Error and attack tolerance of synchronization in Hindmarsh–Rose neural networks with community structure

Synchronization is one of the most important features observed in large-scale complex networks of interacting dynamical systems. As is well known, there is a close relation between the network topology and the network synchronizability. Using the coupled Hindmarsh–Rose neurons with community structure as a model network, in this paper we explore how failures of the nodes due to random errors or intentional attacks affect the synchronizability of community networks. The intentional attacks are realized by removing a fraction of the nodes with high values in some centrality measure such as the centralities of degree, eigenvector, betweenness and closeness. According to the master stability function method, we employ the algebraic connectivity of the considered community network as an indicator to examine the network synchronizability. Numerical evidences show that the node failure strategy based on the betweenness centrality has the most influence on the synchronizability of community networks. With this node failure strategy for a given network with a fixed number of communities, we find that the larger the degree of communities, the worse the network synchronizability; however, for a given network with a fixed degree of communities, we observe that the more the number of communities, the better the network synchronizability.     

Analysis and implementation of theFMLMS algorithm in AANC

I.IntroductionInthefieldofnoisecontrol,whenthecharacteristicsofthenoisesourcevary,theAANCsystemcanadaptivelyadjustthecontrollerofthecancellingsystemtoachievetheoptimal'complexstrengthofthesecondarysourceandconsequentlyensurethatthenoisecontrolsystemcanworkattheoptimalstatusfrombeginningtoend.So,thetechniqueoftheAANChasbeenappliedtoalmostallofthe3-Dspatialactivenoisecontrol.'ThealgorithmhastakenanimportantroleintheAANC.OneofthemainalgorithmsusedintheAANCistheFiltered-XLMS(FLMS)algori…     

L_2-L_∞ learning of dynamic neural networks

This paper proposes an L2 -L∞ learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the L2-L∞ learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an L2-L∞ induced norm constraint. It is shown that the design of the L2-L∞ learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.     

Applying Bayesian neural networks to identify pion, kaon and proton in BESⅡ

The Monte-Carlo samples of pion, kaon and proton generated from 0.3GeV/c to 1.2GeV/c by the `tester' generator from SIMBES which are used to simulate the detector of BESⅡ are identified with the Bayesian neural networks (BNN). The pion identification and misidentification efficiencies are obviously better at high momentum region using BNN than the methods of χ² analysis of dE/dX and TOF information. The kaon identification and misidentification efficiencies are obviously better from 0.3GeV/c to 1.2GeV/c using BNN than the methods of χ² analysis. The proton identification and misidentification efficiencies using BNN are basically consistent with the ones of χ² analysis. The anti-proton identification and misidentification efficiencies are better below 0.6GeV/c using BNN than the methods of χ² analysis.     

Global exponential stability of reaction diffusion neural networks with discrete and distributed time-varying delays

This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays.By constructing a more general type of Lyapunov-Krasovskii functional combined with a free-weighting matrix approach and analysis techniques,delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities.The obtained results are dependent on the size of the time-varying delays and the measure of the space,which are usually less conservative than delay-independent and space-independent ones.These results are easy to check,and improve upon the existing stability results.Some remarks are given to show the advantages of the obtained results over the previous results.A numerical example has been presented to show the usefulness of the derived linear matrix inequality(LMI)-based stability conditions.     

H∞ synchronization of chaotic neural networks with time-varying delays

In this paper,we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays.A new model of the networks with disturbances in both master and slave systems is presented.By constructing a suitable Lyapunov–Krasovskii functional and using a reciprocally convex approach,a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities(LMIs)which can be easily solved by various effective optimization algorithms.Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Robust adaptive synchronization of chaotic neural networks by slide technique

In this paper, we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay. In order to increase the robustness of the two coupled neural networks, the key idea is that a sliding-mode-type controller is employed. Moreover, without the estimate values of the network unknown parameters taken as an updating object, a new updating object is introduced in the constructing of controller. Using the proposed controller, without any requirements for the boundedness, monotonicity and differentiability of activation functions, and symmetry of connections, the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are. Finally, the numerical simulation validates the effectiveness and feasibility of the proposed technique.     

Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen–Grossberg neural networks

This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order CohenGrossberg neural networks(FOCGNNs) with time delays.Based on Brouwer's fixed point theorem,sufficient conditions are established to ensure the existence of Π_(i=1)~n(2 K_i+1) equilibrium points for FOCGNNs.Through the use of Hardy inequality,fractional Halanay inequality,and Lyapunov theory,some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Π_(i=1)~n(K_i+1) equilibrium points for FOCGNNs·The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases.The activation functions are nonlinear and nonmonotonic.There could be many corner points in this general class of activation functions.The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points.Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories.Finally,two numerical examples are provided to illustrate the effectiveness of the obtained results.     

