Results 41 to 50 of about 4,000 (161)
Characterizing binary simplical matroids
Discrete Mathematics, 1976 AbstractIn an earlier paper we defined a class of matroids whose circuit are combinatorial generalizations of simple polytopes; these matroids are the binary analogue of the simplical geometrics of Crapo and Rota. Here we find necessary and sufficient conditions for a matroid to be isomorphic to such a binary simplical matroid.
openaire +1 more source
Girth in GF(q)$\textsf {GF}(q)$‐representable matroids
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3401-3407, November 2025.Abstract We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field GF(q)$\textsf {GF}(q)$ and any integer t$t$, every cosimple GF(q)$\textsf {GF}(q)$‐representable matroid with sufficiently large girth contains either M(Kt)$M(K_t)$ or M(Kt)∗$M(K_t)^*$ as a minor.
James Davies +4 more
wiley +1 more source
A New Approach to Rough Set Based on Remote Neighborhood Systems
Mathematical Problems in Engineering, Volume 2019, Issue 1, 2019., 2019 The notion of neighborhood systems is abstracted from the geometric notion of “near”, and it is primitive in the theory of topological spaces. Now, neighborhood systems have been applied in the study of rough set by many researches. The notion of remote neighborhood systems is initial in the theory of topological molecular lattice, and it is abstracted
Shoubin Sun +3 more
wiley +1 more source
The critical number of dense triangle-free binary matroids
, 2016 We show that, for each real number $\epsilon > 0$ there is an integer $c$ such that, if $M$ is a simple triangle-free binary matroid with $|M| \ge (\tfrac{1}{4} + \epsilon) 2^{r(M)}$, then $M$ has critical number at most $c$.
Geelen, Jim, Nelson, Peter
core +1 more source
Approximate‐Guided Representation Learning in Vision Transformer
CAAI Transactions on Intelligence Technology, Volume 10, Issue 5, Page 1459-1477, October 2025.ABSTRACT In recent years, the transformer model has demonstrated excellent performance in computer vision (CV) applications. The key lies in its guided representation attention mechanism, which uses dot‐product to depict complex feature relationships, and comprehensively understands the context semantics to obtain feature weights.
Kaili Wang +4 more
wiley +1 more source
Wireless Communications and Mobile Computing, Volume 2018, Issue 1, 2018., 2018 Cache‐enabled heterogeneous cellular networks (HCNs) have been investigated extensively to alleviate backhaul congestion and reduce content delivery delay. In this paper, we jointly optimize content placement and user association to minimize the average content delivery delay in cache‐enabled HCNs based on flow‐level models. This formulation considers (
Hua Qu +5 more
wiley +1 more source
, 2013 We investigate the computational difficulty of approximating the partition function of the ferromagnetic Ising model on a regular matroid. Jerrum and Sinclair have shown that there is a fully polynomial randomised approximation scheme (FPRAS) for the ...
Goldberg, Leslie Ann, Jerrum, Mark
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New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
wiley +1 more source
Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016 In cellular heterogeneous networks (HetNets), offloading users to small cell base stations (SBSs) leads to a degradation in signal to interference plus noise ratio (SINR) and results in high outage probabilities for offloaded users. In this paper, we propose a novel framework to solve the cell association problem with the intention of improving user ...
Gongchao Su +5 more
wiley +1 more source
Basilica: New canonical decomposition in matching theory
Journal of Graph Theory, Volume 108, Issue 3, Page 508-542, March 2025.Abstract In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are ...
Nanao Kita
wiley +1 more source