Uniquely Solvable Puzzles and Fast Matrix Multiplication

In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplications, with several conjectures that would imply the matrix multiplication exponent $\omega$ is 2. Their methods have been used to match one of the fastest known algorithms by Coppersmith and Winograd, which runs in $O(n^{2.376})$ time and implies that $\omega \leq 2.376$. This thesis discusses the framework that Cohn and Umans came up with and presents some new results in constructing combinatorial objects called uniquely solvable puzzles that were introduced in a 2005 follow-up paper, and which play a crucial role in one of the $\omega = 2$ conjectures

The Best Reporter in America

This research looks at the life of the infamous Nellie Bly, born Elizabeth Cochran, a woman reporter in the late nineteenth and early twentieth centuries. She was one of the pioneers of “stunt” journalism, a form of reporting reliant upon thorough investigation. Her first big feat during her career was feigning insanity to be committed to a women\u27s insane asylum in order to write an article on the terrible living conditions there. The feat for which she is best known however, was her trip around the world in less time than anyone else at the time. This research seeks to bring to light the accomplishments of Nellie Bly, “the best reporter in America.

The Persistence of Population III Star Formation

We present a semi-analytic model of star formation in the early universe, beginning with the first metal-free stars. By employing a completely feedback-limited star formation prescription, stars form at maximum efficiency until the self-consistently calculated feedback processes halt formation. We account for a number of feedback processes including a meta-galactic Lyman-Werner background, supernovae, photoionization, and chemical feedback. Halos are evolved combining mass accretion rates found through abundance matching with our feedback-limited star formation prescription, allowing for a variety of Population III (Pop III) initial mass functions (IMFs). We find that, for a number of models, massive Pop III star formation can continue on until at least $z \sim 20$ and potentially past $z \sim 6$ at rates of around $10^{-4}$ to $10^{-5}$ M$_\odot$ yr$^{-1}$ Mpc$^{-3}$, assuming these stars form in isolation. At this point Lyman-Werner feedback pushes the minimum halo mass for star formation above the atomic cooling threshold, cutting off the formation of massive Pop III stars. We find that, in most models, Pop II and Pop III star formation co-exist over cosmological time-scales, with the total star formation rate density and resulting radiation background strongly dominated by the former before Pop III star formation finally ends. These halos form at most $\sim 10^3$ M$_\odot$ of massive Pop III stars during this phase and typically have absolute magnitudes in the range of $M_\text{AB} = -5$ to $-10$. We also briefly discuss how future observations from telescopes such as JWST or WFIRST and 21-cm experiments may be able to constrain unknown parameters in our model such as the IMF, star formation prescription, or the physics of massive Pop III stars.Comment: 16 pages, 13 figures, submitted to MNRA

Constraints on Electroweak Effective Operators at One Loop

We derive bounds on nine dimension-six operators involving electroweak gauge bosons and the Higgs boson from precision electroweak data. Four of these operators contribute at tree level, and five contribute only at one loop. Using the full power of effective field theory, we show that the bounds on the five loop-level operators are much weaker than previously claimed, and thus much weaker than bounds from tree-level processes at high-energy colliders.Comment: 15 page

Confidence in Arguments in Dialogues for Practical Reasoning

For the context of practical reasoning, this paper suggests a method of assessing the level of confidence we should rationally have in arguments. It draws from dialectic which induces the elaboration of reasons for a position and on auditors’ prior knowledge. Accurate assessment depends on evidential standards, on selecting dialogue moves according to their practical and epistemic importance, and on selecting auditors according to their competence and diversity of relevant knowledge

The electrochemical interface and stochastic functions: A data-driven approach to modeling non-ideal behavior in concentrated systems

