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A method is given for analyzing in the frequency domain the performance of linear networks containing nonlinear resistors. The method is applied to the evaluation of the frequency performance of a reactively terminated mixer.

This Memorandum provides a theorem which illustrates why a general adaptive feed-forward layered network with linear output units can perform well as a pattern classification device. The central result is that minimizing the error at the output of the network is equivalent to maximizing a particular norm, the Network Cost Function, at the output of the hidden units. If the total covariance matrix is full rank and the targets are appropriately chosen, then this cost function relates the inverse of the total covariance matrix and the weighted between class covariance matrix of the hidden unit patterns. In a linear network it is shown how our theorem can reproduce the result recently obtained by Gallinari et al as a special case. We present numerical simulations to illustrate the theorem and to show that alternative choices for the cost function at the hidden layer are not maximized, generally, in a nonlinear situation. Great Britain,

A network of nonlinear coupled oscillators is presented, and a convergence proof is given along with physical motivation. Next, the network architecture is generalized by allowing interconnections between oscillators to be controlled in an adaptive fashion, and convergence of the generalized network is proved. An example network is presented to illustrate the utility of such networks and to show why the problem of undesired stable equilibria must be addressed. Two alternative approaches are then presented which overcome the problem of undesired stable equilibria appearing in the network dynamics. Finally, an analog VLSI approach to implementation of such networks is presented, and tradeoffs among power dissipation, bandwidth, and network size are discussed.

There has been a tremendous recent interest in the development of second-order nonlinear optical (NLO) polymeric materials for photonic applications. However, a major drawback of second-order NLO polymers that prevents them from being used in device applications is the instability of their electric field induced dipolar alignment. The randomization of the dipole orientation leads to the decay of second-order optical nonlinearities. Numerous efforts have been made to increase the stability of the second-order NLO properties of polymers. The search for new approaches to develop NLO polymers with optimal properties has been an active research area since the past decade. A novel approach, combining the hybrid properties of high glass transition temperatures, extensively crosslinked networks, and permanent entanglements, based on interpenetrating polymer networks (IPN) is introduced to develop stable second-order NLO materials. Two types of IPN systems are prepared and their properties are investigated. The designing criteria and the rationale for the selection of polymers are discussed. The IPN samples show excellent temporal stability at elevated temperatures. Long term stability of the optical nonlinearity at 100 C has been observed in these materials. Temporal stability of the NLO properties of these IPNs is synergistically enhanced. Relaxation behavior of the optical nonlinearity of an IPN system has been studied and compared with that of a typical guest/host system. The improved temporal stability of the second-order NLO properties of this IPN system is a result of the combination of the high rigidity of the polymer backbones, crosslinked matrices, and permanent entanglements of the polymer networks. A slight modification of the chemical structure resulted in an improvement of the optical quality of the sample.

This report describes an experimental investigation to determine if a procedure reported upon for reducing third order Intermodulation Products (IMP's) in an RF amplifier stage could be implemented in the laboratory. The third order IMP reduction procedure is based upon altering the RF amplifier linear out-of-band response by adding passive compensating networks. For this experiment, an RF amplifier tuned at 10 MHz was selected. The RF amplifier was excited by two CW signals at frequencies f1 = 9.0 MHz and f2 = 9.5 MHz in order to obtain a third order IMP at the frequency 2f2 - f1 = 10 MHz. The objective of the experiment was to determine if a significant reduction in this third order IMP could be obtained by connecting properly designed compensating networks to the basic RF amplifier stage. A linear model for the basic RF amplifier stage was developed. This model yielded calculated results that were in relatively good agreement with measured results for the magnitude and phase of the linear transfer function VOUT/VIN. Using the linear model for the basic amplifier stage, compensating networks were synthesized.

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In this technical note we address the problem of achieving consensus in a network of homogeneous nonlinear systems. The communication network is supposed to be switching within a finite set of topologies which may be disconnected for finite time intervals. We prove that if the length of the time intervals in which connected topologies are active satisfy an average dwell-time condition consensus is achieved. Lyapunov arguments proposed in the field of hybrid nonlinear systems are adopted to prove the result.

