We investigate the effects of patchy (clustered) connectivity in sparsely connected attractor neural networks (NNs). This study is motivated by the fact that the connectivity of pyramidal neurons in layer II/III of the mammalian visual cortex is patchy and sparse. The storage capacity of hypercolumnar attractor NNs that use the Hopfield and Willshaw learning rules with this kind of connectivity...

INTRODUCTION Low-frequency (<0.1Hz) spontaneous fluctuations in resting-state fMRI have been used to study functional connectivity in brain networks (1, 2). However, the underlying mechanism and contrast-to-noise ratio (CNR) of the connectivity remain inconclusive (3). While the CNR of stimulation-induced brain activation has been well studied, much less is known about the optimization of funct...

the atom-bond connectivity index of graph is a topological index proposed by estrada et al.as abc (g)  uve (g ) (du dv  2) / dudv , where the summation goes over all edges ofg, du and dv are the degrees of the terminal vertices u and v of edge uv. in the present paper,some upper bounds for the second type of atom-bond connectivity index are computed.

let $g$ be a non-abelian group. the non-commuting graph $gamma_g$ of $g$ is defined as the graph whose vertex set is the non-central elements of $g$ and two vertices are joined if and only if they do not commute.in this paper we study some properties of $gamma_g$ and introduce $n$-regular $ac$-groups. also we then obtain a formula for szeged index of $gamma_g$ in terms of $n$, $|z(g)|$ and $|g|...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

In many neuroimaging studies functional connectivity measurements are collected across a cohort of multiple subjects. Given such data, a fundamental problem corresponds to accurately quantifying variability across subjects. In this vignette we provide a brief illustration of the recently proposed Mixed Neighborhood Selection (MNS) algorithm which is able to simultaneously estimate connectivity ...

We prove that given any fixed edge ra in a 4-connected graph G, there exists a cycle C through ra such that G − (V (C) − {r}) is 2-connected. This will provide the first step in a decomposition for 4-connected graphs. We also prove that for any given edge e in a 5-connected graph G there exists an induced cycle C through e in G such that G−V (C) is 2-connected. This provides evidence for a conj...

It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a chord. This conjecture is verified for locally 4-connected planar graphs, that is, let N be the set of natural numbers; then there is a function h : N → N such that, for every 4-connected graph G embedded in a surface S w...

Let Tn denote the set of all unrooted and unlabeled trees with n vertices, and (i, j) a double-star. By assuming that every tree of Tn is equally likely, we show that the limiting distribution of the number of occurrences of the double-star (i, j) in Tn is normal. Based on this result, we obtain the asymptotic value of Randić index for trees. Fajtlowicz conjectured that for any connected graph ...