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The disordered fibrous networks provide load-bearing and main structural to different biological materials such as soft tissues. These networks display a highly nonlinear stress-strain relationship behavior when subjected to mechanical loads. This nonlinear strain-stiffening behavior is dependent on the network microstructure and properties of constituting fiber. We conduct a comprehensive computational study to characterize the importance of material properties of individual fibers as well as the local connectivity or coordination number and bending rigidity in the overall nonlinear mechanical response of a 3D random fiber network. The presented model shows the nonlinear stiffening with increasing applied shear strain more than critical shear strain. We determine the amount of strain-stiffening as a function of network microstructure parameters and the amount of nonlinearity of the fibers. The results show that the constitutive behavior of fibers displays much more strain-stiffening than networks made up of linear fibers. We find that the importance of the nonlinear reaction of individual fiber materials in the general mechanical behavior of networks becomes more important with increasing network connectivity. Furthermore, the amount of stress created in the network under shear increases with the enhanced connectivity of the network due to an increase in the network stiffness. Our model points to the important role of the mechanical response of individual fiber as well as the microstructure of the network in determining the overall mechanical properties of the 3D random network, which could be used to design and better understand the complex biomimetic network systems such as biological tissues and artificial engineering networks.

The performance of the cognitive non-orthogonal multiple access (NOMA) systems with random locations is examined in the present paper. More precisely, the positions of the secondary receivers (SRs) are randomly distributed inside a disk with the centre at the secondary transmitter (ST). The primary networks (PNs), on the other hand, are not necessarily inside the transmission range of the ST. Two user selection schemes namely, path-loss-based and channel-gain-based approaches, are adopted to serve two SRs according to the power domain NOMA technique. Additionally, the impact of the imperfect hardware impairments (HIs) on both transmitters and receivers is also taken into consideration. Furthermore, a recently proposed transmit power allocation at the ST is employed to concurrently maximize the system performance of the secondary networks (SNs) and to strictly protect the quality-of-service (QoS) of the PNs. The correctness of the developed mathematical frameworks is corroborated by simulation results based on the Monte Carlo method. Finally, we unveil that there is no scheme that always outperforms another. Thus, an adaptive scheme can be proposed to optimize the networks' performance. Our findings also reveal that the outage probability (OP) under the harmful effect of HI can be effectively mitigated by increasing the transmit power of the ST. Additionally, increasing the transmit power of the PT is also beneficial for the SNs with the adopted transmit power allocation at the ST.

Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While many methods have been proposed to address this problem in recent years, they usually assume that the true model belongs to a known class, which is not verifiable in most real-world applications. Consequently, network modeling based on these methods either suffers from model misspecification or relies on additional model selection procedures that are not well understood in theory and can potentially be unstable in practice. To address this difficulty, we propose a mixing strategy that leverages available arbitrary models to improve their individual performances. The proposed method is computationally efficient and almost tuning-free for network modeling. We show that the proposed method performs equally well as the oracle estimate when the true model is included as individual candidates. More importantly, the method remains robust and outperforms all current estimates even when the models are misspecified. Extensive simulation examples are used to verify the advantage of the proposed mixing method. Evaluation of link prediction performance on more than 500 real-world networks from different domains also demonstrates the universal competitiveness of the mixing method across multiple domains. for this article are available online. [ABSTRACT FROM AUTHOR]

The performance of the cognitive non-orthogonal multiple access (NOMA) systems with random locations is examined in the present paper. More precisely, the positions of the secondary receivers (SRs) are randomly distributed inside a disk with the centre at the secondary transmitter (ST). The primary networks (PNs), on the other hand, are not necessarily inside the transmission range of the ST. Two user selection schemes namely, path-loss-based and channel-gain-based approaches, are adopted to serve two SRs according to the power domain NOMA technique. Additionally, the impact of the imperfect hardware impairments (HIs) on both transmitters and receivers is also taken into consideration. Furthermore, a recently proposed transmit power allocation at the ST is employed to concurrently maximize the system performance of the secondary networks (SNs) and to strictly protect the quality-of-service (QoS) of the PNs. The correctness of the developed mathematical frameworks is corroborated by simulation results based on the Monte Carlo method. Finally, we unveil that there is no scheme that always outperforms another. Thus, an adaptive scheme can be proposed to optimize the networks' performance. Our findings also reveal that the outage probability (OP) under the harmful effect of HI can be effectively mitigated by increasing the transmit power of the ST. Additionally, increasing the transmit power of the PT is also beneficial for the SNs with the adopted transmit power allocation at the ST. [ABSTRACT FROM AUTHOR]

