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<p> This thesis is concerned with a necessary and sufficient condition for the existence of non-zero linear continuous functionals on Fréchet or more general topological vector spaces. The main idea is based on the famous Hahn-Banach theorem. Since the connection between Hahn-Banach theorem and separation theorems is well known, here we study some separation theorems as well.</p> / Thesis / Master of Science (MSc)

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Information extraction aims to automatically extract structured information from unstructured texts. Supervised information extraction requires large quantities of labeled training data, which is time-consuming and labor-intensive. This dissertation focuses on information extraction, especially relation extraction and attribute-value extraction in e-commerce, with few labeled (few-shot learning) or even no labeled (zero-shot learning) training data. We explore multi-source auxiliary information and novel learning techniques to integrate semantic auxiliary information with the input text to improve few-shot learning and zero-shot learning. For zero-shot and few-shot relation extraction, the first method explores the existing data statistics and leverages auxiliary information including labels, synonyms of labels, keywords, and hypernyms of name entities to enable zero-shot learning for the unlabeled data. We build an automatic hypernym extraction framework to help acquire hypernyms of different entities directly from the web. The second method explores the relations between seen classes and new classes. We propose a prompt-based model with semantic knowledge augmentation to recognize new relation triplets under the zero-shot setting. In this method, we transform the problem of zero-shot learning into supervised learning with the generated augmented data for new relations. We design the prompts for training using the auxiliary information based on an external knowledge graph to integrate semantic knowledge learned from seen relations. The third work utilizes auxiliary information from images to enhance few-shot learning. We propose a multi-modal few-shot relation extraction model that leverages both textual and visual semantic information to learn a multi-modal representation jointly. To supplement the missing contexts in text, this work integrates both local features (object-level) and global features (pixel-level) from different modalities through image-guided attention, object-guided attention, and hybrid feature attention to solve the problem of sparsity and noise. We then explore the few-shot and zero-shot aspect (attribute-value) extraction in the e-commerce application field. The first work studies the multi-label few-shot learning by leveraging the auxiliary information of anchor (label) and category description based on the prototypical networks, where the hybrid attention helps alleviate ambiguity and capture more informative semantics by calculating both the label-relevant and query-related weights. A dynamic threshold is learned by integrating the semantic information from support and query sets to achieve multi-label inference. The second work explores multi-label zero-shot learning via semi-inductive link prediction of the heterogeneous hypergraph. The heterogeneous hypergraph is built with higher-order relations (generated by the auxiliary information of user behavior data and product inventory data) to capture the complex and interconnected relations between users and the products. / Doctor of Philosophy / Information extraction is the process of automatically extracting structured information from unstructured sources, such as plain text documents, web pages, images, and so on. In this dissertation, we will first focus on general relation extraction, which aims at identifying and classifying semantic relations between entities. For example, given the sentence `Peter was born in Manchester.' in the newspaper, structured information (Peter, place of birth, Manchester) can be extracted. Then, we focus on attribute-value (aspect) extraction in the application field, which aims at extracting attribute-value pairs from product descriptions or images on e-commerce websites. For example, given a product description or image of a handbag, the brand (i.e. brand: Chanel), color (i.e. color: black), and other structured information can be extracted from the product, which provides a better search and recommendation experience for customers. With the advancement of deep learning techniques, machines (models) trained with large quantities of example input data and the corresponding desired output data, can perform automatic information extraction tasks with high accuracy. Such example input data and the corresponding desired output data are also named annotated data. However, across technological innovation and social change, new data (i.e. articles, products, etc.) is being generated continuously. It is difficult, time-consuming, and costly to annotate large quantities of new data for training. In this dissertation, we explore several different methods to help the model achieve good performance with only a few (few-shot learning) or even no labeled data (zero-shot learning) for training. Humans are born with no prior knowledge, but they can still recognize new information based on their existing knowledge by continuously learning. Inspired by how human beings learn new knowledge, we explore different auxiliary information that can benefit few-shot and zero-shot information extraction. We studied the auxiliary information from existing data statistics, knowledge graphs, corresponding images, labels, user behavior data, product inventory data, optical characters, etc. We enable few-shot and zero-shot learning by adding auxiliary information to the training data. For example, we study the data statistics of both labeled and unlabeled data. We use data augmentation and prompts to generate training samples for no labeled data. We utilize graphs to learn general patterns and representations that can potentially transfer to unseen nodes and relations. This dissertation provides the exploration of how utilizing the above different auxiliary information to help improve the performance of information extraction with few annotated or even no annotated training data.

Yes / Trait inferences occur routinely and rapidly during social interaction, sometimes based on scant or fleeting information. In this research, participants (perceivers) made inferences of targets' big‐five traits after briefly watching or listening to an unfamiliar target (a third party) performing various mundane activities (telling a scripted joke or answering questions about him/herself or reading aloud a paragraph of promotional material). Across three studies, when perceivers judged targets to be either low or high in one or more dimensions of the big‐five traits, they tended to be correct, but they did not tend to be correct when they judged targets as average. Such inferences seemed to vary in effectiveness across different trait dimensions and depending on whether the target's behaviour was presented either in a video with audio, a silent video, or just in an audio track—perceivers generally were less often correct when they judged targets as average in each of the big‐five traits across various information channels (videos with audio, silent videos, and audios). Study 3 replicated these findings in a different culture. We conclude with discussion of the scope and the adaptive value of this trait inferential ability.

Mimicking human motion with a humanoid robot can prove to be useful for studying gaits, designing better prostheses, or assisting the elderly or disabled. Directly mimicking and implementing a motion of a human on a humanoid robot may not be successful because of the different dynamic characteristics between them, which may cause the robot to fall down due to instability. Using the Zero Moment Point as the stability criteria, this work proposes an Analytical Motion Filter (AMF), which stabilizes a reference motion that can come from human motion capture data, gait synthesis using kinematics, or animation software, while satisfying common constraints. In order to determine how the AMF stabilized a motion, the different kinds of instabilities were identified and classified when examining the reference motions. The different cases of instability gave more insight as to why a particular motion was unstable: the motion was too fast, too slow, or inherently unstable. In order to stabilize the gait two primary methods were utilized: time and spatial scaling. Spatial scaling scaled the COM trajectory down towards a known stable trajectory. Time scaling worked similarly by changing the speed of the motion, but was limited in effectiveness based on the types of instabilities in the motion and the coupling of the spatial directions. Other constraints applied to the AMF and combinations of the different methods produced interesting results that gave more insight into the stability of the gait. The AMF was tested using both simulations and physical experiments using the DARwIn miniature humanoid robot developed by RoMeLa at Virginia Tech as the test platform. The simulations proved successful and provided more insight to understanding instabilities that can occur for different gait generation methods. The physical experiments worked well for non-walking motions, but because of insufficient controllability in the joint actuators of the humanoid robot used for the experiment, the high loads during walking motions prevented them from proper testing. The algorithms used in this work could also be expanded to legged robots or entirely different platforms that depend on stability and can use the ZMP as a stability criterion. One of the primary contributions of this work was showing that an entire reference motion could be stabilized using a single set of closed form solutions and equations. Previous work by others considered optimization functions and numeric schemes to stabilize all or a portion of a gait. Instead, the Analytical Motion Filter gives a direct relationship between the input reference motion and the resulting filtered output motion. / Ph. D.

Human-building relationships impact everyone in industrialized society. We spend approximately 90% of our lives in the built environment. Buildings have a large impact on the environment; consuming 20% of worldwide energy (40% of U.S. energy) annually. Buildings are complex systems, yet architecture, engineering, and construction (AEC) professionals often perform their work without considering the human factors that affect the operational performance of the building system. The AEC industry currently employs a linear design and delivery approach, lacking verified performance standards and real-time feedback once a certificate of occupancy is issued. We rely on static monthly utility bills that lag and mask occupant behavior. We rely on lawsuits and anecdotal business development trends as our feedback mechanisms for the evaluation of a complex, system-based product. The omission of human factors in the design and delivery of high performance building systems creates risk for the AEC industry. Neglecting an iterative, human-centered design approach inhibits our ability to relinquish the building industry's position as the top energy consuming sector. Therefore, this research aims to explore, identify, and propose optimizations to critical human-building relationships in the multifamily housing system. This work is grounded in Sociotechnical Systems theory (STS). STS provides the most appropriate theoretical construct for this work because 1) human-building interactions (HBI) are fundamentally, human-technology interactions, 2) understanding HBI will improve total system performance, and 3) the interrelationships among human-building subsystems and the potential for interventions to effect the dynamics of the system are not currently well understood. STS was developed in the 1940's as a result of work system design changes with coal mining in the United Kingdom. STS consists of four subsystems and provides a theoretical framework to approach the joint optimization of complex social and technical problems. In the context of this work, multidisciplinary approaches were leveraged from human factors engineering and building construction to explore relationships among the four STS subsystems. An exploratory case study transformed the work from theoretical construct toward an applied STS model. Data are gathered from each STS subsystem using a mixed-methods research design. Methods include Systematic Review (SR), a descriptive case study of zero energy housing, and the Macroergonomics Analysis and Design (MEAD) of three builder-developers. This work contributes to bridging the bodies of knowledge between human factors engineering and the AEC industry. An output of this work is a framework and work system recommendations to produce human-centered, adaptive buildings. This work specifically examined the system inputs and outputs of multifamily housing in the United States. The findings are supportive of existing scientific society, government, and industry standards and goals. Relevant standards and goals include the Human Factors and Ergonomics Society (HFES) Macroergonomics and Environmental Design Technical Groups, International Energy Agency's Energy in Buildings ANNEX 79 Occupant Behavior-Centric Building Design and Operation, the U.S. Department of Energy's Building America Research to Market Plan and zero energy building goals of the American Society of Heating Refrigeration and Air-Conditioning Engineers (ASHRAE). / Doctor of Philosophy / We spend approximately 90% of our lives in the built environment. Buildings have a large impact on the environment; consuming 20% of worldwide energy (40% of U.S. energy) annually. As we work to reduce energy use in buildings, new challenges have emerged. As buildings become more complex, the architecture, engineering, and construction industry (AEC) must adapt. The industry historically employs a linear design and delivery approach, lacking verified performance standards and real-time feedback once a certificate of occupancy is issued. We rely on static monthly utility bills that lag and mask occupant behavior. We rely on lawsuits and anecdotal business development trends as our feedback mechanisms for the evaluation of a complex, system-based product. The omission of human factors in the design and delivery of high-performance building systems creates risk for the industry and occupants. To better understand that risk, a comparative analysis of zero energy housing explores the relationship between humans and the buildings of the future. A second case study explores the work systems of builder-developers by using the Macroergonomic Analysis and Design method. The work reports risks and barriers in the system, as well as opportunities to create human-centered, adaptive housing. Specifically, this project enhances our understanding of 1) high performance housing, 2) their occupants, and 3) the builder-developers that produce high performance housing.

