Complete moment convergence for ND random variables under the sub-linear expectations

In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.

STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20].We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent literature.Powerful tools such as moment inequality and Kolmogorov’s exponential inequality are established for these kinds of extended negatively independent random variables,and these tools improve a lot upon those of Chen,Chen and Ng[1].The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.

CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.

Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation

In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.

Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations

In this article,we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.Our results of strong limit theorems are more general than some related results previously obtained by Thrum(1987),Li et al.(1995)and Wu(2010)in classical probability space.

A Note on the Expectation Value of Time

In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.

提高湖羊圈养空间利用率的建模方案优化设计

为提高湖羊圈养的空间利用率,采用分期分批连续方式安排交配,根据交配期、怀孕期、哺乳期、休整期、育肥期等5个阶段的期长、容量、流转倍率等参数值,建立各期羊栏需求数的计算模型。针对养殖场现有的羊栏规格,经试算搜索得到其羊只的最佳流转速度,由此编制具体的生产方案,使得年化出栏羊只数量达到最大。继而针对5项不确定因素,构建参数重新选定的计算公式,并在合理范围内,调整哺乳期和空怀期时长,得到多种备选方案,再通过分层次计算比较各方案的期望损失,确定最优方案。

高校图书馆创客空间用户持续使用意愿实证研究

用户的持续使用意愿关系到图书馆创客空间的可持续发展。文章在期望确认模型的基础上,加入对环境的假设及自我决定理论,构建了高校图书馆创客空间用户持续使用意愿模型。实证发现,期望确认度、感知有用性及环境满意度对用户持续使用意愿产生正向影响。自我决定理论中,自主需求正向影响满意度,胜任需求正向影响期望确认度,归属需求对持续使用意愿的影响显著。文章进一步提出应增加创客空间的宣传力度、营造创客空间品牌效应、充分发挥创客空间自主学习优势、结合专业指导和互动学习模式、调动用户积极性等建议。

次线性期望空间下独立同分布序列的一个强大数定律

利用与概率空间不同的研究方法,研究次线性期望空间中独立同分布随机变量序列的加权和在某些条件下的一个强大数定律,从而将该定理从传统概率空间扩展到次线性期望空间.

The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations

In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on R^(∞) under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given.

Joint channel estimation and symbol detection for space-time block code

The simplified joint channel estimation and symbol detection based on the EM (expectation-maximization) algorithm for space-time block code (STBC) are proposed. By assuming channel to be invariant within only one STBC word and utilizing the orthogonal structure of STBC, the computational complexity and cost of this algorithm are both very low, so it is very suitable to implementation in real systems.

元宇宙:概念演进、技术想象与社会期待

技术对新产品的赋能、用户对新体验的期待、资本对新利好的嗅觉、新冠疫情“宅居”生活的刺激让元宇宙这个不温不火的概念迅即成为传媒、经济、文化、教育等领域聚焦的热点。如果将这一概念简单地理解为某种技术现实、应用场景、媒介体验,抑或产业形态都未免浅薄,因此有必要基于这一概念的变迁反思其背后蕴含的技术想象、社会期待,并在检视其实践应用的基础上把握其可能性影响。从“赛博空间”到“电子游戏”,到“虚拟空间”,再到“虚实连接”,元宇宙概念变迁承载了人们从“抽象的文学想象”到“具象化的游戏交互”,再到“愈加丰富充实的数字生活”,最终指向“沉浸式的、消除边界的、融合共生的生命体验”的愿景。

公共文化空间中城市图书馆角色的三重视野

[目的/意义]城市图书馆是公共文化空间治理的基本单元,其角色定位指引着图书馆新馆建设与改扩建行动方向及其空间价值的社会化表达。[研究设计/方法]采用质性文本分析、演绎归纳、文献与网络调查等方法,从政策安排、实践需要和公众期待三个维度考察城市图书馆在公共文化空间中的角色定位。[结论/发现]国家文化治理政策指向城市图书馆从“参与者”转向“主导者”、由“用户中心”趋于“社会介入”“人民中心”与“高质量发展”并重。行业实践需要城市图书馆成为城市公共“正义空间”的建构者、“韧性空间”的培育者与“发展空间”的提供者。社会公众期待城市图书馆提供情绪疗愈、泛在互联和全纳融合的公共文化空间样态。为全面参与公共文化空间建设,城市图书馆应该以品牌建设凝练空间价值融合体系、以机理革新完善空间协同治理框架和以数实融合重塑空间文化场景样态。[创新/价值]从国家公共文化空间视角考察和明晰了城市图书馆空间建设与服务的行动路向,为空间变革提供多维审视框架。

Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications

In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.

Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm

We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.

The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations

Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distribution of Sn are equivalent.In this paper,we prove similar results for the independent random variables under the sub-linear expectations,and give a group of sufficient and necessary conditions for these convergence.For proving the results,the Levy and Kolmogorov maximal inequalities for independent random variables under the sub-linear expectation are established.As an application of the maximal inequalities,the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random variables are also obtained.

基于信道特征高精度提取的空地信道密钥量化

针对无人机空地信道,基于空间期望最大化算法(SAGE)对信道特征参数进行高精确度估计。在提取了多径时延、多径功率等空地信道小尺度衰落特征后,利用均匀量化和非均匀量化方法,对实测数据的主径功率、主径-多径功率差开展无线信道密钥量化。分别针对起飞和巡航场景分析了密钥的量化效率、随机性以及算法运行时间等指标,并与基于大尺度特征的密钥量化结果进行比较。密钥量化效率结果表明:基于非均匀量化优于均匀量化;基于信道特征高精确度估计的量化方法优于传统基于大尺度特征的量化;起飞场景下的量化优于巡航场景的量化。密钥随机性测试结果表明本次量化所获得的密钥都具有较好的随机性;算法运行时间结果则表明不同量化方法的运行时间差异较小。因此基于高精确度提取的2种量化方法复杂度较低。

Lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.

基于GAPSO优化的神经网络无线信道参数预测

针对复杂环境中无线信道参数的预测问题展开深入研究,基于反向传播神经网络(Back Propagation Neural Network,BPNN),提出了遗传算法(Genetic Algorithm,GA)与粒子群优化(Particle Swarm Optimization,PSO)算法联合优化的神经网络预测无线信道参数的方法。在利用QuaDriGa平台生成非视距(Non-Line-of-Sight,NLoS)环境下的信道冲激响应(Channel Impulse Response,CIR)的基础上,结合GA在搜索最优解方面的优势与PSO算法加快收敛的特点,利用优化后的BP神经网络模型对相关信道参数进行学习和预测,解决了学习过程中收敛速度慢、预测精确度有限等问题。仿真结果表明,GAPSO-BPNN模型对NLoS环境下的信道参数的预测有较好的效果,能够在未来适应更多的复杂环境。

On the laws of the iterated logarithm under sub-linear expectations

In this paper,we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space,where the random variables are not necessarily identically distributed.Exponential inequalities for the maximum sum of independent random variables and Kolmogorov’s converse exponential inequalities are established as tools for showing the law of the iterated logarithm.As an application,the sufficient and necessary conditions of the law of the iterated logarithm for independent and identically distributed random variables under the sub-linear expectation are obtained.In the paper,it is also shown that if the sub-linear expectation space is rich enough,it will have no continuous capacity.The laws of the iterated logarithm are established without the assumption on the continuity of capacities.