We investigate three related problems concerning sampling minorities in attributed networks. This is guided by a general attributed network model which can incorporate several levels of homophily and heterophily, and whose degree and Page-rank distributions have known properties. The first problem investigates sampling schemes that favor the representation of the minority over majority nodes and give preference to "more popular" minority nodes (i.e. higher degree/Page-rank) for a given homophily scenario. We show that (in-)degree and Page-rank sampling schemes increase the probability of sampling a minority node. The second problem concerns the relative ranking of minorities compared to majorities in degree and Page-rank based sampling schemes for several homophily and heterophily scenarios. We provide analytical conditions for the minority nodes to rank higher as a function of the model parameters for the degree based samplings and investigate the problem numerically for Page-rank based sampling schemes. The third problem considers subgraph sampling schemes and the bias of the proportion of minority nodes in top ranked degree nodes in several homophily and heterophily scenarios. Finally, the results and findings obtained from the sampling analysis are assessed on real-world networks. [ABSTRACT FROM AUTHOR]

Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers. [ABSTRACT FROM AUTHOR]

The disordered fibrous networks provide load-bearing and main structural to different biological materials such as soft tissues. These networks display a highly nonlinear stress-strain relationship behavior when subjected to mechanical loads. This nonlinear strain-stiffening behavior is dependent on the network microstructure and properties of constituting fiber. We conduct a comprehensive computational study to characterize the importance of material properties of individual fibers as well as the local connectivity or coordination number and bending rigidity in the overall nonlinear mechanical response of a 3D random fiber network. The presented model shows the nonlinear stiffening with increasing applied shear strain more than critical shear strain. We determine the amount of strain-stiffening as a function of network microstructure parameters and the amount of nonlinearity of the fibers. The results show that the constitutive behavior of fibers displays much more strain-stiffening than networks made up of linear fibers. We find that the importance of the nonlinear reaction of individual fiber materials in the general mechanical behavior of networks becomes more important with increasing network connectivity. Furthermore, the amount of stress created in the network under shear increases with the enhanced connectivity of the network due to an increase in the network stiffness. Our model points to the important role of the mechanical response of individual fiber as well as the microstructure of the network in determining the overall mechanical properties of the 3D random network, which could be used to design and better understand the complex biomimetic network systems such as biological tissues and artificial engineering networks. [ABSTRACT FROM AUTHOR]

Optical backbone networks constitute the fundamental infrastructure employed today by network operators to deliver services to users. As network capacity is a key factor influencing optical network performance, it is important to understand how topological and physical properties impact its behavior and to have the capability to estimate its value. In this context, we propose here a method to evaluate the network capacity that relies on the optical reach to account for physical layer aspects in conjunction with constrained routing techniques for traffic routing. As this type of routing can lead to traffic blocking, particularly due to the limitation on the number of wavelengths per fiber, we also propose a fiber assignment algorithm designed to deal with this problem. We apply this method to a set of randomly generated networks using a modified Waxman model, and for a network with 60 nodes, in a scenario without blocking, we obtain capacities of about 2.5 Pbit/s for a symbol rate of 64 Gbaud and about 5 Pbit/s for a symbol rate of 128 Gbaud. Remarkably, this duplication in the total network capacity is achieved by an increase in the total fiber length of only about 51%. [ABSTRACT FROM AUTHOR]

The performance of physical layer secrecy approach in non-orthogonal multiple access (NOMA)-enabled heterogeneous networks (HetNets) is analyzed in this paper. A K-tier multi-cell HetNet is considered, comprising NOMA adopted in all tiers. The base stations, legitimate users (in a two-user NOMA setup), and passive eavesdroppers, all with single-antenna, are randomly distributed. Assuming independent Poisson point processes for node distribution, stochastic geometry approaches are exploited to characterize the ergodic secrecy rate. A lower bound on the ergodic secrecy rate along with closed-form expressions for the lower bound on the ergodic rates of the legitimate users in a special case are derived. Moreover, simpler expressions for the ergodic secrecy rate are obtained in the interference-limited regime with vanishing noise variance. The effect of multi-tier technology, NOMA, and physical layer secrecy are investigated using numerical results. The results reveal that applying HetNet to a secure multi-cell NOMA system improves the spectrum efficiency performance.

