The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.The research of this paper is partially supported by the University of Kashan under grant no 159020/12

Social Software: For the People, By the People

Social networking software is an emergent phenomenon of the information systems landscape whose novelty has ensured that it has largely eluded academic scrutiny. Given that social software is primarily within the province of the young at this stage, a playfully meandering exposition of its definition and quasi-philosophical ramifications will be delivered in essay form

An empirical investigation of high relational orientation sport club members

Relationships between businesses, businesses and end customers, as well as between customers are an important area of practical and scientific interest. In the present era, largely due to digital technologies such as the database, public and private networks, and data collection and information distribution via TCP/IP (Transmission Control Protocol/Internet Protocol) interface tools such as the World Wide Web (Web), the interest in relationships and related aspects such as trust as it relates to Web interactivity continues. An important antecedent empirical study established that arts patrons (customers) of a New York theatre company could be segmented according to their relational orientation, and that this orientation mediated between component attitudes and future purchase intentions. The study reported in this paper employs Web-based data collection and postal data collection methods in an investigation of the mediation effects of these data collection methods used with the same population of a premier football club in Australia. While a future aim is to more closely compare the outcomes established in the arts study with those from a similarly constructed study in the sporting arena, the focus of this initial paper is the differences in response exhibited by online respondents relative to postal survey respondents. The paper reports findings which do not support those of the antecedent arts and entertainment study concerning the weakness of overall satisfaction on the purchase intentions of high relational orientation customers. The paper also reports findings which give confidence to users of online surveys that despite differences in demographic profiles of these respondents and postal survey respondents, there is a degree of similarity in the responses of the two groups on the measures used in this study. The paper also suggests the need for further research into these data collection effects as they relate to relationship marketing.<br /

Dysconnection and cognition in schizophrenia: A spectral dynamic causal modeling study

Schizophrenia (SZ) is a severe mental disorder characterized by failure of functional integration (aka dysconnection) across the brain. Recent functional connectivity (FC) studies have adopted functional parcellations to define subnetworks of large-scale networks, and to characterize the (dys)connection between them, in normal and clinical populations. While FC examines statistical dependencies between observations, model-based effective connectivity (EC) can disclose the causal influences that underwrite the observed dependencies. In this study, we investigated resting state EC within seven large-scale networks, in 66 SZ and 74 healthy subjects from a public dataset. The results showed that a remarkable 33% of the effective connections (among subnetworks) of the cognitive control network had been pathologically modulated in SZ. Further dysconnection was identified within the visual, default mode and sensorimotor networks of SZ subjects, with 24%, 20%, and 11% aberrant couplings. Overall, the proportion of discriminative connections was remarkably larger in EC (24%) than FC (1%) analysis. Subsequently, to study the neural correlates of impaired cognition in SZ, we conducted a canonical correlation analysis between the EC parameters and the cognitive scores of the patients. As such, the self-inhibitions of supplementary motor area and paracentral lobule (in the sensorimotor network) and the excitatory connection from parahippocampal gyrus to inferior temporal gyrus (in the cognitive control network) were significantly correlated with the social cognition, reasoning/problem solving and working memory capabilities of the patients. Future research can investigate the potential of whole-brain EC as a biomarker for diagnosis of brain disorders and for neuroimaging-based cognitive assessment

Finite element modeling of coupled optical microdisk resonators for displacement sensing

We analyze normal mode splitting in a pair of vertically coupled microdisk resonators. A full vectorial finite element model is used to find the eigen frequencies of the symmetric and antisymmetric composite modes as a function of coupling distance. We find that the coupled microdisks can compete with the best Fabry-Perot resonators in displacement sensing. We also show how we configured FreeFem++ for the sphere eigenvalue problem.Comment: 10 pages, 4 figures, 1 FreeFem++ script (download and unzip the paper source