to provide performance and dependability measures). This paper investigates a unifying view between formal methods and stochastic methods by proposing an analysis methodology of hybrid systems based on Fluid Petri Nets (FPNs). FPNs can be analyzed directly using appropriate tools. Our paper shows that the same FPN model can be fed to different functional analyzers for model checking. In order to extensively explore the capability of the technique, we have converted the original FPN into languages for discrete as well as hybrid as well as stochastic model checkers. In this way, a first comparison among the modeling power of well known tools can be carried out. Our approach is illustrated by means of a 'real world' hybrid system: the temperature control system of a co-generative plant
Reachability analysis of real-time systems using time Petri nets.
Wang, J; Deng, Y; Xu, G
2000-01-01
Time Petri nets (TPNs) are a popular Petri net model for specification and verification of real-time systems. A fundamental and most widely applied method for analyzing Petri nets is reachability analysis. The existing technique for reachability analysis of TPNs, however, is not suitable for timing property verification because one cannot derive end-to-end delay in task execution, an important issue for time-critical systems, from the reachability tree constructed using the technique. In this paper, we present a new reachability based analysis technique for TPNs for timing property analysis and verification that effectively addresses the problem. Our technique is based on a concept called clock-stamped state class (CS-class). With the reachability tree generated based on CS-classes, we can directly compute the end-to-end time delay in task execution. Moreover, a CS-class can be uniquely mapped to a traditional state class based on which the conventional reachability tree is constructed. Therefore, our CS-class-based analysis technique is more general than the existing technique. We show how to apply this technique to timing property verification of the TPN model of a command and control (C2) system.
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
Do stochastic Schroedinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schroedinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schroedinger equation introduced by Strunz, Diosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction
Directory of Open Access Journals (Sweden)
Araújo, Maria Valéria Pereira de
2014-12-01
Full Text Available The case teaching "The Petri dishes of Samuel" mentions a real situation occurred in a small business Medical Laboratory located in the city of Natal-RN. The dilemma of the case comes to a decision-making situation involving João, Director of the Laboratory Tércio Rosado and responsible for the human resources sector of the organization. The case is narrated from his point of view which faces a situation where one employee who works at the company for 25 years can not get adapted to the new technologies of the Medical Laboratory area, although the employee possesses behavioral and attitudinal competences which sets it apart from other professionals. After several attempts of training processes, trying to make Samuel adapt his behavior to the new technological requirements of the position, none of them were successful. Facing the situation the Director had a dilemma to solve: keep him in the company or not? If the company remains the employee, it might discourage the learning development of the other ones? On the other hand, the company would have other alternatives of training him in order to develop the required skills? What could be done? The case was constructed from observational data and informal conversations with employees and with the former owners of the company. Fictitious names were used to preserve the identity of the involved.
Application of Petri Nets in Bone Remodeling
Directory of Open Access Journals (Sweden)
Lingxi Li
2009-07-01
Full Text Available Understanding a mechanism of bone remodeling is a challenging task for both life scientists and model builders, since this highly interactive and nonlinear process can seldom be grasped by simple intuition. A set of ordinary differential equations (ODEs have been built for simulating bone formation as well as bone resorption. Although solving ODEs numerically can provide useful predictions for dynamical behaviors in a continuous time frame, an actual bone remodeling process in living tissues is driven by discrete events of molecular and cellular interactions. Thus, an event-driven tool such as Petri nets (PNs, which may dynamically and graphically mimic individual molecular collisions or cellular interactions, seems to augment the existing ODE-based systems analysis. Here, we applied PNs to expand the ODE-based approach and examined discrete, dynamical behaviors of key regulatory molecules and bone cells. PNs have been used in many engineering areas, but their application to biological systems needs to be explored. Our PN model was based on 8 ODEs that described an osteoprotegerin linked molecular pathway consisting of 4 types of bone cells. The models allowed us to conduct both qualitative and quantitative evaluations and evaluate homeostatic equilibrium states. The results support that application of PN models assists understanding of an event-driven bone remodeling mechanism using PN-specific procedures such as places, transitions, and firings.
Stochastic quantization and gravity
International Nuclear Information System (INIS)
Rumpf, H.
1984-01-01
We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)
A general analytical solution for the stochastic Milne problem using Karhunen–Loeve (K–L) expansion
International Nuclear Information System (INIS)
Hussein, A.; Selim, M.M.
2013-01-01
This paper considers the solution of the stochastic integro-differential equation of Milne problem with random operator. The Pomraning–Eddington method is implemented to get a closed form solution deterministically. Relying on the spectral properties of the covariance function, the Karhunen–Loeve (K–L) expansion is used to represent the input stochastic process in the deterministic solution. This leads to an explicit expression for the solution process as a multivariate functional of a set of uncorrelated random variables. By using different distributions for these variables, the work is realized through computing the mean and the variance of the solution. The numerical results are found in agreement with those obtained in the literature. -- Highlights: •The solution of the stochastic Milne problem is considered. •We dealt with the random cross-section itself not with the optical transformation of it. •Pomraning–Eddington method together with the (K–L) expansion were implemented. •The solution process is obtained as a functional of a set of uncorrelated random variables. •Good results are obtained for different distributions of these variables
The equivalency between logic Petri workflow nets and workflow nets.
Wang, Jing; Yu, ShuXia; Du, YuYue
2015-01-01
Logic Petri nets (LPNs) can describe and analyze batch processing functions and passing value indeterminacy in cooperative systems. Logic Petri workflow nets (LPWNs) are proposed based on LPNs in this paper. Process mining is regarded as an important bridge between modeling and analysis of data mining and business process. Workflow nets (WF-nets) are the extension to Petri nets (PNs), and have successfully been used to process mining. Some shortcomings cannot be avoided in process mining, such as duplicate tasks, invisible tasks, and the noise of logs. The online shop in electronic commerce in this paper is modeled to prove the equivalence between LPWNs and WF-nets, and advantages of LPWNs are presented.
The Equivalency between Logic Petri Workflow Nets and Workflow Nets
Wang, Jing; Yu, ShuXia; Du, YuYue
2015-01-01
Logic Petri nets (LPNs) can describe and analyze batch processing functions and passing value indeterminacy in cooperative systems. Logic Petri workflow nets (LPWNs) are proposed based on LPNs in this paper. Process mining is regarded as an important bridge between modeling and analysis of data mining and business process. Workflow nets (WF-nets) are the extension to Petri nets (PNs), and have successfully been used to process mining. Some shortcomings cannot be avoided in process mining, such as duplicate tasks, invisible tasks, and the noise of logs. The online shop in electronic commerce in this paper is modeled to prove the equivalence between LPWNs and WF-nets, and advantages of LPWNs are presented. PMID:25821845
CPN Tools for Editing, Simulating, and Analysing Coloured Petri Nets
DEFF Research Database (Denmark)
Ratzer, Anne Vinter; Wells, Lisa Marie; Lassen, Henry Michael
2003-01-01
CPN Tools is a tool for editing, simulating and analysing Coloured Petri Nets. The GUI is based on advanced interaction techniques, such as toolglasses, marking menus, and bi-manual interaction. Feedback facilities provide contextual error messages and indicate dependency relationships between ne...... information such as boundedness properties and liveness properties. The functionality of the simulation engine and state space facilities are similar to the corresponding components in Design/CPN, which is a widespread tool for Coloured Petri Nets.......CPN Tools is a tool for editing, simulating and analysing Coloured Petri Nets. The GUI is based on advanced interaction techniques, such as toolglasses, marking menus, and bi-manual interaction. Feedback facilities provide contextual error messages and indicate dependency relationships between net...
Generalized Asynchronous Systems
Directory of Open Access Journals (Sweden)
E. S. Kudryashova
2012-01-01
Full Text Available The paper consider a mathematical model of a concurrent system, the special case of which is an asynchronous system. Distributed asynchronous automata are introduced here. It is proved that Petri nets and transition systems with independence can be considered as distributed asynchronous automata. Time distributed asynchronous automata are defined in a standard way by correspondence which relates events with time intervals. It is proved that the time distributed asynchronous automata generalize time Petri nets and asynchronous systems.
A simulator for high-level Petri nets: An ePNK application
DEFF Research Database (Denmark)
Kindler, Ekkart; Laganeckas, Mindaugas
2013-01-01
The ePNK is a platform for Petri net tools based on the PNML transfer format. One of its important features is its extensibility, which allows developers to plug in new Petri net types and new functions and applications for different kinds of Petri nets. The basic version of the ePNK provides...
Pragmatics annotated coloured petri nets for protocol software generation and verification
DEFF Research Database (Denmark)
Simonsen, Kent Inge Fagerland; Kristensen, Lars M.; Kindler, Ekkart
2016-01-01
Pragmatics Annotated Coloured Petri Nets (PA-CPNs) are a restricted class of Coloured Petri Nets (CPNs) developed to support automated generation of protocol software. The practical application of PA-CPNs and the supporting PetriCode software tool have been discussed and evaluated in earlier papers...
Approximating Preemptive Stochastic Scheduling
Megow Nicole; Vredeveld Tjark
2009-01-01
We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...
The stochastic goodwill problem
Marinelli, Carlo
2003-01-01
Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionar...
Stochastic and non-stochastic effects - a conceptual analysis
International Nuclear Information System (INIS)
Karhausen, L.R.
1980-01-01
The attempt to divide radiation effects into stochastic and non-stochastic effects is discussed. It is argued that radiation or toxicological effects are contingently related to radiation or chemical exposure. Biological effects in general can be described by general laws but these laws never represent a necessary connection. Actually stochastic effects express contingent, or empirical, connections while non-stochastic effects represent semantic and non-factual connections. These two expressions stem from two different levels of discourse. The consequence of this analysis for radiation biology and radiation protection is discussed. (author)
International Nuclear Information System (INIS)
Wu Zhi-Hai; Peng Li; Xie Lin-Bo; Wen Ji-Wei
2013-01-01
In this paper we provide a unified framework for consensus tracking of leader-follower multi-agent systems with measurement noises based on sampled data with a general sampling delay. First, a stochastic bounded consensus tracking protocol based on sampled data with a general sampling delay is presented by employing the delay decomposition technique. Then, necessary and sufficient conditions are derived for guaranteeing leader-follower multi-agent systems with measurement noises and a time-varying reference state to achieve mean square bounded consensus tracking. The obtained results cover no sampling delay, a small sampling delay and a large sampling delay as three special cases. Last, simulations are provided to demonstrate the effectiveness of the theoretical results. (interdisciplinary physics and related areas of science and technology)
Petri nets and fault diagnosis in nuclear reactors
International Nuclear Information System (INIS)
Jalel, N.A.; Nicholson, H.
1990-11-01
The possibility of applying Petri nets (Pns) as a modelling tool to represent any fault or accident that might occur in the Loss Of Fluid Test (LOFT) reactor, small scale pressurised water reactor, is discussed and analysed. Pns are developed to assist the nuclear reactor operator in identifying any fault or alarm that might arise in the power station. (author)
Transactions on Petri Nets and Other Models of Concurrency VI
DEFF Research Database (Denmark)
The sixth volume of ToPNoC includes revised versions of selected papers from workshops and tutorials held at the 32nd International Conference on Application and Theory of Petri Nets and Concurrency. It also contains a special section on Networks, Protocols, and Services, as well as a contributed...
Application of Coloured Petri Nets in System Development
DEFF Research Database (Denmark)
Kristensen, Lars Michael; Jørgensen, Jens Bæk; Jensen, Kurt
2004-01-01
Coloured Petri Nets (CP-nets or CPNs) and their supporting computer tools have been used in a wide range of application areas such as communication protocols, software designs, and embedded systems. The practical application of CP-nets has also covered many phases of system development ranging fr...
Completeness Results for Linear Logic on Petri Nets
DEFF Research Database (Denmark)
Engberg, Uffe Henrik; Winskel, Glynn
1993-01-01
Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic linear logic, with $otimes$, $-!circ$, &, $oplus$ and the exponential ! (''of course´´), and forms of quantification. This logic ...
A Petri Net Definition of a System Description Language
DEFF Research Database (Denmark)
Jensen, Kurt; Kyng, Morten; Madsen, Ole Lehrmann
1979-01-01
This paper introduces a language for the description of systems with concurrency, and presents a formal definition of its semantics. The language is based on Delta and the semantic model is an extension of Petri nets with a data part and with expressions attached to transitions and to places....
Accurate Complex Systems Design: Integrating Serious Games with Petri Nets
Directory of Open Access Journals (Sweden)
Kirsten Sinclair
2016-03-01
Full Text Available Difficulty understanding the large number of interactions involved in complex systems makes their successful engineering a problem. Petri Nets are one graphical modelling technique used to describe and check proposed designs of complex systems thoroughly. While automatic analysis capabilities of Petri Nets are useful, their visual form is less so, particularly for communicating the design they represent. In engineering projects, this can lead to a gap in communications between people with different areas of expertise, negatively impacting achieving accurate designs.In contrast, although capable of representing a variety of real and imaginary objects effectively, behaviour of serious games can only be analysed manually through interactive simulation. This paper examines combining the complementary strengths of Petri Nets and serious games. The novel contribution of this work is a serious game prototype of a complex system design that has been checked thoroughly. Underpinned by Petri Net analysis, the serious game can be used as a high-level interface to communicate and refine the design.Improvement of a complex system design is demonstrated by applying the integration to a proof-of-concept case study.
Online Conformance Checking for Petri Nets and Event Streams
DEFF Research Database (Denmark)
Burattin, Andrea
2017-01-01
Within process mining, we can identify conformance checking as the task of computing the extent to which executions of a process model are in line with the reference behavior. Most approaches currently available in the literature (for imperative models, such as Petri nets) perform just a-posterio...
A Generalised Approach to Petri Nets and Algebraic Specifications
International Nuclear Information System (INIS)
Sivertsen, Terje
1998-02-01
The present report represents a continuation of the work on Petri nets and algebraic specifications. The reported research has focused on generalising the approach introduced in HWR-454, with the aim of facilitating the translation of a wider class of Petri nets into algebraic specification. This includes autonomous Petri nets with increased descriptive power, as well as non-autonomous Petri nets allowing the modelling of systems (1) involving extensive data processing; (2) with transitions synchronized on external events; (3) whose evolutions are time dependent. The generalised approach has the important property of being modular in the sense that the translated specifications can be gradually extended to include data processing, synchronization, and timing. The report also discusses the relative merits of state-based and transition-based specifications, and includes a non-trivial case study involving automated proofs of a large number of interrelated theorems. The examples in the report illustrate the use of the new HRP Prover. Of particular importance in this context is the automatic transformation between state-based and transitionbased specifications. It is expected that the approach introduced in HWR-454 and generalised in the present report will prove useful in future work on combination of wide variety of specification techniques
International Nuclear Information System (INIS)
Son, Han Seong; Seong, Poong Hyun
1998-01-01
Generally, FLC design causes the designer to spend too much efforts and time. If a design support is provided to apply various membership functions to and simulate a FLC without coding at the early development stage, the cost problem may be solved to a remarkable degree. In order to offer the systematic approach to support FLC design, Fuzzy Colored Petri Nets (FCPN) is introduced as design support in this work. The feasibility of FCPN is demonstrated through a controller design example
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Introduction to stochastic calculus
Karandikar, Rajeeva L
2018-01-01
This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...
Dynamical and hamiltonian dilations of stochastic processes
International Nuclear Information System (INIS)
Baumgartner, B.; Gruemm, H.-R.
1982-01-01
This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)
Directory of Open Access Journals (Sweden)
Muhammad Ali Nasir
2016-12-01
Full Text Available This study derives an optimal macroeconomic policy combination for financial sector stability in the United Kingdom by employing a New Keynesian Dynamic Stochastic General Equilibrium (NK-DSGE framework. The empirical results obtained show that disciplined fiscal and accommodative monetary policies stance is optimal for financial sector stability. Furthermore, fiscal indiscipline countered by contractionary monetary stance adversely affects financial sector stability. Financial markets, e.g. stocks and Gilts show a short-term asymmetric response to macroeconomic policy interaction and to each other. The asymmetry is a reflection of portfolio adjustment. However in the long-run, the responses to suggested optimal policy combination had homogenous effects and there was evidence of co-movement in the stock and Gilt markets.
Parzen, Emanuel
1962-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Directory of Open Access Journals (Sweden)
Misbah Razzaq
Full Text Available Internet worms are analogous to biological viruses since they can infect a host and have the ability to propagate through a chosen medium. To prevent the spread of a worm or to grasp how to regulate a prevailing worm, compartmental models are commonly used as a means to examine and understand the patterns and mechanisms of a worm spread. However, one of the greatest challenge is to produce methods to verify and validate the behavioural properties of a compartmental model. This is why in this study we suggest a framework based on Petri Nets and Model Checking through which we can meticulously examine and validate these models. We investigate Susceptible-Exposed-Infectious-Recovered (SEIR model and propose a new model Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered (SEIDQR(S/I along with hybrid quarantine strategy, which is then constructed and analysed using Stochastic Petri Nets and Continuous Time Markov Chain. The analysis shows that the hybrid quarantine strategy is extremely effective in reducing the risk of propagating the worm. Through Model Checking, we gained insight into the functionality of compartmental models. Model Checking results validate simulation ones well, which fully support the proposed framework.
Marine Traffic Optimization Using Petri Net and Genetic Algorithm
Directory of Open Access Journals (Sweden)
Anita Gudelj
2012-11-01
Full Text Available The paper deals with the traffic control and job optimization in the marine canal system. The moving of vessels can be described as a set of discrete events and states. Some of these states can be undesirable such as conflicts and deadlocks. It is necessary to apply adequate control policy to avoid deadlocks and blocks the vessels’ moving only in the case of dangerous situation. This paper addresses the use of Petri net as modelling and scheduling tool in this context. To find better solutions the authors propose the integration of Petri net with a genetic algorithm. Also, a matrix based formal method is proposed for analyzing discrete event dynamic system (DEDS. The algorithm is developed to deal with multi-project, multi-constrained scheduling problem with shared resources. It is verified by a computer simulation using MATLAB environment.
Knowledge base verification based on enhanced colored petri net
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Hyun; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1997-12-31
Verification is a process aimed at demonstrating whether a system meets it`s specified requirements. As expert systems are used in various applications, the knowledge base verification of systems takes an important position. The conventional Petri net approach that has been studied recently in order to verify the knowledge base is found that it is inadequate to verify the knowledge base of large and complex system, such as alarm processing system of nuclear power plant. Thus, we propose an improved method that models the knowledge base as enhanced colored Petri net. In this study, we analyze the reachability and the error characteristics of the knowledge base and apply the method to verification of simple knowledge base. 8 refs., 4 figs. (Author)
Knowledge base verification based on enhanced colored petri net
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Hyun; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-12-31
Verification is a process aimed at demonstrating whether a system meets it`s specified requirements. As expert systems are used in various applications, the knowledge base verification of systems takes an important position. The conventional Petri net approach that has been studied recently in order to verify the knowledge base is found that it is inadequate to verify the knowledge base of large and complex system, such as alarm processing system of nuclear power plant. Thus, we propose an improved method that models the knowledge base as enhanced colored Petri net. In this study, we analyze the reachability and the error characteristics of the knowledge base and apply the method to verification of simple knowledge base. 8 refs., 4 figs. (Author)
APPLYING PETRI NETS EXTENSIONS TO MODELING COMMERCIAL BANK ACTIVITY
Directory of Open Access Journals (Sweden)
Igor ENICOV
2017-02-01
Full Text Available The relevance of the study is determined by the need to improve the methods of modeling andsimulating commercial bank activity, including for the purpose of calculating, controlling and managingthe risk of the bank, in the context of the transition to the application of Basel III standards. Thisimprovement becomes necessary due to a direct transition to new regulatory standards when the internalassessments of the main risks become the initial data for calculating the capital adequacy of a bank. Thepurpose of this article is to argue the opportunity to formulate a theory of the commercial bank model onthe extensions of Petri nets theory. The main methods of research were the method of scientific abstractionand method of logical analysis. The main result obtained in the study and presented in the article is theargumentation of the possibility to analyze the quantitative and qualitative characteristics of acommercial bank with the help of Petri net extensions.
