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Grothendieck predicted that the cohomological Brauer group of a regular scheme X is insensitive to removing a closed subscheme Z of X of codimension>=2. By Gabber's several results, the conjecture was...
We first consider the basic theory of algebraic curves, including the compact Riemann surface, Riemann-Hurwitz formula, Baker-Akhiezer function, three kinds of Abelian differentials, the construction ...
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expres...
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expres...
Sparse constraints on signal decompositions are justified bytypical sensor data used in a variety of signal processing fields such as acoustics, medical imaging, or wireless, but moreover can lead to ...
The purpose of this paper is twofold. First we show that the dynamics ofa Sun-Jupiter-Comet system and under some simplifying assumptions has a semi-infiniteregion of instability. This is done by redu...
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on th...
In this paper, we introduce a modified version of linear discriminant analysis, called the “shrunken centroids regularized discriminant analysis” (SCRDA). This method generalizes the idea of the “near...
Conditional Random Sampling (CRS) was originally proposed for efficiently computing pairwise (l2, l1) distances, in static, large-scale, and sparse data. This study modifies the original CRS and exten...
We present a general approach to quantifying a mechanism’s susceptibility to strategic manipulation, based on the premise that agents report their preferences truthfully if the potential gain from b...
We propose an algorithm for extracting the diagonal of the inverse matrices arising from electronic structure calculation. The proposed algorithm uses a hierarchical decomposition ofthe computational ...

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