Discrete Stochastic Model Research Articles

Phase transition approach to bursting in neuronal cultures: quorum percolation models

The Quorum Percolation model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of statistical physics rather than from a dynamical synchronization approach. It is based upon information propagation on a directed graph with a threshold activation rule; this leads to a phase diagram which exhibits a giant percolation cluster below some critical value mC of the excitability. We describe the main characteristics of the original model and derive extensions according to additional relevant biological features. Firstly, we investigate the effects of an excitability variability on the phase diagram and show that the percolation transition can be destroyed by a sufficient amount of such a disorder; we stress the weakly averaging character of the order parameter and show that connectivity and excitability can be seen as two overlapping aspects of the same reality. Secondly, we elaborate a discrete time stochastic model taking into account the decay originating from ionic leakage through the membrane of neurons and synaptic depression; we give evidence that the decay softens and shifts the transition, and conjecture than decay destroys the transition in the thermodynamical limit. We were able to develop mean-field theories associated with each of the two effects; we discuss the framework of their agreement with Monte Carlo simulations. It turns out that the the critical point mC from which information on the connectivity of the network can be inferred is affected by each of these additional effects. Lastly, we show how dynamical simulations of bursts with an adaptive exponential integrateand- fire model can be interpreted in terms of Quorum Percolation. Moreover, the usefulness of the percolation model including the set of sophistication we investigated can be extended to many scientific fields involving information propagation, such as the spread of rumors in sociology, ethology, ecology.

Double Gamma Stochastic Volatility Model in Discrete Time

In an affine term structure framework we propose a discrete time stochastic volatility model. We derive the characteristic function of the log swap rate under swap measure. Having the characteristic function, we employ the Fourier cosine (COS) technique to price swaptions. Using data on tweleve years of swap rates and swaption premiums, model parameters are estimated using an unscented Kalman filter algorithm.

Three-dimensional computational fluid dynamics (volume of fluid) modelling coupled with a stochastic discrete phase model for the performance analysis of an invert trap experimentally validated using field sewer solids

Invert traps are used to trap sewer solids flowing into a sewer drainage system. The performance of the invert trap in an open rectangular channel was experimentally and numerically analysed using field sewer solids collected from a sewer drain. Experiments showed that the free water surface rises over the central opening (slot) of the invert trap, which reduces the velocity near the slot and allows more sediment to be trapped in comparison with the case for the fixed-lid model (assuming closed conduit flow with a shear-free top wall) used by earlier investigators. This phenomenon cannot be modelled using a closed conduit model as no extra space is provided for the fluctuation of the water surface, whereas this space is provided in the volume of fluid (VOF) model in the form of air space in ANSYS Fluent 14.0 software. Additionally, the zero atmospheric pressure at the free water surface cannot be modelled in a fixed-lid model. In the present study, experimental trap efficiencies of the invert trap using field sewer solids were fairly validated using a three-dimensional computational fluid dynamics model (VOF model) coupled with a stochastic discrete phase model. The flow field (i.e., velocities) predicted by the VOF model were compared with experimental velocities obtained employing particle image velocimetry. The water surface profile above the invert trap predicted by the VOF model was found to be in good agreement with the experimentally measured profile. The present study thus showed that the VOF model can be used with the stochastic discrete phase model to well predict the performance of invert traps.

Discrete stochastic models and global information risk treatment operations in strategic processes

Formulating, investigating, and applying in various practical disciplines of discrete stochastic models incorporating discrete random sums are considered as significant research activities. The present paper makes use of a discrete random sum and a discrete random variable to formulate a stochastic model and investigate the corresponding probability distribution. In addition, the present paper establishes applications of the formulated discrete stochastic model in the practical disciplines of strategic thinking and strategic management.

Evaluation of Control Strategies for Porcine Reproductive and Respiratory Syndrome (PRRS) in Swine Breeding Herds Using a Discrete Event Agent-Based Model.

The objective of this study was to develop a discrete event agent-based stochastic model to explore the likelihood of the occurrence of porcine reproductive and respiratory syndrome (PRRS) outbreaks in swine herds with different PRRS control measures in place. The control measures evaluated included vaccination with a modified-live attenuated vaccine and live-virus inoculation of gilts, and both were compared to a baseline scenario where no control measures were in place. A typical North American 1,000-sow farrow-to-wean swine herd was used as a model, with production and disease parameters estimated from the literature and expert opinion. The model constructed herein was not only able to capture individual animal heterogeneity in immunity to and shedding of the PRRS virus, but also the dynamic animal flow and contact structure typical in such herds under field conditions. The model outcomes included maximum number of females infected per simulation, and time at which that happened and the incidence of infected weaned piglets during the first year of challenge-virus introduction. Results showed that the baseline scenario produced a larger percentage of simulations resulting in outbreaks compared to the control scenarios, and interestingly some of the outbreaks occurred over long periods after virus introduction. The live-virus inoculation scenario showed promising results, with fewer simulations resulting in outbreaks than the other scenarios, but the negative impacts of maintaining a PRRS-positive population should be considered. Finally, under the assumptions of the current model, neither of the control strategies prevented the infection from spreading to the piglet population, which highlights the importance of maintaining internal biosecurity practices at the farrowing room level.

Determination of the Optimal Concession Period for BOT Contract Projects Based on a Discrete Stochastic Process Model

The concession period is one of the most important issues in the contractual arrangement of build-operate-transfer (BOT) projects. When planning a BOT project, the government should aim for a trade-off between the concerned government’s satisfaction and the private concessionaire’s profit. The objective of this paper is to present a discrete stochastic process model to obtain an optimal concession period considering the trade-off. The process model is developed for a highway project by analyzing the actual traffic data. The net present value (NPV) is calculated for use as a constraint condition that indicates the boundary of risk preference in a utility function. Using a utility function, this paper estimates the duration of concession periods at which the government can both attract investments from private concessionaires and satisfy public opinion. A numerical simulation is applied to demonstrate the applicability of the methodology presented. The result of the simulation shows that the discrete stochastic process model contributes to a better understanding of trade-offs in determining the optimal concession period.

Finite state projection based bounds to compare chemical master equation models using single-cell data.

Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.

Stochastic prediction of high-speed train dynamics to long-term evolution of track irregularities

There is a great interest to predict the long-term evolution of the track irregularities for a given track stretch of the high-speed train network, in order to be able to anticipate the start off of the maintenance operations. In this paper, a stochastic predictive model, based on big data made up of a lot of experimental measurements performed on the French high-speed train network, is proposed for predicting the statistical quantities of a vector-valued random indicator related to the nonlinear dynamic responses of the high-speed train excited by stochastic track irregularities. The long-term evolution of the vector-valued random indicator is modeled by a discrete non-Gaussian nonstationary stochastic model (ARMA type model), for which the coefficients are time-dependent. These coefficients are identified by a least-squares method and fitted on long time, using experimental measurements. The quality assessment of the stochastic predictive model is presented, which validates the proposed stochastic model.

Three dimensional discrete stochastic model of occluded corrosion cell

We present a stochastic three dimensional (3D) model for corrosion at a mesoscopic scale. The competition between uniform and localized corrosion is studied, with special emphasis given to the connection between the anodic and cathodic reactions. Even if the reactions happen at different places, they are linked and occur simultaneously, maintaining an electric balance. We focused on the particular case of an occluded corrosion on a metal covered by a non reactive layer, where two growth regimes are evidenced and controlled by the diffusion of species in the electrolyte.

3D CFD validation of invert trap efficiency for sewer solid management using VOF model

Earlier investigators have numerically carried out performance analysis of the invert trap fitted in an open channel using the stochastic discrete phase model (DPM) by assuming the open channel flow to be closed conduit flow under pressure and assuming zero shear stress at the top wall. This is known as the fixed lid model. By assuming the top wall to be a shear free wall, they have been able to show that the velocity distribution looks similar to that of an open channel flow with zero velocity at the bottom and maximum velocity at the top, representing the free water surface, but no information has been provided for the pressure at the free water surface. Because of this assumption, the validation of the model in predicting the trap efficiency has performed significantly poorly. In addition, the free water surface subject to zero gauge pressure cannot be modeled using the fixed lid model because there is no provision of extra space in the form of air space for the fluctuating part of the water surface profile. It can, however, be modeled using the volume of fluid (VOF) model because the VOF model is the appropriate model for open channel or free surface flow. Therefore, in the present study, three-dimensional (3D) computational fluid dynamics (CFD) modeling with the VOF model, which considers open channel flow with a free water surface, along with the stochastic DPM, was used to model the trap efficiency of an invert trap fitted in an open rectangular channel. The governing mathematical flow equations of the VOF model were solved using the ANSYS Fluent 14.0 software, reproducing the experimental conditions exactly. The results show that the 3D CFD predictions using the VOF model closely fit the experimental data for glass bead particles.

