Abstract:
Random walks are one of the best investigated dynamical processes on graphs. A particularly fascinating phenomenon is the scaling relationship of fluctuations $\sigma $ with the average flux $\langle f \rangle $. Here we analyze how network topology and nodes with finite capacity lead to deviations from a simple scaling law $\sigma \sim \langle f \rangle ^\alpha$. Sources of randomness are the random walk itself (internal noise) and the fluctuation of the number of walkers (external noise). We obtained exact results for the extreme case of a star network which are indicative of the behavior of large scale systems with a broad degree distribution.The latter are subsequently studied using Monte Carlo simulations. We find that the network heterogeneity amplifies the effects of external noise. By computing the `effective' scaling of each node we show that multiple scaling relationships can coexist in a graph with a heterogeneous degree distribution at an intermediate level of external noise. Finally, we analyze the effect of a finite capacity of nodes for random walkers and find that this also can lead to a heterogeneous scaling of fluctuations.

Abstract:
To improve the accessing performance in a heterogeneous cellular domain, a new relay node clustering strategy was adopted into heterogeneous wireless network. At first, the heterogeneous interference models for relay network were derived, which have great influence on wireless accessing performance. Secondly, system outage probability was given under heterogeneous relay network, so as to get symbol error rate. On the basis of these, Closest neighbor clustering algorithm was used to achieve an good performance. As a comparison, fixed node deployment strategy was adopted to understand cooperative performance. In numerical simulation, the Closest neighbor solution shows an effectively performance improvement in the heterogeneous cellular network.

Abstract:
Based on complex network theory, we propose a computational methodology that addresses the spatial distribution of fuel breaks for the inhibition of the spread and size of wildland fires on heterogeneous landscapes. This is a two-tire approach where the dynamics of fire spread are modeled as a random Markov field process on a directed network whose edge weights, are provided by a state-of-the-art cellular automata model that integrates detailed GIS, landscape and meteorological data. Within this framework, the spatial distribution of fuel breaks is reduced to the problem of finding the network nodes among which the fire spreads faster, thus their removal favours the inhibition of the fire propagation. Here this is accomplished exploiting the information centrality statistics. We illustrate the proposed approach through (a) an artificial forest of randomly distributed density of vegetation, and (b) a real-world case concerning the island of Rhodes in Greece whose a major part of its forest burned in 2008. Simulation results show that the methodology outperforms significantly the benchmark tactic of random distribution of fuel breaks.

Abstract:
Network theory provides a rich toolbox consisting of methods, measures, and models for studying the structure and dynamics of complex systems found in nature, society, or technology. Recently, it has been pointed out that many real-world complex systems are more adequately mapped by networks of interacting or interdependent networks, e.g., a power grid showing interdependency with a communication network. Additionally, in many real-world situations it is reasonable to include node weights into complex network statistics to reflect the varying size or importance of subsystems that are represented by nodes in the network of interest. E.g., nodes can represent vastly different surface area in climate networks, volume in brain networks or economic capacity in trade networks. In this letter, combining both ideas, we derive a novel class of statistical measures for analysing the structure of networks of interacting networks with heterogeneous node weights. Using a prototypical spatial network model, we show that the newly introduced node-weighted interacting network measures indeed provide an improved representation of the underlying system's properties as compared to their unweighted analogues. We apply our method to study the complex network structure of cross-boundary trade between European Union (EU) and non-EU countries finding that it provides important information on trade balance and economic robustness.

Abstract:
Delay tolerant network (DTN) is opportunistic network where each node searches best opportunity to deliver the message called bundle to the destination. DTN implements a store and forward message switching system by simply introducing another new protocol layer called the Bundle Layer on top of the transport layer. The bundle layer is responsible for storing and forwarding entire message in message segments called bundles between source node and destination node. This paper evaluates the performance of delay tolerant network layer in heterogeneous highly dense mobile node environment. The heterogeneous network is created with the help of stationary wired node and Base Station node by introducing dynamic dense Mobile node network. Mobile nodes are assigned with continuous mobility. Three parameters are suggested $\Delta$, $\Theta$ and $\lambda$ to correlate the results obtained using rigorous simulation. Results show that after some threshold values, dense feature about mobile node does not pretend the delay cause for delay tolerant network packets. Also, increase in number of mobile node and number of File Transfer connection rarely change the overall performance of the delay tolerant network.

