ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

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.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

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.

Distributed IRS-Aided DF Relaying Systems:Performance Analysis and Optimization

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.

The Generalized-Fisher composite fading model for the next generation of mobile communication systems

The new generation of communication systems is moving towards using a millimeter-wave spectrum.Since the shadowing effects are undeniable in this type of propagation,the proposed Generalized Fisher(GF)distribution can be useful in modeling shadowed fading channels,considering the non-linearity and the multi-cluster nature of the diffusion medium.After introducing the model,its main statistics,including Probability Density Function(PDF),Cumulative Distribution Function(CDF),Moment Generating Function(MGF),and the distribution of the sum of an arbitrary number of independent and non-identically distributed(i.n.i.d.)random variables with GF distribution are calculated.Subsequently,some wireless communication application criteria such as ergodic and outage capacities,are computed.Finally,considering the classic Wyner's wiretap model and passive eavesdropping scenario,specific security criteria,such as the probability of non-zero secrecy capacity and secrecy outage probability,are also determined.These expressions are measured in terms of either univariate or multivariate Fox's H-function.

Mathematical Modeling of Possibility Markov Chains by Possibility Theory

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.

Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

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∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L2(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) .

Ergodic capacity analysis for device-to-device communication underlaying cellular networks

The ergodic capacity of device-to-device （D2D） communication underlaying cellular networks is analyzed. First,the D2D communication model is introduced and the interference during uplink period and downlink period is analyzed.In a D2D communication system,since it is very difficult to obtain the instantaneous channel state information （CSI）,assume that only the transmitters know the statistical CSI and the channel coefficient follows an independent complex Gaussian distribution.Based on the assumptions,for the uplink period,the signal to interference plus noise ratio （SINR）of the D2D user equipments（DUEs）is expressed. Then the cumulative distribution function （CDF ） and probability distribution function （PDF）formulae of the SINR of the DUEs are presented.Based on the SINR formulae during the uplink period,the ergodic capacity formula of the uplink period is derived. Subsequently, using the same methods,the ergodic capacity formula of the downlink period is derived.The simulation results show that the DUEs can still obtain a high ergodic capacity even in the case of a large number of DUEs.This result can be applied to the design and optimization of D2D communications.

期货经纪公司保证金的一种确定方法

本文基于马尔可夫链在存储论中的应用,结合Ergodic定理,得到确定期货经纪公司保证金的Ergodic模型,即一个双目标规划问题,然后应用乘积最大化准则,将该模型转化为单目标规划问题来求解。该方法考虑期货经纪公司承担的风险和对投资者的吸引程度,为保证金的确定提供新的思路。

无穷个增生映射和的半隐式算法、Ergodic收敛及Curvature系统（英文）

在实一致凸且q一致光滑Banach空间中,构造无穷个m增生映射和μ_i逆强增生映射和的公共零点的半隐式迭代算法.证明ergodic收敛性.与近期研究成果相比,限定条件更弱.此外,还研究了一类curvature系统并证明其解恰好是无穷个m增生映射和μ_i逆强增生映射和的公共零点,进而验证了迭代算法的有效性.

Close-formed bound on generalized distributed antenna system capacity

The composite channel models of the generalized distributed antenna system （GDAS） such as Rayleigh-lognormal fading are studied. Then comparisons are performed between the GDAS and the traditional multiple-input multiple-output （MIMO） system to analyze the ergodic capacity of the GDAS and make conclusions that it is impossible to achieve an analytical expression for the ergodic capacity of the GDAS. Moreover, in order to evaluate the performance of the ergodic capacity of the GDAS conveniently, the analytical lower bound and upper bound of the ergodic capacity of the GDAS are derived by using the results from multivariate statistics and matrix inequalities, under the scenarios of Rayleigh-lognormal fading and equal power allocation scheme at transmitter. Finally, the analytical bounds are verified by comparisons with the numerical results.

A Resistant Quantum Key Exchange Protocol and Its Corresponding Encryption Scheme

The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.

SL(2,R)上的Hardy-Littlewood极大函数的性质

本文给出了SL(2,R)上的Hardy-Littlewood极大函数mf的定义,利用Ergodic定理证明了Hardy-Littlewood极大函数的强(p,p)型性质,p>1.

Performance Analysis of Cooperative NOMA with Energy Harvesting in Multi-Cell Networks

In this paper,an energy harvesting enabled cooperative non-orthogonal multiple access(NOMA)system for a multi-cell network is investigated.Particularly,during the direct transmission phase,base stations send their superposed messages to the near users and far users simultaneously according to a NOMA principle,while the near users act as energy harvesting enabled relays employing a power splitting protocol.During the cooperative phase,the near users transmit their decoded messages to the corresponding far users using harvested energy.Using tools from stochastic geometry,we firstly calculate the signal to interference ratios of the users in each NOMA group including one near user and one far user.Then,the closed-form expressions of the coverage probability,ergodic rate,and energy efficiency are derived respectively.Numerical results validate the derived expressions and show that the energy harvesting enabled cooperative NOMA system in a multi-cell network can improve the coverage probability,ergodic rate,and energy efficiency compared to its counterpart OMA system.

