A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be a good alternative. In addition, for a parameter with a small value, the Bell distribution approaches the Poisson distribution. In this paper, we introduce a new first-order, non-negative, integer-valued autoregressive model with Bell innovations based on the binomial thinning operator. Compared with other models, the new model is not only simple but also particularly suitable for time series of counts exhibiting overdispersion. Some properties of the model are established here, such as the mean, variance, joint distribution functions, and multi-step-ahead conditional measures. Conditional least squares, Yule–Walker, and conditional maximum likelihood are used for estimating the parameters. Some simulation results are presented to access these estimates’ performances. Real data examples are provided.     

Message Passing-Based Inference for Time-Varying Autoregressive Models

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite “AR node” with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.     

Low-Frequency Periodic Processes in Spectroscopy and Chemical Transformations

It has been shown that the low-frequency periodic processes in spectroscopy and chemical transformations that proceed without a change in the total energy of a complex molecular system can be explained as a result of synchronized radiationless transitions between the resonant ground states of quantum systems of a different structure. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 325–329, May–June, 2005.     

Statistical Inference for Ergodic Algorithmic Model (EAM), Applied to Hydrophobic Hydration Processes

The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Thermal Partition Function {T-PF}. By development of {DS-PF}, parabolic binding potential functions α) RlnK_dual = (−ΔG°_dual/T) ={f(1/T)*g(T)} and β) RTlnK_dual = (−ΔG°_dual) = {f(T)*g(lnT)} have been calculated. The resulting binding functions are “convoluted” functions dependent on the reciprocal interactions between the primary function f(1/T) or f(T) with the secondary function g(T) or g(lnT), respectively. The binding potential functions carry the essential thermodynamic information elements of each system. The analysis of the binding potential functions experimentally determined at different temperatures by means of the Thermal Equivalent Dilution (TED) principle has made possible the evaluation, for each compound, of the pseudo-stoichiometric coefficient ±ξ_w, from the curvature of the binding potential functions. The positive value indicates convex binding functions (Class A), whereas the negative value indicates concave binding function (Class B). All the information elements concern sets of compounds that are very different from one set to another, in molecular dimension, in chemical function, and in aggregation state. Notwithstanding the differences between, surprising equal unitary values of niche (cavity) formation in Class A <Δh_for>_A = −22.7 ± 0.7 kJ·mol⁻¹ ·ξ_w⁻¹ sets with standard deviation σ = ±3.1% and <Δs_for>_A = −445 ± 3J·K⁻¹·mol⁻¹·ξ_w⁻¹J·K⁻¹·mol⁻¹·ξ_w⁻¹ with standard deviation σ = ±0.7%. Other surprising similarities have been found, demonstrating that all the data analyzed belong to the same normal statistical population. The Ergodic Algorithmic Model (EAM) has been applied to the analysis of important classes of reactions, such as thermal and chemical denaturation, denaturation of proteins, iceberg formation or reduction, hydrophobic bonding, and null thermal free energy. The statistical analysis of errors has shown that EAM has a general validity, well beyond the limits of our experiments. Specifically, the properties of hydrophobic hydration processes as biphasic systems generating convoluted binding potential functions, with water as the implicit solvent, hold for all biochemical and biological solutions, on the ground that they also are necessarily diluted solutions, statistically validated.     

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.     

No periodic orbits for the type A Bianchi's systems

It is known that the 6 models of Bianchi class A have no periodic solutions. In this article we provide a new, direct, unified and easier proof of this result.     

Threshold Property of Photoresist Film for Two-photon Optical Memory

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计算周期解时出现刚性问题的一种处理方法

给出计算周期解时出现刚性问题的一种具体处理方法,采用MATLAB软件中求解刚性初值问题的解题器ODE15s,同时在处理问题的过程中,为便于计算和减少工作量使用变步长的Gear方法,给出相应的计算公式,并给出数值实例.     

Thresholding Approach for Low-Rank Correlation Matrix Based on MM Algorithm

Background: Low-rank approximation is used to interpret the features of a correlation matrix using visualization tools; however, a low-rank approximation may result in an estimation that is far from zero, even if the corresponding original value is zero. In such a case, the results lead to a misinterpretation. Methods: To overcome this, we propose a novel approach to estimate a sparse low-rank correlation matrix based on threshold values. We introduce a new cross-validation function to tune the corresponding threshold values. To calculate the value of a function, the MM algorithm is used to estimate the sparse low-rank correlation matrix, and a grid search was performed to select the threshold values. Results: Through numerical simulation, we found that the false positive rate (FPR), interpretability, and average relative error of the proposed method were superior to those of the tandem approach. For the application of microarray gene expression, the FPRs of the proposed approach with d=2,3 and 5 were 0.128, 0.139, and 0.197, respectively, while the FPR of the tandem approach was 0.285. Conclusions: We propose a novel approach to estimate sparse low-rank correlation matrices. The advantage of the proposed method is that it provides results that are interpretable using a heatmap, thereby avoiding result misinterpretations. We demonstrated the superiority of the proposed method through both numerical simulations and real examples.     

