Search

Improving the user performance and spectrum efficiency are urgent problems for 5G and beyond 5G (B5G) cellular networks to support high Quality of Services such as enhanced mobile broadband, ultra-reliable, and low latency communications. Together with Fractional Frequency Reuse (FFR), Time Division Duplex (TDD) and Non-Orthogonal Multi-Access (NOMA) are promising the potential solutions for these problems. While the related researches focus on the single or combination two of three techniques, this paper proposes a system that combination of all three techniques to improve the data rate on the uplink sub-band. Specifically, each couple of Cell-Center User (CCU) and Cell-Edge User (CEU) in a given cell, that is defined by the FFR technique, is allowed to transmit on the same sub-band by the meaning of power-domain NOMA technique. In addition, the TDD technique allow the sharing sub-band between the user and Base Station (BS). The analytical results in Nakagami-m fading and regular path loss model shows that achievable total data rate on the shared sub-band in the proposed system model is 18.2% and 125% higher than that in the regular one with TDD and NOMA, respectively. The data rate improvement of the proposed system model proves the feasibility of co-exits of these techniques in the B5G systems.

Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. Algebraic properties of the asymptotic covariance matrix are studied as the intensity of the underlying homogeneous Poisson point process increases. This includes a systematic discussion of matrix properties like rank, definiteness, determinant, eigenspaces or decompositions of interest. For the formulation of the results a case distinction is necessary. In the three possible regimes the respective covariance matrix is of quite different nature which leads to different statements. Stochastic consequences for random geometric graphs are derived. [ABSTRACT FROM AUTHOR]

Species distribution models (SDMs) are usually based on a single data type, such as presence‐only (PO), presence‐absence (PA) or abundance (AA). Results from SDMs using single sources of data will suffer from inherent biases and limitations to that data type. For example, PO data contain sampling‐bias and PA/AA data are often less expansive and more sparse. Integrated SDMs (ISDMs) combine multiple data types and have recently emerged as a way to leverage strengths and minimise weaknesses of the different data types. They pose a common (distribution) model and separate observation models for each of the data types. The 'RISDM' package for the R environment (www.r‐project.org) provides access to this modelling framework using functions for preparation, fitting, interpreting and diagnosing models. The functionality of the package is demonstrated here using synthetic data sets. [ABSTRACT FROM AUTHOR]

Improving the user performance and spectrum efficiency are urgent problems for 5G and beyond 5G (B5G) cellular networks to support high Quality of Services such as enhanced mobile broadband, ultra-reliable, and low latency communications. Together with Fractional Frequency Reuse (FFR), Time Division Duplex (TDD) and Non-Orthogonal Multi-Access (NOMA) are promising the potential solutions for these problems. While the related researches focus on the single or combination two of three techniques, this paper proposes a system that combination of all three techniques to improve the data rate on the uplink sub-band. Specifically, each couple of Cell-Center User (CCU) and Cell-Edge User (CEU) in a given cell, that is defined by the FFR technique, is allowed to transmit on the same sub-band by the meaning of power-domain NOMA technique. In addition, the TDD technique allow the sharing sub-band between the user and Base Station (BS). The analytical results in Nakagami-m fading and regular path loss model shows that achievable total data rate on the shared sub-band in the proposed system model is 18.2% and 125% higher than that in the regular one with TDD and NOMA, respectively. The data rate improvement of the proposed system model proves the feasibility of co-exits of these techniques in the B5G systems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we study point processes on the complex plane and illustrate their uses in several statistical areas, where the quantities of interest requiring estimation involve Fourier expansions. In particular, for any problem where we can describe a quantity in terms of its Fourier expansion, we propose modeling the coefficients of the expansion using a point process on the complex plane. We utilize the Poisson complex point process and model its intensity function using log-linear and mixture models. The proposed models are exemplified via applications to general density approximation, via modeling of the characteristic function, and time series analysis, via modeling of the spectral density. [ABSTRACT FROM AUTHOR]