Joint Beamforming for Intelligent Reflecting Surface Aided Wireless Communication Using Statistical CSI

A joint beamforming algorithm is proposed for intelligent reflecting surface(IRS) aided wireless multiple-input multiple-output(MIMO) communication using statistical channel state information(CSI). The beamforming is done by alternatively optimizing the IRS reflecting coefficients and the covariance matrix of the transmit symbol vector, such that the ergodic rate of the system is maximized. The algorithm utilizes only the second order momentum of the random channel matrices and does assume any specific channel distribution, leading to a general framework for ergodic rate evaluation. A practical channel correlation model is configured to validate the performance gain. It is found that the rate can be enlarged by the joint optimization algorithm, however, the gain over that of randomly deployed reflecting coefficients depends highly on the relative correlation distance of the IRS elements and the spatial position of the IRS. In particular, the results suggest that IRS should be placed in the vicinity of either the transmitter or the receiver. Placing IRS far away from those positions is non-beneficial.

Review of Divertor Studies in LHD

In the Large Helical Device （LHD）, two different divertor configurations, i.e. helical divertor （HD） and local island divertor （LID）, are utilized to control the edge plasma. The HD with two X-points is an intrinsic divertor for heliotron devices, accompanied with a relatively thick ergodic layer outside the confinement region. Edge and divertor plasma behavior from low density to high density regimes is presented, referring to the divertor detachment. The effect of the ergodic layer on the edge transport is also discussed. On the other hand, the LID is an advanced divertor concept which realizes a high pumping efficiency by the combination of an externally induced magnetic island and a closed pumping system. Experimental results to confirm the fundamental divertor performance of the LID are presented.

Public Key Cryptography Based on Ergodic Matrices over Finite Field

A new public key encryption scheme is proposed in this paper, which is based on a hard problem over ergodic matrices. The security of this scheme is equal to the MQ-problem： multivariate quadratic equations over finite fields. This problem has been shown to be NP-complete and can＇t be solved with polynomial time algorithm.

Performance Analysis of NOMA-Based Cooperative Networks with Relay Selection

Non-orthogonal multiple access(NOMA)technique is an expert on channel differences exploiting.In this paper,a dual-hop NOMA-based cooperative relaying network where a best relay is selected as an active node to accomplish the communication between a source and a destination is discussed.We assume that both decode-and-forward(DF)and amplify-and-forward(AF)protocols are applied to the selected relay.The metrics that ergodic sum-rate and outage probability are investigated,and the closed-form expressions of the latter for DF and AF protocols are derived.Numerical and simulation results are conducted to verify the validity of the theoretical analysis,in which we can see that the NOMA based DF relaying is better than the NOMA based AF relaying and other existing NOMA-based cooperative communication schemes.

Hierarchical Content Caching in Fog Radio Access Networks:Ergodic Rate and Transmit Latency

In order to alleviate capacity constraints on the fronthaul and decrease the transmit latency, a hierarchical content caching paradigm is applied in the fog radio access networks(F-RANs). In particular, a specific cluster of remote radio heads is formed through a common centralized cloud at the baseband unit pool, while the local content is directly delivered at fog access points with edge cache and distributed radio signal processing capability. Focusing on a downlink F-RAN, the explicit expressions of ergodic rate for the hierarchical paradigm is derived. Meanwhile, both the waiting delay and latency ratio for users requiring a single content are exploited. According to the evaluation results of ergodic rate on waiting delay, the transmit latency can be effectively reduced through improving the capacity of both fronthaul and radio access links. Moreover, to fully explore the potential of hierarchical content caching, the transmit latency for users requiring multiple content objects is optimized as well in three content transmission cases with different radio access links. The simulation results verify the accuracy of the analysis, further show the latency decreases significantly due to the hierarchical paradigm.

Secrecy Rate Analysis for Reconfigurable Intelligent Surface-Assisted MIMO Communications with Statistical CSI

In this paper,a reconfigurable intelligent surface(RIS)-assisted MIMO wireless secure communication system is considered,in which a base station(BS)equipped with multiple antennas exploits statistical channel state information to communicate with a legitimate multi-antenna user,in the presence of an eavesdropper,also equipped with multiple antennas.We firstly obtain an analytical expression of the ergodic secrecy rate based on the results of largedimensional random matrix theory.Then,a jointly alternating optimization algorithm with the method of Taylor series expansion and the projected gradient ascent method is proposed to design the transmit covariance matrix at the BS,as well as the diagonal phaseshifting matrix to maximize the ergodic secrecy rate.Simulations are conducted to demonstrate the accuracy of the derived analytical expressions,as well as the superior performance of our proposed algorithm.

Interference Cancellation in Device-to-Device Communications underlying MU-MIMO Cellular Networks

This paper investigates the device-to-device(D2 D) communication underlaying multi-user multi-input multi-output(MU-MIMO) cellular networks. It is assumed that D2 D users reuse the downlink time-frequency resources of cellular links, and the base station(BS) is assumed to be equipped with multiple antennas. We investigate the ergodic achievable sum rate of the system when the interference cancellation(IC) precoding strategy is employed at the BS. The distributions of the received signal-to-interference-plus-noise ratio(SINR) for each link are firstly analyzed, and an exact ergodic achievable sum rate of the whole system with closedform expressions is then derived. Furthermore, we present novel upper and lower bounds with simpler expressions, which are later verified to be fairly close to the Monte-Carlo simulations. All the expressions we presented are suitable for arbitrary network topology and arbitrary number of antennas at BS. Based on the derived bounds, the influence of the antennas at BS on system performance is then analyzed. We reveal that the system performance increases along with the number of antennas at BS in a logarithmic way. The accuracy of our analytical results is validated via comparisons with Monte-Carlo simulations.