Modeling With Bivariate Geometric Distributions, 2010 New Jersey Institute of Technology

#### Modeling With Bivariate Geometric Distributions, Jing Li

*Dissertations*

This dissertation studied systems with several components which were subject to different types of failures. Systems with two components having frequency counts in the domain of positive integers, and the survival time of each component following geometric or mixture geometric distribution can be classified into this category. Examples of such systems include twin engines of an airplane and the paired organs in a human body. It was found that such a system, using conditional arguments, can be characterized as multivariate geometric distributions. It was proved that these characterizations of the geometric models can be achieved using conditional probabilities, conditional failure ...

A Nonlinear Ode Model Of Tumor Growth And Effect Of Immunotherapy And Chemotherapy Treatment In Colorectal Cancer, 2010 Harvey Mudd College

#### A Nonlinear Ode Model Of Tumor Growth And Effect Of Immunotherapy And Chemotherapy Treatment In Colorectal Cancer, Hannah P. Savage

*HMC Senior Theses*

Colorectal cancer will kill approximately 50,000 people in the United States this year. Current treatment options, including surgery, chemotherapy, and radiation, are often able to force the cancer into remission, but better treatments are needed to help those who don't respond to current treatments. A new and promising treatment option, monoclonal-antibody therapy, has the potential to help reduce the deaths caused by colorectal cancer, but most monoclonal-antibody drugs are currently still in trial phases, and the variations in the dosing schedule of those currently approved for use have not been heavily explored. We have modified a nonlinear ODE ...

A Multistage Incidence Estimation Model For Diseases With Differential Mortality, 2010 Harvey Mudd College

#### A Multistage Incidence Estimation Model For Diseases With Differential Mortality, Alyssa W. Dray

*HMC Senior Theses*

According to theWorld Health Organization, surgically removable cataract remains the leading cause of blindness worldwide. In sub-Saharan Africa, cataract surgical rate targets should ideally be set based on cataract incidence (the number of new cataracts developed each year). Unfortunately, the longitudinal studies necessary to measure incidence have not yet been feasible in these areas. Our research instead proposes a method for estimating incidence based on available cataract prevalence data. We extend a method proposed by Podgor and Leske (1986) to estimate age-specific incidence from age-specific prevalence in single diseases with differential mortality. A two-stage disease extension is created in order ...

Optimizing Restaurant Reservation Scheduling, 2010 Harvey Mudd College

#### Optimizing Restaurant Reservation Scheduling, Jacob Feldman

*HMC Senior Theses*

We consider a yield-management approach to determine whether a restaurant should accept or reject a pending reservation request. This approach was examined by Bossert (2009), where the decision for each request is evaluated by an approximate dynamic program (ADP) that bases its decision on a realization of future demand. This model only considers assigning requests to their desired time slot. We expand Bossert's ADP model to incorporate an element of flexibility that allows requests to be assigned to a time slot that differs from the customer's initially requested time. To estimate the future seat utilization given a particular ...

Computational Feasibility Of Increasing The Visibility Of Vertices In Covert Networks, 2010 Harvey Mudd College

#### Computational Feasibility Of Increasing The Visibility Of Vertices In Covert Networks, Yaniv J. Ovadia

*HMC Senior Theses*

Disrupting terrorist and other covert networks requires identifying and capturing key leaders. Previous research by Martonosi et al. (2009) defines a load metric on vertices of a covert network representing the amount of communication in which a vertex is expected to participate. They suggest that the visibility of a target vertex can be increased by removing other, more accessible members of the network. This report evaluates the feasibility of efficiently calculating the optimal subset of vertices to remove. We begin by proving that the general problem of identifying the optimally load maximizing vertex set removal is NP-complete. We then consider ...

