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The aim of this paper is to numerically solve the Fokker-Planck-Kolmogorov fractional-time differential equations using the Legendre wavelet. Also, we analyzed the convergence of function approximation using Legendre wavelets. Introduced the absolute value between the exact answer and the approximate answer obtained by the given numerical methods, and analyzed the error of the numerical method. This method has the advantage of being simple to solve. The results revealed that the suggested numerical method is highly accurate and effective. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. The simulation was carried out using MATLAB software. In this paper and for the first time, the authors presented results on the numerical simulation for classes of time-fractional differential equations. The authors applied the reproducing Legendre wavelet method for the numerical solutions of nonlinear Fokker-Planck-Kolmogorov time-fractional differential equation. The method presented in the present study can be used by programmers, engineers, and other researchers in this field. [ABSTRACT FROM AUTHOR]

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In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form. The proposed scheme is based on a spectral collocation approach to obtain the two independent variables. Our approach is accurate, efficient, and feasible for the model problem under consideration. The proposed Jacobi spectral collocation method yields an exponential rate of convergence with a relatively small number of degrees of freedom. Finally, a series of numerical examples are provided to demonstrate the efficiency and flexibility of the numerical scheme. [ABSTRACT FROM AUTHOR]

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from the perspective of the Liu process. The class or problems considered here are Caputo fuzzy differential equations with Caputo derivatives of order b 2 (1, 2), C 0 Db t u(t, z) = Au(t, z)+ f (t, u(t, z))dCt + Bx(t)Cx(t)dt with initial conditions u(0) = u0, u0(0) = u1, where u(t, z) takes values from U(- EN),V(- EN) is the other bounded space, and EN represents the set of all upper semi-continuously convex fuzzy numbers on R. In addition, several numerical solutions have been provided to verify the correctness and effectiveness of the main result. Finally, an example is given, which expresses the fuzzy fractional differential equations. [ABSTRACT FROM AUTHOR]

Abstract The foremost objective of this study was to analyze the performance of a Markov chain/cellular automata model for predicting land use/land cover changes in environments predisposed to desertification. The study area is the Vieira river basin, located in Montes Claros (MG, Brazil). Land use/land cover prognosis was performed for the year 2005 so that this result could be compared with the ranked image for the same year, taken as ground truth. Kappa indices were used to evaluate the change level that occurred between these two cases. Results from cellular automata were evaluated from those of the Markov chain model. The latter proved to be efficient in the quantitative prediction of changes in land use/land cover. Regarding the cellular automata, an average performance was noted in the spatial distribution of classes. Specifically, with regard to desertification, the use of the CA-Markov model was effective at estimating the total area of the most susceptible class to this process, Bare Soil; however, it was inefficient in its spatialization. Even with the caveats related to the performance of cellular automata, the overall prediction capacity of CA-Markov models can be considered as good. Graphical abstract Image 1 Highlights • Markov chain and cellular automata were used to predict areas susceptible to desertification. • CA-Markov model was efficient in estimating the total and inefficient area in desertification area spatialization. • CA-Markov model can be used as a starting point for studies on desertification. [ABSTRACT FROM AUTHOR]

For a fixed right process X we investigate those functions u for which u(X) is a quasimartingale. We prove that u(X) is a quasimartingale if and only if u is the difference of two finite excessive functions. In particular, we show that the quasimartingale nature of u is preserved under killing, time change, or Bochner subordination. The study relies on an analytic reformulation of the quasimartingale property for u(X) in terms of a certain variation of u with respect to the transition function of the process. We provide sufficient conditions under which u(X) is a quasimartingale, and finally, we extend to the case of semi-Dirichlet forms a semimartingale characterization of such functionals for symmetric Markov processes, due to Fukushima. [ABSTRACT FROM AUTHOR]

Two limit theorems are established on the extremes of a family of stationary Markov processes, known as q -Ornstein–Uhlenbeck processes with q ∈ ( − 1 , 1 ) . Both results are crucially based on the weak convergence of the tangent process at the lower boundary of the domain of the process, a positive self-similar Markov process little investigated so far in the literature. The first result is the asymptotic excursion probability established by the double-sum method, with an explicit formula for the Pickands constant in this context. The second result is a Brown–Resnick-type limit theorem on the minimum process of i.i.d. copies of the q -Ornstein–Uhlenbeck process: with appropriate scalings in both time and magnitude, a new semi-min-stable process arises in the limit. [ABSTRACT FROM AUTHOR]

