Statistics and Probability Commons^™

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 …

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 …

Generating Indexing Functions Of Regularly Sparse Arrays For Array Compilers, Scott Thibault, Lenore Mullin, Matt Insall

Computer Science Technical Reports

There are many applications involving arrays that contain non-zero components in regular geometric partitions. These include triangular, diagonal, tridiagonal, banded, etc. When computing with this type of arrays, they are usually stored in a packed form and computations are performed with only the non-zero components. This packed form requires an indexing function that maps an index of the array to an index of the packed lexico-graphically stored array. This paper presents a method of describing regular partitions and of automatically generating an indexing function from that description. These methods enable an array compiler to compile array operations on these type …

Conjugating Polynomials On Finite Rings, M. Insall, L. Mullin, R. Wilkerson

Computer Science Technical Reports

No abstract provided.

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

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.

Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho

Mathematics and Statistics Faculty Publications

Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.

Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We describe a class of measurable subsets Ω in R^d such that L²(Ω) has an orthogonal basis of frequencies e_λ(x) = e^i2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ R^d. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L²(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …

Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim

Mathematical Sciences Technical Reports (MSTR)

To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use.

Dynamic Id3: A Symbolic Learning Algorithm For Many-Valued Attribute Domains, Roger Gallion, Chaman Sabharwal, Daniel C. St. Clair, William E. Bond

Computer Science Faculty Research & Creative Works

Quinlan's ID3 machine learning algorithm induces classification trees (rules) from a set of training examples. The algorithm is extremely effective when training examples are composed of attributes whose values are taken from small discrete domains. The classification accuracy of ID3-produced trees on domains whose attributes are many-valued tends to be marginal due to the large number of possible values which may be associated with each attribute. Attempts to solve this problem by a priori grouping of attribute values into distinct subsets has met with limited success. The dynamic ID3 algorithm improves the performance of ID3 on this type of problem …

Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito

Mathematics and Statistics Faculty Publications

A mathematical model is developed for the new nondestructive optical technique called laser-beam-induced currents (LBIC), which can be used to detect electrically active regions and defects in semiconductors. The wellposedness of the model equations is shown, and an approximate model that simplifies the numerical implementation of the identification problem is obtained. Some numerical results are presented to show that the approximate model preserves the significant features that the LBIC technique has been experimentally shown to possess.

The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer

Mathematics and Statistics Faculty Publications

We study the group of all ''R-automorphisms'' of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R. A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for R-automorphisms. Finally we show that this group always contains copies of free …

Feasibility Test Verification Method For Nonsymmetric Release Time Task Scheduling, R. G. Karl, T. L. Lo, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

This paper discusses problems associated with scheduling periodic task on a uniprocessor in a hard, real-time processing environment using a static-priority, preemptive-resume operating system. Task sets containing a single periodic task with two Ned release periocis of unequal length are examined. Ihe nonsymmetric scheduling algorithm is based on the rate monotonic scheduling algorithm which assigns higher task priorities to tasks with shorter release periods. me effects on processor utilization using two dirkrent priority assignment schemes are examined; one with task priorities sorted by the average release periods and the other with priorities sorted using the short nonsymmetric task period with …

Fixed Points For Pairs Of Mappings In D-Complete Topological Spaces, Troy L. Hicks, B. E. Rhoades

Mathematics and Statistics Faculty Research & Creative Works

Several important metric space fixed point theorems axe proved for a large class of non-metric spaces. In some cases, the metric space proofs need only minor changes. This is surprising since the distance function used need not be symmetric and need not satisfy the triangular inequality. © 1993, Hindawi Publishing Corporation. All rights reserved.

The Next Linear Collider Test Accelerator, R. D. Ruth, C. Adolphsen, K. Bane, R. F. Boyce, D. L. Burke, R. Calin, G. Caryotakis, R. Cassel, Stephen L. Clark, H. Deruyter, K. Fant, R. Fuller, S. Heifets, H. Hoag, R. Humphrey, S. Kheifets, R. Koontz, N. M. Kroll, R. T. Lavine, G. A. Loew, A. Menegat, R. H. Miller, C. Nantista, J. M. Patterson, C. Pearson, R. Phillips, J. Rifkin, J. Spencer, S. Tantawi, K. A. Thompson, A. Vlieks, V. Vylet, J. W. Wang, P. B. Wilson, A. Yeremian, B. Youngman

Mathematics and Statistics Faculty Research & Creative Works

During the past several years, there has been tremendous progress on the development of the RF system and accelerating structures for a Next Linear Collider (NLC). Developments include high-power klystrons, RF pulse compression systems and damped/detuned accelerator structures to reduce wakefields. In order to integrate these separate development efforts into an actual X-band accelerator capable of accelerating the electron beams necessary for an NLC, we are building an NLC Test Accelerator (NLCTA). The goal of the NLCTA is to bring together all elements of the entire accelerating system by constructing and reliably operating an engineered model of a high-gradient linac …

On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Mathematics Faculty Publications

The existence of bounded solutions and periodic solutions is studied for a system of infinite delay integral equations having nonlinear perturbations. An equivalent system of equations is obtained in terms of the resolvent kernel. Then the existence results are shown for the equivalent equations. Contraction principle, Schauder’s fixed point theorem, and monotone method are used in the study.