The purpose of this study was to determine what change, if any, existed in the number and percentage of student discipline referrals and exclusionary discipline practices of students by race, gender, and those with disabilities after the introduction of a division-wide, systematic approach to discipline that aligned behavior, social-emotional wellness, and academics into one decision-making framework. This research used quantitative data with a nonexperimental descriptive design. The researcher sought to answer the questions: 1. What is the number and percentage of students receiving an office discipline referral by race, gender, and those with a disability? 2. What is the number and percentage of students receiving suspensions, both in-school and out-of-school, related to office discipline referrals for students by race, gender, and those with a disability? 3. How has the number and percentage changed for incidents over the three years of implementing a systematic approach that aligns behavior, social-emotional wellness, and academics into one decision-making framework for students of different races, genders, and those with a disability? 4. How has the number and percentage changed for consequences over the three years of implementing a systematic approach that behavior, social-emotional wellness, and academics into one decision-making framework for students of different races, genders, and those with a disability? This study included 39 schools (24 elementary schools, seven middle schools, five high schools, one middle/high school, one specialty high school, and one alternative school) of an urban school division in the Commonwealth of Virginia. The selected division leadership team established an outcome to decrease office discipline referrals (ODRs), In-School Suspension (ISS), and Out-of-School Suspensions (OSS) in order to increase instructional time in the classroom. The sampled schools had evidence of varying levels of implementation. This study examined the effects of a multi-tiered system of support on student discipline. This study found that the proportion of students receiving ODRs was not reduced by the implementation of a multitiered framework. Additionally, the number of ODRs increased for most subgroups over the period of the study. However, the study did find that the disproportionality for SWD decreased for ODRs. The study also found that the gap in proportions between Black students receiving ISS and White students receiving ISS increased. Despite the growing disparity between Black and White students, disproportionality for SWD receiving ISS decreased. Conversely, the proportion of Black students receiving OSS decreased over the 3-year period of the study. In conjunction to the findings related to ISS, the disproportionality of SWD receiving OSS decreased during this study period. Finally, the study found that the proportion of female students receiving LTS increased over the 3-year period of the study. This study did not include an analysis of the critical features of a multi-tiered system of support. / Doctor of Education / The purpose of this study was to determine what change, if any, existed in the number and percentage of student discipline referrals and exclusionary discipline practices of students by race, gender, and those with disabilities after the introduction of a division-wide, systematic approach to discipline that aligned behavior, social-emotional wellness, and academics into one decision-making framework. This research used quantitative data with a nonexperimental descriptive design. This study found that the proportion of students receiving ODRs was not reduced by the implementation of a multitiered framework. Additionally, the number of ODRs increased for most subgroups over the period of the study. However, the study did find that the disproportionality for SWD decreased for ODRs. The study also found that the gap in proportions between Black students receiving ISS and White students receiving ISS increased. Despite the growing disparity between Black and White students, disproportionality for SWD receiving ISS decreased. Conversely, the proportion of Black students receiving OSS decreased over the 3-year period of the study. In conjunction to the findings related to ISS, the disproportionality of SWD receiving OSS decreased during this study period. Finally, the study found that the proportion of female students receiving LTS increased over the 3-year period of the study. This study did not include an analysis of the critical features of a multi-tiered system of support.