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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Computational Feasibility Of Increasing The Visibility Of Vertices In Covert Networks, Yaniv J. Ovadia
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, Bo Chen
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, Ross C. Merriam
Arithmetic On Specializable Continued Fractions, Ross C. Merriam
HMC Senior Theses
No abstract provided.
Minimal Circuits For Very Incompletely Specified Boolean Functions, Richard Strong Bowen
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, Kwang B. Ketcham
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.
A Nonlinear Ode Model Of Tumor Growth And Effect Of Immunotherapy And Chemotherapy Treatment In Colorectal Cancer, Hannah P. Savage
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 tumor/treatment model …
Optimizing Restaurant Reservation Scheduling, Jacob Feldman
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 decision, a …
Understanding Voting For Committees Using Wreath Products, Stephen C. Lee
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 Multistage Incidence Estimation Model For Diseases With Differential Mortality, Alyssa W. Dray
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 …
Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger
Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger
CMC Senior Theses
Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.