Statistical Mechanics describes the macroscopic behavior of a system through the analysis of its microscopic components. It is therefore a framework to move from a probabilistic, high-dimensional description of a system to its macroscopic description through averaging. This approach, now one of the pillars of physics, has seen successes in other fields, such as statistics or mathematical finance. This broadening of the applications of statistical physics has opened new avenues of research in the field itself. Ideas from information theory, differential geometry, and approximate computation are making their way into modern statistical physics. The research presented in this dissertation straddles this boundary: we start by showing how concepts from statistical physics can be applied to statistical learning, then show how modern statistical physics can provide insights into molecular transport phenomena. The first three chapters focus on building an understanding of statistical learning as a thermodynamic relaxation process in a high-dimensional space: in the same way that a statistical mechanical system is composed of a large number of particles relaxing to their equilibrium distribution, a statistical learning system is a parametric function whose optimal parameters minimize an empirical loss. We present this process as a trajectory in a high-dimensional probability Riemannian manifold, and show how this conceptual framework can lead to practical improvements in learning algorithms for large scale neural networks. The second part of this thesis focuses on two applications of modern statistical mechanics to molecular transport. First, I propose a statistical mechanical interpretation of metabolon formation through cross-diffusion, a generalization of the reaction-diffusion framework to multiple reacting species with non-diagonal terms in the diffusion matrix. These theoretical results are validated by experimental results obtained using a microfluidic system. Second, I demonstrate how fluctuation analysis in motility assays can allow us to infer nanoscale properties from microscale measurements. I accomplish this using computational Langevin dynamics simulations and show how this setup can be used to simplify the testing of theoretical non-equilibrium statistical mechanics hypotheses.

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Thesis (M. Nurs.)--University of Hong Kong, 2009. / Includes bibliographical references (p. 56-63).

Teaching science using an inquiry approach is encouraged by several organisations responsible for defining teaching and learning guidelines in North America. However, using this approach can be difficult because of the complexity of inquiry. One source of difficulty is an inability to make sense of the data. Error variation, in particular, poses a significant barrier to the correct interpretation of data and therefore successful inquiry learning. A study was conducted to examine middle school students' ability to make sense of the data they collected in three related experiments. These data involved taking measurements of two continuous variables that were affected by error variation. The results indicated that students tended not to use abstract patterns to describe the data but rather used more local patterns that did not make use of the whole data set. However, many students also indicated an intuitive understanding that a greater amount of data could be used to generate results that are more accurate. This suggests a disparity between what the students understand about data and what they are capable of doing with data. Educational implications are that students may benefit from learning ideal patterns that can be compared to non-ideal data they collect.

Statistical methods based on nonparametric and distribution-free procedures require the use of order statistics. Order statistics are also used in many parametric estimation and testing problems. With the introduction of modern high speed computers, order statistics have gained more importance in recent years in statistical inference - the main reason being that ranking a large number of observations manually was difficult and time consuming in the past, which is no longer the case at present because of the availability of high speed computers. Also, applications of order statistics require in many cases the use of numerical tables and computer is needed to construct these tables.In this thesis, some basic concepts and results involving order statistics are provided. Typically, application of the Theory of Permanents in the distribution of order statistics are discussed. Further, the correlation coefficient between the smallest observation (Y1) and the largest observation (Y,,) of a random sample of size n from two gamma populations, where (n-1) observations of the sample are from one population and the remaining observation is from the other population, is presented. / Department of Mathematical Sciences

This thesis covers the uncertainty of empirical prediction. As opposed to objectivity, I will discuss the practicality of statistics. Practicality defined as "useful" in an unbiased sense, in relation to something in the external world that we care about. We want our model of prediction to give us unbiased inference whilst also being able to speak about something we care about. For the reasons explained, the inherent uncertainty of statistics undermines the unbiased inference for many methods. Bayesian Statistics, by valuing hypotheses is more plausible but ultimately cannot arrive at an unbiased inference. I posit the value theory of money as a concept that might be able to allow us to derive unbiased inferences from while still being something we care about. However, money is of instrumental value, ultimately being worth less than an object of “transcendental value.” Which I define as something that is worth more than money since money’s purpose is to help us achieve “transcendental value” under the value theory. Ultimately, as long as an individual has faith in a given hypothesis it will be worth more than any hypothesis valued with money. From there we undermine statistic’s practicality as it seems as though without the concept of money we have no manner of valuing hypotheses unbiasedly, and uncertainty undermines the “objective” inferences we might have been able to make.

Thesis (M.S.)--Georgia Southern University, 2008. / "A dissertation submitted to the Graduate Faculty of Georgia Southern University in partial fulfillment of the requirements for the degree Master of Science." Under the direction of Pat Humphrey. ETD. Electronic version approved: May 2008. Includes bibliographical references (p. 79-80) and appendices.

Thesis (Ph.D.)--Pennsylvania State University, 2006. / Mode of access: World Wide Web.

Berlin, Humboldt-Univ., Diss., 2009

Thesis (Ph. D.)--Stockholm University, 1996. / Includes bibliographical references (p. 206-217).