Combinatorial Proofs Using Complex Weights, 2010 Harvey Mudd College

#### Combinatorial Proofs Using Complex Weights, Bo Chen

*HMC Senior Theses*

In 1961, Kasteleyn, Fisher, and Temperley gave a result for the number of possible tilings of a 2m 2n checkerboard with dominoes. Their proof involves the evaluation of a complicated Pfaffian. In this thesis we investigate combinatorial strategies to evaluate the sum of evenly spaced binomial coefficients, and present steps towards a purely combinatorial proof of the 1961 result.

Arithmetic On Specializable Continued Fractions, 2010 Harvey Mudd College

#### Arithmetic On Specializable Continued Fractions, Ross C. Merriam

*HMC Senior Theses*

No abstract provided.

Minimal Circuits For Very Incompletely Specified Boolean Functions, 2010 Harvey Mudd College

#### Minimal Circuits For Very Incompletely Specified Boolean Functions, Richard Strong Bowen

*HMC Senior Theses*

In this report, asymptotic upper and lower bounds are given for the minimum number of gates required to compute a function which is only partially specified and for which we allow a certain amount of error. The upper and lower bounds match. Hence, the behavior of these minimum circuit sizes is completely (asymptotically) determined.

Group Frames And Partially Ranked Data, 2010 Harvey Mudd College

#### Group Frames And Partially Ranked Data, Kwang B. Ketcham

*HMC Senior Theses*

We give an overview of finite group frames and their applications to calculating summary statistics from partially ranked data, drawing upon the work of Rachel Cranfill (2009). We also provide a summary of the representation theory of compact Lie groups. We introduce both of these concepts as possible avenues beyond finite group representations, and also to suggest exploration into calculating summary statistics on Hilbert spaces using representations of Lie groups acting upon those spaces.

Understanding Voting For Committees Using Wreath Products, 2010 Harvey Mudd College

#### Understanding Voting For Committees Using Wreath Products, Stephen C. Lee

*HMC Senior Theses*

In this thesis, we construct an algebraic framework for analyzing committee elections. In this framework, module homomorphisms are used to model positional voting procedures. Using the action of the wreath product group S2[Sn] on these modules, we obtain module decompositions which help us to gain an understanding of the module homomorphism. We use these decompositions to construct some interesting voting paradoxes.

A Lift Of Cohomology Eigenclasses Of Hecke Operators, 2010 Brigham Young University - Provo

#### A Lift Of Cohomology Eigenclasses Of Hecke Operators, Brian Francis Hansen

*All Theses and Dissertations*

A considerable amount of evidence has shown that for every prime p &neq; N observed, a simultaneous eigenvector v_0 of Hecke operators T(l,i), i=1,2, in H^3(Γ_0(N),F(0,0,0)) has a “lift” v in H^3(Γ_0(N),F(p−1,0,0)) — i.e., a simultaneous eigenvector v of Hecke operators having the same system of eigenvalues that v_0 has. For each prime p>3 and N=11 and 17, we construct a vector v that is in the cohomology group H^3(Γ_0(N),F(p−1,0,0)). This is ...

An Exponentially Convergent Nonpolynomial Finite Element Method For Time-Harmonic Scattering From Polygons, 2010 Dartmouth College

#### An Exponentially Convergent Nonpolynomial Finite Element Method For Time-Harmonic Scattering From Polygons, A. H. Barnett, T. Betcke

*Open Dartmouth: Faculty Open Access Articles*

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination ...

Results From Electrostatic Calibrations For Measuring The Casimir Force In The Cylinder-Plane Geometry, 2010 Dartmouth College

#### Results From Electrostatic Calibrations For Measuring The Casimir Force In The Cylinder-Plane Geometry, Q. Wei, D. A. R. Dalvit, F. C. Lombardo, F. D. Mazzitelli, R. Onofrio

*Open Dartmouth: Faculty Open Access Articles*

We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurements performed in the parallel-plane configuration, showing that the dependence on distance of the minimizing potential, if present ...

