A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in al...A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.展开更多
The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysi...The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions,which implies that the theoretical results are able to be applied to stochastic feedback systems.Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation.We employ analysis techniques such as stochastic Lyapunov function,stability theory of stochastic systems,and algebraic graph theory to deal with the above issue.The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal,the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way.At last,we illustrate the property of the proposed distributed KF algorithm by a simulation example.展开更多
In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and co...In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.展开更多
This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI)systems under additive stochastic disturbances.It first constructs a probabilistic invariant set a...This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI)systems under additive stochastic disturbances.It first constructs a probabilistic invariant set and a probabilistic reachable set based on the priori knowledge of system uncertainties.Assisted with enhanced robust tubes,the chance constraints are then formulated into a deterministic form.To alleviate the online computational burden,a novel event-triggered stochastic model predictive control is developed,where the triggering condition is designed based on the past and future optimal trajectory tracking errors in order to achieve a good trade-off between system resource utilization and control performance.Two triggering parametersσandγare used to adjust the frequency of solving the optimization problem.The probabilistic feasibility and stability of the system under the event-triggered mechanism are also examined.Finally,numerical studies on the control of a heating,ventilation,and air conditioning(HVAC)system confirm the efficacy of the proposed control.展开更多
In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6...In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.展开更多
A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncer...A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.展开更多
Streptococcus suis(S.suis)is a major disease impacting pig farming globally.It can also be transferred to humans by eating raw pork.A comprehensive study was recently carried out to determine the indices throughmultip...Streptococcus suis(S.suis)is a major disease impacting pig farming globally.It can also be transferred to humans by eating raw pork.A comprehensive study was recently carried out to determine the indices throughmultiple geographic regions in China.Methods:The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features,including positivity,boundedness equilibria,reproduction number,and parameter sensitivity.Stochastic Euler,Runge Kutta,and EulerMaruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population.However,the dynamic qualities of the suggested model cannot be restored using these techniques.Results:For the stochastic delay differential equations of the model,the non-standard finite difference approach in the sense of stochasticity is developed to avoid several problems such as negativity,unboundedness,inconsistency,and instability of the findings.Results from traditional stochastic methods either converge conditionally or diverge over time.The stochastic non-negative step size convergence nonstandard finite difference(NSFD)method unconditionally converges to the model’s true states.Conclusions:This study improves our understanding of the dynamics of streptococcus suis infection using versions of stochastic with delay approaches and opens up new avenues for the study of cognitive processes and neuronal analysis.Theplotted interaction behaviour and new solution comparison profiles.展开更多
In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher prec...In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.展开更多
Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fl...Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.展开更多
In this paper, deterministic and stochastic models for schistosomiasis involving four sub-populations are developed. Conditions are given under which system exhibits thresholds behavior. The disease-free equilibrium i...In this paper, deterministic and stochastic models for schistosomiasis involving four sub-populations are developed. Conditions are given under which system exhibits thresholds behavior. The disease-free equilibrium is globally asymptotically stable if R0 ?and the unique endemic equilibrium is globally asymptotically stable when R0 >?1. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and the stochastic model.展开更多
Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactio...Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.展开更多
Obtaining complete information regarding discovered vulnerabilities looks extremely difficult. Yet, developing statistical models requires a great deal of such complete information about the vulnerabilities. In our pr...Obtaining complete information regarding discovered vulnerabilities looks extremely difficult. Yet, developing statistical models requires a great deal of such complete information about the vulnerabilities. In our previous studies, we introduced a new concept of “Risk Factor” of vulnerability which was calculated as a function of time. We introduced the use of Markovian approach to estimate the probability of a particular vulnerability being at a particular “state” of the vulnerability life cycle. In this study, we further develop our models, use available data sources in a probabilistic foundation to enhance the reliability and also introduce some useful new modeling strategies for vulnerability risk estimation. Finally, we present a new set of Non-Linear Statistical Models that can be used in estimating the probability of being exploited as a function of time. Our study is based on the typical security system and vulnerability data that are available. However, our methodology and system structure can be applied to a specific security system by any software engineer and using their own vulnerabilities to obtain their probability of being exploited as a function of time. This information is very important to a company’s security system in its strategic plan to monitor and improve its process for not being exploited.展开更多
Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting...Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills.In this paper,we proposed a method for searching the seasonal autoregressive integrated moving average(SARIMA)model parameters to predict the behavior of groundwater time series affected by the issues mentioned.Based on the analysis of statistical indices,8 stations among 44 available within the Campania region(Italy)have been selected as the highest quality measurements.Different SARIMA models,with different autoregressive,moving average and differentiation orders had been used.By reviewing the criteria used to determine the consistency and goodness-of-fit of the model,it is revealed that the model with specific combination of parameters,SARIMA(0,1,3)(0,1,2)_(12),has a high R^(2) value,larger than 92%,for each of the 8 selected stations.The same model has also good performances for what concern the forecasting skills,with an average NSE of about 96%.Therefore,this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area.展开更多
