We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...

A wireless sensor network (WSN) is a composed group of a small tiny battery-equipped device capable of sensing, communication and computation which can be scattered over a vast region for the purpose of detecting or monitoring region perfectly. Sensing coverage and network connectivity are two of the most fundamental problem in WSNs. In WSN is usually defined as a measure of how well the sensin...

Sensing coverage and network connectivity are two of the most fundamental problems in wireless sensor networks. Finding an optimal node deployment strategy that would minimize cost, reduce computation and communication overhead, be resilient to node failures, and provide a high degree of coverage with network connectivity is extremely challenging. Coverage and connectivity together can be treat...

Background: Schizophrenia is a mental disorder that severely affects the perception and relations of individuals. Nowadays, this disease is diagnosed by psychiatrists based on psychiatric tests, which is highly dependent on their experience and knowledge. This study aimed to design a fully automated framework for the diagnosis of schizophrenia from electroencephalogram signals using advanced de...

D.R. Fulkerson 1976] described a two-phase greedy algorithm to nd a minimum cost spanning arborescence and to solve the dual linear program. This was extended by the present author for "kernel systems", a model including the rooted edge-connectivity augmentation problem, as well. A similar type of method was developed by D. Kornblum 1978] for "lattice polyhedra", a notion introduced by A. Hooma...

We propose the use of force-directed graph layout as an explorative tool for connectivity-based brain parcellation studies. The method can be used as a heuristic to find the number of clusters intrinsically present in the data (if any) and to investigate their organisation. It provides an intuitive representation of the structure of the data and facilitates interactive exploration of properties...

Today, neuroscientists are interested in discovering human brain functions through brain networks. In this regard, the evaluation of dynamic changes in functional connectivity of the brain regions by using functional magnetic resonance imaging data has attracted their attention. In this paper, we focus on two model-based approaches, called the exponential weighted moving average model and the d...

Coverage and connectivity both are important in wireless sensor network (WSN). Coverage means how well an area of interest is being monitored by the deployed network. It depends on sensing model that has been used to design the network model. Connectivity ensures the establishment of a wireless link between two nodes. A link model studies the connectivity between two nodes. The probability of e...

The notion of element-connectivity has found several important applications. An important tool for these applications is a graph reduction step that preserves element-connectivity [19, 4]. In this article we survey several open problems related to this reduction step as well as some related problems on edge-connectivity.

Effective spatial management in the ocean requires a network of conservation areas that are connected by larval and adult dispersal. We propose a conceptual framework for including the likely impacts of a changing climate on marine connectivity, and synthesize information on the relationships between changing ocean temperature and acidification, connectivity and conservation tools. Our framewor...