Abstract.In this work, we consider a randomized version of the deterministic pseudofractal graph model, which was first proposed in the physical literature. Our model is a sequence of dynamic networks, in which the increment of network size at each time depends on the current size and a sequence of evolving parameters. We first show that the network size is closely related to a branching process in the varying environment. Under a mild assumption, we then prove that the asymptotic degree distribution in our model obeys the power law with an exponent three. Based on this asymptotic degree distribution, we show that the clustering coefficient of our network model converges to a given constant in probability. [ABSTRACT FROM AUTHOR]

Optical backbone networks constitute the fundamental infrastructure employed today by network operators to deliver services to users. As network capacity is a key factor influencing optical network performance, it is important to understand how topological and physical properties impact its behavior and to have the capability to estimate its value. In this context, we propose here a method to evaluate the network capacity that relies on the optical reach to account for physical layer aspects in conjunction with constrained routing techniques for traffic routing. As this type of routing can lead to traffic blocking, particularly due to the limitation on the number of wavelengths per fiber, we also propose a fiber assignment algorithm designed to deal with this problem. We apply this method to a set of randomly generated networks using a modified Waxman model, and for a network with 60 nodes, in a scenario without blocking, we obtain capacities of about 2.5 Pbit/s for a symbol rate of 64 Gbaud and about 5 Pbit/s for a symbol rate of 128 Gbaud. Remarkably, this duplication in the total network capacity is achieved by an increase in the total fiber length of only about 51%.

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization. [ABSTRACT FROM AUTHOR]

This paper evaluates outage probability (OP) and intercept probability (IP) of physical-layer security based MIMO networks adopting cooperative jamming (Coop-Jam). In the considered scenario, a multi-antenna source communicates with a multi-antenna destination employing transmit antenna selection (TAS)/ selection combining (SC), in presence of a multi-antenna eavesdropper using SC. One of jammers appearing near the destination is selected for generating jamming noises on the eavesdropper. Moreover, the destination supports the wireless energy for the chosen jammer, and cooperates with it to remove the jamming noises. We consider two jammer selection approaches, named RAND and SHORT. In RAND, the destination randomly selects the jammer, and in SHORT, the jammer, which is nearest to the destination, is chosen. We derive exact and asymptotic expressions of OP and IP over Rayleigh fading, and perform Monte-Carlo simulations to verify the correction of our derivation. The results present advantages of the proposed RAND and SHORT methods, as compared with the corresponding one without using Coop-Jam.

Graphs have become crucial for representing and examining biological, social and technological interactions. In this context, the graph spectrum is an exciting feature to be studied because it encodes the structural and dynamic characteristics of the graph. Hence, it becomes essential to efficiently compute the graph's spectral distribution (eigenvalue's density function). Recently, some authors proposed degree-based methods to obtain the spectral density of locally tree-like networks in linear time. The bottleneck of their approach is that they assumed that the graph's assortativity is zero. However, most real-world networks, such as social and biological networks, present assortativity. Consequently, their spectral density approximations may be inaccurate. Here, we propose a method that considers assortativity. Our algorithm's time and space complexities are |$\mathscr{O}(d_{\max}^{2})$|⁠ , where |$d_{\max}$| is the largest degree of the graph. Finally, we show our method's efficacy in simulated and empirical networks. [ABSTRACT FROM AUTHOR]

We study the spread of misinformation in a social network characterized by unequal access to learning resources. Agents use social learning to uncover an unknown state of the world, and a principal strategically injects misinformation into the network to distort this learning process. A subset of agents throughout the network is endowed with knowledge of the true state. This gives rise to a natural definition of inequality: privileged communities have unrestricted access to these agents, whereas marginalized communities do not. We show that the role that this inequality plays in the spread of misinformation is highly complex. For instance, communities who hoard resources and deny them to the larger population can end up exposing themselves to more misinformation. Conversely, although more inequality generally leads to worse outcomes, the prevalence of misinformation in society is nonmonotone in the level of inequality. This implies that policies that decrease inequality without substantially reducing it can leave society more vulnerable to misinformation. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.4376. [ABSTRACT FROM AUTHOR]

We study a model of innovation with a large number of firms that create new technologies by combining several discrete ideas. These ideas are created via private investment and spread between firms. Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates learning from others. Their decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a learning network. Higher interaction rates impose both positive and negative externalities, as there is more learning but also more competition. We show that the equilibrium learning network is at a critical threshold between sparse and dense networks. At equilibrium, the positive externality from interaction dominates: the innovation rate and welfare would be dramatically higher if the network were denser. So there are large returns to increasing interaction rates above the critical threshold. Nevertheless, several natural types of interventions fail to move the equilibrium away from criticality. One effective policy solution is to introduce informational intermediaries, such as public innovators who do not have incentives to be secretive. These intermediaries can facilitate a high-innovation equilibrium by transmitting ideas from one private firm to another. [ABSTRACT FROM AUTHOR]

