Notes on sufficient conditions for a graph to be Hamiltonian

The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant. The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.

Network construction and graph theoretical analysis of functional language networks in pediatric epilepsy

This dissertation introduces a new approach for assessing the effects of pediatric epilepsy on the language connectome. Two novel data-driven network construction approaches are presented. These methods rely on connecting different brain regions using either extent or intensity of language related activations as identified by independent component analysis of fMRI data. An auditory description decision task (ADDT) paradigm was used to activate the language network for 29 patients and 30 controls recruited from three major pediatric hospitals. Empirical evaluations illustrated that pediatric epilepsy can cause, or is associated with, a network efficiency reduction. Patients showed a propensity to inefficiently employ the whole brain network to perform the ADDT language task; on the contrary, controls seemed to efficiently use smaller segregated network components to achieve the same task. To explain the causes of the decreased efficiency, graph theoretical analysis was carried out. The analysis revealed no substantial global network feature differences between the patient and control groups. It also showed that for both subject groups the language network exhibited small-world characteristics; however, the patient's extent of activation network showed a tendency towards more random networks. It was also shown that the intensity of activation network displayed ipsilateral hub reorganization on the local level. The left hemispheric hubs displayed greater centrality values for patients, whereas the right hemispheric hubs displayed greater centrality values for controls. This hub hemispheric disparity was not correlated with a right atypical language laterality found in six patients. Finally it was shown that a multi-level unsupervised clustering scheme based on self-organizing maps, a type of artificial neural network, and k-means was able to fairly and blindly separate the subjects into their respective patient or control groups. The clustering was initiated using the local nodal centrality measurements only. Compared to the extent of activation network, the intensity of activation network clustering demonstrated better precision. This outcome supports the assertion that the local centrality differences presented by the intensity of activation network can be associated with focal epilepsy.^

Intracranial Volume Estimation and Graph Theoretical Analysis of Brain Functional Connectivity Networks

Understanding pathways of neurological disorders requires extensive research on both functional and structural characteristics of the brain. This dissertation introduced two interrelated research endeavors, describing (1) a novel integrated approach for constructing functional connectivity networks (FCNs) of brain using non-invasive scalp EEG recordings; and (2) a decision aid for estimating intracranial volume (ICV). The approach in (1) was developed to study the alterations of networks in patients with pediatric epilepsy. Results demonstrated the existence of statistically significant (p

Text analytics of social media: Sentiment analysis, event detection and summarization

In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. ^ Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. ^ In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data. ^

Text Analytics of Social Media: Sentiment Analysis, Event Detection and Summarization

In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data.

Network Construction and Graph Theoretical Analysis of Functional Language Networks in Pediatric Epilepsy

This dissertation introduces a new approach for assessing the effects of pediatric epilepsy on the language connectome. Two novel data-driven network construction approaches are presented. These methods rely on connecting different brain regions using either extent or intensity of language related activations as identified by independent component analysis of fMRI data. An auditory description decision task (ADDT) paradigm was used to activate the language network for 29 patients and 30 controls recruited from three major pediatric hospitals. Empirical evaluations illustrated that pediatric epilepsy can cause, or is associated with, a network efficiency reduction. Patients showed a propensity to inefficiently employ the whole brain network to perform the ADDT language task; on the contrary, controls seemed to efficiently use smaller segregated network components to achieve the same task. To explain the causes of the decreased efficiency, graph theoretical analysis was carried out. The analysis revealed no substantial global network feature differences between the patient and control groups. It also showed that for both subject groups the language network exhibited small-world characteristics; however, the patient’s extent of activation network showed a tendency towards more random networks. It was also shown that the intensity of activation network displayed ipsilateral hub reorganization on the local level. The left hemispheric hubs displayed greater centrality values for patients, whereas the right hemispheric hubs displayed greater centrality values for controls. This hub hemispheric disparity was not correlated with a right atypical language laterality found in six patients. Finally it was shown that a multi-level unsupervised clustering scheme based on self-organizing maps, a type of artificial neural network, and k-means was able to fairly and blindly separate the subjects into their respective patient or control groups. The clustering was initiated using the local nodal centrality measurements only. Compared to the extent of activation network, the intensity of activation network clustering demonstrated better precision. This outcome supports the assertion that the local centrality differences presented by the intensity of activation network can be associated with focal epilepsy.