Recurrent Neural Networks (RNN) and Nonlinear Autoregressive Neural Network with External Input (NARX) are recently applied in predicting energy consumption. Energy consumption prediction for depth analysis of how electrical energy consumption is managed on Tower 2 Engineering Building is critical in order to reduce the energy usage and the operational cost. Prediction of energy consumption in this building will bring great benefits to the Faculty of Electrical Engineering UiTM Shah Alam. In this work, we present the comparative study on the performance of prediction of energy consumption in Tower 2 Engineering Building using RNN and NARX method. The model of RNN and NARX are trained using data collected using smart meters installed inside the building. The results after training and testing using RNN and NARX show that by using the recorded data we can accurately predict the energy consumption in the building. We also show that RNN model trained with normalized data performs better than NARX model. 

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) resistors. Generalizing work of Curtis, Ingerman, Morrow, Colin de Verdiere, Gitler, and Vertigan, we characterize the circular planar graphs for which the inverse boundary value problem has a solution in this generalized non-linear setting. The answer is the same as in the linear setting. Our method of proof never requires that the resistors behave in a continuous or monotone fashion; this allows us to recover signed conductances in many cases. We apply this to the problem of recovery in graphs that are not circular planar. We also use our results to make a frivolous knot-theoretic statement, and to slightly generalize a fact proved by Lam and Pylyavskyy about factorization schemes in their electrical linear group.

The objective of this research is to develop a Back-propagation Neural Network (BNN) to control certain classes of unknown nonlinear systems and explore the network's capabilities. The structure of the Direct Model Reference Adaptive Controller (DMRAC) for Linear Time Invariant (LTI) systems with unknown parameters is first analyzed. This structure is then extended using a BNN for adaptive control of unknown nonlinear systems. The specific structure of the BNN DMRAC is developed for control of four general classes of nonlinear systems modeled in discrete time. Experiments are conducted by placing a representative system from each class under the BNN's control. The condition under which the BNN DMRAC can successfully control these systems are investigated. The design and training of the BNN are also studied. The results of the experiments show that the BNN DMRAC works for the representative systems considered, while the conventional least-squares estimator DMRAC fails. Based on analysis and experimental findings, some genera conditions required to ensure that this technique works are postulated and discussed. General guidelines used to achieve the stability of the BNN learning process and good learning convergence are also discussed. To establish this as a general and significant control technique, further research is required to obtain analytically, the conditions for stability of the controlled system, and to develop more specific rules and guidelines in the BNN design and training.

Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave generation and propagation on circular subgraphs of a complex network. On circle networks, in the continuum limit, this model is equivalent to the over-damped Frenkel-Kontorova model. The new model is shown to keep the essential features of those well-known models such as the diffusively coupled B\"ar-Eiswirth model but with much simplified expression such that analytic analysis becomes possible. We classify traveling wave solutions on circle networks and show the universality of its features with perturbation analysis and numerical computation.

Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave generation and propagation on circular subgraphs of a complex network. On circle networks, in the continuum limit, this model is equivalent to the over-damped Frenkel-Kontorova model. The new model is shown to keep the essential features of those well-known models such as the diffusively coupled B\"ar-Eiswirth model but with much simplified expression such that analytic analysis becomes possible. We classify traveling wave solutions on circle networks and show the universality of its features with perturbation analysis and numerical computation.

In this paper, we study the leader-following consensus problem for a class of uncertain nonlinear multi-agent systems under jointly connected directed switching networks. The uncertainty includes constant unbounded parameters and external disturbances. We first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence. Then, by integrating the conventional adaptive control technique with the adaptive distributed observer, we present our solution by a distributed adaptive state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of van der Pol oscillators.

Bell System Technical Journal, 48: 5. May-June 1969 pp 1293-1311. Some Network-Theoretic Properties of Nonlinear DC Transistor Networks. (Sandberg, I.W.; Willson, A.N. Jr.)

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents alpha and beta, the stationary states the degree distributions evolve towards exhibit a second order phase transition - from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at alpha = beta. Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power-laws, of exponents -alpha and 1-alpha.