In the face of disease occurrence, susceptible individuals tend to protect themselves by rewiring their links, i.e., cutting off connection with infected person and switching to contact with healthy ones. Therefore, the adaptive rewiring mechanism is considered in the network epidemic model. Moreover, the infection periods for different diseases do not always follow exponential distributions in the process of disease transmission, which may be of fixed length. Using the idea of age-structure, we establish the susceptible–infected–recovered epidemic model for each node and each link, resulting in a delayed non-Markovian SIR pairwise model with fixed infectious period and preventive rewiring, then give the pairwise reproduction number R 0 p and provide the formula for the final epidemic size by rigorous analysis and tedious computation. The simulation results show that adaptive rewiring inhibits the spread of disease and decreases the size of disease outbreak, while the extension of the infectious period promotes disease transmission. In addition, the numerical simulation results are in good agreement with the stochastic simulation. To our best knowledge, the approach in building our model is novel, the results may provide new insights into the study of the network disease transmission. [ABSTRACT FROM AUTHOR]

A unified mathematical model of Green–Naghdi’s thermoelasticty theories (GN), based on fractional time-derivative of heat transfer is constructed. The model is applied to solve a one-dimensional problem of a perfect conducting unbounded body with a cylindrical cavity subjected to sinusoidal pulse heating in the presence of an axial uniform magnetic field. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Comparisons are made with the results predicted by the two theories. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed. [ABSTRACT FROM PUBLISHER]

A two-dimensional sparse-data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer-aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS-based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X-ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic reliability analysis of three-state fc-out-of-n:G systems in case of a non-homogeneous continuous time Markov (NH CTM ) degradation process assumption. This assumption provides time-dependent transition rates between states of the components which is more realistic for real life applications. It is assumed that the components and the system have three states:perfect functioning, partial performance and complete failure. W e study some performance characteristics of two type of three-state k-out-of-n systems by using the marginal and joint survival functions for the lifetime of those three-state k-out-of-n:G systems that consist of independent and nonidentical components. W e consider permanent based representations for the survival probabilities. Numerical results for the performance characteristics of the two different types of systems are provided. The results are also supported with some graphical illustrations. [ABSTRACT FROM AUTHOR]

In this paper I argue that constitutive relevance relations in mechanisms behave like a special kind of causal relation in at least one important respect: Under suitable circumstances constitutive relevance relations produce the Markov factorization. Based on this observation one may wonder whether standard methods for causal discovery could be fruitfully applied to uncover constitutive relevance relations. This paper is intended as a first step into this new area of philosophical research. I investigate to what extent the PC algorithm, originally developed for causal search, can be used for constitutive relevance discovery. I also discuss possible objections and certain limitations of a constitutive relevance discovery procedure based on PC. [ABSTRACT FROM AUTHOR]

This paper presents a predictive probabilistic model to estimate the overall economic impacts of pitting corrosion by considering both the corrosion costs and significant losses that may occur if failures occur because of pitting corrosion. The major loss categories are considered as business loss and accidental loss. Models are proposed to estimate the elements in each loss category. Corrosion prevention, monitoring, maintenance and management (CPM3) costs are considered as the main categories of corrosion costs and the probabilistic models are proposed to estimate these costs. The Monte Carlo (MC) method is used to integrate the loss and cost models and also to address the uncertainties in these models. The effect of inflation on loss values and the mitigating impact of CPM3 costs are also taken into consideration in the developed models. The application of the proposed risk model is demonstrated using a piping case study. As highlighted in the case study, the developed models help to assess corrosion economic risk, which is used for corrosion prevention and control's decision-making. [ABSTRACT FROM AUTHOR]

We consider the controlled tandem queuing network with two single-server finite-length queues with non-stationary Poisson input flow of packets. The first station controls the service rate and drops any incoming packet if its buffer is full. The second station controls the packet acceptance probability. The tandem is described by a controlled finite-state Markov process and optimized on a fixed time interval by minimizing average number of dropped packets with constraints on the average sojourn time and energy consumption. [ABSTRACT FROM AUTHOR]

A nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on the model parameters, the nonlocal steady and unsteady state master equations are shown to be well-posed in a weak sense. Then the nonlocal operator is shown to be the generator of finite-range nonsymmetric jump processes and, when certain conditions on the model parameters hold, the generators of finite and infinite activity Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator. [ABSTRACT FROM AUTHOR]

There is demonstrated in the present paper, that the H -theorem in the case of explicit time discretization of the physico-chemical kinetic equations, generally speaking, is not valid. We prove the H -theorem, when the system of the physico-chemical kinetic equations with explicit time discretization has the form of non-linear analogue of the Markov process with doubly stochastic matrix, and for more general cases. In these cases the proof is reduced to the proof of the H -theorem for Markov chains. The simplest discrete velocity models of the Boltzmann equation with explicit time discretization –the Carleman and Broadwell models are discussed and the H -theorem for them in the case of discrete time is proved. [ABSTRACT FROM AUTHOR]

We develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms. [ABSTRACT FROM AUTHOR]

This paper focuses on the evaluation of the probability that both components of a bivariate stochastic process ever simultaneously exceed some large level; a leading example is that of two Markov fluid queues driven by the same background process ever reaching the set (u, ∞)×(u, ∞), for u>0. Exact analysis being prohibitive, we resort to asymptotic techniques and efficient simulation, focusing on large values of u. The first contribution concerns various expressions for the decay rate of the probability of interest, which are valid under Gärtner–Ellis-type conditions. The second contribution is an importance-sampling-based rare-event simulation technique for the bivariate Markov modulated fluid model, which is capable of asymptotically efficiently estimating the probability of interest; the efficiency of this procedure is assessed in a series of numerical experiments. [ABSTRACT FROM PUBLISHER]

This paper proposes a unified approximation method for various options whose pay-offs depend on the volume weighted average price (VWAP). Despite their popularity in practice, very few pricing models have been developed in the literature. Also, in previous works, the underlying asset process has been restricted to a geometric Brownian motion. In contrast, our method is applicable to the general class of continuous Markov processes such as local volatility models. Moreover, our method can be used for any type of VWAP options with fixed-strike, floating-strike, continuously sampled, discretely sampled, forward-start and in-progress transactions. [ABSTRACT FROM AUTHOR]

In this research article, the Variational Iteration method coupled with the polynomial approximation is used to find numerical solution to some homogenous and non-homogenous ordinary differential equations arising in mechanics. [ABSTRACT FROM AUTHOR]

We show that all Lindblad operators (i.e., generators of quantum Markov semigroups) on a finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems. [ABSTRACT FROM AUTHOR]

The stability of iterations of affine linear maps Ψn(x)=Anx+Bn,n=1,2,... is studied in the presence of a Markovian environment, more precisely, for the situation when (An,Bn)n≥1 is modulated by an ergodic Markov chain (Mn)n≥0 with countable state space SS and stationary distribution ππ. We provide necessary and sufficient conditions for the a.s. and the distributional convergence of the backward iterations Ψ1O...OΨn(Z0) and also describe all possible limit laws as solutions to a certain Markovian stochastic fixed-point equation. As a consequence of the random environment, these limit laws are stochastic kernels from SS to RR rather than distributions on RR, thus reflecting their dependence on where the driving chain is started. We give also necessary and sufficient conditions for the distributional convergence of the forward iterations ΨnO...OΨ1. The main differences caused by the Markovian environment as opposed to the extensively studied case of independent and identically distributed (iid) Ψ1,Ψ2,... are that: (1) backward iterations may still converge in distribution if a.s. convergence fails, (2) the degenerate case when A1cM1+B1=cM0 a.s. for suitable constants cici, i∈S, is by far more complex than the degenerate case for iid (An,Bn) when A1c+B1=cA a.s. for some c∈R, and (3) forward and backward iterations generally have different laws given M0=i for i∈S so that the former ones need a separate analysis. Our proofs draw on related results for the iid-case, notably by Vervaat, Grincevičius, and Goldie and Maller, in combination with recent results by the authors on fluctuation theory for Markov random walks. [ABSTRACT FROM AUTHOR]

