Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.

Characteristic Functions over C*-Probability Spaces

Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.

Study of Nonlinear Earthquake Flow Functions and Their Application to the Space Increased Probability of Strong Earthquake (SIP)

The definition and abnormality discriminatory criteria of earthquake flow function are introduced in this paper based on the algorithm of Space Increased Probability (SIP). Nine earthquake flow functions were defined by the method. The retrospect test that applied the SIP algorithm with the nonlinear earthquake flow function to 7 earthquakes, which occurred from 1975 to 1989 in Eastern China, with a magnitude of 6 or greater depicted that 6 of the 7 strong earthquakes (86%) were located in the SIP areas, and the SIP covers about 32% of the total research time-space domain. These suggest that the R-value, an effective scale for earthquake forecast, is 54% and may imply that the nonlinear earthquake flow function introduced in this paper can be applied to the intermediate-term earthquake forecast research.

因素空间理论下的因果概率推理分类算法研究

机器学习方法与因果推理结合能极大地提升方法性能。为探究因果概率正逆向推理的分类效果,基于因素空间理论下的因素概率论,利用条件概率,研究正向因素概率推理原理及模型并提出正向因果概率推理分类法(forward causal probabilistic inference classification algorithm,FCPIC)和简化条件的可取度分类法;研究逆向因素概率推理原理及模型并结合贝叶斯网络提出逆向因果概率推理分类法(reverse causal probabilistic inference classification algorithm,RCPIC)。将3个分类算法与KNN(K-Nearest neighbor)和SVM(support vector machine)算法进行实例对比验证,研究结果表明:FCPIC算法、可取度分类算法和RCPIC算法简单有效、具有可行性和实用性,且可取度分类法和RCPIC算法性能优于SVM和KNN算法,FCPIC算法对实际数据预测中必要类有查全需求的情况更优。研究结论丰富了因素空间的理论研究和应用价值。

基于碰撞概率的GEO业务卫星空间安全规避策略

针对GEO业务卫星空间规避问题,提出一种基于碰撞概率优化的GEO卫星空间规避策略.建立脉冲推力控制下的位保模型,解释碰撞概率的假设条件与计算原理,针对GEO卫星对原有碰撞概率计算方法进行改进,提出了一种考虑了速度误差的碰撞概率计算方法,以脉冲速度大小为变量,以消耗速度冲量最小和碰撞概率最小为优化目标,基于非支配排序多目标遗传算法(NSGA-Ⅱ)进行多目标优化,对碰撞概率较大的问题求出其帕累托最优解.考虑GEO卫星定点保持的业务要求,得到满足其位保精度的空间规避策略,并进行仿真验证了空间规避策略的有效性.研究结果可为在轨业务卫星实现满足位保要求的空间安全规避提供思路.

基于潜在空间生成器的联邦知识蒸馏

用户的异质性对联邦学习(FL)构成了显著挑战,这可能导致全局模型偏移和收敛速度缓慢。针对此问题,提出一种结合知识蒸馏和潜在空间生成器的联邦学习方法(FedLSG)。该方法通过中央服务器学习一个搭载潜在空间生成器的生成模型,该模型能够提取并模拟不同用户端样本标签的概率分布,从而生成更加丰富和多样的伪样本来指导用户端模型的训练。这种方法旨在有效解决FL中的用户异质性问题。通过理论分析和实验验证,展示了与现有FedGen方法相比,FedLSG普遍比FedGen的测试精度高出1%左右,前20轮的通信效率优于FedGen,同时还能提供一定程度的用户隐私保护。

基于量子Bernoulli噪声的一维时空非齐次开放量子游荡

用量子Bernoulli噪声方法研究一维时空非齐次开放量子游荡,给出该游荡的演化性质以及极限概率分布,并表明以局部基态作为初始态时,基于量子Bernoulli噪声的一维时空非齐次开放量子游荡具有与经典随机游荡相同的极限概率分布.

基于行为轨迹的中庭式酒店COVID-19感染概率研究

中庭式酒店建筑因中庭空间人员密集、气流波动大,属呼吸道传染疾病高感染概率区域,建筑高大公共空间的传染概率有待研究.以某中庭式酒店为研究对象,基于该酒店人流状况、行为轨迹的实测,通过回归分析,得到该酒店人流密度的分布规律;运用Anylogic软件,结合Wells-Riley感染概率计算模型,对不同类型人员感染后的酒店人群感染概率进行模拟.通过模拟可知,住宿人群、就餐人群、商务会议三类人群中单一人群感染时,感染概率分别为29.3%,17.9%,36.4%;当三类人员及后勤人员共同耦合感染时,感染概率增加至42.6%.通过对污染物颗粒的时空分布规律的分析发现三层、标准层污染物颗粒较多;人员交叉与感染概率呈正相关;流线交叉较多的就餐空间、滞留时间较长休闲空间、竖向交通空间等应重点考虑设计措施以降低其感染概率;该研究为人员行为轨迹下的酒店空间的布局优化提供研究思路,为疫情背景下寒冷地区中庭式酒店平疫结合酒店空间布局设计研究提供理论依据.

On Performance Characteristics of a Nonparametric Subset Selection Procedure with a Small Randomized Block Experimental Design

This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e., that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.

