On the best location of signal detectors

An event may occur anywhere in a planar area or on a linear region such as a route. One or more detectors are to be located within this region with the objective of maximizing the smallest probability of the detection of an event anywhere in the region. In other words, the minimum protection in the region is to be maximized. The probability that an event is detected by a detector is a decreasing function of the distance. For example, the probability may decrease with some power (say, 2) of distance, or this decrease could be approximately exponential with distance. Two solution procedures are proposed for the problem on a line segment: a mathematical programming model and a specially designed algorithm. The problem in an area is solved by a univariate search, a Demjanov-type algorithm, a mathematical programming model, and simulated annealing. Computational experience is reported.     

CUMULATIVE DAMAGE UNDER TWO LEVEL CYCLING: SOME THEORETICAL PREDICTIONS AND TEST DATA

Abstract— Predictions of a new cumulative damage theory established by Hashin and Rotem (HR) are compared with an extensive series of test data for two-level shear strain cycling and a double linear exponential damage rule, all given by Miller and Zachariah (MZ), demonstrating good agreement. While MZ requires determination of two parameters to assess crack development by fit to the two level test data the only testing parameter needed for HR is the fatigue lifetime N_e beyond which the fatigue limit occurs. This parameter has here been estimated on the basis of recent advances in understanding cyclic deformation.     

REPLACEMENT OF TECHNOLOGY WHEN A NEW TECHNOLOGICAL BREAKTHROUGH IS EXPECTED

A replacement problem is presented in which two technologies are involved. One technology is immediately available while the second, considered a technological breakthrough, is expected at some uncertain time in the future. The technological environment is dynamic. Therefore, special attention is given to the availability and reliability of data. Decision horizon stopping rules are suggested when long time horizons are considered. The algorithm is different from currently known standard procedures. It does not rely on the monotonicity properties of the optimal solution that occur when the horizon is extended, nor on action elimination considerations based on non-homogeneous Markov decision analysis. Rather, a special procedure is suggested in which an auxiliary problem binds the solution of the original problem. Interrelationships between the two problems lead to the desired horizon results. The procedure detects much shorter forecast horizons than the Bess and Sethi (1988) procedure without increasing the computational effort needed.     

Modelling the application of adaptive optics to wide-field microscope live imaging

Wide‐field fluorescence microscopy is an essential tool in modern cell biology. Unfortunately the image quality of fluorescence microscopes is often significantly degraded due to aberrations that occur under normal imaging conditions. In this article, we examine the use of adaptive optics technology to dynamically correct these problems to achieve close to ideal diffraction limited performance. Simultaneously, this technology also allows ultra‐rapid focusing without having to move either the stage or the objective lens. We perform optical simulations to demonstrate the degree of correction that can be achieved.