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In this series of work, we aim at improving the bootstrapping paradigm for fully homomorphic encryption (FHE). Our main goal is to show that the amortized cost of bootstrapping within a polynomial mod...
Deep learning based methods have shown great potential for solving Vehicle Routing Problems (VRPs) in recent years. In the current learning based models, attention mechanism plays an important role an...
Lattice reduction algorithms have been proved to be one of the most powerful and versatile tools in public key cryptanalysis. In this talk, we primarily concentrate on lattice attacks against (EC)DSA ...
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators l_r M^r+?+l_1 M+l_0 where l_0,…,l_r are polynomials in x and Mx=x^b M for some...
Passengers left behind is an important measure to describe the degree of congestion in metro systems. Note that passengers' left behind probabilities are different for their different tap-in times. Th...
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars:Multiple solutions for semilinear subelliptic Dirichlet problem
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted So...
In this talk we consider the maximum absolute value in the autocorrelation spectrum (not considering the zero point) of balanced Boolean function. The long-standing open question in this area is to ob...
数学作为一门基础学科,在科学的研究中扮演着无可替代的角色。但是数学的研究与工程应用之间存在着一道鸿沟。如何针对实际问题的需求,进行相关数学研究是目前应用数学与计算数学研究的一个热点方法。在本报告,我们主要介绍了我们团队最近的两项相关的研究成果。1、基于微分方程模型的由局部信息重构全局信息的问题,即从方程的内部观测值如何重构方程解的问题。这是一个具有重要实际和应用前景的问题。但是,数学理论的结果说明...
电磁建模与计算在雷达目标探测与识别、隐身与反隐身、电磁兼容性分析、无线通讯等诸多领域有着重要的需求,是长期以来国内外同行关注的重点方向。随着科学计算方法和高性能计算技术的飞速发展,电磁建模与计算研究取得了长足的进步,然而针对计算目标越来越复杂,计算需求越来越高,电磁建模与计算面临一系列的挑战。本报告重点介绍了区域分解方法研究及进展,包括基于积分方程方法、有限元方法、有限元-边界元混合方法的区域分解...
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
近日,由北京大学主办/承办的FrontiersofMathematics和《数学进展》先后举行2023年编委会议。
The key to electrochemical energy storage systems such as Li/Na-ion batteries is materials. The traditional method for exploring new materials is trial-and-error, which often takes a dozen years durin...

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