Unknown Endpoints Research Articles

Parallel Implementation of the Deterministic Ensemble Kalman Filter for Reservoir History Matching

In this paper, the deterministic ensemble Kalman filter is implemented with a parallel technique of the message passing interface based on our in-house black oil simulator. The implementation is separated into two cases: (1) the ensemble size is greater than the processor number and (2) the ensemble size is smaller than or equal to the processor number. Numerical experiments for estimations of three-phase relative permeabilities represented by power-law models with both known endpoints and unknown endpoints are presented. It is shown that with known endpoints, good estimations can be obtained. With unknown endpoints, good estimations can still be obtained using more observations and a larger ensemble size. Computational time is reported to show that the run time is greatly reduced with more CPU cores. The MPI speedup is over 70% for a small ensemble size and 77% for a large ensemble size with up to 640 CPU cores.

Erratum to "Detecting Curves with Unknown Endpoints and Arbitary Topology Using Minimal Paths"

The authors of Detecting Curves with Unknown Endpoints and Arbitrary Topology Using Minimal Paths which appeared in the October 2012 issue of this journal point out and correct an error that occurred in equation (14) of the paper.

Analysis of Interval-Censored Data with Random Unknown End Points: An Application to Soft Error Rate Estimation

Summary The paper presents a Bayesian approach to analysing interval-censored data with random unknown end points. Such data occur when the event of interest is interval censored but, because of the measurement process, the interval end points are not known exactly. Modelling the measurement process permits inference that accounts for this source of variability. Our results are motivated by an experimental study that was designed to characterize the cosmic-ray–neutron-induced soft error rate of a semiconductor device.

Detecting Curves with Unknown Endpoints and Arbitrary Topology Using Minimal Paths

Existing state-of-the-art minimal path techniques work well to extract simple open curves in images when both endpoints of the curve are given as user input or when one input is given and the total length of the curve is known in advance. Curves which branch require even further prior input from the user, namely, each branch endpoint. In this work, we present a novel minimal path-based algorithm which works on much more general curve topologies with far fewer demands on the user for initial input compared to prior minimal path-based algorithms. The two key novelties and benefits of this new approach are that 1) it may be used to detect both open and closed curves, including more complex topologies containing both multiple branch points and multiple closed cycles without requiring a priori knowledge about which of these types is to be extracted, and 2) it requires only a single input point which, in contrast to existing methods, is no longer constrained to be an endpoint of the desired curve but may in fact be ANY point along the desired curve (even an internal point). We perform quantitative evaluation of the algorithm on 48 images (44 pavement crack images, 1 catheter tube image, and 3 retinal images) against human supplied ground truth. The results demonstrate that the algorithm is indeed able to extract curve-like objects accurately from images with far less prior knowledge and less user interaction compared to existing state-of-the-art minimal path-based image processing algorithms. In the future, the algorithm can be applied to other 2D curve-like objects and it can be extended to detect 3D curves.

Estimation of Message Source and Destination From Network Intercepts

We consider the problem of estimating the endpoints (source and destination) of a transmission in a network based on partial measurement of the transmission path. Possibly asynchronous sensors placed at various points within the network provide the basis for endpoint estimation by indicating that a specific transmission has been intercepted at their assigned locations. During a training phase, test transmissions are made between various pairs of endpoints in the network and the sensors they activate are noted. Sensor activations corresponding to transmissions with unknown endpoints are also observed in a monitoring phase. A semidefinite programming relaxation is used in conjunction with the measurements and linear prior information to produce likely sample topologies given the data. These samples are used to generate Monte Carlo approximations of the posterior distributions of source/destination pairs for measurements obtained in the monitoring phase. The posteriors allow for maximum a posteriori (MAP) estimation of the endpoints along with computation of some resolution measures. We illustrate the method using simulations of random topologies

Maximum Likelihood Estimation for the 4-Parameter Beta Distribution

This paper addresses the problem of obtaining maximum likelihood estimates for the parameters of the Pearson Type I distribution (beta distribution with unknown end points and shape parameters). Since they do not seem to have appeared in the literature, the likelihood equations and the information matrix are derived. The regularity conditions which ensure asymptotic normality and efficiency are examined, and some apparent conflicts in the literature are noted. To ensure regularity, the shape parameters must be greater than two, giving an (assymmetrical) bell-shaped distribution with high contact in the tails. A numerical investigation was carried out to explore the bias and variance of the maximum likelihood estimates and their dependence on sample size. The numerical study indicated that only for large samples (n ≥ 1000) does the bias in the estimates become small and does the Cramer-Rao bound give a good approximation for their variance. The likelihood function has a global maximum which corresponds to ...

The Optimal Cross-Sectional Shape of a Thin-Walled Composite Tube for Maximizing Torsional Rigidity*

ABSTRACT ABSTRACT In this paper the optimal cross-sectional shape of a thin-walled composite tube for maximum torsional rigidity is studied. Optimality conditions are presented, using variational principles. Due to unknown end points, transver-sality conditions are used to find boundary conditions. It is shown that a circular section is the optimal shape for a tube with helically-wound reinforced composite material. For an orthotropic tube, the optimal shape is found to be C continuous only for cases in which the degree of orthotropism is less than or equal to a critical value. Otherwise, the optimal shape contains cusps at the end points.

Concavity of the Log Likelihood

Abstract For a very general regression model with an ordinal dependent variable, the log likelihood is proved concave if the derivative of the underlying response function has concave logarithm. For a binary dependent variable, a weaker condition suffices, namely, that the response function and its complement each have concave logarithm. The normal, logistic, sine, and extreme-value distributions, among others, satisfy the stronger condition, the t (including Cauchy) distributions only the weaker. Some converses and generalizations are also given. The model is that which arises from an ordinary linear regression model with a continuous dependent variable that is partly unobservable, being either grouped into intervals with unknown endpoints, or censored, or, more generally, grouped in some regions, censored in others, and observed exactly elsewhere.

Concavity of the Log Likelihood

Abstract For a very general regression model with an ordinal dependent variable, the log likelihood is proved concave if the derivative of the underlying response function has concave logarithm. For a binary dependent variable, a weaker condition suffices, namely, that the response function and its complement each have concave logarithm. The normal, logistic, sine, and extreme-value distributions, among others, satisfy the stronger condition, the t (including Cauchy) distributions only the weaker. Some converses and generalizations are also given. The model is that which arises from an ordinary linear regression model with a continuous dependent variable that is partly unobservable, being either grouped into intervals with unknown endpoints, or censored, or, more generally, grouped in some regions, censored in others, and observed exactly elsewhere.

On tests of uniformity

Let X1,…,Xn be independent observations from a distribution on the interval (a,b). Fur each of three types of nonuniformity, we consider tests of uniformity (a and b known) designed to detect alternatives of that type. The types of nonuniformity are (i) U-shaped, (ii) unimodal symmetric or nearly symmetric, and (iii) nonsymmetric distributions that have decreasing density or that are unimodal with mode close to a. A Monte Carlo power study is given. The application to testing the distributional hypothesis of exponentiality against specific types of nonexponentiality is discussed. An easy extension of tests of uniformity to the case of unknown endpoints is pointed out; and an investigation of power properties, including a Monte Carlo study, is given.

The use of splines with unknown end points in the identification of systems

The use of splines with unknown end points in the identification of systems