let r be a fnite commutative ring and n(r) be the set of non unit elements of r. the non unit graph of r, denoted by gamma(r), is the graph obtained by setting all the elements of n(r) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin n(r). in this paper, the basic properties of gamma(r) are investigated and some characterization results regarding co...

The aim of this work is to characterize quantitatively the performance of a body of techniques in the frequency domain for the estimation of cortical connectivity from high-resolution EEG recordings in different operative conditions commonly encountered in practice. Connectivity pattern estimators investigated are the Directed Transfer Function (DTF), its modification known as direct DTF (dDTF)...

Connectivity is an increasingly important part of statistical computing, and interfaces to databases are becoming important both in large-scale data mining applications and from the use of smaller personal databases. In this paper we present current work and future plans on interfacing the S language (R and S-PLUS) to databases, in particular to relational database management systems (DBMS).

For any finite abelian group G and any subset S ⊆ G, we determine the connectivity of the addition Cayley graph induced by S on G. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a special, explicitly described form.

The authors previously published an iterative process to generate a class of projectiveplanarK3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4free projective-planar graphs which we call Möbi...

We prove a new adjunction theorem for n-equivalences. This theorem enables us to produce a simple geometric version of proof of the triad connectivity theorem of Blakers and Massey. An important intermediate step is a study of the collapsing map S∨X → S,

Most brain activity occurs in an ongoing manner not directly locked to external events or stimuli. Regional ongoing activity fluctuates in unison with some brain regions but not others, and the degree of long-range coupling is called functional connectivity, often measured with correlation. Strength and spatial distributions of functional connectivity dynamically change in an ongoing manner ove...

Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane was imagined. Further, the ide...

Abst rac t . Given an undirected graph G = (V, E0) with IVI-n, and a feasible set E of m weighted edges on V, the optimal 2-edge (2-vertex) connectivity augmentation problem is to find a subset S* __ E such that G(V, E0 U S*) is 2-edge (2-vertex) connected and the weighted sum of edges in S* is minimized. We devise NC approximation algorithms for the optimal 2-edge connectivity and the optimal ...

For a connected graph G = (V, E), an edge set S ⊆ E is a k-restricted edge cut if G−S is disconnected and every component of G− S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G) = min{|[X, X ]| : |X | = k,G[X ] is connected}. G is λk -optimal if λk(G) = ξk(G). Moreover, G is super-λk ...