Digital Commons Network^™

A Development Of Transfer Entropy In Continuous-Time, Christopher David Edgar

Theses and Dissertations

The quantification of causal relationships between time series data is a fundamen- tal problem in fields including neuroscience, social networking, finance, and machine learning. Amongst the various means of measuring such relationships, information- theoretic approaches are a rapidly developing area in concert with other methods. One such approach is to make use of the notion of transfer entropy (TE). Broadly speaking, TE is an information-theoretic measure of information transfer between two stochastic processes. Schreiber’s 2001 definition of TE characterizes information transfer as an informational divergence between conditional probability mass func- tions. The original definition is native to discrete-time stochastic processes …

Dynamical Entropy Of Quantum Random Walks, Duncan Wright

Theses and Dissertations

In this manuscript, we study discrete-time dynamics of systems that arise in physics and information theory, and the measure of disorder in these systems known as dy- namical entropy. The study of dynamics in classical systems is done from two distinct viewpoints: random walks and dynamical systems. Random walks are probabilistic in nature and are described by stochastic processes. On the other hand, dynami- cal systems are described algebraically and deterministic in nature. The measure of disorder from either viewpoint is known as dynamical entropy.

Entropy is an essential notion in physics and information theory. Motivated by the study of …

Applications Of Pattern Recognition Entropy (Pre) And Informatics To Data Analysis, Shiladitya Chatterjee

Theses and Dissertations

The primary focus of my work is the application of informatics methods to the fields of materials science and analytical chemistry. The statistical analysis of data has become increasingly important in understanding the properties of materials and analytes. Statistical methods like principal component analysis (PCA) and multivariate curve resolution (MCR) are widely used for analysis in chemistry and other fields given their ability to categorize spectra in an unsupervised way. PCA is relatively easy to apply and has appealing mathematical properties. However, the results can be challenging to interpret, even for experienced users. In contrast, MCR results can be more …