Timed-Arc Petri Nets vs. Networks of Timed Automata
DEFF Research Database (Denmark)
Srba, Jiri
We establish mutual translations between the classes of 1-safe timed-arc Petri nets (and its extension with testing arcs) and networks of timed automata (and its subclass where every clock used in the guard has to be reset). The presented translations are very tight (up to isomorphism of labelled...... transition systems with time). This provides a convenient characterization from the theoretical point of view but is not always satisfactory from the practical point of view because of the possible non-polynomial blow up in the size (in the direction from automata to nets). Hence we relax the isomorphism...... requirement and provide efficient (polynomial time) reductions between networks of timed automata and 1-safe timed-arc Petri nets preserving the answer to the reachability question. This makes our techniques suitable for automatic translation into a format required by tools like UPPAAL and KRONOS. A direct...
Towards a Notion of Distributed Time for Petri Nets
DEFF Research Database (Denmark)
Nielsen, Mogens; Sassone, Vladimiro; Srba, Jiří
2001-01-01
We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks — possibly o...... per place — allowing a local timing as well as distributed time synchronisation. We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of processes of the respective models.......We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks — possibly one...
International Nuclear Information System (INIS)
Klauder, J.R.
1983-01-01
The author provides an introductory survey to stochastic quantization in which he outlines this new approach for scalar fields, gauge fields, fermion fields, and condensed matter problems such as electrons in solids and the statistical mechanics of quantum spins. (Auth.)
Properties of Distributed Timed-Arc Petri Nets
DEFF Research Database (Denmark)
Nielsen, M.; Sassone, V.; Srba, J.
2001-01-01
In [12] we started a research on a distributed-timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. This formalism enables to model e.g. hardware architectures like GALS. We give a formal...... definition of process semantics for our model and investigate several properties of local versus global timing: expressiveness, reachability and coverability....
International Nuclear Information System (INIS)
Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas
2004-01-01
We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise
Numerical and experimental dosimetry of petri dish exposure setups
Energy Technology Data Exchange (ETDEWEB)
Burkhardt, M.; Pokovic, K.; Gnos, M.; Schmid, T.; Kuster, N. [Swiss Federal Inst. of Tech., Zurich (Switzerland)
1996-12-31
Crawford TEM cells are often used to exposure cell cultures or small animals in order to study the effects caused by high-frequency fields. They are self-contained, easy-to-use setups that provide a rather homogeneous field distribution in a large area around its center, corresponding approximately to far-field conditions. However, a number of conditions must be met if such TEM cells are intended to be used for in vitro experiments. For instance, poor interaction with the incident field must be maintained to avoid significant field disturbances in the TEM cell. This is best achieved with E-polarization, i.e., when the E-field vector is normal to the investigated cell layer lining the bottom of a synthetic Petri dish. In addition, E-polarization provides the most homogeneous field distribution of all polarizations within the entire layer of cells. In this paper, the authors present a detailed dosimetric assessment for 60 and 100 mm Petri dishes as well as for a 48-well titer plate at 835 MHz. The dosimetry was performed by using numerical computations. The modeling and the simplifications are validated by a second numerical technique and by experimental measurements. For thin liquid layers, an approximation formula is provided with which the induced field strength for many other experiments conducted in Petri dishes can be assessed reliably.
STOCHASTIC ASSESSMENT OF NIGERIAN STOCHASTIC ...
African Journals Online (AJOL)
eobe
STOCHASTIC ASSESSMENT OF NIGERIAN WOOD FOR BRIDGE DECKS ... abandoned bridges with defects only in their decks in both rural and urban locations can be effectively .... which can be seen as the detection of rare physical.
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Verification of the safety communication protocol in train control system using colored Petri net
International Nuclear Information System (INIS)
Chen Lijie; Tang Tao; Zhao Xianqiong; Schnieder, Eckehard
2012-01-01
This paper deals with formal and simulation-based verification of the safety communication protocol in ETCS (European Train Control System). The safety communication protocol controls the establishment of safety connection between train and trackside. Because of its graphical user interface and modeling flexibility upon the changes in the system conditions, this paper proposes a composition Colored Petri Net (CPN) representation for both the logic and the timed model. The logic of the protocol is proved to be safe by means of state space analysis: the dead markings are correct; there are no dead transitions; being fair. Further analysis results have been obtained using formal and simulation-based verification approach. The timed models for the open transmit system and the application process are created for the purpose of performance analysis of the safety communication protocol. The models describe the procedure of data transmission and processing, and also provide relevant timed and stochastic factors, as well as time delay and lost packet, which may influence the time for establishment of safety connection of the protocol. Time for establishment of safety connection of the protocol in normal state is verified by formal verification, and then time for establishment of safety connection with different probability of lost packet is simulated. After verification it is found that the time for establishment of safety connection of the safety communication protocol satisfies the safety requirements.
Fault Diagnosis System of Wind Turbine Generator Based on Petri Net
Zhang, Han
Petri net is an important tool for discrete event dynamic systems modeling and analysis. And it has great ability to handle concurrent phenomena and non-deterministic phenomena. Currently Petri nets used in wind turbine fault diagnosis have not participated in the actual system. This article will combine the existing fuzzy Petri net algorithms; build wind turbine control system simulation based on Siemens S7-1200 PLC, while making matlab gui interface for migration of the system to different platforms.
Coloured Petri Nets and CPN Tools for Modelling and Validation of Concurrent Systems
DEFF Research Database (Denmark)
Jensen, Kurt; Kristensen, Lars Michael; Wells, Lisa Marie
2007-01-01
Coloured Petri Nets (CPNs) is a language for the modeling and validation og systems in which concurrency, communication, and synchronisation play a major role. Coloured Petri Nets is a descrete-event modeling language combining Petri Nets with the funcitonal programming language Standard ML. Petr...... with user-defined Standard ML functions. A license for CPN Tools can be obtained free of charge, also for commercial use....
Directory of Open Access Journals (Sweden)
Elisa Alòs
2008-01-01
Full Text Available We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.
CPN Tools-Assisted Simulation and Verification of Nested Petri Nets
Directory of Open Access Journals (Sweden)
L. W. Dworza´nski
2012-01-01
Full Text Available Nested Petri nets (NP-nets are an extension of Petri net formalism within the “netswithin-nets” approach, when tokens in a marking are Petri nets, which have an autonomous behavior and are synchronized with the system net. The formalism of NP-nets allows modeling multi-level multi-agent systems with dynamic structure in a natural way. Currently, there is no tool for supporting NP-nets simulation and analysis. The paper proposes the translation of NP-nets into Colored Petri nets and the use of CPN Tools as a virtual machine for NP-nets modeling, simulation and automatic verification.
Pragmatics Annotated Coloured Petri Nets for Protocol Software Generation and Verification
DEFF Research Database (Denmark)
Simonsen, Kent Inge; Kristensen, Lars Michael; Kindler, Ekkart
This paper presents the formal definition of Pragmatics Annotated Coloured Petri Nets (PA-CPNs). PA-CPNs represent a class of Coloured Petri Nets (CPNs) that are designed to support automated code genera-tion of protocol software. PA-CPNs restrict the structure of CPN models and allow Petri net...... elements to be annotated with so-called pragmatics, which are exploited for code generation. The approach and tool for gen-erating code is called PetriCode and has been discussed and evaluated in earlier work already. The contribution of this paper is to give a formal def-inition for PA-CPNs; in addition...
International Nuclear Information System (INIS)
Rumpf, H.
1987-01-01
We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Han, Shurong; Huang, Yeqing
2017-07-07
The study analysed the medical imaging technology business cycle from 1981 to 2009 and found that the volatility of consumption in Chinese medical imaging business was higher than that of the developed countries. The volatility of gross domestic product (GDP) and the correlation between consumption and GDP is also higher than that of the developed countries. Prior to the early 1990s the volatility of consumption is even higher than GDP. This fact makes it difficult to explain the volatile market using the standard one sector real economic cycle (REC) model. Contrary to the other domestic studies, this study considers a three-sector dynamical stochastic general equilibrium REC model. In this model there are two consumption sectors, whereby one is labour intensive and another is capital intensive. The more capital intensive investment sector only introduces technology shocks in the medical imaging market. Our response functions and Monte-Carlo simulation results show that the model can explain 90% of the volatility of consummation relative to GDP, and explain the correlation between consumption and GDP. The results demonstrated the significant correlation between the technological reform in medical imaging and volatility in the labour market on Chinese macro economy development.
Model petri net of adaptive traffic lights and its collaboration with a special event
Directory of Open Access Journals (Sweden)
Tristono Tomi
2018-01-01
Full Text Available Traffic lights have an important role as the system control of vehicles flow on the urban network. Commonly, most countries still using fixed time strategy. Our research proposes the adaptive traffic lights model to response the traffic demand. It uses basic Petri net as a general modeling framework. Foractuating method of minimum and maximum green signal time interval, the green traffic lights have three-time extension units. Next, we collaborate on a case of the existence of railways that crosses on the southern arm of an intersection. We introduce both of collaboration model design of traffic lights and the railway's gate which always closes while a train passing. Verification and validation of the model are based on the simulation result of vehicles queue. The collaboration model design of traffic lights has excellent performance, and it can resolve the congestion problem better than conventional schedule.
A PetriNet-Based Approach for Supporting Traceability in Cyber-Physical Manufacturing Systems.
Huang, Jiwei; Zhu, Yeping; Cheng, Bo; Lin, Chuang; Chen, Junliang
2016-03-17
With the growing popularity of complex dynamic activities in manufacturing processes, traceability of the entire life of every product has drawn significant attention especially for food, clinical materials, and similar items. This paper studies the traceability issue in cyber-physical manufacturing systems from a theoretical viewpoint. Petri net models are generalized for formulating dynamic manufacturing processes, based on which a detailed approach for enabling traceability analysis is presented. Models as well as algorithms are carefully designed, which can trace back the lifecycle of a possibly contaminated item. A practical prototype system for supporting traceability is designed, and a real-life case study of a quality control system for bee products is presented to validate the effectiveness of the approach.
A PetriNet-Based Approach for Supporting Traceability in Cyber-Physical Manufacturing Systems
Directory of Open Access Journals (Sweden)
Jiwei Huang
2016-03-01
Full Text Available With the growing popularity of complex dynamic activities in manufacturing processes, traceability of the entire life of every product has drawn significant attention especially for food, clinical materials, and similar items. This paper studies the traceability issue in cyber-physical manufacturing systems from a theoretical viewpoint. Petri net models are generalized for formulating dynamic manufacturing processes, based on which a detailed approach for enabling traceability analysis is presented. Models as well as algorithms are carefully designed, which can trace back the lifecycle of a possibly contaminated item. A practical prototype system for supporting traceability is designed, and a real-life case study of a quality control system for bee products is presented to validate the effectiveness of the approach.
Gods, Germs, and Petri Dishes: Toward a Nonsecular Medical Anthropology.
Roberts, Elizabeth F S
2016-01-01
This commentary calls on medical anthropology to become programmatically non-secular. Despite recent anthropological critiques of secularity, within and outside of anthropology, most contemporary medical anthropologists continue to leave deities and religiosity out of their examinations of healing practices, especially in their accounts of biomedicine. Through a critical, relational constructionist lens, which traces how all entities are both constructed and real, a non-secular medical anthropology would insist that when deities are part of medical practice, they are integral to analysis. Importantly then, within the symmetrical nature of this same constructionist lens, biomedical entities like germs and petri dishes need to be accounted for just as much as deities.
A vector matching method for analysing logic Petri nets
Du, YuYue; Qi, Liang; Zhou, MengChu
2011-11-01
Batch processing function and passing value indeterminacy in cooperative systems can be described and analysed by logic Petri nets (LPNs). To directly analyse the properties of LPNs, the concept of transition enabling vector sets is presented and a vector matching method used to judge the enabling transitions is proposed in this article. The incidence matrix of LPNs is defined; an equation about marking change due to a transition's firing is given; and a reachable tree is constructed. The state space explosion is mitigated to a certain extent from directly analysing LPNs. Finally, the validity and reliability of the proposed method are illustrated by an example in electronic commerce.
Petri net modeling of encrypted information flow in federated cloud
Khushk, Abdul Rauf; Li, Xiaozhong
2017-08-01
Solutions proposed and developed for the cost-effective cloud systems suffer from a combination of secure private clouds and less secure public clouds. Need to locate applications within different clouds poses a security risk to the information flow of the entire system. This study addresses this by assigning security levels of a given lattice to the entities of a federated cloud system. A dynamic flow sensitive security model featuring Bell-LaPadula procedures is explored that tracks and authenticates the secure information flow in federated clouds. Additionally, a Petri net model is considered as a case study to represent the proposed system and further validate the performance of the said system.
The Practitioner's guide to Coloured Petri Nets
DEFF Research Database (Denmark)
Kristensen, Lars Michael; Christensen, Søren; Jensen, Kurt
1998-01-01
four hundred commercial companies. It is available free of charge, also for commercial use. This paper provides a comprehensive road map to the practical use of CP-nets and the Design/CPN tool. We give an informal introduction to the basic concepts and ideas underliying CP-nets. The key components...... and facilities of the Design/CPN tool are presented and their use illustrated. The paper is self-contained and does not assume any prior kowledge of Petri nets and CP-nets nor any experience with the Design/CPN tool...
Formal Verification of Computerized Procedure with Colored Petri Nets
International Nuclear Information System (INIS)
Kim, Yun Goo; Shin, Yeong Cheol
2008-01-01
Computerized Procedure System (CPS) supports nuclear power plant operators in performing operating procedures which are instructions to guide in monitoring, decision making and controlling nuclear power plants. Computerized Procedure (CP) should be loaded to CPS. Due to its execution characteristic, computerized procedure acts like a software in CPS. For example, procedure flows are determined by operator evaluation and computerized procedure logic which are pre-defined. So the verification of Computerized Procedure logic and execution flow is needed before computerized procedures are installed in the system. Formal verification methods are proposed and the modeling of operating procedures with Coloured Petri Nets(CP-nets) is presented
International Nuclear Information System (INIS)
Bisognano, J.; Leemann, C.
1982-03-01
Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron
A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets
DEFF Research Database (Denmark)
David, Alexandre; Jacobsen, Lasse; Jacobsen, Morten
2012-01-01
Timed-arc Petri nets (TAPN) are a well-known time extension of thePetri net model and several translations to networks of timedautomata have been proposed for this model.We present a direct, DBM-basedalgorithm for forward reachability analysis of bounded TAPNs extended with transport arcs...
A Method to Compare the Descriptive Power of Different Types of Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1980-01-01
The purpose of this paper is to show how the descriptive power of different types of Petri nets can be compared, without the use of Petri net languages. Moreover the paper proposes an extension of condition/event-nets and it is shown that this extension has the same descriptive power as condition/event-nets....
A primer on the Petri Net Markup Language and ISO/IEC 15909-2
DEFF Research Database (Denmark)
Hillah, L. M.; Kindler, Ekkart; Kordon, F.
2009-01-01
Standard, defines a transfer format for high-level nets. The transfer format defined in Part 2 of ISO/IEC 15909 is (or is based on) the \\emph{Petri Net Markup Language} (PNML), which was originally introduced as an interchange format for different kinds of Petri nets. In ISO/IEC 15909-2, however...
PetriCode: A Tool for Template-Based Code Generation from CPN Models
DEFF Research Database (Denmark)
Simonsen, Kent Inge
2014-01-01
Code generation is an important part of model driven methodologies. In this paper, we present PetriCode, a software tool for generating protocol software from a subclass of Coloured Petri Nets (CPNs). The CPN subclass is comprised of hierarchical CPN models describing a protocol system at different...
State Space Analysis of Hierarchical Coloured Petri Nets
DEFF Research Database (Denmark)
Christensen, Søren; Kristensen, Lars Michael
2003-01-01
In this paper, we consider state space analysis of Coloured Petri Nets. It is well-known that almost all dynamic properties of the considered system can be verified when the state space is finite. However, state space analysis is more than just formulating a set of formal requirements and invokin...... supporting computation and storage of state spaces which exploi the hierarchical structure of the models....... in which formal verification, partial state spaces, and analysis by means of graphical feedback and simulation are integrated entities. The focus of the paper is twofold: the support for graphical feedback and the way it has been integrated with simulation, and the underlying algorithms and data-structures......In this paper, we consider state space analysis of Coloured Petri Nets. It is well-known that almost all dynamic properties of the considered system can be verified when the state space is finite. However, state space analysis is more than just formulating a set of formal requirements and invoking...
Applying Petri nets in modelling the human factor
International Nuclear Information System (INIS)
Bedreaga, Luminita; Constntinescu, Cristina; Guzun, Basarab
2007-01-01
Usually, in the reliability analysis performed for complex systems, we determine the success probability to work with other performance indices, i.e. the likelihood associated with a given state. The possible values assigned to system states can be derived using inductive methods. If one wants to calculate the probability to occur a particular event in the system, then deductive methods should be applied. In the particular case of the human reliability analysis, as part of probabilistic safety analysis, the international regulatory commission have developed specific guides and procedures to perform such assessments. The paper presents the modality to obtain the human reliability quantification using the Petri nets approach. This is an efficient means to assess reliability systems because of their specific features. The examples showed in the paper are from human reliability documentation without a detailed human factor analysis (qualitative). We present human action modelling using event trees and Petri nets approach. The obtained results by these two kinds of methods are in good concordance. (authors)
Linear stochastic neutron transport theory
International Nuclear Information System (INIS)
Lewins, J.
1978-01-01
A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Borodin, Andrei N
2017-01-01
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Entropy Production in Stochastics
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Demetris Koutsoyiannis
2017-10-01
Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.
Directory of Open Access Journals (Sweden)
Özgür ARMANERİ
2006-01-01
Full Text Available As in many engineering fields, the design of manufacturing systems can be carried out using models. Petri nets have been used extensively to model and analyze manufacturing systems. Petri Nets, as graphical and mathematical tools, provide a uniform environment for modeling, format analysis and design of discrete event systems. The modeling, simulation and analysis of simple one machine-two product systems using Petri nets will be presented in this paper. Behavioral and structural properties of the Petri net model will be considered in details. Then, the Petri net model of one machine-two product system will be simulated using a simulation program.
