Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence

Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].

Energy Efficiency Optimization for Heterogeneous Cellular Networks Modeled by Matérn Hard-Core Point Process

The Poisson point process(PPP) has been widely used in wireless network modeling and performance analysis due to the independence between its nodes. Therefore, it may not be a suitable model for many of the exclusive networks between the nodes. This paper analyzes the energy efficiency(EE) and optimizes the two-tier heterogeneous cellular networks(Het Nets). Considering the mutual exclusion between macro base stations(MBSs) distribution, the deployment of MBSs is modeled by the Matérn hard-core point process(MHCPP), and the deployment of pico base stations(PBSs) is modeled by the PPP. We adopt a simple approximation method to study the signal to interference ratio(SIR) distribution in two-tier MHCPP-PPP networks and then derive the coverage probabilities, the average data rates and the energy efficiency of Het Nets. Finally, an optimization algorithm is proposed to improve the EE of Het Nets by controlling the transmit power of PBSs. The simulation results show that the EE of a system can be effectively improved by selecting the appropriate transmit power for the PBSs. In addition, two-tier MHCPP-PPP Het Nets have higher energy efficiency than two-tier PPP-PPP Het Nets.

Model for Failure Point Process of a Repairable System and Application

A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process. This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed, and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time, and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality.

Standby Redundancy Allocation for a Coherent System under Its Signature Point Process Representation

Willing to work in reliability theory in a general set up, under stochastically dependence conditions, we intend to characterize a not identically spare standby redundancy operation through compensator transform under a complete information level, the physic approach, that is, observing its component lifetime. We intend to optimize system reliability under standby redundancy allocation of its components, particularly, under minimal standby redundancy. To get results, we will use a coherent system representation through a signature point process.

Reliability Analysis of Repairable Systems Using Stochastic Point Processes

In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system because the rate of occurrence of failures (ROCOF) of the system changes over time rather than remains stable. However, from a practical point of view, it is always preferred to apply the simplest method to address problems and to obtain useful practical results. Therefore, we attempted to use the HPP model to analyze the failure data from real repairable systems. A graphic method and the Laplace test were also used in the analysis. Results of numerical applications show that the HPP model may be a useful tool for the entire life cycle of repairable systems.

Gaussian limit for determinantal point processes with J-Hermitian kernels

We show that the central limit theorem for linear statistics over determinantal point processes with J-Hermitian kernels holds under fairly general conditions.In particular,we establish the Gaussian limit for linear statistics over determinantal point processes on the union of two copies of Rdwhen the correlation kernels are J-Hermitian translation-invariant.

Aggregate Point Cloud Geometric Features for Processing

As 3D acquisition technology develops and 3D sensors become increasingly affordable,large quantities of 3D point cloud data are emerging.How to effectively learn and extract the geometric features from these point clouds has become an urgent problem to be solved.The point cloud geometric information is hidden in disordered,unstructured points,making point cloud analysis a very challenging problem.To address this problem,we propose a novel network framework,called Tree Graph Network(TGNet),which can sample,group,and aggregate local geometric features.Specifically,we construct a Tree Graph by explicit rules,which consists of curves extending in all directions in point cloud feature space,and then aggregate the features of the graph through a cross-attention mechanism.In this way,we incorporate more point cloud geometric structure information into the representation of local geometric features,which makes our network perform better.Our model performs well on several basic point clouds processing tasks such as classification,segmentation,and normal estimation,demonstrating the effectiveness and superiority of our network.Furthermore,we provide ablation experiments and visualizations to better understand our network.

Point Cloud Processing Methods for 3D Point Cloud Detection Tasks

Light detection and ranging(LiDAR)sensors play a vital role in acquiring 3D point cloud data and extracting valuable information about objects for tasks such as autonomous driving,robotics,and virtual reality(VR).However,the sparse and disordered nature of the 3D point cloud poses significant challenges to feature extraction.Overcoming limitations is critical for 3D point cloud processing.3D point cloud object detection is a very challenging and crucial task,in which point cloud processing and feature extraction methods play a crucial role and have a significant impact on subsequent object detection performance.In this overview of outstanding work in object detection from the 3D point cloud,we specifically focus on summarizing methods employed in 3D point cloud processing.We introduce the way point clouds are processed in classical 3D object detection algorithms,and their improvements to solve the problems existing in point cloud processing.Different voxelization methods and point cloud sampling strategies will influence the extracted features,thereby impacting the final detection performance.

THINNING OF POINT PROCESSES,REVISITED

Let N, N1, N2 be simple point processes on a LCCB space (E,) such that N=N1+N2, and p() be a measurable function with 0<p()<1 on (E,). Then any two of the following statements yield another two:(Ⅰ) N is a Poisson process;(Ⅱ) N1 is the p( )thinning of N, N2 is the (1-p())-thinning of N;(Ⅲ) N1 and N2 are independent;(Ⅳ) N1, N2 are Poisson processes with respect to a filtration {F(A), A}, whereF(A)={N1(B), N2(B), B, BA},i.e., for each bounded set A, N1(A) and N2(A) are Poisson variables, independent of F(A ).Indeed, only the fact, (Ⅱ)+(Ⅲ)(Ⅳ)+(Ⅰ), is new.

