Random Networks

Some scaling properties of the topological width function for an infinite population of networks obeying the random model are analyzed. A Monte Carlo procedure is applied to generate width functions according to the hypothesis of topological randomness. The probability distributions of both peak and distance to peak of the topological width functions, conditioned (1) on the network diameter X and (2) on X and parameter/3 = [log (2/x -1)]/log X, are studied. The parameter/3 can be considered a shape factor of the network; indeed, low/3 values describe elongated networks, while high/3 values refer to fan-like networks. Scale invariance for both random variables is established in the first case by using X as a scale parameter. Also in the second case, scale invariance is observed for both the peak and the distance to peak of the topological width function; in particular, the invariance property for the peak involves a scaling function which is directly related to the shape factor/3, allowing determination of the statistical similarity between random networks indexed by the same/3. Then, a coarse-graining procedure is applied to a set of 15,000 width functions with X = 512; a scaling behavior of peaks of the original width function and aggregated ones is observed over a wide range of aggregation scales. Consequently, a statistical self-similarity for the peaks is also observed, which involved the same/3-related scaling function. Finally, possible implication of the present results on the hydrologic response, at the basin scale, is discussed.

We consider a high contrast two phase composite such as a ceramic/polymer composite or a fiberglass composite. Our objective is to determine the dependence of the effective conductivity  (or the effective dielectric constant or the effective shear modulus) of the composite on the random locations of the inclusions (ceramic particles or fibers) when the concentration of the inclusions is high. We consider a two dimensional model and show that the continuum problem can be approximated by a discrete random network (graph). We use variational techniques to provide rigorous mathematical justification for this approximation. In particular, we have shown asymptotic equivalence of the effective constant  for the discrete and continuum models in the limit when the relative interparticle distance goes to zero. We introduce the geometrical interparticle distance parameter using Voronoi tessellation, and emphasize the relevance of this parameter due to the fact that for irregular (non periodic) geometries it is not uniquely determined by the volume fraction of the inclusions. We use the discrete network to compute  numerically. For this purpose we employ a computer program which generates a random distribution of disks on the plane. Using this distribution we obtain the corresponding discrete network. Furthermore the computer program provides the distribution of fluxes in the network which is based on the Keller's formula for two closely spaced disks. We compute the dependence of  on the volume fraction of the inclusions V for monodispersed composites and obtained results which are consistent with the percolation theory predictions. For polydispersed composites (random inclusions of two different sizes) the dependence Â(V ) is not simple and is determined by the relative volume fraction Vr of large and small particles. We found some special values of Vr for which the effective coefficient is significantly decreased. The computer program which is based on our network model is very efficient and it allows us to collect the statistical data for a large number of random configurations.

Raman scattering and modulated-DSC experiments on Potassium Germanate glasses* N. WANG, D. NOVITA, P. BOOLCHAND, University of Cincinnati -We have synthesized titled glasses in the 0 < x < 0.16 range by traditional melt-quenching, and have examined them in Raman scattering and modulated-DSC (MDSC) experiments. Raman lineshapes observed in the present work are quite similar to those reported by Henderson and Wang 1 . Preliminary MDSC experiments reveal glass transition temperatures, T g (x), starting from a value of 570˚C at x = 0, to decrease to 508˚C near x = 0.06, and to increase thereafter almost linearly to 552˚C as x increases to 0.15. On the other hand, the non-reversing enthalpy associated with T g provides evidence of a global minimum in the 0.08 < x < 0.10 range, the reversibility window 2 . These results are consistent with glasses at x < 0.08 as Stressed-Rigid, those at x > 0.10 as Floppy, while those in the reversibility window as representing the Intermediate Phase 2 . The space filling nature of the Intermediate Phase is, independently, corroborated by trends in molar volumes which show a broad global minimum in the 9-11% range. Identification of the three elastic phases provides a physical basis to understand the origin of the Germanate anomaly, and the electrical conductivity threshold when glasses become mechanically floppy. *Supported by NSF grant DMR 04-56472. 1

It has been suggested, based on x-ray absorption spectroscopy (XAS) experiments on liquid water [Wernet, Ph., et al. (2004) Science 304, 995–999], that a condensed-phase water molecule’s asymmetric electron density results in only two hydrogen bonds per water molecule on average. The larger implication of the XAS interpretation is that the conventional view of liquid water being a tetrahedrally coordinated random network is now replaced by a structural organization that instead strongly favors hydrogen-bonded water chains or large rings embedded in a weakly hydrogen-bonded disordered network. This work reports that the asymmetry of the hydrogen density exhibited in the XAS experiments agrees with reported x-ray scattering structure factors and intensities for Q &gt; 6.5 Å −1 . However, the assumption that the asymmetry in the hydrogen electron density does not fluctuate and is persistent in all local molecular liquid water environments is inconsistent with longer-ranged tetrahedral ...

