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Stochastic Activity Networks (SANs) are a stochastic generalization of Petri nets which have been defined for the modeling and analysis of distributed real-time systems. In this paper, a new definiton for these models is presented. This definition is based on a unified view of the system in three settings: nondeterministic, probabilistic and stochastic. Some general properties of these models are also investigated  

Using the cross-correlation of the wavelet transformation, we propose a general method of studying the scale dependence of the direction of coupling for coupled time series. The method is first demonstrated by applying it to coupled van der Pol forced oscillators and coupled nonlinear stochastic equations. We then apply the method to the analysis of the log-return time series of the stock values of the IBM and General Electric (GE) companies. Our analysis indicates that, on average, IBM stocks react earlier to possible common sector price movements than those of GE  

Jumps are discontinuous variations in time series and one expects that the higher jump activity will cause higher uncertainty in the stochastic behavior of measured time series. Here we study jump events in beat-to-beat fluctuations in the heart rates of healthy subjects, as well as those with congestive heart failure (CHF). The analysis shows that the interbeat time series belong to the class of non-continuous stochastic processes. The estimated drift and diffusion coefficients and jump characteristics of healthy and CHF subjects reveal the distinguishability of two subjects. © 2019 IOP Publishing Ltd and SISSA Medialab srl  

We introduce a method by which stochastic processes are mapped onto complex networks. As examples, we construct the networks for such time series as those for free-jet and low-temperature helium turbulence, the German stock market index (the DAX), and white noise. The networks are further studied by contrasting their geometrical properties, such as the mean length, diameter, clustering, and average number of connections per node. By comparing the network properties of the original time series investigated with those for the shuffled and surrogate series, we are able to quantify the effect of the long-range correlations and the fatness of the probability distribution functions of the series... 

Analysis of flow in fluidized beds, a common chemical reactor, is of much current interest due to its fundamental as well as industrial importance. Experimental data for the successive increments of the pressure fluctuations time series in a fluidized bed are analyzed by computing a multiscale probability density function (PDF) of the increments. The results demonstrate the evolution of the shape of the PDF from the short to long time scales. The deformation of the PDF across time scales may be modeled by the log-normal cascade model. The results are also in contrast to the previously proposed PDFs for the pressure fluctuations that include a Gaussian distribution and a PDF with a power-law... 

We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network features which is in agreement with recent empirical studies  

In this paper, we investigate the statistical and scaling properties of the California earthquakes' inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events. © Versita... 

In this paper, we consider acyclic networks of queues as a model to support the design of a dynamic production system. Each service station in the network represents a manufacturing or assembly operation. Only one type of product is produced by the system, but there exist several distinct production processes for manufacturing this product, each one corresponding with a directed path in the network of queues. In each network node, the number of servers in the corresponding service station is either one or infinity. The service time in each station is either exponentially distributed or belongs to a special class of Coxian distribution. Only in the source node, the service system may be... 

In this paper, we apply the stochastic dynamic programming to find the dynamic shortest path from the source node to the sink node in stochastic dynamic networks, in which the arc lengths are independent random variables with exponential distributions. In each node there is an environmental variable, which evolves in accordance with a continuous time Markov process. The parameter of the exponential distribution of the transition time of each arc is also a function of the state of the environmental variable of its initiative node. Upon arriving at each node, we can move toward the sink node through the best outgoing arc or wait. At the beginning, it is assumed that upon arriving at each node,... 

We have studied the effect of annealing temperature on the statistical properties of WO3 surface using atomic force microscopy (AFM) techniques. We have applied both level crossing and structure function methods. Level crossing analysis indicates an optimum annealing temperature of around 400°C at which the effective area of the WO3 thin film is maximum, whereas the composition of the surface remains stoichiometric. The complexity of the height fluctuation of surfaces was characterized by roughness, the roughness exponent and the lateral size of surface features. We have found that there is a phase transition at around 400°C from one set to two sets of roughness parameters. This happens due... 

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science,... 

We use multifractal detrended fluctuation analysis (MF-DFA) to study the electrical discharge current fluctuations in plasma and show that it has multifractal properties and behaves as a weak anti-correlated process. Comparison of the MF-DFA results for the original series with those for the shuffled and surrogate series shows that correlation of the fluctuations is responsible for the multifractal nature of the electrical discharge current. © 2009 IOP Publishing Ltd. and SISSA  

It is well known that the ballistic deposition and the restricted solid-on-solid models belong to the same universality class, having the same roughness and growth exponents. In this paper, we determine some new statistical properties of the two models, such as the Kramers-Moyal coefficients and the Markov length scale, and show them to be distinct for the two models. © 2008 IOP Publishing Ltd  

Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Furthermore, the source node can include an M/G/∞ queuing system. The length of the arcs connecting the nodes of the network is assumed to be independent random variables. In the proposed method, the network of queues is transformed into a relevant stochastic network. Then, we compute the distribution... 

From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent β characterizing the growth of the mean squared displacement 〈 (δh)(2)〉 of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments 〈 {divides}δh{divides}(q)〉 with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity... 

A time series study of the electrical energy generated by wind turbines and solar cells shows that the energy produced has a lot of fluctuations due to the geographic conditions. These ups and downs have caused not only the share of these sources to be marginal, but also they lead to the volatility of electric power plants. By examining several different data from different countries and regions with the frequency of second and minute, we show that different scale behaviors exist at different time intervals and reveal their other random and nonlinear characteristics. We also compare the non-Gaussian behavior of these regions together, showing that studying the properties of such data helps... 

In this chapter we provide mathematical tools to study the stochastic process from the physical point of view. © 2019, Springer Nature Switzerland AG  

In this chapter we provide mathematical tools to study the stochastic process from the physical point of view. © 2019, Springer Nature Switzerland AG  

Caching at network edges has attracted more and more research interests recently for the purpose of alleviating the network traffic pressure especially in backhaul links and improving user experience. We study Heterogeneous Cellular Caching Networks (HCCNs) consisting of macro cells in which N small cell base stations (SBSs) equipped with cache memory operate in conjunction with the macro cell base station (MBS). We provide closed-form expressions of the MBS and SBSs utilization factors and average user-experienced-delay in HCCNs with overlapping coverage regions, considering general traffic models for the request arrivals based on the Independent Reference Model (IRM) and renewal traffic...