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This thesis studies the large scale dimension theory of metric spaces. Background on dimension theory is provided, including topological and asymptotic dimension, and notions of nonpositive curvature in metric spaces are reviewed. The hyperbolic dimension of Buyalo and Schroeder is surveyed. Miscellaneous new results on hyperbolic dimension are proved, including a union theorem, an estimate for central group extensions, and the vanishing of hyperbolic dimension for countable abelian groups. A new quasi-isometry invariant called weak hyperbolic dimension (abbreviated $\wdim$) is introduced and developed. Weak hyperbolic dimension is computed for a variety of metric spaces, including the fundamental computation $\wdim \Hyp^n = n-1$. An estimate is proved for (not necessarily central) group extensions. Weak dimension is used to obtain the quasi-isometric nonembedding result $\Hyp^4 \not \rightarrow \Sol \times \Sol$ and possible directions for further nonembedding applications are explored. / Thesis / Doctor of Philosophy (PhD) / Shapes and spaces are studied from the "large scale" or "far away" point of view. Various notions of dimension for such spaces are studied.

I report on the iterative process of designing a mobile AI poetry system, along with a series of broad scale use cases in which different variants of the system has been tested in the wild. The project has so far resulted in the generation of about 20 million individual poems, co-created by the system together with millions of users. Apart from the design of the technical side of the system, my focus has been on how the system could be adapted to and deployed in different commercial settings. I discuss my insights related to systems support for creative processes, and how findings from these use cases could be applicable also to other AI content generation systems. / Här beskrivs den iterativa utformningen av en mobilapplikation för AI-genererad poesi, samt en serie storskaliga kommersiella kampanjer där olika varianter av systemet har testats i verklig användning. Genom detta genererades cirka 20 miljoner enskilda dikter, producerade av systemet tillsammans med miljontals användare. Förutom systemets tekniska funktionalitet beskrivs hur systemet anpassats för att distribueras i olika kommersiella sammanhang. Utifrån denna process diskuteras insikter relaterade till systemstöd för kreativa processer, och hur lärdomar från denna process kan tillämpas även i andra system för AI-genererat innehåll.

The objective of the research is to study optimal routing policy (ORP) problems and to develop an optimal adaptive routing algorithm practical for large-scale Stochastic Time-Dependent (STD) real-life networks, where a traveler could revise the route choice based upon en route information. The routing problems studied can be viewed as counterparts of shortest path problems in deterministic networks. A routing policy is defined as a decision rule that specifies what node to take next at each decision node based on realized link travel times and the current time. The existing routing policy algorithm is for explorative purpose and can only be applied to hypothetical simplified network. In this research, important changes have been made to make it practical in a large-scale real-life network. Important changes in the new algorithm include piece-wise linear travel time representation, turn-based, label-correcting, criterion of stochastic links, and dynamic blocked links. Complete dependency perfect online information (CDPI) variant is then studied in a real-life network (Pioneer Valley, Massachusetts). Link travel times are modeled as random variables with time-dependent distributions which are obtained by running Dynamic Traffic Assignment (DTA) using data provided by Pioneer Valley Planning Commission (PVPC). A comprehensive explanation of the changes by comparing the two algorithms and an in-depth discussion of the parameters that affects the runtime of the new algorithm is given. Computational tests on the runtime changing with different parameters are then carried out and the summary of its effectiveness are presented. To further and fully understand the applicability and efficiency, this algorithm is then tested in another large-scale network, Stockholm in Sweden, and in small random networks. This research is also a good starting point to investigate strategic route choice models and strategic route choice behavior in a real-life network. The major tasks are to acquire data, generate time-adaptive routing policies, and estimate the runtime of the algorithm by changing the parameters in two large-scale real-life networks, and to test the algorithm in small random networks. The research contributes to the knowledge base of ORP problems in stochastic time-dependent (STD) networks by developing an algorithm practical for large-scale networks that considers complete time-wise and link-wise stochastic dependency.

Search engines play a very important role in daily life. As multimedia product becomes more and more popular, people have developed search engines for images and videos. In the first part of this thesis, I propose a prototype of a book image search engine. I discuss tag representation for the book images, as well as the way to apply the probabilistic model to generate image tags. Then I propose the random walk refinement method using tag similarity graph. The image search system is built on the Galago search engine developed in UMASS CIIR lab. Consider the large amount of data the search engines need to process, I bring in cloud environment for the large-scale distributed computing in the second part of this thesis. I discuss two models, one is the MapReduce model, which is currently one of the most popular technologies in the IT industry, and the other one is the Maiter model. The asynchronous accumulative update mechanism of Maiter model is a great fit for the random walk refinement process, which takes up 84% of the entire run time, and it accelerates the refinement process by 46 times.

<p>This is a dissertation by Funing Li submitted to the Faculty of Purdue University in partial fulfillment of the requirements for the degree of Doctor of Philosophy.</p>

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We investigate several techniques to identify voids in the galaxy distribution of matter in the universe. We utilize galaxy number counts as a function of apparent magnitude and Wolf plots to search a two- or three-dimensional data set in a pencil-beam fashion to locate voids within the field of view. The technique is able to distinguish between voids that represent simply a decrease in density as well as those that show a build up of galaxies on the front or back side of the void. This method turns out to be primarily useable only at relatively short range (out to about 200 Mpc). Beyond this distance, the characteristics indicating a void become increasingly difficult to separate from the statistical background noise. We apply the technique to a very simplified model as well as to the Millennium Run dark matter simulation. We then compare results with those obtained on the Sloan Digital Sky Survey. We also created the Watershed Void Examiner (WaVE) which treats densities in a fashion similar to elevation on a topographical map, and then we allow the "terrain" to flood. The flooded low-lying regions are identified as voids, which are allowed to grow and merge as the level of flooding becomes higher (the overdensity threshold increases). Void statistics can be calculated for each void. We also determine that within the Millennium Run semi-analytic galaxy catalog, the walls that separate the voids are permeable at a scale of 4 Mpc. For each resolution that we tested, there existed a characteristic density at which the walls could be penetrated, allowing a single void to grow to dominate the volume. With WaVE, we are able to get comparable results to those previously published, but often with fewer choices of parameters that could bias the results. We are also able to determine the the density at which the number of voids peaks for different resolutions as well as the expected number of void galaxies. The number of void galaxies is amazingly consistent at an overdensity of −0.600 at all resolutions, indicating that this could be a good choice for comparing models.