Mathematics Commons^™

Advances And Applications Of Dezert-Smarandache Theory (Dsmt), Vol. 1, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

The Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning is a natural extension of the classical Dempster-Shafer Theory (DST) but includes fundamental differences with the DST. DSmT allows to formally combine any types of independent sources of information represented in term of belief functions, but is mainly focused on the fusion of uncertain, highly conflicting and imprecise quantitative or qualitative sources of evidence. DSmT is able to solve complex, static or dynamic fusion problems beyond the limits of the DST framework, especially when conflicts between sources become large and when the refinement of the frame of the problem under consideration …

Stage Based Interventions For Low Fat Diet With Middle School Students, Marilyn Frenn, Shelly Malin, Naveen K. Bansal

College of Nursing Faculty Research and Publications

Preventing obesity and cardiovascular disease at early ages is important; however, few effective interventions for early adolescents have been reported. In this study, low-income, culturally diverse students from an urban middle school (n = 60) received four classroom interventions with the use of a combined Health Promotion/Transtheoretical Model to control fat in diet and increase physical activity. A control group (n = 57) received the usual classroom education. Pretest percentage fat in diet was regressed on demographics, access to low-fat foods, perceived self-efficacy, benefits/barriers, and stage of change with results as proposed by the model [F(9,64) …

A Mathematical Model Of Immune Response To Tumor Invasion, Lisette De Pillis, Ami Radunskaya

All HMC Faculty Publications and Research

Recent experimental studies by Diefenbach et al. [1] have brought to light new information about how the immune system of the mouse responds to the presence of a tumor. In the Diefenbach studies, tumor cells are modified to express higher levels of immune stimulating NKG2D ligands. Experimental results show that sufficiently high levels of ligand expression create a significant barrier to tumor establishment in the mouse. Additionally, ligand transduced tumor cells stimulate protective immunity to tumor rechallenge. Based on the results of the Diefenbach experiments, we have developed a mathematical model of tumor growth to address some of the questions …

A Contrast-Based Neural Control System For Ant Navigation, Joanna R. Wares, Predrag-Peter Ilich, Daniel P. Dougherty

Department of Math & Statistics Faculty Publications

A mathematical model for a neural control system of ant locomotion was developed. Contrast-based detectors using excitation and inhibition were tuned to specific contrast orientations. A control system using multiple orientation contrast detectors was then developed and optimized for a model ant, which could move via a biased random walk. The system allowed sufficient control to guide the ant through various mazes.

Medical Inference System On Arthritis Using Fuzzy Relational Theory, Chee Kau Lim

Student Works (2000-2009)

Fuzzy relational theory is a branch in the study of fuzzy sets theory. According to this theory, mapping among two sets can be carried out in four ways, which arc represented by circle product, sub-triangular product, super-triangular product and square product. Each of these products can be abstracted into inference structures. which is useful in designing the inference engine of an expert system. Based on the revised version [DeBaets and Kerre 1993. Hallam and Yew l998a] of fuzzy relational theory. a series of 18 inference structures, namely sub-K inference structures (denoted as Kt to Kl8) are constructed. Based on these …

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …

A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan

Department of Math & Statistics Faculty Publications

This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample's exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for …

Signal Processing With Neural Networks, Pero Smrzlic

Masters Theses

In this study, we introduce the Adaptive Back Propagation (ABP) learning algorithm, computationally superior to the standard Back Propagation. The ABP is based on the new activation function, with its corresponding adaptive learning parameter. By using the combination of computer simulations and analysis in the domain of activation function, the Method of One Hidden layer was developed for the effective utilization of units in one-hidden layer networks. A parallel version of the ABP was designed and implemented on a nCUBE-2 supercomputer with 128 processors.

The simulation results suggested a strong correlation between frequency of signals and the role of hidden …

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.

A Sensitivity Analysis Of The Coefficients For The Transformation Of The Electrocardiographic Orthogonal Three-Lead System (Frank) To The Standard Twelve-Lead System, Rasa Ona Draugelis

Loma Linda University Electronic Theses, Dissertations & Projects

The SENSITIVITY ANALYSIS is performed on the transformation coefficients of the Frank XYZ signals generating standard 12-lead ECG with respect to diagnosis. The analysis is adapted for the individual waveform and per each lead. The disease/abnormality categories are described in terms of discrete pattern classes based on criteria used by Marquette Electronics, Inc. The nonlinear global sensitivity analysis method developed by Shuler, et al, is selected for this project. The diagnostic change in the waveform is denoted by a distance measurement from the pattern class boundary corresponding to the best-experimental coefficient estimates (Dower coefficients) to the alternate coefficient specification measurement …

Estimation Of Growth Curves By Least Square Splines, Dorothy Rybaczyk Pathak

Mathematics & Statistics ETDs

The primary object of this dissertation is to present some con­tributions to the theory of estimation of growth curves by least square splines in the presence of unknown unequal variances. The theoretical developments rest heavily on the standard least square theory and the theory of polynomial spline functions. A modifica­tion of the Aitken procedure of weighted least squares is used to estimate regression parameters. It is shown that this modification of the Aitken procedure does not unduly influence the nice least square properties of estimators so obtained; the estimators re­ main unbiased, consistent and asymptotically efficient.

The techniques developed in …

Models For Estimating Psychiatric Bed Needs, Patricia A. Brenneman

Loma Linda University Electronic Theses, Dissertations & Projects

Inland Counties Comprehensive Health Planning Council wished to estimate the psychiatric bed needs by type (such as state hospitals, board and care homes, etc.) in San Bernardino County from the distributions of patient arrivals and of lengths of stay. A statistical description of the system during 1973 was considered the first step toward estimating future bed needs. A computer simulation model using IBM's programming language General Purpose Simulation System (GPSS) was developed and was found to be unsatisfactory.

Theorems were then developed for a statistical model, seeking to predict future bed needs. The most convenient of these theorems states that …