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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...
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 ...
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...
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...
We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the nth copy is −n. We prove...
New associative product of three states generalizing free, monotone, anti-monotone, Boolean, conditionally free and conditionally monotone products
Conditionally free independence free independence monotone indepen-dence Boolean independence cumulants
2010/12/1
We define a new independence in three states called indented independence which unifies many independences: free, monotone, anti-monotone, Boolean, conditionally free, condi-tionally monotone and cond...
On the parity complexity measures of Boolean functions
Computational complexity Communication complexity Parity decision tree Log-Rank conjecture
2012/11/30
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Bool...
Boolean delay equations on networks: An application to economic damage propagation
Boolean delay equations networks economic damage propagation
2010/4/27
We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for stu...
Boolean delay equations on networks: An application to economic damage propagation
Boolean delay equations networks economic damage
2010/4/6
We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for stu...