Summary: In the rapidly evolving landscape of fifth generation Internet of Things (5G‐IoT) networks, Device‐to‐Device (D2D) communication has emerged as a promising paradigm to enhance secrecy transmission rate (STR) and connectivity. However, the security of D2D communications in the presence of eavesdroppers remains a critical challenge. This article investigates the problem of optimizing D2D transmit power to achieve secure D2D communication while considering the presence of random eavesdroppers in 5G‐IoT networks. We propose a novel secrecy‐based power control approach (SRMWPCA) approach to model the random distribution of eavesdroppers in the network, taking into account their varying distances from D2D pairs and deliberately increasing interference at the eavesdropper's link. By leveraging tools from stochastic geometry, we derive an analytical expression for the secrecy transmission probability (STP), which quantifies the probability of eavesdroppers successfully decoding the D2D transmission. In this analysis, we have incorporated practical considerations such as channel fading, path loss, and interference from other devices. To enhance the security of D2D communication, we formulate an optimization problem to determine the optimal transmit power levels for D2D pairs, subject to constraints on the secrecy transmission probability and interference to the cellular network. We propose an efficient algorithm to find the power allocation that maximizes the secrecy outage performance while meeting these constraints. Simulation results demonstrate the effectiveness of the proposed approach in achieving secure D2D communication in 5G‐IoT networks with random eavesdroppers. The performance of the proposed SRMWPCA approach improved by 23.25% and 20.9% compared with standard approaches in terms of the secrecy rate and throughput of the users from malicious attacks. [ABSTRACT FROM AUTHOR]

The beyond 5G millimeter-wave cellular network system is expected to provide high-quality service in indoor areas. Due to the high density of obstacles, cooperative communication techniques are employed to improve the user's desired signal power by finding more than one appropriate station to serve that user. While the conventional system utilizes additional equipment such as Reconfigurable Intelligent Surfaces (RIS) and relays to enable cooperative features, the paper introduces a new network paradigm that utilizes the second nearest Base Station (BS) of the typical user as the Decode and Forward (DF) relay. Thus, depending on the success of decoding the message from the user's serving BS or the second nearest BS, the typical user can work with or without assistance from the relay, whose operation follows the discipline of the power-domain NOMA technique. In the case of relay assistance, the Maximum Ratio Combining technique is utilized by the typical user to combine the desired signals. To examine the performance of the proposed system, the Nakagamim and the newly developed path loss model, which considers the density of walls and their properties, are adopted to derive the coverage probability of the user with and without relay assistance. The closedform expressions of this performance metric are derived using Gauss quadrature and Welch-Satterthwaite approximation. Through analytical and simulation results, it is seen that the proposed system can improve the user coverage probability by up to 10%. [ABSTRACT FROM AUTHOR]

Spatial capture-recapture (SCR) is now routinely used for estimating abundance and density of wildlife populations. A standard SCR model includes sub-models for the distribution of individual activity centers (ACs) and for individual detections conditional on the locations of these ACs. Both sub-models can be expressed as point processes taking place in continuous space, but there is a lack of accessible and efficient tools to fit such models in a Bayesian paradigm. Here, we describe a set of custom functions and distributions to achieve this. Our work allows for more efficient model fitting with spatial covariates on population density, offers the option to fit SCR models using the semi-complete data likelihood (SCDL) approach instead of data augmentation, and better reflects the spatially continuous detection process in SCR studies that use area searches. In addition, the SCDL approach is more efficient than data augmentation for simple SCR models while losing its advantages for more complicated models that account for spatial variation in either population density or detection. We present the model formulation, test it with simulations, quantify computational efficiency gains, and conclude with a real-life example using non-invasive genetic sampling data for an elusive large carnivore, the wolverine (Gulo gulo) in Norway.

Abstract In building a robust knowledge base or validating existing models for use in ecological spatial modelling, having plentiful high‐quality data is paramount. Careful survey design helps attain that goal and, in part due to financial constraints, such design requires the balancing of hard monetary costs and the intangible benefit of improved ecological models. We propose a framework that quantifies a location's value to the modeller by accounting for both the probability of obtaining new samples and their expected contribution to the model. The approach is illustrated on a citizen science database of roadkills in Taiwan, modelled as a Poisson point process on a linear road network. Our method has revealed some valuable locations that were not self‐evident, for example, highlighting the possibility of sending volunteers to mountainous areas that despite being hard to reach, would provide valuable samples. We have also highlighted some ex situ sampling opportunities to avoid wasting resources by over‐sampling hard to access locations. Our technique is not restricted to presence‐only data, and in fact we present a general framework that can be applied to a wide range of settings by tuning its formulation. Our method is quite flexible and allows for more elaborate value functions, enabling managers to precisely quantify varied goals within the same framework.