The methodology of multicriterial assessment of Petri nets’ apparatus
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Pashchenko Dmitry
2016-01-01
Full Text Available This article emphasizes the effectiveness and relevance of the using of the apparatus of Petri nets for modeling of complex computing systems. Due to the fact that the methods of analysis existing in this theory do not allow estimating the resources required to build the desired model of the system, there is a problem of shortage of criteria for its evaluation in terms of the complexity of the construction. In the article we consider the method of analysis of a random Petri net based on the complexity of its building and relationships of internal units - subnets. The purpose of this article is a software implementation of such an assessment within the theory of PN structures. Due to the fact, that structural approach allows to perform the operation of decomposition of the original system, this model can be divided into subnets of minimal dimension, that will allow to make its quantitative assessment - ranking. To determine the total assessment of the input and output data of the system we will perform the analysis of head and tail positions of the net taking into account the weights of the input and output arcs of these positions. In order to identify an extent of the cost required to build the system, the number of operations of union of subnet transitions and positions. These subnets have minimal dimension in the original PN. Thus, the article demonstrates the formal implementation of assessment technique modules with using of algebra of sets, and the rules of splitting the PN structure into elementary blocks are formulated. The example of a comparative assessment of the two Petri nets based on the proposed complexity criteria is given; the plots of PN in different coordinate systems are displayed. The article presents the results of the research - a plot of PN structures in three-dimensional space, implemented using described software. It demonstrates the accuracy of PN assessment by structural analysis in comparing with a non
Stochastic quantization of gravity and string fields
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
The stochastic quantization method of Parisi and Wu is generalized so as to make it applicable to Einstein's theory of gravitation. The generalization is based on the existence of a preferred metric in field configuration space, involves Ito's calculus, and introduces a complex stochastic process adapted to Lorentzian spacetime. It implies formally the path integral measure of DeWitt, a causual Feynman propagator, and a consistent stochastic perturbation theory. The lineraized version of the theory is also obtained from the stochastic quantization of the free string field theory of Siegel and Zwiebach. (Author)
Manufacturing Scheduling Using Colored Petri Nets and Reinforcement Learning
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Maria Drakaki
2017-02-01
Full Text Available Agent-based intelligent manufacturing control systems are capable to efficiently respond and adapt to environmental changes. Manufacturing system adaptation and evolution can be addressed with learning mechanisms that increase the intelligence of agents. In this paper a manufacturing scheduling method is presented based on Timed Colored Petri Nets (CTPNs and reinforcement learning (RL. CTPNs model the manufacturing system and implement the scheduling. In the search for an optimal solution a scheduling agent uses RL and in particular the Q-learning algorithm. A warehouse order-picking scheduling is presented as a case study to illustrate the method. The proposed scheduling method is compared to existing methods. Simulation and state space results are used to evaluate performance and identify system properties.
Formal Requirements Modeling for Reactive Systems with Coloured Petri Nets
DEFF Research Database (Denmark)
Tjell, Simon
This dissertation presents the contributions of seven publications all concerned with the application of Coloured Petri Nets (CPN) to requirements modeling for reactive systems. The publications are introduced along with relevant background material and related work, and their contributions...... to take into concern that the behavior of human actors is less likely to be predictable than the behavior of e.g. mechanical components. In the second approach, the CPN model is parameterized and utilizes a generic and reusable CPN module operating as an SD interpreter. In addition to distinguishing...... and events. A tool is presented that allows automated validation of the structure of CPN models with respect to the guidelines. Next, three publications on integrating Jackson's Problem Frames with CPN requirements models are presented: The first publication introduces a method for systematically structuring...
A Concurrent Multiple Negotiation Protocol Based on Colored Petri Nets.
Niu, Lei; Ren, Fenghui; Zhang, Minjie; Bai, Quan
2017-11-01
Concurrent multiple negotiation (CMN) provides a mechanism for an agent to simultaneously conduct more than one negotiation. There may exist different interdependency relationships among these negotiations and these interdependency relationships can impact the outcomes of these negotiations. The outcomes of these concurrent negotiations contribute together for the agent to achieve an overall negotiation goal. Handling a CMN while considering interdependency relationships among multiple negotiations is a challenging research problem. This paper: 1) comprehensively highlights research problems of negotiations at concurrent negotiation level; 2) provides a graph-based CMN model with consideration of the interdependency relationships; and 3) proposes a colored Petri net-based negotiation protocol for conducting CMNs. With the proposed protocol, a CMN can be efficiently and concurrently processed and negotiation agreements can be efficiently achieved. Experimental results indicate the effectiveness and efficiency of the proposed protocol in terms of the negotiation success rate, the negotiation time and the negotiation outcome.
Control Design for Untimed Petri Nets Using Markov Decision Processes
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Cherki Daoui
2017-01-01
Full Text Available Design of control sequences for discrete event systems (DESs has been presented modelled by untimed Petri nets (PNs. PNs are well-known mathematical and graphical models that are widely used to describe distributed DESs, including choices, synchronizations and parallelisms. The domains of application include, but are not restricted to, manufacturing systems, computer science and transportation networks. We are motivated by the observation that such systems need to plan their production or services. The paper is more particularly concerned with control issues in uncertain environments when unexpected events occur or when control errors disturb the behaviour of the system. To deal with such uncertainties, a new approach based on discrete time Markov decision processes (MDPs has been proposed that associates the modelling power of PNs with the planning power of MDPs. Finally, the simulation results illustrate the benefit of our method from the computational point of view. (original abstract
Detection and Modeling of Cyber Attacks with Petri Nets
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Bartosz Jasiul
2014-12-01
Full Text Available The aim of this article is to present an approach to develop and verify a method of formal modeling of cyber threats directed at computer systems. Moreover, the goal is to prove that the method enables one to create models resembling the behavior of malware that support the detection process of selected cyber attacks and facilitate the application of countermeasures. The most common cyber threats targeting end users and terminals are caused by malicious software, called malware. The malware detection process can be performed either by matching their digital signatures or analyzing their behavioral models. As the obfuscation techniques make the malware almost undetectable, the classic signature-based anti-virus tools must be supported with behavioral analysis. The proposed approach to modeling of malware behavior is based on colored Petri nets. This article is addressed to cyber defense researchers, security architects and developers solving up-to-date problems regarding the detection and prevention of advanced persistent threats.
Automatic Structure-Based Code Generation from Coloured Petri Nets
DEFF Research Database (Denmark)
Kristensen, Lars Michael; Westergaard, Michael
2010-01-01
Automatic code generation based on Coloured Petri Net (CPN) models is challenging because CPNs allow for the construction of abstract models that intermix control flow and data processing, making translation into conventional programming constructs difficult. We introduce Process-Partitioned CPNs...... (PP-CPNs) which is a subclass of CPNs equipped with an explicit separation of process control flow, message passing, and access to shared and local data. We show how PP-CPNs caters for a four phase structure-based automatic code generation process directed by the control flow of processes....... The viability of our approach is demonstrated by applying it to automatically generate an Erlang implementation of the Dynamic MANET On-demand (DYMO) routing protocol specified by the Internet Engineering Task Force (IETF)....
A Method of Sample Models of Program Construction in Terms of Petri Nets
Directory of Open Access Journals (Sweden)
D. I. Kharitonov
2015-01-01
Full Text Available In the article a method of automated construction of Petri nets simulating the behaviour of imperative programs is considered from the formal point of view. Petri net samples with certain characteristics are necessary in programming new algorithms for program analysis; in particular, they can be used for developing or optimizing algorithms of Petri nets compositions and decompositions, building the reachability tree, checking invariants and so on. The generation process consists of two stages. At the ﬁrst stage, construction templates for a resulting net and parameters for construction are described. With the help of these parameters it is possible to regulate the ﬁnal size and the absolute or relative amount of certain structures in the resulting net. At the second stage, iterative process of automated net construction is used for Petri net generation of any size, limited only by an available computer memory. In the ﬁrst section of the article the minimum necessary deﬁnitions are given and a new version of Petri nets composition operation by places is introduced. Commutative and associative properties of introduced binary operation allow to synchronize any number of Petri nets in arbitrary order. Then construction template is deﬁned as a marked Petri net with input and output interfaces and rules for templates composition using this interfaces. A number of construction templates can be united in a collection, for which the evolution rules are deﬁned. The completeness property of a collection guarantees that the collection evolution results in a Petri net that simulates the imperative program behavior. The article provides a version of the construction templates complete collection and an example of Petri net simulating sequential imperative program construction.
International Nuclear Information System (INIS)
Colombino, A.; Mosiello, R.; Norelli, F.; Jorio, V.M.; Pacilio, N.
1975-01-01
A nuclear system kinetics is formulated according to a stochastic approach. The detailed probability balance equations are written for the probability of finding the mixed population of neutrons and detected neutrons, i.e. detectrons, at a given level for a given instant of time. Equations are integrated in search of a probability profile: a series of cases is analyzed through a progressive criterium. It tends to take into account an increasing number of physical processes within the chosen model. The most important contribution is that solutions interpret analytically experimental conditions of equilibrium (moise analysis) and non equilibrium (pulsed neutron measurements, source drop technique, start up procedures)
Directory of Open Access Journals (Sweden)
Romanu Ekaterini
2006-01-01
Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.
Stochastic theories of quantum mechanics
International Nuclear Information System (INIS)
De la Pena, L.; Cetto, A.M.
1991-01-01
The material of this article is organized into five sections. In Sect. I the basic characteristics of quantum systems are briefly discussed, with emphasis on their stochastic properties. In Sect. II a version of stochastic quantum mechanics is presented, to conclude that the quantum formalism admits an interpretation in terms of stochastic processes. In Sect. III the elements of stochastic electrodynamics are described, and its possibilities and limitations as a fundamental theory of quantum systems are discussed. Section IV contains a recent reformulation that overcomes the limitations of the theory discussed in the foregoing section. Finally, in Sect. V the theorems of EPR, Von Neumann and Bell are discussed briefly. The material is pedagogically presented and includes an ample list of references, but the details of the derivations are generally omitted. (Author)
Reliability modelling of repairable systems using Petri nets and fuzzy Lambda-Tau methodology
International Nuclear Information System (INIS)
Knezevic, J.; Odoom, E.R.
2001-01-01
A methodology is developed which uses Petri nets instead of the fault tree methodology and solves for reliability indices utilising fuzzy Lambda-Tau method. Fuzzy set theory is used for representing the failure rate and repair time instead of the classical (crisp) set theory because fuzzy numbers allow expert opinions, linguistic variables, operating conditions, uncertainty and imprecision in reliability information to be incorporated into the system model. Petri nets are used because unlike the fault tree methodology, the use of Petri nets allows efficient simultaneous generation of minimal cut and path sets
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Stochastic calculus and applications
Cohen, Samuel N
2015-01-01
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
The stochastic quality calculus
DEFF Research Database (Denmark)
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...... with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...
On Lipschitzian quantum stochastic differential inclusions
International Nuclear Information System (INIS)
Ekhaguere, G.O.S.
1990-12-01
Quantum stochastic differential inclusions are introduced and studied within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus. Results concerning the existence of solutions of a Lipschitzian quantum stochastic differential inclusion and the relationship between the solutions of such an inclusion and those of its convexification are presented. These generalize the Filippov existence theorem and the Filippov-Wazewski Relaxation Theorem for classical differential inclusions to the present noncommutative setting. (author). 9 refs
Ambit processes and stochastic partial differential equations
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....
The Robustness of Stochastic Switching Networks
Loh, Po-Ling; Zhou, Hongchao; Bruck, Jehoshua
2009-01-01
Many natural systems, including chemical and biological systems, can be modeled using stochastic switching circuits. These circuits consist of stochastic switches, called pswitches, which operate with a fixed probability of being open or closed. We study the effect caused by introducing an error of size ∈ to each pswitch in a stochastic circuit. We analyze two constructions – simple series-parallel and general series-parallel circuits – and prove that simple series-parallel circuits are robus...
Time Extensions of Petri Nets for Modelling and Verification of Hard Real-Time Systems
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Tomasz Szmuc
2002-01-01
Full Text Available The main aim ofthe paper is a presentation of time extensions of Petri nets appropriate for modelling and analysis of hard real-time systems. It is assumed, that the extensions must provide a model of time flow an ability to force a transition to fire within a stated timing constraint (the so-called the strong firing rule, and timing constraints represented by intervals. The presented survey includes extensions of classical Place/Transition Petri nets, as well as the ones applied to high-level Petri nets. An expressiveness of each time extension is illustrated using simple hard real-time system. The paper includes also a brief description of analysis and veryication methods related to the extensions, and a survey of software tools supporting modelling and analysis ofthe considered Petri nets.
An Efficient Translation of Timed-Arc Petri Nets to Networks of Timed Automata
DEFF Research Database (Denmark)
Byg, Joakim; Jørgensen, Kenneth Yrke; Srba, Jiri
2009-01-01
Bounded timed-arc Petri nets with read-arcs were recently proven equivalent to networks of timed automata, though the Petri net model cannot express urgent behaviour and the described mutual trans- lations are rather inefficient. We propose an extension of timed-arc Petri nets with invariants...... to enforce urgency and with transport arcs to generalise the read-arcs. We also describe a novel translation from the extended timed-arc Petri net model to networks of timed automata. The translation is implemented in the tool TAPAAL and it uses UPPAAL as the verification engine. Our experiments confirm...... the efficiency of the translation and in some cases the translated models verify significantly faster than the native UPPAAL models do....
Ninth Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools
DEFF Research Database (Denmark)
Daniel Moldt, Gremany Laure Petrucci, France Rüdiger Vlak, Germany Lee Wagenhals, USA Karsten Wolf, Germany Jianli Xu, Finland The programme committee has accepted 10 papers for presentation. Most of these deal with different projects in which Coloured Petri Nets and their tools have been put......This booklet contains the proceedings of the Ninth Workshop on Pratical Use of Coloured Petri Nets and CPN Tools, October 20-22, 2008. The workshop is organised by the CPN group at the Department of Computer Science, Aarhus University, Denmark. Coloured Petri Nets and the CPN Tools are now licensed...... to more than 7,200 users in 138 countries. The aim of the workshop is to bring together some of the users and in this way provide a forum for those who are interested in the practical use of Coloured Petri nets and their tools. The submitted papers were evaluated by a programme committee...
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Directory of Open Access Journals (Sweden)
Jennifer Scheidel
2015-12-01
Full Text Available The insulin-dependent activation and recycling of the insulin receptor play an essential role in the regulation of the energy metabolism, leading to a special interest for pharmaceutical applications. Thus, the recycling of the insulin receptor has been intensively investigated, experimentally as well as theoretically. We developed a time-resolved, discrete model to describe stochastic dynamics and study the approximation of non-linear dynamics in the context of timed Petri nets. Additionally, using a graph-theoretical approach, we analyzed the structure of the regulatory system and demonstrated the close interrelation of structural network properties with the kinetic behavior. The transition invariants decomposed the model into overlapping subnetworks of various sizes, which represent basic functional modules. Moreover, we computed the quasi-steady states of these subnetworks and demonstrated that they are fundamental to understand the dynamic behavior of the system. The Petri net approach confirms the experimental results of insulin-stimulated degradation of the insulin receptor, which represents a common feature of insulin-resistant, hyperinsulinaemic states.
Modeling biological gradient formation: combining partial differential equations and Petri nets.
Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J
2016-01-01
Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.
Workshop on Practical Use of Coloured Petri Nets and Design/CPN
DEFF Research Database (Denmark)
This booklet contains the proceedings of the 1998 Workshop on Practical use of Coloured Petri Nets and Design/CPN. The papers are also available in electronic form via the CPN Web pages at University of Aarhus.......This booklet contains the proceedings of the 1998 Workshop on Practical use of Coloured Petri Nets and Design/CPN. The papers are also available in electronic form via the CPN Web pages at University of Aarhus....
Stochasticity Modeling in Memristors
Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.
2015-01-01
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Stochastic quantization of instantons
International Nuclear Information System (INIS)
Grandati, Y.; Berard, A.; Grange, P.
1996-01-01
The method of Parisi and Wu to quantize classical fields is applied to instanton solutions var-phi I of euclidian non-linear theory in one dimension. The solution var-phi var-epsilon of the corresponding Langevin equation is built through a singular perturbative expansion in var-epsilon=h 1/2 in the frame of the center of the mass of the instanton, where the difference var-phi var-epsilon -var-phi I carries only fluctuations of the instanton form. The relevance of the method is shown for the stochastic K dV equation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, the authors obtain explicit expressions for the first two orders in var-epsilon of the pertrubed instanton of its Green function. Specializing to the Sine-Gordon and var-phi 4 models, the first anaharmonic correction is obtained analytically. The calculation is carried to second order for the var-phi 4 model, showing good convergence. 21 refs., 5 fig
Gambling addiction in primary care: a survey of general practitioners ...
African Journals Online (AJOL)
Arun Kumar Agnihotri
experiences of, and confidence in, managing these patients in primary care, their perceived role and ... KEY WORDS: Gambling addiction; Primary care; General practitioners; Management ..... Petry NM, Blanco C, Auriacombe M, Borges.
International Nuclear Information System (INIS)
Wu, Xin-yang; Wu, Xiao-Yue
2015-01-01
Phased Mission Systems (PMS) have several phases with different success criteria. Generally, traditional analytical methods need to make some assumptions when they are applied for reliability evaluation and analysis of complex PMS, for example, the components are non-repairable or components are not subjected to common cause failures (CCF). However, the evaluation and analysis results may be inapplicable when the assumptions do not agree with practical situation. In this article, we propose an extended object-oriented Petri net (EOOPN) model for mission reliability simulation of repairable PMS with CCFs. Based on object-oriented Petri net (OOPN), EOOPN defines four reusable sub-models to depict PMS at system, phase, or component levels respectively, logic transitions to depict complex components reliability logics in a more readable form, and broadcast place to transmit shared information among components synchronously. After extension, EOOPN could deal with repairable PMS with both external and internal CCFs conveniently. The mission reliability modelling, simulation and analysis using EOOPN are illustrated by a PMS example. The results demonstrate that the proposed EOOPN model is effective. - Highlights: • EOOPN model was effective in reliability simulation for repairable PMS with CCFs. • EOOPN had modular and hierarchical structure. • New elements of EOOPN made the modelling process more convenient and friendlier. • EOOPN had better model reusability and readability than other PNs
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Analytic stochastic regularization and gange invariance
International Nuclear Information System (INIS)
Abdalla, E.; Gomes, M.; Lima-Santos, A.
1986-05-01
A proof that analytic stochastic regularization breaks gauge invariance is presented. This is done by an explicit one loop calculation of the vaccum polarization tensor in scalar electrodynamics, which turns out not to be transversal. The counterterm structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization, are also analysed. (Author) [pt
Fast substation service restoration using intelligent petri-nets models
Energy Technology Data Exchange (ETDEWEB)
Yang, H.T.; Peng, P.C.; Jiang, H.L. [Chung Yuan Christian Univ., Chung Li, Taiwan (China)
2006-07-01
Service restoration of a substation is a stressful and immediate task that must be conducted by system operators following a blackout. Operators, including those of Taiwan Power Company (TPC), normally restore power loads on the basis of their past experiences and engineering heuristics. Due to the significant number of switching operations to be evaluated, a computer-aided decision support system can be quite valuable. In distribution system automation, installation of unmanned substations requires an automated restoration computer system to rapidly devise a switching plan after a fault event. The modeling technique of Petri Nets (PNs) encompasses fault diagnosis of distribution systems, protective scheming of relays, and generic restoration schedule of power transmission systems. Knowledge or configuration about the system concerned can be expressed systematically through a structured model with parallelism and synchronization. This paper proposed a new PNs knowledge representation scheme to achieve a fast, on-line service restoration plan of a substation. The paper described the task of service restoration in a substation as well as the heuristic rules adopted by the dispatchers of the TPC distribution systems. The paper also introduced the topic of Typical PN properties and the proposed matrix operations for PNs reasoning. The proposed basic PNs model for service restoration on the basis of the engineering heuristics were also identified. It was concluded that the proposed approach not only facilitated software programming, but was highly adaptive to the extension or maintenance of the developed programs, arising from the changes of the substation configuration. 18 refs., 1 tab., 8 figs.