Abstract:
It is well-known that General Relativity with positive cosmological constant can be formulated as a gauge theory with a broken SO(1,4) symmetry. This symmetry is broken by the presence of an internal space-like vector $V^A$, $A=0,...,4$, with SO(1,3) as a residual invariance group. Attempts to ascribe dynamics to the field $V^{A}$ have been made in the literature but so far with limited success. Regardless of this issue we can take the view that $V^A$ might actually vary across spacetime and in particular become null or time-like. In this paper we will study the case where $V^A$ is null. This is shown to correspond to a Lorentz violating modified theory of gravity. Using the isomorphism between the de Sitter group and the spatial conformal group, $SO(1,4)\simeq C(3)$, we show that the resulting gravitational field equations are invariant under all the symmetries, but spatial translations, of the conformal group C(3).

Abstract:
In the next generation of the mobile network there will be the future of the heterogeneous interface. As it provides the multiple interface at the same time hence will connect to the many interfaces at the same time but will connect to the best one at the time so it will provide the better connectivity at all time. The 4G’s main feature is always providing best connectivity to speedy network. As 4G is providing the mobile-ip connectivity hence will support the voice over ip. This project will provide multiple interfaces to the NS hence will helpful for the research and educational purpose. This paper will provide the idea of creating heterogeneous interface to mobile node architecture in NS. The NS2 is open source so this will provide good environment for the research work. In this paper we are going to explain the architecture of the adding multiple interface to NS2 model.

Abstract:
An important first step when deploying a wireless ad hoc network is neighbor discovery in which every node attempts to determine the set of nodes it can communicate with in one wireless hop. In the recent years, cognitive radio (CR) technology has gained attention as an attractive approach to alleviate spectrum congestion. A cognitive radio transceiver can operate over a wide range of frequencies, possibly scanning multiple frequency bands. A cognitive radio node can opportunistically utilize unused wireless spectrum without interference from other wireless devices in its vicinity. Due to spatial variations in frequency usage and hardware variations in radio transceivers, different nodes in the network may perceive different subsets of frequencies available to them for communication. This heterogeneity in the available channel sets across the network increases the complexity of solving the neighbor discovery problem in a cognitive radio network. In this work, we design and analyze several randomized algorithms for neighbor discovery in such a (heterogeneous) network under a variety of assumptions (e.g. maximum node degree known or unknown) for both synchronous and asynchronous systems under minimal knowledge. We also show that our randomized algorithms are naturally suited to tolerate unreliable channels and adversarial attacks.

Abstract:
Motivated by its relevance to various types of dynamical behavior of network systems, the maximum eigenvalue $\lambda_Q$ of the adjacency matrix $A$ of a network has been considered, and mean-field-type approximations to $\lambda_Q$ have been developed for different kinds of networks. Here $A$ is defined by $A_{ij} = 1$ ($A_{ij} = 0$) if there is (is not) a directed network link to $i$ from $j$. However, in at least two recent problems involving networks with heterogeneous node properties (percolation on a directed network and the stability of Boolean models of gene networks), an analogous but different eigenvalue problem arises, namely, that of finding the largest eigenvalue $\lambda_Q$ of the matrix $Q$, where $Q_{ij} = q_i A_{ij}$ and the `bias' $q_i$ may be different at each node $i$. (In the previously mentioned percolation and gene network contexts, $q_i$ is a probability and so lies in the range $0 \le q_i \le 1$.) The purposes of this paper are to extend the previous considerations of the maximum eigenvalue $\lambda_A$ of $A$ to $\lambda_Q$, to develop suitable analytic approximations to $\lambda_Q$, and to test these approximations with numerical experiments. In particular, three issues considered are (i) the effect of the correlation (or anticorrelation) between the value of $q_i$ and the number of links to and from node $i$; (ii) the effect of correlation between the properties of two nodes at either end of a network link (`assortativity'); and (iii) the effect of community structure allowing for a situation in which different $q$-values are associated with different communities.

Abstract:
We analyze the resistance between two notes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M by N cobweb network of resistors with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.