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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Balanced Boolean Functions with Good Autocorrelation Spectra and Their Applications
自相关谱 平衡 布尔函数
2023/4/26
In this talk we consider the maximum absolute value in the autocorrelation spectrum (not considering the zero point) of balanced Boolean function. The long-standing open question in this area is to ob...
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...
How to Find Good Finite-Length Codes: From Art Towards Science
LDPC coding transmission binary probability
2015/8/21
We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn...
On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields
Elliptic Curves over Number Fields Mordell-Weil Group Two-Descent
2013/1/30
We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data inc...
Existence of good moduli spaces for A_k-stable curves
Existence of good moduli spaces A_k-stable curves Algebraic Geometry
2012/6/25
We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a weak analog of the Keel-Mori theorem, which guarantees the existence of a coarse mo...
Let A be the adjacency matrix of a graph $X$ and suppose U(t)=exp(itA). We view A as acting on $\cx^{V(X)}$ and take the standard basis of this space to be the vectors $e_u$ for $u$ in $V(X)$. Physici...
Good measures on locally compact Cantor sets
Good measures locally compact Cantor sets Dynamical Systems
2012/4/17
We study the set M(X) of full non-atomic Borel (finite or infinite) measures on a non-compact locally compact Cantor set X. For an infinite measure $\mu$ in M(X), the set $\mathfrak{M}_\mu = \{x \in X...
Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields
Non-existence of elliptic curves quadratic fields Number Theory
2011/9/19
Abstract: We prove the non-existence of elliptic curves having good reduction everywhere over some real quadratic fields.
Cohomology rings of good contact toric manifolds
contact toric cohomology equivariant cohomology
2011/1/20
A good contact toric manifold M is determined by its moment cone C. We compute the equivariant cohomology ring with Z coefficient of M in terms of the combinatorial data of C. Then under a smoothness ...
Good tilting modules and recollements of derived module categories
Commutative algebras Coproducts Derived categories p-adic numbers Recollements Ring epimorphisms Tilting
2011/1/20
Let T be an infinitely generated tilting module of projective dimension at most one over an arbitrary associative ring A, and let B be the endomorphism ring of T.
Partial desingularizations of good moduli spaces of Artin toric stacks
Partial desingularizations good moduli spaces of Artin toric stacks
2011/1/19
Let X be an Artin stack with good moduli space X → M. We define the Reichstein transform of X relative to a closed substack C ⊂ X to be the complement of the strict transform of the saturation o...
Extension theorems, Non-vanishing and the existence of good minimal models
Extension theorems Non-vanishing existence of good minimal models
2011/1/17
We prove an extension theorem for effective plt pairs (X, S+B) of non-negative Kodaira dimension (KX +S+B) ≥ 0.The main new ingredient is a refinement of the Ohsawa-Takegoshi
L2 extension theorem in...
For a smooth and projective variety over a number field with torsion free geometric Picard group and finite transcendental Brauer group we show that only the archimedean places, the primes of bad redu...
A family of sequences with large size and good correlation property arising from $M$-ary Sidelnikov sequences of period $q^d-1$
Correlation Family size Sidelnikov sequence Array structure
2010/12/1
Let q be any prime power and let d be a positive integer greater than 1. In this paper, we construct a family of Mary sequences of period q−1 from a given M-ary.
m solutions good, m-1 solutions better
computability optimization solving systems of equations
2010/9/10
One of the main objectives of theoretical research in computational complexity and feasibility is to explain experimentally observed difference in complexity. Empirical evidence shows that the more so...