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.

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.

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.

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.

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.

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.

Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

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.

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].

EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS

A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.

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.

ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS

Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.

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.

Performance Evaluation of Mobility Anchor Point with Guard Load Reservation in Hierarchical Mobile IPv6

Hierarchical mobile IPv6 （HMIPv6） introduces a mobility anchor point to reduce the signaling overhead and handoff latency. In this paper, we apply the matrix-analytical approach to explore the performance measures of the ongoing mobile nodes （MNs） drop and new MNs block probabilities of mobility anchor point with a guard bandwidth reservation scheme. We apply the Markovian arrival process （MAP） to model ongoing MNs and new MNs. Five related performance measures are derived, including the long-term new MN block and ongoing MN drop probabilities, and the three short-term measures of average length of a block period and a non-block period, as well as the conditional ongoing MN drop probability during a block period. These performance measures greatly assist the guard bandwidth reservation mechanism in determining a proper threshold guard bandwidth. The results presented in this paper can provide guidelines for designing adaptive algorithms to adjust the threshold in the guard bandwidth reservation scheme.

Research on 3D Laser Scanning Reconstruction of Ancient Buildings Combined with BIM Technology

After more than 30 years of scientific and social development, surveying and mapping technology by leaps and bounds, engineering surveying technology has undergone tremendous changes. In the process of protecting ancient buildings, it is necessary to obtain the precise dimensions of architectural details. In this study, the path of 3D laser scanning combined with BIM technology is explored. Taking the observation and protection of the ancestral hall of the Liu family as an example, this study aims to draw drawings that reflect the relevant information about the ancient buildings, the accurate three-dimensional model of ancient buildings is established with BIM technology, which provides new methods and ideas for the research and protection of ancient buildings. .

Load-Aware Offloading Strategy in Two-Tier Heterogeneous Network

Although small cell offloading technology can alleviate the congestion in macrocell, aggressively offloading data traffic from macrocell to small cell can also degrade the performance of small cell due to the heavy load. Because of collision and backoff, the degradation is significant especially in network with contention-based channel access, and finally decreases throughput of the whole network. To find an optimal fraction of traffic to be offloaded in heterogeneous network, we combine Markov chain with the Poisson point process model to analyze contention-based throughput in irregularly deployment networks. Then we derive the close-form solution of the throughput and find that it is a function of the transmit power and density of base stations.Based on this, we propose the load-aware offloading strategies via power control and base station density adjustment. The numerical results verify our analysis and show a great performance gain compared with non-load-aware offloading.

Modeling forest fires in Mazandaran Province, Iran

We used a spafio-temporal shot-noise Cox process to study the distribution of forest fires reported between 2006 and 2010 in the Mazandaran Province＇s forests. The fitted model shows that daily temperature, altitude, and slope-exposure impacted fire occurrence. Forest fire occurred in the region had an aggregated behavior, which increased in radius below 1-km away from fired areas; a periodic pattern of fire occurrence in the region was verified. The risk of forest fire is significantly higher for areas with southern exposure and slope between 30° and 50°, northern exposure and slope between 0° and 50°, and eastern exposure and slope between 0° and 30°. The risk of fire was also significantly higher at altitudes between 1350 and 3000 m asl. Human causes were the main ignition source for forest fires in the region. The fire occurrence rate stayed above average during the drought period from September 2008 to September 2009. Our findings could lead to the development of fire-response and fire-suppression strategies appropriate to specific regions.

Characterizing the Seasonal and Directional Varying Properties in A Marine Environment

With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite important. It is recognized that a possible improvement in the traditional modeling of environmental characteristics, which are the basis for the load models for structural analysis and design, may be needed. In this paper, the seasonal and directional varying properties in modeling the ocean parameter, the wave height, are studied. The peak over threshold（POT） method is selected to model the extreme wave height by utilizing a non-stationary discrete statistical extreme model. The varying parameters are taken into account with a changing pattern to reflect the seasonal and directional dependent behavior. Both the magnitude and the occurrence rate of the extreme values are investigated. Detailed discussion on the continuity of the established model is also given. The importance of the proposed model is demonstrated in reliability analysis for a jacket structure. The sensitivity to the changing marine environment in reliability analyses is investigated.

Existence results for unilateral contact problem with friction of thermo-electro-elasticity

This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini＇s conditions and Tresca＇s friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is de- rived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.