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- 13P10 Commutative Rings and Algebras/Computational Aspects/Grobner Bases (1)
- 60C05 Combinatorial Probability (1)
- 60E15 Inequalities; stochastic orderings (1)
- 60G42 Martingales with Discrete Parameters (1)
- 60J20 Probability theory and stochastic processes/Markov processes/Applications of Markov chains and discrete-time Markov processes on general state spaces (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
The Quantum Dialectic, Logan Kelley
The Quantum Dialectic, Logan Kelley
Pitzer Senior Theses
A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
HMC Senior Theses
Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool …
Martingale Couplings And Bounds On Tails Of Probability Distributions, Kyle Luh
Martingale Couplings And Bounds On Tails Of Probability Distributions, Kyle Luh
HMC Senior Theses
Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears in Hoeffding's paper. I have then used and extended my urn construction to create new inequalities.
How Other Drivers’ Vehicle Characteristics Influence Your Driving Speed, Russell Brockett
How Other Drivers’ Vehicle Characteristics Influence Your Driving Speed, Russell Brockett
CMC Senior Theses
An analysis of the effect of passing vehicles’ characteristics and their impact on other drivers’ velocities was investigated. Three experimental studies were proposed and likely outcomes were discussed. Experiment 1 focused on the effect of passing vehicle type (SUV, sedan or truck) on driver speed. Drivers were hypothesized as going faster when the same vehicle type as they were driving passed them versus when no vehicle or a different vehicle passed them. Experiment 2 focused on the effect of passing SUV age on driver’s speed. Evidence suggests passing older SUVs will increase the driver’s speed more than new SUVs. Experiment …
Applying Localized Realized Volatility Modeling To Futures Indices, Luella Fu
Applying Localized Realized Volatility Modeling To Futures Indices, Luella Fu
CMC Senior Theses
This thesis extends the application of the localized realized volatility model created by Ying Chen, Wolfgang Karl Härdle, and Uta Pigorsch to other futures markets, particularly the CAC 40 and the NI 225. The research attempted to replicate results though ultimately, those results were invalidated by procedural difficulties.