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.

The world is observing unprecedented, devastating, yet growing effects of climate change. GDP has been slow for decades; Covid-19 has disturbed the economy; energy prices are rising; unemployment remains high; consumer debt and budget deficit are climbing; wealth inequality is at an all-time high. Still, 89% of the energy consumed in the United States comes from non-renewable sources. Amid this challenging time, the question this work tries to answer is how can we protect our climate and environment through innovative development policies and practices that concurrently promote social equity and preserve economic viability? To answer this question, I explore five sustainable housing goals: climate protection, policy innovation, environmental protection, social equity, and economic growth. I use data and empirical analysis to show sustainable development challenges and conflicts are significant. I share lessons learned from cities and states that act as pioneers of climate and environmental protection; I explore a balanced integration of economic, environmental, and social goals through zero-energy building in the traditionally siloed policy sector of low-income housing; I show that a lack of consideration for social equity can turn environmental initiatives into luxury goods that surrender equity to profitability; I show that a lack of consideration for economic viability can lead to underinvestment in environmental and social equity initiatives. The overall insights derived from this study suggest that state housing agencies and local governments, particularly in large cities and in communities that are more vulnerable to environmental risks, are in a unique position to stimulate and drive climate and environmental protection. Significant between-agency differences in housing policy innovation persist, and future policy innovation research should explore factors that impact the utility of policy innovation and barriers the environmental sustainability movement faces at the organization level and beyond. Existing challenges to distributed energy generation need further study. This research highlights the need for greater policy attention to affordable housing needs in core urban areas, neighborhood diversity, and costs of gentrification. / Doctor of Philosophy / The world is now observing unprecedented, devastating, yet growing effects of climate change. Covid-19 has slowed the economy; energy prices are rising; unemployment remains high; consumer debt and budget deficit are climbing, and wealth inequality has reached an all-time high. While renewable energy is rapidly growing in worldwide adoption, still 89% of the energy consumed in the United States comes from non-renewable sources. Sustainability thinking encourages integrated, interdisciplinary approaches and policies that holistically address multiple contemporary problems. Sustainable development requires a balanced integration of economic, environmental, and social justice goals with traditionally siloed policy sectors, such as housing, as a goal of governance. Policy integration is deemed necessary because some policy sectors – like environment and climate – alone are not capable of achieving all objectives and, thus, must work with other sectors. Despite the importance of sustainability to the future of the planet, there are inherent economic, environmental, and social justice conflicts involved in reaching sustainable development, and conflict resolution has not been easy. The overarching question in this work is how can we protect our climate and environment through innovative housing policies and practices that promote social equity and preserve economic viability? I explore five glocal sustainable housing goals, namely climate protection, policy innovation, environmental protection, social equity, and economic growth. The overall insights derived from this study suggest that state housing agencies and local governments, particularly in large cities and in communities vulnerable to environmental risks, are in a unique position to stimulate and drive climate and environmental protection. Significant between-agency differences in housing policy innovation persist, and future policy innovation research should explore factors that impact the utility of policy innovation and barriers the environmental sustainability movement faces at the organization level and beyond. This research highlights the need for greater policy attention to affordable housing needs in core urban areas, neighborhood diversity, and costs of gentrification. There are barriers to distributed energy generation that need to be studied.

The immutability, validity and confidentiality of an audit log is crucial when operating over sensitive data to comply to standard data regulations (e.g., HIPAA). Despite its critical needs, state-of-the-art privacy-preserving audit log schemes (e.g., Ghostor (NSDI '20), Calypso (VLDB '19)) do not fully obtain a high level of privacy, integrity, and immutability simultaneously, in which certain information (e.g., user identities) is still leaked in the log. In this work, we propose Harpocrates, a new privacy-preserving and immutable audit log scheme. Harpocrates permits data store, share, and access operations to be recorded in the audit log without leaking sensitive information (e.g., data identifier, user identity), while permitting the validity of data operations to be publicly verifiable. Harpocrates makes use of blockchain techniques to achieve immutability and avoid a single point of failure, while cryptographic zero-knowledge proofs are harnessed for confidentiality and public verifiability. We analyze the security of our proposed technique and prove that it achieves non-malleability and indistinguishability. We fully implemented Harpocrates and evaluated its performance on a real blockchain system (i.e., Hyperledger Fabric) deployed on a commodity platform (i.e., Amazon EC2). Experimental results demonstrated that Harpocrates is highly scalable and achieves practical performance. / Master of Science / Audit logs are an essential part of data storage systems as they allow to check if the system is working as intended. They are usually maintained on a server, a server with ill intentions can easily modify records of the log and make it appear that the system is working correctly. To store these records in an un-modifiable manner, prior works have leveraged special audit log storing mechanisms for e.g., blockchain due to its immutable nature. However, these works do not focus on the privacy of the records which is a crucial aspect for conforming to certain data regulations like HIPAA. In our work, we propose Harpocrates, an immutable and privacy-preserving audit log platform that supports recording operations (share/access) on sensitive data. Harpocrates leverages blockchain to achieve immutability of the audit log. Harpocrates use specific cryptographic primitives to achieve public verifiability and confidentiality of the audit log. Real world deployment of Harpocrates shows that it is practical and achieves strong security guarantees.