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces \emph{separably estimable} observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the $\mathcal{NU}$ (with its linear counterpart $\mathcal{LU}$) and the $\mathcal{NLU}$. Their update rule combines a \emph{consensus} step (where each sensor updates the state by weight averaging it with its neighbors' states) and an \emph{innovation} step (where each sensor processes its local current observation.) This makes the three algorithms of the \textit{consensus + innovations} type, very different from traditional consensus. The paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value,) efficiency, and asymptotic unbiasedness. For $\mathcal{LU}$ and $\mathcal{NU}$, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms $\mathcal{LU}$ and $\mathcal{NU}$ are analyzed in the framework of stochastic approximation theory; algorithm $\mathcal{NLU}$ exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in the paper.

It is shown from computer simulations that the current-voltage ($I$-$V$) characteristics for the two-dimensional XY model with resistively-shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear $I$-$V$ exponent $a$ can be determined to good precision. This determination supports the conclusion $a=z+1$, where $z$ is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B {\bf 67}, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. {\bf 78}, 4324 (1997)].

Broadcast radio, especially pirate radio, persists among marginalized communities, despite web radio's rise. In Brooklyn, over 100 stations fill the airwaves with dozens of musics and languages, ephemerally reclaiming spaces like taxi interiors, restaurant kitchens and city streets for particular communities. Listeners and broadcasters also innovate with radio: Immigrant and diasporic broadcasters use subcarrier frequencies, conference call systems and dedicated radio-by-phone services to reach their communities. As well, immigrant communities circulate information and music through semi-offline networks integrating pirate radio, posters and flyers in specific neighborhoods and commuting routes. Pirate radio's value is not only as marginal media for marginal people, but as sites of relative autonomy. This autonomy is fostered due to what are often called limitations: ephemerality, local/geographically-bound communication, unprofessionalism, illegality. Such limitations can be affordances for autonomy. This helps explain why technological and legal movements towards integration, legalization and visibility are not easily embraced by many oppressed communities. For example, low power FM stations that serve ethnic minority communities in particular are vastly outnumbered by pirate radio stations that do so. It also explains why many marginalized communities don’t make use of the latest web radio or internet-based communication. These "older" technologies center values that internet technologies are not usually designed to center, and make use of shared knowledge that is deeply rooted in many communities already. Through my research on pirate radio in New York and London, I have identified locality, collective intimacy, and synchronous and ephemeral sonic connection as values that are important for marginalized communities. Taking account of these values and using similar methods to identify values and strengths particular to specific marginalized communities can help us better support autonomous media making. Along the way, they remind us that innovation is not linear, and that the visions of the future grow from different pasts. Larisa Kingston Mann Radical Networks - Spektrum Berlin 21 Oct. 2018

This paper focuses on analyzing the finite-time convergence of a nonlinear consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis of the closed-loop system under the proposed consensus algorithm are more challenging than those under the well-studied consensus algorithms for known linear systems. For this purpose, we propose a novel stability tool based on a generalized comparison lemma. With the aid of the novel stability tool, it is shown that the proposed nonlinear consensus algorithm can guarantee finite-time convergence if the directed switching interaction graph has a directed spanning tree at each time interval. Specifically, the finite-time convergence is shown by comparing the closed-loop system under the proposed consensus algorithm with some well-designed closed-loop system whose stability properties are easier to obtain. Moreover, the stability and the finite-time convergence of the closed-loop system using the proposed consensus algorithm under a (general) directed switching interaction graph can even be guaranteed by the stability and the finite-time convergence of some special well-designed nonlinear closed-loop system under some special directed switching interaction graph, where each agent has at most one neighbor whose state is either the maximum of those states that are smaller than its own state or the minimum of those states that are larger than its own state. This provides a stimulating example for the potential applications of the proposed novel stability tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems. For illustration of the theoretical result, we provide a simulation example.

We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites across the lattice. Using localized initial conditions we focus on the time averaged probability of occupation of the initial site as a function of the degree of complexity of the lattice and nonlinearity. We observe that selftrapping occurs at increasingly larger values of the nonlinearity parameter as the lattice connectivity increases, while close to the fully coupled network limit, localization becomes more preferred. For nonlinearity values above a certain threshold we find a reentrant localization transition, viz. localization when the number of long distant bonds is small followed by delocalization and enhanced transport at intermediate bond numbers while close to the fully connected limit localization reappears.

