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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...
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 ...
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...
Computation of the maximum H_infinity-norm of parameter-dependent linear systems by a branch and bound algorithm
Calculation algorithm parameter linear system a branch and bound algorithm linear system
2015/8/12
For linear systems that contain unspecified parameters that lie in given intervals, we present a branch and bound algorithm for computing the maximum H_infinity-norm over the set of uncertain paramete...
A sharp bound on the L2 norm of the solution of a random elliptic difference equation
sharp bound L2 norm random elliptic difference equation
2015/7/14
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
Statistical Estimation and Testing via the Sorted 1 Norm
Sparse regression variable selection false discovery rate lasso sorted 1 penalized estimation (SLOPE) prox operator
2015/6/17
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = Xβ + z, then we ...
A Method for Generating Uniformly Scattered Points on the L p-norm Unit Sphere and Its Applications
Generating Uniformly Scattered Points L p-norm Unit Sphere and Its Applications
2015/3/20
A Method for Generating Uniformly Scattered Points on the L p-norm Unit Sphere and Its Applications.
A Method for Generating Uniformly Scattered Points on the L p-norm Unit Sphere and Its Applications
Generating Uniformly Scattered Points L p-norm Unit Sphere
2015/3/18
In this paper we propose a method associated with an algorithm for
generating uniformly scattered points on the the Lp-norm unit sphere and
discuss its applications in statistical simulation, repres...
Physiologic norm for vitamin D supported, not challenged
Physiologic norm vitamin D challenged
2018/12/20
The results presented in your recent article, “25-Hydroxyvitamin D in African-origin populations at varying latitudes challenges the construct of a physiologic norm” (1), provide excellent evidence in...