Joint Limit Distributions of Exceedances Point Processes and Partial Sums of Gaussian Vector Sequence

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

Point process models, the dimensions of biodiversity and the importance of small-scale biotic interactions

Aims Recent mechanistic explanations for community assembly focus on the debates surrounding niche-based deterministic and dispersalbased stochastic models.This body of work has emphasized the importance of both habitat filtering and dispersal limitation,and many of these works have utilized the assumption of species spatial independence to simplify the complexity of the spatial modeling in natural communities when given dispersal limitation and/or habitat filtering.One potential drawback of this simplification is that it does not consider species interactions and how they may influence the spatial distribution of species,phylogenetic and functional diversity.Here,we assess the validity of the assumption of species spatial independence using data from a subtropical forest plot in southeastern China.Methods We use the four most commonly employed spatial statistical models—the homogeneous Poisson process representing pure random effect,the heterogeneous Poisson process for the effect of habitat heterogeneity,the homogenous Thomas process for sole dispersal limitation and the heterogeneous Thomas process for joint effect of habitat heterogeneity and dispersal limitation—to investigate the contribution of different mechanisms in shaping the species,phylogenetic and functional structures of communities.Important Findings Our evidence from species,phylogenetic and functional diversity demonstrates that the habitat filtering and/or dispersal-based models perform well and the assumption of species spatial independence is relatively valid at larger scales(50×50 m).Conversely,at local scales(10×10 and 20×20 m),the models often fail to predict the species,phylogenetic and functional diversity,suggesting that the assumption of species spatial independence is invalid and that biotic interactions are increasingly important at these spatial scales.

Stochastic Differential Equations Driven by Multi-fractional Brownian Motion and Poisson Point Process

In this paper,we study a class of stochastic differential equations with additive noise that contains a non-stationary multifractional Brownian motion(mBm)with a Hurst parameter as a function of time and a Poisson point process of class(QL).The differential equation of this kind is motivated by the reserve processes in a general insurance model,in which between the claim payment and the past history of liability present the long term dependence.By using the variable order fractional calculus on the fractional Wiener-Poisson space and a multifractional derivative operator,and employing Girsanov theorem for multifractional Brownian motion,we prove the existence of weak solutions to the SDEs under consideration,As a consequence,we deduce the uniqueness in law and the pathwise uniqueness.

THE POINT PROCESS OF STATETRANSITIONS IN AREGULAR MARKOV CHAIN

In this paper, we study the point process of state transitions in a regular Markov chain.Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution,the renewal distribution and the entering probability. As an applicstion, using these formulas we derive the LS transform of the busy period for the M/M/∞ queue.

The SCUSUM Estimation of Variance Change Point in Linear Process

这份报纸在线性过程考虑一个变化变化点的评价问题。一个 SCUSUM 类型变化点评估者的一致性被证明，它集中的率被建立。平均数未知的盒子也被考虑。

RATE OF CONVERGENCE FOR MULTIPLE CHANGEPOINTS ESTIMATION OF MOVING-AVERAGE PROCESSES

In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions.

ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESS CONVOLUTION SEMIGROUPS

Let D be a convolution semigroup of random measures or point processes on a locally compact second countable T 2space. There is a topological isomorphism from D into a subsemigroup of product topological semigroup (R +,+) N.D is a sequentially stable and D-separable ZH-semigroup, as well as a metrizable, stable and normable Hun semigroup, so it has the corresponding properties. In particular the author has a new and simple proof byZH-semigroup approach or Hun semigroup approach to show that D has property ILID (an infinitesimal array limit is infinitely divisible), and know the Baire types which some subsets of D belong in.

Computer Processing of the Intersection of Two Cones with Their Axes Intersecting and a Method to Get the Special Points

The analytic expression of the special points on the intersection of two cones with their axes intersecting(ITCTAI) is given. It also presents a method to construct the special points graphically according to the analytic expression of them. Finally, with computer programming language, it gives a program to generate the intersection in several different cases.

New Approach in Processing of the Infrared Image Sequence for Moving Dim Point Targets Detection

The development of an efficient moving target detection algorithm in IR-image sequence is considered one of the most critical research fields in modern IRST (Infrared Search and Track) systems, especially when dealing with moving dim point targets. In this paper we propose a new approach in processing of the Infrared image sequence for moving dim point targets detection built on the transformation of the IR-image sequence into 4-vectors for each frame in the sequence. The results of testing the proposed approach on a set of frames having a simple single pixel target performing a different motion patterns show the validity of the approach for detecting the motion, with simplicity in calculation and low time consumption.

Pre-process algorithm for satellite laser ranging data based on curve recognition from points cloud

The satellite laser ranging （SLR） data quality from the COMPASS was analyzed, and the difference between curve recognition in computer vision and pre-process of SLR data finally proposed a new algorithm for SLR was discussed data based on curve recognition from points cloud is proposed. The results obtained by the new algorithm are 85 % （or even higher） consistent with that of the screen displaying method, furthermore, the new method can process SLR data automatically, which makes it possible to be used in the development of the COMPASS navigation system.

Modeling and Performance Analysis of UAV-Aided Millimeter Wave Cellular Networks with Stochastic Geometry

UAV-aided cellular networks,millimeter wave(mm-wave)communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G)and even 6G communications.By leveraging the power of stochastic geometry,this paper aims at providing an effective framework for modeling and analyzing a UAV-aided heterogeneous cellular network,where the terrestrial base stations(TBSs)and the UAV base stations(UBSs)coexist,and the UBSs are provided with mm-wave and multi-antenna techniques.By modeling the TBSs as a PPP and the UBSs as a Matern hard-core point pro-´cess of type II(MPH-II),approximated but accurate analytical results for the average rate of the typical user of both tiers are derived through an approximation method based on the mean interference-to-signal ratio(MISR)gain.The influence of some relevant parameters is discussed in detail,and some insights into the network deployment and optimization are revealed.Numerical results show that some trade-offs are worthy of being considered,such as the antenna array size,the altitude of the UAVs and the power control factor of the UBSs.