scholarly journals Simulation of cluster point processes without edge effects

2002 ◽  
Vol 34 (02) ◽  
pp. 267-280 ◽  
Author(s):  
Anders Brix ◽  
Wilfrid S. Kendall
Keyword(s):  
Edge Effects ◽  
Point Processes ◽  
Direct Method ◽  
A Priori ◽  
Simulation Method ◽  
Observation Window ◽  
Cox Processes ◽  
Cluster Distribution ◽  
Actual Observation ◽  
Parent Point

The usual direct method of simulation for cluster processes requires the generation of the parent point process over a region larger than the actual observation window, since we have to allow for all possible parents giving rise to observed daughter points, and some of these parents may fall outwith the observation window. When there is no a priori bound on the distance between parent and child then we have to take care to control approximations arising from edge effects. In this paper, we present a simulation method which requires simulation only of those parent points actually giving rise to observed daughter points, thus avoiding edge effect approximation. The idea is to replace the cluster distribution by one which is conditioned to plant at least one daughter point in the observation window, and to modify the parent process to have an inhomogeneous intensity exactly balancing the effect of the conditioning. We furthermore show how the method extends to cases involving infinitely many potential parents, for example gamma-Poisson processes and shot-noise G-Cox processes, allowing us to avoid approximation due to truncation of the parent process.

scholarly journals Simulation of cluster point processes without edge effects

2002 ◽  
Vol 34 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Anders Brix ◽  
Wilfrid S. Kendall
Keyword(s):  
Edge Effects ◽  
Point Processes ◽  
Direct Method ◽  
A Priori ◽  
Simulation Method ◽  
Observation Window ◽  
Cox Processes ◽  
Cluster Distribution ◽  
Actual Observation ◽  
Parent Point

The usual direct method of simulation for cluster processes requires the generation of the parent point process over a region larger than the actual observation window, since we have to allow for all possible parents giving rise to observed daughter points, and some of these parents may fall outwith the observation window. When there is no a priori bound on the distance between parent and child then we have to take care to control approximations arising from edge effects. In this paper, we present a simulation method which requires simulation only of those parent points actually giving rise to observed daughter points, thus avoiding edge effect approximation. The idea is to replace the cluster distribution by one which is conditioned to plant at least one daughter point in the observation window, and to modify the parent process to have an inhomogeneous intensity exactly balancing the effect of the conditioning. We furthermore show how the method extends to cases involving infinitely many potential parents, for example gamma-Poisson processes and shot-noise G-Cox processes, allowing us to avoid approximation due to truncation of the parent process.

Cognate Space Identification for Forced Response Structural Redesign

2003 ◽  
Vol 127 (3) ◽  
pp. 227-233
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas
Keyword(s):  
Direct Method ◽  
A Priori ◽  
Normal Modes ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Practical Guidelines ◽  
Structural Redesign ◽  
Large Admissible Perturbations ◽  
Perturbation Equations

Large admissible perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the incremental method (IM) and the direct method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate spaces, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.

scholarly journals Theory of Second Order Numerical Simulation Method of Enhanced Oil Production

2019 ◽  
Vol 11 (2) ◽  
pp. 73
Author(s):  
Yirang Yuan ◽  
Aijie Cheng ◽  
Danping Yang ◽  
Changfeng Li
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Oil Production ◽  
Coupled System ◽  
Simulation Method ◽  
Second Order ◽  
Optimal Order ◽  
Difference Operators ◽  
Order Error ◽  
L2 Norm

A kind of second-order implicit upwind fractional steps finite difference method is presented in this paper to numerically simulate the coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and optimal order error estimates in l2 norm are derived.