The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are ...The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.展开更多
For a stochastic non-minimum phase multivariable system,a multiple models direct adaptive controller is presented.It is composed of multiple fixed models with two adaptive models.The fixed models are used to cover the...For a stochastic non-minimum phase multivariable system,a multiple models direct adaptive controller is presented.It is composed of multiple fixed models with two adaptive models.The fixed models are used to cover the region where the system parameters jump and improve the transient response,while another two adaptive models are used to guarantee the stability.Utilizing generalized minimum variance design method,it adopts the stochastic system estimation algorithm with optimal controller design method to identify the controller parameter directly.Finally,the global convergence is given.The simulation proves the effectives of the controller proposed.展开更多
In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in...In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.展开更多
A stochastic economic growth model may be transformed into a deterministic economic growth model with an infiaite dimentional Banach space of state-contingent capital stocks[6].This paper proves that under the framewo...A stochastic economic growth model may be transformed into a deterministic economic growth model with an infiaite dimentional Banach space of state-contingent capital stocks[6].This paper proves that under the framework,the stochastic analogUes of the asymptotic turnpike theorems in the standard deterministic economic growth model[5]will continue tO hold if we assume that essentially smooth programs satisfy uniformly essentially dominant diagonal condition.展开更多
This paper deals with the construction of approximate series solutions of diffusion models with stochastic excitation and nonlinear losses using the homotopy analysis method (HAM). The mean, variance and other statist...This paper deals with the construction of approximate series solutions of diffusion models with stochastic excitation and nonlinear losses using the homotopy analysis method (HAM). The mean, variance and other statistical properties of the stochastic solution are computed. The solution technique was applied successfully to the 1D and 2D diffusion models. The scheme shows importance of choice of convergence-control parameter to guarantee the convergence of the solutions of nonlinear differential Equations. The results are compared with the Wiener-Hermite expansion with perturbation (WHEP) technique and good agreements are obtained.展开更多
The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the...The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.展开更多
Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a n...Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.展开更多
基金Supported by the National Science Foundation of China.
文摘A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.
基金supported in part by Sichuan Science and Technology Program under Grant No.2025ZNSFSC151in part by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No.XDA27030201+1 种基金the Natural Science Foundation of China under Grant No.U21B6001in part by the Natural Science Foundation of Tianjin under Grant No.24JCQNJC01930.
文摘The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions,which implies that the theoretical results are able to be applied to stochastic feedback systems.Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation.We employ analysis techniques such as stochastic Lyapunov function,stability theory of stochastic systems,and algebraic graph theory to deal with the above issue.The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal,the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way.At last,we illustrate the property of the proposed distributed KF algorithm by a simulation example.
基金supported by the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.
基金supported by the National Nature Science Foundation of China(62073194)the Natural Science Foundation of Shandong Province of China(ZR2023MF028)the Taishan Scholars Program of Shandong Province(tsqn202312008)
文摘This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI)systems under additive stochastic disturbances.It first constructs a probabilistic invariant set and a probabilistic reachable set based on the priori knowledge of system uncertainties.Assisted with enhanced robust tubes,the chance constraints are then formulated into a deterministic form.To alleviate the online computational burden,a novel event-triggered stochastic model predictive control is developed,where the triggering condition is designed based on the past and future optimal trajectory tracking errors in order to achieve a good trade-off between system resource utilization and control performance.Two triggering parametersσandγare used to adjust the frequency of solving the optimization problem.The probabilistic feasibility and stability of the system under the event-triggered mechanism are also examined.Finally,numerical studies on the control of a heating,ventilation,and air conditioning(HVAC)system confirm the efficacy of the proposed control.
基金supported by the Fundacao para a Ciencia e Tecnologia,FCT,under the project https://doi.org/10.54499/UIDB/04674/2020(accessed on 1 January 2025).
文摘In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.
基金Supported by the National Natural Science Foundation of China(No.U24B20156)the National Defense Basic Scientific Research Program of China(No.JCKY2021204B051)the National Laboratory of Space Intelligent Control of China(Nos.HTKJ2023KL502005 and HTKJ2024KL502007)。
文摘A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[KFU250259].
文摘Streptococcus suis(S.suis)is a major disease impacting pig farming globally.It can also be transferred to humans by eating raw pork.A comprehensive study was recently carried out to determine the indices throughmultiple geographic regions in China.Methods:The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features,including positivity,boundedness equilibria,reproduction number,and parameter sensitivity.Stochastic Euler,Runge Kutta,and EulerMaruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population.However,the dynamic qualities of the suggested model cannot be restored using these techniques.Results:For the stochastic delay differential equations of the model,the non-standard finite difference approach in the sense of stochasticity is developed to avoid several problems such as negativity,unboundedness,inconsistency,and instability of the findings.Results from traditional stochastic methods either converge conditionally or diverge over time.The stochastic non-negative step size convergence nonstandard finite difference(NSFD)method unconditionally converges to the model’s true states.Conclusions:This study improves our understanding of the dynamics of streptococcus suis infection using versions of stochastic with delay approaches and opens up new avenues for the study of cognitive processes and neuronal analysis.Theplotted interaction behaviour and new solution comparison profiles.