The Birational Geometry Of Tropical Compactifications, 2010 University of Pennsylvania

#### The Birational Geometry Of Tropical Compactifications, Colin Diemer

*Publicly Accessible Penn Dissertations*

We study compactifications of subvarieties of algebraic tori using methods from the still developing subject of tropical geometry. Associated to each ``tropical" compactification is a polyhedral object called a tropical fan. Techniques developed by Hacking, Keel, and Tevelev relate the polyhedral geometry of the tropical variety to the algebraic geometry of the compactification. We compare these constructions to similar classical constructions. The main results of this thesis involve the application of methods from logarithmic geometry in the sense of Iitaka \cite{iitaka} to these compactifications. We derive a precise formula for the log Kodaira dimension and log irregularity in terms ...

Isolated Hypersurface Singularities As Noncommutative Spaces, 2010 University of Pennsylvania

#### Isolated Hypersurface Singularities As Noncommutative Spaces, Tobias Dyckerhoff

*Publicly Accessible Penn Dissertations*

We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. This category is shown to admit a compact generator which is given by the stabilization of the residue field. We deduce a quasi-equivalence between the category of matrix factorizations and the dg derived category of an explicitly computable dg algebra. Building on this result, we employ a variant of Toen's derived Morita theory to identify continuous functors between matrix factorization categories as integral transforms. This enables us to calculate the Hochschild chain and cochain complexes of these categories. Finally, we give interpretations of ...

An Overview Of The Geometry And Combinatorics Of The Macdonald Polynomial And Q-T Catalan Number, 2010 University of Pennsylvania

#### An Overview Of The Geometry And Combinatorics Of The Macdonald Polynomial And Q-T Catalan Number, Tian Liang

*Publicly Accessible Penn Dissertations*

We will explore the combinatorial and geometric properties related to the Macdonald polynomials and the diagonal harmonics. We have the combinatorial Macdonald polynomial formula that ts the dening conditions directly. The shue conjecture gives an elegant expression of the Frobenius series of the diagonal harmonics. While the geometric properties of the Hilbert scheme and schemes over it provides explanations from a dierent perspective. We use examples to show that these two approaches arrive at the same goal.

Factorizations In The Irreducible Characters Of Compact Semisimple Lie Groups, 2010 University of Pennsylvania

#### Factorizations In The Irreducible Characters Of Compact Semisimple Lie Groups, Andrew Rupinski

*Publicly Accessible Penn Dissertations*

Our goal is to describe factorizations of the characters of irreducible representations of compact semisimple Lie groups. It is well-known that for a given Lie group G of rank n, the Virtual Representation Ring R(G) with the operations of tensor product, direct sum, and direct difference is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, R(G) is a Unique Factorization Domain and thus, viewing a given representation of G as an element of this ring, it makes sense to ask questions about how a representation factors. Using various approaches ...

An Iterated Pseudospectral Method For Functional Partial Differential Equations, 2010 Boise State University

#### An Iterated Pseudospectral Method For Functional Partial Differential Equations, J. Mead, B. Zubik-Kowal

*Barbara Zubik-Kowal*

Chebyshev pseudospectral spatial discretization preconditioned by the Kosloff and Tal-Ezer transformation [10] is applied to hyperbolic and parabolic functional equations. A Jacobi waveform relaxation method is then applied to the resulting semi-discrete functional systems, and the result is a simple system of ordinary differential equations d/dtUk+1(t) = MαUk+1(t)+f(t,U kt). Here Mα is a diagonal matrix, k is the index of waveform relaxation iterations, U kt is a functional argument computed from the previous iterate and the function f, like the matrix Mα, depends on the process of semi-discretization. This waveform relaxation splitting has ...

Noncommutative Topology And The World’S Simplest Index Theorem, 2010 Dartmouth College

#### Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp

*Open Dartmouth: Faculty Open Access Articles*

In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool ...

Scalable Probabilistic Databases With Factor Graphs And Mcmc, 2010 University of Massachusetts - Amherst

#### Scalable Probabilistic Databases With Factor Graphs And Mcmc, Michael Wick, Andrew Mccallum, Gerome Miklau

*Andrew McCallum*

Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary ...