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# Hexagonal Pixels and Indexing Scheme for Binary Images

Friday, 13 April 2007

For some purposes, this scheme is superior to rectangular pixels.
A scheme for resampling binaryimage data from a rectangular grid to a regular hexagonal grid and an associated tree - structured pixel - indexing scheme keyed to the level of resolution have been devised. This scheme could be utilized in conjunction with appropriate image - data - processing algorithms to enable automated retrieval and/or recognition of images. For some purposes, this scheme is superior to a prior scheme that relies on rectangular pixels: One example of such a purpose is recognition of fingerprints, which can be approximated more closely by use of line segments along hexagonal axes than by line segments along rectangular axes. This scheme could also be combined with algorithms for query - image - based retrieval of images via the Internet.

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# Finding Minimum-Power Broadcast Trees for Wireless Networks

Friday, 13 April 2007

Algorithms for identifying viable trees have been derived.
Some algorithms have been devised for use in a method of constructing tree graphs that represent connections among the nodes of a wireless ommunication network. These algorithms provide for determining the viability of any given candidate connection tree and for generating an initial set of viable trees that can be used in any of a variety of search algorithms (e.g., a genetic algorithm) to find a tree that enables the network to broadcast from a source node to all other nodes while consuming the minimum amount of total power. The method yields solutions better than those of a prior algorithm known as the broadcast incremental power algorithm, albeit at a slightly greater computational cost.

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# Automation of Design Engineering Processes

Friday, 13 April 2007

A method facilitates ISO 9001 compliance and eliminates voluminous, difficult-to-manage paper files.
A method, and a computer program that helps to implement the method, have been developed to automate and systematize the retention and retrieval of all the written records generated during the process of designing a complex engineering system. It cannot be emphasized strongly enough that “all the written records” as used here is meant to be taken literally: it signifies not only final drawings and final engineering calculations but also such ancillary documents as minutes of meetings, memoranda, requests for design changes, approval and review documents, and reports of tests. One important purpose served by the method is to make the records readily available to all involved users via their computer workstations from one computer archive while eliminating the need for voluminous paper files stored in different places. Another important purpose served by the method is to facilitate the work of engineers who are charged with sustaining the system and were not involved in the original design decisions. The method helps the sustaining engineers to retrieve information that enables them to retrace the reasoning that led to the original design decisions, thereby helping them to understand the system better and to make informed engineering choices pertaining to maintenance and/or modifications of the system. The software used to implement the method is written in Microsoft Access. All of the documents pertaining to the design of a given system are stored in one relational database in such a manner that they can be related to each other via a single tracking number. In addition to improving the management of records of the design process, the method can be utilized to improve the design process itself in a number of ways that include the following:

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# Higher-Order Finite Elements for Computing Thermal Radiation

Friday, 13 April 2007

Computationally efficient methods yield close approximations of exact solutions.
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higherorder finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times.One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications.

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# Making the Monte Carlo Approach Easier and Faster

Friday, 13 April 2007

Libraries of random number generators can make implementing Monte Carlo simulations easier.
Originally introduced by Nicholas Metropolis during the Manhattan Project, Monte Carlo methods today have very broad and extensive use in various areas of science and technology. Random number generators (RNGs) are a core part of any Monte Carlo method, having a significant impact on the overall quality and performance of Monte Carlo simulations. Libraries of RNGs can make implementing Monte Carlo simulations much easier and faster. The most important role of high-performance libraries is to provide facilities that can make writing programs simpler, substantially speed up development, and improve program efficiency in terms of performance.

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# Algorithm for Training a Recurrent Multilayer Perceptron

Friday, 13 April 2007

An improved algorithm has been devised for training a recurrent multilayer perceptron (RMLP) for optimal performance in predicting the behavior of a complex, dynamic, and noisy system multiple time steps into the future. [An RMLP is a computational neural network with self-feedback and cross-talk (both delayed by one time step) among neurons in hidden layers]. Like other neural-network-training algorithms, this algorithm adjusts network biases and synaptic-connection weights according to a gradientdescent rule. The distinguishing feature of this algorithm is a combination of global feedback (the use of predictions as well as the current output value in computing the gradient at each time step) and recursiveness. The recursive aspect of the algorithm lies in the inclusion of the gradient of predictions at each time step with respect to the predictions at the preceding time step; this recursion enables the RMLP to learn the dynamics. It has been conjectured that carrying the recursion to even earlier time steps would enable the RMLP to represent a noisier, morecomplex system.

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# System for Better Spacing of Airplanes En Route

Friday, 13 April 2007

Deviations from preferred trajectories can be reduced.
An improved method of computing the spacing of airplanes en route, and software to implement the method, have been invented. The purpose of the invention is to help air-traffic controllers minimize those deviations of the airplanes from the trajectories preferred by their pilots that are needed to make the airplanes comply with miles-in-trail spacing requirements (defined below). The software is meant to be a modular component of the Center-TRACON Automation System (CTAS) (TRACON signifies "terminal radar approach control"). The invention reduces controllers’ workloads and reduces fuel consumption by reducing the number of corrective clearances needed to achieve conformance with specified flow rates, without causing conflicts, while providing for more efficient distribution of spacing workload upstream and across air-traffic-control sectors.

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