SOFTWARE FOR FAULT DIAGNOSIS USING KNOWLEDGE MODELS IN PETRI NETS
Directory of Open Access Journals (Sweden)
ADRIAN ARBOLEDA
2012-01-01
Full Text Available Los sistemas de diagnóstico de fallas en empresas asociadas al sector eléctrico requieren propiedades de precisión y flexibilidad cuando surgen eventos de falla. Actualmente existen sistemas que pretenden mejorar el proceso de diagnóstico mediante varios métodos y técnicas computacionales, reduciendo el tiempo de respuesta a perturbaciones. Sin embargo, son pocas las propuestas que unifican modelos gráficos de conocimiento con las señales de un proceso que pueden ofrecer dispositivos como controladores lógicos programables (PLCs. Este artículo propone un software novedoso guiado por modelos basados en redes de Petri e integrado con señales del proceso, para el diagnóstico de falla en centrales de generación eléctrica. Un caso de estudio demuestra la flexibilidad y adaptabilidad del software cuando nuevas nociones en los modelos de conocimiento cambian, sin realizar procedimientos de reingeniería al software.
Evaluation of software architecture using fuzzy colored Petri nets
Directory of Open Access Journals (Sweden)
Vahid Abroshan
2013-02-01
Full Text Available Software Architecture (SA is one of the most important artifacts for life cycle of a software system because it incorporates some important decisions and principles for the system development. On the other hand, developing the systems based on uncertain and ambiguous requirement has been increased, significantly. Therefore, there have been significant attentions on SA requirements. In this paper, we present a new method for evaluation of performance characteristics based on a use case, response time, and queue length of SA. Since there are some ambiguities associated with considered systems, we use the idea of Fuzzy UML (F-UML diagrams. In addition, these diagrams have been enriched with performance annotations using proposed Fuzzy-SPT sub profile, the extended version of SPT profile proposed by OMG. Then, these diagrams are mapped into an executable model based on Fuzzy Colored Petri Nets (FCPN and finally the performance metrics are calculated using the proposed algorithms. We have implemented CPN-Tools for creating and evaluating the FCPN model.
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Stochastic models: theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Stochastic quantization of Einstein gravity
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
We determine a one-parameter family of covariant Langevin equations for the metric tensor of general relativity corresponding to DeWitt's one-parameter family of supermetrics. The stochastic source term in these equations can be expressed in terms of a Gaussian white noise upon the introduction of a stochastic tetrad field. The only physically acceptable resolution of a mathematical ambiguity in the ansatz for the source term is the adoption of Ito's calculus. By taking the formal equilibrium limit of the stochastic metric a one-parameter family of covariant path-integral measures for general relativity is obtained. There is a unique parameter value, distinguished by any one of the following three properties: (i) the metric is harmonic with respect to the supermetric, (ii) the path-integral measure is that of DeWitt, (iii) the supermetric governs the linearized Einstein dynamics. Moreover the Feynman propagator corresponding to this parameter is causal. Finally we show that a consistent stochastic perturbation theory gives rise to a new type of diagram containing ''stochastic vertices.''
Petrišin, Grigori
2009-01-01
Riigikogu liikme, endise Tallinna abilinnapea Kalev Kallo poole pöördus ettevõtja Grigori Petrišin, keda kaitsepolitsei oli sundinud väidetavalt oma firma nimel kirjutama linnajuhte kompromiteerivaid kirju. Nüüd väidab ettevõtja, et teda on ära kasutatud valimiseelsetes võimumängudes
Stochastic mechanics and quantum theory
International Nuclear Information System (INIS)
Goldstein, S.
1987-01-01
Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic) physical reality. Stochastic mechanics presents a unified treatment of the microscopic and macroscopic domains, in which the process of measurement plays no special physical role and which reduces to Newtonian mechanics in the macroscopic limit
Fundamentals of stochastic nature sciences
Klyatskin, Valery I
2017-01-01
This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under wh...
Stochastic quantization and topological theories
International Nuclear Information System (INIS)
Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.
1992-01-01
In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones
Stochastic tools in turbulence
Lumey, John L
2012-01-01
Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the
Modelling of Biometric Identification System with Given Parameters Using Colored Petri Nets
Petrosyan, G.; Ter-Vardanyan, L.; Gaboutchian, A.
2017-05-01
Biometric identification systems use given parameters and function on the basis of Colored Petri Nets as a modelling language developed for systems in which communication, synchronization and distributed resources play an important role. Colored Petri Nets combine the strengths of Classical Petri Nets with the power of a high-level programming language. Coloured Petri Nets have both, formal intuitive and graphical presentations. Graphical CPN model consists of a set of interacting modules which include a network of places, transitions and arcs. Mathematical representation has a well-defined syntax and semantics, as well as defines system behavioural properties. One of the best known features used in biometric is the human finger print pattern. During the last decade other human features have become of interest, such as iris-based or face recognition. The objective of this paper is to introduce the fundamental concepts of Petri Nets in relation to tooth shape analysis. Biometric identification systems functioning has two phases: data enrollment phase and identification phase. During the data enrollment phase images of teeth are added to database. This record contains enrollment data as a noisy version of the biometrical data corresponding to the individual. During the identification phase an unknown individual is observed again and is compared to the enrollment data in the database and then system estimates the individual. The purpose of modeling biometric identification system by means of Petri Nets is to reveal the following aspects of the functioning model: the efficiency of the model, behavior of the model, mistakes and accidents in the model, feasibility of the model simplification or substitution of its separate components for more effective components without interfering system functioning. The results of biometric identification system modeling and evaluating are presented and discussed.
Perturbation theory for continuous stochastic equations
International Nuclear Information System (INIS)
Chechetkin, V.R.; Lutovinov, V.S.
1987-01-01
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Modelado de redes de Petri con retroalimentación de activación
López Eslava, Eduardo
2016-01-01
Muchos sistemas no pueden ser descritos por ecuaciones diferenciales, sistemas en los cuales la ocurrencia de algún evento puede llevar al sistema de un estado a otro, y en los cuales un evento puede ocurrir abruptamente o en un instante de tiempo indeterminado. Las redes de Petri son una herramienta matemática y gráfica para sistemas que presentan este tipo de características. El carácter visual de las redes de Petri nos permite observar el flujo de comportamiento de un sistema en cada una d...
METHOD OF DISPLAYING AN EXECUTABLE BUSINESS PROCESS MODELS INTO PETRI NETS
Directory of Open Access Journals (Sweden)
Igor G. Fedorov
2013-01-01
Full Text Available Executable business process models, as well as programs, require evidence of a defect-free finish. The methods based on the formalism of Petri nets are widely used. A business process is a network of dishes, and its properties are set by the analysis of the properties of the network. The aim is to study the methods of displaying an executable business process model in a Petri net. Analysis of the properties of the resulting model allows us to prove a number of important properties: it is a network of free choice and clean without looping.
Propuesta de un tipo de redes de Petri temporizadas para el modelado de procesos
Gonzaléz, Ariel; Vaisman, Gabriel David
2001-01-01
Las Redes de Petri (RP) son un formalismo gráfico para la especificación de sistemas, las cuales pertenecen a la clase de modelos operacionales y son apropiadas cuando se desean describir las propiedades dinámicas de los sistemas. Además, la flexibilidad del modelo permite extenderlo en varias direcciones manteniendo su filosofía original. En el presente trabajo utilizaremos como base un modelo de Red de Petri Temporizada basadas en relojes para luego extenderlo con el concepto de Subredes au...
Quantization of dynamical systems and stochastic control theory
International Nuclear Information System (INIS)
Guerra, F.; Morato, L.M.
1982-09-01
In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
Environmental Stochasticity and the Speed of Evolution
Danino, Matan; Kessler, David A.; Shnerb, Nadav M.
2018-03-01
Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.
Fastest Rates for Stochastic Mirror Descent Methods
Hanzely, Filip
2018-03-20
Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.
Fastest Rates for Stochastic Mirror Descent Methods
Hanzely, Filip; Richtarik, Peter
2018-01-01
Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.
Model checking of time Petri nets using the state class timed automaton
DEFF Research Database (Denmark)
Lime, Didier; Roux, Olivier H.
2006-01-01
In this paper, we propose a method for building the state class graph of a bounded time Petri net (TPN) as a timed automaton (TA), which we call the state class timed automaton. We consider bounded TPN, whose underlying net is not necessarily bounded. We prove that our translation preserves the b...
A Case Study on Coloured Petri Nets in Object-oriented Analysis and Design
DEFF Research Database (Denmark)
Barros, Joao Paulo; Jørgensen, Jens Bæk
2005-01-01
In this paper, we first demonstrate how a coloured Petri nets (CPN) model can be used to capture requirements for a considered example system, an elevator controller. Then, we show how this requirements-level CPN model is transformed into a design-level object-oriented CPN model, which...
DEFF Research Database (Denmark)
Tjell, Simon; Lassen, Kristian Bisgaard
2008-01-01
In this paper, we describe a formal foundation for a specialized approach to automatically checking traces against real-time requirements. The traces are obtained from simulation of Coloured Petri Net (CPN) models of reactive systems. The real-time requirements are expressed in terms of a derivat...
Polymorphism and Module-Reuse Mechanisms for Algebraic Petri Nets in CoopnTools
Buffo, Mathieu; Buchs, Didier; Donatelli, S.; Kleijn, J.
1999-01-01
This paper introduces CoopnTools, a tool set allowing the support of object-oriented specifications written by means of the language CO-OPN/2, based on synchronised algebraic Petri nets. In particular, this paper shows how concrete mechanisms dealing with polymorphism and module-reuse are implemented in CoopnTools.
Model-Based Testing of a Reactive System with Coloured Petri Nets
DEFF Research Database (Denmark)
Tjell, Simon
2006-01-01
In this paper, a reactive and nondeterministic system is tested. This is doneby applying a generic model that has been specified as a configurable Coloured PetriNet. In this way, model-based testing is possible for a wide class of reactive system atthe level of discrete events. Concurrently...
Protos2CPN: using colored Petri nets for confuguring and testing business processes
Gottschalk, F.; Aalst, van der W.M.P.; Vullers - Jansen, M.H.; Verbeek, H.M.W.
2008-01-01
Protos is a popular tool for business process modelling used in more than 1,500 organizations. It has a built-in Petri-net-based simulation engine which shows key performance indicators for the modelled processes. Reference process models offered for Protos reduce modelling efforts by providing
Pascal Semantics by a Combination of Denotational Semantics and High-level Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt; Schmidt, Erik Meineche
1986-01-01
This paper describes the formal semantics of a subset of PASCAL, by means of a semantic model based on a combination of denotational semantics and high-level Petri nets. It is our intention that the paper can be used as part of the written material for an introductory course in computer science....
Beta Instability and Stochastic Market Weights
David H. Goldenberg
1985-01-01
An argument is given for individual firm beta instability based upon the stochastic character of the market weights defining the market portfolio and the constancy of its beta. This argument is generalized to market weighted portfolios and the form of the stochastic process generating betas is linked to that of the market return process. The implications of this analysis for adequacy of models of beta nonstationarity and estimation of betas are considered in light of the available empirical e...
Approximative solutions of stochastic optimization problem
Czech Academy of Sciences Publication Activity Database
Lachout, Petr
2010-01-01
Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Quantum stochastic calculus associated with quadratic quantum noises
International Nuclear Information System (INIS)
Ji, Un Cig; Sinha, Kalyan B.
2016-01-01
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus
Quantum stochastic calculus associated with quadratic quantum noises
Energy Technology Data Exchange (ETDEWEB)
Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)
2016-02-15
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Aspects regarding at 13C isotope separation column control using Petri nets system
International Nuclear Information System (INIS)
Boca, M L; Ciortea, M E
2015-01-01
This paper is intended to show that Petri nets can be also applicable in the chemical industry. It used linear programming, modeling underlying Petri nets, especially discrete event systems for isotopic separation, the purpose of considering and control events in real-time through graphical representations. In this paper it is simulate the control of 13 C Isotope Separation column using Petri nets. The major problem with 13 C comes from the difficulty of obtaining it and raising its natural fraction. Carbon isotopes can be obtained using many methods, one of them being the cryogenic distillation of carbon monoxide. Some few aspects regarding operating conditions and the construction of such cryogenic plants are known today, and even less information are available as far as the separation process modeling and control are concerned. In fact, the efficient control of the carbon monoxide distillation process represents a necessity for large-scale 13 C production. Referring to a classic distillation process, some models for carbon isotope separation have been proposed, some based on mass, component and energy balance equations, some on the nonlinear wave theory or the Cohen equations. For modeling the system it was used Petri nets because in this case it is deal with discrete event systems. In use of the non-timed and with auxiliary times Petri model, the transport stream was divided into sections and these sections will be analyzed successively. Because of the complexity of the system and the large amount of calculations required it was not possible to analyze the system as a unitary whole. A first attempt to model the system as a unitary whole led to the blocking of the model during simulation, because of the large processing times. (paper)
Using UML and Petri nets for visualization of business document flow
Directory of Open Access Journals (Sweden)
Ivana Rábová
2012-01-01
Full Text Available The article deals with two principles of business workflow modeling, Petri nets and UML notation, that are the acceptable approaches to business modeling and can be used also for business documents workflow. The special type of Petri nets, WF-nets and UML activity diagrams are used in this article and both modeling ways are presented on the concrete business workflow and then there are presented and specified their advantage and disadvantage for business documents flows. At beginning it is explained the word workflow in context business documents, its features, principles and using in business environment. After that it is clarified that the UML is OMG’s most-used specification, and the way the world models not only application structure, behavior, and architecture, but also business process, workflows and data structure. Activity diagram UML is good way to show how different workflows in the business are managed, how they start, go and stop. Diagrams also show many different decision paths that can be taken from start to finish. State charts can be used as a detail the transitions or changes of states when documents can go through in the business. They show how a documents moves from one state to another and the rules that govern that change. Petri-nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution. Unlike UML Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis. In the article there are modeled a special type of Petri nets, the WF-nets. The practical part of article incorporates two models of concrete business documents workflows presented in these notations, their comparison and recommendation for using these diagrams in business process management.
Analysis and reconstruction of stochastic coupled map lattice models
International Nuclear Information System (INIS)
Coca, Daniel; Billings, Stephen A.
2003-01-01
The Letter introduces a general stochastic coupled lattice map model together with an algorithm to estimate the nodal equations involved based only on a small set of observable variables and in the presence of stochastic perturbations. More general forms of the Frobenius-Perron and the transfer operators, which describe the evolution of densities under the action of the CML transformation, are derived
Elitism and Stochastic Dominance
Bazen, Stephen; Moyes, Patrick
2011-01-01
Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the...
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Planning under uncertainty solving large-scale stochastic linear programs
Energy Technology Data Exchange (ETDEWEB)
Infanger, G. [Stanford Univ., CA (United States). Dept. of Operations Research]|[Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft
1992-12-01
For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.
BRS invariant stochastic quantization of Einstein gravity
International Nuclear Information System (INIS)
Nakazawa, Naohito.
1989-11-01
We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)
Double stochastic matrices in quantum mechanics
International Nuclear Information System (INIS)
Louck, J.D.
1997-01-01
The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Stochastic Effects; Application in Nuclear Physics
International Nuclear Information System (INIS)
Mazonka, O.
2000-04-01
Stochastic effects in nuclear physics refer to the study of the dynamics of nuclear systems evolving under stochastic equations of motion. In this dissertation we restrict our attention to classical scattering models. We begin with introduction of the model of nuclear dynamics and deterministic equations of evolution. We apply a Langevin approach - an additional property of the model, which reflect the statistical nature of low energy nuclear behaviour. We than concentrate our attention on the problem of calculating tails of distribution functions, which actually is the problem of calculating probabilities of rare outcomes. Two general strategies are proposed. Result and discussion follow. Finally in the appendix we consider stochastic effects in nonequilibrium systems. A few exactly solvable models are presented. For one model we show explicitly that stochastic behaviour in a microscopic description can lead to ordered collective effects on the macroscopic scale. Two others are solved to confirm the predictions of the fluctuation theorem. (author)
Stochastic analytic regularization
International Nuclear Information System (INIS)
Alfaro, J.
1984-07-01
Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)
Instantaneous stochastic perturbation theory
International Nuclear Information System (INIS)
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.
2017-01-01
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of
Meyer, Joerg M.
2018-01-01
The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.
Micro-level stochastic loss reserving
Antonio, K.; Plat, R.
2010-01-01
To meet future liabilities general insurance companies will set-up reserves. Predicting future cash-flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general
Symmetries of stochastic differential equations: A geometric approach
Energy Technology Data Exchange (ETDEWEB)
De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)
2016-06-15
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.
Invariant measures for stochastic nonlinear beam and wave equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Ondreját, Martin; Seidler, Jan
2016-01-01
Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf
Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps
Li, Yan; Hu, Junhao
2013-01-01
We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Directory of Open Access Journals (Sweden)
Kaidesoja Tuukka
2015-09-01
Full Text Available This paper is a reply to the discussions of Ruth Groff, Dave Elder-Vass, Daniel Little, and Petri Ylikoski of Tuukka Kaidesoja (2013: Naturalizing Critical Realist Social Ontology (London: Routledge.
2–stage stochastic Runge–Kutta for stochastic delay differential equations
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Jusoh Awang, Rahimah [Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Gambang, Pahang (Malaysia); Bahar, Arifah; Yeak, S. H. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-05-15
This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.
GRIFFITHS, MARK D.; VAN ROOIJ, ANTONIUS J.; KARDEFELT-WINTHER, DANIEL; STARCEVIC, VLADAN; KIRÁLY, ORSOLYA; PALLESEN, STÅLE; MÜLLER, KAI; DREIER, MICHAEL; CARRAS, MICHELLE; PRAUSE, NICOLE; KING, DANIEL L.; ABOUJAOUDE, ELLIAS; KUSS, DARIA J.; PONTES, HALLEY M.; FERNANDEZ, OLATZ LOPEZ
2016-01-01
This commentary paper critically discusses the recent debate paper by Petry et al. (2014) that argued there was now an international consensus for assessing Internet Gaming Disorder (IGD). Our collective opinions vary considerably regarding many different aspects of online gaming. However, we contend that the paper by Petry and colleagues does not provide a true and representative international community of researchers in this area. This paper critically discusses and provides ...