基于后验概率空间变化向量分析的NSCT高分辨率遥感影像变化检测

非下采样轮廓波变换(non-subsampled contourlet transform,NSCT)和变化向量分析法(change vector analysis,CVA)在高分辨率遥感影像变化检测中,会因不同地物的变化幅度有显著差异,而在单一阈值下无法保证较高的检测精度。为此,文章在后验概率空间变化向量分析(change vector analysis in posterior probability space,CVAPS)的框架下,提出了一种基于模糊C均值聚类(fuzzy C-means,FCM)和简单贝叶斯网络(simple Bayesian network,SBN)的NSCT变化检测方法(FCM-SBN-CVAPS-NSCT)。该方法首先将FCM与SBN耦合,计算出后验概率变化强度图;之后,通过NSCT将后验概率变化强度图分解为不同尺度和方向的子图,通过保留高频子图中的细节并消除噪声,优化了重构后的后验概率变化强度图,实现了后验概率空间下的多尺度、多方向的变化检测,最终提高了变化检测的精度。实验结果表明,所提方法在3个研究区中得到的Kappa系数比FCM-SBN-CVAPS分别高出了0.1009,0.0566和0.0674,具有一定的优越性。

基于空间光学传感技术的变电站设备高热故障红外识别方法

无论对技术还是操作人员,变电站设备故障识别过程都有着非常严格的要求,而故障识别精度依旧较低。为此,提出基于空间光学传感技术的变电站设备高热故障红外识别方法。在采集得到变电站设备红外图像后,对其展开阈值分割、图像增强、光照分量估计一系列处理,削弱背景对目标识别的影响,找出目标所在区域;计算目标所在区域的温度概率密度,与温度范围比照,确定高温区域范围,完成对变电站设备高热故障的精准识别。利用所提方法分别识别避雷器、主变套管、电流互感器和隔离开关的故障位置,结果表明,所提方法识别到的目标故障位置非常精准,没有出现误检测或漏识别的情况。

数据科学中的最优逼近算法问题

文章介绍了数据科学与计算数学交叉学科中概率宽度问题的研究现状,阐明了计算复杂性与宽度理论之间的联系,给出了不同框架下Gel̓fand宽度的定义,并研究了信息函数类在不同计算模型下的逼近特性。基于离散化思想,文章精确刻画了赋予Gussian测度的多元Sobolev空间MWr 2在Sq尺度下的概率Gel̓fand宽度的阶数。

针长大于间距的蒲丰投针问题及应用

本文聚焦于针长l大于平行线间距d的蒲丰投针问题.首先,探讨了d<l<2d时针与平行线恰好有两个交点的概率.接着,研究了l<2d时针与平行线至少有两个交点的概率.然后,对于边长分别为l_(1)、l_(2)、l_(3)的三角形,在l_(1)<l_(2)<l_(3)的条件下,应用得到的引理求解了该三角形与平行线相交的概率.进一步,通过数值模拟,得到该三角形与平行线相交概率的变化趋势.

基于state-space-split法的滞回非线性系统随机动力响应分析

采用SSS(state-space-split)法,建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数(PDF)的近似求解方法,分析了其随机动力响应变化规律。首先,将Bouc-Wen滞回模型引入杜芬非线性系统,分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响。随后,对该模型进行了等效线性化(EQL)处理,基于等效线性化法结果,介绍了SSS法的简化方法和计算原理,并通过该方法求解了三维FPK方程的近似联合概率密度函数。最后,将该方法应用于三个案例和一个工程实例,通过求解其概率密度函数分布及动力可靠度验证了提出方法的适用性、可行性和优越性。

Probability Density Function Method for Observing Reconstructed Attractor Structure

Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.

A New Version of Unified Field Theory—Stochastic Quantum Space Theory on Particle Physics and Cosmology

Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.

PROBABILISTIC NORM OF LINEAR OPERATORS ON PN SPACE

In this paper, the new definition of probabilistic norm of linear operators on a PN space is given. In virtue of this, the boundedness of linear operators is described and the completeness of the PN space composed of all bounded linear operators is showed.

A Carrier Synchronization Algorithm for AutonomousRadio Receiver in Deep Space

The carrier synchronization algorithm of the autonomous radio for deep space is studied.When the signal modulation is unknown,this paper improves the existing universal carrier synchronization loop for multiple modulations,expands the frequency tracking range of the loop,proposes a Tong detection-based M-ary Phase Shift Keying(M-PSK)signal locking detection algorithm to rapidly and effectively determine whether the current phase discrimination mode matches the modulation mode,so as to independently choose whether to switch the phase discrimination mode.Through theoretical analysis and comparison,it is described that the total detection probability of the algorithm proposed in this paper is significantly higher than the probability of single lock detection.Simulation results show that the algorithm has high detection probabiUty and low computational complexity at a low signal to noise ratio.

Model of constant probability event and its application in information fusion

A model of constant probability event is constructed rigorously in event space of PSCEA. It is showed that the numericalbased fusion and the algebraicbased fusion have a consistent result when the weight is regarded as a constant probability event. From the point of view of algebra, we present a novel similarity measure in product space. Based on the similarity degree, we use a similarity aggregation method to fusion experts' evaluation. We also give a numerical example to illustrate the method.