Physics Commons^™

Interdisciplinary Studies Of Complex Network And Machine Learning And Its Applications, Shaojun Luo

Dissertations, Theses, and Capstone Projects

In this dissertation, we introduce the concept of network-based statistical inference methods of two types: network structure inference and variable inference. For network structure inference, we introduce correlation matrix, graphical Lasso, network clustering and identify the influencer in the network. For variable inference, we also introduce from Bayesian network, to Random Markov Field and Ising Model, Boltzmann and Restricted Boltzmann machine and the algorithm of Belief Propagation. Last but not the least, we introduce the most widely used neural network family and its two main types: Convolutional Neural Network and Recurrent Neural Network.

In Chapter 3 we provide an example …

A Network Theoretical Approach To Real-World Problems: Application Of The K-Core Algorithm To Various Systems, Kate Burleson-Lesser

Dissertations, Theses, and Capstone Projects

The study of complex networks is, at its core, an exploration of the mechanisms that control the world in which we live at every scale, from particles no bigger than a grain of sand and amino acids that comprise proteins, to social networks, ecosystems, and even countries. Indeed, we find that, regardless of the physical size of the network's components, we may apply principles of complex network theory, thermodynamics, and statistical mechanics to not only better understand these specific networks, but to formulate theories which may be applied to problems on a more general level. This thesis explores several networks …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

Standard And Anomalous Wave Transport Inside Random Media, Xujun Ma

Dissertations, Theses, and Capstone Projects

This thesis is a study of wave transport inside random media using random matrix theory. Anderson localization plays a central role in wave transport in random media. As a consequence of destructive interference in multiple scattering, the wave function decays exponentially inside random systems. Anderson localization is a wave effect that applies to both classical waves and quantum waves. Random matrix theory has been successfully applied to study the statistical properties of transport and localization of waves. Particularly, the solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation gives the distribution of transmission.

For wave transport in standard one dimensional random systems in …

Developing A 3d In Vitro Model By Microfluidics, Hung-Ta Chien

Dissertations and Theses

In vitro tissue models play an important role in providing a platform that mimics the realistic tissue microenvironment for stimulating and characterizing the cellular behavior. In particular, the hydrogel-based 3D in vitro models allow the cells to grow and interact with their surroundings in all directions, thus better mimicking in vivo than their 2D counterparts. The objective of this thesis is to establish a 3D in vitro model that mimics the anatomical and functional complexity of the realistic cancer microenvironment for conveniently studying the transport coupling in porous tissue structures. We pack uniform-sized PEGDA-GelMA microgels in a microfluidic chip to …