A modeling method of semiconductor fabrication flows with extended knowledge hybrid Petri nets
Institute of Scientific and Technical Information of China (English)
Zhou Binghai; Jiang Shuyu; Wang Shijin; Wu bin
2008-01-01
A modeling method of extended knowledge hybrid Petri nets (EKHPNs), incorporating object-oriented methods into hybrid Petri nets (HPNs), was presented and used for the representation and modeling of semiconductor wafer fabrication flows. To model the discrete and continuous parts of a complex semiconductor wafer fabrication flow, the HPNs were introduced into the EKHPNs. Object-oriented methods were combined into the EKHPNs for coping with the complexity of the fabrication flow. Knowledge annotations were introduced to solve input and output conflicts of the EKHPNs.Finally, to demonstrate the validity of the EKHPN method, a real semiconductor wafer fabrication case was used to illustrate the modeling procedure. The modeling results indicate that the proposed method can be used to model a complex semiconductor wafer fabrication flow expediently.
Petri Net-Based R&D Process Modeling and Optimization for Composite Materials
Directory of Open Access Journals (Sweden)
Xiaomei Hu
2013-01-01
Full Text Available Considering the current R&D process for new composite materials involves some complex details, such as formula design, specimen/sample production, materials/sample test, assessment, materials/sample feedback from customers, and mass production, the workflow model of Petri net-based R&D process for new composite materials’ is proposed. By analyzing the time property of the whole Petri net, the optimized model for new composite materials R&D workflow is further proposed. By analyzing the experiment data and application in some materials R&D enterprise, it is demonstrated that the workflow optimization model shortens the period of R&D on new materials for 15%, definitely improving the R&D efficiency. This indicates the feasibility and availability of the model.
A knowledge-base verification of NPP expert systems using extended Petri nets
International Nuclear Information System (INIS)
Kwon, Il Won; Seong, Poong Hyun
1995-01-01
The verification phase of knowledge base is an important part for developing reliable expert systems, especially in nuclear industry. Although several strategies or tools have been developed to perform potential error checking, they often neglect the reliability of verification methods. Because a Petri net provides a uniform mathematical formalization of knowledge base, it has been employed for knowledge base verification. In this work, we devise and suggest an automated tool, called COKEP (Checker Of Knowledge base using Extended Petri net), for detecting incorrectness, inconsistency, and incompleteness in a knowledge base. The scope of the verification problem is expanded to chained errors, unlike previous studies that assumed error incidence to be limited to rule pairs only. In addition, we consider certainty factor in checking, because most of knowledge bases have certainty factors
A Petri Net-Based Software Process Model for Developing Process-Oriented Information Systems
Li, Yu; Oberweis, Andreas
Aiming at increasing flexibility, efficiency, effectiveness, and transparency of information processing and resource deployment in organizations to ensure customer satisfaction and high quality of products and services, process-oriented information systems (POIS) represent a promising realization form of computerized business information systems. Due to the complexity of POIS, explicit and specialized software process models are required to guide POIS development. In this chapter we characterize POIS with an architecture framework and present a Petri net-based software process model tailored for POIS development with consideration of organizational roles. As integrated parts of the software process model, we also introduce XML nets, a variant of high-level Petri nets as basic methodology for business processes modeling, and an XML net-based software toolset providing comprehensive functionalities for POIS development.
Moutinho, Filipe de Carvalho
2016-01-01
This book describes a model-based development approach for globally-asynchronous locally-synchronous distributed embedded controllers. This approach uses Petri nets as modeling formalism to create platform and network independent models supporting the use of design automation tools. To support this development approach, the Petri nets class in use is extended with time-domains and asynchronous-channels. The authors’ approach uses models not only providing a better understanding of the distributed controller and improving the communication among the stakeholders, but also to be ready to support the entire lifecycle, including the simulation, the verification (using model-checking tools), the implementation (relying on automatic code generators), and the deployment of the distributed controller into specific platforms. Uses a graphical and intuitive modeling formalism supported by design automation tools; Enables verification, ensuring that the distributed controller was correctly specified; Provides flex...
Coupling of Petri Net Models of the Mycobacterial Infection Process and Innate Immune Response
Directory of Open Access Journals (Sweden)
Rafael V. Carvalho
2015-04-01
Full Text Available Computational and mathematical modeling is important in support of a better understanding of complex behavior in biology. For the investigation of biological systems, researchers have used computers to construct, verify, and validate models that describe the mechanisms behind biological processes in multi-scale representations. In this paper we combine Petri net models that represent the mycobacterial infection process and innate immune response at various levels of organization, from molecular interaction to granuloma dissemination. In addition to the conventional graphical representation of the Petri net, the outcome of the model is projected onto a 3D model representing the zebrafish embryo. In this manner we provide a visualization of the process in a simulation framework that portrays the infection in the living system.
Design and verification of distributed logic controllers with application of Petri nets
Energy Technology Data Exchange (ETDEWEB)
Wiśniewski, Remigiusz; Grobelna, Iwona; Grobelny, Michał; Wiśniewska, Monika [University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland)
2015-12-31
The paper deals with the designing and verification of distributed logic controllers. The control system is initially modelled with Petri nets and formally verified against structural and behavioral properties with the application of the temporal logic and model checking technique. After that it is decomposed into separate sequential automata that are working concurrently. Each of them is re-verified and if the validation is successful, the system can be finally implemented.
An Evaluation of Automated Code Generation with the PetriCode Approach
DEFF Research Database (Denmark)
Simonsen, Kent Inge
2014-01-01
Automated code generation is an important element of model driven development methodologies. We have previously proposed an approach for code generation based on Coloured Petri Net models annotated with textual pragmatics for the network protocol domain. In this paper, we present and evaluate thr...... important properties of our approach: platform independence, code integratability, and code readability. The evaluation shows that our approach can generate code for a wide range of platforms which is integratable and readable....
CHERNENOK S.A.; NEPOMNIASCHY V.A.
2015-01-01
The language of message sequence charts (MSC) is a popular scenario-based specification language used to describe the interaction of components in distributed systems. However, the methods for validation of MSC diagrams are underdeveloped. This paper describes a method for translation of MSC diagrams into coloured Petri nets (CPN). The method is applied to the property verification of these diagrams. The considered set of diagram elements is extended by the elements of UML sequence diagrams a...
Opening the stable door: new initiatives at the Petrie Museum of Egyptian Archaeology
Directory of Open Access Journals (Sweden)
Sally MacDonald
2000-11-01
Full Text Available The Petrie Museum ut UCL contains u world-class collection of Egyptian objects that ranges chronologically from early prehistoric to Islamic times, but it is inadequately housed and remains little known outside Egyptology. It has now been designated us of national importance and its stuff have ambitious plans to provide greater access, via the Internet and in other ways, to the 80000 objects it contains.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-10-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
Design of River System Deadlock Avoidance Supervisor by Using Petri Net
Directory of Open Access Journals (Sweden)
Danko Kezić
2010-05-01
Full Text Available Advanced function of the computer-based river traffic management system should automatically predict and prevent possible conflict and deadlock states between vessels by using adequate control policy (supervisor. This paper proposes a formal method for calculating maximally permissive deadlock prevention supervisor. To model the river system, the authors use a class of Petri net suitable for describing multiple re-entrant flowlines with disjoint sets of resources, jobs and control places, and matrix-based formal method to analyze the system. By using matrix algebra, the structural characteristics of the Petri net (circular waits, P-invariants, critical siphons and subsystem, key resource have been analyzed and the steps for supervisor design proposed. The first and the second level deadlocks can be avoided by maintaining the number of tokens in the critical subsystems and ensuring that the key resource would not be the last available resource in the system. The derived supervisor has been verified by a computer simulation using MATLAB environment. KEYWORDS: traffic management system, deadlock avoidance, discrete event system, Petri net
The risk management of perishable supply chain based on coloured Petri Net modeling
Directory of Open Access Journals (Sweden)
Lu Liu
2018-03-01
Full Text Available The supply chain of perishable products is a combination of information organization, sharing and integration. The information modeling of supply chain is constructed to abstract key quality information including environment information, processing procedures and product quality assessments based on principle of quality safety factors and property of decay rate. The coloured Petri Net is applied for integrated description of independent information classification, aiming at risk identification and risk management framework. Well, according to the quality deterioration tendency, risk grades management and decision-making system are established. Practically, the circulation system of aquatic products is studied in this paper for full processing description. The simulation experiments are manipulated on environmental information, processing information and product quality information by the coloured Petri Net. Eventually, the conclusion turns out precisely as such that the coloured Petri Net conclusive for information classification and information transmission while integrated information management is available of efficient risk identification and decision-making system in supply chain of perishable products. Meanwhile, the validity of evaluating management and shelf-life estimation of perishable products are technically feasible.
Reliability Analysis of Core Protection Calculator System by Combining Petri Net and Fault Tree
International Nuclear Information System (INIS)
Kim, Hyejin; Kim, Jonghyun
2013-01-01
This paper proposes an approach to analyzing the reliability of digital systems by combining Petri net (PN) and Fault tree. The Petri net allows modeling event dependencies and interaction, to represent the time sequence, and to model assumptions for dynamic events. The Petri net model can be straightforwardly transformed to fault tree using the gate. Then, the FT can be integrated into the existing PSA. This paper applies the approach to the reliability analysis of Core Protection Calculator System (CPCS). Digital technology is replacing the analog instrumentation and control (I and C) systems in both new and upgraded nuclear power plants. As digital systems are introduced to nuclear power plants, issues related with reliability analyses of these digital systems are being raised. One of these issues is that static fault tree (FT) and event tree (ET) approach cannot properly account for dynamic interactions in the digital systems, such as multiple top events, logic loops and time delay. Many methods have been proposed to solve the problems, but there is no single method that is universally accepted for the application to the current generation probabilistic safety analysis (PSA)
Reliability Analysis of Core Protection Calculator System by Combining Petri Net and Fault Tree
Energy Technology Data Exchange (ETDEWEB)
Kim, Hyejin; Kim, Jonghyun [KEPCO International Nuclear Graduate School, Ulsan (Korea, Republic of)
2013-10-15
This paper proposes an approach to analyzing the reliability of digital systems by combining Petri net (PN) and Fault tree. The Petri net allows modeling event dependencies and interaction, to represent the time sequence, and to model assumptions for dynamic events. The Petri net model can be straightforwardly transformed to fault tree using the gate. Then, the FT can be integrated into the existing PSA. This paper applies the approach to the reliability analysis of Core Protection Calculator System (CPCS). Digital technology is replacing the analog instrumentation and control (I and C) systems in both new and upgraded nuclear power plants. As digital systems are introduced to nuclear power plants, issues related with reliability analyses of these digital systems are being raised. One of these issues is that static fault tree (FT) and event tree (ET) approach cannot properly account for dynamic interactions in the digital systems, such as multiple top events, logic loops and time delay. Many methods have been proposed to solve the problems, but there is no single method that is universally accepted for the application to the current generation probabilistic safety analysis (PSA)
Multiple fields in stochastic inflation
Energy Technology Data Exchange (ETDEWEB)
Assadullahi, Hooshyar [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Noorbala, Mahdiyar [Department of Physics, University of Tehran,P.O. Box 14395-547, Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Vennin, Vincent; Wands, David [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom)
2016-06-24
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Remarks on stochastic acceleration
International Nuclear Information System (INIS)
Graeff, P.
1982-12-01
Stochastic acceleration and turbulent diffusion are strong turbulence problems since no expansion parameter exists. Hence the problem of finding rigorous results is of major interest both for checking approximations and for reference models. Since we have found a way of constructing such models in the turbulent diffusion case the question of the extension to stochastic acceleration now arises. The paper offers some possibilities illustrated by the case of 'stochastic free fall' which may be particularly interesting in the context of linear response theory. (orig.)
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Time-ordered product expansions for computational stochastic system biology
International Nuclear Information System (INIS)
Mjolsness, Eric
2013-01-01
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. (paper)
Stochastic variables in N=1 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Lechtenfeld, O.
1984-06-01
The stochastic structure of N=1 supersymmetric Yang-Mills theory is rederived by using a previously developed method for the construction of the (nonlocal) Nicolai map. The stochastic variables correspond to the fixed points of this mapping. The relations are derived in a light cone gauge and in general covariant gauges. (orig.)
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input....... This gives rise to Generalised Semi-Markov Decision Processes for which few analytical techniques are available. We restrict delays on output actions to be exponentially distributed while still admitting real-time constraints on the quality binders. This facilitates developing analytical techniques based...
Structural factoring approach for analyzing stochastic networks
Hayhurst, Kelly J.; Shier, Douglas R.
1991-01-01
The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.
Doberkat, Ernst-Erich
2009-01-01
Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.
International Nuclear Information System (INIS)
Hueffel, H.
1990-01-01
After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2012-01-01
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
The interpolation method of stochastic functions and the stochastic variational principle
International Nuclear Information System (INIS)
Liu Xianbin; Chen Qiu
1993-01-01
Uncertainties have been attaching more importance to increasingly in modern engineering structural design. Viewed on an appropriate scale, the inherent physical attributes (material properties) of many structural systems always exhibit some patterns of random variation in space and time, generally the random variation shows a small parameter fluctuation. For a linear mechanical system, the random variation is modeled as a random one of a linear partial differential operator and, in stochastic finite element method, a random variation of a stiffness matrix. Besides the stochasticity of the structural physical properties, the influences of random loads which always represent themselves as the random boundary conditions bring about much more complexities in structural analysis. Now the stochastic finite element method or the probabilistic finite element method is used to study the structural systems with random physical parameters, whether or not the loads are random. Differing from the general finite element theory, the main difficulty which the stochastic finite element method faces is the inverse operation of stochastic operators and stochastic matrices, since the inverse operators and the inverse matrices are statistically correlated to the random parameters and random loads. So far, many efforts have been made to obtain the reasonably approximate expressions of the inverse operators and inverse matrices, such as Perturbation Method, Neumann Expansion Method, Galerkin Method (in appropriate Hilbert Spaces defined for random functions), Orthogonal Expansion Method. Among these methods, Perturbation Method appear to be the most available. The advantage of these methods is that the fairly accurate response statistics can be obtained under the condition of the finite information of the input. However, the second-order statistics obtained by use of Perturbation Method and Neumann Expansion Method are not always the appropriate ones, because the relevant second
Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com [Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce (Turkey); Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr [Department of Mathematics, Institute of Science and Arts, Afyon Kocatepe University, Afyonkarahisar (Turkey); Çelik, Nuri, E-mail: ncelik@bartin.edu.tr [Department of Statistics, Faculty of Science, Bartın University, Bartın-Turkey (Turkey)
2016-04-18
The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.
Stochastic resonance in a stochastic bistable system with additive noises and square–wave signal
International Nuclear Information System (INIS)
Feng, Guo; Xiang-Dong, Luo; Shao-Fu, Li; Yu-Rong, Zhou
2010-01-01
This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated. (general)
Frank, T D; Beek, P J
2001-08-01
Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.
Topological superposition of abstractions of stochastic processes
Bujorianu, L.M.; Bujorianu, M.C.
2008-01-01
In this paper, we present a sound integration mechanism for Markov processes that are abstractions of stochastic hybrid systems (SHS). In a previous work, we have defined a very general model of SHS and we proved that the realization of an SHS is a Markov process. Moreover, we have developed a
Stochastic electromagnetic radiation of complex sources
Naus, H.W.L.
2007-01-01
The emission of electromagnetic radiation by localized complex electric charge and current distributions is studied. A statistical formalism in terms of general dynamical multipole fields is developed. The appearing coefficients are treated as stochastic variables. Hereby as much as possible a
Active fault diagnosis based on stochastic tests
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad; Niemann, Hans Henrik
2008-01-01
The focus of this paper is on stochastic change detection applied in connection with active fault diagnosis (AFD). An auxiliary input signal is applied in AFD. This signal injection in the system will in general allow us to obtain a fast change detection/isolation by considering the output...
Degenerate parabolic stochastic partial differential equations
Czech Academy of Sciences Publication Activity Database
span class="emphasis">Hofmanová, Martinaspan>
2013-01-01
Roč. 123, č. 12 (2013), s. 4294-4336 ISSN 0304-4149 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : kinetic solutions * degenerate stochastic parabolic equations Subject RIV: BA - General Mathematics Impact factor: 1.046, year: 2013 http://library.utia.cas.cz/separaty/2013/SI/hofmanova-0397241.pdf
ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES
RUSCHENDORF, L; DEVALK, [No Value
We construct a.s. nonlinear regression representations of general stochastic processes (X(n))n is-an-element-of N. As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive
Efficient Diversification According to Stochastic Dominance Criteria
Kuosmanen, T.K.
2004-01-01
This paper develops the first operational tests of portfolio efficiency based on the general stochastic dominance (SD) criteria that account for an infinite set of diversification strategies. The main insight is to preserve the cross-sectional dependence of asset returns when forming portfolios by
Generalized Langevin Equation Description of Stochastic ...
Indian Academy of Sciences (India)
dissipation theorems. The vertical ... luminosity is also obtained, and it is shown that it has non-standard values. The theoretical .... black hole (a), for A = 0.0015 and a = 0.03 (red curve), a = 0.1 (green curve) and a = 0.001. (black curve) ...
Stochastic Oscillations of General Relativistic Disks Described
Indian Academy of Sciences (India)
4
spectral slope at high frequencies of the power spectrum density of disk ..... has a negative sign, the process is antipersistence or anti-correlated. ..... We can find that the computation of a Grünwald-Letnikov derivative requires knowledge of.
Communication nets stochastic message flow and delay
Kleinrock, Leonard
2007-01-01
Considerable research has been devoted to the formulation and solution of problems involving flow within connected networks. Independent of these surveys, an extensive body of knowledge has accumulated on the subject of queues, particularly in regard to stochastic flow through single-node servicing facilities. This text combines studies of connected networks with those of stochastic flow, providing a basis for understanding the general behavior and operation of communication networks in realistic situations.Author Leonard Kleinrock of the Computer Science Department at UCLA created the basic p
Stochastic Modeling of Traffic Air Pollution
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
2014-01-01
In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...
Scattering theory of stochastic electromagnetic light waves.
Wang, Tao; Zhao, Daomu
2010-07-15
We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.
International Nuclear Information System (INIS)
Haran, O.; Shvarts, D.; Thieberger, R.
1998-01-01
Classical transport of neutral particles in a binary, scattering, stochastic media is discussed. It is assumed that the cross-sections of the constituent materials and their volume fractions are known. The inner structure of the media is stochastic, but there exist a statistical knowledge about the lump sizes, shapes and arrangement. The transmission through the composite media depends on the specific heterogeneous realization of the media. The current research focuses on the averaged transmission through an ensemble of realizations, frm which an effective cross-section for the media can be derived. The problem of one dimensional transport in stochastic media has been studied extensively [1]. In the one dimensional description of the problem, particles are transported along a line populated with alternating material segments of random lengths. The current work discusses transport in two-dimensional stochastic media. The phenomenon that is unique to the multi-dimensional description of the problem is obstacle bypassing. Obstacle bypassing tends to reduce the opacity of the media, thereby reducing its effective cross-section. The importance of this phenomenon depends on the manner in which the obstacles are arranged in the media. Results of transport simulations in multi-dimensional stochastic media are presented. Effective cross-sections derived from the simulations are compared against those obtained for the one-dimensional problem, and against those obtained from effective multi-dimensional models, which are partially based on a Markovian assumption
Lectures on Topics in Spatial Stochastic Processes
Capasso, Vincenzo; Ivanoff, B Gail; Dozzi, Marco; Dalang, Robert C; Mountford, Thomas S
2003-01-01
The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.
Stochastic partial differential equations an introduction
Liu, Wei
2015-01-01
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...