This paper studies the min–max group consensus of discrete-time multi-agent systems under a directed random graph, where the presence of each directed edge is randomly determined by a probability and independent of the presence of other edges. Firstly, we propose a min–max consensus protocol without memory, and give the necessary and sufficient conditions to ensure that the multi-agent system can achieve the min–max group consensus in the sense of almost sure and mean square, respectively. Secondly, we design a novel consensus protocol with memory and a behavior mechanism. Using the stochastic analysis theory and the extremal algebra, some necessary and sufficient conditions are obtained for achieving the min–max group consensus in the sense of almost sure and mean square, respectively. It is shown that the protocol with memory can solve the loss problem of the maximum and minimum initial states. Finally, the effectiveness of the two group consensus protocols and the behavior mechanism is verified by four numerical simulations. [ABSTRACT FROM AUTHOR]

This paper focuses on the study of the min–max consensus problem for multi-agent systems in random networks. A min–max consensus algorithm is proposed, which incorporates the weighted average of the agent's state, the maximum value of its neighbors' states, and the minimum value of its neighbors' states. The interaction network is composed of a directed random network where edges exist with probability and are independent of each other. Then, the convergence of the min–max consensus algorithm is investigated utilizing max-plus algebra, min-plus algebra, and stochastic analysis theory. Sufficient and necessary conditions are given to ensure that the multi-agent systems achieve min–max consensus almost surely and in mean-square, respectively. Finally, some numerical simulations are conducted to confirm the effectiveness of the proposed consensus algorithm. [ABSTRACT FROM AUTHOR]

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, N. In this paper, we present a novel derivation of the small-world property for Gilbert–Erdös–Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime. [ABSTRACT FROM AUTHOR]

Networks are all around us and can be in the Euclidean space of concrete objects such as power grids, the Internet, highways or subway systems, and neural networks, or in an abstractly defined space, such as networks of familiarity or cooperation between people. To express the general properties of such networks, their modeling is in the form of graphs that show the nodes as oscillators (the dynamic unit) and the edges as the existence of interaction between oscillators We applied the Kuramato model to networks of oscillators connected in a small-world network pattern and considered the influence of oscillators on each other as conformist and contrarian. Based on this, we examined the synchronization in the network. We showed that if the number of contrarian oscillators in the network reaches a certain value, it will cause more of the network, which is due to the weakening of defects created in compatible oscillators. [ABSTRACT FROM AUTHOR]

Linear regression on network‐linked observations has been an essential tool in modelling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with non‐parametric network effects. The model does not assume that the relational data or network structure is exactly observed and can be provably robust to network perturbations. Asymptotic inference framework is established under a general requirement of the network observational errors, and the robustness of this method is studied in the specific setting when the errors come from random network models. We discover a phase‐transition phenomenon of the inference validity concerning the network density when no prior knowledge of the network model is available while also showing a significant improvement achieved by knowing the network model. Simulation studies are conducted to verify these theoretical results and demonstrate the advantage of the proposed method over existing work in terms of accuracy and computational efficiency under different data‐generating models. The method is then applied to middle school students' network data to study the effectiveness of educational workshops in reducing school conflicts. [ABSTRACT FROM AUTHOR]

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment rules. When a new edge is created, with probability p ∈ (0 , 1) , it follows the PA rule. Otherwise, this new edge is added between two uniformly chosen nodes. Such mixture makes the in- and out-degrees of a fixed node grow at a slower rate, compared to the pure PA case, thus leading to lighter distributional tails. For estimation and inference, we develop two numerical methods which are applied to both synthetic and real network data. We see that with extra flexibility given by the parameter p, the hybrid random network provides a better fit to real-world scenarios, where lighter tails from in- and out-degrees are observed. [ABSTRACT FROM AUTHOR]

Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree distributions, number of edges, and other relevant network metrics which support the scale-free structure of networks. Previous work on such graphs imposes a marginal assumption of univariate regular variation (e.g., power-law tail) on the bivariate generating graphex function. In this paper, we study sparse exchangeable graphs generated by graphex functions which are multivariate regularly varying. We also focus on a different metric for our study: the distribution of the number of common vertices (connections) shared by a pair of vertices. The number being high for a fixed pair is an indicator of the original pair of vertices being connected. We find that the distribution of number of common connections are regularly varying as well, where the tail indices of regular variation are governed by the type of graphex function used. Our results are verified on simulated graphs by estimating the relevant tail index parameters. [ABSTRACT FROM AUTHOR]

The activation function deployed in a deep neural network has great influence on the performance of the network at initialisation, which in turn has implications for training. In this paper we study how to avoid two problems at initialisation identified in prior works: rapid convergence of pairwise input correlations, and vanishing and exploding gradients. We prove that both these problems can be avoided by choosing an activation function possessing a sufficiently large linear region around the origin, relative to the bias variance σ b 2 of the network's random initialisation. We demonstrate empirically that using such activation functions leads to tangible benefits in practice, both in terms of test and training accuracy and in terms of training time. Furthermore, we observe that the shape of the nonlinear activation outside the linear region appears to have a relatively limited impact on training. Finally, our results also allow us to train networks in a new hyperparameter regime, with a much larger bias variance than has previously been possible. [ABSTRACT FROM AUTHOR]

The SARS-CoV-2 epidemic has impacted children's education, with schools required to implement infection control measures that have led to periods of absence and classroom closures. We developed an agent-based epidemiological model of SARS-CoV-2 transmission in a school classroom that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties. Our approach is based on a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies in suppressing infection outbreaks and limiting pupil absence are considered. COVID-19 infections in primary schools in England in autumn 2020 were re-examined and the model was then used to estimate infection levels in autumn 2021, as the Delta variant was emerging and it was thought likely that school transmission would play a major role in an incipient new wave of the epidemic. Our results were in good agreement with available data. These findings indicate that testing-based surveillance is more effective than bubble quarantine, both for reducing transmission and avoiding pupil absence, even accounting for insensitivity of self-administered tests. Bubble quarantine entails large numbers of absences, with only modest impact on classroom infections. However, maintaining reduced contact rates within the classroom can have a major benefit for managing COVID-19 in school settings.

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization.

The "random intersection graph with communities" (RIGC) models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups may overlap. The group memberships are generated by a bipartite configuration model. The model generalizes the classical random intersection graph model, a special case where each community is a complete graph. The RIGC model is analytically tractable. We prove a phase transition in the size of the largest connected component in terms of the model parameters. We prove that percolation on RIGC produces a graph within the RIGC family, also undergoing a phase transition with respect to size of the largest component. Our proofs rely on the connection to the bipartite configuration model. Our related results on the bipartite configuration model are of independent interest, since they shed light on interesting differences from the unipartite case. [ABSTRACT FROM AUTHOR]

This brief investigates the resilient consensus control for multiagent systems over a time-varying directed random network. We propose a median-based consensus strategy, which is purely distributed and, as opposed to the Weighted-Mean-Subsequence-Reduced approaches in the existing literature, shared estimate regarding the number of malicious agents in the neighborhood of each cooperative agent is not required. This offers more applicability and flexibility as seeking a shared estimate of surrounding threats is often difficult in practice. In addition to malicious agents, random availability of communication edges is accommodated in the random network framework. Sufficient conditions are derived for reaching almost sure consensus by using a martingale convergence theorem. Finally, the theoretical findings are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

Understanding charge transport mechanisms in thin-film transistors based on random networks of single-wall carbon nanotubes (SWCNT-TFTs) is essential for further advances to improve the potential for various nanoelectronic applications. Herein, a comprehensive investigation of the two-dimensional (2D) charge transport mechanism in SWCNT-TFTs is reported by analyzing the temperature-dependent electrical characteristics determined from the direct-current and non-quasi-static transient measurements at 80–300 K. To elucidate the time-domain charge transport characteristics of the random networks in the SWCNTs, an empirical equation was derived from a theoretical trapping model, and a carrier velocity distribution was determined from the differentiation of the transient response. Furthermore, charge trapping and de-trapping in shallow- and deep-traps in SWCNT-TFTs were analyzed by investigating charge transport based on their trapping/de-trapping rate. The comprehensive analysis of this study provides fundamental insights into the 2D charge transport mechanism in TFTs based on random networks of nanomaterial channels. [ABSTRACT FROM AUTHOR]

Due to the fully-connected complex structure of Artificial Neural Networks (ANNs), systems based on ANN may consume much computational time, energy and space. Therefore, intense research has been recently centered on changing the topology and design of ANNs to obtain high performance. To explore the influence of network structure on ANNs complex systems topologies have been applied in these networks to have more efficient and less complex structures while they are more similar to biological systems at the same time. In this paper, the methodology and results of some recent papers are summarized and discussed in which the authors investigated the efficacy of random complex networks on the performance of Hopfield associative memory and multi-layer ANNs compared with ANNs with small-world, scale-free and regular structures.

