Results 31 to 40 of about 76,534 (153)
Lower bounds for cube‐ideal set‐systems
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract A set‐system S⊆{0,1}n$S\subseteq \lbrace 0,1\rbrace ^n$ is cube‐ideal if its convex hull can be described by capacity and generalized set covering inequalities. In this paper, we use combinatorics, convex geometry, and polyhedral theory to give exponential lower bounds on the size of cube‐ideal set‐systems, and linear lower bounds on their ...
Ahmad Abdi +3 more
wiley +1 more source
Variational Inference on the Boolean Hypercube with the Quantum Entropy
CoRRIn this paper, we derive variational inference upper-bounds on the log-partition function of pairwise Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the
Beyler, Eliot, Bach, Francis
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Sensitivity and Hamming Graphs
Journal of Graph Theory, Volume 112, Issue 3, Page 296-305, July 2026.ABSTRACT For any m ≥ 3 we show that the Hamming graph H ( n , m ) admits an imbalanced partition into m sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong m‐ary Sensitivity Conjecture of Asensio, García‐Marco, and Knauer.
Sara Asensio +3 more
wiley +1 more source
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Dedekind's problem, dating back to 1897, asks for the total number ψ(n)$\psi (n)$ of antichains contained in the Boolean lattice Bn$B_n$ on n$n$ elements. We study Dedekind's problem using a recently developed method based on the cluster expansion from statistical physics, and as a result, obtain several new results on the number and typical ...
Matthew Jenssen +2 more
wiley +1 more source
A Maker--Breaker Game on the Boolean Hypercube With Subcubes as Winning Set
Integers, 2018 See the abstract in the attached pdf.
Klay Kruczek, Eric Sundberg 0001
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Equiorthogonal Frequency Hypercubes: Preliminary Theory
, 1998 Using a strong definition of frequency hypercube, we define a strengthened form of orthogonality, called equiorthogonality, for sets of such hypercubes.
Morgan, Ilene H.
core +1 more source
Interpretable Machine Learning: A Comprehensive Review of Foundations, Methods, and the Path Forward
WIREs Data Mining and Knowledge Discovery, Volume 16, Issue 1, March 2026.This systematic review of 352 studies establishes a comprehensive taxonomy for Interpretable Machine Learning, transitioning from foundational intrinsic models to advanced deep learning explanations. It reveals a critical paradigm shift toward “mechanistic interpretability” and actionable recourse, emphasizing that future AI systems must be rigorously ...
Shimon Fridkin, Michael Bendersky
wiley +1 more source
Cumulative Differences Between Paired Samples
Statistical Analysis and Data Mining: An ASA Data Science Journal, Volume 19, Issue 1, February 2026.ABSTRACT Paired samples are observations from two populations, commonly with each observed response from one population corresponding to an observed response from the other population at the same value of an ordinal covariate. Such pairs of responses at the same covariate values are called “matched pairs.” Graphing cumulative differences between the ...
Isabel Kloumann +4 more
wiley +1 more source
On devising Boolean Routing Schemes
, 1997 In this paper, the problem of routing messages along shortest paths in a network of processors without using complete routing tables is considered. The Boolean Routing model is proposed and it is shown that it provides optimal representations of all ...
Gambosi, G +2 more
core +1 more source
A Refined Graph Container Lemma and Applications to the Hard‐Core Model on Bipartite Expanders
Random Structures &Algorithms, Volume 68, Issue 1, January 2026.ABSTRACT We establish a refined version of a graph container lemma due to Galvin and discuss several applications related to the hard‐core model on bipartite expander graphs. Given a graph G$$ G $$ and λ>0$$ \lambda >0 $$, the hard‐core model on G$$ G $$ at activity λ$$ \lambda $$ is the probability distribution μG,λ$$ {\mu}_{G,\lambda } $$ on ...
Matthew Jenssen +2 more
wiley +1 more source