Método para el Modelado y Prueba de Diagramas de Actividades Mediante Redes de Petri
Directory of Open Access Journals (Sweden)
Lionel Baquero Hernández
2015-11-01
Full Text Available Las redes de Petri son ideales para describir y estudiar sistemas que procesan información y con características concurrentes, asíncronas, distribuidas, paralelas, no determinísticas y/o estocásticas. . Sin embargo, la teoría clásica de estas redes se enfrenta al desafío de adecuarse a las nuevas necesidades de los sistemas informáticos que los ingenieros diseñan en la actualidad. Un diagrama de actividades representa una secuencia de actividades. Podría aplicarse a cualquier propósito, pero se considera especialmente útil para visualizar los flujos de trabajo y los procesos del negocio, o casos de uso. El presente trabajo se ha desarrollado con el objetivo de diseñar un método para el modelado y prueba de diagramas de actividades mediante redes de Petri. El método propuesto brinda una serie de pasos necesarios para modelar un diagrama de actividades con redes de Petri y a partir de dicha red obtener una representación matemática de la misma. Esta representación matemática se utiliza para con ella realizar una serie de operaciones basadas en el marcaje de la red que permiten realizar pruebas al diagrama. Este método es capaz de identificar errores comunes que se cometen en el modelado de los diagramas de actividades, lo cual se demostró a través del método de experimentación.
Jung, Jinmyung; Kwon, Mijin; Bae, Sunghwa; Yim, Soorin; Lee, Doheon
2018-03-05
Muscle atrophy, an involuntary loss of muscle mass, is involved in various diseases and sometimes leads to mortality. However, therapeutics for muscle atrophy thus far have had limited effects. Here, we present a new approach for therapeutic target prediction using Petri net simulation of the status of phosphorylation, with a reasonable assumption that the recovery of abnormally phosphorylated proteins can be a treatment for muscle atrophy. The Petri net model was employed to simulate phosphorylation status in three states, i.e. reference, atrophic and each gene-inhibited state based on the myocyte-specific phosphorylation network. Here, we newly devised a phosphorylation specific Petri net that involves two types of transitions (phosphorylation or de-phosphorylation) and two types of places (activation with or without phosphorylation). Before predicting therapeutic targets, the simulation results in reference and atrophic states were validated by Western blotting experiments detecting five marker proteins, i.e. RELA, SMAD2, SMAD3, FOXO1 and FOXO3. Finally, we determined 37 potential therapeutic targets whose inhibition recovers the phosphorylation status from an atrophic state as indicated by the five validated marker proteins. In the evaluation, we confirmed that the 37 potential targets were enriched for muscle atrophy-related terms such as actin and muscle contraction processes, and they were also significantly overlapping with the genes associated with muscle atrophy reported in the Comparative Toxicogenomics Database (p-value net. We generated a list of the potential therapeutic targets whose inhibition recovers abnormally phosphorylated proteins in an atrophic state. They were evaluated by various approaches, such as Western blotting, GO terms, literature, known muscle atrophy-related genes and shortest path analysis. We expect the new proposed strategy to provide an understanding of phosphorylation status in muscle atrophy and to provide assistance towards
A Stochastic Multiobjective Optimization Framework for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Shibo He
2010-01-01
Full Text Available In wireless sensor networks (WSNs, there generally exist many different objective functions to be optimized. In this paper, we propose a stochastic multiobjective optimization approach to solve such kind of problem. We first formulate a general multiobjective optimization problem. We then decompose the optimization formulation through Lagrange dual decomposition and adopt the stochastic quasigradient algorithm to solve the primal-dual problem in a distributed way. We show theoretically that our algorithm converges to the optimal solution of the primal problem by using the knowledge of stochastic programming. Furthermore, the formulation provides a general stochastic multiobjective optimization framework for WSNs. We illustrate how the general framework works by considering an example of the optimal rate allocation problem in multipath WSNs with time-varying channel. Extensive simulation results are given to demonstrate the effectiveness of our algorithm.
Formal Abstractions for Automated Verification and Synthesis of Stochastic Systems
Esmaeil Zadeh Soudjani, S.
2014-01-01
Stochastic hybrid systems involve the coupling of discrete, continuous, and probabilistic phenomena, in which the composition of continuous and discrete variables captures the behavior of physical systems interacting with digital, computational devices. Because of their versatility and generality,
Verification of Liveness Properties on Closed Timed-Arc Petri Nets
DEFF Research Database (Denmark)
Andersen, Mathias; Larsen, Heine G.; Srba, Jiri
2012-01-01
Verification of closed timed models by explicit state-space exploration methods is an alternative to the wide-spread symbolic techniques based on difference bound matrices (DBMs). A few experiments found in the literature confirm that for the reachability analysis of timed automata explicit...... techniques can compete with DBM-based algorithms, at least for situations where the constants used in the models are relatively small. To the best of our knowledge, the explicit methods have not yet been employed in the verification of liveness properties in Petri net models extended with time. We present...
Ritning som byggande: Lewerentz och ritningarna till S:t Petri
DEFF Research Database (Denmark)
Foote, Jonathan
2016-01-01
from the site and into drawing studios. Today, with complex tools of virtual communication between builders and designers, it is quite common for an architect to design buildings without ever setting foot on the construction site. In contrast to the strong distinction between drawing and building made...... and S:t Petri. Through close collaborations with materials and builders, Lewerentz translated his ideas into an architecture that was deeply personal. What is more, such an approach was thoroughly inseparable from his unique method of engaging construction through drawing and sketching. Upon examining...
The Perspective on Data and Control Flow Analysis in Topological Functioning Models by Petri Nets
Directory of Open Access Journals (Sweden)
Asnina Erika
2014-12-01
Full Text Available The perspective on integration of two mathematical formalisms, i.e., Colored Petri Nets (CPNs and Topological Functioning Model (TFM, is discussed in the paper. The roots of CPNs are in modeling system functionality. The TFM joins principles of system theory and algebraic topology, and formally bridges the solution domain with the problem domain. It is a base for further automated construction of software design models. The paper discusses a perspective on check of control and data flows in the TFM by CPNs formalism. The research result is definition of mappings from TFMs to CPNs.
Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 1, Basic Concepts
DEFF Research Database (Denmark)
Jensen, Kurt
This three-volume work presents a coherent description of the theoretical and practical aspects of coloured Petri nets. These CP-nets are shown to be a full-fledged language for the design, specification, simulation, validation and implementation of large software systems. The introductory first...... volume contains the formal definition of CP-nets and the mathematical theory behind their analysis methods. It gives a detailed presentation of many small examples and a brief overview of some industrial applications. The purpose of the book is to teach the reader how to construct CP-net models...
A Case Study on Coloured Petri Nets in Object-oriented Analysis and Design
DEFF Research Database (Denmark)
Barros, Joao Paulo; Jørgensen, Jens Bæk
2005-01-01
is structurally and conceptually closer to class diagrams and object-oriented programming languages. The CPN models reduce the gap between user-level requirements and the respective implementation, thus simplifying the implementation or code generation. Finally, we discuss the code generation from object-oriented......In this paper, we first demonstrate how a coloured Petri nets (CPN) model can be used to capture requirements for a considered example system, an elevator controller. Then, we show how this requirements-level CPN model is transformed into a design-level object-oriented CPN model, which...
Distinguishing Environment and System in Coloured Petri Net Models of Reactive Systems
DEFF Research Database (Denmark)
Tjell, Simon
2007-01-01
This paper introduces and formally defines the environment-and-system-partitioned property for behavioral models of reactive systems expressed in the formal modeling language Coloured Petri Net. The purpose of the formalization is to make it possible to automatically validate any CPN model...... with respect to this property based on structural analysis. A model has the environment-and-system-partitioned property if it is based on a clear division between environment and system. This division is important in many model-driven approaches to software development such as model-based testing and automated...
Performance Estimation for Hardware/Software codesign using Hierarchical Colored Petri Nets
DEFF Research Database (Denmark)
Grode, Jesper Nicolai Riis; Madsen, Jan; Jerraya, Ahmed-Amine
1998-01-01
This paper presents an approach for abstract modeling of the functional behavior of hardware architectures using Hierarchical Colored Petri Nets (HCPNs). Using HCPNs as architectural models has several advantages such as higher estimation accuracy, higher flexibility, and the need for only one...... estimation tool. This makes the approach very useful for designing component models used for performance estimation in Hardware/Software Codesign frameworks such as the LYCOS system. The paper presents the methodology and rules for designing component models using HCPNs. Two examples of architectural models...
A Method for Modeling the Virtual Instrument Automatic Test System Based on the Petri Net
Institute of Scientific and Technical Information of China (English)
MA Min; CHEN Guang-ju
2005-01-01
Virtual instrument is playing the important role in automatic test system. This paper introduces a composition of a virtual instrument automatic test system and takes the VXIbus based a test software platform which is developed by CAT lab of the UESTC as an example. Then a method to model this system based on Petri net is proposed. Through this method, we can analyze the test task scheduling to prevent the deadlock or resources conflict. At last, this paper analyzes the feasibility of this method.
International Nuclear Information System (INIS)
Charles, M.W.
1990-01-01
Recent biological data from man and pig on the non-stochastic effects following exposure with a range of β-emitters are combined with recent epidemiological analyses of skin cancer risks in man to form a basis for suggested improved protection criteria following whole- or partial-body skin exposures. Specific consideration is given to the choice of an organ weighting factor for evaluation of effective dose-equivalent. Since stochastic and non-stochastic end-points involve different cell types at different depths in the skin, the design of an ideal physical dosemeter may depend on the proportion of the body skin exposed and the radiation penetrating power. Possible choices of design parameters for skin dosemeters are discussed. Limitation of skin exposure from small radioactive sources ('hot particles') is addressed using animal data. (author)
Stochastic approach to microphysics
Energy Technology Data Exchange (ETDEWEB)
Aron, J.C.
1987-01-01
The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e/sup +/e/sup -/ collisions, or pp -> ..pi../sup 0/ + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...).
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
Stochastic cooling at Fermilab
International Nuclear Information System (INIS)
Marriner, J.
1986-08-01
The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system
Stochastic Feedforward Control Technique
Halyo, Nesim
1990-01-01
Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.
Markov stochasticity coordinates
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
DEFF Research Database (Denmark)
Simonsen, Maria
This thesis treats stochastic systems with switching dynamics. Models with these characteristics are studied from several perspectives. Initially in a simple framework given in the form of stochastic differential equations and, later, in an extended form which fits into the framework of sliding...... mode control. It is investigated how to understand and interpret solutions to models of switched systems, which are exposed to discontinuous dynamics and uncertainties (primarily) in the form of white noise. The goal is to gain knowledge about the performance of the system by interpreting the solution...
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
CSIR Research Space (South Africa)
Roux, FS
2013-09-01
Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...
Foundations of stochastic analysis
Rao, M M; Lukacs, E
1981-01-01
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Stochastic quantisation: theme and variation
International Nuclear Information System (INIS)
Klauder, J.R.; Kyoto Univ.
1987-01-01
The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)
Lyapunov functionals and stability of stochastic functional differential equations
Shaikhet, Leonid
2013-01-01
Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...
Parameter-free resolution of the superposition of stochastic signals
Energy Technology Data Exchange (ETDEWEB)
Scholz, Teresa, E-mail: tascholz@fc.ul.pt [Center for Theoretical and Computational Physics, University of Lisbon (Portugal); Raischel, Frank [Center for Geophysics, IDL, University of Lisbon (Portugal); Closer Consulting, Av. Eng. Duarte Pacheco Torre 1 15" 0, 1070-101 Lisboa (Portugal); Lopes, Vitor V. [DEIO-CIO, University of Lisbon (Portugal); UTEC–Universidad de Ingeniería y Tecnología, Lima (Peru); Lehle, Bernd; Wächter, Matthias; Peinke, Joachim [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Lind, Pedro G. [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Institute of Physics, University of Osnabrück, Osnabrück (Germany)
2017-01-30
This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent stochastic processes, one of which is an Ornstein–Uhlenbeck process and the other a general (non-linear) Langevin process. The method is able to distinguish between the stochastic processes, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.
Directory of Open Access Journals (Sweden)
A. A. Gurskiy
2016-09-01
Full Text Available The coordinating control system by drives of the robot-manipulator is presented in this article. The purpose of the scientific work is the development and research of the new algorithms for parametric synthesis of the coordinating control systems. To achieve this aim it is necessary to develop the system generating the required parametric synthesis algorithms and performing the necessary procedures according to the generated algorithm. This scientific work deals with the synthesis of Petri net in the specific case with the automatic generation of Petri nets.
Stochastic quantization of Proca field
International Nuclear Information System (INIS)
Lim, S.C.
1981-03-01
We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)
Stochastic Estimation via Polynomial Chaos
2015-10-01
AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic
Hierarchical Colored Petri Nets for Modeling and Analysis of Transit Signal Priority Control Systems
Directory of Open Access Journals (Sweden)
Yisheng An
2018-01-01
Full Text Available In this paper, we consider the problem of developing a model for traffic signal control with transit priority using Hierarchical Colored Petri nets (HCPN. Petri nets (PN are useful for state analysis of discrete event systems due to their powerful modeling capability and mathematical formalism. This paper focuses on their use to formalize the transit signal priority (TSP control model. In a four-phase traffic signal control model, the transit detection and two kinds of transit priority strategies are integrated to obtain the HCPN-based TSP control models. One of the advantages to use these models is the clear presentation of traffic light behaviors in terms of conditions and events that cause the detection of a priority request by a transit vehicle. Another advantage of the resulting models is that the correctness and reliability of the proposed strategies are easily analyzed. After their full reachable states are generated, the boundness, liveness, and fairness of the proposed models are verified. Experimental results show that the proposed control model provides transit vehicles with better effectiveness at intersections. This work helps advance the state of the art in the design of signal control models related to the intersection of roadways.
Specification and Verification of Medical Monitoring System Using Petri-nets.
Majma, Negar; Babamir, Seyed Morteza
2014-07-01
To monitor the patient behavior, data are collected from patient's body by a medical monitoring device so as to calculate the output using embedded software. Incorrect calculations may endanger the patient's life if the software fails to meet the patient's requirements. Accordingly, the veracity of the software behavior is a matter of concern in the medicine; moreover, the data collected from the patient's body are fuzzy. Some methods have already dealt with monitoring the medical monitoring devices; however, model based monitoring fuzzy computations of such devices have been addressed less. The present paper aims to present synthesizing a fuzzy Petri-net (FPN) model to verify behavior of a sample medical monitoring device called continuous infusion insulin (INS) because Petri-net (PN) is one of the formal and visual methods to verify the software's behavior. The device is worn by the diabetic patients and then the software calculates the INS dose and makes a decision for injection. The input and output of the infusion INS software are not crisp in the real world; therefore, we present them in fuzzy variables. Afterwards, we use FPN instead of clear PN to model the fuzzy variables. The paper follows three steps to synthesize an FPN to deal with verification of the infusion INS device: (1) Definition of fuzzy variables, (2) definition of fuzzy rules and (3) design of the FPN model to verify the software behavior.
International Nuclear Information System (INIS)
Kwon, I. W.; Seong, P. H.
1996-01-01
The adoption of expert systems mainly as operator supporting systems is becoming increasingly popular as the control algorithms of system become more and more sophisticated and complicated. The verification phase of knowledge base is an important part for developing reliable expert systems, especially in nuclear industry. Although several strategies or tools have been developed to perform potential error checking, they often neglect the reliability of verification methods. Because a Petri net provides a uniform mathematical formalization of knowledge base, it has been employed for knowledge base verification. In this work, we devise and suggest an automated tool, called COKEP(Checker of Knowledge base using Extended Petri net), for detecting incorrectness, inconsistency, and incompleteness in a knowledge base. The scope of the verification problem is expended to chained errors, unlike previous studies that assume error incidence to be limited to rule pairs only. In addition, we consider certainty factor in checking, because most of knowledge bases have certainly factors. 8 refs,. 2 figs,. 4 tabs. (author)
Nano Petri dishes: a new polystyrene platform for studying cell-nanoengineered surface interactions
International Nuclear Information System (INIS)
Cha, Kyoung Je; Na, Moon-Hee; Kim, Hyung Woo; Kim, Dong Sung
2014-01-01
In this study, we fabricated and fully characterized a new type of polystyrene (PS) cell-culture platform containing nanoengineered surfaces (NES), referred to as a nano Petri dish, which can be used at the transition stage of basic cell–NES interaction studies for clinical applications. Nano-injection molding in this study was used for the mass production of the nano Petri dish having nanopore arrays. The effects of processing parameters of the injection molding on the replication quality of the nanopore arrays were quantitatively evaluated by means of design of experiments based on the Taguchi method. This allowed efficient and reliable cell culture studies by providing large numbers of the same dishes, in addition to removing the fixation step of the NES plates inside the cell-culture container. Physical, chemical and mechanical properties of the NES, as well as cell behavior including attachment and proliferation of human osteosarcoma MG-63 cells on the NES, were then characterized, with and without the oxygen plasma surface treatment. (paper)
Nano Petri dishes: a new polystyrene platform for studying cell-nanoengineered surface interactions
Cha, Kyoung Je; Na, Moon-Hee; Kim, Hyung Woo; Kim, Dong Sung
2014-05-01
In this study, we fabricated and fully characterized a new type of polystyrene (PS) cell-culture platform containing nanoengineered surfaces (NES), referred to as a nano Petri dish, which can be used at the transition stage of basic cell-NES interaction studies for clinical applications. Nano-injection molding in this study was used for the mass production of the nano Petri dish having nanopore arrays. The effects of processing parameters of the injection molding on the replication quality of the nanopore arrays were quantitatively evaluated by means of design of experiments based on the Taguchi method. This allowed efficient and reliable cell culture studies by providing large numbers of the same dishes, in addition to removing the fixation step of the NES plates inside the cell-culture container. Physical, chemical and mechanical properties of the NES, as well as cell behavior including attachment and proliferation of human osteosarcoma MG-63 cells on the NES, were then characterized, with and without the oxygen plasma surface treatment.
Control of Discrete-Event Systems Automata and Petri Net Perspectives
Silva, Manuel; Schuppen, Jan
2013-01-01
Control of Discrete-event Systems provides a survey of the most important topics in the discrete-event systems theory with particular focus on finite-state automata, Petri nets and max-plus algebra. Coverage ranges from introductory material on the basic notions and definitions of discrete-event systems to more recent results. Special attention is given to results on supervisory control, state estimation and fault diagnosis of both centralized and distributed/decentralized systems developed in the framework of the Distributed Supervisory Control of Large Plants (DISC) project. Later parts of the text are devoted to the study of congested systems though fluidization, an over approximation allowing a much more efficient study of observation and control problems of timed Petri nets. Finally, the max-plus algebraic approach to the analysis and control of choice-free systems is also considered. Control of Discrete-event Systems provides an introduction to discrete-event systems for readers that are not familiar wi...
Software hazard analysis for nuclear digital protection system by Colored Petri Net
International Nuclear Information System (INIS)
Bai, Tao; Chen, Wei-Hua; Liu, Zhen; Gao, Feng
2017-01-01
Highlights: •A dynamic hazard analysis method is proposed for the safety-critical software. •The mechanism relies on Colored Petri Net. •Complex interactions between software and hardware are captured properly. •Common failure mode in software are identified effectively. -- Abstract: The software safety of a nuclear digital protection system is critical for the safety of nuclear power plants as any software defect may result in severe damage. In order to ensure the safety and reliability of safety-critical digital system products and their applications, software hazard analysis is required to be performed during the lifecycle of software development. The dynamic software hazard modeling and analysis method based on Colored Petri Net is proposed and applied to the safety-critical control software of the nuclear digital protection system in this paper. The analysis results show that the proposed method can explain the complex interactions between software and hardware and identify the potential common cause failure in software properly and effectively. Moreover, the method can find the dominant software induced hazard to safety control actions, which aids in increasing software quality.