Signal of new physics and chemical composition of matter in core-crossing neutrinos

We consider the non-standard matter effect in flavor conversion of neutrinos crossing the core of the Earth. We show that oscillations of core-crossing neutrinos with E≳0.5 GeV can well be described by first order perturbation theory. We show that due to the non-standard matter effect a varying chemical composition in the Earth can modify the neutrino flavor conversion by 100%. The effects of CP violating phases in non-standard neutral current interactions are emphasized in particular.     

Techniques of laser spectroscopy in investigations of lanthanides’ free atoms and ions

Various experimental methods, used in Chair of Quantum Engineering and Metrology for determination of the hyperfine structure of electronic levels in lanthanides atoms and ions, are presented. In turn the spectroscopic methods on an atomic beam (laser induced fluorescence and laser-rf double resonance ABMR-LIRF), laser-rf double resonance in a Paul trap and spectroscopic methods in a hollow cathode discharge (optogalvanic detection and laser induced fluorescence) are presented. Each method has been characterized with its potential accuracy and domain of application. The results achieved for the atoms and the ions of lanthanum, praseodymium, neodymium and europium have been published in numerous articles (compiled in the reference list).     

“Eigen-Operator” Method of the Square of Schroedinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers

We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.     

Coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.     

Coherent periodic activity in excitatory Erdös-Renyi neural networks: the role of network connectivity

In this article, we investigate the role of connectivity in promoting coherent activity in excitatory neural networks. In particular, we would like to understand if the onset of collective oscillations can be related to a minimal average connectivity and how this critical connectivity depends on the number of neurons in the networks. For these purposes, we consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erdo?s-Renyi graph with average connectivity scaling as a power law with the number of neurons in the network. The scaling is controlled by a parameter γ, which allows to pass from massively connected to sparse networks and therefore to modify the topology of the system. At a macroscopic level, we observe two distinct dynamical phases: an asynchronous state corresponding to a desynchronized dynamics of the neurons and a regime of partial synchronization (PS) associated with a coherent periodic activity of the network. At low connectivity, the system is in an asynchronous state, while PS emerges above a certain critical average connectivity (c). For sufficiently large networks, (c) saturates to a constant value suggesting that a minimal average connectivity is sufficient to observe coherent activity in systems of any size irrespectively of the kind of considered network: sparse or massively connected. However, this value depends on the nature of the synapses: reliable or unreliable. For unreliable synapses, the critical value required to observe the onset of macroscopic behaviors is noticeably smaller than for reliable synaptic transmission. Due to the disorder present in the system, for finite number of neurons we have inhomogeneities in the neuronal behaviors, inducing a weak form of chaos, which vanishes in the thermodynamic limit. In such a limit, the disordered systems exhibit regular (non chaotic) dynamics and their properties correspond to that of a homogeneous fully connected network for any γ-value. Apart for the peculiar exception of sparse networks, which remain intrinsically inhomogeneous at any system size.     

Role of copper ions in dielectric and structural investigations of lead– borate glasses

Glasses in the system 0.1CuO-(x-0.1)PbO-(1-x)B₂O₃ (0.3≤ x ≤ 0.7) were synthesized by using the melt quench technique. A number of studies such as X-ray diffraction (XRD), differential scanning calorimetry (DSC), fourier-transform infrared (FTIR) and Raman spectroscopy, electron paramagnetic resonance (EPR) and dielectric properties (viz., dielectric constant ??, dielectric loss and ac conductivity σ_ac) are employed to characterize the glasses. The amorphous nature of the glasses was confirmed using XRD while the glass transition temperature (T_g) of glass samples have been estimated from DSC investigation and found that the T_g decreases with increasing PbO content. Raman and FTIR spectroscopy reveals that when increasing lead ions, the tetrahedral [BO₄] units are gradually replaced by trigonal [BO₃] units. The EPR study leads to determine the local site of Cu²⁺ ions and its transformation with the Pb content in the studied glasses.     

A comparison of genetic programming and neural networks; new formulations for electrical resistivity of Zn–Fe alloys

It is difficult to automatically solve a problem in a systematic method without using computers. In this study, a comparison between Neural Network (NN) and genetic programming (GEP) soft computing techniques as alternative tools for the formulation of electrical resistivity of zinc–iron (Zn–Fe) alloys for various compositions is proposed. Different formulations are supplied to control the verity and robustness of NN and GEP for the formulation to design composition and electrolyte conditions in certain ranges. The input parameters of the NN and GEP models are weight percentages of zinc and iron in the film and in the electrolyte, measurement temperature, and corrosion voltage of the films. The NN- and GEP-based formulation results are compared with experimental results and found to be quite reliable with a very high correlation (R ²=0.998 for GEP and 0.999 for NN).