Change-point detection within random networks is essential for many applications. Generally, the typical methods focus on the Erdös-Rényi random networks, or assume that the anomalous subnetworks only have high link probability with the fixed membership. In this paper, we consider the stochastic block model of random graphs, and study the change-point detection regarding to the scenario that after a change-point, the connectivity of subnetworks becomes denser or sparser while the membership of nodes also changes. Based on local graph features, we explore a local statistic with dynamic vertex selection for detecting the emergence of an abrupt change-point. In addition, we derive an analytic expression with respect to average run length to set detection threshold in a theoretical fashion, and achieve the probability bounds related to the dynamic vertex selection to characterize the performance of the presented algorithm. As a result, the proposed scheme can provide performance improvement as well as reduce the computational complexity. The proposed algorithm can address a more general problem than the typical methods. Numerical experiments are provided to show the effectiveness of our method.

Additive noise is known to tune the stability of nonlinear systems. Using a network of two randomly connected interacting excitatory and inhibitory neural populations driven by additive noise, we derive a closed mean-field representation that captures the global network dynamics. Building on the spectral properties of Erdös-Rényi networks, mean-field dynamics are obtained via a projection of the network dynamics onto the random network’s principal eigenmode. We consider Gaussian zero-mean and Poisson-like noise stimuli to excitatory neurons and show that these noise types induce coherence resonance. Specifically, the stochastic stimulation induces coherent stochastic oscillations in the γ-frequency range at intermediate noise intensity. We further show that this is valid for both global stimulation and partial stimulation, i.e. whenever a subset of excitatory neurons is stimulated only. The mean-field dynamics exposes the coherence resonance dynamics in the γ-range by a transition from a stable non-oscillatory equilibrium to an oscillatory equilibrium via a saddle-node bifurcation. We evaluate the transition between non-coherent and coherent state by various power spectra, Spike Field Coherence and information-theoretic measures.

This paper analyzes the behavior of the discrete stochastic reaction-diffusion algorithm Greenberg-Hastings in a random network with dynamic links. The main research questions of this study are: 1. Can the stochastic Greenberg-Hastings reach an 'acceptable' steady state in a dynamic network with multiple topological and neighborhood variations? and 2. What is the critical value of the relevant model parameters?. To answer these questions, the model has been implemented by using multiple test scenarios and, as the main constraint is the network links variability, it has been defined in such a manner so that the parameters take low, medium, and high values. This paper presents some numerical experiments which demonstrate its robustness and stability since, in many of the scenarios experienced, the 'acceptable' steady state has been reached. Additionally, the critical values have been identified by the model parameters and iterations, and the behaviors for all the generated scenarios are described. This analysis allows for deducing from the results obtained that, given the robustness of the model, it is possible to conceive a stochastic control algorithm to modify, reach and maintain the 'acceptable' steady state in all analyzed scenarios. [ABSTRACT FROM AUTHOR]

Epilepsy has been found to be modulated by the astrocyte systems in experiments, and tremendous modeling studies have unveiled the roles of astrocyte cellular functions such as the calcium and potassium channels in the epileptic seizures. However, little attention has been paid to the structure changes of astrocytes in the epileptic seizures in the scale of networks. This paper first constructs a neuron–astrocyte network model to explain the experimental observation that astrocytes mainly induce epilepsy by blocking the channels of the astrocyte gap junction in the network scale. Such model is used to discuss potential seizure induction process in the network by changing the connection intensity of the astrocyte gap junction. The simulation results show that a decrease of the gap junction intensity changes the firing pattern of the population of neurons from slow periodical firing to high-frequency epileptic seizures, featuring epileptic patterns of depolarization blocks. This further verifies that epileptic seizures are experimentally induced via the channel block of the astrocyte gap junctions. Because of the heterogeneous structure of the real neuron–astrocyte network, the effect of changing astrocyte network structures on the seizure activities is then studied in two typical network structures: the regular neighboring connection and the random connection. The results show that an increase of the number of regular connections of the regular neighboring astrocyte network could inhibit the induction and spread of the epileptic seizures. The epileptic inhibition can be achieved similarly by increasing the connection probability of the random astrocyte network. These findings further provide evidence for the experimental phenomena of the protective response of gliosis to epilepsy with increasing gap junctions. Above all, the simulation results suggest a potential pathway of epilepsy treatment by targeting the astrocyte gap junctions. [ABSTRACT FROM AUTHOR]