Dynamical Scheduling and Robust Control in Uncertain Environments with Petri Nets for DESs
Directory of Open Access Journals (Sweden)
Dimitri Lefebvre
2017-10-01
Full Text Available This paper is about the incremental computation of control sequences for discrete event systems in uncertain environments where uncontrollable events may occur. Timed Petri nets are used for this purpose. The aim is to drive the marking of the net from an initial value to a reference one, in minimal or near-minimal time, by avoiding forbidden markings, deadlocks, and dead branches. The approach is similar to model predictive control with a finite set of control actions. At each step only a small area of the reachability graph is explored: this leads to a reasonable computational complexity. The robustness of the resulting trajectory is also evaluated according to a risk probability. A sufficient condition is provided to compute robust trajectories. The proposed results are applicable to a large class of discrete event systems, in particular in the domains of flexible manufacturing. However, they are also applicable to other domains as communication, computer science, transportation, and traffic as long as the considered systems admit Petri Nets (PNs models. They are suitable for dynamical deadlock-free scheduling and reconfiguration problems in uncertain environments.
Evaluation of Cyber Security and Modelling of Risk Propagation with Petri Nets
Directory of Open Access Journals (Sweden)
Marcin Szpyrka
2017-02-01
Full Text Available This article presents a new method of risk propagation among associated elements. On thebasis of coloured Petri nets, a new class called propagation nets is defined. This class providesa formal model of a risk propagation. The proposed method allows for model relations betweennodes forming the network structure. Additionally, it takes into account the bidirectional relationsbetween components as well as relations between isomorphic, symmetrical components in variousbranches of the network. This method is agnostic in terms of use in various systems and it canbe adapted to the propagation model of any systems’ characteristics; however, it is intentionallyproposed to assess the risk of critical infrastructures. In this paper, as a proof of concept example, weshow the formal model of risk propagation proposed within the project Cyberspace Security ThreatsEvaluation System of the Republic of Poland. In the article, the idea of the method is presented aswell as its use case for evaluation of risk for cyber threats. With the adaptation of Petri nets, it ispossible to evaluate the risk for the particular node and assess the impact of this risk for all relatednodes including hierarchic relations of components as well as isomorphism of elements.
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2004-01-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction
Energy Technology Data Exchange (ETDEWEB)
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Schrager, D.F.
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing
Composite stochastic processes
Kampen, N.G. van
Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
Research in Stochastic Processes.
1982-10-31
Office of Scientific Research Grant AFOSR F49620 82 C 0009 Period: 1 Noveber 1981 through 31 October 1982 Title: Research in Stochastic Processes Co...STA4ATIS CAMBANIS The work briefly described here was developed in connection with problems arising from and related to the statistical comunication
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
Modularization of biochemical networks based on classification of Petri net t-invariants.
Grafahrend-Belau, Eva; Schreiber, Falk; Heiner, Monika; Sackmann, Andrea; Junker, Björn H; Grunwald, Stefanie; Speer, Astrid; Winder, Katja; Koch, Ina
2008-02-08
Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find
Modularization of biochemical networks based on classification of Petri net t-invariants
Directory of Open Access Journals (Sweden)
Grunwald Stefanie
2008-02-01
Full Text Available Abstract Background Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior. With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. Methods Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t
Stochastic modeling of soil salinity
Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.
2010-12-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.
Stochastic Galerkin methods for the steady-state Navier–Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Sousedík, Bedřich, E-mail: sousedik@umbc.edu [Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States); Elman, Howard C., E-mail: elman@cs.umd.edu [Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 (United States)
2016-07-01
We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.
Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate
Directory of Open Access Journals (Sweden)
Ji-Hun Yoon
2014-01-01
Full Text Available Even though interest rates fluctuate randomly in the marketplace, many option-pricing models do not fully consider their stochastic nature owing to their generally limited impact on option prices. However, stochastic dynamics in stochastic interest rates may have a significant impact on option prices as we take account of issues of maturity, hedging, or stochastic volatility. In this paper, we derive a closed form solution for European options in Black-Scholes model with stochastic interest rate using Mellin transform techniques.
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Energy Technology Data Exchange (ETDEWEB)
Wang, Lijin, E-mail: ljwang@ucas.ac.cn [School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049 (China)
2016-06-08
The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.
Stochastic control with rough paths
International Nuclear Information System (INIS)
Diehl, Joscha; Friz, Peter K.; Gassiat, Paul
2017-01-01
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
BRS symmetry in stochastic quantization of the gravitational field
International Nuclear Information System (INIS)
Nakazawa, Naohito.
1989-12-01
We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in a sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)
Stochastic analysis in discrete and continuous settings with normal martingales
Privault, Nicolas
2009-01-01
This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.
Some remarks on stochastic collective oscillations in ECRIS plasmas
International Nuclear Information System (INIS)
Golovanivsky, K.S.
1993-08-01
It is proposed that the thermal fluctuations in plasmas in general and in ECRIS plasmas in particular create rather strong stochastic electrical fields affecting both confinement and heating of an ECRIS plasma. The amplitude, range and characteristic frequency of the stochastic fields as well as the perpendicular diffusion coefficient and the upper density limit for the mirror confinement are determined on the level of the approximate evaluations. Some aspects of the ECRIS plasma's peculiarities due to the stochastic electrical fields are discussed. (author) 7 refs., 5 figs
A concise course on stochastic partial differential equations
Prévôt, Claudia
2007-01-01
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.
Stochastic theory for classical and quantum mechanical systems
International Nuclear Information System (INIS)
Pena, L. de la; Cetto, A.M.
1975-01-01
From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section
Some illustrations of stochasticity
International Nuclear Information System (INIS)
Laslett, L.J.
1977-01-01
A complex, and apparently stochastic, character frequently can be seen to occur in the solutions to simple Hamiltonian problems. Such behavior is of interest, and potentially of importance, to designers of particle accelerators--as well as to workers in other fields of physics and related disciplines. Even a slow development of disorder in the motion of particles in a circular accelerator or storage ring could be troublesome, because a practical design requires the beam particles to remain confined in an orderly manner within a narrow beam tube for literally tens of billions of revolutions. The material presented is primarily the result of computer calculations made to investigate the occurrence of ''stochasticity,'' and is organized in a manner similar to that adopted for presentation at a 1974 accelerator conference
Stochastic ice stream dynamics.
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-09
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Fractional Stochastic Field Theory
Honkonen, Juha
2018-02-01
Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Stochastic stacking without filters
International Nuclear Information System (INIS)
Johnson, R.P.; Marriner, J.
1982-12-01
The rate of accumulation of antiprotons is a critical factor in the design of p anti p colliders. A design of a system to accumulate higher anti p fluxes is presented here which is an alternative to the schemes used at the CERN AA and in the Fermilab Tevatron I design. Contrary to these stacking schemes, which use a system of notch filters to protect the dense core of antiprotons from the high power of the stack tail stochastic cooling, an eddy current shutter is used to protect the core in the region of the stack tail cooling kicker. Without filters one can have larger cooling bandwidths, better mixing for stochastic cooling, and easier operational criteria for the power amplifiers. In the case considered here a flux of 1.4 x 10 8 per sec is achieved with a 4 to 8 GHz bandwidth
Multistage stochastic optimization
Pflug, Georg Ch
2014-01-01
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Stochastic split determinant algorithms
International Nuclear Information System (INIS)
Horvatha, Ivan
2000-01-01
I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algorithms of practical relevance might be based on Markov processes so constructed
Network interdiction and stochastic integer programming
2003-01-01
On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part....
Sparse Learning with Stochastic Composite Optimization.
Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei
2017-06-01
In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).
The role of stochasticity in sawtooth oscillation
International Nuclear Information System (INIS)
Lichtenberg, A.J.; Itoh, Kimitaka; Itoh, Sanae; Fukuyama, Atsushi.
1991-08-01
In this paper we have demonstrated that stochastization of field lines, resulting from the interaction of the fundamental m/n=1/1 helical mode with other periodicities, plays an important role in sawtooth oscillations. The time scale for the stochastic temperature diffusion has been determined. It was shown to be sufficiently fast to account for the fast sawtooth crash, and is generally shorter than the time scales for the redistribution of current. The enhancement of the electron and ion viscosity, arising from the stochastic field lines, has been calculated. The enhanced electron viscosity always leads to an initial increase in the growth rate of the mode; the enhanced ion viscosity can ultimately lead to mode stabilization before a complete temperature redistribution or flux reconnection has occurred. A dynamical model has been introduced to calculate the path of the sawtooth oscillation through a parameter space of shear and amplitude of the helical perturbation. The stochastic trigger to the enhanced growth rate and the stabilization by the ion viscosity are also included in the mode. A reasonable prescription for the flux reconnection at the end of the growth phase allows us to determine the initial q-value for the successive sawtooth ramps. (J.P.N.)
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
Directory of Open Access Journals (Sweden)
Shaolin Ji
2013-01-01
Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
Chekroun, Mickaël D; Wang, Shouhong
2015-01-01
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Almost Periodic Solutions for Impulsive Fractional Stochastic Evolution Equations
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Toufik Guendouzi
2014-08-01
Full Text Available In this paper, we consider the existence of square-mean piecewise almost periodic solutions for impulsive fractional stochastic evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, fractional calculus, fixed point technique and stochastic analysis theory and methods adopted directly from deterministic fractional equations. Some known results are improved and generalized.
On changes of measure in stochastic volatility models
Directory of Open Access Journals (Sweden)
Bernard Wong
2006-01-01
models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.
Path probability of stochastic motion: A functional approach
Hattori, Masayuki; Abe, Sumiyoshi
2016-06-01
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.
Automatic Supervisory System Synthesis for Port Cranes Collision Prevention by Using Petri Net
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Danko Kezić
2006-05-01
Full Text Available The article deals with the system of port cranes comprisingtwo independently controlled cranes which are simultaneouslyengaged in the transhipment of cargo between a vessel and arailway wagon assembly alongside. The crane operator's errorcan lead to tlie collision of cranes. Therefore, it is necessary toinstall the supervisor in an automatic control system with thefunctions of continuous supervision of the process of cranemovement, and blocking of commands that can lead to collision.The article shows the method of crane system modellingas a discrete event system by using PIT and P-timed Petri nets.There is a proposal of a formal mathematic method for calculationof the state supervisor by P-invariant method. The supervisorcalculated in this way is maximally permissive supervisor.The efficiency of the supervisor is verified by a computer simulation.
Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 2, Analysis Methods
DEFF Research Database (Denmark)
Jensen, Kurt
ideas behind the analysis methods are described as well as the mathematics on which they are based and also how the methods are supported by computer tools. Some parts of the volume are theoretical while others are application oriented. The purpose of the volume is to teach the reader how to use......This three-volume work presents a coherent description of the theoretical and practical aspects of coloured Petri nets (CP-nets). The second volume contains a detailed presentation of the analysis methods for CP-nets. They allow the modeller to investigate dynamic properties of CP-nets. The main...... the formal analysis methods, which does not require a deep understanding of the underlying mathematical theory....
Directory of Open Access Journals (Sweden)
Alecsander Pereira Martins
2015-10-01
Full Text Available This paper proposes an automatic method based on computer vision implemented in mobile platform capable of monitoring the growth of microbial colonies incubated in Petri dishes. The developed optimized image processing algorithm performs this task without human intervention from images of colonies of the microorganism in different evolution phases. The contribution of this paper is the development of a fast and robust mobile tool to assist bioprocess experts in monitoring the growth of colonies without using the conventional error prone evaluation techniques. The obtained results successfully demonstrated dimensional alterations in colonies in a faster and more precise fashion when compared with the conventional method, with the additional advantage of versatility in producing reliable estimation of the growth rates with higher statistical significance.
Requirements Engineering for Reactive Systems: Coloured Petri Nets for an Elevator Controller
DEFF Research Database (Denmark)
Jørgensen, Jens Bæk; Fernandes, Joao Miguel; Tjell, Simon
2007-01-01
This paper presents a model-based approach to requirements engineering for reactive systems; we use an elevator controller as case study. We identify and justify two key properties that a model which we construct must have, namely: (1) controller-and-environment-partitioned, which means...... constituting a description of both the controller and the environment, and distinguishing between these two domains and between desired and assumed behaviour; (2) use case-based, which means constructed on the basis of a given use case diagram and reproducing the behaviour described in accompanying scenario...... descriptions. For the case study, we build an executable model in the formal modelling language Coloured Petri Nets. We demonstrate how this model is useful for requirements engineering, since it provides a solid basis for addressing behavioural issues early in the development process, for example regarding...
Simulación de un sistema de manufactura flexible con redes de Petri coloreadas
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Luis Diego Murillo Soto
2010-10-01
Full Text Available Una forma de estudiar un sistema de manufactura flexible es por medio de un modelo del sistema y someterlo a un simulacro para observar sus índices de comportamiento, gráficas, etc. Siguiendo esta pauta, el presente trabajo plantea la simulación de una línea de producción con tres máquinas, dos robots y tres tipos de productos distintos. Con dicho sistema se desea obtener, en forma automática, porcentajes del uso de las máquinas, tamaño promedio de las colas, gráficas del comportamiento de las colas y el diagrama Gantt. El modelado de la línea de producción se realizó con Redes de Petri Coloreadas (RdPC y su implementación se realizó con la herramienta CPNTool.
Tareen, Samar Hayat Khan; Ahmad, Jamil
2015-01-01
Circadian rhythms are certain periodic behaviours exhibited by living organism at different levels, including cellular and system-wide scales. Recent studies have found that the circadian rhythms of several peripheral organs in mammals, such as the liver, are able to entrain their clocks to received signals independent of other system level clocks, in particular when responding to signals generated during feeding. These studies have found SIRT1, PARP1, and HSF1 proteins to be the major influencers of the core CLOCKBMAL1:PER-CRY circadian clock. These entities, along with abstracted feeding induced signals were modelled collectively in this study using Petri Nets. The properties of the model show that the circadian system itself is strongly robust, and is able to continually evolve. The modelled feeding regimens suggest that the usual 3 meals/day and 2 meals/day feeding regimens are beneficial with any more or less meals/day negatively affecting the system. PMID:25789928
A High-Level Petri Net Framework for Genetic Regulatory Networks
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Banks Richard
2007-12-01
Full Text Available To understand the function of genetic regulatory networks in the development of cellular systems, we must not only realise the individual network entities, but also the manner by which they interact. Multi-valued networks are a promising qualitative approach for modelling such genetic regulatory networks, however, at present they have limited formal analysis techniques and tools. We present a flexible formal framework for modelling and analysing multi-valued genetic regulatory networks using high-level Petri nets and logic minimization techniques. We demonstrate our approach with a detailed case study in which part of the genetic regulatory network responsible for the carbon starvation stress response in Escherichia coli is modelled and analysed. We then compare and contrast this multivalued model to a corresponding Boolean model and consider their formal relationship.
International Nuclear Information System (INIS)
Lee, Seung Jun; Seong, Poong Hyun
2002-01-01
In this work, AuTomated Operating Procedure System (ATOPS) is developed. ATOPS is an automation system for operation of a nuclear power plant (NPP) which can monitor signals, diagnose statuses, and generate control actions according to corresponding operating procedures, without any human operator's help. Main functions of ATOPS are anomaly detection function and procedure execution function, but only the procedure execution function is implemented because this work is just the first step. In the procedure execution function, operating procedures of NPP are analyzed and modeled using Fuzzy Colored Petri Nets (FCPN), and executed depending on decision making of the inference engine. In this work, an ATOPS prototype is developed in order to demonstrate its feasibility and it is also validated using FISA-2/WS simulator. The validation is performed for the cases of a loss of coolant accident (LOCA) and a steam generator tube rupture (SGTR). The simulation results show that ATOPS works correctly in the emergency situations
System of failures diagnosis for energy transmission systems, using Petri nets
International Nuclear Information System (INIS)
Zapata, German; Grisales, John Faber; Gomez, Juan Camilo; Quintero Henao, Luis Fernando
2005-01-01
An expert system of second generation was used integrating the inverse Petri nets (RPN) and the systems based on rules (rule-based system) for the accomplishment of a program in Visual Basic that helps in the obtaining of an opportune and fast analysis of transmission of energy at the time of happening a fault in anymore of its components (line or bus). The program is proven in a portion of system IEEE -118 standard bus test system, in which two extracted cases of literature are developed and are the obtained results. Finally tests realized with the method developed in the laboratory of machines of the national university of Colombia, Medellin campus, simulating a system of transmission with two lines and two buses
Petri Nets Based Modelling of Control Flow for Memory-Aid Interactive Programs in Telemedicine
Khoromskaia, V K
2004-01-01
Petri Nets (PN) based modelling of the control flow for the interactive memory assistance programs designed for personal pocket computers and having special requirements for robustness is considered. The proposed concept allows one to elaborate the programs which can give users a variety of possibilities for a day-time planning in the presence of environmental and time restrictions. First, a PN model for a known simple algorithm is constructed and analyzed using the corresponding state equations and incidence matrix. Then a PN graph for a complicated algorithm with overlapping actions and choice possibilities is designed, supplemented by an example of its analysis. Dynamic behaviour of this graph is tested by tracing of all possible paths of the flow of control using the PN simulator. It is shown that PN based modelling provides reliably predictable performance of interactive algorithms with branched structures and concurrency requirements.
A Petri net-based modelling of replacement strategies under technological obsolescence
Energy Technology Data Exchange (ETDEWEB)
Clavareau, Julien [Universite Libre de Bruxelles (U.L.B.), Service de Metrologie Nucleaire, Av. F.D. Roosevelt, 50 (CP165/84), Bruxelles B-1050 (Belgium)], E-mail: jclavare@ulb.ac.be; Labeau, Pierre-Etienne [Universite Libre de Bruxelles (U.L.B.), Service de Metrologie Nucleaire, Av. F.D. Roosevelt, 50 (CP165/84), Bruxelles B-1050 (Belgium)
2009-02-15
The technological obsolescence of a unit is characterised by the existence of challenger units displaying identical functionalities, but with higher performances. Though this issue is commonly encountered in practice, it has received little consideration in the literature. Previous exploratory works have treated the problem of replacing old-technology items by new ones, for identical components facing a unique new generation of items. This paper aims to define, in a realistic way, possible replacement policies when several types of challenger units are available and when the performances of these newly available units improve with time. Since no fully generic model can exist in maintenance optimisation, a modular modelling of the problem, allowing easy adaptations to features corresponding to specific applications is highly desirable. This work therefore proposes a modular Petri net model for this problem, underlying a Monte Carlo (MC) estimation of the costs incurred by the different possible replacement strategies under consideration.
