Background: Ensuring adequate depth of anesthesia during surgery is essential for anesthesiologists to prevent the occurrence of unwanted alertness during surgery or failure to return to consciousness. Since the purpose of using anesthetics is to affect the central nervous system, brain signal processing such as electroencephalography (EEG) can be used to predict different levels of anesthesia....

The source location problem is a problem of computing a minimum cost source set in an undirected graph so that the connectivity between the source set and a vertex is at least the demand of the vertex. In this paper, the connectivity between a source set S and a vertex v is defined as the maximum number of paths between v and S no two of which have common vertex except v. We propose an O(d∗ log...

Recurrent networks that have transfer functions that fulfill the Lipschitz continuity with L = 1, may be echo state networks if certain limitations on the recurrent connectivity are applied. Initially it has been shown that it is sufficient if the largest singular value of the recurrent connectivity S is smaller than 1. The main achievement of this paper is a proof under which conditions the ne...

The Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights (d(u)d(v))− 1 2 over all edges e = uv ofG. We prove that R(G) ≥ d(G)/2, where d(G) is the diameter of G. This immediately implies that R(G) ≥ r(G)/2, which is the closest result to the well-known Grafiti conjecture R(G) ≥ r(G) − 1 of Fajtlowicz [4], where r(G) is the radius of G. Asymptotically, our res...

The problem in which the object is to add a minimum weight set of edges to a graph so as to satisfy a given condition is called the augmentation problem. This problem has a wide variety [3-5, 10, 11, 14-201. If such a given condition is concerned with the vertexor edge-connectivity of a graph then the problem is referred to as the (vertexor edge-) connectivity augmentation problem. Frank and Ch...

• Random Sampling: X are iid uniform from unit sphere in S`. • Random Subspace: S` are spanned by d iid uniform vectors in R. GRAPH CONNECTIVITY What about the second design objective? • Nashihatkon & Hartley nailed that connectivity is NOT a generic property for SSC in general when d ≥ 4. • What about for LRR? Assume random sampling and random subspace, we have: Proposition 1 Under independent...

in this paper we discuss about tenacity and its properties in stability calculation. we indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. we also give good lower and upper bounds for tenacity.

The S and LG alleles of the serotonin transporter-linked polymorphic region (5-HTTLPR) lower serotonin transporter expression. These low-expressing alleles are linked to increased risk for depression and brain activation patterns found in depression (increased amygdala activation and decreased amygdala-prefrontal cortex connectivity). Paradoxically, serotonin transporter blockade relieves depre...

The right and left hand Motor Imagery (MI) analysis based on the electroencephalogram (EEG) signal can directly link the central nervous system to a computer or a device. This study aims to identify a set of robust and nonlinear effective brain connectivity features quantified by transfer entropy (TE) to characterize the relationship between brain regions from EEG signals and create a hierarchi...

Given a graph H = (U,E) and connectivity requirements r = {r(u, v) : u, v ∈ R ⊆ U}, we say that H satisfies r if it contains r(u, v) pairwise internally-disjoint uv-paths for all u, v ∈ R. We consider the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set V of points in a normed space (M, ‖·‖) and connectivity requirements, find a minimum size set S ⊂ ...