Receptive field (RF) sizes and cortical magnification factor (CMF) are fundamental organization properties of the visual cortex. At increasing visual eccentricity, RF sizes increase and CMF decreases. A relationship between RF size and CMF suggests constancies in cortical architecture, as their product, the cortical representation of an RF (point image), may be constant. Previous animal neuroph...

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Sch...

Given a graph G = (V; E) we deene e(X), the mean eccentricity of a vertex X, as the average distance from X to all the other vertices of the graph. The computation of this parameter appears to be nontrivial in the case of the de Bruijn networks. In this paper we consider upper and lower bounds for e(X). For the directed de Bruijn network, we provide tight bounds as well as the extremal vertices...

In this section, we provide basic definitions and interpretations for the different network characteristics that we consider. At the household level, we study: • Degree: the number of links that a household has. This is a measure of how well connected a node is in the graph. • Clustering coefficient: the fraction of a household’s neighbors that are themselves neighbors. This is a measure of how...

a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...