We study a continuous-time power policy to maximize the ergodic channel throughput of an energy harvesting transmitter over a Markov fading channel. In particular, we consider transmission power policies that are adapted to the fading process of the channel as well as the storage process of the battery. We obtain a set of equations that determine the probability density of the energy in the battery at each channel state. Specifically, for an ergodic battery storage process, these equations describe the relation between the probability density of stored energy and the transmission power at each channel state. From these equations, we derive an upper bound on the average transmission power and an upper bound on the average transmission rate. To compute a lower bound on the average transmission rate, we apply a calculus of variations technique to a non-linear throughput maximization problem. As a result, we obtain a system of coupled ordinary differential equations for locally optimal power policies. We then focus on the Gilbert–Elliot channel as a special case and derive some structural results for specific classes of fast and slow fading channels. Furthermore, we numerically find a locally optimal transmission power policy for the two channel state scenario. [ABSTRACT FROM PUBLISHER]

The moments of the random future liabilities of health insurance policies are key quantities for studying distributional properties of the future liabilities. Assuming that the randomness of the future health status of individual policyholders can be described by a semi-Markovian multistate model, integral and differential equations are derived for moments of any order and for the moment generating function. Different representations are derived and discussed with a view to numerical solution methods. [ABSTRACT FROM AUTHOR]

The online shortest path problem is a type of stochastic shortest path problem in which certain arc costs are revealed en route, and the path is updated accordingly to minimize expected cost. This note addresses the open problem of determining whether a problem instance admits a finite optimal solution in the presence of negative arc costs. We formulate the problem as a Markov decision process and show ways to detect such instances in the course of solving the problem using standard algorithms such as value and policy iteration. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(4), 270-276 2016 [ABSTRACT FROM AUTHOR]

We consider the scheduling problem in downlink wireless networks with heterogeneous, Markov-modulated, on/off channels. It is well known that the performance of scheduling over fading channels relies heavily on the accuracy of the available channel state information (CSI), which is costly to acquire. Thus, we consider the CSI acquisition via a practical ARQ-based feedback mechanism whereby channel states are revealed at the end of only scheduled users’ transmissions. In the assumed presence of temporally correlated channel evolutions, the desired scheduler must optimally balance the exploitation–exploration tradeoff, whereby it schedules transmissions both to exploit those channels with up-to-date CSI and to explore the current state of those with outdated CSI. In earlier works, Whittle’s Index Policy had been suggested as a low-complexity and high-performance solution to this problem. However, analyzing its performance in the typical scenario of statistically heterogeneous channel state processes has remained elusive and challenging, mainly because of the highly coupled and complex dynamics it possesses. In this work, we overcome these difficulties to rigorously establish the asymptotic optimality properties of Whittle’s Index Policy in the limiting regime of many users. More specifically: 1) we prove the local optimality of Whittle’s Index Policy, provided that the initial state of the system is within a certain neighborhood of a carefully selected state; (2) we then establish the global optimality of Whittle’s Index Policy under a recurrence assumption that is verified numerically for our problem. These results establish that Whittle’s Index Policy possesses analytically provable optimality characteristics for scheduling over heterogeneous and temporally correlated channels. [ABSTRACT FROM PUBLISHER]

This paper considers consensus problems with random networks. A key object of our analysis is a sequence of stochastic matrices which involve Markovian switches and decreasing step sizes. We establish ergodicity of the backward products of these stochastic matrices. The basic technique is to consider the second moment dynamics of an associated Markovian jump linear system and exploit its two-scale interaction property resulting from the decreasing step sizes. The mean square convergence rate of the backward products is also obtained. The ergodicity results are used to prove mean square consensus of stochastic approximation algorithms where agents collect noisy information. The approach is further applied to a token scheduled averaging model. [ABSTRACT FROM AUTHOR]

