The secondary structures of ribonucleic acid (RNA) have been successfully modeled with graph-theoretic structures. Often, simple graphs are used to represent secondary RNA structures; however, in this research, a multigraph representation of RNA is used, in which vertices represent stems and edges represent the internal motifs. Any type of RNA secondary structure may be represented by a graph in this manner. We define novel graphical invariants to quantify the multigraphs and obtain characteristic descriptors of the secondary structures. These descriptors are used to train an artificial neural network (ANN) to recognize the characteristics of secondary RNA structure. Using the ANN, we classify the multigraphs as either RNA-like or not RNA-like. This classification method produced results similar to other classification methods. Given the expanding library of secondary RNA motifs, this method may provide a tool to help identify new structures and to guide the rational design of RNA molecules.

A multi-commodity flow problem consists of moving several commodities from their respective sources to their sinks through a network where each edge has different costs and capacity constraints. This paper explores different linear programming algorithms and their performance regarding finding an optimal solution for multi-commodity flow problems. By testing several of different network constraints, we examine which algorithms are most suitable for specific network and problem structures. Furthermore, we implement our own multi-commodity solver and compare its performance against state-of-the-art linear programming solvers. The results show that for the methods we tested it is difficult to discern which class of linear programming methods are optimal solvers for multi-commodity flow problems and that their performance depends on how the network and commodities are structured.

The aim of this thesis is to examine clustering based outlier detection algorithms on their ability to detect abnormal events in flight traffic. A nominal model is trained on a data-set containing only flights which are labeled as normal. A detection scoring function based on the nominal model is used to decide if a new and in forehand unseen data-point behaves like the nominal model or not. Due to the unknown structure of the data-set three different clustering algorithms are examined for training the nominal model, K-means, Gaussian Mixture Model and Spectral Clustering. Depending on the nominal model different methods to obtain a detection scoring is used, such as metric distance, probability and OneClass Support Vector Machine. This thesis concludes that a clustering based outlier detection algorithm is feasible for detecting abnormal events in flight traffic. The best performance was obtained by using Spectral Clustering combined with a Oneclass Support Vector Machine. The accuracy on the test data-set was 95.8%. The algorithm managed to correctly classify 89.4% of the datapoints labeled as abnormal and correctly classified 96.2% of the datapoints labeled as normal. / Syftet med detta arbete är att undersöka huruvida klusterbaserad anomalidetektering kan upptäcka onormala händelser inom flygtrafik. En normalmodell är anpassad till data som endast innehåller flygturer som är märkta som normala. Givet denna normalmodell så anpassas en anomalidetekteringsfunktion så att data-punkter som är lika normalmodellen klassificeras som normala och data-punkter som är avvikande som anomalier. På grund av att strukturen av nomraldatan är okänd så är tre olika klustermetoder testade, K-means, Gaussian Mixture Model och Spektralklustering. Beroende på hur normalmodellen är modellerad så har olika metoder för anpassa en detekteringsfunktion används, så som baserat på avstånd, sannolikhet och slutligen genom One-class Support Vector Machine. Detta arbete kan dra slutsatsen att det är möjligt att detektera anomalier med hjälp av en klusterbaserad anomalidetektering. Den algoritm som presterade bäst var den som kombinerade spektralklustring med One-class Support Vector Machine. På test-datan så klassificerade algoritmen $95.8\%$ av all data korrekt. Av alla data-punkter som var märka som anomalier så klassificerade denna algoritm 89.4% rätt, och på de data-punkter som var märka som normala så klassificerade algoritmen 96.2% rätt.

When attempting to mitigate the spread of an epidemic without the use of a vaccine, many measures may be made to dampen the spread of the disease such as physically distancing and wearing masks. The implementation of an effective test and quarantine strategy on a population has the potential to make a large impact on the spread of the disease as well. Testing and quarantining strategies become difficult when a portion of the population are asymptomatic spreaders of the disease. Additionally, a study has shown that randomly testing a portion of a population for asymptomatic individuals makes a small impact on the spread of a disease. This thesis simulates the transmission of the virus that causes COVID-19, SARSCoV- 2, in contact networks gathered from real world interactions in five different environments. In these simulations, several testing and quarantining strategies are implemented with a varying number of tests per day. These strategies include a random testing strategy and several uniform testing strategies, based on knowledge of the underlying network. By modeling the population interactions as a graph, we are able to extract properties of the graph and test based on those metrics, namely the degree of the network. This thesis found many of the strategies had a similar performance to randomly testing the population, save for testing by degree and testing the cliques of the graph, which was found to consistently outperform other strategies, especially on networks that are more dense. Additionally, we found that any testing and quarantining of a population could significantly reduce the peak number of infections in a community.

A well-known result in spectral graph theory states that if a graph has an equitable partition then the eigenvalues of the associated divisor graph are a subset of the graph's eigenvalues. A natural question question is whether it is possible to recover the remaining eigenvalues of the graph. Here we show that if a graph has a Hermitian adjacency matrix then the spectrum of the graph can be decomposed into a collection of smaller graphs whose eigenvalues are collectively the remaining eigenvalues of the graph. This we refer to as a complete equitable decomposition of the graph.

Correlated stocks should, in equilibrium, have correlated momenta, but in practice momenta do not always correlate. We use short-term inconsistencies between correlations and momenta to predict price corrections, produce more meaningful investment indicators, and improve upon accepted investing strategies. In particular, our approaches integrate inconsistencies within an entire security class rather than relying only on individual or pairwise security data. We use this theory to improve upon not only the standard momentum portfolio but also Pair Trading and Momentum Reversion methods. This results in three strategies for portfolio allocation that outperforms overlying indices and market benchmarks by 5%-10% in annual gain with an increase of CAPM alpha over the standard momentum portfolio from -0.1 to 5.4. We expand on these strategies by showing applications generalized to comparable investing indicators including volatility.

As the capabilities of autonomous systems have increased so has interest in utilizing teams of autonomous systems to accomplish tasks more efficiently. This dissertation takes steps toward enabling the cooperation of unmanned systems in scenarios that are challenging, such as GPS-denied or perceptually aliased environments. This work begins by developing a cooperative navigation framework that is scalable in the number of agents, robust against communication latency or dropout, and requires little a priori information. Additionally, this framework is designed to be easily adopted by existing single-agent systems with minimal changes to existing software and software architectures. All systems in the framework are validated through Monte Carlo simulations. The second part of this dissertation focuses on making cooperative navigation robust in challenging environments. This work first focuses on enabling a more robust version of pose graph SLAM, called cycle-based pose graph optimization, to be run in real-time by implementing and validating an algorithm to incrementally approximate a minimum cycle basis. A new algorithm is proposed that is tailored to multi-agent systems by approximating the cycle basis of two graphs that have been joined. These algorithms are validated through extensive simulation and hardware experiments. The last part of this dissertation focuses on scenarios where perceptual aliasing and incorrect or unknown data association are present. This work presents a unification of the framework of consistency maximization, and extends the concept of pairwise consistency to group consistency. This work shows that by using group consistency, low-degree-of-freedom measurements can be rejected in high-outlier regimes if the measurements do not fit the distribution of other measurements. The efficacy of this method is verified extensively using both simulation and hardware experiments.

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付記する学位プログラム名: デザイン学大学院連携プログラム / 京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24031号 / 情博第787号 / 新制||情||134(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 阿久津 達也, 教授 山本 章博, 教授 鹿島 久嗣 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM