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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Spectral rigidity and joint integrability for Anosov diffeomorphisms on tori
环形 阿诺索夫微分同胚 谱刚度 联合可积性
2023/4/14
In this talk, we address on the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with s...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak multisymplectic spectral integrators with a resolution of Gibbs phenomenon
吉布斯现象 分辨率 弱多辛谱 积分器
2023/4/28
We will report our recent work on weak multisymplectic spectral integrators for a wide range of nonsmooth Hamiltonian partial differential equations, which appear in quite a few physical applications ...
SURFACE GROUP REPRESENTATIONS TO SL(2, C) AND HIGGS BUNDLES WITH SMOOTH SPECTRAL DATA
SURFACE GROUP SL(2, C) HIGGS BUNDLES SPECTRAL DATA
2015/12/17
We show that for every nonelementary representation of a surface group into SL(2, C) there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the d...
The study of the spectrum of the Laplace operator has produced an extensive literature. (See [Cha] and the references therein.) Of special interest to recent applications has been the behavior of spec...
SOME SPECTRAL PROPERTIES OF PSEUDO-DIFFERENTIAL OPERATORS ON THE SIERPINSKI GASKET
Analysis on fractals localized eigenfunctions Sierpiński gasket Szego limit theorem
2015/12/10
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
STRONG SHIFT EQUIVALENCE AND THE GENERALIZED SPECTRAL CONJECTURE FOR NONNEGATIVE MATRICES
STRONG SHIFT EQUIVALENCE GENERALIZED SPECTRAL CONJECTURE NONNEGATIVE MATRICES
2015/9/29
Given matrices A and B shift equivalent over a dense subring R of R,with A primitive, we show that B is strong shift equivalent over R to a primitive matrix. This result shows that the weak form of th...
This note is related to Theorem 1 of the ICA-BSS Conference’paper “AR Processes and Sources can be Reconstructed from Degenerate Mixtures” [1]. Here we study further the uniqueness of the decompositio...
MICROPHONE ARRAY SPEECH ENHANCEMENT BY BAYESIAN ESTIMATION OF SPECTRAL AMPLITUDE AND PHASE
MICROPHONE ARRAY SPEECH ENHANCEMENT BAYESIAN ESTIMATION SPECTRAL AMPLITUDE AND PHASE
2015/9/29
Microphone arrays provide new opportunities for noise reduction and speech enhancement. This paper presents anovel decomposition of the estimation problems for short-time spectral amplitude (STSA), lo...
THE NONCOMMUTATIVE WIENER LEMMA,LINEAR INDEPENDENCE,AND SPECTRAL PROPERTIES OF THE ALGEBRA OF TIME-FREQUENCY SHIFT OPERATORS
NONCOMMUTATIVE WIENER LEMMA LINEAR INDEPENDENCE SPECTRAL PROPERTIES OF THE ALGEBRA TIME-FREQUENCY SHIFT OPERATORS
2015/9/29
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
Asymptotic Equivalence of Spectral Density Estimation and Gaussian White Noise
Stationary Gaussian process spectral density Sobolev classes Le Cam distance asymptotic equivalence Whittle likelihood log-periodogram regression nonparametric Gaussian scale model signal in Gaussian white noise
2015/8/25
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam’s...
ASYMPTOTIC EQUIVALENCE OF SPECTRAL DENSITY ESTIMATION AND GAUSSIAN WHITE NOISE
ASYMPTOTIC EQUIVALENCE SPECTRAL DENSITY ESTIMATION GAUSSIAN WHITE NOISE
2015/8/25
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f . Asymptotic equivalence, in the sense of Le Cam’...
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
collaborative filtering nuclear norm spectral regularization netflix prize large scale convex optimization
2015/8/21
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and...
FIR filter design via spectral factorization and convex optimization
Finite impulse response filter filter coefficient variables spectral decomposition linear and nonlinear convex programming
2015/8/11
We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the filter coefficient...
A FAST SPECTRAL ALGORITHM FOR THE QUANTUM BOLTZMANN COLLISION OPERATOR
Quantum Boltzmann equation fast spectral method
2015/7/14
This paper introduces a fast spectral algorithm for the quantum Boltzmann collision operator. In the usual spectral framework, one of the terms in the operator cannot be evaluatedefficiently. The new ...