The magnetic rare earth element gadolinium (Gd) was doped into thin films of amorphous carbon (hydrogenated a-C:H, or hydrogen-free a-C) using magnetron co-sputtering. The Gd acted as a magnetic as well as an electrical dopant, resulting in an enormous negative magnetoresistance below a temperature (T ′ ). Hydrogen was introduced to control the amorphous carbon bonding structure. High-resolution electron microscopy, ion-beam analysis and Raman spectroscopy were used to characterize the influence of Gd doping on the a-Gd x C 1-x (:H y ) film morphology, composition, density and bonding. The films were largely amorphous and homogeneous up to x=22.0 at.%. As the Gd doping increased, the sp 2 -bonded carbon atoms evolved from carbon chains to 6-member graphitic rings. Incorporation of H opened up the graphitic rings and stabilized a sp 2 -rich carbonchain random network. The transport properties not only depended on Gd doping, but were also very sensitive to the sp 2 ordering. Magnetic properties, such as the spin-glass freezing temperature and susceptibility, scaled with the Gd concentration.

The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R × R. We extend the earlier work of Arratia and of Tóth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including convergence of the system of all coalescing random walks to the BW under diffusive spacetime scaling. In this paper, we present a number of results concerning the characterization of and convergence to a striking stochastic object called the Brownian web (BW). Several of the main results were previously announced, with sketches of the proofs, in . Roughly speaking, the BW is the collection of graphs of coalescing onedimensional Brownian motions (with unit diffusion constant and zero drift) starting from all possible starting points in one plus one-dimensional (continuous) space-time. This object was originally studied more than twenty years ago by Arratia [5], motivated by asymptotics of one-dimensional voter models, and then about five years ago by Tóth and Werner , motivated by the problem of constructing continuum "self-repelling motions." Our own interest in this object arose because of its relevance to "aging" in statistical physics models of onedimensional coarsening -which returns us to Arratia's original context of voter models, or equivalently coalescing random walks in one dimension. This motivation leads to our primary concern with weak convergence results, which in turn requires a careful choice of space for the BW so as to obtain useful characterization criteria for its distribution.

Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we study the network structure for a fractional percolation process [Shang, Phys. Rev. E 89, 012813 (2014)], in which the state of a node can be either fully functional (FF), partially functional (PF), or dysfunctional (D). We develop new equations to calculate the relative size of the percolating cluster of FF and PF nodes, that are in agreement with our stochastic simulations. In addition, we find a regime in which the percolating cluster can be described as a coarse-grained bipartite network, namely, as a set of finite groups of FF nodes connected by PF nodes. Moreover, these groups behave as a set of ``supernodes'' with a power-law degree distribution. Finally, we show how this emergent structure explains the values of several critical exponents around the percolation threshold.

The static and dynamic elastic properties of two-dimensional random networks composed of Hookean springs are analyzed. These networks are proved to be nonrigid with respect to small deformations, and the floppy mode ratio is calculated exactly. The vibrational spectrum is shown to consist only of zerofrequency and localized modes. The exponential decay of the amplitude and velocity of the transient wave front are shown to be exactly described by a quasi-one-dimensional model of noninteracting paths of propagation. [S0031-9007(96)

We consider a one-dimensional network in which the nodes at Euclidean distance l can have long range connections with a probabilty P (l) ∼ l -δ in addition to nearest neighbour connections. This system has been shown to exhibit small world behaviour for δ < 2 above which its behaviour is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at δ = 1. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicate that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behaviour of a single quantity, the average bond length. The phase transitions in all dimensions are non-trivial in nature.

By restricting the motion of high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum-mechanically, the interplay of backscattering, and of the bending action of a weak magnetic field. Backscattering limits the mobility, while bending initiates quantization of the Hall conductivity. We demonstrate that, in restricted geometry, electron motion reduces to two Chalker-Coddington networks, with opposite directions of propagation along the links, which are weakly coupled by disorder. Interplay of backscattering and bending results in the quantum Hall transition in a non-quantizing magnetic field, which decreases with increasing mobility. This is in accord with scenario of floating up delocalized states.

