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  1. Free, publicly-accessible full text available July 23, 2025
  2. Bringmann, Karl ; Grohe, Martin ; Puppis, Gabriele ; Svensson, Ola (Ed.)
    The hereditary discrepancy of a set system is a quantitative measure of the pseudorandom properties of the system. Roughly speaking, hereditary discrepancy measures how well one can 2-color the elements of the system so that each set contains approximately the same number of elements of each color. Hereditary discrepancy has numerous applications in computational geometry, communication complexity and derandomization. More recently, the hereditary discrepancy of the set system of shortest paths has found applications in differential privacy [Chen et al. SODA 23]. The contribution of this paper is to improve the upper and lower bounds on the hereditary discrepancy of set systems of unique shortest paths in graphs. In particular, we show that any system of unique shortest paths in an undirected weighted graph has hereditary discrepancy O(n^{1/4}), and we construct lower bound examples demonstrating that this bound is tight up to polylog n factors. Our lower bounds hold even for planar graphs and bipartite graphs, and improve a previous lower bound of Ω(n^{1/6}) obtained by applying the trace bound of Chazelle and Lvov [SoCG'00] to a classical point-line system of Erdős. As applications, we improve the lower bound on the additive error for differentially-private all pairs shortest distances from Ω(n^{1/6}) [Chen et al. SODA 23] to Ω̃(n^{1/4}), and we improve the lower bound on additive error for the differentially-private all sets range queries problem to Ω̃(n^{1/4}), which is tight up to polylog n factors [Deng et al. WADS 23]. 
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  3. Izatt, Joseph A. ; Fujimoto, James G. (Ed.)
  4. Kidney cancer is a kind of high mortality cancer because of the difficulty in early diagnosis and the high metastatic dissemination in treatments. The surgical resection of tumors is the most effective treatment for renal cancer patients. However, precise assessment of tumor margins is a challenge during surgical resection. The objective of this study is to demonstrate an optical imaging tool in precisely distinguishing kidney tumor borders and identifying tumor zones from normal tissues to assist surgeons in accurately resecting tumors from kidneys during the surgery. 30 samples from six human kidneys were imaged using polarization-sensitive optical coherence tomography (PS-OCT). Cross-sectional, enface, and spatial information of kidney samples were obtained for microenvironment reconstruction. Polarization parameters (phase retardation, optic axis direction, and degree of polarization uniformity (DOPU) and Stokes parameters (Q, U, and V) were utilized for multiparameter analysis. To verify the detection accuracy of PS-OCT, H&E histology staining and dice-coefficient were utilized to quantify the performance of PS-OCT in identifying tumor borders and regions. In this study, tumor borders were clearly identified by PS-OCT imaging, which outperformed the conventional intensity-based OCT. With H&E histological staining as golden standard, PS-OCT precisely identified the tumor regions and tissue distributions at different locations and different depths based on polarization and Stokes parameters. Compared to the traditional attenuation coefficient quantification method, PS-OCT demonstrated enhanced contrast of tissue characteristics between normal and cancerous tissues due to the birefringence effects. Our results demonstrated that PS-OCT was promising to provide imaging guidance for the surgical resection of kidney tumors and had the potential to be used for other human kidney surgeries in clinics such as renal biopsy. 
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  5. Free, publicly-accessible full text available August 13, 2025