Spectral and Stochastic Solutions to Boundary Value Problems on Magnetic Graphs

A magnetic graph is a graph G equipped with an orientation structure σ on its edges. The discrete magnetic Laplace operator LσG, a second-order difference operator for complex-valued functions on the vertices of G, has been an interesting and useful tool in discrete analysis for over twenty years. Its role in the study of quantum mechanics has been examined closely since its debut in a classic paper by Lieb and Loss in 1993. In this paper, we pose some boundary value problems associated to this operator, and adapt two classic techniques to the setting of magnetic graphs to solve them. The first technique uses the spectral properties of the operator, and the second technique utilizes random walks adjusted to this particular setting. Throughout, we will prove some useful results including a Green’s identity, mean value characterization of harmonic functions, and extensions of the solution techniques to Kronecker product graphs.Biography:Sawyer Jack Robertson is a Norman native and a sophomore undergraduate student in the Department of Mathematics. He has been participating in undergraduate research for one academic year, and has presented at conferences in four states across the country. He is also a recipient of National Merit, Court, and Rust scholarships and has been recognized nationally for his achievements in academics and research. A passionate mathematics major, he hopes to one day attend graduate school at a top institution and become a research mathematician helping to solve problems arising in research areas across many scientific disciplines.University of Oklahoma Libraries Undergraduate Research Awardsundergraduat

Graphical models for zero-inflated single cell gene expression

Bulk gene expression experiments relied on aggregations of thousands of cells to measure the average expression in an organism. Advances in microfluidic and droplet sequencing now permit expression profiling in single cells. This study of cell-to-cell variation reveals that individual cells lack detectable expression of transcripts that appear abundant on a population level, giving rise to zero-inflated expression patterns. To infer gene co-regulatory networks from such data, we propose a multivariate Hurdle model. It is comprised of a mixture of singular Gaussian distributions. We employ neighborhood selection with the pseudo-likelihood and a group lasso penalty to select and fit undirected graphical models that capture conditional independences between genes. The proposed method is more sensitive than existing approaches in simulations, even under departures from our Hurdle model. The method is applied to data for T follicular helper cells, and a high-dimensional profile of mouse dendritic cells. It infers network structure not revealed by other methods; or in bulk data sets. An R implementation is available at https://github.com/amcdavid/HurdleNormal .Comment: Fixed error in software UR

A Type-Based Blocking Technique for Efficient Entity Resolution over Large-Scale Data

In data integration, entity resolution is an important technique to improve data quality. Existing researches typically assume that the target dataset only contain string-type data and use single similarity metric. For larger high-dimensional dataset, redundant information needs to be verified using traditional blocking or windowing techniques. In this work, we propose a novel ER-resolving method using a hybrid approach, including type-based multiblocks, varying window size, and more flexible similarity metrics. In our new ER workflow, we reduce the searching space for entity pairs by the constraint of redundant attributes and matching likelihood. We develop a reference implementation of our proposed approach and validate its performance using real-life dataset from one Internet of Things project. We evaluate the data processing system using five standard metrics including effectiveness, efficiency, accuracy, recall, and precision. Experimental results indicate that the proposed approach could be a promising alternative for entity resolution and could be feasibly applied in real-world data cleaning for large datasets

Decision Support Systems

Decision support systems (DSS) have evolved over the past four decades from theoretical concepts into real world computerized applications. DSS architecture contains three key components: knowledge base, computerized model, and user interface. DSS simulate cognitive decision-making functions of humans based on artificial intelligence methodologies (including expert systems, data mining, machine learning, connectionism, logistical reasoning, etc.) in order to perform decision support functions. The applications of DSS cover many domains, ranging from aviation monitoring, transportation safety, clinical diagnosis, weather forecast, business management to internet search strategy. By combining knowledge bases with inference rules, DSS are able to provide suggestions to end users to improve decisions and outcomes. This book is written as a textbook so that it can be used in formal courses examining decision support systems. It may be used by both undergraduate and graduate students from diverse computer-related fields. It will also be of value to established professionals as a text for self-study or for reference