基金supported by the National High Technology Research and Development Program of China(863 Program)(2014AA06A503)the National Natural Science Foundation of China(61422307,61673361)+3 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars and Ministry of Education of Chinasupports from the Youth Top-notch Talent Support Programthe 1000-talent Youth Programthe Youth Yangtze River Scholarship
文摘In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.
文摘Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.
文摘In this paper, deterministic and stochastic models for schistosomiasis involving four sub-populations are developed. Conditions are given under which system exhibits thresholds behavior. The disease-free equilibrium is globally asymptotically stable if R0 ?and the unique endemic equilibrium is globally asymptotically stable when R0 >?1. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and the stochastic model.
文摘Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.
文摘Obtaining complete information regarding discovered vulnerabilities looks extremely difficult. Yet, developing statistical models requires a great deal of such complete information about the vulnerabilities. In our previous studies, we introduced a new concept of “Risk Factor” of vulnerability which was calculated as a function of time. We introduced the use of Markovian approach to estimate the probability of a particular vulnerability being at a particular “state” of the vulnerability life cycle. In this study, we further develop our models, use available data sources in a probabilistic foundation to enhance the reliability and also introduce some useful new modeling strategies for vulnerability risk estimation. Finally, we present a new set of Non-Linear Statistical Models that can be used in estimating the probability of being exploited as a function of time. Our study is based on the typical security system and vulnerability data that are available. However, our methodology and system structure can be applied to a specific security system by any software engineer and using their own vulnerabilities to obtain their probability of being exploited as a function of time. This information is very important to a company’s security system in its strategic plan to monitor and improve its process for not being exploited.
文摘Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills.In this paper,we proposed a method for searching the seasonal autoregressive integrated moving average(SARIMA)model parameters to predict the behavior of groundwater time series affected by the issues mentioned.Based on the analysis of statistical indices,8 stations among 44 available within the Campania region(Italy)have been selected as the highest quality measurements.Different SARIMA models,with different autoregressive,moving average and differentiation orders had been used.By reviewing the criteria used to determine the consistency and goodness-of-fit of the model,it is revealed that the model with specific combination of parameters,SARIMA(0,1,3)(0,1,2)_(12),has a high R^(2) value,larger than 92%,for each of the 8 selected stations.The same model has also good performances for what concern the forecasting skills,with an average NSE of about 96%.Therefore,this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area.
文摘The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.
基金the National Natural Science Foundation of China (Nos.60504010 and 60774015)the National High Technology Research and Development Program (863) of China (No.2008AA04Z129)+1 种基金the Disbursal Budget Program of Shanghai Municipal Education Commission of China (No.2008093) the Innovation Program of Shanghai Municipal Education Commission of China (No.09YZ241)
文摘For a stochastic non-minimum phase multivariable system,a multiple models direct adaptive controller is presented.It is composed of multiple fixed models with two adaptive models.The fixed models are used to cover the region where the system parameters jump and improve the transient response,while another two adaptive models are used to guarantee the stability.Utilizing generalized minimum variance design method,it adopts the stochastic system estimation algorithm with optimal controller design method to identify the controller parameter directly.Finally,the global convergence is given.The simulation proves the effectives of the controller proposed.
文摘In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.
基金Supported by the National Science Foundation of China and the Natural Seience Fund of Central China Normal University.
文摘A stochastic economic growth model may be transformed into a deterministic economic growth model with an infiaite dimentional Banach space of state-contingent capital stocks[6].This paper proves that under the framework,the stochastic analogUes of the asymptotic turnpike theorems in the standard deterministic economic growth model[5]will continue tO hold if we assume that essentially smooth programs satisfy uniformly essentially dominant diagonal condition.
文摘This paper deals with the construction of approximate series solutions of diffusion models with stochastic excitation and nonlinear losses using the homotopy analysis method (HAM). The mean, variance and other statistical properties of the stochastic solution are computed. The solution technique was applied successfully to the 1D and 2D diffusion models. The scheme shows importance of choice of convergence-control parameter to guarantee the convergence of the solutions of nonlinear differential Equations. The results are compared with the Wiener-Hermite expansion with perturbation (WHEP) technique and good agreements are obtained.
文摘The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.
基金supported by Comunidad de Madrid within the framework of the Multiannual Agreement with Universidad Politécnica de Madrid to encourage research by young doctors(PRINCE).
文摘Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.
