The quantum walk is a unitary analogue to the discrete random walk, and its properties have been increasingly studied since the turn of the millennium. In comparison with the classical random walk, the quantum walk exhibits linear spreading and initial condition dependent asymmetries. As noted early on in the conjecture and subsequent calculation of absorption probabilities in the one dimensional Hadamard walk, the interaction of the quantum walk with an absorbing boundary is fundamentally divergent from classical case. Here, we will survey absorption probabilities for a more general collection of one dimensional quantum walks and extend the method to consider d-dimensional walks in the presence of d-1 dimensional absorbing walls. However, these results are concerned only with local behavior at the boundary in the form of absorption probabilities. The main results of this thesis are concerned with the global behavior of finite quantum walks, which can be described by linear spreading in the short term, modal phenomena in the mid term, and stable distributions in the exceedingly long term. These theorems will be rigorously proved in the one-dimensional case and extrapolated to higher dimensional quantum walks. To this end we introduce QWSim, a new and robust computational engine for displaying finite two dimensional quantum walks.

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Much of the walking that we do in our daily lives is dull, but sometimes, unexpectedly, it can be revelatory. During these moments, through what phenomenologist Maurice Merleau-Ponty calls the "lived perspective" of walking, we experience a merging of our inner and outer worlds and achieve greater self-awareness. Although most of our experience in the landscape is through movement, we rarely design for such spaces. Using the hypothesis that terrorist threats and an aging infrastructure may lead to the rerouting of the CSX Railway south of Washington, D.C., shutting down the existing line, I propose to convert the CSX Railway bridge that crosses the Anacostia River in Southeast Washington to an open public space. While other portions of the track may be demolished and returned to the wide avenues envisioned by L'Enfant or renovated as trolley tracks, the CSX bridge could be renovated to provide a link between the neighborhood of Capitol Hill and the Anacostia River through a pedestrian walkway. The methodology I use to explore this thesis is two-fold. I study several environments, from site-specific artworks to monuments to large urban parks. I also study fields that explore the experiential nature of perception such as art and philosophy, and use the freedom of expression that drawing allows as a tool to inform the design of spaces that can enable us to experience a state in which our mind, body, and vision are intertwined. / Master of Landscape Architecture

Online Social Networks (OSNs) such as Facebook, Twitter, and YouTube are among the most popular sites on the Internet. Billions of users are connected through these sites, building strong and effective communities to share views and ideas, and make recommendations nowadays. Therefore, by choosing an appropriate user-base from billions of people is required to analyze the structure and key characteristics of the large social graphs to improve current systems and to design new applications. For this reason, node sampling technique plays an important role to study large-scale social networks. As a basic requirement, the sampled nodes and their links should possess similar statistical features of the original network, otherwise the conclusion drawn from the sampled network may not be appropriate for the entire population. Hence, good sampling strategies are key to many online social network applications. For instance, before introducing a new product or adding new feature(s) of a product to the online social network community, that specific new product or the additional feature has to be exposed to only a small set of users, who are carefully chosen to represent the complete set of users. As such, different random walk-based sampling techniques have been introduced to produce samples of nodes that not only are internally well-connected but also capture the statistical features of the whole network. Traditionally, walk-based techniques do not have the restriction on the number of times that a node can be re-visited while sampling. This may lead to an inefficient sampling method, because the walk may be "stuck" at a small number of high-degree nodes without being able to reach out to the rest of the nodes. A random walk, even after a large number of hops, may not be able to obtain a sampled network that captures the statistical features of the entire network. In this thesis, we propose two walk-based sampling techniques to address the above problem, called K-Avoiding Random Walk (KARW) and Neighborhood-Avoiding Random Walk (NARW). With KARW, the number of times that a node can be re-visited is constrained within a given number K. With NARW, the random walk works in a "jump" fashion, since the walk starts outside of the N-hop neighborhood from the current node chosen randomly. By avoiding the current nodes neighboring area of level-N, NARW is expected to reach out the other nodes within the entire network quickly. We apply these techniques to construct multiple independent subgraphs from a social graph, consisting of 63K users with around a million connections between users collected from a Facebook dataset. By simulating our proposed strategies, we collect performance metrics and compare the results with the current state-of-the-art sampling techniques (Uniform Random Sampling, Random Walk, and Metropolis Hastings Random Walk). We also calculate some of the key statistical features (i.e., degree distribution, betweenness centrality, closeness centrality, modularity, and clustering coefficient) of the sampled graphs to get an idea about the network structures that essentially represent the original social graph. / Graduate / 0984 / shahed.anwar@gmail.com

