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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with potentials
Calabi-Yau 曲线计数 4-folds
2023/4/23
I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4...
Counting Chromosomes:Plant Scientists Solve A Century-Old Mystery About Reproduction（图）
Counting Chromosomes Plant Scientists Century-Old Mystery Reproduction
2018/2/1
Counting is vital in nature. Counting chromosomes is something that most animals, plants and even single-celled organisms need to know how to do to assure viability and to reproduce. Today, a team of ...
2018年SPIE光学感应，成像和光子计数会议（SPIE Optical Sensing,Imaging,and Photon Counting:From X-Rays to Thz）
2018年 SPIE 光学感应，成像和光子计数 会议
2017/11/27
Nano-structuring of optoelectronic devices enables photonic detectors, sensors, and imagers with functionalities and properties that surpass traditional bulk devices in virtually any metric; for examp...
2017SPIE光子计数应用会议（2017 Conference on Photon Counting Applications）。
Counting good truth assignments of random k-SAT formulae
Random k-SAT Correlation Decay Uniqueness Gibbs Distribution
2015/8/21
We present a deterministic approximation algorithm to compute logarithm of the number of ‘good’ truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by ‘good’ we m...
Wald Lecture I: Counting Bits with Kolmogorov and Shannon
Rate-Distortion Gaussian Process Entrop Ellipsoids
2015/8/21
Shannon’s Rate-Distortion Theory describes the number of bits needed to approximately
represent typical realizations of a stochastic process X = (X(t) : t ∈ T),while Kolmogorov’s
-entropy describes...
COUNTING THE FACES OF RANDOMLY-PROJECTED HYPERCUBES AND ORTHANTS, WITH APPLICATIONS
RANDOMLY-PROJECTED ORTHANTS
2015/8/21
Let RN
+ denote the positive orthant; the expected number of k-faces of
the random cone ARN
+ obeys Efk(ARN
+)/fk(RN
+) = 1 − PN−n,N−k. The
formula applies to numerous matrix e...
COUNTING FACES OF RANDOMLY-PROJECTED POLYTOPES WHEN THE PROJECTION RADICALLY LOWERS DIMENSION
RANDOMLY-PROJECTED RADICALLY LOWERS DIMENSION
2015/8/21
The modern trend in statistics and probability is to consider the case where both
the number of dimensions d and the sample size n are large [19, 21]. In that case, the
intuition fostered by the cla...
Caporaso and Harris derive recursive formulas counting nodal plane
curves of degree d and geometric genus g in the plane (through the appropriate number of xed
general points). We rephrase their ar...
A BOX-COUNTING METHOD TO CHARACTERIZE DEGREES OF FOLIAGE CLUMPING USING AIRBORNE AND SIMULATED LIDAR DATA
LiDAR leaf area index foliage clumping
2015/5/7
Monitoring forest productivity and health is key to sustainable ecosystem management and informed decision making. A key parameter used in monitoring forest resources is the leaf area index (LAI), w...
Power counting of loop diagrams in general relativity
Cyclic graph the general theory of relativity energy expansion quantum effects physical power calculation
2014/12/23
A class of loop diagrams in general relativity appears to have a behavior which would upset the utility of the energy expansion for quantum effects. We show through the study of specific diagrams that...
Counting the World's Poor: Problems and Possible Solutions
Counting the World's Poor Problems Possible Solutions
2014/3/24
Counting the World's Poor: Problems and Possible Solutions。
An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions
the zero-counting formulae Dirichlet $L$-functions Dedekind zeta-functions Number Theory
2012/6/30
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution o...
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symme...