In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary rando...In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.展开更多
A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epi...A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.展开更多
Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning mas...Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning massive reflecting elements.This paper considers a distributed IRS aided decode-and-forward(DF)relaying system over Nakagami-m fading channels.Based on a tight approximation for the distribution of the received signalto-noise ratio(SNR),we first derive exact closed-form expressions of the outage probability,ergodic capacity,and energy efficiency for the considered system.Moreover,we propose the optimal IRS configuration considering the energy efficiency and pilot overhead.Finally,we compare the performance between the distributed IRS-aided DF relaying and multi-IRS-only systems,and verify the analytical results by using monte carlo simulations.展开更多
Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is propo...Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.展开更多
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to...In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.展开更多
In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a...In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.展开更多
基金supported by the Shenzhen sustainable development project:KCXFZ 20201221173013036 and the National Natural Science Foundation of China(91746107).
文摘In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.
文摘A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.
基金supported in part by National Natural Science Foundation of China under Grant 62371262 and 61971467in part by the Key Research and Development Program of Jiangsu Province of China under Grant BE2021013-1+1 种基金in part by the Qinlan Project of Jiangsu Provincein part by the Scientific Research Program of Nantong under Grant JC22022026
文摘Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning massive reflecting elements.This paper considers a distributed IRS aided decode-and-forward(DF)relaying system over Nakagami-m fading channels.Based on a tight approximation for the distribution of the received signalto-noise ratio(SNR),we first derive exact closed-form expressions of the outage probability,ergodic capacity,and energy efficiency for the considered system.Moreover,we propose the optimal IRS configuration considering the energy efficiency and pilot overhead.Finally,we compare the performance between the distributed IRS-aided DF relaying and multi-IRS-only systems,and verify the analytical results by using monte carlo simulations.
文摘Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
基金supported by the National Science Foundation of China(1067121290820302)the National Science Foundation of Hunan Province
文摘In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.
基金Supported by the National Natural Science Foundation of China(11571372,11771452)the Innovation Program of Central South University(10900-50601010)
文摘In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
