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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations principle for weighted means of a recursive numerical method for ergodic SDEs
遍历 SDE递归 数值方法 加权均值 大偏差原理
2023/4/24
For ergodic SDEs, their ergodic limits are usually approximated by the suitable means of numerical methods. To reveal the numerical asymptotic behavior, we study the large deviations principle (LDP) f...
基于逻辑回归函数的加权K-means聚类算法
欧式距离 特征加权的K-means算法 逻辑回归函数 初始聚类中心
2022/3/15
传统K-means聚类算法通过欧式距离计算样本的相似度，将数据所有的属性特征均平等对待，忽略每个属性特征的不同贡献，导致样本相似度计算的准确率不高。针对这个不足，提出一种特征加权的K-means算法进行优化。首先，运用Softmax和Sigmoid逻辑回归函数计算特征权重，使得加权的欧式距离更能准确地表示样本相似度；其次，优化初始聚类中心选择策略，选择距离较大的K个样本作为初始聚类中心，可有效避免...
Tests atternative to higher criticism for high dimensional means under sparsity and column-wise dependence
Large deviation Large p, small n Optimal detection boundary Sparse signal Thresholding Weak dependence
2016/1/25
We consider two alternative tests to the Higher Criticism test of Donoho and Jin (2004) for high dimensional means under the spar-sity of the non-zero means for sub-Gaussian distributed data with unkn...
Inversion of circular means and the wave equation on general planar domains
Inversion of circular equation general planar domains Analysis of PDEs
2012/6/25
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on an arbitrarily shaped bounded domain $\Omega \subset \R^2$. As a main result we ...
Approximation of functions from Lp(w)b by matrix means of their Fourier series
Rate of approximation summability of Fourier series Lipschitz classes
2012/4/16
We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, wher...
Inversion Formulas for the Spherical Means in Constant Curvature Spaces
The spherical mean Radon transform thermoacoustic tomography the method of analytic continuation
2011/9/23
Abstract: The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections...
Sets of Injectivity for Weighted Twisted Spherical Means and Support Theorems
Heisenberg group twisted spherical means twisted con-volution
2011/2/25
We prove that spheres are sets of injectivity for certain weighted twisted spherical means on Cn. We also prove an analog of Helgason’s support theorem for weighted Euclidean and twisted spheri-cal me...
On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Differential Galois Theory Darboux theory of Integrability Poincar´ e problem,
2011/2/24
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type folia-tion.
Confidence interval for the difference of two normal population means with a known ratio of variances
Coverage probability Expected length
2010/9/20
Motivated by the recent work of Schechtman and Sherman [The twosample t-test with a known ratio of variances. Statistical Methodology 4, 508-514, (2007).], we investigate, in this paper, a new exact c...
A note on the Euclidean norms of matrices with arithmetic-geometric-harmonic means
Euclidean norm arithmetic-geometric-harmonic mean
2010/9/25
A note on the Euclidean norms of matrices with arithmetic-geometric-harmonic means.
Recurrence-based time series analysis by means of complex network methods
Chaotic Dynamics (nlin.CD) Social and Information Networks (cs.SI) Data Analysis Statistics and Probability (physics.data-an) Physics and Society (physics.soc-ph)
2010/11/10
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. Dur...
Solving a Generalized Heron Problem by means of Convex Analysis
Generalized Heron Problem Convex Analysis
2010/11/19
The classical Heron problem states: \emph{on a given straight line in the plane, find a point $C$ such that the sum of the distances from $C$ to the given points $A$ and $B$ is minimal}. This problem ...
Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
Reconstruction of a function spherical (circular) means certain polygons and polyhedra
2010/11/26
We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). ...
Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk
reaction-diffusion equation random walk
2010/4/1
We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the re...
R. Supper, Spherical Means of Subharmonic Functions
holomorphic functions in the unit disk subharmonic functions in the unit ball zeros of holomorphic functions Riesz measures Blaschke condition
2009/6/16
This article is devoted to subharmonic functions u in the unit ball. It studies how
growth conditions on u impact on the Riesz measure associated to u. More precisely,
the growth hypotheses involve ...