Statistical inference for point-process models of rainfall

1984 ◽  
Vol 16 (1) ◽  
pp. 22-22 ◽  
Author(s):  
James A. Smtih ◽  
Alan F. Karr
Keyword(s):  
Parameter Estimation ◽  
Statistical Inference ◽  
Point Processes ◽  
Process Models ◽  
Renewal Processes ◽  
Cox Processes ◽  
The Family ◽  
Point Process Models ◽  
Image Position ◽  
Rainfall Occurrences

In this paper we develop maximum likelihood procedures for parameter estimation and hypothesis testing for three classes of point processes that have been used to model rainfall occurrences; renewal processes, Neyman-Scott processes, and RCM processes (which are members of the family of Cox processes). The statistical inference procedures developed in this paper are based on the intensity process

Determination of Wastewater Accidental Contamination by Antibiotics

2019 ◽  
Vol 7 (5) ◽  
pp. 3-8
Author(s):  
В. Алексеев ◽  
V. Alekseev ◽  
В. Усольцев ◽  
V. Usol'cev ◽  
С. Юран ◽  
...  
Keyword(s):  
Laser Radiation ◽  
Direct Method ◽  
A Priori ◽  
Sewage Treatment ◽  
Control Procedure ◽  
Real Time Control ◽  
Short Period ◽  
Quantitative Characteristics ◽  
Definition Of

The way for solving the task of enterprises sewage treatment from emergency discharge of antibiotics is offered. Emergency discharge of antibiotics into sewage can arise at enterprises of chemical-pharmaceutical and processing industry. Emergency discharge happens in a short period that gives the chance for its detection and utilization into a settler. Standards for emergency discharges have been presented. The main form for detection of antibiotics in water, their kind and concentration identification is analysis of flowing sewage. This analysis includes two elements: obtaining information on the actual existence of antibiotics (their qualitative and quantitative characteristics), and comparison of obtained information with available indicators for the purpose of definition of their compliance. The control procedure includes operations of measurement and identification. Determination of numerical values for indicators of quantitative characteristics is based on information obtained when using technical means of measurements. For the task solution have been considered characteristics of various methods for detection of antibiotics in sewage. Classification of methods according to quantitative and qualitative indicators of sewage on antibiotics existence has been carried out. Have been allocated methods providing the real time control, among which a specific place is occupied by optical-electronic control methods with use of laser radiation. For implementation of real spectroscopy it is offered to use laser radiation with radiation wavelength corresponding to antibiotic range extremes. In such a case, a spectral characteristic of an antibiotic, which can appear in emergency discharge of enterprise’s sewer, is a priori known. For verification of this technical offer an experiment was set up, which had showed a possibility to use a direct method of spectroscopy — translucency on laser radiation’s chosen wavelength for definition of emergency discharge of antibiotic into enterprise’s sewage.

Motion Artifacts Comparision for Subjective and Objective Results

2012 ◽  
Vol 433-440 ◽  
pp. 5349-5353
Author(s):  
Ye Tian ◽  
Tong Sheng Mou ◽  
Hai Yan Xi
Keyword(s):  
Direct Method ◽  
Simulation Method ◽  
Test System ◽  
Statistical Correlation ◽  
Motion Artifacts ◽  
System Structure ◽  
Flat Panel Display ◽  
Flat Panel ◽  
High System ◽  
Homogeneous Good

In this paper, an integrated test system involving direct racking and simulation test systems is presented for evaluate the motion artifacts of flat panel display, to refrain from the high system requirements of direct method and environment limitations of simulation method. And then system structure and operating principle are expatiated and analyzed. Although the testing results are not exactly the same as subjective observing, they are still essentially homogeneous. Good statistical correlation illustrates the value of this study. The work presented here has implications for future contribution to research and measurement of motion artifacts of flat panel display.

scholarly journals Persistence and Equilibria of Branching Populations with Exponential Intensity

2012 ◽  
Vol 49 (1) ◽  
pp. 226-244
Author(s):  
Zakhar Kabluchko
Keyword(s):  
Laplace Transform ◽  
Random Walks ◽  
Point Process ◽  
Poisson Point Process ◽  
Point Processes ◽  
Local Extinction ◽  
Branching Random Walks ◽  
Cluster Distribution

We consider a system of independent branching random walks on R which start from a Poisson point process with intensity of the form eλ(du) = e-λudu, where λ ∈ R is chosen in such a way that the overall intensity of particles is preserved. Denote by χ the cluster distribution, and let φ be the log-Laplace transform of the intensity of χ. If λφ'(λ) > 0, we show that the system is persistent, meaning that the point process formed by the particles in the nth generation converges as n → ∞ to a non-trivial point process Πeλχ with intensity eλ. If λφ'(λ) < 0 then the branching population suffers local extinction, meaning that the limiting point process is empty. We characterize point processes on R which are cluster invariant with respect to the cluster distribution χ as mixtures of the point processes Πceλχ over c > 0 and λ ∈ Kst, where Kst = {λ ∈ R: φ(λ) = 0, λφ'(λ) > 0}.

