Point Process Techniques Research Articles

A machine learning framework for the quantification of experimental uveitis in murine OCT.

This paper presents methods for the detection and assessment of non-infectious uveitis, a leading cause of vision loss in working age adults. In the first part, we propose a classification model that can accurately predict the presence of uveitis and differentiate between different stages of the disease using optical coherence tomography (OCT) images. We utilize the Grad-CAM visualization technique to elucidate the decision-making process of the classifier and gain deeper insights into the results obtained. In the second part, we apply and compare three methods for the detection of detached particles in the retina that are indicative of uveitis. The first is a fully supervised detection method, the second is a marked point process (MPP) technique, and the third is a weakly supervised segmentation that produces per-pixel masks as output. The segmentation model is used as a backbone for a fully automated pipeline that can segment small particles of uveitis in two-dimensional (2-D) slices of the retina, reconstruct the volume, and produce centroids as points distribution in space. The number of particles in retinas is used to grade the disease, and point process analysis on centroids in three-dimensional (3-D) shows clustering patterns in the distribution of the particles on the retina.

Spatial Pattern Simulation of Antenna Base Station Positions Using Point Process Techniques

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.

Spatial point processes and neural networks: A convenient couple

Different spatial point process models and techniques have been developed in the past decades to facilitate the statistical analysis of spatial point patterns. However, in some cases the spatial point process methodology is scarce and no flexible models nor suitable statistical methods are available. For example, due to its complexity, the statistical analysis of spatial point patterns of several groups observed at a number of time instances has not been studied in-depth, and there are a few limited models and methods available for such data. In the present work, we provide a mathematical framework for coupling neural network methods with the statistical analysis of point patterns. In particular, we discuss an example of deep neural networks in the statistical analysis of highly multivariate spatial point patterns and provide a new strategy for building spatio-temporal point processes using variational autoencoder generative neural networks.

Large sample autocovariance matrices of linear processes with heavy tails

We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time. Assuming that the dimension increases with the sample size, we provide theory for the eigenvectors of the sample autocovariance matrices and find explicit approximations of a simple structure, whose finite sample quality is illustrated for simulated data. We also obtain the limits of the normalized eigenvalues of functions of the sample autocovariance matrices in terms of cluster Poisson point processes. In turn, we derive the distributional limits of the largest eigenvalues and functionals acting on them. In our proofs, we use large deviation techniques for heavy-tailed processes, point process techniques motivated by extreme value theory, and related continuous mapping arguments.

Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration

We describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton–Watson processes with regularly varying immigration with tail index α∈(1,2). The limit law is the ratio of two dependent stable random variables with indices α∕2 and 2α∕3, respectively, and it has a continuously differentiable density function. We use point process technique in the proofs.

Stochastic point process applied in aggregates composition for concrete

The objective of this work is to apply a stochastic point process technique in the evaluation of aggregate composition parameters for concrete. Several experimental, numeric and computational methods have been used for determining an ideal packing of aggregates for concrete, based on the principle of the lowest content of voids. Experimental method is quite hard-working. On the other hand, the mathematical and computational models need potent computer and be tested experimentally. Equipment and computational methods have been developed, to provide images of the particle distribution, approaching the actual distribution of aggregates and allowing to obtain ideal aggregates compositions. This work uses a stochastic point process, based on the point processes method, which a simple sequential inhibition (SSI) process on the arbitrary closed region places the particles. The SSI generates image of spherical particles distributions for viewing and checking compliance of parameters of aggregates compositions. The characteristics of aggregates (porosity, granulometry, proportion of each aggregate composition, and specific mass) and the problem’s domain are input data. The SSI’s output data of interest are virtual image of particles distribution, particles composition, porosity of each composition, diameter and number of particles. From SSI’s output data, it can be determined the packing factor and a histogram of particles diameters. This information is evaluated and compared with the input composition. As a result, the stochastic SSI demonstrates to be efficient in comparing the output and experimental data, complying with the purpose of the study.