A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The precision matrix assumes Gaussian data and its entries are zero for those pairs of variable which are conditionally independent. Here, we propose the Distance Precision Matrix which is based on a measure of possibly non-linear association, the distance covarince. We provide evidence that the Distance Precision Matrix can successfully compute networks from non-linear data and does so in a very consistent manner across many data situations.

The structure of a stochastic nonlinear gene regulatory network is uncovered by studying its response to input signal generators. Four applications are studied in detail: a nonlinear connection of two linear systems, the design of a logic pulse, a molecular amplifier and the interference of three signal generators in E2F1 regulatory element. The gene interactions are presented using molecular diagrams that have a precise mathematical structure and retain the biological meaning of the processes.

We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and corresponding time-averaged velocities derived from the Laplacian matrix, which reflects the network's topology. In terms of these coordinates, synchronization manifests itself as a contraction of the dynamics onto progressively lower-dimensional submanifolds of phase space spanned by Laplacian eigenvectors with lower eigenvalues. Differences between high and low clustering networks can be correlated with features of the Laplacian spectrum. For example, the inhibition of full synchoronization at high clustering is associated with a group of low-lying modes that fail to lock even at strong coupling, while the advanced partial synchronizationat low coupling noted elsewhere is associated with high-eigenvalue modes.

Advances in research have been made in the following areas: (1) The detailed test and characterization of the first ever ARAM in the CNN Chip Set Architecture; (2) The constructive use of the local activity principle in designing Cellular Nonlinear Networks with complex behavior; (3) Analogic CNN subroutine design for various practical applications, including coding, and optical flow estimation; and (4) Advances in testing qualitative properties of CNN, including stability test of non-symmetric feedback CNN.

A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors, are differential-difference KdV-type with perturbations. In the case of large Hill coefficient the proteomic signal along the gene network is given by a superposition of perturbed dark solitons of defocusing differential-difference mKdV equation. Biological implications are discussed.

A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors, are differential-difference KdV-type with perturbations. In the case of large Hill coefficient the proteomic signal along the gene network is given by a superposition of perturbed dark solitons of defocusing differential-difference mKdV equation. Biological implications are discussed.

A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors, are differential-difference KdV-type with perturbations. In the case of large Hill coefficient the proteomic signal along the gene network is given by a superposition of perturbed dark solitons of defocusing differential-difference mKdV equation. Biological implications are discussed.

In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and the networks weight. The gradient descent algorithm is a widely used weight adjustment algorithm in most of neural networks training algorithm. However, the method is known for its weakness for easily trap in local minima. It suffers from a random weight generated for the networks during initial stage of training at input layer to hidden layer networks. The performance of radial basis function networks (RBFN) has been improved from different perspectives, including centroid initialization problem to weight correction stage over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the weight produces by the algorithm. To solve this problem, an improved gradient descent algorithm for finding initial weight and improve the overall networks weight is proposed. This improved version algorithm is incorporated into RBFN training algorithm for updating weight. Hence, this paper presented an improved RBFN in term of algorithm for improving the weight adjustment in RBFN during training process. The proposed training algorithm, which uses improved gradient descent algorithm for weight adjustment for training RBFN, obtained significant improvement in predictions compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment. The proposed improved network called IRBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to IRBFN for root mean square error (RMSE) values with standard RBFN. The IRBFN yielded a promising result with an average improvement percentage more than 40 percent in RMSE.

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Joint optimization of nonlinear precoders and receive filters is studied for both the uplink and downlink in a cellular system. For the uplink, the base transceiver station (BTS) receiver implements successive interference cancellation, and for the downlink, the BTS station pre-compensates for the interference with Tomlinson-Harashima precoding (THP). Convergence of alternating optimization of receivers and transmitters in a single cell is established when filters are updated according to a minimum mean squared error (MMSE) criterion, subject to appropriate power constraints. Adaptive algorithms are then introduced for updating the precoders and receivers in the absence of channel state information, assuming time-division duplex transmissions with channel reciprocity. Instead of estimating the channels, the filters are directly estimated according to a least squares criterion via bi-directional training: Uplink pilots are used to update the feedforward and feedback filters, which are then used as interference pre-compensation filters for downlink training of the mobile receivers. Numerical results show that nonlinear filters can provide substantial gains relative to linear filters with limited forward-backward iterations.