Advance of Optimization Methods for Identifing Groundwater Pollution Source Porperties

2012 ◽  
Vol 178-181 ◽  
pp. 603-608 ◽  
Author(s):  
Yu Qiao Long ◽  
Wei Li ◽  
Ju Huang
Keyword(s):  
Heuristic Algorithm ◽  
Groundwater Pollution ◽  
Direct Method ◽  
Groundwater Resources ◽  
Field Tests ◽  
Simulation Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Pollution Source ◽  
Groundwater Environment

China has to confront the groundwater resources crisis and the deterioration of groundwater environment. Reinforcing the studies on groundwater pollution source identification (GPSI) could be an important support to contamination removing, groundwater protecting, drinking water security, and development of society and economy. Exploring the new theory and method on GPSI could push the studies on ill-posed problems, and improve the techniques of contamination remediation. GPSI has been studied for thirty years, and a brief review is given to conclude the characteristics of GPSI problems. The mathematical simulation method can be classified into four types: optimization method, analytical and regression method, direct method, and stochastic method. A specific review of optimization approaches is given in this paper. The configuration, simulation procedures, common optimization algorithms used by the optimization methods are discussed in detail. Both non-heuristic and heuristic algorithm can be used to solve the PSI problem. The heuristic algorithm is more suitable for complex numerical and field cases, but it is time-consuming. The non-heuristic algorithm, especially the algorithm combined with analytical method, is time-economical, but is not suitable for complicated numerical and field tests. Further researches may focus on more complex GPSI problems, expressing physical chemistry and biological process, improving efficiency and model uncertainty of GPSI modeling.

Shot noise Cox processes

2003 ◽  
Vol 35 (3) ◽  
pp. 614-640 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Large Class ◽  
Edge Effects ◽  
Shot Noise ◽  
Conditional Simulation ◽  
Intensity Function ◽  
Summary Statistics ◽  
Cox Processes ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Cluster Processes

Shot noise Cox processes constitute a large class of Cox and Poisson cluster processes in ℝd, including Neyman-Scott, Poisson-gamma and shot noise G Cox processes. It is demonstrated that, due to the structure of such models, a number of useful and general results can easily be established. The focus is on the probabilistic aspects with a view to statistical applications, particularly results for summary statistics, reduced Palm distributions, simulation with or without edge effects, conditional simulation of the intensity function and local and spatial Markov properties.

scholarly journals Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications

2009 ◽  
Vol 41 (03) ◽  
pp. 623-646 ◽  
Author(s):  
Bartłomiej Błaszczyszyn ◽  
D. Yogeshwaran
Keyword(s):  
Shot Noise ◽  
Point Processes ◽  
Pair Correlation ◽  
Dependence Structure ◽  
Convex Order ◽  
Random Measures ◽  
Convex Ordering ◽  
Cox Processes ◽  
The Impact ◽  
Directionally Convex Order

Directionally convex ordering is a useful tool for comparing the dependence structure of random vectors, which also takes into account the variability of the marginal distributions. It can be extended to random fields by comparing all finite-dimensional distributions. Viewing locally finite measures as nonnegative fields of measure values indexed by the bounded Borel subsets of the space, in this paper we formulate and study directionally convex ordering of random measures on locally compact spaces. We show that the directionally convex order is preserved under some of the natural operations considered on random measures and point processes, such as deterministic displacement of points, independent superposition, and thinning, as well as independent, identically distributed marking. Further operations on Cox point processes such as position-dependent marking and displacement of points are shown to preserve the order. We also examine the impact of the directionally convex order on the second moment properties, in particular on clustering and on Palm distributions. Comparisons of Ripley's functions and pair correlation functions, as well as examples, seem to indicate that point processes higher in the directionally convex order cluster more. In our main result we show that nonnegative integral shot noise fields with respect to the directionally convex ordered random measures inherit this ordering from the measures. Numerous applications of this result are shown, in particular to comparison of various Cox processes and some performance measures of wireless networks, in both of which shot noise fields appear as key ingredients. We also mention a few pertinent open questions.

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