多注行波管周期永磁聚焦系统

利用自行开发的3维行波管仿真软件研究了五注耦合腔行波管周期永磁聚焦系统,分析了各个电子注通道内的静磁场分布和电子注聚焦性能。讨论了在有无初始横向速度的情况下各电子注的聚焦情况。并对外层电子注通道内的横向磁场的性质和其造成的对电子注聚焦的影响进行了分析,结果表明:该多注周期永磁聚焦系统具有良好的静磁场分布特性与电子注聚焦性能,在结构设计合理时,横向磁场对外层通道内电子注的聚焦影响很小,可以忽略。     

Periodic Folded Wave Patterns for (2+1)-Dimensional Higher-Order Broer-Kaup Equation

A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-order Broer-Kaup equation by means of WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are found to be completely elastic.     

A Spatially Correlated Model with Generalized Autoregressive Conditionally Heteroskedastic Structure for Counts of Crimes

Crime is a negative phenomenon that affects the daily life of the population and its development. When modeling crime data, assumptions on either the spatial or the temporal relationship between observations are necessary if any statistical analysis is to be performed. In this paper, we structure space–time dependency for count data by considering a stochastic difference equation for the intensity of the space–time process rather than placing structure on a latent space–time process, as Cox processes would do. We introduce a class of spatially correlated self-exciting spatio-temporal models for count data that capture both dependence due to self-excitation, as well as dependence in an underlying spatial process. We follow the principles in Clark and Dixon (2021) but considering a generalized additive structure on spatio-temporal varying covariates. A Bayesian framework is proposed for inference of model parameters. We analyze three distinct crime datasets in the city of Riobamba (Ecuador). Our model fits the data well and provides better predictions than other alternatives.     

非均匀混响统计建模与功率估计

针对非均匀混响中进行恒虚警(CFAR)检测所需的背景功率估计问题,通过对非均匀混响进行统计建模分析,提出一种非均匀混响功率自适应估计方法。所提方法基于排序统计、功率分类等处理,对混响数据服从的统计模型进行判别,根据均匀混响、参杂强干扰混响、混响边缘等具有不同特性的混响成分,选择不同的处理方式进行功率估计。进一步将所提出的混响功率估计方法应用于CFAR检测中,获得一种新的CFAR检测器。仿真和实测混响数据的处理结果表明,提出的混响功率估计方法可以对强干扰和混响边缘等非均匀混响背景进行有效判别和功率估计,提出的CFAR检测器有效提高了非均匀混响背景中的目标检测性能。     

Doubly Periodic Propagating Wave for （2d-1）-Dimensional Breaking Soliton Equation

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.     

Direct Approach to Construct the Periodic Wave Solutions for Two Nonlinear Evolution Equations

With symbolic computation, the Hirota method and Riemann theta function are employed to directly construct the periodic wave solutions for the Hirota-Satsuma equation for shallow water waves and Boiti-Leon-Manna- Pempinelli equation. Then, the corresponding figures of the periodic wave solutions are given. Fhrthermore, it is shown that the known soliton solutions can be reduced from the periodic wave solutions.     

CRE Method for Solving m Kd V Equation and New Interactions Between Solitons and Cnoidal Periodic Waves

In nonlinear physics, the modified Korteweg de-Vries(m Kd V) as one of the important equation of nonlinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the m Kd V equation, the consistent Riccati expansion(CRE) method can unearth other equations.     

最大似然参数估计水声通信帧同步技术研究

水声通信中传统帧同步方法仅仅依赖于匹配滤波输出的相关系数,在复杂信道条件下,容易出现误触发和漏同步。针对这一问题,分析了水声信道中噪声、多普勒和多径对帧同步的影响,提出了一种基于参数估计的帧同步方法.在同步过程中引入参数估计,将信号参数作为检测判决依据,以降低误触发率和漏检率;同时对最大似然估计算法进行适当简化,以降低实现复杂度。计算机仿真实验验证了新的帧同步方法相对于传统方法在定时精度和相关系数方面的优势。实际水声通信实验结果表明,无论是静止平台还是移动平台之间的通信,新的帧同步方法均能有效提高匹配滤波器输出的相关系数,提升接收机检测能力,从而避免出现误触发和漏同步。     

Data-Based Optimal Bandwidth for Kernel Density Estimation of Statistical Samples

It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples, since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%~3% for sample size larger than 10⁴. This approach can also be generalized easily to cases of variable kernel estimations.