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Full-Text Articles in Mathematics

Computing Χ² Values, John F. Dooley, Daniel C. St Clair, William E. Bond Dec 1994

Computing Χ² Values, John F. Dooley, Daniel C. St Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Textbooks and courses on numerical algorithms contain numerous examples which lead students to believe that the algorithm of choice for computing the zeros of a function f1994 is Newton's algorithm. In many of these courses little or no time is spent in providing students with "real world" experiences where Newton's method fails. The work presented in this paper describes a slow convergence problem encountered while trying to use Newton to estimate values for the 2 distributions. The problem occurred while the authors were trying to implement a well-known machine learning algorithm from the field of artificial intelligence. The function being …


Classification Characteristics Of Som And Art2, J. J. Aleshunas, Daniel C. St. Clair, William E. Bond Apr 1994

Classification Characteristics Of Som And Art2, J. J. Aleshunas, Daniel C. St. Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Artificial neural network algorithms were originally designed to model human neural activities. They attempt to recreate the processes involved in such activities as learning, short term memory, and long-term memory. Two widely used unsupervised artificial neural network algorithms are the Self-Organizing Map (SOM) and Adaptive Resonance Theory (ART2). Each was designed to simulate a particular biological neural activity. Both can be used as unsupervised data classifiers. This paper compares performance characteristics of two unsupervised artificial neural network architectures; the SOM and the ART2 networks. The primary factors analyzed were classification accuracy, sensitivity to data noise, and sensitivity of the algorithm …


Using The Id3 Symbolic Classification Algorithm To Reduce Data Density, Barry Fiachsbart, Daniel C. St. Clair, Jeff Holland Apr 1994

Using The Id3 Symbolic Classification Algorithm To Reduce Data Density, Barry Fiachsbart, Daniel C. St. Clair, Jeff Holland

Mathematics and Statistics Faculty Research & Creative Works

Effective data reduction is mandatory for modeling complex domains. The work described here demonstrates how to use a symbolic classifier algorithm from machine learning to effectively reduce large amounts of data. The algorithm, Quirdan's ID3, uses input data records and corresponding classifications to produce a decision tree. The resulting tree can be used to classify previously unseen inputs. Alternatively, the attributes found in the tree can be used as the basis to develop other system modeling techniques such as neural networks or mathematical programming algorithms. This approach has been used to effectively reduce data from a large complex domain. The …


Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley Jan 1994

Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley

Mathematics and Statistics Faculty Research & Creative Works

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." This survey takes a brief look at background information related to harmonics, including their sources, effects, and characteristics. Then, the evolution of the harmonics elimination approaches of current compensation and active filtering, which are becoming more feasible due to research and technological improvements, are discussed in order to give some insight into the directions that research is taking.


Fixed Point Theorems For Non-Self Maps I, Troy L. Hicks, Unda Marie Sauga Jan 1994

Fixed Point Theorems For Non-Self Maps I, Troy L. Hicks, Unda Marie Sauga

Mathematics and Statistics Faculty Research & Creative Works

Suppose f:C→X where C is a closed subset of X. Necessary and sufficient conditions are given for f to have a fixed point. All results hold when X is complete metric space. Several results hold in a much more general setting. © 1994, Hindawi Publishing Corporation. All rights reserved.