Directory of Open Access Journals (Sweden)
Samar Hayat Khan Tareen
Full Text Available Circadian rhythms are certain periodic behaviours exhibited by living organism at different levels, including cellular and system-wide scales. Recent studies have found that the circadian rhythms of several peripheral organs in mammals, such as the liver, are able to entrain their clocks to received signals independent of other system level clocks, in particular when responding to signals generated during feeding. These studies have found SIRT1, PARP1, and HSF1 proteins to be the major influencers of the core CLOCKBMAL1:PER-CRY circadian clock. These entities, along with abstracted feeding induced signals were modelled collectively in this study using Petri Nets. The properties of the model show that the circadian system itself is strongly robust, and is able to continually evolve. The modelled feeding regimens suggest that the usual 3 meals/day and 2 meals/day feeding regimens are beneficial with any more or less meals/day negatively affecting the system.
Efficient Data-Structures and Algorithms for a Coloured Petri Nets Simulator
DEFF Research Database (Denmark)
Mortensen, Kjeld Høyer
2001-01-01
In this paper we describe how efficient data-structures and algorithms are used to dramatically improve the performance of a simulator for Coloured Petri Nets compared with earlier versions. We have improved the simulator with respect to three areas: Firstly we have improved the transition...... of other transitions. Secondly we have improved the data-structures which hold multi-sets for markings. A kind of weight-balanced trees, called BB-trees. are used instead of lists as in the original version of the simulator. Although this kind of trees are more difficult to maintain at run...... "recipe" which is specially generated and optimised for each individual transition. The improved simulator is implemented in both the Design/CPN and CPN tools software packages, and has been used in several industrial projects....
Modeling and Application of Vehicular Cyber Physical System Based Petri Nets
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Lin Chen
2014-11-01
Full Text Available Mobile cyber physical system (MCPS has been a hot research area, where mobile nodes can mobile, and communicate with each other. As a typical MCPS, vehicular cyber physical system (VCPS plays an important role in intelligent transportation, especially in collision avoidance. There is no, however, a formal modeling and analysis method for VCPS. In the paper, the modeling method based Petri nets (PN is presented. Furthermore, the behavior expression analysis method is also presented which can deal with arbitrary distribution timed transitions. Finally, a case is introduced to verify the effectiveness about proposed method, and the results show that VCPS can greatly reduce the reaction time of vehicles behind when emergent accident occurs and then enhance the traffic safety.
Directory of Open Access Journals (Sweden)
Leonardo Rodriguez-Urrego
2015-01-01
Full Text Available This paper presents a fault diagnosis application of the Latent Nestling Method to IGBTs. The paper extends the Latent Nestling Method based in Coloured Petri Nets (CPNs to hybrid systems in such a manner that IGBTs performance can be modeled. CPNs allow for an enhanced capability for synthesis and modeling in contrast to the classical phenomena of combinational state explosion when Finite State Machine methods are applied. We present an IGBT model with different fault modes including those of intermittent nature that can be used advantageously as predictive symptoms within a predictive maintenance strategy. Ageing stress tests have been experimentally applied to the IGBTs modules and intermittent faults are diagnosed as precursors of permanent failures. In addition, ageing is validated with morphological analysis (Scanning Electron Microscopy and semiqualitative analysis (Energy Dispersive Spectrometry.
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
Stochastic aspects of Lanchester's theory of warfare
Kingman, J. F. C.
2002-01-01
A Markov chain model for a battle between two opposing forces is formulated, which is a stochastic version of one studied by F. W. Lanchester. Solutions of the backward equations for the final state yield martingales and stopping identities, but a more powerful technique is a time-reversal analogue of a known method for studying urn models. A general version of a remarkable result of Williams and McIlroy (1998) is proved.
The theory of hybrid stochastic algorithms
International Nuclear Information System (INIS)
Duane, S.; Kogut, J.B.
1986-01-01
The theory of hybrid stochastic algorithms is developed. A generalized Fokker-Planck equation is derived and is used to prove that the correct equilibrium distribution is generated by the algorithm. Systematic errors following from the discrete time-step used in the numerical implementation of the scheme are computed. Hybrid algorithms which simulate lattice gauge theory with dynamical fermions are presented. They are optimized in computer simulations and their systematic errors and efficiencies are studied. (orig.)
Compressible fluid flows driven by stochastic forcing
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Maslowski, B.; Novotný, A.
2013-01-01
Roč. 254, č. 3 (2013), s. 1342-1358 ISSN 0022-0396 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Institutional support: RVO:67985840 Keywords : stochastic Navier-Stokes equations * compressible fluid * random driving force Subject RIV: BA - General Mathematics Impact factor: 1.570, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022039612004135
Analytic stochastic regularization and gauge theories
International Nuclear Information System (INIS)
Abdalla, E.; Gomes, M.; Lima-Santos, A.
1987-04-01
We prove that analytic stochatic regularization braks gauge invariance. This is done by an explicit one loop calculation of the two three and four point vertex functions of the gluon field in scalar chromodynamics, which turns out not to be geuge invariant. We analyse the counter term structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization. (author) [pt
Planning and Optimization of AGV Jobs by Petri Net and Genetic Algorithm
Directory of Open Access Journals (Sweden)
Anita Gudelj
2012-12-01
Full Text Available The following article presents the possibilities of job optimization on a maritime container terminal, in order to increase the system productivity and optimize the terminal capacity. Automated guided vehicles (AGVs are now becoming popular mode of container transport in seaport terminals. The moving of vehicles can be described as the set of discrete events and states. Some of these states can be undesirable such as conflicts and deadlocks. It is necessary to apply adequate control policy to avoid deadlocks and block the vehicles’ moving only in the case of dangerous situation.This paper addresses the use a Petri net as modeling and scheduling tool in this context. The aim of AGV scheduling is to dispatch a set of AGVs to improve the productivity of a system and reduce delay in a batch of pickup/drop-off jobs under certain constraints such as deadlines, priority, etc. The final goals are related to optimization of processing time and minimization of the number of AGVs involved while maintaining the system throughput.To find better solutions, the authors propose the integration MRF1 class of Petri net (MRF1PN with a genetic algorithm. Also, the use of a matrix based formal method is proposed to analyze discrete event dynamic system (DEDS. The algorithm is described to deal with multi-project, multi-constrained scheduling problem with shared resources. The developed model was tested and validated by simulation of typical scenarios of the container terminal of Port Koper. Modularity and simplicity of the approach allow using the model to monitor and test the efficiency of the processes, and also to propose future alternative solutions to optimize the schedule of operations and the employment of AGV at the terminal.
Directory of Open Access Journals (Sweden)
Xiaona Leng
2017-06-01
Full Text Available Abstract This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the results of numerical simulations investigating the dynamical effects of stochastic disturbance. Our results significantly improve and generalize the corresponding results in recent literatures. The developed theoretical methods and stochastic inequalities technique can be used to investigate the high-dimensional nonlinear stochastic differential systems.
International Nuclear Information System (INIS)
Song Lina; Zhang Hongqing
2007-01-01
In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.
Factors influencing lysis time stochasticity in bacteriophage λ
Directory of Open Access Journals (Sweden)
Dennehy John J
2011-08-01
Full Text Available Abstract Background Despite identical genotypes and seemingly uniform environments, stochastic gene expression and other dynamic intracellular processes can produce considerable phenotypic diversity within clonal microbes. One trait that provides a good model to explore the molecular basis of stochastic variation is the timing of host lysis by bacteriophage (phage. Results Individual lysis events of thermally-inducible λ lysogens were observed using a temperature-controlled perfusion chamber mounted on an inverted microscope. Both mean lysis time (MLT and its associated standard deviation (SD were estimated. Using the SD as a measure of lysis time stochasticity, we showed that lysogenic cells in controlled environments varied widely in lysis times, and that the level of lysis time stochasticity depended on allelic variation in the holin sequence, late promoter (pR' activity, and host growth rate. In general, the MLT was positively correlated with the SD. Both lower pR' activities and lower host growth rates resulted in larger SDs. Results from premature lysis, induced by adding KCN at different time points after lysogen induction, showed a negative correlation between the timing of KCN addition and lysis time stochasticity. Conclusions Taken together with results published by others, we conclude that a large fraction of λ lysis time stochasticity is the result of random events following the expression and diffusion of the holin protein. Consequently, factors influencing the timing of reaching critical holin concentrations in the cell membrane, such as holin production rate, strongly influence the mean lysis time and the lysis time stochasticity.
Multivariate moment closure techniques for stochastic kinetic models
International Nuclear Information System (INIS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-01-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
A retrodictive stochastic simulation algorithm
International Nuclear Information System (INIS)
Vaughan, T.G.; Drummond, P.D.; Drummond, A.J.
2010-01-01
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
Stochastic processes and quantum theory
International Nuclear Information System (INIS)
Klauder, J.R.
1975-01-01
The author analyses a variety of stochastic processes, namely real time diffusion phenomena, which are analogues of imaginary time quantum theory and convariant imaginary time quantum field theory. He elaborates some standard properties involving probability measures and stochastic variables and considers a simple class of examples. Finally he develops the fact that certain stochastic theories actually exhibit divergences that simulate those of covariant quantum field theory and presents examples of both renormaizable and unrenormalizable behavior. (V.J.C.)
Stochastic Coloured Petrinet Based Healthcare Infrastructure Interdependency Model
Nukavarapu, Nivedita; Durbha, Surya
2016-06-01
The Healthcare Critical Infrastructure (HCI) protects all sectors of the society from hazards such as terrorism, infectious disease outbreaks, and natural disasters. HCI plays a significant role in response and recovery across all other sectors in the event of a natural or manmade disaster. However, for its continuity of operations and service delivery HCI is dependent on other interdependent Critical Infrastructures (CI) such as Communications, Electric Supply, Emergency Services, Transportation Systems, and Water Supply System. During a mass casualty due to disasters such as floods, a major challenge that arises for the HCI is to respond to the crisis in a timely manner in an uncertain and variable environment. To address this issue the HCI should be disaster prepared, by fully understanding the complexities and interdependencies that exist in a hospital, emergency department or emergency response event. Modelling and simulation of a disaster scenario with these complexities would help in training and providing an opportunity for all the stakeholders to work together in a coordinated response to a disaster. The paper would present interdependencies related to HCI based on Stochastic Coloured Petri Nets (SCPN) modelling and simulation approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The entire model would be integrated with Geographic information based decision support system to visualize the dynamic behaviour of the interdependency of the Healthcare and related CI network in a geographically based environment.
STOCHASTIC COLOURED PETRINET BASED HEALTHCARE INFRASTRUCTURE INTERDEPENDENCY MODEL
Directory of Open Access Journals (Sweden)
N. Nukavarapu
2016-06-01
Full Text Available The Healthcare Critical Infrastructure (HCI protects all sectors of the society from hazards such as terrorism, infectious disease outbreaks, and natural disasters. HCI plays a significant role in response and recovery across all other sectors in the event of a natural or manmade disaster. However, for its continuity of operations and service delivery HCI is dependent on other interdependent Critical Infrastructures (CI such as Communications, Electric Supply, Emergency Services, Transportation Systems, and Water Supply System. During a mass casualty due to disasters such as floods, a major challenge that arises for the HCI is to respond to the crisis in a timely manner in an uncertain and variable environment. To address this issue the HCI should be disaster prepared, by fully understanding the complexities and interdependencies that exist in a hospital, emergency department or emergency response event. Modelling and simulation of a disaster scenario with these complexities would help in training and providing an opportunity for all the stakeholders to work together in a coordinated response to a disaster. The paper would present interdependencies related to HCI based on Stochastic Coloured Petri Nets (SCPN modelling and simulation approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The entire model would be integrated with Geographic information based decision support system to visualize the dynamic behaviour of the interdependency of the Healthcare and related CI network in a geographically based environment.
Stochastic Analysis with Financial Applications
Kohatsu-Higa, Arturo; Sheu, Shuenn-Jyi
2011-01-01
Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. This book also covers the areas of backward stochastic differential equations via the (non-li
Energy Technology Data Exchange (ETDEWEB)
Hardwick, Robert J.; Vennin, Vincent; Wands, David [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom); Byrnes, Christian T.; Torrado, Jesús, E-mail: robert.hardwick@port.ac.uk, E-mail: vincent.vennin@port.ac.uk, E-mail: c.byrnes@sussex.ac.uk, E-mail: jesus.torrado@sussex.ac.uk, E-mail: david.wands@port.ac.uk [Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH (United Kingdom)
2017-10-01
We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.
International Nuclear Information System (INIS)
Hardwick, Robert J.; Vennin, Vincent; Wands, David; Byrnes, Christian T.; Torrado, Jesús
2017-01-01
We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Modeling and performance analysis of a closed-loop supply chain using first-order hybrid Petri nets
Directory of Open Access Journals (Sweden)
Imane Outmal
2016-05-01
Full Text Available Green or closed-loop supply chain had been the focus of many manufacturers during the last decade. The application of closed-loop supply chain in today’s manufacturing is not only due to growing environmental concerns and the recognition of its benefits in reducing greenhouse gas emissions, energy consumption, and meeting a more strict environmental regulations but it also offers economic competitive advantages if appropriately managed. First-order hybrid Petri nets represent a powerful graphical and mathematical formalism to map and analyze the dynamics of complex systems such as closed-loop supply chain networks. This article aims at illustrating the use of first-order hybrid Petri nets to model a closed-loop supply chain network and evaluate its operational, financial, and environmental performance measures under different management policies. Actual data from auto manufacturer in the United States are used to validate network’s performance under both tactical and strategic decision-making, namely, (1 tactical decision—production policies: increase of recovered versus new components and (2 strategic decision—closed-loop supply chain network structure: manufacturer internal recovery process or recovery process done by a third-party collection and recovery center. The work presented in this article is an extension of the use of first-order hybrid Petri nets as a modeling and performance analysis tool from supply chain to closed-loop supply chain. The modularity property of first-order hybrid Petri nets has been used in the modeling process, and the simulation and analysis of the modeled network are done in MATLAB® environment. The results of the experiments depict that first-order hybrid Petri nets are a powerful modeling and analysis formalism for closed-loop supply chain networks and can be further used as an efficient decision-making tool at both tactical and strategic levels. Unlike other researches on modeling supply chain
Stochastic calculus in physics
International Nuclear Information System (INIS)
Fox, R.F.
1987-01-01
The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations
Stochastic conditional intensity processes
DEFF Research Database (Denmark)
Bauwens, Luc; Hautsch, Nikolaus
2006-01-01
model allows for a wide range of (cross-)autocorrelation structures in multivariate point processes. The model is estimated by simulated maximum likelihood (SML) using the efficient importance sampling (EIS) technique. By modeling price intensities based on NYSE trading, we provide significant evidence......In this article, we introduce the so-called stochastic conditional intensity (SCI) model by extending Russell’s (1999) autoregressive conditional intensity (ACI) model by a latent common dynamic factor that jointly drives the individual intensity components. We show by simulations that the proposed...... for a joint latent factor and show that its inclusion allows for an improved and more parsimonious specification of the multivariate intensity process...
Stochastic cooling for beginners
International Nuclear Information System (INIS)
Moehl, D.
1984-01-01
These two lectures have been prepared to give a simple introduction to the principles. In Part I we try to explain stochastic cooling using the time-domain picture which starts from the pulse response of the system. In Part II the discussion is repeated, looking more closely at the frequency-domain response. An attempt is made to familiarize the beginners with some of the elementary cooling equations, from the 'single particle case' up to equations which describe the evolution of the particle distribution. (orig.)
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic
Markovian approach: From Ising model to stochastic radiative transfer
International Nuclear Information System (INIS)
Kassianov, E.; Veron, D.
2009-01-01
The origin of the Markovian approach can be traced back to 1906; however, it gained explicit recognition in the last few decades. This overview outlines some important applications of the Markovian approach, which illustrate its immense prestige, respect, and success. These applications include examples in the statistical physics, astronomy, mathematics, computational science and the stochastic transport problem. In particular, the overview highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics. Using simple probabilistic assumptions (Markovian approximation), they have introduced a simplified, but quite realistic, representation of the neutron/radiation transfer through a two-component discrete stochastic mixture. New concepts and methodologies introduced by these two distinguished scientists allow us to generalize the Markovian treatment to the stochastic medium with inhomogeneous statistics and demonstrate its improved predictive performance for the down-welling shortwave fluxes. (authors)
Cheetham, Paul
2010-01-01
Muusikamanageride Paul Cheethami, Tapio Korjuse, Petri H. Lundeni, Kari Pössi ja Rasmus Stolbergi arvamusi oma tööst ja nõuannetest eesti ansamblitele, kes tahavad oma karjääri teha rahvusvahelisel areenil
Stochastic differential equations and a biological system
DEFF Research Database (Denmark)
Wang, Chunyan
1994-01-01
The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based...... on experimental data is considered. As an example, the growth of bacteria Pseudomonas fluorescens is taken. Due to the specific features of stochastic differential equations, namely that their solutions do not exist in the general sense, two new integrals - the Ito integral and the Stratonovich integral - have...... description. In order to identify the parameters, a Maximum likelihood estimation method is used together with a simplified truncated second order filter. Because of the continuity feature of the predictor equation, two numerical integration methods, called the Odeint and the Discretization method...
Stochastic Blind Motion Deblurring
Xiao, Lei
2015-05-13
Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.
AA, stochastic precooling pickup
CERN PhotoLab
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...
Behavioral Stochastic Resonance
Freund, Jan A.; Schimansky-Geier, Lutz; Beisner, Beatrix; Neiman, Alexander; Russell, David F.; Yakusheva, Tatyana; Moss, Frank
2001-03-01
Zooplankton emit weak electric fields into the surrounding water that originate from their own muscular activities associated with swimming and feeding. Juvenile paddlefish prey upon single zooplankton by detecting and tracking these weak electric signatures. The passive electric sense in the fish is provided by an elaborate array of electroreceptors, Ampullae Lorenzini, spread over the surface of an elongated rostrum. We have previously shown that the fish use stochastic resonance to enhance prey capture near the detection threshold of their sensory system. But stochastic resonance requires an external source of electrical noise in order to function. The required noise can be provided by a swarm of plankton, for example Daphnia. Thus juvenile paddlefish can detect and attack single Daphnia as outliers in the vicinity of the swarm by making use of noise from the swarm itself. From the power spectral density of the noise plus the weak signal from a single Daphnia we calculate the signal-to-noise ratio and the Fisher information at the surface of the paddlefish's rostrum. The results predict a specific attack pattern for the paddlefish that appears to be experimentally testable.
Stochastic Kuramoto oscillators with discrete phase states
Jörg, David J.
2017-09-01
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.
Stochastic Kuramoto oscillators with discrete phase states.
Jörg, David J
2017-09-01
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.
Coherence and extensions of stochastic matrices
Directory of Open Access Journals (Sweden)
Angelo Gilio
1995-11-01
Full Text Available In this paper a review of some general results on coherence of conditional probability assessments is given. Then, a necessary and sufficient condition on coherence of two finite families of discrete conditianal probability distributions, represented by two stochastic matrices P and Q, is obtained. Moreover, the possible extensions of the assessment (P,Q to the marginal distributions are examined and explicit formulas for them are given in some special case. Finally, a general algorithm to check coherence of (P,Q and to derive its extensions is proposed.
Stochastic programming with integer recourse
van der Vlerk, Maarten Hendrikus
1995-01-01
In this thesis we consider two-stage stochastic linear programming models with integer recourse. Such models are at the intersection of two different branches of mathematical programming. On the one hand some of the model parameters are random, which places the problem in the field of stochastic