Rapid development in numerical modelling of materials and the complexity of new models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models from noisy experimental data remains a nontrivial and often computationally exhaustive task. The layered neural networks thus represent a robust and efficient technique to overcome the time-consuming simulations of a calibrated model. The potential of neural networks consists in simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed to accelerate the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) model response, (ii) inverse relationship between the model response and its parameters and (iii) error function quantifying how well the model fits the data. The advantages and drawbacks of particular strategies are demonstrated on the calibration of four parameters of the affinity hydration model from simulated data as well as from experimental measurements. This model is highly nonlinear, but computationally cheap thus allowing its calibration without any approximation and better quantification of results obtained by the examined calibration strategies. The paper can be thus viewed as a guide intended for the engineers to help them select an appropriate strategy in their particular calibration problems.

We investigate a network of coupled superconducting transmission line resonators, each of them made nonlinear with a capacitively shunted Josephson junction coupling to the odd flux modes of the resonator. The resulting eigenmode spectrum shows anticrossings between the plasma mode of the shunted junction and the odd resonator modes. Notably, we find that the combined device can inherit the complete nonlinearity of the junction, allowing for a description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID instead of a single junction, the nonlinearity can be tuned between 10 kHz and 4 MHz while maintaining resonance frequencies of a few gigahertz for realistic device parameters. An array of such nonlinear resonators can be considered a scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The device would be capable of accessing the strongly correlated regime and be particularly well suited for investigating quantum many-body dynamics of interacting particles under the influence of drive and dissipation.

We study nonlinear random resistor diode networks at the transition from the non percolating to the directed percolating phase. The resistor-like bonds and the diode-like bonds under forward bias voltage obey a generalized Ohm's law, $V \sim I^r$. Based on general grounds as symmetries and relevance we develop a field theoretic model. We focus on the average two-port resistance, which is governed at the transition by the resistance exponent $\phi_r$. By employing renormalization group methods we calculate $\phi_r$ for arbitrary $r$ to one-loop order. Then we address the fractal dimensions characterizing directed percolation clusters. Via considering distinct values of the nonlinearity $r$, we determine the dimension of the red bonds, the chemical path and the backbone to two-loop order.

We study nonlinear random resistor diode networks at the transition from the non percolating to the directed percolating phase. The resistor-like bonds and the diode-like bonds under forward bias voltage obey a generalized Ohm's law, $V \sim I^r$. Based on general grounds as symmetries and relevance we develop a field theoretic model. We focus on the average two-port resistance, which is governed at the transition by the resistance exponent $\phi_r$. By employing renormalization group methods we calculate $\phi_r$ for arbitrary $r$ to one-loop order. Then we address the fractal dimensions characterizing directed percolation clusters. Via considering distinct values of the nonlinearity $r$, we determine the dimension of the red bonds, the chemical path and the backbone to two-loop order.

Big networks express various large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to set up a broad class of nonlinear continuous-time block-structured Markov processes, which can be applied to deal with many practical stochastic systems. Firstly, a nonlinear Markov process is derived from a large number of interacting big networks with symmetric interactions, each of which is described as a continuous-time block-structured Markov process. Secondly, some effective algorithms are given for computing the fixed points of the nonlinear Markov process by means of the UL-type RG-factorization. Finally, the Birkhoff center, the Lyapunov functions and the relative entropy are used to analyze stability or metastability of the big network, and several interesting open problems are proposed with detailed interpretation. We believe that the results given in this paper can be useful and effective in the study of big networks.

Bell System Technical Journal, 49: 8. October 1970 pp 1739-1776. Theorems on the Computation of the Transient Response of Nonlinear Networks Containing Transistors and Diodes. (Sandberg, I.W.)

This paper presents a novel framework which combines a non-iterative solution of Real-Time Nonlinear Receding Horizon Control (NRHC) methodology to achieve consensus within complex network topologies with existing time-delays and in presence of switching topologies. In this formulation, we solve the distributed nonlinear optimization problem for multi-agent network systems directly, \emph{in real-time}, without any dependency on iterative processes, where the stability and convergence guarantees are provided for the solution. Three benchmark examples on non-linear chaotic systems provide validated results which demonstrate the significant outcomes of such methodology.