The Sznajd model of socio-physics, that only a group of people sharing the same opinion can convince their neighbors, is applied to a scale-free random network modeled by a deterministic graph. We also study a model for elections based on the Sznajd model and the exponent obtained for the distribution of votes during the transient agrees with those obtained for real elections in Brazil and India. Our results are compared to those obtained using a Barabási-Albert scale-free network.

Cladding stainless steel layer on the inner surface of ferrite pressure vessel is a common method to improve the corrosion resistance and save the economic cost. However, the movement of heat source and temperature gradient in the process of cladded welding will lead to the anisotropy of cladded layer material. When measuring the residual stress of pressure vessel steel plate with stainless steel cladded layers by contour method, it is necessary to know the elastic mechanical properties of stainless steel cladded layers accurately. The assumption of transversely isotropy was employed, and the relationship between the material compliance matrix and the elastic modulus of transversely isotropic material was utilized. Based on the elastic modulus of each cladded layer and the whole steel plate from the longitudinal direction (0°) until the transverse direction (90°) measured by the experiment, the independent constants S11, S13, S33 and S44 in the compliance matrix of each cladded layer and the whole steel plate were obtained by regression analysis method. Furthermore, by using the relationship between the independent constants of the stiffness matrix of the transversely isotropic material and the single crystal material, the independent constants S12 in the compliance matrix of each stainless steel cladded layer and the whole steel plate were obtained. And then the independent constants of the stiffness matrix of each cladded layer and the whole steel plate were acquired. Hence, a method for calculating the anisotropic elastic constants of the stainless steel cladded layer and the whole steel plate was proposed. The results will provide material data support for measuring residual stress of pressure vessel steel plate with stainless steel cladded layers by contour method.

Motivation: Algorithmic and modeling advances in the area of protein-protein interaction (PPI) network analysis could contribute to the understanding of biological processes. Local structure of networks can be measured by the frequency distribution of graphlets, small connected non-isomorphic induced subgraphs. This measure of local structure has been used to show that high-confidence PPI networks have local structure of geometric random graphs. Finding graphlets exhaustively in a large network is computationally intensive. More complete PPI networks, as well as PPI networks of higher organisms, will thus require efficient heuristic approaches. Results: We propose two efficient and scalable heuristics for finding graphlets in high-confidence PPI networks. We show that both PPI and their model geometric random networks, have defined boundaries that are sparser than the 'inner parts' of the networks. In addition, these networks exhibit 'uniformity' of local structure inside the networks. Our first heuristic exploits these two structural properties of PPI and geometric random networks to find good estimates of graphlet frequency distributions in these networks up to 690 times faster than the exhaustive searches. Our second heuristic is a variant of a more standard sampling technique and it produces accurate approximate results up to 377 times faster than the exhaustive searches. We indicate how the combination of these approaches may result in an even better heuristic.

Motivation: Algorithmic and modeling advances in the area of protein–protein interaction (PPI) network analysis could contribute to the understanding of biological processes. Local structure of networks can be measured by the frequency distribution of graphlets, small connected non-isomorphic induced subgraphs. This measure of local structure has been used to show that high-confidence PPI networks have local structure of geometric random graphs. Finding graphlets exhaustively in a large network is computationally intensive. More complete PPI networks, as well as PPI networks of higher organisms, will thus require efficient heuristic approaches. Results: We propose two efficient and scalable heuristics for finding graphlets in high-confidence PPI networks. We show that both PPI and their model geometric random networks, have defined boundaries that are sparser than the ‘inner parts’ of the networks. In addition, these networks exhibit ‘uniformity’ of local structure inside the networ...

In this paper, we study synchronization of complex random networks of nonlinear oscillators, with specifiable expected degree distribution. We review a sufficient condition for synchronization and a sufficient condition for desynchronization, expressed in terms of the eigenvalue distribution of the Laplacian of the graph and the coupling strength. We then provide a general way to approximate the Laplacian eigenvalue distribution for the case of large random graphs produced by a generalization, [2], of the Erdös-Rényi model. Our approach is based on approximating the moments of the eigenvalue density function. The analysis is illustrated by using a complex network of nonlinear oscillators, with a power-law degree distribution.

In this paper, we study synchronization of complex random networks of nonlinear oscillators, with specifiable expected degree distribution. We review a sufficient condition for synchronization and a sufficient condition for desynchronization, expressed in terms of the eigenvalue distribution of the Laplacian of the graph and the coupling strength. We then provide a general way to approximate the Laplacian eigenvalue distribution for the case of large random graphs produced by a generalization, [2], of the Erdös-Rényi model. Our approach is based on approximating the moments of the eigenvalue density function. The analysis is illustrated by using a complex network of nonlinear oscillators, with a power-law degree distribution.

Can we objectively distinguish chemical systems that are able to process meaningful information from those that are not suitable for information processing? Here, we present a formal method to assess the semantic capacity of a chemical reaction network. The semantic capacity of a network can be measured by analyzing the capability of the network to implement molecular codes. We analyzed models of real chemical systems (Martian atmosphere chemistry and various combustion chemistries), bio-chemical systems (gene expression, gene translation, and phosphorylation signaling cascades), as well as an artificial chemistry and random networks. Our study suggests that different chemical systems posses different semantic capacities. Basically no semantic capacity was found in the atmosphere chemistry of Mars and all studied combustion chemistries, as well as in highly connected random networks, i.e., with these chemistries molecular codes cannot be implemented. High semantic capacity was found in the bio-chemical systems, as well as in random networks where the number of second order reactions is at the number of species. Hypotheses concern the origin and evolution of life. We conclude that our approach can be applied to evaluate the information processing capabilities of a chemical system and may thus be a useful tool to understand the origin and evolution of meaningful information, e.g., at the origin of life.

Can we objectively distinguish chemical systems that are able to process meaningful information from those that are not suitable for information processing? Here, we present a formal method to assess the semantic capacity of a chemical reaction network. The semantic capacity of a network can be measured by analyzing the capability of the network to implement molecular codes. We analyzed models of real chemical systems (Martian atmosphere chemistry and various combustion chemistries), bio-chemical systems (gene expression, gene translation, and phosphorylation signaling cascades), as well as an artificial chemistry and random networks. Our study suggests that different chemical systems posses different semantic capacities. Basically no semantic capacity was found in the atmosphere chemistry of Mars and all studied combustion chemistries, as well as in highly connected random networks, i.e., with these chemistries molecular codes cannot be implemented. High semantic capacity was found in the bio-chemical systems, as well as in random networks where the number of second order reactions is at the number of species. Hypotheses concern the origin and evolution of life. We conclude that our approach can be applied to evaluate the information processing capabilities of a chemical system and may thus be a useful tool to understand the origin and evolution of meaningful information, e.g., at the origin of life.

We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s c . Using percolation theory to calculate the average fractional size M SIR of an epidemic, we find that the strength of the spanning link percolation cluster P ∞ is an upper bound to M SIR . For small values of s c , P ∞ is no longer a good approximation, and the average fractional size has to be computed directly. The value of s c for which P ∞ is a good approximation is found to depend on the transmissibility T of the SIR. We also study Q, the probability that an SIR propagation reaches the epidemic mass s c , and find that it is well characterized by percolation theory. We apply our results to real networks (DIMES and Tracerouter) to measure the consequences of the choice s c on predictions of average outcome sizes of computer failure epidemics.

We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state. Traditional voter model behavior can be recovered within the model. We find that on a complete bipartite network, the traditional voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of α, exit time is dominated by diffusive drift of the system state, but as the high nodes become more influential, the exit time becomes becomes dominated by frustration effects. For certain selection processes and parameters values, an intermediate regime occurs where exit occurs after exponential mixing.

1. Introduction 631.1 Outline 631.2 Universals versus realizations in the study of learning and memory 642. Large random cortical networks developing ex vivo 652.1 Preparation 652.2 Measuring electrical activity 673. Spontaneous development 693.1 Activity 693.2 Connectivity 704. Consequences of spontaneous activity: pharmacological manipulations 724.1 Structural consequences 724.2 Functional consequences 735. Effects of stimulation 745.1 Response to focal stimulation 745.2 Stimulation-induced changes in connectivity 746. Embedding functionality in real neural networks 776.1 Facing the physiological definition of ‘reward’: two classes of theories 786.2 Closing the loop 797. Concluding remarks 848. Acknowledgments 859. References 85The phenomena of learning and memory are inherent to neural systems that differ from each other markedly. The differences, at the molecular, cellular and anatomical levels, reflect the wealth of possible instantiations of two neural learning and memory univ...

We consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a wireless network, as the number of nodes in the network becomes large. Two cases of large wireless networks are studied-dense random networks and constant density (extended) random networks. In addition, we also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. We first establish an information-theoretic lower bound on the minimum energy per bit for multicasting in arbitrary wireless networks when the channel state information is not available at the transmitters. Upper bounds are obtained by constructing a simple flooding scheme that requires no information at the receivers about the channel states or the locations and identities of the nodes. The gap between the upper and lower bounds is only a constant factor for dense random networks and regular networks, and differs by a poly-logarithmic factor for extended random networks. Furthermore, we show that the proposed upper and lower bounds for random networks hold almost surely in the node locations as the number of nodes approaches infinity.

