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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Functions of bounded variation and nonlocal functionals
有界 变差函数 非局部泛函
2023/11/29
In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Bourguignon-Gauduchon's variation formula for Dirac operators
Dirac算子 Bourguignon-Gauduchon 变分公式
2023/11/13
我们将介绍由Bar-Gauduchon-Moroianu给出的spin流形上Dirac算子在度量变化时一阶变分公式的证明。作为应用，我们将计算Dirac算子沿Ricci flow的一阶变分。
FIRST VARIATION OF THE GENERAL CURVATURE-DEPENDENT SURFACE ENERGY
Surface energy gradient fl ow mean curvature
2015/12/11
We consider general surface energies, which are weighted integrals
over a closed surface with a weight function depending on the position, the
unit normal and the total curvature of the surface. Ene...
On the Behavior of the Total Variation in CWENO Methods for Conservation Laws
Hyperbolic conservation laws Central difference schemes High-order accuracy Non-oscillatory schemes CWENO reconstruction TVB
2015/10/8
We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interest...
THE LOCUS OF HODGE CLASSES IN AN ADMISSIBLE VARIATION OF MIXED HODGE STRUCTURE
ADMISSIBLE VARIATION HODGE CLASSES
2015/9/29
We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure.
False Discovery Rates and Copy Number Variation
False discovery rate multiple testing grouped hypotheses
2015/8/20
Copy number changes, the gains and losses of chromosome segments, are a common type
of genetic variation among healthy individuals as well as an important feature in tumor
genomes. Microarray techno...
An ADMM algorithm for a class of total variation regularized estimation problems
Signal processing algorithms stochastic parameters parameter estimation convex optimization and regularization
2015/8/7
We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that ...
New Multiscale Transforms, Minimum Total Variation Synthesis: Applications to Edge-Preserving Image Reconstruction
Ridgelets curvelets wavelets pseudo-polar FFT Slant Stack Radon transform trigonometric interpolation total-variation edges edge-preserving tomography/deconvolution thresholding
2015/6/17
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
The discovery of 139 Child Non-syndromic Intellectual Disability associated genetic copy number variation loci with biological insights
Gene copy biological
2014/12/5
Intellectual disability (ID) is a highly heritable mental disease. Especially, the
underlying molecular mechanism of non-syndromic intellectual disability (NSID), a
subtype of ID with no ...
Variation of Hodge structure for generalized complex manifolds
Variation of Hodge structure generalized complex manifolds Differential Geometry
2012/5/9
A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the be...
FunctionaL Regular Variation of Levy-driven Multivariate Mixed Moving Average Processes
cadlag sample paths functional regular variation heavy tails Levy basis mixed moving average process
2012/4/18
We consider the functional regular variation in the space $\mathbb{D}$ of c\`adl\`ag functions of multivariate mixed moving average (MMA) processes of the type $X_t = \int\int f(A, t - s) \Lambda (d A...
Discontinuous Galerkin Method for Total Variation Minimization on one-dimensional Inpainting Problem
finite element method discontinuous Galerkin method total variation minimization inpainting
2011/9/15
Abstract: This paper is concerned with the numerical minimization of energy functionals in $BV(\Omega)$ (the space of bounded variation functions) involving total variation for gray-scale 1-dimensiona...
Total Variation Flow and Sign Fast Diffusion in one dimension
Fast Diffusion Total Variation Flow asymptotic extinction profile convergence rates extinction time
2011/9/1
Abstract: We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the expli...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
Uniqueness of the representation for $G$-martingales with finite variation
niqueness representation theorem G-martingale finite variation G-expectation
2011/1/19
Our purpose is to prove the uniqueness of the representation for G-martingales with finite variation.