In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and spread value. Radial basis function network (RBFN) is a type of feedforward network that capable of perform nonlinear approximation on unknown dataset. It has been widely used in classification, pattern recognition, nonlinear control and image processing. Thus, with the increases in RBFN application, some problems and weakness of RBFN network is identified. Through the combination of quantum computing and RBFN provides a new research idea in design and performance improvement of RBFN system. This paper describes the theory and application of quantum computing and cloning operators, and discusses the superiority of these theories and the feasibility of their optimization algorithms.This proposed improved RBFN (I-RBFN) that combined with cloning operator and quantum computing algorithm demonstrated its ability in global search and local optimization to effectively speed up learning and provides better accuracy in prediction results. Both the algorithms that combined with RBFN optimize the centers and spread value of RBFN. The proposed I-RBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to I-RBFN for root mean square error (RMSE) values with standard RBFN. The proposed I-RBFN yielded better results with an average improvement percentage more than 90 percent in RMSE.

Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behavior over a wide range of network concentrations and strains up to failure of the material.

The purpose of this short paper is to provide a theoretical analysis for the consensus problem under nonlinear protocols. A main contribution of this work is to generalize the previous consensus problems under nonlinear protocols for networks with undirected graphs to directed graphs (information flow). Our theoretical result is that if the directed graph is strongly connected and the nonlinear protocol is strictly increasing, then consensus can be realized. Some simple examples are also provided to demonstrate the validity of our theoretical result.

Here we study the nonlinear hyperbolic equations of the type of equations from theory of flows on networks, for which we prove the solvability theorem under the appropriate conditions and also investigate the behaviour of the solution.

Thesis advisor, Roberto Cristi

This article is from PLoS ONE , volume 9 . Abstract Nonlinear dependence is general in regulation mechanism of gene regulatory networks (GRNs). It is vital to properly measure or test nonlinear dependence from real data for reconstructing GRNs and understanding the complex regulatory mechanisms within the cellular system. A recently developed measurement called the distance correlation (DC) has been shown powerful and computationally effective in nonlinear dependence for many situations. In this work, we incorporate the DC into inferring GRNs from the gene expression data without any underling distribution assumptions. We propose three DC-based GRNs inference algorithms: CLR-DC, MRNET-DC and REL-DC, and then compare them with the mutual information (MI)-based algorithms by analyzing two simulated data: benchmark GRNs from the DREAM challenge and GRNs generated by SynTReN network generator, and an experimentally determined SOS DNA repair network in Escherichia coli. According to both the receiver operator characteristic (ROC) curve and the precision-recall (PR) curve, our proposed algorithms significantly outperform the MI-based algorithms in GRNs inference.

The aim of this paper is a short survey of models and methods that developed by the authors. These models and methods are used to optimize general networks with nonlinear non-convex restrictions and objectives possessing mixed continuous-discrete optimization variables. There are discussed the problem formulations and solution methods for simulation, optimization, sensitivity and stability analysis for flow with nonlinear potential in general networks. These problems and the developed methods and programs have industrial application e.g. by gas networks.

In this paper, we study the problem of synchronization with stochastic interaction among network components. The network components dynamics is nonlinear and modeled in Lure form with linear stochastic interaction among network components. To study this problem we first prove the stochastic version of Positive Real Lemma (PRL). The stochastic PRL result is then used to provide sufficient condition for synchronization of stochastic network system. The sufficiency condition for synchronization, is a function of nominal (mean) coupling Laplacian eigenvalues and the statistics of link uncertainty in the form of coefficient of dispersion (CoD). Contrary to the existing literature on network synchronization, our results indicate that both the largest and the second smallest eigenvalue of the mean Laplacian play an important role in synchronization of stochastic networks. Robust control-based small-gain interpretation is provided for the derived sufficiency condition which allow us to define the margin of synchronization. The margin of synchronization is used to understand the important tradeoff between the component dynamics, network topology, and uncertainty characteristics. For a special class of network system connected over torus topology we provide an analytical expression for the tradeoff between the number of neighbors and the dimension of the torus. Similarly, by exploiting the identical nature of component dynamics computationally efficient sufficient condition independent of network size is provided for general class of network system. Simulation results for network of coupled oscillators with stochastic link uncertainty are presented to verify the developed theoretical framework.

