Results 61 to 70 of about 887,124 (211)
A complex network perspective on brain disease
Biological Reviews, EarlyView.ABSTRACT If brain anatomy and dynamics have a complex network structure as it has become standard to posit, it is reasonable to assume that such a structure should play a key role not only in brain function but also in brain dysfunction. However, exactly how network structure is implicated in brain damage and whether at least some pathologies can be ...
David Papo, Javier M. Buldú
wiley +1 more source
Extremal, enumerative and probabilistic results on ordered hypergraph matchings
Forum of Mathematics, SigmaAn ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders.
Michael Anastos +3 more
doaj +1 more source
Hypergraph removal lemmas via robust sharp threshold theorems
Discrete Analysis, 2020 Hypergraph removal lemmas via robust sharp threshold theorems, Discrete Analysis 2020:10, 46 pp. A central result in additive and extremal combinatorics is the triangle removal lemma, which roughly speaking states that a graph with few triangles can be ...
Noam Lifshitz
doaj +1 more source
Estimates on the decay of the Laplace–Pólya integral
Bulletin of the London Mathematical Society, EarlyView.Abstract The Laplace–Pólya integral, defined by Jn(r)=1π∫−∞∞sincntcos(rt)dt$J_n(r) = \frac{1}{\pi }\int _{-\infty }^\infty \operatorname{sinc}^n t \cos (rt) \,\mathrm{d}t$, appears in several areas of mathematics. We study this quantity by combinatorial methods; accordingly, our investigation focuses on the values at integer rs$r{\rm s}$.
Gergely Ambrus, Barnabás Gárgyán
wiley +1 more source
Cacti with Extremal PI Index [PDF]
, 2016 The vertex PI index $PI(G) = \sum_{xy \in E(G)} [n_{xy}(x) + n_{xy}(y)]$ is a distance-based molecular structure descriptor, where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the
Wang, Chunxiang +2 more
core +1 more source
Degrees and prime power order zeros of characters of symmetric and alternating groups
Bulletin of the London Mathematical Society, EarlyView.Abstract We show that the p$p$‐part of the degree of an irreducible character of a symmetric group is completely determined by the set of vanishing elements of p$p$‐power order. As a corollary, we deduce that the set of zeros of prime power order controls the degree of such a character. The same problem is analysed for alternating groups, where we show
Eugenio Giannelli +2 more
wiley +1 more source
Curves of best approximation on wonderful varieties
Bulletin of the London Mathematical Society, EarlyView.Abstract We give an unconditional proof of the Coba conjecture for wonderful compactifications of adjoint type for semisimple Lie groups of type An$A_n$. We also give a proof of a slightly weaker conjecture for wonderful compactifications of adjoint type for arbitrary Lie groups.
Christopher Manon +2 more
wiley +1 more source
Kneser graphs are like Swiss cheese
Discrete Analysis, 2018 Kneser graphs are like Swiss cheese, Discrete Analysis 2018:2, 18 pp. This paper relates two very interesting areas of research in extremal combinatorics: removal lemmas, and influence of variables.
Ehud Friedgut, Oded Regev
doaj +1 more source
Beyond sum-free sets in the natural numbers [PDF]
, 2014 For an interval [1,N]⊆N, sets S⊆[1,N] with the property that |{(x,y)∈S2:x+y∈S}|=0, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)=|{(x,y)∈S2:x+y∈S}|, and analyze its behaviour ...
Huczynska, Sophie
core
Geometric variational problems of statistical mechanics and of combinatorics
, 2000 We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a ...
Alexander K. +9 more
core +2 more sources