The SARS-CoV-2 coronavirus is responsible for millions of deaths around the world. To help contribute to the understanding of crucial knowledge and to further generate new hypotheses relevant to SARS-CoV-2 and human protein interactions, we make use of the information abundant Biomine probabilistic database and extend the experimentally identified SARS-CoV-2-human protein-protein interaction (PPI) network in silico. We generate an extended network by integrating information from the Biomine database and the PPI network. To generate novel hypotheses, we focus on the high-connectivity sub-communities that overlap most with the PPI network in the extended network. Therefore, we propose a new data analysis pipeline that can efficiently compute core decomposition on the extended network and identify dense subgraphs. We then evaluate the identified dense subgraph and the generated hypotheses in three contexts: literature validation for uncovered virus targeting genes and proteins, gene function enrichment analysis on subgraphs, and literature support on drug repurposing for identified tissues and diseases related to COVID-19. The majority types of the generated hypotheses are proteins with their encoding genes and we rank them by sorting their connections to known PPI network nodes. In addition, we compile a comprehensive list of novel genes, and proteins potentially related to COVID-19, as well as novel diseases which might be comorbidities. Together with the generated hypotheses, our results provide novel knowledge relevant to COVID-19 for further validation. / Graduate

There have been several papers on the subject of traditional peg solitaire on different boards. However, in this paper we consider a generalization of the game to arbitrary boards. These boards are treated as graphs in the combinatorial sense. We present necessary and sufficient conditions for the solvability of several well-known families of graphs. In the major result of this paper, we show that the cartesian product of two solvable graphs is likewise solvable. Several related results are also presented. Finally, several open problems related to this study are given.

In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the Roman domination cover rubbling number of a tree.

The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b completed columns and all other cells empty. We identify reductions of partial latin squares in PLS(2, 3; n) by using permutations described by filled rows and intersections of filled rows and columns. We find that all partial latin squares in PLS(2, 3;n), where n is sufficiently large, can be completed if such a reduction can be completed. We also show that all partial latin squares in PLS(2, 3; n) where the intersection of filled rows and columns form a latin rectangle have completions for n ≥ 8.

Many complicated problems have simple or at least understandable version, which can be pleasant to listen to and to think about. This work presents the reader with an interesting problem about hats, which, as it turns out, surprises with a number of variations, diversity of procedures and unexpected results. Work will (hopefully) serve as entertaining mathematical literature for anyone who wants to look at these problems, or as a good source of logical problems of this kind. The first part is therefore written in a relaxed language and style, problems are set in one (perhaps overly fairy-tale) story. Mathematics hidden behind problem solving is presented in the second part. 1

MSc., Faculty of Science, University of the Witwatersrand, 2011 / A vast array of important practical problems, in many di erent elds, can be modelled and solved as quadratic assignment problems (QAP). This includes problems such as university campus layout, forest management, assignment of runners in a relay team, parallel and distributed computing, etc. The QAP is a di cult combinatorial optimization problem and solving QAP instances of size greater than 22 within a reasonable amount of time is still challenging. In this dissertation, we propose two new solution approaches to the QAP, namely, a Branch-and-Bound method and a discrete dynamic convexized method. These two methods use the standard quadratic integer programming formulation of the QAP. We also present a lower bounding technique for the QAP based on an equivalent separable convex quadratic formulation of the QAP. We nally develop two di erent new techniques for nding initial strictly feasible points for the interior point method used in the Branch-and-Bound method. Numerical results are presented showing the robustness of both methods.

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Several major functional networks in the brain have been identified, based on sub-regions in the brain that display functionally correlated, synchronous activity and perform common cognitive functions. Three such brain networks (default mode network - DMN, central executive network - CEN, and salience network - SN) form a tri-network model of higher cognitive functioning and are found to be dysregulated in a number of psychopathologies, such as PTSD, autism, schizophrenia, anxiety, depression, bipolar disorder and fronto-temporal dementia (FTD). Current therapies that improve the patient’s cognitive and behavioural states are also found to re-normalize these dysregulated networks, suggesting a correlation between network dysfunction and behavioural dysregulation. Hence, assessing tri-network activity and its dynamics can be a powerful tool to objectively assess treatment response in such psychopathologies. Doing so would most likely rely on functional magnetic resonance imaging (fMRI), as one of the most commonly used modalities for studying such brain networks. While fMRI allows for superior spatial resolution, it poses serious challenges to widespread clinical adoption due to MRI's high operational costs and poor temporal resolution of the acquired signal. One potential strategy to overcome this shortcoming is by identifying the activity of these networks using their EEG-based temporal signatures, greatly reducing the cost and increasing accessibility of using such measures. This thesis takes a step towards improving the clinical accessibility of such brain network-based biomarkers. Doing so first required the exploration of a popular EEG-based method currently being used to study brain networks in mental health disorders - Microstates. This work uncovered flaws in the core assumptions made in assessing Microstates, necessitating the development of an alternate method to detect such network activity using EEG. To accomplish this, it was important to understand the healthy dynamics between the three brain networks constituting the tri-network model and test one of the core predictions of this model, i.e. the SN gates the DMN and CEN activation based on interoceptive and exteroceptive task demands. Probing this question next uncovered mechanistic details of this process, discovering that the SN co-activates with the task-relevant network. Using this information, a novel machine learning pipeline was developed that used simultaneous EEG-fMRI data to identify EEG-based signatures of the three networks within the tri-network model, and could use these signatures to predict network activation. Finally, the novel machine learning pipeline was trialed in a study investigating the effects of lifestyle interventions on the network dynamics, showing that CEN-SN synchrony can predict response to intervention, while DMN-SN synchrony can develop in those that fail to respond. The understanding of healthy network dynamics gathered from the earlier study helps interpret these results, suggesting that the non-responders persistently activated DMN as a maladaptive strategy. In conclusion, the studies discussed in this thesis have improved our understanding of healthy network dynamics, uncovered critical flaws in currently popular methods of EEG-based network analysis, provided an alternative methodology to assess network dynamics using EEG, and also validated its use in tracking changes in network synchrony. The identified EEG signatures of widely used functional networks, will greatly increase the clinical accessibility of such brain network measures as biomarkers for neuropathologies. Monitoring the level of network activity in affected subjects may also lead to the development of novel individualized treatments such as brain network-based neurofeedback interventions. / Thesis / Doctor of Philosophy (PhD) / Synergistic activity in specific brain regions gives rise to large-scale brain networks, linked to specific cognitive tasks. Interactions between three such brain networks are believed to underlie healthy behavior and cognition, and these are found to be disrupted in those with mental health disorders. The ability to cheaply and effectively detect these networks can enable routine network-based clinical assessments, improving diagnosis of mental health disorders and tracking their response to treatment. The first study in this thesis found major flaws in a popular method to assess these networks using a suitably cheap imaging method called electroencephalography(EEG). The remainder of the thesis addressed these issues by first identifying healthy patterns of network activity, followed by designing a novel method to identify network activity using EEG. The final study validates the developed method by tracking network changes after lifestyle interventions. In sum, this thesis takes a step towards improving the clinical accessibility of such brain network-based biomarkers.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24737号 / 情博第825号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 青柳 富誌生, 教授 田口 智清, 准教授 寺前 順之介 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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