With rapid advances in technology, there is an ever increasing need for deploying increasingly complex defence systems to be fielded in operation within costs, time and acceptable end-use functionality. The design of such large-scale military systems are done by integrating off-the-shelf sub-systems, and component-based systems along with indigenously developed systems, ensuring interoperability, functionality and performance. As the size and complexity of systems increases, the design problem goes beyond component and subsystem design or the design of algorithms and data structures of the computation in the sub-systems. The proliferation of software systems have triggered a transition from the hardware oriented military systems to systems that are controlled by software and more so towards embedded systems. In this paper, we extend and apply a framework based reliability assessment approach for a naval system architecture based on a scenario analysis. This approach enables us to infer the system reliability from aspect reliabilities based on the composition methods, allowing the application specific aspects to be added dynamically or upgraded at a later stage. The design of a system as a framework that can support plug-in application specific aspects is an effective way of simplifying the system and assuring high quality by making the specification of each aspect as well as composition component more amenable to rigorous analysis. In order to assess the performance of these systems in various real time warfare scenarios, a Discrete Time Markov Chain is constructed. This methodology can be applied in early design stages to allow the designer to understand the effect of operational degradation factors and their effects that occur over the days of war. The methodology has been effectively applied to carry out the sensitivity analysis of the sub-systems with respect to the scenario based operations and compute mission reliability. [ABSTRACT FROM AUTHOR]

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closedform solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. [ABSTRACT FROM AUTHOR]

As many real applications need a large amount of states, the classical methods are intractable for solving large Markov Decision Processes. The decomposition technique basing on the topology of each state in the associated graph and the parallelization technique are very useful methods to cope with this problem. In this paper, the authors propose a Modified Value Iteration algorithm, adding the parallelism technique. They test their implementation on artificial data using an Open MP that offers a significant speed-up. [ABSTRACT FROM AUTHOR]

A class of stochastic particle models for the spatially discretized time-dependent Schrödinger equation is constructed. Each particle is characterized by a complex-valued weight and a position. The particle weights change according to some deterministic rules between the jumps. The jumps are determined by the creation of offspring. The main result is that certain functionals of the particle systems satisfy the Schrödinger equation. The proofs are based on the theory of piecewise deterministic Markov processes. [ABSTRACT FROM AUTHOR]

We study conditions under which the optimal stopping for one-dimensional diffusion process is generated by a threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as the first time when the process exceeds some level (threshold), and the continuation set has a threshold structure. [ABSTRACT FROM AUTHOR]

We consider estimations of parameters of a two-dimensional Markov Gaussian non-stationary process, given by a system of linear stochastic equations with two parameters, which are different from maximum likelihood estimates. We prove that these estimates are asymptotically normal and asymptotically independent, so this permits us to construct confidence intervals simultaneously for two parameters. [ABSTRACT FROM AUTHOR]

We extend Rice Formula to a process which is the sum of two independent processes: a smooth process and a pure jump process with finitely many jumps. Formulas for the mean number of both continuous and discontinuous crossings through a fixed level on a compact time interval are obtained. We present examples in which we compute explicitly the mean number of crossings and compare which kind of crossings dominates for high levels. In one of the examples the leading term of the tail of the distribution function of the maximum of the process over a compact time interval as the level goes to infinity is obtained. We end giving a generalization, to the non-stationary case, of Borovkov-Last's Rice Formula for Piecewise Deterministic Markov Processes. [ABSTRACT FROM AUTHOR]

The central limit theorem is stated for nonuniformly ergodic Markov chains with an arbitrary phase space. The brief description of the modification of the spectral method is given which is used in the proof of this theorem. Previously the spectral method was being applied only to uniformly ergodic Markov chains. [ABSTRACT FROM AUTHOR]

A multi-type continuous state and continuous time branching process with immigration satisfying some moment conditions is identified as a pathwise unique strong solution of certain stochastic differential equation with jumps. [ABSTRACT FROM AUTHOR]

Comparison of the movements in the VIX index, the rand - dollar exchange rate and South African CPI inflation reveals a striking resemblance between them, raising the question as to whether or not there is an empirical relationship among them. The aim of this paper is to determine whether or not changes in market uncertainty, as reflected in the VIX index, influence South African inflation. Given that the VIX index reflects market uncertainty, its impact on the inflation rate may differ between times of heightened uncertainty and normality, thus suggesting the presence of multiple regimes. To cater for this possibility, the analysis first uses the general-to-specific procedure (including squared and cubed values of dependent and independent variables) with impulse indicator saturation dummies to look for non-linear behaviour in the form of statistically significant squared and cubed variables and clustered periods of outlier dummies that might reflect an alternative regime. Finding such periods, the analysis next uses a Markov-switching model to model this non-linear behaviour explicitly. The results show that market volatility as measured by the VIX indeed explains South African inflation. Moreover, as shown by the second regime of the Markov-switching model, when market volatility is elevated, its influence on inflation also increases. [ABSTRACT FROM AUTHOR]