Existing work on the capacity of wireless networks predominantly considers homogeneous random networks with random work load. The most relevant bounds on the network capacity, e.g., take into account only the number of nodes and the area of the network. However, these bounds can significantly overestimate the achievable capacity in real world situations where network topology or traffic patterns often deviate from these simplistic assumptions. To provide analytically tractable yet asymptotically tight approximations of network capacity we propose a novel space-based approach. At the heart of our methodology lie simple functions which indicate the presence of active transmissions near any given location in the network and which constitute a tool well suited to untangle the interactions of simultaneous transmissions. We are able to provide capacity bounds which are tighter than the traditional ones and which involve topology and traffic patterns explicitly, e.g., through the length of Euclidean Minimum Spanning Tree, or through traffic demands between clusters of nodes. As an additional novelty our results cover unicast, multicast and broadcast and are asymptotically tight. Notably, our capacity bounds are simple enough to require only knowledge of node location, and there is no need for solving or optimizing multi-variable equations in our approach.

Centrality measures are important in network analysis and mining. The correlation structures between the centrality measures are subject of the structural network analysis to improve the understanding of the process in that network. The aim of this paper is to extract useful hidden structural information about the structural correlations between centrality measures study. With Data Science analysis and visualization technics, we propose a structural analysis and visualization of the Pearson correlation between centrality measures. Overall experimentations, the same results are shown in 31 social networks with different topologies. The results show the existence of a strong positive and structural correlation between degree and closeness centrality, degree and betweenness centrality, degree and eigenvector centrality. However, we observed a strong positive and non-structural correlation between eigenvector and betweenness centrality, betweenness and closeness centrality, closeness and eigenvector centrality. Furthermore, we suggest some structural implications of these centrality measures in a network. Finally, we identify influential nodes and their state of evolution that build an effective minimization policy for an infectious disease spread. With the strong positive and structural correlations observed, in large networks, high complexity centrality measure can be approximated by low complexity such as degree centrality.

Centrality measures are important in network analysis and mining. The correlation structures between the centrality measures are subject of the structural network analysis to improve the understanding of the process in that network. The aim of this paper is to extract useful hidden structural information about the structural correlations between centrality measures study. With Data Science analysis and visualization technics, we propose a structural analysis and visualization of the Pearson correlation between centrality measures. Overall experimentations, the same results are shown in 31 social networks with different topologies. The results show the existence of a strong positive and structural correlation between degree and closeness centrality, degree and betweenness centrality, degree and eigenvector centrality. However, we observed a strong positive and non-structural correlation between eigenvector and betweenness centrality, betweenness and closeness centrality, closeness and eigenvector centrality. Furthermore, we suggest some structural implications of these centrality measures in a network. Finally, we identify influential nodes and their state of evolution that build an effective minimization policy for an infectious disease spread. With the strong positive and structural correlations observed, in large networks, high complexity centrality measure can be approximated by low complexity such as degree centrality.

Existing work on the capacity of wireless networks predominantly considers homogeneous random networks with random work load. The most relevant bounds on the network capacity, e.g., take into account only the number of nodes and the area of the network. However, these bounds can significantly overestimate the achievable capacity in real world situations where network topology or traffic patterns often deviate from these simplistic assumptions. To provide analytically tractable yet asymptotically tight approximations of network capacity we propose a novel space-based approach. At the heart of our methodology lie simple functions which indicate the presence of active transmissions near any given location in the network and which constitute a tool well suited to untangle the interactions of simultaneous transmissions. We are able to provide capacity bounds which are tighter than the traditional ones and which involve topology and traffic patterns explicitly, e.g., through the length of Euclidean Minimum Spanning Tree, or through traffic demands between clusters of nodes. As an additional novelty our results cover unicast, multicast and broadcast and are asymptotically tight. Notably, our capacity bounds are simple enough to require only knowledge of node location, and there is no need for solving or optimizing multi-variable equations in our approach.