Error Exponents for Dimension-Matched Vector Multiple Access Channels With Additive Noise

We analyze a class of vector multiple access channels with additive noise, where the sum of the dimensions of the transmitted signals matches that of the received signal. We first focus on the case without power constraints, in the Poltyrev sense, using point process techniques. We find the Poltyrev capacity region for noise processes that are independent and identically distributed over channel uses. For each rate vector strictly in the Poltyrev capacity region, we study, for each subset of the transmitters, the exponent of the decay in block length of the smallest possible probability that decoding results in error for each transmitter in that subset. In the case of independent and identically distributed Gaussian noise, with arbitrary positive definite covariance matrix, we derive random coding exponents for each type of error event—these are lower bounds to the true error exponents. This also leads to random coding error exponents in the traditional power-constrained case, where the power constraint at each transmitter is defined by an arbitrary positive definite matrix.

A Stochastically Geometrical Poisson Point Process Approach for the Future 5G D2D Enabled Cooperative Cellular Network

Due to recent developments in the cellular communication system, stochastic process implementation is necessary. The cellular communication system exhibits random patterns in various domains, thereby compelling the utilization of stochastic processes to achieve an optimal output. User behaviors with respect to the variable geographical pattern, population density, architecture, data usage, and mobility over various cells are random in nature. Therefore, the stochastic-geometry-based Poisson point process (PPP) technique can be implemented to accurately analyze these random processes in device-to-device (D2D)-based cooperative cellular networks. The stochastic modeling entails the consideration of transmitters and receivers as the elements of stochastic point processes. The hexagonal method is not applicable for the implementation of heterogeneous network topologies, as it is not suitable for topologies, in which the cell size is not fixed. Therefore, a randomly designed heterogeneous network uses stochastic geometry as a viable solution for predicting the probabilistic parameters, including the cell interference, load distribution, coverage probability, base station (BS) mapping, and signal-to-interference-plus-noise ratio (SINR). Moreover, as a network architecture that is based on relay nodes (RNs), cellular and D2D users can be utilized in the domain of homogeneous random models. The associated phenomenon can be considered independent and Poisson. In this paper, the stochastic-geometric-based PPP approach is introduced for modeling the SINR, success probability, ergodic capacity, and outage probability for the D2D-enabled cooperative cellular network. The proposed PPP realistic model utilizes BS, RN, the cellular user (CU), and D2D user positioning method to design an interference-free network. The success probability, ergodic capacity, and outage probability for cellular and D2D users are used as metrics for evaluating the results with respect to various SINR threshold values and node densities. Moreover, the total success probability, ergodic capacity, and outage probability have been calculated for various multiple-input-multiple-output (MIMO) antenna configurations to validate the results. The results confirmed that the proposed PPP model approach outperforms the grid model and conventional multi-antenna ultra-dense network (UDN) approaches.

3D modelling of the Excavation Damaged Zone using a Marked Point Process technique

The Excavation Damage Zone (EDZ) is a key aspect in the assessment of engineering feasibility and long-term safety of deep geological repositories for radioactive waste. The EDZ represents a possible release path for radionuclides dissolved in the porewater and for gases from corrosion and degradation processes which needs to be addressed quantitatively in Safety Assessment (SA). The EDZ is often represented by a discrete fracture network, whose complexity precludes its implementation in conventional SA models. To overcome this problem, two-dimensional abstraction methodologies have been developed that replace the complex geometry of the discrete fracture network by a hydraulically equivalent continuum model. Although such simple 2D models are amenable to SA modelling, they cannot capture the inherent three-dimensional and stochastic nature of the phenomena associated with the EDZ. In this paper we present a methodology based on Marked Point Processes to infer 3D stochastic continuum models of the EDZ from 2D discrete characterizations of the fracture network. The methodology is illustrated with the calibration of a multi-rate injection experiment in Mont Terri (Switzerland).

Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances

Structural characteristics of random field threshold exceedance sets (e.g., size, connectivity, and boundary regularity) are used in practice for definition of different indicators in spatial and spatio-temporal risk analysis. In this work, point process techniques are applied to study the structural changes derived from random field deformations and blurring transformations, meaningful from both physical and methodological points of view in a variety of contexts. Specifically, based on simulations from a flexible random field model class, features such as aggregation/inhibition of patterns defined by centroids of connected components, as well as by boundary A-exit points, are investigated in relation to the local contraction/dilation effects of deformation and the smoothing properties of blurring. Supplementary materials accompanying this paper appear online.

Closed-Form Approximations for Optimal (r,q) and (S,T) Policies in a Parallel Processing Environment

We consider a single-item continuous-review (r,q) inventory system with a renewal demand process and i.i.d. stochastic leadtimes. Using a stationary marked point process technique and a heavy traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy traffic limit, the first of their kind to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S,T) systems with constant leadtimes.

Reconstructing the reproductive mode of an Ediacaran macro-organism.

Enigmatic macrofossils of late Ediacaran age (580-541 million years ago) provide the oldest known record of diverse complex organisms on Earth, lying between the microbially dominated ecosystems of the Proterozoic and the Cambrian emergence of the modern biosphere. Among the oldest and most enigmatic of these macrofossils are the Rangeomorpha, a group characterized by modular, self-similar branching and a sessile benthic habit. Localized occurrences of large in situ fossilized rangeomorph populations allow fundamental aspects of their biology to be resolved using spatial point process techniques. Here we use such techniques to identify recurrent clustering patterns in the rangeomorph Fractofusus, revealing a complex life history of multigenerational, stolon-like asexual reproduction, interspersed with dispersal by waterborne propagules. Ecologically, such a habit would have allowed both for the rapid colonization of a localized area and for transport to new, previously uncolonized areas. The capacity of Fractofusus to derive adult morphology by two distinct reproductive modes documents the sophistication of its underlying developmental biology.

Proposed 4D GIS for predicting the trend of housing construction in urban areas: application for District 5, Ho Chi Minh city

In this paper, the model of house building in the future will be presented by the 4D GIS, 3D in space and temporal. By mining the building stage 2001-2010 and lidar data in the District 5th of HoChiMinh city, the expecting trend of building is built by combinning some analyses such as point process techniques, Markov, timeseries. By this method, building house points will be generated temporally by the statistical random generating method and the trend in changing will controlled by the factors from timeseries analysing. And the geometric model for house is employed just the level of detail 1 (LOD1), block of house.

Galaxy pairs align with Galactic filaments

Context. Gravitational collapse theory and numerical simulations suggest that the velocity field within large-scale galaxy filaments is dominated by motions along the filaments. Aims. Our aim is to check whether observational data reveal any preferred orientation of galaxy pairs with respect to the underlying filaments as a result of the expectedly anisotropic velocity field. Methods. We use galaxy pairs and galaxy filaments identified from the Sloan Digital Sky Survey data. For filament extraction, we use the Bisous model that is based the marked point process technique. During the filament detection, we use the centre point of each pair instead of the positions of galaxies to avoid a built-in influence of pair orientation on the filament construction. For pairs lying within filaments (3012 cases), we calculate the angle between the line connecting galaxies of each pair and their host filament. To avoid redshift-space distortions, the angle is measured in the plain of the sky. Results. The alignment analysis shows that the orientation of galaxy pairs correlates strongly with their host filaments. The alignment signal is stronger for loose pairs, with at least 25% excess of aligned pairs compared to a random distribution. The alignment of galaxy pairs and filaments measured from the observational data is in good concordance with the alignment in the Millennium simulation and thus provides support to the {\Lambda}CDM formalism.