The original design of zero-tolerance policies was meant to support school safety through an anti-drug and violence campaign but in the years following their implementation, school districts have employed them repeatedly without merit. Exclusionary practices have become controversial, leading to high rates of recidivism, imbalanced implementation toward minority groups, and the loss of learning while suspended or expelled. Just as effective educators respond and intervene to instructional practices that are not proving successful, an overhaul of disciplinary practices was necessary for academic and emotional health. Restorative practices have emerged in recent years as an alternative process to the antiquated system of exclusionary measures. The previously used disciplinary structure inhibited the education of students, diminished opportunities for relationships to form and flourish, and had the potential to damage the well-being of all students involved in a negative event. In recent years, school districts across the country have recognized a need for improvement in the education system. Educators are spearheading efforts to combat the widespread epidemic of illiteracy and increase the level of college and career readiness. As a result, time, funding, professional development opportunities, and research have been dedicated to support this endeavor. While a number of resources are allotted for instructional purposes, the emotional element of student success is often overlooked, only widening the gap between success and stagnation. The purpose of this qualitative study was to examine pre-K through fifth grade teacher perceptions of integrated restorative practices in their respective classrooms and how these practices affected disciplinary measures and intervention.

The Atiyah Conjecture originates from a paper written 40 years ago by Sir Michael Atiyah, a famous mathematician and Fields medalist. Since publication of the paper, mathematicians have been working to solve many questions related to the conjecture, but it is still open. The conjecture is about certain topological invariants attached to a group 𝐺. There are examples showing that the conjecture does not hold in general. These examples involve something like the lamplighter group (the wreath product ℤ/2ℤ ≀ ℤ). We are interested in looking at examples where this is not the case. We are interested in the specific case where 𝐺 is a finitely generated group in which the Prüfer group can be embedded as the center. The Prüfer group is a 𝑝-group for some prime 𝑝 and its finite subgroups have unbounded order, in particular the finite subgroups of G will have unbounded order. To understand whether any form of the Atiyah conjecture is true for 𝐺, it will first help to determine whether the group ring 𝑘𝐺 of the group 𝐺 has a classical ring of quotients for some field 𝑘. To determine this we will need to know the zero divisors for the group ring 𝑘𝐺. Our investigations will be divided into two cases, namely when the characteristic of the field 𝑘 is the same as the prime p for the Prüfer group and when it is different. / Master of Science

Vehicles and mechanisms which must perform very precise tasks or maneuvers require controllers to compensate for their inherent structural flexibility. Many of these applications involve structures that have time-varying dynamics, or have dynamics that are not considered in the traditional off-line controller design. These types of structures necessitate the use of adaptive control algorithms which can redesign themselves on-line in response to changes in the structural dynamics. This work describes an on-line control algorithm that uses the pole-zero spacings of the collocated control-to-output transfer function to design the optimum Positive Position Feedback (PPF) control law. The PPF control law uses second-order filters to add closed-loop damping to resonant structural modes. An on-line PPF design algorithm was developed based on the theoretical model of the collocated control-to-output transfer function. The optimal PPF filter parameters are shown to be a function of the pole-zero spacing in the collocated transfer function. These parameters were found by solving the pole placement problem using a theoretical model for various pole-zero spacings. The parameters are then stored in a lookup table in the realtime controller, and a frequency sweep algorithm identifies the pole-zero spacing on-line and designs the PPF filters using the parameters in the lookup table. A Phase-Locked Loop (PLL) was also studied as a means for adaptively tuning the PPF filters on-line. The PLL behavior in the presence of random and deterministic signals was characterized. The PLL was used experimentally to tune a PPF filter to a changing modal frequency. Analysis of the theoretical model indicated the amount of closed-loop damping a PPF filter can add monotonically increases with the amount of frequency spacing of the pole/zero pair. Experimental results with the on-line optimal PPF control algorithm proved it to be effective at adding damping to structures and suppressing vibration. The poles and zeros of the control-to-output transfer function were accurately identified by the pole/zero identification routine. However, the closed-loop performance was shown to be very dependent on the correct placement of sensor and actuator pairs. Tests with pointing control problems showed the algorithm to be better suited to vibration suppression rather than vibration isolation. Simulations and experiments with the phase-locked loop showed it to be unable to track a modal frequency of a structure excited by broadband noise. Bandpass prefilters would be necessary to eliminate the frequency content of the other modes, limiting the usefulness of the PLL. / Master of Science

This thesis covers the Cantor Ternary Set and generalizations of the Cantor Set, and gives a complete existential theory for three set properties: denumerability, exhaustibility, and zero measure.

Approved for public release; distribution in unlimited. / In this thesis, a new fictitious play (FP) procedure is presented to solve two-person zero-sum (TPZS) Blotto games. The FP solution procedure solves TPZS games by assuming that the two players take turns selecting optimal responses to the opponent's strategy observed so far. It is known that FP converges to an optimal solution, and it may be the only realistic approach to solve large games. The algorithm uses dynamic programming (DP) to solve FP subproblems. Efficiency is obtained by limiting the growth of the DP state space. Blotto games are frequently used to solve simple missile defense problems. While it may be unlikely that the models presented in this paper can be used directly to solve realistic offense and defense problems, it is hoped that they will provide insight into the basic structure of optimal and near-optimal solutions to these important, large games, and provide a foundation for solution of more realistic, and more complex, problems. / Captain, Republic of Korea Air Force