General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function

We present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. This generalization expresses the exact solutions for general-relativistic self-gravitating N-body systems in one spatial and one time dimension, and a previously unknown mathematical link between the (1+1) gravity problem and the Schrödinger wave equation.     

A GENERALIZED APPROACH TO MODELING THE HIERARCHICAL MAXIMAL COVERING LOCATION PROBLEM WITH REFERRAL

ABSTRACT Several investigators have developed hierarchically structured maximal covering location problems, especially for hierarchies with two levels such as clinics and hospitals: Moore and ReVelle developed and applied a hierarchical covering model to a medical service delivery problem in Houduras; and Church and Falon developed two alternate model forms of hierarchical covering that were applied to a medical services planning, problem in Colombia. In this paper, we proposed a hybrid formulation that encompasses all three of these previous models and which allows for the trade-off of up of four different objectives. This new model formulation is also an improvement in that it has a significantly more efficient and compact structure, even while encompassing a more complete location problem, of which the three previous works are special cases. Example solutions are given for two different data sels involving regions in Colombia and Uganda. In addition, two further model formulations of a closely related nature are presented without computational results.     

Detection of sudden pedestrian crossings for driving assistance systems

In this paper, we study the problem of detecting sudden pedestrian crossings to assist drivers in avoiding accidents. This application has two major requirements: to detect crossing pedestrians as early as possible just as they enter the view of the car-mounted camera and to maintain a false alarm rate as low as possible for practical purposes. Although many current sliding-window-based approaches using various features and classification algorithms have been proposed for image-/video-based pedestrian detection, their performance in terms of accuracy and processing speed falls far short of practical application requirements. To address this problem, we propose a three-level coarse-to-fine video-based framework that detects partially visible pedestrians just as they enter the camera view, with low false alarm rate and high speed. The framework is tested on a new collection of high-resolution videos captured from a moving vehicle and yields a performance better than that of state-of-the-art pedestrian detection while running at a frame rate of 55 fps.     

Stock trading strategy creation using GP on GPU

This paper investigates the speed improvements available when using a graphics processing unit (GPU) for evaluation of individuals in a genetic programming (GP) environment. An existing GP system is modified to enable parallel evaluation of individuals on a GPU device. Several issues related to implementing GP on GPU are discussed, including how to perform tree-based GP on a device without recursion support, as well as the effect that proper memory layout can have on speed increases when using CUDA-enabled nVidia GPU devices. The specific GP implementation is designed to evolve stock trading strategies using technical analysis indicators. The second goal of this research is to investigate the possible improvement in performance when training individuals on a larger number of stocks and training days. This increased training size (nearly 100,000 training points) is enabled due to the speedups realized by GPU evaluation. Several different scenarios were used to test various speed optimizations of GP evaluation on the GPU device, with a peak speedup factor of over 600 (when compared to sequential evaluation on a 2.4 GHz CPU). Also, it is found that increasing the number of stocks and the length of the training period can result in higher out-of-training testing profitability.     

Mining the change of customer behavior in fuzzy time-interval sequential patterns

Comprehending changes of customer behavior is an essential problem that must be faced for survival in a fast-changing business environment. Particularly in the management of electronic commerce (EC), many companies have developed on-line shopping stores to serve customers and immediately collect buying logs in databases. This trend has led to the development of data-mining applications. Fuzzy time-interval sequential pattern mining is one type of serviceable data-mining technique that discovers customer behavioral patterns over time. To take a shopping example, (Bread, Short, Milk, Long, Jam), means that Bread is bought before Milk in a Short period, and Jam is bought after Milk in a Long period, where Short and Long are predetermined linguistic terms given by managers. This information shown in this example reveals more general and concise knowledge for managers, allowing them to make quick-response decisions, especially in business. However, no studies, to our knowledge, have yet to address the issue of changes in fuzzy time-interval sequential patterns. The fuzzy time-interval sequential pattern, (Bread, Short, Milk, Long, Jam), became available in last year; however, is not a trend this year, and has been substituted by (Bread, Short, Yogurt, Short, Jam). Without updating this knowledge, managers might map out inappropriate marketing plans for products or services and dated inventory strategies with respect to time-intervals. To deal with this problem, we propose a novel change mining model, MineFuzzChange, to detect the change in fuzzy time-interval sequential patterns. Using a brick-and-mortar transactional dataset collected from a retail chain in Taiwan and a B2C EC dataset, experiments are carried out to evaluate the proposed model. We empirically demonstrate how the model helps managers to understand the changing behaviors of their customers and to formulate timely marketing and inventory strategies.     

Nonmonotonic behavior of the maximum collapse pressure in a cavitation bubble

Calculations which are relevant to the determination of the maximum collapse pressure generated inside a microbubble as a function of peak pressure in the driving ultrasonic pulse are presented. It is found that above the threshold for transient cavitation, the maximum collapse pressure has a nonmonotonic variation. This result is explained on the basis of phase differences between the external applied acoustic pulse and the resulting bubble response.     

Vinyl bottle performance with the addition of vinyl bottle flake

The effect of adding recycled vinyl bottle flake to virgin bottle compound has been studied. Vinyl bottles contains 10 to 50% recycled vinyl bottle flake were produced on a Bekum extrusion blow molding machine. The performance properties of the vinyl bottles were evaluated, and the optimum level of recycled flake was determined.