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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures
正交投影 混合范数 度量维度 分析插值
2023/5/5
We obtain new mixed-norm estimates and geometric results on projections. In the proof we introduce a new quantity called s-amplitude, and interpolate analytically not only on p,q, but also on dimensio...
More Efficient Algorithms for the NTRU Key Generation using the Field Norm
lattice techniques public-key cryptography quantum cryptography
2019/1/9
NTRU lattices are a class of polynomial rings which allow for compact and efficient representations of the lattice basis, thereby offering very good performance characteristics for the asymmetric algo...
Improved Algorithms for the Approximate k-List Problem in Euclidean Norm
sieving SVP cryptanalysis
2017/2/20
We present an algorithm for the approximate kk-List problem for the Euclidean distance that improves upon the Bai-Laarhoven-Stehle (BLS) algorithm from ANTS'16. The improvement stems from the observat...
FHPKE with Zero Norm Noises based on DLA&CDH
fully homomorphic public-key encryption discrete logarithm assimption computational Diffie–Hellman assumption
2016/7/29
In this paper I propose the fully homomorphic public-key encryption(FHPKE) scheme with zero norm noises that is based on the discrete logarithm assumption(DLA) and computational Diffie–Hellman assumpt...
Fully Homomorphic Encryption with Zero Norm Cipher Text
fully homomorphic encryption octonion factoring
2016/6/29
Gentry抯 bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak...
Solving Random Subset Sum Problem by $l_{p}$-norm SVP Oracle
SVP random subset sum problems lattice
2016/1/26
HYBRID SUP-NORM BOUNDS FOR HECKE-MAASS CUSP FORMS
Cutting-edge characteristic value hyperbolic measure
2015/8/25
Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0(N)) = 1 and the form f such that kfk2 = 1. It is shown that kfk1 ≪1...
The Asymptotic Minimax Constant for Sup-Norm Loss in Nonparametric Density Estimation
Density estimation exact constant optimal recovery uniform norm risk white noise
2015/8/25
We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussian ...
Fast Solution of `1-norm Minimization Problems When the Solution May be Sparse
LASSO. LARS Homotopy Methods Basis Pursuit.
2015/8/21
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax,
is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property
is of interest i...
For Most Large Underdetermined Systems of Equations, the Minimal ` 1 -norm Near-Solution Approximates the Sparsest Near-Solution
Solution of Underdetermined Linear Systems Approximate Sparse Solution of Linear equations
2015/8/21
We consider inexact linear equations y ≈ Φα where y is a given vector in R
n
, Φ is a
given n by m matrix, and we wish to find an α0, which is sparse and gives an approximate
solution, obey...
For Most Large Underdetermined Systems of Linear Equations the Minimal ` 1 -norm Solution is also the Sparsest Solution
Solution of Underdetermined Linear Systems Overcomplete Representations
2015/8/21
We consider linear equations y = Φα where y is a given vector in R
n
, Φ is a given n by m
matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns
of Φ are normalized ...
The standard 2-norm SVM is known for its good performance in twoclass classification. In this paper, we consider the 1-norm SVM. We argue that the 1-norm SVM may have some advantage over the standard ...
On computing the H_infinity-norm of a transfer matrix
Transfer matrix the bisection algorithm computation the transfer matrix the norm
2015/8/13
We present a simple bisection algorithm to compute the H_infinity norm of a transfer matrix. The bisection method is far more efficient than algorithms which involve a search over frequencies, and mor...
A bisection method for computing the H_infinity-norm of a transfer matrix and related problems
Transfer matrix singular value assessment the Hamiltonian matrix characteristic values of linear algebra
2015/8/13
Inspired by recent work of Byers we establish a simple connection between the singular values of a transfer matrix evaluated along the imaginary axis and the imaginary eigenvalues of a related Hamilto...
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...