探花视频 - 国产探花 - 免费在线观看

In this talk we discuss some monotonicity questions related to Fredholm matrices and operators. A function $f(x)$ is called completely monotonic if $(-1)^mf^{(m)}(x)>0$. It is known that the expectation of having $m$ eigenvalues of a random Hermitian matrix in an interval is a multiple of $(-1)^{m}$ times the $m$-th derivative of a Fredholm determinant at $/lambda=1$. In this work we extend the positivity to half-real line $(-/infty,1]$, and we also study the completely monotonicity of some special functions which arise as Fredholm determinants.

We survey results on q-analogue of the normal distribution and the corresponding orthogonal polynomials.

In this talk, we will investigate a complex short pulse equation and its two-component generalization. First, we will derive them starting from Maxwell equations. Then we will study their various soliton solutions such as bright, dark, breather and rogue wave solutions by using Hirota’s bilinear method and Darboux transformation method.

We generalize the notions of ordinary points and singularities from linear ordinary differential equations to D-finite systems. Ordinary points and apparent singularities of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms are presented for removing and detecting apparent singularities. In addition, an algorithm is given for computing formal power series solutions of a D-finite system at apparent singularities. This is a joint work with Manuel Kauers, Ziming Li and Yi Zhang.

Log Fano manifold are generalization of Fano manifolds, and the canonical metrics on them are conic Kahler-Einstein metrics. I will talk about the existence of such metrics on log K-polystable log Fano manifolds.

We establish spreading properties of the Lotka-Volterra competition-diffusion system. When the initial data vanish on a right half-line, we show that there are two successive invasions. We derive the formulas of the exact spreading speeds and prove the convergence to homogeneous equilibrium states in between the invasion fronts. Our method is inspired by the geometric optics approach for Fisher-KPP equation due to the work of Freidlin, and that of Evans and Souganidis. Our main result settles an open question raised by Shigesada and Kawasaki in 1997, and shows that one of the species spreads to the right with a speed which is linearly, but non-locally, determined.

Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regularized variations with large regularization parameter will degradate the performance in several important machine learning applications, and small regularization parameter will fail due to numerical stability issues with existing algorithms. We address this challenge by developing an Inexact Proximal point method for exact Optimal Transport problem (IPOT) with the proximal operator approximately evaluated at each iteration using projections to the probability simplex. The algorithm (a) converges to exact Wasserstein distance with theoretical guarantee and robust regularization parameter selection,

Let be an array of i.i.d. random variables, and let be a sequence of positive integers such that is bounded away from 0 and . The sample correlation matrix is generated from , , such that is the Pearson correlation coefficient between and . In this talk, we provide a supplement to Jiang's asymptotic distribution of the largest entry . We show that, for given nondecreasing function with ，there exists an array of symmetric i.i.d. random variables such that and, for some subsequence of , almost surely; does not exist almost surely; ， ，and does not convergence in distribution, where