Cellulose nanopapers provide diverse, strong and lightweight templates prepared entirely from sustainable raw materials, cellulose nanofibers (CNFs). Yet the strength of CNFs has not been fully capitalized in the resulting nanopapers and the relative influence of CNF strength, their bonding, and biological origin to nanopaper strength are unknown. Here, we show that basic principles from paper physics can be applied to CNF nanopapers to illuminate those relationships. Importantly, it appeared that ~ 200 MPa was the theoretical maximum for nanopapers with random fibril orientation. Furthermore, we demonstrate the contrast in tensile strength for nanopapers prepared from bacterial cellulose (BC) and wood-based nanofibrillated cellulose (NFC). Endemic amorphous polysaccharides (hemicelluloses) in NFC act as matrix in NFC nanopapers, strengthening the bonding between CNFs just like it improves the bonding between CNFs in the primary cell wall of plants. The conclusions apply to all composites containing non-woven fiber mats as reinforcement. [ABSTRACT FROM AUTHOR]

Networks are a convenient way to represent many interactions among different entities as they provide an efficient and clear methodology to evaluate and organize relevant data. While there are many features for characterizing networks, a quantity seems rather elusive: Complexity. The quantification of the complexity of networks is nowadays a fundamental problem. Here, we present a novel tool for identifying the complexity of ecological networks. We compare the behavior of two relevant indices of complexity: K-complexity and Single Value Decomposition (SVD) entropy. For that, we use real data and two types of null models. Both null models consist of randomized networks built by swapping a controlled number of links of the original ones. We analyze 23 plant–pollinator and 19 host-parasite networks as case studies. Our results show that (a) it is necessary to calculate, not only the original network K-complexity and SVD entropy but also to calculate the corresponding indices of the randomized networks (b) the density and degree distribution are essential in the characterization of a network and the randomized networks are a suitable tool to detect the network complexity, and (c) plant–pollinator networks are more complex than host-parasite networks. We found that, for the first null model, K-complexity and SVD did not change with link swapping in both pollinator-plant and host-parasite networks. For the second null model, K-complexity for pollinator-plant networks generally decreased with an increasing number of links swapped (i.e. negative slope), showing that plant–pollinator networks lose complexity with increasing link swapping. In contrast, there was a positive slope between K-complexity and link swapping for host-parasite networks, showing that these networks are less complex than plant–pollinator networks. For both types of networks, in general, the slope between K-complexity and the number of links swapped became more positive with network density. Overall, SVD entropy was less responsive to link swapping. Our analyses show that although SVD entropy has been widely used to characterize network complexity, K-complexity is a more reliable tool. Additionally, they show that degree distribution and density are important drivers of network complexity and should be accounted for in future studies. [ABSTRACT FROM AUTHOR]

Abstract We introduce the random intersection graph with communities, a new model for networks with overlapping communities with arbitrary internal structure. We construct the model from a list of arbitrary community graphs that are the building blocks, and a separate list of individuals, each with a prescribed number of community membership tokens. Randomness is introduced by matching these tokens uniformly at random to vertices of the community graphs. We then identify the community members assigned to the same individual, thus overlaps arise due to individuals having several tokens. This gives a highly flexible model for networks with community structure. We are able to derive a wide range of analytic results on this model. We derive an asymptotic description of the local structure of the graph, which further yields the asymptotic degree distribution, local clustering coefficient, and results on the overlapping structure of the communities. For the global connectivity structure, we identify a phase transition in the size of the largest component. When the largest component constitutes a positive proportion of the graph, we can further characterize its asymptotic local structure. Finally, we study how the connectivity structure changes under a randomized attack, where we remove edges randomly, according to independent coin flips.