A novel two-stage extended Kalman filter algorithm for reaction flywheels fault estimation

This paper investigates the problem of two-stage extended Kalman filter (TSEKF)-based fault estimation for reaction flywheels in satellite attitude control systems (ACSs). Firstly, based on the separate-bias principle, a satellite ACSs with actuator fault is transformed into an augmented nonlinear discrete stochastic model; then, a novel TSEKF is suggested such that it can simultaneously estimate satellite attitude information and actuator faults no matter they are additive or multiplicative; finally, the proposed approach is respectively applied to estimating bias faults and loss of effectiveness for reaction flywheels in satellite ACSs, and simulation results demonstrate the effectiveness of the proposed fault estimation approach.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System

So far many optimization models based on Nash Bargaining Theory associated with reservoir operation have been developed. Most of them have aimed to provide practical and efficient solutions for water allocation in order to alleviate conflicts among water users. These models can be discussed from two viewpoints: (i) having a discrete nature; and (ii) working on an annual basis. Although discrete dynamic game models provide appropriate reservoir operator policies, their discretization of variables increases the run time and causes dimensionality problems. In this study, two monthly based non-discrete optimization models based on the Nash Bargaining Solution are developed for a reservoir system. In the first model, based on constrained state formulation, the first and second moments (mean and variance) of the state variable (water level in the reservoir) is calculated. Using moment equations as the constraint, the long-term utility of the reservoir manager and water users are optimized. The second model is a dynamic approach structured based on continuous state Markov decision models. The corresponding solution based on the collocation method is structured for a reservoir system. In this model, the reward function is defined based on the Nash Bargaining Solution. Indeed, it is used to yield equilibrium in every proper sub-game, thereby satisfying the Markov perfect equilibrium. Both approaches are applicable for water allocation in arid and semi-arid regions. A case study was carried out at the Zayandeh-Rud river basin located in central Iran to identify the effectiveness of the presented methods. The results are compared with the results of an annual form of dynamic game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that both models are capable of tackling conflict issues in water allocation in situations of water scarcity properly. Also, comparing the annual dynamic game models, the presented models result in superior results in practice. Furthermore, unlike discrete dynamic game models, the presented models can significantly reduce the runtime thereby avoiding dimensionality problems.

Efficient water management policies for irrigation adaptation to climate change in Southern Europe

This paper evaluates economic and environmental effects of two incentive-based water management policies to address climate change impacts on irrigated agriculture: water markets and irrigation subsidies. A Southern European case study assesses farmers' long and short-run adaptation responses under climate change and policy interventions with a discrete stochastic programming model. Results indicate that climate change will likely have negative impacts on irrigation activities and water-dependent ecosystems in Southern Europe. However, the severity of impacts depends on government policy settings and farmers' adaptation responses. The comparison between water market and irrigation subsidy policies shows the advantages of water markets over irrigation subsidies in terms of both private and social benefits. These findings could guide policymakers on the design of efficient water institutions and policies to address climate change in the irrigated agriculture of Southern Europe.

Effect of Substrate and Its Shape on in-Flight Particle Characteristics in Suspension Plasma Spraying

Obtaining a uniform coating on curved mechanical parts such as gas turbine blades is one of the industrial challenges in suspension plasma spraying. Through a three dimensional numerical analysis, this study is aimed at providing a better understanding of the effect of substrate curvature on in-flight particle temperature, velocity, and trajectory. The high temperature and high velocity plasma flow is simulated inside the plasma torch using a uniform volumetric heat source in the energy equation. The suspension of yttria-stabilized zirconia particles is molded as a multicomponent droplet while catastrophic breakup regime is considered for simulating the secondary break up when the suspension interacts with the plasma flow. A two-way coupled Eulerian-Lagrangian approach along with a stochastic discrete model was used to track the particle trajectory. Particle size distribution in the vicinity of the substrate at different stand-off distances has been investigated. The results show that sub-micron particles obtain higher velocity and temperature compared to the larger particles. However, due to the small Stokes number associated with sub-micron particles, they are more sensitive to the change of the gas flow streamlines in the vicinity of a curved substrate.

On a stochastic epidemic SEIHR model and its diffusion approximation

To model the evolution of diseases with extended latency periods like varicella, we generalise a simple discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases. Analytical results of the proposed Markovian model are provided. The basic reproduction number \(R_0\) of the former and new models as well as a diffusion approximation are derived, leading to a stochastic differential equation with multiple delays in a natural way.