Existing work on the capacity of wireless networks predominantly considers homogeneous random networks with random work load. The most relevant bounds on the network capacity, e.g., take into account only the number of nodes and the area of the network. However, these bounds can significantly overestimate the achievable capacity in real world situations where network topology or traffic patterns often deviate from these simplistic assumptions. To provide analytically tractable yet asymptotically tight approximations of network capacity we propose a novel space-based approach. At the heart of our methodology lie simple functions which indicate the presence of active transmissions near any given location in the network and which constitute a tool well suited to untangle the interactions of simultaneous transmissions. We are able to provide capacity bounds which are tighter than the traditional ones and which involve topology and traffic patterns explicitly, e.g., through the length of Euclidean Minimum Spanning Tree, or through traffic demands between clusters of nodes. As an additional novelty our results cover unicast, multicast and broadcast and are asymptotically tight. Notably, our capacity bounds are simple enough to require only knowledge of node location, and there is no need for solving or optimizing multi-variable equations in our approach.

We study behavior and equilibrium selection in experimental network games. We vary two important factors: (a) actions are either strategic substitutes or strategic complements, and (b) subjects have either complete or incomplete information about the structure of a random network. Play conforms strongly to the theoretical predictions, providing an impressive behavioral confirmation of the Galeotti, Goyal, Jackson, Vega-Redondo, and Yariv (2010) model. The degree of equilibrium play is striking, even with incomplete information. We find that under complete information, subjects typically play the stochastically-stable (inefficient) equilibrium when the game involves strategic substitutes, but play the efficient one with strategic complements. Our results suggest that equilibrium multiplicity may not be a major concern. Subjects' actions and realized outcomes under incomplete information depend strongly on both the degree and the connectivity. When there are multiple equilibria, subjects begin by playing the efficient equilibrium, but eventually converge to the inefficient one.

We study behavior and equilibrium selection in experimental network games. We vary two important factors: (a) actions are either strategic substitutes or strategic complements, and (b) subjects have either complete or incomplete information about the structure of a random network. Play conforms strongly to the theoretical predictions, providing an impressive behavioral confirmation of the Galeotti, Goyal, Jackson, Vega-Redondo, and Yariv (2010) model. The degree of equilibrium play is striking, even with incomplete information. We find that under complete information, subjects typically play the stochastically-stable (inefficient) equilibrium when the game involves strategic substitutes, but play the efficient one with strategic complements. Our results suggest that equilibrium multiplicity may not be a major concern. Subjects' actions and realized outcomes under incomplete information depend strongly on both the degree and the connectivity. When there are multiple equilibria, subjects begin by playing the efficient equilibrium, but eventually converge to the inefficient one.

In this paper, we describe a series of laboratory experiments that implement specific examples of a more general network structure and we examine equilibrium selection. Specifically, actions are either strategic substitutes or strategic complements, and participants have either complete or incomplete information about the structure of a random network. Since economic environments typically have a considerable degree of complementarity or substitutability, this framework applies to a wide variety of settings. The degree of equilibrium play is striking, in particular with incomplete information. Behavior closely resembles the theoretical equilibrium whenever this is unique; when there are multiple equilibria, general features of networks, such as connectivity, clustering, and the degree of the players, help to predict informed behavior in the lab. People appear to be strongly attracted to maximizing aggregate payoffs (social efficiency), but there are forces that moderate this attraction: 1) people seem content with (in the aggregate) capturing only the lion's share of the efficient profits in exchange for reduced exposure to loss, and 2) uncertainty about the network structure makes it considerably more difficult to coordinate on a demanding, but efficient, equilibrium that is typically implemented with complete information.

Secret sharing schemes are ideally suited to save highly sensitive information in distributed systems. On the other hand, Zigzag-Decodable (ZD) codes are employed in wireless distributed platforms for encoding data using only bit-wise shift and XOR operations. Recently, Vandermondebased ZD codes have been utilized in secret sharing schemes to achieve high computational efficiency such that sharing and recovering of secrets can be realized by lightweight operations. However, the storage overhead of using these ZD codes remains a problem which is addressed in the present paper. Here, a ramp secret sharing scheme is proposed based on an efficient ZD code with less storage overhead in comparison with existing literature. The novelty of the proposed scheme lies in the careful selection of the number of positions to shift the bits of the secret such that security and zigzag decodability are guaranteed simultaneously. In addition to prove gaining these features, we show that the scheme improves speed of recovery.

This paper is focused on the description, as to how to represent the network topology. It is very important to know the network topology and to understand its properties. This work describes how to find all the Giant Connected Component in directed network. The growing complex networks with preferential linking were used for experimental testing within this research. Roulettewheel selection method was used as a preferential selection algorithm in the task of generation of complex networks.

