Physical Sciences and Mathematics Commons^™

Graduate Colloquium, Borbala Mazzag

Borbala Mazzag

No abstract provided.

A Bayesian Approach To Wireless Location Problems, Ivan Zorych

Dissertations

Several approaches for indoor location estimation in wireless networks are proposed. We explore non-hierarchical and hierarchical Bayesian graphical models that use prior knowledge about physics of signal propagation, as well as different modifications of Bayesian bivariate spline models. The hierarchical Bayesian model that incorporates information about locations of access points achieves accuracy that is similar to other published models and algorithms, but by using prior knowledge, this model drastically reduces the requirement for training data when compared to existing approaches. Proposed Bayesian bivariate spline models for location surpass predictive accuracy of existing methods. It has been shown that different versions …

Thermal Imaging Of Circular Inclusions Within A Two-Dimensional Region, Shannon Talbott, Hilary Spring

Mathematical Sciences Technical Reports (MSTR)

The ability to study the interior of an object without destroying it is an important industrial tool. One method of recent interest is steady-state thermal or impedance imaging. In this paper we will use the steady-state heat equation to locate one or more circular inclusions within a two-dimensional region, where the boundaries of the inclusions have partially disbonded from the surrounding material; this disbond is modelled as between the heat flux and jump discontinuity at the disbonded interface.

A Survey On Intrusion Detection Approaches, A Murali M. Rao

International Conference on Information and Communication Technologies

Intrusion detection plays one of the key roles in computer security techniques and is one of the prime areas of research. Usages of computer network services are tremendously increasing day by day and at the same time intruders are also playing a major role to deny network services, compromising the crucial services for Email, FTP and Web. Realizing the importance of the problem due to intrusions, many researchers have taken up research in this area and have proposed several solutions. It has come to a stage to take a stock of the research results and project a comprehensive view so …

Building Efficient Systems From Data In A Computational Intelligence Framework, Debrup Chakraborty Dr.

Doctoral Theses

There are problems of interest for which precise mathematical or physical understanding is yet to come. Let us illustrate this with an example. Suppose, for a mining operation one needs to blast a certain portion of the soil/rock using some specific ex- plosives. Before the blast is made, the miners want to know the intensity of vibration that would be produced at a certain distance from the site of blasting. The intensity of vibration may de pend on several factors. For example, it will depend on the characteristics and quantity of the explosive used, the rock characteristics of the region, …

Specific Ige Response To Purified And Recombinant Allergens In Latex Allergy, Viswanath P. Kurup, Gordon L. Sussman, Hoong Y. Yeang, Nancy Elms, Heimo Breiteneder, Siti Am Arif, Kevin J. Kelly, Naveen K. Bansal, Jordan N. Fink

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

In recent years, allergy to natural rubber latex has emerged as a major allergy among certain occupational groups and patients with underlying diseases. The sensitization and development of latex allergy has been attributed to exposure to products containing residual latex proteins. Although improved manufacturing procedures resulted in a considerable reduction of new cases, the potential risk for some patient groups is still great. In addition the prevalent cross-reactivity of latex proteins with other food allergens poses a major concern. A number of purified allergens and a few commercial kits are currently available, but no concerted effort was undertaken to …

Analyzing The Combination Of Polymorphisms Associating With Antidepressant Response By Exact Conditional Test, Baofu Ma

Mathematics Theses

Genetic factors have been shown to be involved in etiology of a poor response to the antidepressant treatment with sufficient dosage and duration. Our goal was to identify the role of polymorphisms in the poor response to the treatment. To this end, 5 functional polymorphisms in 109 patients diagnosed with unipolar, major depressive disorder are analyzed. Due to the small sample size, exact conditional tests are utilized to analyze the contingency table. The data analysis involves: (1) Exact test for conditional independence in a high dimensional contingency table; (2) Marginal independence test; (3) Exact test for three-way interactions. The efficiency …

A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su

All HMC Faculty Publications and Research

We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sⁿ that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version.

Upper Estimates For The Energy Of Solutions Of Nonhomogeneous Boundary Value Problems, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We establish upper bounds for the energy of critical levels of the functional associated to a perturbed superlinear elliptic boundary value problem. We show that the perturbed problem satisfies the estimates obtained by Bahri and Lions (1988) for the symmetric problem. We use these estimates to prove the existence of nonradial solutions to a radial elliptic boundary value problem. Our results fill a gap in an earlier paper by Aduén and Castro.

Construction Of M^4 Run Linear Graphs By Finite Geometries, Chung Yi Suen

Mathematics and Statistics Faculty Publications

Finite projective geometries are used to obtain some series of Taguchi's linear graphs involving m^4 runs, where m is a prime or a prime power. The concept of maximal linear graph is introduced to reduce the number of nonisomorphic linear graphs. Some 81-run maximal linear graphs are given as examples. A table of 27 nonisomorphic 16-run maximal linear graphs, which is believed to be complete, is provided.