Self-insurance and multi-peril grassland crop insurance: the case of French suckler cow farms

Purpose – From the perspectives of the probable replacement of the national calamity funds by multi-peril grassland insurance, the purpose of this paper is to estimate demand for grassland production insurance. Design/methodology/approach – A discrete stochastic programming model with a three-year planning horizon was used to run simulations for farms raising suckler cows primarily with grasslands. In this model, the annual area insured and some production decisions are optimized under grasland yield uncertainty, with possible ex post production-system adjustments. The effects of insurance loading cost (14 levels), insurance coverage level (three levels), risk aversion (two levels) and stock levels (forage and animal stocks vary according to grassland yields and to farm management of the previous years) were analyzed. Findings – The results show that grassland insurance could be used as a flexible risk management tool, when farm becomes vulnerable to fodder shortfall. According to previous years’ grassland yields and to the subsequent states of hay stock and animal liveweight, the area insured could vary between nearly the none and full. Farmers with low-average stocking rate and important hay storage capacity have less incentive to buy grassland insurance. The author also demonstrates that for a given loading cost, more insurance is purchased at a coverage level of 70 percent of average yield than at higher coverage levels. The cost of self-insurance increases for important and rare losses while multi-peril grassland insurance premium decreases. Higher levels of risk aversion also raise the quantity of insurance subscribed. Eventually, insurance price is a key factor. Almost no insurance is bought for loading costs greater than 1.1 under low-risk aversion and for loading costs greater than 1.3 under moderate risk aversion. Research limitations/implications – The willingness to pay for insurance could have been overestimated for different reasons. First, basis risks have not been introduced in the simulation framework. Although the Forage Production Index performed quite well, basis risks are high enough to trigger inappropriate indemnifications in some cases. Consequences of these risks should be estimated in further research. Second, other self-insurance options and public emergency measures such as subsidized loan or reduction in social security contributions should also be considered to assess and reduce farmers vulnerability to risks. Practical implications – The launching of the multi-peril grassland insurance is likely to be successful thanks to the 65 percent of public subsidies on insurance premiuml. However, considering that the loading cost is likely to be high and that demand for grassland production insurance is rather low, multi-peril grassland production insurance may struggle to continue unsubsidized. Originality/value – This paper provides a framework that enables to estimate demand for grassland production insurance factoring in substitution with self-insurance and taking into account successive risks.

Numerical study of the particle residence time and flow characters in an Opposed Multi-Burner gasifier

As one of the most efficient and reliable entrained flow coal gasification technologies, the Opposed Multi-Burner (OMB) coal-water slurry gasification technology has been applied in 38 plants. The particle residence time in a commercial scale OMB gasifier is studied in this work by using a 3D numerical model. The Realizable k-ε model and discrete particle stochastic trajectory model are employed to solve the gas–solid two-phase flow. The model is validated with the particle residence distribution (RTD) obtained from the bench scale gasifier. The Direct Simulation Monte Carlo (DSMC) method and hard sphere model are used to calculate the gas–solid flow in gasifier impinging zone to consider the effects of the inter-particle collision. In order to reveal the intrinsic factors that dominate the particle residence time, the particle flow behavior is investigated and the mechanical analysis is conducted. A criterion is proposed and used to evaluate the dominant factor of particle flow in different flow regions of the OMB gasifier. The following results are obtained: The inter-particle collisions in Jet Zones and Impinging Zone of the OMB gasifier slightly reduce the particle residence time in these regions. In the regions close to the Impinging Zone, nearly all of the particles are completely controlled by the drag force, while the gravity is the dominant factor to most of the particles in the Outlet Zone. In the middle part of the down flow Impinging Flow Zone, the dominant factor of particle flow can be significantly affected by the particle diameter and inlet gas velocity.

First assembly times and equilibration in stochastic coagulation-fragmentation.

We develop a fully stochastic theory for coagulation and fragmentation (CF) in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we find exact analytical results for the expected equilibrium cluster distributions. If coagulation is fast relative to fragmentation and if the total system mass is indivisible by the mass of the largest allowed cluster, we find a mean cluster-size distribution that is strikingly broader than that predicted by the corresponding mass-action equations. Combinations of total mass and maximum cluster size under which equilibration is accelerated, eluding late-stage coarsening, are also delineated. Finally, we compute the mean time it takes particles to first assemble into a maximum-sized cluster. Through careful state-space enumeration, the scaling of mean assembly times is derived for all combinations of total mass and maximum cluster size. We find that CF accelerates assembly relative to monomer kinetic only in special cases. All of our results hold in the infinite system limit and can be only derived from a high-dimensional discrete stochastic model, highlighting how classical mass-action models of self-assembly can fail.

Survival probability for a diffusive process on a growing domain.

We consider the motion of a diffusive population on a growing domain, 0<x<L(t), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x=0, and an absorbing boundary at x=L(t), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t). Using this solution, we derive an exact expression for the survival probability, S(t), and an accurate approximation for the long-time limit, S=lim(t→∞)S(t). Unlike traditional analyses on a nongrowing domain, where S≡0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x=L(t) from other situations where the diffusive population never reaches the moving boundary at x=L(t). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.