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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Asymptotic log-concavity of dominant lower Bruhat intervals
显性 Bruhat区间 渐近对数凹性
2023/11/13
The unimodality of lower Bruhat intervals for the “upper half” remains as an open problem. For affine Weyl group W with corresponding finite Weyl group W_f, we prove that lower W_f-parabolic Bruhat in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Log-Brunn-Minkowski inequality
对数 布伦 闵可夫斯基不等式
2023/4/17
In 2012, Boroczky, Lutwak, Yang, and Zhang posed the log-Brunn-Minkowski conjecture, which represents an enhanced version of the classical Brunn-Minkowski inequality for convex bodies. We will recall ...
Discussion of ‘Maximum likelihood estimation of a multi-dimensional log-concave density’ by M. Cule, R. Samworth and M. Stewart
likelihood estimation multi-dimensional log-concave density
2015/8/20
I started looking at log-concave distributions when I was searching for an appropriate model
for subpopulations of multivariate flow cytometry data about ten years ago. The use of log-concave
...
Inference and Modeling with Log-concave Distributions
Log-concave Distributions Inference and Modeling
2015/8/20
Log-concave distributions are an attractive choice for modeling
and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions ...
Clustering with mixtures of log-concave distributions
EM algorithm Log-concave distribution Clustering Normal copula
2015/8/20
The EM algorithm is a popular tool for clustering observations via a parametric mixture model. Two disadvantages of this
approach are that its success depends on the appropriateness of the assumed pa...
Distribution-Free Multivariate Process Control Based On Log-Linear Modeling
Association Discrete measurements
2015/3/18
This pa p e r c o nsider s sta tistica l pr o cess c o ntr o l (SP C ) w hen the pr o cess mea sur e ment is
multiva r ia te. I n the liter a tur e, mo st existing multiva r ia te SP C pr o cedur es ...
Zeta Functions and the Log-behavior of Combinatorial Sequences
log-convexity Riemann zeta function Bernoulli number Bell number Bessel zeta function Narayana number Hö lder's inequality
2014/6/3
In this paper, we use the Riemann zeta function ζ(x) and the Bessel zeta function ζμ(x) to study the log-behavior of combinatorial sequences. We prove that ζ(x) is log-convex for x>1. As a consequence...
The Boros-Moll polynomials Pm(a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that...
Infinitely Log-monotonic Combinatorial Sequences
logarithmically completely monotonic function infinitely logmonotonic sequence ratio log-concave Riemann zeta function
2014/6/3
We introduce the notion of infinitely log-monotonic sequences. By establishing a connection between completely monotonic functions and infinitely log-monotonic sequences, we show that the sequences of...
Log-Harnack Inequality for Gruschin Type Semigroups
Gruschin semigroup log-Harnack inequality coupling regular conditional probability
2012/6/19
By constructing a coupling in two steps and using the Girsanov theorem under a regular conditional probability, the log-Harnack inequality is established for a large class of Gruschin type semigroups ...
There always exists at least one prime between x and x+log^2(x) when x> =8
Prime distribution of primes
2011/9/21
In this paper one has shown that there always exists at least one pseudo prime number between x and x+log^2(x), so it also is true that there always exists at least one real prime number for the real ...
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
GNS inequality Log-HLS inequality critical mass Keller-Segel equation Analysis of PDEs
2011/9/23
Abstract: Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev inequality...
Families of canonically polarized manifolds over log Fano varieties
Families of canonically polarized manifolds log Fano varieties Algebraic Geometry
2011/9/19
Abstract: Let (X,D) be a dlt pair, where X is a normal projective variety. Let S denote the support of the rounddown of D, and K the canonical divisor of X. We show that any smooth family of canonical...
The Log-Convex Density Conjecture and vertical surface area in warped products
The Log-Convex Density Conjecture vertical surface area warped products Differential Geometry
2011/9/19
Abstract: We examine the vertical component of surface area in the warped product of a Euclidean interval and a fiber manifold with product density. We determine general conditions under which vertica...
On Finiteness of B-representatoin and Semi-log Canonical Abundance
Finiteness of B-representatoin Semi-log Canonical Abundance Algebraic Geometry
2011/9/16
Abstract: We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) a...