For each finite field F of prime order there is a constant c such that every 4-connected matroid has at most c inequivalent representations over F. We had hoped that this would extend to all finite fields, however, it was not to be. The (m,n)-mace is the matroid obtained by adding a point freely to M(Km,n). For all n ≥ 3, the (3, n)-mace is 4-connected and has at least 2 representations over an...

We show that every 4-connected planar graph has a B3-EPG representation, i.e., every vertex is represented by a curve on the grid with at most three bends, and two vertices are adjacent if and only if the corresponding curves share an edge of the grid. Our construction is based on a modification of the representation by touching thickened L-shapes proposed by Gonçalves et al. [4].

Introduction: Long-term stressful situations can drastically influence one’s mental life. However, the effect of mental stress on recognition of emotional stimuli needs to be explored. In this study, recognition of emotional stimuli in a stressful situation was investigated. Four emotional conditions, including positive and negative states in both low and high levels of arousal were analy...

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 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...

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.

A sensor network is a network with large number of sensors. Each node in the network is defined with some energy parameters. With each communication over the network some amount of energy is consumed. The proposed work is related to improve the network life by using the concept of prioritization along with the mobile base station over circular path in a clustered network in such a way that maxi...

This paper describes the definition and testing of a new type of median filter for images. The topological median filter implements some existing ideas and some new ideas on fuzzy connectedness to improve, over a conventional median filter, the extraction of edges in noise. The concept of alpha-connectivity is defined and used to create an algorithm for computing the degree of connectedness of ...