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Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.

This project's purpose was to understand the workings of a new theorem introduced in a professional paper on the cutwidth of meshes and then use this knowledge to apply it to the search for the cyclic cutwidth of the n-cube.

An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination number for ladders, specific families of prisms, mobius ladders and related products including categorical products $G\times K_2$ and lexicographic products $G\cdot K_2$. Finally, we will conclude with open problems.

An Italian dominating function, abbreviated IDF, of $G$ is a function $f \colon V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that for every vertex $v \in V(G)$ with $f(v)=0$, we have $\sum_{u \in N(v)} f(u) \ge 2$. That is, either $v$ is adjacent to at least one vertex $u$ with $f(u) = 2$, or to at least two vertices $x$ and $y$ with $f(x) = f(y) = 1$. The Italian domination number, denoted $\gamma_I$(G), is the minimum weight of an IDF in $G$. In this thesis, we use operations that join two trees with a single edge in order to build trees with unique $\gamma_I$-functions.

Comparing genomes in a computationally efficient manner is a difficult problem. Methods that provide the highest resolution are too inefficient and methods that are efficient are too low resolution. In this thesis, we show that the Colored de Bruijn Graph (CdBG) is a suitable method for comparing genomes because it is efficient while maintaining a useful amount of resolution. To illustrate the usefulness of the CdBG, the phylogenetic tree for 12 species in the Drosophila genus is reconstructed using pseudo-homologous regions of the genome contained in the CdBG.

Shared micromobility defines as the shared use of light and low-speed vehicles such as bike and scooter in which users have short-term access on an as-needed basis. As shared micromobility, as one of the most viable and sustainable modes of transportation, has emerged in the U.S. over the last decade., understanding different aspects of these modes of transportation help decision-makers and stakeholders to have better insights into the problems related to these transportation options. Designing efficient and effective shared micromobility programs improves overall system performance, enhances accessibility, and is essential to increase ridership and benefit commuters. This dissertation aims to address three vital aspects of emerging shared micromobility transportation options with three essays that each contribute to the practice and literature of sustainable transportation. Chapter one of this dissertation investigates public opinion towards dockless bikes sharing using a mix of statistical and natural language processing methods. This study finds the underlying topics and the corresponding polarity in public discussion by analyzing tweets to give better insight into the emerging phenomenon across the U.S. Chapter two of this dissertation proposes a new framework for the micromobility network to improve accessibility and reduce operator costs. The framework focuses on highly centralized clubs (known as k-club) as virtual docking hubs. The study suggests an integer programming model and a heuristic approach as well as a cost-benefit analysis of the proposed model. Chapter three of this dissertation address the risk perception of bicycle and scooter riders’ risky behaviors. This study investigates twenty dangerous maneuvers and their corresponding frequency and severity from U.S. resident’s perspective. The resultant risk matrix and regression model provides a clear picture of the public risk perception associated with these two micromobility options. Overall, the research outcomes will provide decision-makers and stakeholders with scientific information, practical implications, and necessary tools that will enable them to offer better and sustainable micromobility services to their residents.

Working memory is a mental workspace which utilizes short and long-term memory to maintain and manipulate information. It is crucial in enabling cognitive control and is largely controlled by interactions within and between frontal and parietal cortices. Recent work has identified visual nonspatial, spatial, and visuospatial working memory spectral characteristics of the local field potential through simultaneous recordings from various areas across the monkey frontoparietal network. However, the reports are minimal in number, and there is no clear narrative tying together the heterogenous functionality of the characteristics. Here, a new spectral model of monkey visual working memory is proposed to address these shortcomings. It highlights functional roles for low, mid, and high frequency bands. Next, the organization of structural connectivity which gives rise to these spectral characteristics is investigated. A new binary association matrix representing connections in the frontoparietal network is proposed. A graph theoretic analysis on the matrix found that a 3-node dynamical relaying M9 motif was a fundamental building block of the network. It is optimally structured for the synchrony found in the spectral model. The network was also found to have a small-world architecture, which confers the integration and specialization of function required by visual working memory. Afterwards, three hypotheses generated by the spectral model are tested on non-spatial data. The low and mid band hypotheses were supported by evidence, while the high band hypothesized activity was not observed. This adds credibility to the roles identified in the model for the low and mid band and identifies a need for further investigation of the high band role. Finally, opportunities to expand the spectral model, analyze the M9 motif, and further test the model are explored. In the future, the spectral model could evolve to apply its predictions to humans in the pursuit of treatments for neurological disorders. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection

Data clustering is a process of grouping unlabeled objects based on the imformation describing their relationship. And it has obtained a lot of attentions in data mining for its wide applications in life. For example, in marketing, companys are interested in finding groups of customers with similar purchase behavior, which will help them to make suitable plans to gain more profits. Besides, in biology, we can make use of data clustering to distinguish planets and animals given their features. Whats more, in earthquake analysis, by clustering observed earthquake epicenters, dangerous area can be identified, it would be helpful for people to take measures to protect them from earthquake in advance. In general, there isnt one clustering algorithm which can solve all the problems. Algorithms are specifically designed to analyze different data categories. In this thesis, we study several novel numerical algorithms for data clustering mainly applied on multi-view data and tensor data. More accurate clustering result can be achieved on multi-view data by integrating information from multiple graphs. However, Most existing multi-view clustering method assume the degree of association among all the graphs are the same. One significant truth is some graphs may be strongly or weakly associated with other graphs in reality. Determining the degree of association between graphs is a key issue when clustering multi-view data. In Chapter 2, 3 and 4, we propose three different models to solve this problem. In chapter 2, a block signed matrix is constructed to integrate information in each graph with association among graphs together. Then we apply spectral clustering on it to seek different cluster structure for each graph respectively and determine the degree of association among graphs using their own cluster structure at the same time. Numerical experiments including simulations, neuron activity data and gene expression data are conducted to illustrate the state-of-art performance of algorithm in clustering and graph association. In Chapter 3, we further consider multiple graphs clustering with graph association solved by self-consistent field iterative algorithm. By using the block graph clustering framework, graphs association are considered to enhance clustering result, and then better clustering result would be used to calculate more accurate association. Self-consistent field iterative method is employed to solve this problem, and the convergence analysis is also presented. Simulations are also carried out to demonstrate the outperformance of our method. Two gene expression data are used to evaluate the effectiveness of proposed model. In Chapter 4, we formulate the multiple graphs clustering problem with the graph association as an objective function, and the graph association is considered as a term in the objective function. The proposed model can be solved efficiently by using gradient flow method. We also present its convergence analysis. Experiments on synthetic data sets and two gene expression data are given to show the efficiency in clustering and capability in graphs association. In the last three chapters, we use multiple graphs to represent the multi-view data. A key challenge is high dimensionality when the number of graphs or objects is large-scale. Moreover, tensor is another common technique to describe multi-view data. Thus tensor decomposition method can be used to learn a low-dimensional representation for high dimensional data firstly and then perform clustering efficiently, which has attract worldwide attention of researchers. In Chapter 5, we propose an orthogonal nonnegative Tucker decomposition method to decompose high-dimensional nonnegative tensor into tensor with smaller size for dimension reduction, and then perform clustering analysis. A convex relaxation algorithm of the augmented Lagrangian function is devoloped to solve the optimization problem and the convergence of the algorithm is discussed. We employ our proposed method on several real image data sets from different real world application, including face recognition, image representation and hyperspectral unmixing problem to illustrate the effectiveness of proposed algorithm.