With the development of fifth-generation (5G) networks, the number of user equipments (UE) increases dramatically. However, the potential health risks from electromagnetic fields (EMF) tend to be a public concern. Generally, EMF exposure-related analysis mainly considers the passive exposure from base stations (BSs) and active exposure that results from the user’s personal devices while communicating. However, the passive radiation that is generated by nearby devices of other users is typically ignored. In fact, with the increase in the density of UE, their passive exposure to human bodies can no longer be ignored. In this work, we propose a stochastic geometry framework to analyze the EMF exposure from active and passive radiation sources. In particular, considering a typical user, we account for their exposure to EMF from BSs, their own UE, and other UE. We derive the distribution of the Exposure index (EI) and the coverage probability for two typical models for spatial distributions of UE, i.e., i) a Poisson point process (PPP); ii) a Matern cluster process. Also, we show the trade-off between the EMF exposure and the coverage probability. Our numerical results suggest that the passive exposure from other users is non-negligible compared to the exposure from BSs when user density is 102 times higher than BS density, and non-negligible compared to active exposure from the user’s own UE when user density is 105 times the BS density.

We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al. (2022), we consider an urban environment, represented by line segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device. Inspired by wireless network architectures, the network is additionally equipped with a second class of agents able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to chase–escape dynamics. We give conditions for parameter configurations that guarantee existence and absence of global survival as well as an in-and-out of the survival regime, depending on the speed of the devices. We also provide complementary results for the setting in which the chase–escape dynamics is defined as an independent process on the connectivity graph. The proofs mainly rest on percolation arguments via discretization and multiscale analysis. [ABSTRACT FROM AUTHOR]

We consider the spectrum of random Laplacian matrices of the form L n = A n - D n where A n is a real symmetric random matrix and D n is a diagonal matrix whose entries are equal to the corresponding row sums of A n . If A n is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of L n is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices A n with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of L n converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which L n converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure. [ABSTRACT FROM AUTHOR]

The probabilistic representations of solutions of pantograph equations are presented. In some cases these can be functionals of standard Brownian motion, while in others they are functionals of an appropriately constructed Poisson point process. The study of the probabilistic representations lead to surprising phenomena of the so called triangle coefficients, which are generated by a recurrence formula and form some interesting structures. [ABSTRACT FROM AUTHOR]

In building a robust knowledge base or validating existing models for use in ecological spatial modelling, having plentiful high‐quality data is paramount. Careful survey design helps attain that goal and, in part due to financial constraints, such design requires the balancing of hard monetary costs and the intangible benefit of improved ecological models.We propose a framework that quantifies a location's value to the modeller by accounting for both the probability of obtaining new samples and their expected contribution to the model. The approach is illustrated on a citizen science database of roadkills in Taiwan, modelled as a Poisson point process on a linear road network.Our method has revealed some valuable locations that were not self‐evident, for example, highlighting the possibility of sending volunteers to mountainous areas that despite being hard to reach, would provide valuable samples. We have also highlighted some ex situ sampling opportunities to avoid wasting resources by over‐sampling hard to access locations.Our technique is not restricted to presence‐only data, and in fact we present a general framework that can be applied to a wide range of settings by tuning its formulation. Our method is quite flexible and allows for more elaborate value functions, enabling managers to precisely quantify varied goals within the same framework. [ABSTRACT FROM AUTHOR]

The convex hull peeling of a point set is obtained by taking the convex hull of the set and repeating iteratively the operation on the interior points until no point remains. The boundary of each hull is called a layer. We study the number of k-dimensional faces and the outer defect intrinsic volumes of the first layers of the convex hull peeling of a homogeneous Poisson point process in the unit ball whose intensity goes to infinity. More precisely we provide asymptotic limits for their expectation and variance as well as a central limit theorem. In particular, the growth rates do not depend on the layer. [ABSTRACT FROM AUTHOR]

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in R 2 as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed. [ABSTRACT FROM AUTHOR]

Financial market data are abundant with outliers, and the search for an appropriate extreme value theory (EVT) approach to apply is an endless debate in the statistics of extremes research. This paper uses EVT methods to model the five-year daily all-share total return index (ALSTRI) and the daily United States dollar (USD) against the South African rand (ZAR) exchange rate of the Johannesburg stock exchange (JSE). The study compares the block maxima approach and the peaks-over-threshold (POT) approach in terms of their ability to model financial market data. The 100-year return levels for the block maxima approach were found to be almost equal to the maximum observations of the financial markets of 10,860 and R18.99 for the ALSTRI and the USD–ZAR, respectively. For the peaks-over-threshold (POT) approach, the results show that the ALSTRI and the USD–ZAR exchange rate will surpass 17,501.63 and R23.72, respectively, at least once in 100 years. The findings in this study reveal a clear distinction between block maxima and POT return level estimates. The POT approach return level estimates were comparably higher than the block maxima estimates. The study further revealed that the blended generalised extreme value (bGEVD) is more suitable for relatively short-term forecasting, since it cuts off at the 50-year return level. Therefore, this study will add value to the literature and knowledge of statistics and econometrics. In the future, more studies on bGEVD, vine copulas, and the r-largest-order bGEVD can be conducted in the financial markets. [ABSTRACT FROM AUTHOR]

