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Distributed teams of air and ground robots have the potential to be very useful in a variety of application domains, and much work is being done to design distributed algorithms that produce useful behaviors. This thesis presents a set of distributed algorithms that operate under minimal human input for patrol and cordon tasks. The algorithms allow the team to surround and travel between objects of interest. Empirical analyses indicate that the surrounding behaviors are robust to variations on the shape of the object of interest, communication loss, and robot failures.

Spectral-domain optical coherence tomography (SD-OCT) is a non-invasive imaging modality that allows for the quantitative study of retinal structures. SD-OCT has begun to find widespread use in the diagnosis and management of various ocular diseases. While commercial scanners provide limited analysis of a small number of retinal layers, the automated segmentation of retinal layers and other structures within these volumetric images is quite a challenging problem, especially in the presence of disease-induced changes. The incorporation of a priori information, ranging from qualitative assessments of the data to automatically learned features, can significantly improve the performance of automated methods. Here, a combined machine learning-based approach and graph-theoretic approach is presented for the automated segmentation of retinal structures in SD-OCT images. Machine-learning based approaches are used to learn textural features from a training set, which are then incorporated into the graph- theoretic approach. The impact of the learned features on the final segmentation accuracy of the graph-theoretic approach is carefully evaluated so as to avoid incorporating learned components that do not improve the method. The adaptability of this versatile combination of a machine-learning and graph-theoretic approach is demonstrated through the segmentation of retinal surfaces in images obtained from humans, mice and canines. In addition to this framework, a novel formulation of the graph-theoretic approach is described whereby surfaces with a disruption can be segmented. By incorporating the boundary of the "hole" into the feasibility definition of the set of surfaces, the final result consists of not only the surfaces but the boundary of the hole as well. Such a formulation can be used to model the neural canal opening (NCO) in SD-OCT images, which appears as a 3-D planar hole disrupting the surfaces in its vicinity. A machine-learning based approach was also used here to learn descriptive features of the NCO. Thus, the major contributions of this work include 1) a method for the automated correction of axial artifacts in SD-OCT images, 2) a combined machine-learning and graph-theoretic framework for the segmentation of retinal surfaces in SD-OCT images (applied to humans, mice and canines), 3) a novel formulation of the graph-theoretic approach for the segmentation of multiple surfaces and their shared hole (applied to the segmentation of the neural canal opening), and 4) the investigation of textural markers that could precede structural and functional change in degenerative retinal diseases.

The PDZ domain of proteins mediates a protein-protein interaction by recognizing the hydrophobic C-terminal tail of the target protein. One of the challenges put forth by the DREAM (Discussions on Reverse Engineering Assessment and Methods) 2009 Challenge consists of predicting a position weight matrix (PWM) that describes the specificity profile of five PDZ domains to their target peptides. We consider the primary structures of each of the five PDZ domains as a numerical sequence derived from graph-theoretic models of each of the individual amino acids in the protein sequence. Using available PDZ domain databases to obtain known targets, the graph-theoretic based numerical sequences are then used to train a neural network to recognize their targets. Given the challenge sequences, the target probabilities are computed and a corresponding position weight matrix is derived. In this work we present our method. The results of our method placed second in the DREAM 2009 challenge.

Traditional clustering is typically based on a single feature set. In some domains, several feature sets may be available to represent the same objects, but it may not be easy to compute a useful and effective integrated feature set. We hypothesize that clustering individual datasets and then combining them using a suitable ensemble algorithm will yield better quality clusters compared to the individual clustering or clustering based on an integrated feature set. We present two classes of algorithms to address the problem of combining the results of clustering obtained from multiple related datasets where the datasets represent identical or overlapping sets of objects but use different feature sets. One class of algorithms was developed for combining hierarchical clustering generated from multiple datasets and another class of algorithms was developed for combining partitional clustering generated from multiple datasets. The first class of algorithms, called EPaCH, are based on graph-theoretic principles and use the association strengths of objects in the individual cluster hierarchies. The second class of algorithms, called CEMENT, use an EM (Expectation Maximization) approach to progressively refine the individual clusterings until the mutual entropy between them converges toward a maximum. We have applied our methods to the problem of clustering a document collection consisting of journal abstracts from ten different Library of Congress categories. After several natural language preprocessing steps, both syntactic and semantic feature sets were extracted. We present empirical results that include the comparison of our algorithms with several baseline clustering schemes using different cluster validation indices. We also present the results of one-tailed paired emph{T}-tests performed on cluster qualities. Our methods are shown to yield higher quality clusters than the baseline clustering schemes that include the clustering based on individual feature sets and clustering based on concatenated feature sets. When the sets of objects represented in two datasets are overlapping but not identical, our algorithms outperform all baseline methods for all indices.

