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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Projective measure without Projective Baire
投射贝尔 投射测量 勒贝格可测
2023/5/6
In this talk, I will give some of the context and a sketch of the proof of the following result which I proved a while ago: It is consistent (relative to a Mahlo catrdinal) that there is a projective ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/17
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
High Dimensional Influence Measure
Cook’s distance High dimensional diagnosis Influential obser- vation Lasso
2016/1/25
Influence diagnosis is important since presence of influential ob-servations could lead to distorted analysis and misleading interpreta-tions. For high dimensional data, it is particularly so, as the ...
Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates
Law of large numbers branching Hunt processes spine approach h-transform spectral gap
2016/1/20
We establish weak and strong law of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the ...
WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS,GRAPHS AND METRIC MEASURE SPACES
Uncertainty principle p.c.f. fractal Heisenberg’s inequality measure metric spaces Poincar′ e inequality self-similar graphs Sierpinski ′ gasket uniform finitely ramified graphs
2015/12/10
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept ...
NEW EXAMPLES OF S-UNIMODAL MAPS WITH A SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
S-UNIMODAL MAPS SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
2015/9/25
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...
Entropy and Renormalized Solutions for the p(x)-Kaokacuab Equation with Measure Data
Variable exponents Entropy solutions Renormalized solutions Exist- ence Uniqueness
2015/5/4
In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L 1 (Ω) +...
Robustness of an Odds-ratio Test in a Stratified Group Sequential Trial with a Binary Outcome Measure
Binary outcome Odds-ratio Stratification
2015/3/18
Many clinical trials compare two or more treatment groups by using a binary outcome measure.
For example, the goal could be to determine whether the frequency of pain episodes is
significantly reduc...
Multistage Evaluation of Measure ment Error in a Reliability Study
nterim analysis Intraclass correlation
2015/3/18
We introduce sequential testing procedures for the planning
and analysis of reliability studies to assess an exposure’s measurement error.
The designs allow repeated evaluation of reliability of the...
CONFORMAL INVARIANTS ASSOCIATED TO A MEASURE: CONFORMALLY COVARIANT OPERATORS
CONFORMAL INVARIANTS ASSOCIATED MEASURE CONFORMALLY COVARIANT OPERATORS
2014/4/3
In this paper we study Riemannian manifolds (Mn, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling...
In this note we study some conformal invariants of a Riemannanian manifold (Mn;g) equipped with a smooth measure m. In particular, we show that there is a natural de nition of the Ricci and scalar cur...
Numerical Modeling of the Measure of Global Environmental Needs with Applications Laser-LIDAR
Transmission Lasers Optical Propagation Atmospheric Effects
2013/1/30
The functions of Bessel are used extensively in the various problems of the science and the technology. A laser offers practical remote sensing technologies for measuring environmental changes on both...
Topology of probability measure spaces, II
Topology of probability measure spaces General Topology
2012/6/29
This paper is a follow-up to the author's work "Topology of probability measure space, I" devoted to investigation of the functors $\hat P$ and $P_\tau$ of spaces of probability $\tau$-smooth and Rado...
A moderate deviation principle for empirical bootstrap measure
Large deviations moderate deviations bootstrap empirical measure
2012/6/27
We establish two moderate deviation principles (MDP) in the bootstrap setting. We prove MDP for the joint distribution of the empirical measure and the empirical bootstrap measure (empirical measure o...