Temperature-modulated differential scanning calorimetry ͑MDSC͒ measurements on Si x Se 1Ϫx glasses show glass transitions to be thermally reversing in character in the composition window 0.20ϽxϽ0.27. Raman scattering shows a trimodal distribution of vibrational modes, identified with corner-sharing ͑CS͒, edge-sharing ͑ES͒, and Se-chain modes ͑CM͒. In the floppy region, 0ϽxϽ0.19, these modes are symmetric and are characteristic of a random network. In the transition region, 0.20ϽxϽ0.27, the ES and CM split into doublets suggesting appearance of extended range structural correlations. In the percolatively rigid region, xϾ0.27, the CS mode in addition to the ES and CM also splits into a doublet indicating growth of substantial medium range structure. The large compositional width (0.20ϽxϽ0.27) associated with Raman elastic thresholds coincides with the thermally reversing window from MDSC.

This report comprises the complete D5.4.1 deliverable as specified for workpackage WP5.4 in Subproject SP5 of the DELIS (Dynamically Evolving Large-scale Information Systems) Integrated Project. The essential goal of the DELIS project is to understand, predict, engineer and control large evolving information systems. In this workpackage we wish to tie together, hitherto, independent research lines on evolving network “form” and “function”. Both in naturally found networks (e.g., biological and software networks) and artificial networks (e.g., dynamic peer-to-peer networks) there appear to be various levels of selection and evolution and interesting relationships between form and function. It is becoming increasingly clear that form does not follow directly from function (or vice versa) in many observed evolving networks. What then is the relationship and how can it be detected and characterised? We summarise two main lines of work, the first section covers detailed analysis of motif...

A detailed microstructural analysis of amorphous silicon is performed by means of a numerical modeling technique. Paracrystalline models of amorphous silicon, first proposed by Treacy, Gibson and Keblinski, have been generated. Nanocrystallites of various sizes and concentrations have been introduced into a continuous random network that was generated with a vacancy model. Using the conjugate gradient method, the structures have been relaxed by minimizing their total strain energy described by the anharmonic Keating model. The computed pair correlation functions of these structural models bring to the fore a unique behavior of the paracrystalline networks in the context of diffraction experiments; they appear amorphous as the continuous random network model. The paracrystalline model remains denser than the crystalline phase, contrary to experimental observations. However, the former is found to be less homogenous than the CRN model, thus giving a satisfactory explanation of the nanoscale fluctuation electron microscopy data reported recently by Treacy and coworkers.

A detailed microstructural analysis of amorphous silicon is performed via numerical modeling technique. Nanoporous paracrystalline models have been proposed. Intermixed nanocrystallites and nanovoids of various sizes and concentrations have been introduced into a continuous random network that was generated with a vacancy model. Using the conjugate gradient method, the structures have been relaxed by minimizing their total strain energy described by the anharmonic Keating model. The obtained nanoporous structures are energetically competitive with the voidless paracrystalline networks. Nanoporous models with large voids are energetically more favorable than those with small voids. The nanoporous paracrystalline model is less dense than the crystalline phase, contrary to the paracrystalline model. This density decreases with increasing the void size for a fixed void volume fraction. Nanoporous paracrystalline structures reproduce the experimental structure factor better than the paracrystalline network. They account for, in particular, the intense small-angle scattering observed for some a-Si samples. The paracrystallites form amorphous zones but with local and topological ordering neatly better than the surrounding matrix. Such structural heterogeneity gives so a satisfactory explanation of the nanoscale fluctuation electron microscopy data reported recently by Treacy and Gibson.

The concentration dependence of the structure of fibrin gels, formed following fibrinogen activation by thrombin at a constant molar ratio, was investigated by means of elastic light scattering techniques. The scattered intensity distributions were measured in absolute units over a wave-vector range q of about three decades (ϳ3ϫ10 2 -3ϫ10 5 cm Ϫ1 ). A set of gel-characterizing parameters were recovered by accurately fitting the data with a single function recently developed by us ͓F. Ferri et al., Phys. Rev. E 63, 031401 ͑2001͔͒, based on a simple structural model. Accordingly, the gels can be described as random networks of fibers of average diameter d and density , entangled together to form densely packed and spatially correlated blobs of mass fractal dimension D m and average size ͑or crossover length͒ . As previously done for d, we show here that the recovered is also a good approximation of a weight average, namely, dϳͱ͗d 2 ͘ w and ϳ͗͘ w . By varying the fibrinogen concentration c F between 0.034 -0.81 mg/ml, gels with 100уу10 m, 100рdр200 nm, 1.2рD m р1.4, and constant ϳ0.4 mg/ml were obtained. The power-law c F dependencies that we found for both and d are consistent with the model, provided that the blobs are allowed to partially overlap by a factor likewise scaling with c F (2уу1). Recasting the whole dataset on a single master curve provided further evidence of the similarity between the structures of all the gels, and confirmed the self-consistency of the model.