We find that sensory noise delivered together with a weak periodic signal not only enhances nonlinear response of neuronal networks, but also improves the synchronization of the response to the signal. We reveal this phenomenon in neuronal networks that are in a dynamical state near a saddle-node bifurcation corresponding to appearance of sustained network oscillations. In this state, even a weak periodic signal can evoke sharp nonlinear oscillations of neuronal activity. These sharp network oscillations have a deterministic form and amplitude determined by nonlinear dynamical equations. The signal-to-noise ratio reaches a maximum at an optimum level of sensory noise, manifesting stochastic resonance (SR) at the population level. We demonstrate SR by use of simulations and numerical integration of rate equations in a cortical model with stochastic neurons. Using this model, we mimic the experiments of Gluckman et al. [B. J. Gluckman et al, Phys. Rev. Lett., v. 77, 4098 (1996)] that have given evidence of SR in mammalian brain. We also study neuronal networks in which neurons are grouped in modules and every module works in the regime of SR. We find that even a few modules can strongly enhance the reliability of signal detection in comparison with the case when a modular organization is absent.

In this paper, we consider the problem of sparse recovery from nonlinear measurements, which has applications in state estimation and bad data detection for power networks. An iterative mixed $\ell_1$ and $\ell_2$ convex program is used to estimate the true state by locally linearizing the nonlinear measurements. When the measurements are linear, through using the almost Euclidean property for a linear subspace, we derive a new performance bound for the state estimation error under sparse bad data and additive observation noise. As a byproduct, in this paper we provide sharp bounds on the almost Euclidean property of a linear subspace, using the "escape-through-the-mesh" theorem from geometric functional analysis. When the measurements are nonlinear, we give conditions under which the solution of the iterative algorithm converges to the true state even though the locally linearized measurements may not be the actual nonlinear measurements. We numerically evaluate our iterative convex programming approach to perform bad data detections in nonlinear electrical power networks problems. We are able to use semidefinite programming to verify the conditions for convergence of the proposed iterative sparse recovery algorithms from nonlinear measurements.

We present a general approach to the study of synchrony in networks of weakly nonlinear systems described by singularly perturbed equations of the type $x''+x+\epsilon f(x,x')=0$. By performing a perturbative calculation based on normal form theory we analytically obtain an $\O(\epsilon)$ approximation to the Floquet multipliers that determine the stability of the synchronous solution. The technique allows us to prove and generalize recent results obtained using heuristic approaches, as well as reveal the structure of the approximating equations. We illustrate the results in several examples, and discuss extensions to the analysis of stability of multisynchronous states in networks with complex architectures.

An approach to creating Amorphous Recurrent Neural Networks (ARNN) using Genetic Algorithms (GA) called 2pGA has been developed and shown to be effective in evolving neural networks for the control and stabilization of both linear and nonlinear plants, the optimal control for a nonlinear regulator problem, the XOR problem, and an amplitude modulation (AM) detector. This new approach consists of a two-phase GA with the first phase using a set of Lindenmayer System (L-System) production rules to evolve the NN architectures, and the second phase using genetic hill-climbing for connectivity weight tuning. The resulting amorphous (non-layered) recurrent NNs are real-valued as opposed to the binary-valued nets generated by the original GANNET program. Integral absolute error was the fitness function used in these experiments. A striking indirect result of this research is the few number of neurons which are required to effect the compensation and stabilization. Typical networks are from 4-15 neurons. The inclusion of a neural insertion/deletion operator in both the 2pGA and GANNET2 methods allows for the size of the NN to be evolved. This capability has been used to develop an empirical relationship between problem complexity and the required NN complexity. Problem complexity is measured by the number of symbols required to differentiate among binary patterns in a pattern recognition task. NN complexity is measured by number of neurons. while not yet definitive, empirical data from ARNNs evolved by GANNET2 show what appears to be a logarithmic relationship between the complexity of a regular expression and the size of a recurrent neural network which recognize it. Additional experiments are being performed to extend the region of evolved data to improve our confidence in this conclusion.