Analysis of relative influence of nodes in directed networks

Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the relative importance of nodes specifically in directed networks. We analyze such a centrality measure called the influence. The influence represents the importance of nodes in various dynamics such as synchronization, evolutionary dynamics, random walk, and social dynamics. We analytically calculate the influence in various networks, including directed multipartite networks and a directed version of the Watts-Strogatz small-world network. The global properties of networks such as hierarchy and position of shortcuts, rather than local properties of the nodes, such as the degree, are shown to be the chief determinants of the influence of nodes in many cases. The developed method is also applicable to the calculation of the PageRank. We also numerically show that in a coupled oscillator system, the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes. For a type of random network, the analytically derived threshold is approximately equal to the inverse of the influence. We numerically show that this relationship also holds true in a random scale-free network and a neural network.Comment: 9 figure

A REVIEW ON ANCIENT CONCEPTS OF KUMARAGARA, KRIDABHOOMI AND KRIDANAKA W.S.R.TO PEDIATRIC CARE UNIT, PLAY GROUND AND TOYS

Ayurveda is one of the earliest medical systems that have got a strong scientific foundation formulated by experiments and observations of ancient wisdom. Kaumarbhritya (pediatrics) is one among eight branches of Ayurveda. Acharya Kashyapa has given prime importance to Kaumarbhritya for the very first time. As far as the branch pediatrics is concerned, in Ayurveda it accompanies a broad area. Virtually every aspect of a growing child is connected with play. Now days, many textbooks of pediatrics are focusing more on pediatric diseases and its management, but the concept of toys, play and its importance remain untouched. Years ago, Acharyas has described characteristics of Kumaragara (Neonatal care unit/pediatric ward), Kumaradhara (guardian), Kridanaka (toys) and Kridabhumi (play ground) which all are the pillars of a healthy and prosperous human being. Here, an effort is made to collect those aspects and validating that data with available evidence based references.

Collective dynamical response of coupled oscillators with any network structure

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is also developed. General formulae for the collective phase sensitivity and the effective phase coupling between the oscillator networks are found. Our theory is applicable to a wide variety of oscillator networks undergoing frequency synchronization. Any network structure can systematically be treated. A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure

Collective fluctuations in networks of noisy components

Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve fluctuations, which may crucially affect functioning of the system. However, the relation between the fluctuations in isolated individual components and those in collective dynamics is unclear. Here we study a linear dynamical system of networked components subjected to independent Gaussian noise and analytically show that the connectivity of networks determines the intensity of fluctuations in the collective dynamics. Remarkably, in general directed networks including scale-free networks, the fluctuations decrease more slowly with the system size than the standard law stated by the central limit theorem. They even remain finite for a large system size when global directionality of the network exists. Moreover, such nontrivial behavior appears even in undirected networks when nonlinear dynamical systems are considered. We demonstrate it with a coupled oscillator system.Comment: 5 figure

Dynamics-based centrality for general directed networks

Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.Comment: 7 figure

Strong Effects of Network Architecture in the Entrainment of Coupled Oscillator Systems

Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization. However, the entrainment is significantly facilitated if the networks are directionally biased, i.e., closer to the feedforward networks. Furthermore, we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes. The neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results.Comment: 15 pages, 11 figures, RevTe

Synchronization Engineering: Theoretical Framework and Application to Dynamical Clustering

A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.Comment: To appear in CHAO

Cancer risk and parental pesticide application in children of Agricultural Health Study participants.

Parental exposure to pesticides may contribute to childhood cancer risk. Through the Agricultural Health Study, a prospective study of pesticide applicators in Iowa and North Carolina, we examined childhood cancer risk and associations with parental pesticide application. Identifying information for 17,357 children of Iowa pesticide applicators was provided by parents via questionnaires (1993-1997) and matched against the Iowa Cancer Registry. Fifty incident childhood cancers were identified (1975-1998). Risk of all childhood cancers combined was increased [standardized incidence ratio (SIR) = 1.36; 95% confidence interval (CI), 1.03-1.79]. Risk of all lymphomas combined was also increased (SIR = 2.18; 95% CI, 1.13-4.19), as was risk of Hodgkin's lymphoma (SIR = 2.56; 95% CI, 1.06-6.14). We used logistic regression to explore associations between self-reported parental pesticide application practices and childhood cancer risk. No association was detected between frequency of parental pesticide application and childhood cancer risk. An increased risk of cancer was detected among children whose fathers did not use chemically resistant gloves [odds ratio (OR) = 1.98; 95% CI, 1.05-3.76] compared with children whose fathers used gloves. Of 16 specific pesticides used by fathers prenatally, ORs were increased for aldrin (OR = 2.66), dichlorvos (OR = 2.06), and ethyl dipropylthiocarbamate (OR = 1.91). However, these results were based on small numbers and not supported by prior biologic evidence. Identification of excess lymphoma risk suggests that farm exposures including pesticides may play a role in the etiology of childhood lymphoma