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 Title
 Assessment of functional connectivity in the human brain : multivariate and graph signal processing methods
 Creator
 VillafañeDelgado, Marisel
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"Advances in neurophysiological recording have provided a noninvasive way of inferring cognitive processes. Recent studies have shown that cognition relies on the functional integration or connectivity of segregated specialized regions in the brain. Functional connectivity quantifies the statistical relationships among different regions in the brain. However, current functional connectivity measures have certain limitations in the quantification of global integration and characterization of...
Show more"Advances in neurophysiological recording have provided a noninvasive way of inferring cognitive processes. Recent studies have shown that cognition relies on the functional integration or connectivity of segregated specialized regions in the brain. Functional connectivity quantifies the statistical relationships among different regions in the brain. However, current functional connectivity measures have certain limitations in the quantification of global integration and characterization of network structure. These limitations include the bivariate nature of most functional connectivity measures, the computational complexity of multivariate measures, and graph theoretic measures that are not robust to network size and degree distribution. Therefore, there is a need of computationally efficient and novel measures that can quantify the functional integration across brain regions and characterize the structure of these networks. This thesis makes contributions in three different areas for the assessment of multivariate functional connectivity. First, we present a novel multivariate phase synchrony measure for quantifying the common functional connectivity within different brain regions. This measure overcomes the drawbacks of bivariate functional connectivity measures and provides insights into the mechanisms of cognitive control not accountable by bivariate measures. Following the assessment of functional connectivity from a graph theoretic perspective, we propose a graph to signal transformation for both binary and weighted networks. This provides the means for characterizing the network structure and quantifying information in the graph by overcoming some drawbacks of traditional graph based measures. Finally, we introduce a new approach to studying dynamic functional connectivity networks through signals defined over networks. In this area, we define a dynamic graph Fourier transform in which a common subspace is found from the networks over time based on the tensor decomposition of the graph Laplacian over time."Pages iiiii.
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 Title
 Distance preserving graphs
 Creator
 Zahedi, Emad
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"The computational complexity of exploring distance properties of large graphs such as realworld social networks which consist of millions of nodes is extremely expensive. Recomputing distances in subgraphs of the original graph will add to the cost. One way to avoid this is to use subgraphs where the distance between any pair of vertices is the same as in the original graph. Such a subgraph is called isometric. A connected graph is distance preserving, for which we use the abbreviation dp,...
Show more"The computational complexity of exploring distance properties of large graphs such as realworld social networks which consist of millions of nodes is extremely expensive. Recomputing distances in subgraphs of the original graph will add to the cost. One way to avoid this is to use subgraphs where the distance between any pair of vertices is the same as in the original graph. Such a subgraph is called isometric. A connected graph is distance preserving, for which we use the abbreviation dp, if it has an isometric subgraph of every order. In this framework we study dp graphs from both the structural and algorithmic perspectives. First, we study the structural nature of dp graphs. This involves classifying graphs based on the dp property and the relation between dp graphs to other graph classes. Second, we study the recognition problem of dp graphs. We intend to develop efficient algorithms for finding isometric subgraphs as well as deciding whether a graph is dp or not."Page ii.
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 Title
 Graphs and their chromatic numbers
 Creator
 Behzad, Mehdi
 Date
 1965
 Collection
 Electronic Theses & Dissertations
 Title
 Enhancing graphical literacy skills in the high school science classroom via authentic, intensive data collection and graphical representation exposure
 Creator
 Palmeri, Anthony
 Date
 2013
 Collection
 Electronic Theses & Dissertations
 Description

ABSTRACTENHANCING GRAPHICAL LITERACY SKILLS IN THE HIGH SCHOOL SCIENCE CLASSROOM VIA AUTHENTIC, INTENSIVE DATA COLLECTION AND GRAPHICAL REPRESENTATION EXPOSUREByAnthony Palmeri This research project was developed to provide extensive practice and exposure to data collection and data representation in a high school science classroom. The student population engaged in this study included 40 high school sophomores enrolled in two microbiology classes. Laboratory investigations and activities...