On The Construction Of Mixed Orthogonal Arrays Of Strength Two, Chung Yi Suen, Warren F. Kuhfeld

Mathematics and Statistics Faculty Publications

The generalized Kronecker sum was used by Wang and Wu (J. Amer. Statist. Assoc. 86 (1991) 450) and Dey and Midha (Statist. Probab. Lett. 28 (1996) 211; Proc. AP Akad. Sci. 5 (2001) 39) to construct mixed orthogonal arrays. We modify their methods to obtain several families of mixed orthogonal arrays. Some new arrays with run size less than 100 are found.

Hypersurfaces Of Prescribed Curvature In Hyperbolic Space, Marek Szapiel

Doctoral Dissertations

In this paper we consider the problem of existence of hypersurfaces with prescribed curvature in hyperbolic space. We use the upper half-space model of hyperbolic space. The hypersurfaces we consider are given as graphs of positive functions on some domain Ω ∈ Rⁿ satisfying equations of form

f (A) = f (κ₁, . . . , κ_n) = ψ,

where A is the second fundamental form of a hypersurface, f (A) is a smooth sym- metric function of the eigenvalues of A and ψ is a function of position. If we impose certain conditions …

Lebesgue ▼-Measure And Riemann ▼-Integration, Heather Bjorum

Masters Theses & Specialist Projects

Throughout the study of dynamic equations on time-scales, one traditionally finds many theorems involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a Mathematica program for finding the Riemann ▼-integral of a function on various time-scales is provided.

Direct Numerical Simulation For Flow Transition Over A Flat Plate, Shutian Deng

Mathematics Dissertations

In this paper, direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number of 0.5 and a Reynolds number of 1000 based on the free stream velocity and inflow displacement thickness has been carried out. The time-dependent Navier-Stokes equations are solved directly by a third-order TVD Runge-Kutta method from Shu(1998). A sixth order central compact scheme from Lele (1992) that facilitates high resolution of the flow field is used for spatial discretization together with a sixth order implicit compact filter. To avoid possible non-physical wave reflection from the boundaries, the non-reflecting boundary conditions …

On The Image Of The Totalling Functor, Kristen Ann Beck

Mathematics Theses

Let A denote a DG algebra and k a field. The totalling functor, from the category of chain complexes over the graded A-modules to the catagory of DG modules over A, can be extended to one between their derived categories. If this extension were onto, the derived category of the category of DG modules would be superfluous. This paper investigates the image of the extension of Tot in the fundamental case when A is the polynomial ring in d variables over k. When d is at least 2, there are semifree DG modules of rank n, where n is at …

The Classification Of Links Of Up To And Including Thirteen Crossings, Dylan Joshua Faullin

Masters Theses

The prime links of up to 13 crossings are classified up to unoriented equivalence.

Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal

Mathematical Sciences Technical Reports (MSTR)

This paper considers the inverse problem of locating one or more circular inclusions in a two-dimensional domain using thermal boundary data, specifically, the input heat flux and measured boundary temperature. The forward problem is governed by the heat equation. We show how the position and size of such defects can be recovered using the boundary data and various approximations of the solution to the forward problem. We also consider the stability of the algorithm involved to recover the defects.

Mathematics, Meaning, And Identity : A Study Of The Practice Of Mathematics Education In A Rural High School, Rick Anderson

Dissertations and Theses

The purposes of this study were (1) to explore the relationship between mathematics education and the rural context and (2) to determine the usefulness of a social theory of learning (Wenger, 1998) to account for students' participation in advanced high school mathematics courses. Qualitative methods were used to gather data in a small, rural high school in the Pacific Northwest. Data gathered included a student survey, interviews with students and mathematics teachers, observations in mathematics classes, and documents related to the curriculum, the school, and the community.

The findings suggest that high school mathematics education is related to the rural …

Two-Dimensional Self-Assembly In Diblock Copolymers, Anette E. Hosoi, Dmitriy Kogan '03, Caitlin E. Devereaux '02, Andrew J. Bernoff, Shenda M. Baker

All HMC Faculty Publications and Research

Diblock copolymers confined to a two-dimensional surface may produce uniform features of macromolecular dimensions (∼10–100  nm). We present a mathematical model for nanoscale pattern formation in such polymers that captures the dynamic evolution of a solution of poly(styrene)-b-poly(ethylene oxide), PS-b-PEO, in solvent at an air-water interface. The model has no fitting parameters and incorporates the effects of surface tension gradients, entanglement or vitrification, and diffusion. The resultant morphologies are quantitatively compared with experimental data.

A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson

Theses and Dissertations

This thesis presents a simple force-based model of moving and interacting cells that incorporates a realistic description of cell adhesion and applies it to a system of spherical cells. In addition, several results in matrix theory are proved with the end of showing that the equations produced by the model uniquely determine the motion of the system or cells.