This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite-state Markov process that modulates the arrival and service rates in the system. Various cases are considered: fast changing environment, fixed environment, and slowly changing environment. In all cases, the arrival rates are environment dependent, whereas the service rates are environment dependent when the environment Markov process is changing fast, and are assumed to be constant in the other two cases. In each of the cases, using weak convergence analysis, in particular functional limit theorems for Poisson processes and ergodic Markov processes, it is shown that an appropriate 'averaged' version of the classical $$c\mu $$ -policy (the priority policy that favors classes with higher values of the product of holding cost $$c$$ and service rate $$\mu $$ ) is asymptotically optimal for an infinite horizon discounted cost criterion. [ABSTRACT FROM AUTHOR]

The ultracontractivity is well studied and several equivalent conditions are known. In this paper, we introduce the dual notion of the ultracontractivity, which we call the dual ultracontractivity. We give necessary and sufficient conditions for the dual ultracontractivity. As an application, we discuss one-dimensional diffusion processes. We can write the conditions for the dual ultracontractivity in terms of speed measures. [ABSTRACT FROM AUTHOR]

Background Studies have shown the strong association between histone modification levels and gene expression levels. The detailed relationships between the two can vary substantially due to differential regulation, and hence a simple regression model may not be adequate. We apply a regression hidden Markov model (regHMM) to further investigate the potential multiple relationships between genes and histone methylation levels in mouse embryonic stem cells. Results Seven histone methylation levels are used in the study. Averaged histone modifications over nonoverlapping 200 bp windows on the range transcription starting site (TSS) ± 1 Kb are used as predictors, and in total 70 explanatory variables are generated. Based on regHMM results, genes segregated into two groups, referred to as State 1 and State 2, have distinct association strengths. Genes in State 1 are better explained by histone methylation levels with R² = .72 while those in State 2 have weaker association strength with R² = .38. The regression coefficients in the two states are not very different in magnitude except in the intercept, .25 and 1.15 for State 1 and State 2, respectively. We found specific GO categories that may be attributed to the different relationships. The GO categories more frequently observed in State 2 match those of housekeeping genes, such as cytoplasm, nucleus, and protein binding. In addition, the housekeeping gene expression levels are significantly less explained by histone methylation in mouse embryonic stem cells, which is consistent with the constitutive expression patterns that would be expected. Conclusion Gene expression levels are not universally affected by histone methylation levels, and the relationships between the two differ by the gene functions. The expression levels of the genes that perform the most common housekeeping genes' GO categories are less strongly associated with histone methylation levels. We suspect that additional biological factors may also be strongly associated with the gene expression levels in State 2. We discover that the effect of the presence of CpG island in TSS ± 1 Kb is larger in State 2. [ABSTRACT FROM AUTHOR]

Let z be a stochastic exponential, i.e., zt = 1+∫t0zs-dMs, of a local martingale M with jumps ΔMt > -1. Then z is a nonnegative local martingale with Ezt ≤ 1. If EzT = 1, then z is a martingale on the time interval [0, T]. The martingale property plays an important role in many applications. It is therefore of interest to give natural and easily verifiable conditions for the martingale property. In this paper, the property EzT = 1 is verified with the so-called linear growth conditions involved in the definition of parameters of M, proposed by Girsanov [Theory Probab. Appl., 5 (1960), pp. 285-301]. These conditions generalize the Beneš idea [SIAM J. Control, 9 (1971), pp. 446-475] and avoid the technology of piecewise approximation. These conditions are applicable even if the Novikov [Theory Probab. Appl., 24 (1979), pp. 820-824] and Kazamaki [Tôhoku Math. J., 29 (1977), pp. 597-600] conditions fail. They are effective for Markov processes that explode, Markov processes with jumps, and also non-Markov processes. Our approach is different from the recently published paper [P. Cheredito, D. Filipović, and M. Yor, Ann. Appl. Probab., 15 (2005), pp. 1713-1732] and preprint [A. Mijitović and M. Urusov, arXiv:0905.3701v1[math.PR], 2009]. [ABSTRACT FROM AUTHOR]

