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Symmetric functions, which take as input an unordered, fixed-size s et, find practical application in myriad physical settings based on indistinguishable points or particles, and are also used as intermediate building blocks to construct networks with other invariances. Symmetric functionsare known to be universally representable by neural networks that enforce permutation invariance. However the theoretical tools that characterize the approximation, optimization and generalization of typical networks fail to adequately characterize architectures that enforce invariance.

Adolescence stands out as a crucial stage in the complex fabric of the human experience, one that is characterised by the convergence of self-definition, growth, and discovery. But in the midst of all the unending opportunities and goals that come with being young, depression is a silent cloud that hangs over a lot of young people. The pressures and difficulties that young people encounter in today's fast-paced, globally connected world are constantly changing, and this has a significant negative influence on their mental health. "Finding Light: A Guide to Overcoming Youth Depression" shines as a beacon of understanding, compassion, and perseverance within this complex landscape of emotions and experiences

This study started in February, 2013 at the Collider-Accelerator Department of BNL. During the study, the technique of independent component analysis (ICA) was first introduced to RHIC for a systematic estimation of RHIC BPM noise performance and turn-by-turn (TBT) beam position monitor (BPM) data based optics measure- ment. The beta-beat response matrix based global correction scheme and the method of arc beta-beat correction using horizontal closed orbit at sextupoles were developed for RHIC. These techniques were successfully demonstrated in two beam experiments with a total of 4 hours' beam time. In the meantime, various software packages were developed to facilitate the beam experiments and future studies.

This is a three-part project concerning methods for the study of political semantics -how the 'meaning' of political concepts is represented and organized in memory and implications for political attitudes and behavior. The first chapter proposes a framework for the estimation of group differences in memory representations of political concepts and applies it to evaluate partisan representational differences in the U.S. The second chapter proposes amemory-centered approach to the study of ideology along with the requisite methods for its implementation. The third chapter centers on word embeddings, a deep learning method to estimate word representations from large collections of text. Along with a conceptual overview, it provides practitioners with a series of tests to perform model comparison and validation, including a novel Turing-style test

Scripting involves an ambiguity. First, it indicates a directive, as in the commands of "scripture"; or, in the disappointment that an apparently spontaneous happening was in fact "scripted." This engages a familiar outlook on computing: code is language operating in a "prescriptive" register. Additionally, however, scripting also hints towards the materiality of graphic "inscription," such as the traces expressed in the written form of a "manuscript." Thehistory of computing presented here is situated at the joints of these two senses. Working between them prompts an archaic image of the computer, far removed from advanced technologies of electronic machinery. It instead suggests its deep historical heritage in clerical labor, affording a perspective on computation as a manual, incorporated, and lived activity-that is, as the product of scribes.

This research is an original approach that applies industrial engineering and operations research tools to the sociological problem of sex trafficking victimization. Such an approach enables quantitative evaluation of the impacts on an individual's lifetime by anti-trafficking efforts and public policies. A fully interconnected, lifetime model for the experience of sex trafficking victimization is defined as the result of a comprehensive review of literature. Beginning with victimization risk, the defined model is an anticipatory tool to understand the incidences and consequences toindividuals during their lifetime.

Conflict is not only inevitable in a romantic relationship, but also a primary predictor of relationship satisfaction and commitment. The purpose of this quantitative correlational study was to examine if and to what extent a correlation exists between the five mechanisms of mindfulness identified in the Five Facet Mindfulness Questionnaire and the conflict strategy subdomains identified in the Romantic Partner Conflict Scale as used byadults in a committed romantic relationship living in the mid-Atlantic region of the US. Jon Kabat-Zinn's model of mindfulness and Albert Chavannes's social exchange theory serve as the theoretical foundations for this study.