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Between 1960 and 1980, urban renewal transformed many cities, creating vast handwritten records. These documents posed a significant challenge for researchers due to their volume and handwritten nature. The launch of GPT-4V in November 2023 offered a breakthrough, enabling large-scale, efficient transcription and analysis of these historical urban renewal documents., Comment: Published in Digital Humanities (DH 2024). Aug 6-9. Arlington, VA

In a recent paper [16], the authors proposed a BGK model for relativistic gas mixtures based on the Marle-type approximation, which satisfies the fundamental kinetic properties: non-negativity of distribution functions, conservation laws, H-theorem, and indifferentiability principle. In this paper, we are concerned with the stationary problems to the relativistic BGK model for gas mixtures in slab geometry. We establish the existence of a unique mild solution with the fixed inflow boundary data when the collision frequencies for each species are sufficiently small., Comment: 17 pagas

In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on the aggregate cost function and the smoothness assumption on each local cost function, we prove the algorithm converges exponentially fast to a small neighborhood of the optimizer whose radius depends on the stepsizes. Based on our convergence result, we suggest an effective selection of stepsizes which repeats diminishing the stepsizes after a number of specific iterations. Both the convergence results and the effectiveness of the suggested stepsize selection are also verified by the numerical experiments., Comment: 21 pages, 4 figures

Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results %\cite{Kremer,Kremer3,KP} in which such relativistic BGK models for gas mixture are employed to compute transport coefficients. However, to the best knowledge of authors, relativistic BGK models for gas mixtures with complete presentation of the relaxation operators are missing in the literature. In this paper, we fill this gap by suggesting a BGK model for relativistic gas mixtures for which the existence of each equilibrium coefficients in the relaxation operator is rigorously guaranteed in a way that all the essential physical properties are satisfied such as the conservation laws, the H-theorem, the capturing of the correct equilibrium state, the indifferentiability principle, and the recovery of the classical BGK model in the Newtonian limit.

In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We obtain sharp estimates on the dynamic regret of the algorithm when the regular part of the cost is convex and smooth. If the Bregman distance is given by the Euclidean distance, our result also improves the previous work in two ways: (i) We establish a sharper regret bound compared to the previous work in the sense that our estimate does not involve $O(T)$ term appearing in that work. (ii) We also obtain the result when the domain is the whole space $\mathbb{R}^n$, whereas the previous work was obtained only for bounded domains. We also provide numerical tests for problems involving the errors in the gradient and proximal operator., Comment: 16 pages, 5 figures

In this paper, we establish the entropy-entropy production estimate for the ES-BGK model, a generalized version of the BGK model of the Boltzmann equation introduced for better approximation in the Navier-Stokes limit. Our result improves the previous entropy production estimate [39] in that (1) the full range of Prandtl parameters $-1/2\leq\nu <1$ including the critical case $\nu=-1/2$ is covered, and (2) a sharper entropy production bound is obtained. An explicit characterization of the coefficient of the entropy-entropy production estimate is also presented., Comment: 13 pages

The COVID-19 pandemic has brought both tangible and intangible damage to our society. Many researchers studied about its societal impacts in the countries that had implemented strong social distancing measures such as stay-at-home orders. Among them, human mobility has been studied extensively due to its importance in flattening the curve. However, mobility has not been actively studied in the context of mild social distancing. Insufficient understanding of human mobility in diverse contexts might provide limited implications for any technological interventions to alleviate the situation. To this end, we collected a dataset consisting of more than 1M daily smart device users in the third-largest city of South Korea, which has implemented mild social distancing policies. We analyze how COVID-19 shaped human mobility in the city from geographical, socio-economic, and socio-political perspectives. We also examine mobility changes for points of interest and special occasions such as transportation stations and the case of legislative elections. We identify a typology of populations through these analyses as a means to provide design implications for technological interventions. This paper contributes to social sciences through in-depth analyses of human mobility and to the CSCW community with new design challenges and potential implications., Comment: 26 pages

We study the boundary value problem of two stationary BGK-type models - the BGK model for fast chemical reaction and the BGK model for slow chemical reaction - and provide a unified argument to establish the existence and uniqueness of stationary flows of reactive BGK models in a slab. For both models, the main difficulty arises in the uniform control of the reactive parameters from above and below, since, unlike the BGK models for non-reactive gases, the reactive parameters for the reactive BGK models are defined through highly nonlinear relations. To overcome this difficulty, we introduce several nonlinear functionals that capture essential structures of such nonlinear relations such as the monotonicity in specific variables, that enable one to derive necessary estimates for the reactive equilibrium coefficients., Comment: typo checked