Math and Computer Science Working Papers

Mathematical Modeling and Simulation of Latency Phase HIV-1 Dynamics

Frank Nani et al. — Thu, 05 Jul 2012 08:04:52 PDT

In this paper, the patho-physiological dynamics of HIV-1 induced AIDS is analyzed using a system of deterministic ordinary differential equations. The mathematical model exhibits explicitly the dynamics of the HIV-1 virions during latency phase in the absence of anti-viral therapy. The model presented in this paper is a generalization of previous models of HIV-1 dynamics and incorporates the interactions between the HIV-1 virions, infected helper T-Iymphocytes. uninfected helper r-Iymphocytes, and cytotoxic T-Iymphocytes, as well as contributions to HIV-1 reservoirs. investigative computer simulations using clinically plausible parametric configurations are presented. Clinically relevant criteria are derived depicting the annihilation, control, or persistence of HIV-1 in the absence of anti-viral therapy.

Dynamics of HIV-1 Associated Kaposi Sarcoma During HAART Therapy

Frank Nani et al. — Thu, 05 Jul 2012 08:04:51 PDT

The techniques of mathematical modeling and investigative computer simulations are used to study the qualitative aspects of the patho-physiodynamics of HIV-1 associated Kaposi sarcoma (KS) during Highly Active Anti-Retroviral Therapy (HAART) of AIDS. Using a system of non-linear deterministic differential equations, the model incorporates the biologically measurable and clinically relevant immunological interactions and parameters. In particular, the computer simulations elucidate the role of CD8+ T lymphocyte in the annihilation and persistence of Kaposi sarcoma during HAART.

Computer Simulation of a Mathematical Model of HAART Therapy for HIV-1 AIDS

Frank Nani et al. — Thu, 05 Jul 2012 08:04:50 PDT

A clinically plausible mathematical model is constructed to describe the patho-physiological dynamics or HIV-1 induced AIDS during HAART therapy. The model equations incorporate physiological interactions between non-infected helper T cells, HIV-1 infected helper T cells, HIV-1 virions in the blood plasma, HIV-1 specific cytotoxic T cells and drug molecules or the HAART protocol. Investigative computer simulations arc performed to elucidate some therapeutic scenarios such as viral annihilation and efficacious HAART therapy. In particular, some mathematical criteria are derived for therapeutic outcomes such as viral persistence and viral annihilation.

Generalized Necessary and Sufficient Conditions for Annihilation of HIV-1 Virions During HAART

Frank Nani et al. — Thu, 05 Jul 2012 08:04:49 PDT

In this paper, the patho-physiological dynamics of Human Immuno-deficiency Virus type 1( HIV-1) induced AIDS during Highly Active Anti Retroviral Therapy (HAART) is modeled using a system of non-linear deterministic differential equations. The physiologically relevant and clinically plausible equations depict the dynamics of uninfected CD4+ T cells (x1), HIV-1 infected CD4+ T cells (x2), HIV-1 virions in the blood plasma (x3), HIV-1 specific CD8+ T cells (x4), and the concentration of HAART drug molecules (x5). Criteria for the existence of therapeutic outcomes are presented. In particular, the necessary and sufficient conditions for the annihilation of HIV-1 virions, and HIV-1 infected helper T cells are clearly exhibited in terms of biological measureable model physiological parameters. Investigative computer simulations are presented elucidating the patho-physiodynamics of HIV-1 induced AIDS and various hypothetical patient parametric configurations. The mathematical analysis of the model equations and the computer simulations are performed with regard to HAART protocols with constant continuous intravenous and transdermal drug infusions.

Mathematical Modeling and Simulation of 1 Acute and Chronic Phase HIV-1 Dynamics

Frank Nani et al. — Thu, 05 Jul 2012 08:04:47 PDT

Aims: To construct a clinically plausible mathematical model of the patho-physiological dynamics of HIV-1 induced AIDS during the acute and chronic phases which incorporates the interactions between uninfected CD4+ T cells, HIV-1 infected CD4+ T cells, HIV-1 virions in the blood plasma, and specific cytotoxic CD8+ T cells. In particular, the model describes quantitatively the time evolution of AIDS in the patient during the acute phase and the asymptomatic chronic clinical latency phase and elucidates the effect of latent HIV-1 reservoirs on the prognosis of AIDS. The major objective is to derive mathematical criteria depicting the necessary and sufficient conditions under which the HIV-1 virions can be maintained definitely at the subclinical viral blood plasma level such that the HIV-1 seriopositive person does not develop full-blown AIDS.
Study design: The model is based on contemporary published patho-physiological data on acute and clinical chronic phase HIV-1 induced AIDS. These data are meticulously condensed into a clinically plausible four compartmental mathematical model that incorporates the dynamics and interactions between non-HIV-1 infected CD4+ T lymphocytes. HIV-1 infected lymphocytes, free HIV-1 virions in the blood plasma, and HIV-1 specific cytotoxic CD8+ T lymphocytes. The relevant stoichiometric interaction rate constants, apoptotic rate constants, rate constants for viral recruitment from latent reservoirs, and other relevant parameters are clearly exhibited in the mathematical model.
Place and Duration of Study: This research was done at Fayetteville State University, North Carolina USA, and is sponsored by the FSU Mini-Grant Award and the HBCU Graduate STEM Grant. The research was done during the Spring of 2012.
Methodology: The deterministic nonlinear HIV-1 AIDS patho-physio-dynamical equations are analyzed using the techniques of dynamical system theory, principles of linearized stability, Hartman-Grobman theory, and other relevant mathematical techniques. The clinically desirable equilibrium states are and their local existence and global stability are analyzed. Investigative computer simulations are performed illustrating some physiological outcomes.
Results: Mathematical criteria are derived under which the clinically desired outcomes can occur. Investigative computer simulations are presented which elucidate a number of physiological scenarios of primary HIV-1 infection, involving the annihilation, and persistence of HIV-1 in the absence of AIDS Pharmacotherapy.
Conclusion: Mathematical modeling can be a useful technique in the derivation of prognostic criteria and quantitative analysis of AIDS during the acute and chronic phases.

Symmetry reductions for the Tzitzeica curve equation

Nicoleta Bila — Fri, 29 Jun 2012 09:59:53 PDT

The purpose of the paper is to analyze the Tzitzeica curve equation from the point of view of symmetry analysis theory. The Tzitzeica curve equation is a nonlinear ordinary differential equation that arises from differential geometry that may be regarded as a differential equation in three unknown functions, namely, the functions that give the parametrical representation of the curve. The extended classical symmetries, the generalized equivalence transformations and the equivalence transformations related to this nonlinear ordinary differential equation are determined.

Particular solutions to the Tzitzeica curve equation

Nicoleta V. Bila et al. — Fri, 29 Jun 2012 09:59:52 PDT

The aim of this paper is to study a particular reduction case of the nonlinear ordinary differential equation that defines a Tzitzeica curve. It is shown that the Tzitzeica curve equation can be reduced to an auxiliary third order linear homogeneous ordinary differential equation with constant coeficients for the defining functions of the curve and a linear equation for the equation's constant. Consequently, it can be proven that any three linearly independent solutions of the auxiliary ordinary differential equation define a Tzitzeica curve.

Symmetry reductions related to specific nonlinear models

Nicoleta Bila — Fri, 29 Jun 2012 09:59:51 PDT

The purpose of this work is to explore possible side conditions involving high order differential invariants with the aim of reducing the original mathematical model. It is shown that, in the case of the Tzitzeica curve equation, a suitable side condition that leads to exact solutions is a system consisting of two third order differential invariants involving the arbitrary functions and a third order differential invariant involving the dependent variable of the equation. In this situation, the equation can be reduced to a linear equation for the equation's constant. Similarly, in the case of a proposed generalization of the Tzitzeica curve equation, the above side condition also leads to a reduced model.

On the Existance of Certain Circulant Weighing Matrices

Vassil Yorgov — Wed, 27 Jun 2012 12:14:26 PDT

We prove nonexistence of circulant weighing matrices with parameters from ten previously open entries of the updated Strassler's table. The method of proof utilizes some modular constraints on circulant weighing matrices with multipliers.

Stability and Liapunov Functionals for Fractional Differential Equations

Bo Zhang — Mon, 18 Jun 2012 13:31:21 PDT

Abstract.

This project is devoted to developing Liapunov direct method for fractional differential equations and systems. The method (constructing a system related scalar function) enables investigators to analyze the qualitative behavior of solutions of a differential equation without actually solving it. We are able to convert some fractional differential equations (semi-linear) to integral equations with singular kernels and construct Liapunov functionals for the integral equations to deduce conditions for boundedness and stability of solutions. Extending such a method to fully nonlinear equations presents a significant challenge to investigators and will be a major area of research for many years to come.