Palaeo‐ice sheets leave behind a rich database regarding their past behaviour, recorded in the landscape in the form of glacial geomorphology. The most numerous landform created by these ice sheets are subglacial lineations, which generate snapshots of the direction of ice flow at fixed (yet typically unknown) points in time. Despite their relative density within the landform record, the information provided by subglacial lineations is currently underutilised in tests of numerical ice sheet models. To some extent, this is a consequence of ongoing debate regarding lineation formation, but predominantly, it reflects the lack of rigorous model‐data comparison techniques that would enable lineation information to be properly integrated. Here, we present the Likelihood of Accordant Lineations Analysis (LALA) tool. LALA provides a statistically rigorous measure of the log‐likelihood of a supplied ice sheet simulation through comparison of simulation output with both the location and direction of observed lineations. Given an ensemble of ice sheet simulations, LALA provides a formal, and statistically underpinned, quantitative assessment of each simulation's quality‐of‐fit to mapped lineations. This enables a comparison of each simulation's relative plausibility, including identification of the most likely ice sheet simulations amongst the ensemble. This is achieved by modelling lineation formation as a marked Poisson point process and comparison of observed to modelled flow directions using the von Mises distribution. LALA is flexible—users can adapt parameters to account for differing assumptions regarding lineation formation, and for variations in the level of precision required for differing model‐data comparison experiments. We provide guidelines and rationale for assigning parameter values, including an assessment of the variability between users when mapping lineations. Finally, we demonstrate the utility of LALA through application to an ensemble of simulations of the last British‐Irish Ice Sheet. This comparison highlights the benefits of LALA over previous tools and demonstrates some of the considerations of experimental design required when identifying the fit between ice sheet model simulations and the landform record. [ABSTRACT FROM AUTHOR]

Abstract Haphazard and opportunistic species occurrence (PO) data are widely used in species distribution models (SDMs) instead of high-quality species data gathered using appropriate and structured sampling methods, which is expensive and often spatially limited. Despite their widespread use in ecology, PO data are prone to errors and uncertainties, such as imperfect detectability, positional imprecision, and spatial niche truncation, which make their use analytically challenging for effective and adaptive biodiversity management and conservation. Using simulated data, this study investigates the effects of these uncertainties on the performance of spatial point process based presence-only and integrated SDMs. We investigated three SDMs in this study, one that ignores imperfect detectability: the presence-only model (PO model), and two that account for it: the thinned presence-only model (THINPO model) and the integrated model (PBPC model). The ability of these SDMs to produce accurate maximum likelihood estimates of intensity model coefficients and reliable predictions of species distributions under different data quality scenarios was investigated. The results show that SDMs that account for imperfect detectability (THINPO or PBPC models) are not applicable in situations of high detectability. In this situation, the PO model produces the most accurate maximum likelihood estimates of the models’ coefficients ( $${\hat{\beta }}_k$$ β ^ k ), and consequently the most accurate predictions of species distributions ( $${\hat{\lambda }}(s)$$ λ ^ ( s ) ). The effects of positional uncertainty and spatial niche truncation on this SDM output are minimal. However, in situations of low detectability, it is preferable to use the PBPC model. Positional uncertainty and spatial niche truncation have negligible effects on the output of this SDM, except when positionally uncertain PO data are analyzed along with truncated PC data. These minimal effects of spatial niche truncation on SDM outputs demonstrate the transferability of SDMs. However, the effects of all these uncertainties may depend on the characteristics of the species. Prior to modeling species distributions, a multivariate environmental similarity surface analysis should be performed to test the similarity between data from the restricted region to be used for model calibration and data from the entire range. If this analysis reveals dissimilarities, larger spatial and ecological scales should be considered to address the issue of spatial niche truncation. Further efforts could address the effects of species characteristics on SDMs performance and assess the effects of species-specific uncertainties.

