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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Results on Partial Inverse Spanning Tree Problems
部分逆生成树 有权函数 非循环边子集
2023/11/6
Given a graph G with weight function w and an acyclic edge subset E', the partial inverse spanning tree problem on (G, w; E') is to find a new weight function w* so that E' can be extended to a maximu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On strongly quasiconvex functions: existence results and proximal point algorithms
强准孔函数 存在结果 近端点算法
2023/5/4
The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompass...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Extremal results on 4-cycles
4 个周期 极值结果 图兰型问题
2023/4/28
The study of the 4-cycle has an important enlightening effect on the development of Turan type problems, especially the degenerate cases. In this talk, we focus on two conjectures about 4-cycles: a co...
THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE:INTEGRALITY RESULTS
RELATIONS FOR THE RING INVARIANTS OF n POINTS ON THE LINE INTEGRALITY RESULTS
2015/10/14
Consider the projective coordinate ring of the GIT quotient (P1)n//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [HMSV2]we s...
The LASSO risk: asymptotic results and real world examples
Coefficient vector linear observation construct sparse the lasso matrix sequence
2015/8/21
We consider the problem of learning a coefficient vector x0 ∈ RN from noisy linear observation y = Ax0 + w ∈ Rn. In many contexts (ranging from model
selection to image processing) it is desirable to...
WAVELET SHRINKAGE FOR CORRELATED DATA AND INVERSE PROBLEMS: ADAPTIVITY RESULTS
Adaptation correlated data fractional brownian motion
2015/8/20
Johnstone and Silverman (1997) described a level-dependent thresholding
method for extracting signals from correlated noise. The thresholds were chosen
to minimize a data based unbiased risk criteri...
The peak algebra Pn is a unital subalgebra of the symmetric group algebra,
linearly spanned by sums of permutations with a common set of peaks. By exploiting
the combinatorics of sparse subsets of [...
Numerical Results for the Metropolis Algorithm。
New Results for Stepwise Tests in Orthogonal Saturated Designs
Stepwise Tests Orthogonal Saturated Designs
2015/3/20
New Results for Stepwise Tests in Orthogonal Saturated Designs.
During the summer of 1985, after the opening ceremony of Nankai Institute of Mathematics,a beautiful lecture of S.-S. Chern on Chern classes and the Atiyah-Singer index formula introduced me into the ...
On the Muskat problem: global in time results in 2D and 3D
Porous media incompressible ows uid interface global existence.
2014/4/3
This paper considers the three dimensional Muskat problem in the stable regime.We obtain a conservation law which provides an L2 maximum principle for the uid interface. We also show global in time ex...
To Hash or Not to Hash Again?(In)Differentiability Results for H2 and HMAC
Indifferentiability Hash functions HMAC
2012/12/4
We show that the second iterate H2(M) = H(H(M)) of a random oracle H cannot achieve strong security in the sense of indifferentiability from a random oracle. We do so by proving that indifferentiabili...
Symmetry results for the $p(x)$-Laplacian equation
Quasi-linear elliptic equations p(x)-Laplacian operator symmetrization partial symmetry
2012/6/25
We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. For axially symmetric domains we prove that, under suitable assumptions, there exist Mountain-pass solutions which exhibi...
A new approach to the results of Kovari, Sos, and Turan concerning rectangle-free subsets of the grid
Turan concerning rectangle-free subsets of the grid Combinatorics
2012/6/21
For positive integers $m$ and $n$, define $f(m,n)$ to be the smallest integer such that any subset $A$ of the $m \times n$ integer grid with $|A| \geq f(m,n)$ contains a rectangle; that is, there are ...