Simulation Based Performance Analyses on RIPv2, EIGRP, and OSPF Using OPNET

Bing Wu — Wed, 07 Sep 2011 13:19:30 PDT

Extensive experiments has been conducted to analyze and compare a set of characteristics of different routing protocols, such as RIPv2, EIGRP, and OSPF by using sophisticated simulation software called OPNET. The characteristics that will be studied include convergence time, scalability, end-to-end delay, and throughput. Different network topologies, such as the star, ring, and mesh, are being tested in the experiments. The experimental results show that RIPv2 has better performance than others in small and condensed networks. OSPF and EIGRP have better performance for medium-sized and scattered networks. Overall EIGRP is more stable and consistent in both small and relatively large networks. The future work may include the performance analyses on EGP protocols.

Xin Tang's research paper on derivations

Xin Tang — Thu, 09 Jun 2011 17:39:35 PDT

Xin Tang's research paper on two-parameter quantum groups and Ringel-Hall algebras of infinite type

Xin Tang — Thu, 09 Jun 2011 17:39:34 PDT

Additivity of Lie Centralizers on Triangular Rings

Wu Jing — Mon, 16 May 2011 08:24:02 PDT

We introduce the definition of Lie centralizers and investigate the
additivity of Lie centralizers on triangular rings. Characterizations of cen-
tralizers and Lie centralizers on triangular rings and nest algebras are also
presented.

Lie Derivable Mappings on Prime Rings

Wu Jing et al. — Wed, 11 May 2011 12:30:19 PDT

Abstract contains chararcters difficult to render in HTML, please download paper for abstract.

Xin Tang’s paper on the Hopf algebra, please see .pdf

Xin Tang — Tue, 08 Feb 2011 10:12:58 PST

Title and abstract contain characters that cannot be adequately represented in the Digital Commons.

Additivity Of Jordan (Triple) Derivations On Rings

Wu Jing et al. — Wed, 02 Feb 2011 09:06:22 PST

In recent years, there has been a great interest in the study of additivity of mappings on rings as well as operator algebras (see [3] - [8], and references therein). Most of these results focus on the additivity of multiplicative maps, Jordan (triple) multiplicative maps, and Jordan elementary maps on rings, triangular algebras, and operator algebras. The first result in this direction is due to Martindale III who obtained the following pioneer result in 1969.

Simulation of Grass Land

Yufang Bao et al. — Thu, 29 Apr 2010 07:47:49 PDT

A REVIEW OF MOBILE-BASED INITIATIVES ACROSS COLLEGE

Daniel Okunbor et al. — Thu, 30 Oct 2008 17:48:49 PDT

The information era in which we currently live is changing the culture of education. The use of information technologies has resulted in new opportunities that are rapidly evolving to include mobile learning. Keegan (2002) characterizes this evolution of distance learning as a shift from d-learning (distance) to e-learning (electronic) to m-learning (mobile) learning.

Mobile, wireless, and handheld technologies are being used to re-enact approaches and solutions to teaching and learning used in traditional and web-based formats. The goal of mobile learning is to provide opportunities for students to interact through computer-supported learning environments from mobile terminals with low speed wireless connections.

This article provides a review of mobile-based initiatives across college campuses to explore the future of mobile teaching and learning; however, much of what exists in this growing body of literature documents the results of short-term small-scale pilots and trails.

ANALYSIS OF A MOBILE LEARNING PILOT STUDY

Daniel Okunbor et al. — Fri, 25 Jul 2008 06:39:46 PDT

This article documents the results of a pilot study involving the use of mobile phones to enhance student learning. A year-long mobile initiative, identified as Bronco Mobile, was deployed at Fayetteville State University (FSU), a historically Black Institution located in North Carolina. Students were able to manage their academic and social lives using RaveGuardian, RaveAlert, RaveTransit, RaveEmail, RaveAcademics, RaveGroups, RavePolling, and RaveFlashcard--a customized package of applications developed specifically for FSU. The mobile-based applications were developed by Rave Wireless and made available to students on the Sprint/Nextel national network. The results indicate that a large percentage of the study participants found the mobile-based applications to be insignificant.