Show moreABSTRACTENHANCING GRAPHICAL LITERACY SKILLS IN THE HIGH SCHOOL SCIENCE CLASSROOM VIA AUTHENTIC, INTENSIVE DATA COLLECTION AND GRAPHICAL REPRESENTATION EXPOSUREByAnthony Palmeri This research project was developed to provide extensive practice and exposure to data collection and data representation in a high school science classroom. The student population engaged in this study included 40 high school sophomores enrolled in two microbiology classes. Laboratory investigations and activities were deliberately designed to include quantitative data collection that necessitated organization and graphical representation. These activities were embedded into the curriculum and conducted in conjunction with the normal and expected course content, rather than as a separate entity. It was expected that routine practice with graph construction and interpretation would result in improved competency when graphing data and proficiency in analyzing graphs. To objectively test the effectiveness in achieving this goal, a pretest and posttest that included graph construction, interpretation, interpolation, extrapolation, and analysis was administered. Based on the results of a paired TTest, graphical literacy was significantly enhanced by extensive practice and exposure to data representation.
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 Title
 Graphs and their associated linegraphs
 Creator
 Chartrand, Gary
 Date
 1964
 Collection
 Electronic Theses & Dissertations
 Title
 Automorphism groups of graphs
 Creator
 Kateley, Julian
 Date
 1963
 Collection
 Electronic Theses & Dissertations
 Title
 Relative sensitivity of a family of closestpoint graphs in vision applications
 Creator
 Chorzempa, Terrence L.
 Date
 1988
 Collection
 Electronic Theses & Dissertations
 Title
 Community detection in temporal multilayer networks
 Creator
 Alsharoa, Esraa Mustafa
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

"Many real world systems and relational data can be modeled as networks or graphs. With the availability of large amounts of network data, it is important to be able to reduce the network's dimensionality and extract useful information from it. A key approach to network data reduction is community detection. The objective of community detection is to summarize the network by a set of modules, where the similarity within the modules is maximized while the similarity between different modules...
Show more"Many real world systems and relational data can be modeled as networks or graphs. With the availability of large amounts of network data, it is important to be able to reduce the network's dimensionality and extract useful information from it. A key approach to network data reduction is community detection. The objective of community detection is to summarize the network by a set of modules, where the similarity within the modules is maximized while the similarity between different modules is minimized. Early work in graph based community detection methods focused on static or single layer networks. This type of networks is usually considered as an oversimplification of many real world complex systems, such as social networks where there may be different types of relationships that evolve with time. Consequently, there is a need for a meaningful representation of such complex systems. Recently, multilayer networks have been used to model complex systems where the objects may interact through different mechanisms. However, there is limited amount of work in community detection methods for dynamic and multilayer networks. In this thesis, we focus on detecting and tracking the community structure in dynamic and multilayer networks. Two particular applications of interest are considered including temporal social networks and dynamic functional connectivity networks (dFCNs) of the brain. In order to detect the community structure in dynamic singlelayer and multilayer networks, we have developed methods that capture the structure of these complex networks. In Chapter 2, a lowrank + sparse estimation based evolutionary spectral clustering approach is proposed to detect and track the community structure in temporal networks. The proposed method tries to decompose the network into lowrank and sparse parts and obtain smooth cluster assignments by minimizing the subspace distance between consecutive time points, simultaneously. Effectiveness of the proposed approach is evaluated on several synthetic and real social temporal networks and compared to the existing stateoftheart algorithms. As the method developed in Chapter 2 is limited to dynamic singlelayer networks and can only take limited amount of historic information into account, a tensorbased approach is developed in Chapter 3 to detect the community structure in dynamic singlelayer and multilayer networks. The proposed framework is used to track the change points as well as identify the community structure across time and multiple subjects of dFCNs constructed from resting state functional magnetic resonance imaging (rsfMRI) data. The dFCNs are summarized into a set of FC states that are consistent over time and subjects. The detected community structures are evaluated using a consistency measure. In Chapter 4, an informationtheoretic approach is introduced to aggregate the dynamic networks and identify the time points that are topologically similar to combine them into a tensor. The community structure of the reduced network is then detected using a tensor based approach similar to the one described in Chapter 3. In Chapter 5, a temporal block spectral clustering framework is introduced to detect and track the community structure of multilayer temporal networks. A set of intra and interadjacency matrices is constructed and combined to create a set of temporal supraadjacency matrices. In particular, both the connections between nodes of the network within a time window, i.e. intralayer adjacency, as well as the connections between nodes across different time windows, i.e. interlayer adjacency are taken into account. The community structure is then detected by applying spectral clustering to these supraadjacency matrices. The proposed approach is evaluated on dFCNs constructed from rsfMRI across time and subjects revealing dynamic connectivity patterns between the resting state networks (RSNs)."Pages iiiii.
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