Abstract A novel parallel algorithm is presented for generating random scale-free networks using the preferential attachment model. The algorithm, named cuPPA, is custom-designed for “single instruction multiple data (SIMD)” style of parallel processing supported by modern processors such as graphical processing units (GPUs). To the best of our knowledge, our algorithm is the first to exploit GPUs, and also the fastest implementation available today, to generate scale-free networks using the preferential attachment model. A detailed performance study is presented to understand the scalability and runtime characteristics of the cuPPA algorithm. Also another version of the algorithm called cuPPA-Hash tailored for multiple GPUs is presented. On a single GPU, the original cuPPA algorithm delivers the best performance, but is challenging to port to multi-GPU implementation. For multi-GPU implementation, cuPPA-Hash has been used as the parallel algorithm to achieve a perfect linear speedup up to 4 GPUs. In one of the best cases, when executed on an NVidia GeForce 1080 GPU, the original cuPPA generates a scale-free network of two billion edges in less than 3 s. On multi-GPU platforms, cuPPA-Hash generates a scale-free network of 16 billion edges in less than 7 s using a machine consisting of 4 NVidia Tesla P100 GPUs.

This paper continues our previous consensus scheme with only group information when neither absolute states nor inter-agent relative states are available, by considering two special nonlinear cases, L ∞ -norm and L 2 -norm. In the scheme, all the agents are partitioned into two subgroups at each time by certain probability, and then use the relative group information that concerns all agents' states inside for state updating process. It is then shown that almost sure consensus can be achieved under the proposed scheme in both discrete time and continuous time for the two nonlinear cases. When for L ∞ -norm group information, almost sure consensus is achieved if and only if the weighting parameter is greater than one in discrete-time case, and the weighting parameter is positive in continuous-time case. When for L 2 -norm group information, the sufficient conditions to guarantee system consensus almost surely are the weighting parameter greater than n / 2 and positive in discrete-time case and continuous-time case, respectively. Finally, numerical simulations are proposed to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, we use rigorous probabilistic methods to study the asymptotic degree distribution, clustering coefficient, and diameter of geographical attachment networks. As a type of small-world network model, these networks were first proposed in the physical literature, where they were analyzed only with heuristic arguments and computational simulations. [ABSTRACT FROM AUTHOR]

We study behavior and equilibrium selection in experimental network games. We varytwo 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 randomnetwork. Play conforms strongly to the theoretical predictions, providing an impressivebehavioral confirmation of the Galeotti, Goyal, Jackson, Vega-Redondo, and Yariv (2010)model. The degree of equilibrium play is striking, even with incomplete information. We findthat under complete information, subjects typically play the stochastically-stable (inefficient)equilibrium when the game involves strategic substitutes, but play the efficient one with strategiccomplements. Our results suggest that equilibrium multiplicity may not be a major concern.Subjects’ actions and realized outcomes under incomplete information depend strongly on boththe degree and the connectivity. When there are multiple equilibria, subjects begin by playing theefficient equilibrium, but eventually converge to the inefficient one.

In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

Abstract Background Estimation of functional connectivity in gene sets derived from genome-wide or other biological experiments is one of the essential tasks of bioinformatics. A promising approach for solving this problem is to compare gene networks built using experimental gene sets with random networks. One of the resources that make such an analysis possible is CrossTalkZ, which uses the FunCoup database. However, existing methods, including CrossTalkZ, do not take into account individual types of interactions, such as protein/protein interactions, expression regulation, transport regulation, catalytic reactions, etc., but rather work with generalized types characterizing the existence of any connection between network members. Results We developed the online tool FunGeneNet, which utilizes the ANDSystem and STRING to reconstruct gene networks using experimental gene sets and to estimate their difference from random networks. To compare the reconstructed networks with random ones, the node permutation algorithm implemented in CrossTalkZ was taken as a basis. To study the FunGeneNet applicability, the functional connectivity analysis of networks constructed for gene sets involved in the Gene Ontology biological processes was conducted. We showed that the method sensitivity exceeds 0.8 at a specificity of 0.95. We found that the significance level of the difference between gene networks of biological processes and random networks is determined by the type of connections considered between objects. At the same time, the highest reliability is achieved for the generalized form of connections that takes into account all the individual types of connections. By taking examples of the thyroid cancer networks and the apoptosis network, it is demonstrated that key participants in these processes are involved in the interactions of those types by which these networks differ from random ones. Conclusions FunGeneNet is a web tool aimed at proving the functionality of networks in a wide range of sizes of experimental gene sets, both for different global networks and for different types of interactions. Using examples of thyroid cancer and apoptosis networks, we have shown that the links over-represented in the analyzed network in comparison with the random ones make possible a biological interpretation of the original gene/protein sets. The FunGeneNet web tool for assessment of the functional enrichment of networks is available at http://www-bionet.sscc.ru/fungenenet/.