Researchers in the ionics field make frequent use of the mass-action principle – or the assumption of ideal thermodynamic behavior – in its physical models. These models are relatively easy to work with, leading to many useful and convenient formulae. However, they are strictly correct only in the limit of infinite dilution, and over-reliance on mass-action models in concentrated systems can lead to models that are grossly incorrect when compared with experimental reality. Recent microscopic experimental results gathered at surfaces and interfaces of ionic and mixed ionic-electronic conductors provide a striking example: classical models utilizing mass-action assumptions routinely underpredict the thickness of defect accumulation zones by an order of magnitude. Although atomistic models can be employed for concentrated systems, their utility is limited to very small simulation domains: continuum models must be used to predict the behavior of devices. A key issue in any continuum-level thermodynamic treatment is the intractability of the microscopic defect interaction problem: beyond the ideal case, very few closed form solutions for the free energy in terms of concentrations are available. This presentation will introduce a data-driven methodology for determining these functions using either experimental or theoretical datasets. The method utilizes Gaussian process stochastic functions to represent the unknown functional relationships between defect concentrations and free energy, and calibrates these functions to data using Bayesian methods for calibration and model selection. A continuum model for the structure of electrochemical interfaces in concentrated systems is the ‘Poisson-Cahn’ theory, which incorporates defect interactions and, crucially, gradient effects in a model that has proven successful in the replication of both macroscopic and microscopic experimental results. The data-driven approach to model building will be demonstrated in the context of Poisson-Cahn variational approaches applied to microscopic experimental datasets for grain boundaries in calcium-doped ceria

Oral History Interview: Mebane Pritchett

This interview is one of a series conducted concerning the Marshall University Society of Yeager Scholars. At the time of the interview, Mebane Pritchett was president of the Coca-Cola Scholar\u27s Foundation, Inc. She discusses: her personal, educational, and employment background; being Associate & Executive Director of the Morehead Foundation at the University of North Carolina at Chapel Hill, and a detailed discussion of the Morehead Foundation (including its history and the students selected by the program); the Yeager program and how it compares to the Morehead program; individuals such as Dale Nitzschke, Joe Hunnicutt, William Denman, Ralph Albertazzie, Chuck Yeager; the Coca-Cola Scholar\u27s Foundation; and other topics.https://mds.marshall.edu/oral_history/1330/thumbnail.jp

Genetic Optimization Using Derivatives: The rgenoud Package for R

genoud is an R function that combines evolutionary algorithm methods with a derivative-based (quasi-Newton) method to solve difficult optimization problems. genoud may also be used for optimization problems for which derivatives do not exist. genoud solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When the function to be optimized (for example, a log-likelihood) is nonlinear in the model's parameters, the function will generally not be globally concave and may have irregularities such as saddlepoints or discontinuities. Optimization methods that rely on derivatives of the objective function may be unable to find any optimum at all. Multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. On the other hand, algorithms that do not use derivative information (such as pure genetic algorithms) are for many problems needlessly poor at local hill climbing. Most statistical problems are regular in a neighborhood of the solution. Therefore, for some portion of the search space, derivative information is useful. The function supports parallel processing on multiple CPUs on a single machine or a cluster of computers.

Machine Errors and Undervotes in Florida 2006 Revisited

The 2006 election for U.S. House of Representatives District 13 in Sarasota County, Florida, attracted extensive controversy because an unusually high proportion of the ballots cast lacked a vote for that office, and the unusual number of undervotes probably changed the election outcome. Intensive technical studies based on examining software and hardware from the iVotronic touchscreen voting machines used to conduct the election failed to find mechanical flaws sufficient to explain the undervotes. Studies that examined the ballots used in Sarasota and in some other counties concluded the high undervote rate was caused by peculiar features of the ballot\u27s format that confused many voters. I show that recorded events involving power failures and problems with the Personalized Electronic Ballots used with the machines correlate significantly with undervote rates in several Florida counties. The relationships between machine events and undervotes are sufficiently substantial and varied to make it unreasonable to discount the likelihood that mechanical failures contributed substantially to the high numbers of undervotes