Aim: Anthropogenic changes such as land use and climate change affect species' geographic ranges, causing range shifts, contractions, or expansions. However, data on range dynamics are insufficient, heterogeneous, and spatially and temporally biased in most regions. Integrated species distribution models (IDMs) offer a solution as they can complement good quality presence‐absence data with opportunistically collected presence‐only data, simultaneously accounting for heterogeneous sampling effort. However, these methods have seen limited use in the estimation of temporal change of geographic ranges and are not yet widespread as they have a steep learning curve. Here we present a generalisable model and case example. Location: Neotropics ‐ Latin America. Taxon: Herpailurus yagouaroundi. Methods: Using data on presence‐absence and presence‐only on the jaguarundi (Herpailurus yagouaroundi), we modelled the species distribution at two time periods (2000–2013 and 2014–2021) using a Bayesian model based on Poisson point process in JAGS. Our model integrates the different data types while accounting for varying sampling effort and spatial effect. We predicted the species range at the two time periods and quantified their changes. Results: Between the two time periods, the jaguarundi has contracted its southern and northern range limits towards the equator but expanded its area of distribution over the entire species' range. Also, our results show that modelled geographic range, of either time period, is not entirely consistent with the current expert range map from IUCN. Main Conclusions: Our modelling approach provides a working example with the potential to address data gaps and biases in other taxa and regions. Given the increasing number of incidental data being generated by community‐derived initiatives in Latin America, IDMs can become a valuable source for species distribution modelling in the region. This is the first application of the IDM approach with temporal dimension and over the entire species' geographic range. [ABSTRACT FROM AUTHOR]

Recently, federated learning (FL) has been receiving great attention as an effective machine learning method to avoid the security issue in raw data collection, as well as to distribute the computing load to edge devices. However, even though wireless communication is an essential component for implementing FL in edge networks, there have been few works that analyze the effect of wireless networks on FL. In this paper, we investigate FL in small-cell networks where multiple base stations (BSs) and users are located according to a homogeneous Poisson point process (PPP) with different densities. We comprehensively analyze the effects of geographic node deployment on the model aggregation in FL on the basis of stochastic geometry-based analysis. We derive the closed-form expressions of coverage probability with tractable approximations and discuss the minimum required BS density for achieving a target model aggregation rate in small-cell networks. Our analysis and simulation results provide insightful information for understanding the behaviors of FL in small-cell networks; these can be exploited as a guideline for designing the network facilitating wireless FL. [ABSTRACT FROM AUTHOR]

Haphazard and opportunistic species occurrence (PO) data are widely used in species distribution models (SDMs) instead of high-quality species data gathered using appropriate and structured sampling methods, which is expensive and often spatially limited. Despite their widespread use in ecology, PO data are prone to errors and uncertainties, such as imperfect detectability, positional imprecision, and spatial niche truncation, which make their use analytically challenging for effective and adaptive biodiversity management and conservation. Using simulated data, this study investigates the effects of these uncertainties on the performance of spatial point process based presence-only and integrated SDMs. We investigated three SDMs in this study, one that ignores imperfect detectability: the presence-only model (PO model), and two that account for it: the thinned presence-only model (THINPO model) and the integrated model (PBPC model). The ability of these SDMs to produce accurate maximum likelihood estimates of intensity model coefficients and reliable predictions of species distributions under different data quality scenarios was investigated. The results show that SDMs that account for imperfect detectability (THINPO or PBPC models) are not applicable in situations of high detectability. In this situation, the PO model produces the most accurate maximum likelihood estimates of the models' coefficients ( β ^ k ), and consequently the most accurate predictions of species distributions ( λ ^ (s) ). The effects of positional uncertainty and spatial niche truncation on this SDM output are minimal. However, in situations of low detectability, it is preferable to use the PBPC model. Positional uncertainty and spatial niche truncation have negligible effects on the output of this SDM, except when positionally uncertain PO data are analyzed along with truncated PC data. These minimal effects of spatial niche truncation on SDM outputs demonstrate the transferability of SDMs. However, the effects of all these uncertainties may depend on the characteristics of the species. Prior to modeling species distributions, a multivariate environmental similarity surface analysis should be performed to test the similarity between data from the restricted region to be used for model calibration and data from the entire range. If this analysis reveals dissimilarities, larger spatial and ecological scales should be considered to address the issue of spatial niche truncation. Further efforts could address the effects of species characteristics on SDMs performance and assess the effects of species-specific uncertainties. [ABSTRACT FROM AUTHOR]

In this work, we present the performance evaluation of a power beacon-assisted wireless-powered communication system in the presence of multiple co-channel interferers. We consider and compare three distinct interference modeling scenarios, namely the totally induced interference is approximated by the Gamma distribution, interferers are distributed according to a Poisson point process and interferers are distributed according to a binomial point process. Analytical expressions for the outage probability and the ergodic capacity of the considered system under each interference scenario are derived. Furthermore, optimization problems are formulated to determine the optimum switching time maximizing the achieved ergodic capacity. Numerical results accompanied with Monte Carlo simulations are presented to corroborate the proposed theoretical analysis.

Let X 1 , X 2 , ... be independent random uniform points in a bounded domain A ⊂ R d with smooth boundary. Define the coverage threshold R n to be the smallest r such that A is covered by the balls of radius r centred on X 1 , ... , X n . We obtain the limiting distribution of R n and also a strong law of large numbers for R n in the large-n limit. For example, if A has volume 1 and perimeter | ∂ A | , if d = 3 then P [ n π R n 3 - log n - 2 log (log n) ≤ x ] converges to exp (- 2 - 4 π 5 / 3 | ∂ A | e - 2 x / 3) and (n π R n 3) / (log n) → 1 almost surely, and if d = 2 then P [ n π R n 2 - log n - log (log n) ≤ x ] converges to exp (- e - x - | ∂ A | π - 1 / 2 e - x / 2) . We give similar results for general d, and also for the case where A is a polytope. We also generalize to allow for multiple coverage. The analysis relies on classical results by Hall and by Janson, along with a careful treatment of boundary effects. For the strong laws of large numbers, we can relax the requirement that the underlying density on A be uniform. [ABSTRACT FROM AUTHOR]

In this article, the number of vertices of the convex hull and the area between the boundaries of the convex hull and the support are approximated by the sum of stationary sequences for the case when the convex hull is generated by a non-homogeneous Poisson point process inside a parabola. [ABSTRACT FROM AUTHOR]

Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension d at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., a measurable function of the point configurations that commutes with translations), and with the property that the distance between two matched configuration points has a tail distribution that decays as fast as possible in magnitude, namely, as b exp (- c r d) with suitable constants b , c > 0 . This settles the most difficult version of such matching problems: bicolored (versus unicolored) and deterministic (versus randomized). Our proof relies on two earlier results: an allocation ("land-division") rule of similar tail for a Poisson point process by Markó and the author, and a recent breakthrough result of Bowen, Kun and Sabok that enables one to obtain perfect matchings from fractional perfect matchings under suitable conditions. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a user-centric frequency reuse scheme depending on the user classification in the cell in a homogeneous Poisson point process network. Each cell is partitioned into multiple regions delimited by the signal-to-interference ratio of the user considered. A given resource block (RB) is assigned to one user in a cell and cannot be shared by another user in this cell. The typical user only uses a fraction of the RB, and the remaining part is left unused to avoid interference with the other cells. The base stations (BS) interfering set is hence determined by the coverage probability of the typical user, and this set can be approximated by a thinned version of the original PPP. Using this, coverage probability and spectral efficiency (SE) for each user types are derived, and a BS cooperation technique is proposed to improve the SE of the cell edge user. Finally, the average network spectral efficiency and fairness among users are analyzed under the developed theoretical framework. Our results show that the user-centric frequency reuse improves the coverage probability and the SE compared to the conventional frequency reuse scheme.

Spatial statistics is a powerful tool for analyzing data that are illustrated as points or positions in a regular or non-regular state space. Techniques that are proposed to investigate the spatial association between neighboring positions are based on the point process analysis. One of the main goals is to simulate real data positions (such as antenna base stations) using the type of point process that most closely matches the data. Spatial patterns could be detailed describing the observed positions and appropriate models were proposed to simulate these patterns. A common model to simulate spatial patterns is the Poisson point process. In this work analyses of the Poisson point process—as well as modified types such as inhibition point process and determinantal Poisson point process—are presented with simulated data close to the true data (i.e., antenna base station positions). Investigation of the spatial variation of the data led us to the spatial association between positions by applying Ripley’s K-functions and L-Function.

The focus in this paper is on coverage energy-efficient of WSN (wireless sensor networks). Communication path lengths of a randomly distributed BSs and sensor nodes field are characterized by distance distributions. For sensor nodes, this paper will use theory of Poisson point process (PPP) and Boolean Model (BM) to purpose a power allocation scheme results in green communication of sensor nodes. The energy allocation scheme of wireless sensor networks can help to prolong the life of the whole network. In this paper, we prove that the scheduling and allocation scheme can achieve energy saving, so as to prolong the life cycle of the whole wireless sensor networks. In the uniform placement migration case, we simulation 1000 times. In Boolean Model, There is 71.3% for power scheduling and allocation schemes and 28.7% is not. From these results, we see that, in wireless sensor networks, 20%–30% of total energy, which was being consumed from the part of power scheduling and allocation. The scheduling scheme improves response time, throughput and overall energy consumption over base case. Compared with other allocation schemes, the advantage of the scheme proposed in this paper is that the less sensors selected can still provide more than 95% detection area coverage. It will enable robust communication against cross-tier interference and co-layer interference thereby obtaining a substantial improvement in link quality.