A micro spatial analysis of firm demography: the case of food stores in the area of Trento (Italy)

The potential offered by the increasing availability of micro-geographic data is tremendous and still largely not exploited. In this paper, we propose a new methodology to study the spatial dynamics of firm demography making use of such rich source of information. Exploiting the techniques of stochastic spatial point processes (Diggle, Statistical analysis of spatial point patterns, 2003), it is indeed possible to model the firm birth, growth and death explaining the behavior of the individual economic agent. We consider the spatial distribution of the economic activities as the result of a dynamic process occurring in space and time, and we model the micro-spatial patterns as single realizations of marked space–time survival point processes (Rathbun and Cressie, J Am Stat Assoc 89:1164–1174, 1994). Within such a methodological framework firms are created at some random location and some point of time and then operate, grow, and attract (or repulse) the localization of other firms in their neighborhood. The proposed model is fitted to some empirical data on firms’ locations sourced from the ASIA harmonised archive of the Italian National Institute of Statistics. The empirical analysis reveals the presence of local competition behavior in firm creation among small retail food stores, thus shedding light on the phenomena of firm demography.

Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter

Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimates for the autocorrelation parameter f and the unknown location parameter θ by taking the ratio of two sample values chosen with respect to an extreme value criteria for f and by taking the minimum of over the observed series, where represents our estimate for f. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.

Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations

We study the first-order bifurcating autoregressive process X t = ϕ X ⌊ t / 2 ⌋ + ϵ t with Weibull innovations. Using point process technique, we estimate the model parameter ϕ and the tail index α in the Weibull distribution and obtain the joint limit distribution of estimators.

Stochastic analysis of a two-unit cold standby system with two-stage repair and waiting time

In this study we investigated the cost-benefit analysis of a two-unit cold standby system with two-stage repair of a failed unit. We discuss the concept of waiting time with two-stage repair for a two-unit cold standby system. The repair process is divided into two stages. In the first stage, the repairing process of the unit is started but it does not get completed; instead the process is completed in the second stage. The elapsed time between two stages is called the waiting time. Techniques of regenerative point processes have been used to measure the effectiveness. The time dependent availability, steady state availability, reliability, (MTTF) and profit function were obtained numercially and graphically. The MTTF, the steady-state availability and the profit function decreased with respect to the increase of failure rate and waiting rate.

Oil spill detection from SAR intensity imagery using a marked point process

Abstract This paper presents a new algorithm for the detection of oil spill from SAR intensity images. The proposed algorithm combines the marked point process, Bayesian inference and Markov Chain Monte Carlo (MCMC) technique. In this paper, the candidates of oil spills or dark spots in a SAR intensity image are characterized by a Poisson marked point process. The marked point process is formed by a group of random points (as a point process modelling the locations of oil spills) and a set of parameters including geometric parameters of windows centred at the random points and gamma distribution parameters (as the marks attaching to each point). As a result, the candidates of oil spills are represented by a group of windows, in which the intensities of pixels follow independent and identical gamma distribution with lower mean than that for the identical gamma distribution of the pixels out of windows. Following the Bayesian paradigm, the posterior distribution, which characterizes the locations and statistical distributions of oil spills, can be obtained up to a normalizing constant. In order to simulate from the posterior distribution and to estimate the parameters of the posterior distribution, the Revisable Jump MCMC (RJMCMC) algorithm is used. The optimal locations and sizes of dark spots are obtained by a maximum a posteriori (MAP) algorithm. The proposed approach is tested using Radarsat-1 SAR images with oil spills indicated by human analysts. The results show that the proposed approach works well and is very promising.

Stochastic Behavior of a Two-Unit Warm Standby System with Two Types of Repairmen and Patience Time

Problem statement: In this study we investigated the probabilistic analysis of a two-unit warm standby system with constant failure rate and two types of repairmen and patience time. The first repairman, usually called regular repairman, always remained with the repair facility, with the known fact that he might not be able to do some complex repairs within some tolerable (patience) time. An expert repairman was called for the system if and only if the regular repairman is unable to do the job, within some fixed time or on system failure, whichever occurs first. Approach: Techniques of regenerative point processes had been used to measure the system effectiveness Results: The time-dependent availability, steady-state availability, reliability, (MTTF) and profit function were obtained numerically and graphically. Conclusion: The availability and profit decreased with respect to the increase of failure rate.