Positive Solutions For The Beam Equation Under Certain Boundary Conditions, Bo Yang

Faculty Articles

We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established

Differentials In The Homological Homotopy Fixed Point Spectral Sequence, Robert R. Bruner, John Rognes

Mathematics Faculty Research Publications

We analyze in homological terms the homotopy fixed point spectrum of a T–equivariant commutative S–algebra R. There is a homological homotopy fixed point spectral sequence with E^2_(s,t) = H^(−s)_(gp) (��;H_t(R;��_p)), converging conditionally to the continuous homology H^c_(s+t)(R^(h��);��_p) of the homotopy fixed point spectrum. We show that there are Dyer–Lashof operations β^ϵQ^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the E^(2r)–term of the spectral sequence there are 2r other classes in the E^(2r)–term (obtained mostly by Dyer–Lashof operations …

Some Analogs Of Zariski's Theorem On Nodal Line Arrangements, A.D. Raza Choudary, Alexandru Dimca, Ştefan Papadima

Mathematics Faculty Scholarship

For line arrangements in P² with nice combinatorics (in particular, for those which are nodal away the line at infinity), we prove that the combinatorics contains the same information as the fundamental group together with the meridianal basis of the abelianization. We consider higher dimensional analogs of the above situation. For these analogs, we give purely combinatorial complete descriptions of the following topological invariants (over an arbitrary field): the twisted homology of the complement, with arbitrary rank one coefficients; the homology of the associated Milnor fiber and Alexander cover, including monodromy actions; the coinvariants of the first higher non-trivial …

Mapping The Discrete Logarithm, Daniel R. Cloutier

Mathematical Sciences Technical Reports (MSTR)

The discrete logarithm is a problem that surfaces frequently in the field of cryptog- raphy as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional graph is largely dependent on an interaction between g and p-1. In fact, there are precisely as many different functional graph structures as there are divisors of p-1. This paper extracts two of these structures, permutations and binary functional graphs. Estimates exist for the shape of a random permutation, but …

Elemental T.G. Principles Of Relativistic T-Topos (Presheafification Of Matter, Space, And Time), Goro Kato

Mathematics

We would like to solve the following problem: find a mathematical model formulating I) quantum entanglement, II) particle-wave duality, III) universal objects (ur-sub-Planck objects): to be defined in terms of direct or inverse limits (defined by universal mapping properties) giving microcosm behaviors of space-time so as to give the smooth macrocosm space-time, and IV) the “curved” space-time associated with particles with mass in microcosm consistent with the notion of a light cone in macrocosm. Problems I) and II) are treated in Kato G., Europhys. Lett., 68 (2004) 467. In this paper, we will focus on III) and IV). As …

Subdifferential Calculus In Asplund Generated Spaces, Marian Fabian, Philip D. Loewen, Boris S. Mordukhovich

Mathematics Research Reports

We extend the definition of the limiting Frechet subdifferential and the limiting Frechet normal cone from Asplund spaces to Asplund generated spaces. Then we prove a sum rule, a mean value theorem, and other statements for this concept.

A Convergence Theorem For Continued Fractions Of The Form K_{N=1}^{\Infty}A_{N}/1, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

In this paper we present a convergence theorem for continued fractions of the form K∞n=1an/1. By deriving conditions on the an which ensure that the odd and even parts of K∞n=1an/1 converge, these same conditions also ensure that they converge to the same limit. Examples will be given.

Some Effective Diophantine Results Over Q-Bar, Lenny Fukshansky

CMC Faculty Publications and Research

In his 1999 paper D. W. Masser talks about effective search bounds for polynomial equations over integers and rationals. This discussion can also be extended over number fields. Unfortunately, as illustrated by Matiasevich's negative answer to Hilbert's 10-th problem, search bounds in general probably do not exist. Some special cases are understood, but in general very little is known. I will talk about effective search bounds for solutions of polynomial equations over Q-bar with some additional arithmetic conditions. This discussion also naturaly ties into the realm of "absolute" diophantine results, like Siegel's lemma of Roy and Thunder. I will try …

On Convergence To The Denjoy-Wolff Point, P. S. Bourdon, Valentin Matache, J. H. Shapiro

Mathematics Faculty Publications

For holomorphic selfmaps of the open unit disc U that are not elliptic automorphisms, the Schwarz Lemma and the Denjoy-Wolff Theorem combine to yield a remarkable result: each such map φ has a (necessarily unique) "Denjoy-Wolff point"...

The Least-Squares Finite Element Method For Grid Deformation And Meshfree Applications, Dionisio Laeber Fleitas

Mathematics Dissertations

Grid adaptation is often needed to improve the numerical solution of a Partial Differential Equation (PDE), due to, for example, shock waves and boundary layers. In moving boundary problems, the grid needs to be regenerated or adapted to fit the new domain. In this work, a LSFEM deformation method is developed for grid generation on fixed or moving domains. The LSFEM is a finite-elements method which seeks to minimize the PDE residual equation through the least-squares method. A new class of numerical methods currently being researched is the meshfree methods, in which the main goal is to numerically solve PDEs …