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This thesis describes the development of a tool to assist animators in doing walk cycles. In traditional animation, animators create expressive walk cycles with key poses. The process of generating walk cycles by hand is tedious and repetitive. To help animators, many researchers in computer graphics have worked on automating gait generation. However, almost all of them used methods that eliminate animator defined key poses. Although they produce realistic results, their methods are not suitable for expressive walk cycles that can be found in cartoons. The tool described in this thesis attempts to incorporate practices of traditional animators such as comparison of key poses and the use of arc into the program interface. With this tool, animators can concentrate only on setting key poses, which is the most creative task in animating expressive walk. The gait generation program can produce highly expressive walks like the double bounce walk and the sneak. With automated features of the developed tool, animators can save time and effort when animating expressive walk along a curved path.

This study has been conducted in order to determine the existence of predictability for the Stockholm stock exchange. With this purpose the random walk theory has been raised against the theory of mean reversion in order to determine which theory is the most substantial. Data has been collected from Nasdaq OMX Nordic and furtherly been processed using the statistical software EViews. Swedish listed companies’ daily share values between 2000-2014 have been analyzed using two tests; an Augmented Dickey Fuller test and a Variance Ratio test. The results show generally that the null hypothesis - and thus the random walk - is rejected in the short term. This means that both on an aggregated level and on an individual level, the Stockholm stock exchange is predictable in the short term - in the form of mean reversion - and that it is most evident in small cap firms.

A high amount of the US population is not physically active, contributing to rates of heart disease and obesity. One strategy to increase physical activity is to use more active transportation, defined as walking or biking for transit. Besides increasing physical activity levels, active transportation can provide other benefits such as decreased air pollution from cars. College campuses provide opportunities for active transportation as most residences are close to campus. Therefore, we examined reasons for use and barriers to active transportation in students living in a community connected to a large university via a 1.9 mile, paved protected trail. Two pedestrian and bicycle counters were placed to find the number of walkers and bikers on the trail per day and students were recruited to take an online survey. We found that more people used the trail during the weekday compared to the weekend. Students did not receive much support from their friends and family to use the trail. Users of the trail were more likely to believe that using active transportation helps protect the environment while non-users were uncomfortable using a bike. Barriers included the time it took to use the trail and the need to carry items. Both users and non-users indicated that a financial incentive would motivate them to use the trail more. We conclude that non-users may be uncomfortable using a bike and worry about carrying their items for class. Changing university parking fees, providing bike lessons, and placing signs with directions and time to campus may increase active transportation to the university via this trail. / Master of Science / A high amount of the US population is not physically active, contributing to rates of heart disease and obesity. One strategy to increase physical activity is to use more active transportation, defined as walking or biking for transit. Besides increasing physical activity levels, active transportation can provide other benefits such as decreased air pollution from cars. College campuses provide opportunities for active transportation as most residences are close to campus. Therefore, we examined reasons for use and barriers to active transportation in students living in a community connected to a large university via a 1.9 mile, paved protected trail. Two pedestrian and bicycle counters were placed to find the number of walkers and bikers on the trail per day and students were recruited to take an online survey. We found that more people used the trail during the weekday compared to the weekend. Students did not receive much support from their friends and family to use the trail. Users of the trail were more likely to believe that using active transportation helps protect the environment while non-users were uncomfortable using a bike. Barriers included the time it took to use the trail and the need to carry items. Both users and non-users indicated that a financial incentive would motivate them to use the trail more. We conclude that non-users may be uncomfortable using a bike and worry about carrying their items for class. Changing university parking fees, providing bike lessons, and placing signs with directions and time to campus may increase active transportation to the university via this trail.

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