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We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In vari...
Nonconvex constrained optimization (NCO) has been one of the important research fields in optimization community. It has widely appeared in many application fields. However, challenges for solving NCO...
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
We study the performance of fixed-price mechanisms in the bilateral trade problem. We improve the approximation ratios of welfare-optimal mechanisms in several settings. In particular, when we have on...
Waves of all sorts, including electromagnetic waves, acoustic waves, and mechanical vibrations, play a role in shaping our world. In disordered systems, the transport of waves is hindered, resulting i...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was...
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
Modeling non-commutative phenomena in finite dimensional matrix algebras is a central theme of the program Quantitative Linear Algebra. This workshop will focus on a variety of concrete questions aro...
Eigenvalue problems arise in many scientific and engineering applications. They are also important in emerging areas such as big data analysis. For example, eigenvalues (or singular values) can be use...
Spline functions are polynomials that are cut into pieces with care. Although spline functions date back to work of Euler and Bernoulli, it was Iso Schoenberg who began to study them in earnest. In la...
Eigenvalue problems arise in many scientific and engineering applications. They are also important in emerging areas such as big data analysis. For example, eigenvalues (or singular values) can be use...
Classical approximation theory, including polynomial approximation and splines etc., is a fundamental research area in applied mathematics. Development in approximation theory plays an important role ...

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