Prediction Intervals Based On Partial Observations For Some Discrete Distributions, Lee J. Bain, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

Prediction limits of the following type are considered for the binomial, hypergeometric, and negative-binomial distributions. For the binomial distribution, suppose Xr successes have occurred in the first r trials, and based on this partial information it is desired to predict the total number of successes Xs (r < s), which will have occurred by trial s. Similar results are considered for the Poisson and negative-binomial distributions. The results are expressed in terms of well-known distributions which have been tabulated, but it is quite tedious to carry out the procedures based on available tables. Normal (Gaussian) approximations are provided which makes these methods convenient to apply. © 1993 IEEE

Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

On The Positive Solutions Of The Matukuma Equation, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Computational Problems With Binomial Failure Rate Model And Incomplete Common Cause Failure Reliability Data, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In estimating the reliability of a system of components, it is ordinarily assumed that the component lifetimes are independently distributed. This assumption usually alleviates the difficulty of analyzing complex systems, but it is seldom true that the failure of one component in an interactive system has no effect on the lifetimes of the other components. Often, two or more components will fail simultaneously due to a common cause event. Such an incident is called a common cause failure (CCF), and is now recognized as an important contribution to system failure in various applications of reliability. We examine current methods for …

Pseudobases In Direct Powers Of An Algebra, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A subset P of an abstract algebra A is a pseudobasis if every function from P into A extends uniquely to an endomorphism on A. A is called K-free has a pseudobasis of cardinality K; A is minimally free if A has a pseudobasis. (The 0-free algebras are "rigid" in the strong sense; the 1-free groups are always abelian, and are precisely the additive groups of E-rings.) Our interest here is in the existence of pseudobases in direct powers A^I of an algebra A. On the positive side, if A is a rigid …

Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

The identifiability of defects in a semiconductor from its laser-beam-induced current (LBIC) image is studied. It is shown that the LBIC technique is reliable for detecting any spatial defects in the semiconductor material. Continuous dependence of the current measurements on the spatial defects is proved, and sensitivity is also discussed in certain cases.

The Management Of Replicated Data, Hsueh-Chi Shih, C. Y. Ho, S. Alptekin

Computer Science Technical Reports

Data replication, which has the benefits of improving system availability and read performance, proved to be indispensable to many database applications. In a replicated database, the one-copy serializability of transaction executions can be ensured by employing a replica control mechanism on top of the traditional concurrency control mechanism. This work contains two replica control algorithms and a read-only transaction processing algorithm. Both replica control algorithms handle multiple site, communication and partitioning failures. The replica control algorithms achieve read operation efficiency by always translating a logical read operation into one local physical read operation and by taking advantage of the locality …

An Animation System For Shift Reduce Parsers, M. S. Mandl, T. J. Sager, D. C. St. Clair

Computer Science Technical Reports

This paper presents the design and implementation of the Parse Display Utility (POU) system. This system introduces a mechanism to augment traditional methods of exploring parsing theory by providing a PRESENTATION scheme which allows a user to view the operation of a shift-reduce parser.

The overall operation of the tool revolves around an LALR (LookAhead LR) parser/parser generator and is managed by a Graphical User-Interface (GUI) developed using Borland's Turbo Vision product. The GUI allows access to a facility which draws derivation trees in Turbo Pascal graphics. This parse tree facility utilizes an algorithm which can easily be ported to …

Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch

Mathematics and Statistics Faculty Publications

Inverse problems arising from the identification of transistor contact resistivity and contact window location are studied. A one-point boundary measurement of the potential is shown to be sufficient to identify each from a one-parameter monotone family, and such identification is both stable and continuously dependent on the parameter. For a nonmonotone family of locations with resistivity given, similar results are obtained for measurement made on almost all boundary points.

Effects Of Nonsymmetric Release Times On Rate Monotonic Scheduling, R. G. Karl, T. L. Lo, D. C. St. Clair

Computer Science Technical Reports

This paper discusses problems associated with scheduling periodic tasks in a hard, real-time processing or computing environment using a static-priority, preemptive-resume operating system . The scheduling problems associated with a task set containing a single periodic task which has two fixed release periods of unequal length are examined. Some real-world applications may require task release times which are periodic, but whose tasking periods are not symmetric. A scheduling algorithm for task sets with a single nonsymmetric task has been developed for staticpriority, preemptive-resume operating systems. The nonsymmetric scheduling algorithm is based on the rate monotonic scheduling algorithm which assigns higher …

Design Of Backpropagation Neural Network Architectures Using A Decision Tree Classifier, B. M. Van Horn, D. C. St. Clair

Computer Science Technical Reports

The backpropagation neural network algorithm is a popular machine learning methodology. One difficulty with using the algorithm is that the network architecture must be designed before learning can occur. This includes deciding the number of layers, the number of nodes in each layer, and the number of connections. Traditionally this problem is solved by heuristics gained by an expert through experience.

This paper presents an algorithm for using ID3 decision trees to design the network architecture. Previous approaches rely on binary decision trees. The proposed technique utilizes n-ary trees. These trees are easier to understand, are better suited for continuous-valued …

Optimizing Accuracy And Generalization In Numeric Classification Systems, M. D. Walters, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms that take training instances as input and produce a set of rules as output. The classifier systems focused on in this paper represent the knowledge they learn in the form of decision trees, and are built upon Quinlan's [ 1986] inductive algorithm ID3.

The ID3 algorithm suffers from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a continuous domain or from a domain with a large number of discrete values. A number of approaches have been developed for extending ID3 to handle …

The Identification And Processing Of Don't-Care Attribute Values In Id3 Decision Tree Construction, P. D. Dorr, D. C. St. Clair

Computer Science Technical Reports

ID3 is most successful when used with sets of training and testing data that contain no missing attribute values. Many times, however, real-world domains have attributes with missing values. Sometimes these attribute values may not be needed to classify an instance. Such attribute values are called don't-care attribute values. In other cases, the values are needed but are unavailable. These values are called unknown attribute values. This paper describes the difference between unknown and don't-care attribute values and discusses several ways of identifying don't-care attribute values in ID3. Numerical results are described which validate the practicality of these approaches.