A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. [ABSTRACT FROM AUTHOR]

We consider a heterogeneous two-server system processing fixed size jobs. This includes the scheduling system, where jobs wait in a common queue, and the dispatching system, where jobs are assigned to server-specific queues upon arrival. The optimal policy with respect to the delay in both systems is a threshold policy characterized by a single parameter. In this special case, the scheduling and dispatching systems achieve the same performance with the optimal threshold. The optimal threshold depends on the arrival rate and the service rates. It can be determined by means of dynamic programming, where the required value functions can be evaluated only at the necessary points by means of efficient Monte Carlo simulations. We also give the optimal threshold at three different limits, which yield a simple closed-form expression for a near-optimal threshold. The optimal policy is illustrated and compared with several heuristic dispatching policies. [ABSTRACT FROM AUTHOR]

We commonly observe many types of paired nature of competitions in which the objects are compared by the respondents pairwise in a subjective manner. The Bayesian statistics, contrary to the classical statistics, presents a generic tool to incorporate new experimental evidence and update the existing information. These and other properties have ushered the statisticians to focus their attention on the Bayesian analysis of different paired comparison models. The present article focuses on the amended Davidson model for paired comparison in which an amendment has been introduced that accommodates the option of not distinguishing the effects of two treatments when they are compared pairwise. However, Bayesian analysis of the amended Davidson model is performed using the noninformative priors after making another small modification of incorporating the parameter of order effect factor. The joint and marginal posterior distributions of the parameters, their posterior estimates, predictive and posterior probabilities to compare the treatment parameters are obtained. [ABSTRACT FROM AUTHOR]

We investigate the power-law scaling behaviors of returns for a financial price process which is developed by the voter interacting dynamic system in comparison with the real financial market index (Shanghai Composite Index). The voter system is a continuous time Markov process, which originally represents a voter's attitude on a particular topic, that is, voters reconsider their opinions at times distributed according to independent exponential random variables. In this paper, the detrended fluctuation analysis method is employed to explore the long range power-law correlations of return time series for different values of parameters in the financial model. The findings show no indication or very weak long-range power-law correlations for the simulated returns but strong long-range dependence for the absolute returns. The multiplier distribution is studied to demonstrate directly the existence of scale invariance in the actual data of the Shanghai Stock Exchange and the simulation data of the model by comparison. Moreover, the Zipf analysis is applied to investigate the statistical behaviors of frequency functions and the distributions of the returns. By a comparative study, the simulation data for our constructed price model exhibits very similar behaviors to the real stock index, this indicates somewhat rationality of our model to the market application. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic stabilization problem for discrete-time networked control systems with time delay and packet dropout. The message losses and time delay from the sensor to the controller and from the controller to the actuator are considered simultaneously. A two-state Markov chain is used to model the correlated packet dropout process. By introducing free weighting matrices, the sufficient condition on the stochastic stability of such networked control system is obtained. An improved criterion is found by introducing the delay fractioning method and a new Lyapunov-Krasovskii functional. On the basis of the stability condition, the mode-dependent controller is given in terms of linear matrix inequalities. A simulation example is given to show the proposed results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a framework to detect financial crises, pinpoint the end of a crisis in stock markets and support investment decision-making processes. This proposal is based on a hidden Markov model (HMM) and allows for a specific focus on conditional mean returns. By analysing weekly changes in the US stock market indexes over a period of 20 years, this study obtains an accurate detection of stable and turmoil periods and a probabilistic measure of switching between different stock market conditions. The results contribute to the discussion of the capabilities of Markov-switching models of analysing stock market behaviour. In particular, we find evidence that HMM outperforms threshold GARCH model with Student-tinnovations both in-sample and out-of-sample, giving financial operators some appealing investment strategies. [ABSTRACT FROM AUTHOR]