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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...
A BOOLEAN ACTION OF C(M,U(1)) WITHOUT A SPATIAL MODEL AND A RE-EXAMINATION OF THE CAMERON–MARTIN THEOREM
A BOOLEAN ACTION WITHOUT A SPATIAL MODEL RE-EXAMINATION CAMERON–MARTIN THEOREM
2015/8/17
We will demonstrate that if M is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which pr...
Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm
Continuous time Boolean modeling biological signaling application of Gillespie algorithm Molecular Networks
2012/4/28
This article presents an algorithm that allows modeling of biological networks in a qualitative framework with continuous time. Mathematical modeling is used as a systems biology tool to answer biolog...
Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals
Symmetric chain decomposition Boolean algebras cyclic crystals
2011/9/15
Abstract: The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order,...
Noise as a Boolean algebra of sigma-fields. I. Completion
Noise Boolean algebra of sigma-fields Probability
2011/9/9
Abstract: Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more...
Locally monotone Boolean and pseudo-Boolean functions
Boolean function pseudo-Boolean function local monotonicity discrete partial derivative join and meet derivatives
2011/9/29
Abstract: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keep...
Some Quotients of the Boolean Lattice are Symmetric Chain Orders
symmetric chain decomposition Boolean lattice
2011/8/26
Abstract: R. Canfield has conjectured that for all subgroups G of the automorphism group of the Boolean lattice B(n) (which can be regarded as the symmetric group S(n)) the quotient order B(n)/G is a ...
Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes
Competing Boolean Nodes Highly Connected Networks
2011/9/13
Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of ...
On Semigroup of Permutation Factor Circulant Boolean Matrices
Boolean algebra permutation factor circulant Boolean matrix semigroups idempotent Euler-Ferment theorem
2012/9/25
Let ()nPM B denote the set of all nn× permutation factor circulant matrices over the Boolean algebra {0, 1} B = , then ()nPM B forms a semigroup under the usual matrix product. In this paper,...
A Boolean algebra and a Banach space obtained by push-out iteration
Boolean algebra Banach space push-out iteration
2011/2/25
Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(!)/fin has under CH a...
Extension results for boolean maps and a class of systems of linear inequalities
Involution posets boolean maps systems of linear inequalities
2011/2/28
In this paper we introduce the notion of core for two specific classes of boolean maps on finite involution posets (which are a generalization of the boolean lattices) and we prove some extension resu...
On the dangers of Boolean networks: Activity dependent criticality and threshold networks not faithful to biology
Boolean networks Activity dependent criticality
2011/1/6
Spin models of neural networks and genetic networks are considered elegant as they are accessible to statistical mechanics tools for spin glasses and magnetic systems. However, the conventional choice...
Quantum Boolean Algebras
Quantum Boolean Algebras math
2010/11/24
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory
Non Boolean Functions Social Choice Theory
2010/11/22
A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetr...
The extension problem for partial Boolean structures in Quantum Mechanics
partial Boolean structures Quantum Mechanics
2010/11/8
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the ...