The field of chemical graph theory utilizes simple graphs as models of molecules. These models are called molecular graphs, and quantifiers of molecular graphs are known as molecular descriptors or topological indices. Today's chemists use molecular descriptors to develop algorithms for computer aided drug designs, and computer based searching algorithms of chemical databases and the field is now more commonly known as combinatorial or computational chemistry. With the completion of the human genome project, related fields are emerging such as chemical genomics and pharmacogenomics. Recent advances in molecular biology are driving new methodologies and reshaping existing techniques, which in turn produce novel approaches to nucleic acid modeling and protein structure prediction. The origins of chemical graph theory are revisited and new directions in combinatorial chemistry with a special emphasis on biochemistry are explored. Of particular importance is the extension of the set of molecular descriptors to include graphical invariants. We also describe the use of artificial neural networks (ANNs) in predicting biological functional relationships based on molecular descriptor values. Specifically, a brief discussion of the fundamentals of ANNs together with an example of a graph theoretic model of RNA to illustrate the potential for ANN coupled with graphical invariants to predict function and structure of biomolecules is included.

Glaucoma is the second leading cause of blindness worldwide. The clinical standard for monitoring the functional deficits in the retina that are caused by glaucoma is the visual field test. In addition to monitoring the functional loss, evaluating the disease-related structural changes in the human retina also helps with diagnosis and management of this progressive disease. The characteristic changes of retinal structures such as the optic nerve head (ONH) are monitored utilizing imaging modalities such as color (stereo) fundus photography and, more recently, spectral-domain optical coherence tomography (SD-OCT). With the inherent subjectivity and time required for manually segmenting retinal structures, there has been a great interest in automated approaches. Since both fundus and SD-OCT images are often acquired for the assessment of glaucoma, the automated segmentation approaches can benefit from combining the multimodal complementary information from both sources. The goal of the current work is to automatically segment the retinal structures and extract the proper parameters of the optic nerve head related to the diagnosis and management of glaucoma. The structural parameters include the cup-to-disc ratio (CDR) which is a 2D parameter and is obtainable from both fundus and SD-OCT modalities. Bruch's membrane opening-minimum rim width (BMO-MRW) is a recent 3D structural parameter that is obtainable from the SD-OCT modality only. We propose to use the complementary information from both fundus and SD-OCT modalities in order to enhance the segmentation of structures of interest. In order to enable combining information from different modalities, a feature-based registration method is proposed for aligning the fundus and OCT images. In addition, our goal is to incorporate the machine-learning techniques into the graph-theoretic approach that is used for segmenting the structures of interest. Thus, the major contributions of this work include: 1) use of complementary information from SD-OCT and fundus images for segmenting the optic disc and cup boundaries in both modalities, 2) identifying the extent that accounting for the presence of externally oblique border tissue and retinal vessels in rim-width-based parameters affects structure-structure correlations, 3) designing a feature-based registration approach for registering multimodal images of the retina, and 4) developing a multimodal graph-based approach to segment the optic nerve head (ONH) structures such as Internal Limiting Membrane (ILM) surface and Bruch's membrane surface's opening.

For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoffs Matrix-Tree Theorem in graph theory plays an essential role in the approachs development. The approach is successfully applied to several coupled systems well-known in the literature to demonstrate its applicability and effectiveness. / Applied Mathematics

This thesis focuses on decentralized deadbeat output regulation of discrete-time nonlinear plants that are composed of multiple agents. These agents interact, via scalar-valued signals, in a known structured way represented with a graph. This work is motivated by applications where it is infeasible and/or undesirable to introduce control action within each plant agent; instead, control agents are introduced to interact with certain plant agents, where each control agent focuses on regulating a specific plant agent, called its target. Then, two analyses are carried out to determine if regulation is achieved: targeting analysis is used to determine if control laws can be found to regulate all target agents, then growing analysis is used to determine the effect of those control laws on non-target plant agents. The strength of this novel approach is the intuitively-appealing notion of each control agent focusing on the regulation of just one plant agent. This work goes beyond previous research by generalizing the class of allowable plant dynamics, considering not only arbitrary propagation times through plant agents, but also allowing for non-symmetrical influence between the agents. Moreover, new necessary and sufficient algebraic conditions are derived to determine when targeting succeeds. The main contribution of this work, however, is the development of new easily-verifiable conditions necessary for targeting and/or growing to succeed. These new conditions are valuable due to their simplicity and scalability to large systems. They concern the positioning of control agents and targets as well as the propagation time of signals through the plant, and they help significantly with design decisions. Various graph structures (such as queues, grids, spiders, rings, etc.) are considered and for each, these conditions are used to develop a control scheme with the minimum number of control agents needed.

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