The full-information best choice problem asks one to find a strategy maximising the probability of stopping at the minimum (or maximum) of a sequence X 1 , ⋯ , X n of i.i.d. random variables with continuous distribution. In this paper we look at more general models, where independent X j 's may have different distributions, discrete or continuous. A central role in our study is played by the running minimum process, which we first employ to re-visit the classic problem and its limit Poisson counterpart. The approach is further applied to two explicitly solvable models: in the first the distribution of the jth variable is uniform on { j , ⋯ , n } , and in the second it is uniform on { 1 , ⋯ , n } . [ABSTRACT FROM AUTHOR]

This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously prove a verification theorem which provides a sufficient condition for open-loop equilibrium strategies. As special cases, a mean-variance portfolio selection problem and a time-inconsistent problem under non-exponential discounting are discussed. [ABSTRACT FROM AUTHOR]

The magnitudes recorded in seismic catalogues are subject to uncertainties that can have a significant impact when estimating the parameters of seismic recurrence models. In this paper, we propose an innovative approach based on a Poisson point process of dimension 2 that models both the magnitude hazard and the associated uncertainty. We define estimators of the parameters of the Gutenberg Richter model that maximize the likelihood of the data. We apply the approach to the Alps region in France and we compare it to other approaches proposed in the literature. [ABSTRACT FROM AUTHOR]

In this work, we study the effects of geometric confinement on the point statistics in a quasi-low-dimensional system. Specifically, we focus on the nearest-neighbor statistics. Accordingly, we have performed comprehensive numerical simulations of binomial point process on quasi-one-dimensional rectangle strips for different values of the confinement ratio defined as the ratio of the strip width to the mean nearest-neighbor distance. We found that the nearest-neighbor distance distributions (NNDDs) conform to an extreme value Weibull distribution with the shape parameter depending on the confinement ratio, while the process intensity remains constant. This finding reveals the reduction of effective spatial degrees of freedom in a quasi-low-dimensional system under the geometric confinement. The scale dependence of the number of effective spatial degrees of freedom is found to obey the crossover ansatz. We stress that the functional form of the crossover ansatz is determined by the nature of the studied point process. Accordingly, different physical processes in the quasi-low-dimensional system obey different crossover ansatzes. The relevance of these results for quasi-low-dimensional systems is briefly highlighted. [ABSTRACT FROM AUTHOR]

We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained concentration inequalities by application to adaptive intensity estimation. [ABSTRACT FROM AUTHOR]

We investigate the point process of moduli of the Ginibre and hyperbolic ensembles. We show that far from the origin and at an appropriate scale, these processes exhibit Gaussian and Poisson fluctuations. Among the possible Gaussian fluctuations, we can find white noise but also fluctuations with non-trivial covariance at a particular scale. [ABSTRACT FROM AUTHOR]

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in R2 as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed.

Financial market data are abundant with outliers, and the search for an appropriate extreme value theory (EVT) approach to apply is an endless debate in the statistics of extremes research. This paper uses EVT methods to model the five-year daily all-share total return index (ALSTRI) and the daily United States dollar (USD) against the South African rand (ZAR) exchange rate of the Johannesburg stock exchange (JSE). The study compares the block maxima approach and the peaks-over-threshold (POT) approach in terms of their ability to model financial market data. The 100-year return levels for the block maxima approach were found to be almost equal to the maximum observations of the financial markets of 10,860 and R18.99 for the ALSTRI and the USD–ZAR, respectively. For the peaks-over-threshold (POT) approach, the results show that the ALSTRI and the USD–ZAR exchange rate will surpass 17,501.63 and R23.72, respectively, at least once in 100 years. The findings in this study reveal a clear distinction between block maxima and POT return level estimates. The POT approach return level estimates were comparably higher than the block maxima estimates. The study further revealed that the blended generalised extreme value (bGEVD) is more suitable for relatively short-term forecasting, since it cuts off at the 50-year return level. Therefore, this study will add value to the literature and knowledge of statistics and econometrics. In the future, more studies on bGEVD, vine copulas, and the r-largest-order bGEVD can be conducted in the financial markets.

This paper develops a new approach to the modeling and analysis of device-to-device (D2D) underlaying multi-tier cellular network for dense hotspot communications, which consists of macro base stations (MBSs), pico BSs (PBSs), femto BSs (FBSs). A typicl user equipment (UE) can work either in D2D mode or cellular mode. Considering the dense hotspot communications, this work employs Poisson point process (PPP) to model the locations of MBSs and PBSs, and uses Poisson cluster process (PCP) to model the ones of UEs and FBSs. The locations of PBSs are also modeled as the centers of hotspots, referred to as the centers of PCPs. UEs and FBSs cluster around the common parent process PBSs. To guard the cluster-edge UEs, the clustered-UE classification and modified fractional frequency reuse (FFR) are jointly used, by which both the UEs and FBSs are classified two sets, cluster-center UEs and cluster-edge UEs, cluster-center FBSs and cluster-edge FBSs, respectively. The total frequency band is divided into two orthogonal segments, one of which is shared by D2D devices, cluster-edge FBSs, and PBSs, and the other segment of which is shared by cluster-center FBSs and MBSs. For such clustered multi-tier network, by using the methods from PPP, PCP, and PHP, this paper presents a tractable approach for modeling and analyzing the performance of cellular and D2D networks and gives the statistical descriptions of the experienced interferences at a typical D2D or cellular receiver by using the approximated Poisson hole processes (PHP) theory. This yields the derivations of the coverage probabilities of both the D2D receivers and cellular destinations. In additon, during the analysis of cellular UEs, to derive the coverage probabilities, this paper specially constructs one UE association criterion as well as the derivations of both the association probabilities and the statistical descriptions of association distances for cluster-center and cluster-edge UEs. The simulations results exploit the effect of various network parameters on the network performance and give the insights in terms of the proposed schemes as well as the comparison between cluster-center and cluster-edge UEs. [ABSTRACT FROM AUTHOR]

The study presents spatial analysis of traffic violations in Luzhou city, China. Three metrics of spatial point pattern, namely intensity, spatial correlation, and spacing, are evaluated using (i) kernel density and quadrant count; (ii) K and L functions; and (iii) nearest neighbor and empty-space distance methods, respectively. The results show that: (i) three specific places have a high rate of illegal turning movements, disobeying prohibited signs, and illegal parking violations; (ii) all the violation categories have hot spots, among which 53.49% of the total appear at nine different places; (iii) the spatial correlation discloses the existence of spatial dependence and closeness of similar violations; and (iv) the spacing between traffic violations also signifies clustering of violations. Generally, the spatial patterns of traffic violations are nonuniform, have identifiable hot spots, and are clustered. The findings are beneficial for conceiving safety treatment strategies against traffic violations and additional relevant clustering studies. [ABSTRACT FROM AUTHOR]

The present paper proposes a new version of a model for high cycle fatigue of steels able to take load history effects into account. This model is developed in a probabilistic two‐scale framework. The proposed model accounts not only for the failure of samples under high cycle loadings but also for the thermal effects during cycling in a unified theoretical framework. Thus, an ad hoc identification procedure, essentially based on self‐heating tests under cyclic loadings provided in the accompanying paper, is proposed. The model was then validated by predicting the effect of a pre‐cycling loading on S‐N curves. [ABSTRACT FROM AUTHOR]

In this paper we introduce two new classes of stationary random simplicial tessellations, the so-called $\beta$ - and $\beta^{\prime}$ -Delaunay tessellations. Their construction is based on a space–time paraboloid hull process and generalizes that of the classical Poisson–Delaunay tessellation. We explicitly identify the distribution of volume-power-weighted typical cells, establishing thereby a remarkable connection to the classes of $\beta$ - and $\beta^{\prime}$ -polytopes. These representations are used to determine the principal characteristics of such cells, including volume moments, expected angle sums, and cell intensities. [ABSTRACT FROM AUTHOR]

The hyperbolic random geometric graph was introduced by Krioukov et al. (Phys. Rev. E 82 , 2010). Among many equivalent models for the hyperbolic space, we study the d -dimensional Poincaré ball ( $d\ge 2$), with a general connectivity radius. While many phase transitions are known for the expectation asymptotics of certain subgraph counts, very little is known about the second-order results. Two of the distinguishing characteristics of geometric graphs on the hyperbolic space are the presence of tree-like hierarchical structures and the power-law behaviour of the degree distribution. We aim to reveal such characteristics in detail by investigating the behaviour of sub-tree counts. We show multiple phase transitions for expectation and variance in the resulting hyperbolic geometric graph. In particular, the expectation and variance of the sub-tree counts exhibit an intricate dependence on the degree sequence of the tree under consideration. Additionally, unlike the thermodynamic regime of the Euclidean random geometric graph, the expectation and variance may exhibit different growth rates, which is indicative of power-law behaviour. Finally, we also prove a normal approximation for sub-tree counts using the Malliavin–Stein method of Last et al. (Prob. Theory Relat. Fields 165 , 2016), along with the Palm calculus for Poisson point processes. [ABSTRACT FROM AUTHOR]