This paper proposes hybrid ARQ-random network coding frameworks for real-time media broadcast over singlehop wireless networks. We model the wireless channel as a packet erasure channel and our proposed schemes aim at minimizing the packet erasure rate in order to enhance the media quality at receivers. We consider two forms of random network coding: Uniform Random Network Coding (URNC) and Hierarchical Random Network Coding (HRNC) in combination with a number of packet scheduling policies based on a limited number of feedbacks from receivers. Our simulation results show that the hybrid frameworks can improve the quality of media applications significantly compared with the conventional scheme without using network coding.

We investigate extremal dynamics on random networks. In the quenched case, after a transient time the dynamics is localized in the largest cluster. The activity in the largest cluster is nonergodic, with hot spots of activity typically centered around nodes with a high coordination number. The nonergodicity of the activity opens for models of evolving networks, which can self-organize into fractal geometries. [S0031-9007(98)07126-9]

We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz [Mathematical Biology 56 (2008) 293-310].

In this work we propose an alternative DNA sequence analysis tool based on graph theoretical concepts. The methodology investigates the path topology of an organism genome through a triplet network. In this network, triplets in DNA sequence are vertices and two vertices are connected if they occur juxtaposed on the genome. We characterize this network topology by measuring the clustering coefficient. We test our methodology against two main bias: the guaninecytosine (GC) content and 3-bp (base pairs) periodicity of DNA sequence. We perform the test constructing random networks with variable GC content and imposed 3-bp periodicity. A test group of some organisms is constructed and we investigate the methodology in the light of the constructed random networks. We conclude that the clustering coefficient is a valuable tool since it gives information that is not trivially contained in 3-bp periodicity neither in the variable GC content.

Higher order clustering coefficients C(x) are introduced for random networks. The coefficients express probabilities that the shortest distance between any two nearest neighbours of a certain vertex i equals x, when one neglects all paths crossing the node i. Using C(x) we found that in the Barabási-Albert (BA) model the average shortest path length in a node's neighbourhood is smaller than the equivalent quantity of the whole network and the remainder depends only on the network parameter m. Our results show that small values of the standard clustering coefficient in large BA networks are due to random character of the nearest neighbourhood of vertices in such networks.

Despite significant progress made in recent years, a fundamental understanding of immiscible displacements at the macroscale is lacking. In this paper we use a version of percolation theory, based on invasion percolation in a gradient, to connect drainage processes at the pore-network scale with the displacement at the macroscale. When the mobility ratio M is sufficiently small, the displacement is

Visual observations by space shuttle astronauts have described a phenomenon in which spatially distant thunderstorm cells seem to reciprocally ''ignite'' lightning flashes in a semi-cyclic sequence. Lightning occurring in one cell is immediately followed by lightning in other cells, separated by tens or hundreds of kilometers. We present quantitative analysis of lightning observations conducted within the framework of the MEIDEX-sprite campaign on board the space shuttle

We describe the fabrication and electrical performance of p-n homo-junction diode arrays of horizontally aligned single walled carbon nanotubes (SWCNTs). Horizontally aligned SWCNTs grown on stable temperature-cut quartz with a density of ∼6 SWCNTs μm −1 were transferred onto a SiO 2 /Si substrate. After the electrical breakdown, aligned SWCNT field effect transistors (FETs) showed unipolar p-type characteristics with a large current on/off ratio of 10 6 at 1 V and a hole mobility per tube of 1500 cm 2 V −1 s −1. Spin-coating of polyethyleneimine (PEI) onto p-type SWCNT FETs showed the n-type transfer characteristics. Patterning of spin-coated PEI film enabled the fabrication of p-n homo-junction arrays of aligned SWCNTs in an easy way, where the rectifying behavior was observed with a rectification ratio of ∼10 4 at ±2 V. A comparative study with a p-n homo-junction of random networks of SWCNTs confirmed the advantage of aligned SWCNTs for applications in high performance electronic devices.

Structural properties and intermediate range order in sodium-alumino silicate glasses of general formulae Na 2 O•xAl 2 O 3 •(3-x)SiO 2 have been investigated at different concentrations of Al 2 O 3 by means of molecular dynamics simulations. The influence on the calculated structural parameters of the initial randomness expressed by the starting structure has been analysed and discussed. The results obtained support the hypothesis that a continuous transition between two limiting structures is responsible for the anomalous variation in the diffusion properties observed between 5 and 10% of Al 2 O 3 addition.