Univariate approach to the monthly total ozone time series over Kolkata,India: autoregressive integrated moving average (ARIMA) and autoregressive neural network (AR-NN) models

This study reports univariate modelling methodologies applied to the monthly total ozone concentration (TOC) over Kolkata (22°32′, 88°20′), India, derived from the measurements made by the Earth Probe Total Ozone Mapping Spectrometer (EP/TOMS). The univariate models have been generated in two forms, namely autoregressive integrated moving average (ARIMA) and autoregressive neural network (AR-NN). Three ARIMA models in the forms of ARIMA(1,1,1), ARIMA(0,1,1) and ARIMA(0,2,2) and 11 autoregressive neural network models, AR-NN(n), have been generated for a time series. Goodness of fit of the models to the time series of monthly TOC has been assessed using prediction error, Pearson correlation coefficient and Willmott's indices. After rigorous skill assessment, the ARIMA (0,2,2) has been identified as the best predictive model for the time series under study.     

Analysis of toggle protocols

Summary The paper deals with the problem of managing full and empty slots in a slotted ring network. Two solutions are formally described and proved correct. The first solution is deterministic; it recovers inO(N) round trips after the last error, whereN is the number of nodes in the network. The second solution is randomized; the expected number of round trips to recovery after the last error isO(lnN). Jan Pachl works at IBM Zurich Research Laboratory. Previously he worked at BNR in Ottawa and at the University of Waterloo. His interests include communication protocols, distributed systems, skiing and loud music.     

Autoregressive forecast of monthly total ozone concentration: A neurocomputing approach

The present study endeavors to generate autoregressive neural network (AR-NN) models to forecast the monthly total ozone concentration over Kolkata (22°34′, 88°22′), India. The issues associated with the applicability of neural network to geophysical processes are discussed. The autocorrelation structure of the monthly total ozone time series is investigated, and stationarity of the time series is established through the periodogram. From various autoregressive moving average (ARMA) and autoregressive models fit to the time series, the autoregressive model of order 10 is identified as the best. Subsequently, 10 autoregressive neural network (AR-NN) models are generated; the 10th order autoregressive neural network model with extensive input variable selection performs the best among all the competitive models in forecasting the monthly total ozone concentration over the study zone.     

A Modified Version of Chordal Ring

Topological design of intereonnection network is a key factor of developingparallel/distributed processing systems composed of a large number of microcomputermodules. For this purpose a double-chordal ring intereonnection network was proposed. Themost attractive of its advantages is that for an optimally designed network with N modules itsdiameter can he reduced to O(N~(1/3)) compared with O(N~(1/2)) for a simple chordal ring. Theessential properties of double-chordal ring network arc presented, and formulae for calculatingits diameter are derived. These formulae lead to a distributed computational routing algorithmand a way of optimization of the network parameters (maximal number of nedes and optimalchordal lengths) for a given diameter.     

Mathematical modeling of endocrine regulation subject to circadian rhythm

The 2017 Nobel Prize in Physiology or Medicine awarded for discoveries of molecular mechanisms controlling the circadian rhythm has called attention to the challenging area of nonlinear dynamics that deals with synchronization and entrainment of oscillations. Biological circadian clocks keep time in living organisms, orchestrating hormonal cycles and other periodic rhythms. The periodic oscillations of circadian pacemakers are self-sustained; at the same time, they are entrainable by external periodic signals that adjust characteristics of autonomous oscillations. Whereas modeling of biological oscillators is a well-established research topic, mathematical analysis of entrainment, i.e. the nonlinear phenomena imposed by periodic exogenous signals, remains an open problem. Along with sustained periodic rhythms, periodically forced oscillators can exhibit various “irregular” behaviors, such as quasiperiodic or chaotic trajectories.This paper presents an overview of the mathematical models of circadian rhythm with respect to endocrine regulation, as well as biological background. Dynamics of the human endocrine system, comprising numerous glands and hormones operating under neural control, are highly complex. Therefore, only endocrine subsystems (or axes) supporting certain biological functions are usually studied. Low-order dynamical models that capture the essential characteristics and interactions between a few hormones can than be derived. Goodwin’s oscillator often serves as such a model and is widely regarded as a prototypical biological oscillator. A comparative analysis of forced dynamics arising in two versions of Goodwin’s oscillator is provided in the present paper: the classical continuous oscillator and a more recent impulsive one, capturing e.g. pulsatile secretion of hormones due to neural regulation. The main finding of this study is that, while the continuous oscillator is always forced to a periodic solution by a sufficiently large exogenous signal amplitude, the impulsive one commonly exhibits a quasiperiodic or chaotic behavior due to non-smooth dynamics in entrainment.     

Hierarchical Ring Network design

A Hierarchical Ring Network is obtained from a ring network by appending at most one subsidiary ring to each node of the ring and, recursively, to each node of each subsidiary ring. The depth d is the number of levels of the recursive appending of subsidiary rings. There are different definitions according to which rings are appended to nodes created at the preceding level (called an HRN) or to any node (called here an HBN for Hierarchical Bubble Network). The case of an HRN was considered by Aiello et al. who give bounds (not tight) on the diameter of such an HRN as a function of the depth and the number of nodes. Here we determine the exact order of the diameter both for an HRN and an HBN. In fact we consider the optimization problem of maximizing the number of nodes of an HBN (or an HRN) of given depth d and diameter D. We reduce the problem to a system of equations with a complex objective function. Solving this system enables us to determine precisely the structure of an optimal HBN and to show that the maximum number of nodes is of order D ^d /d!.     

Geno-mathematical identification of the multi-layer perceptron

In this paper, we will focus on the use of the three-layer backpropagation network in vector-valued time series estimation problems. The neural network provides a framework for noncomplex calculations to solve the estimation problem, yet the search for optimal or even feasible neural networks for stochastic processes is both time consuming and uncertain. The backpropagation algorithm—written in strict ANSI C—has been implemented as a standalone support library for the genetic hybrid algorithm (GHA) running on any sequential or parallel main frame computer. In order to cope with ill-conditioned time series problems, we extended the original backpropagation algorithm to a K nearest neighbors algorithm (K-NARX), where the number K is determined genetically along with a set of key parameters. In the K-NARX algorithm, the terminal solution at instant t can be used as a starting point for the next t, which tends to stabilize the optimization process when dealing with autocorrelated time series vectors. This possibility has proved to be especially useful in difficult time series problems. Following the prevailing research directions, we use a genetic algorithm to determine optimal parameterizations for the network, including the lag structure for the nonlinear vector time series system, the net structure with one or two hidden layers and the corresponding number of nodes, type of activation function (currently the standard logistic sigmoid, a bipolar transformation, the hyperbolic tangent, an exponential function and the sine function), the type of minimization algorithm, the number K of nearest neighbors in the K-NARX procedure, the initial value of the Levenberg–Marquardt damping parameter and the value of the neural learning (stabilization) coefficient α. We have focused on a flexible structure allowing addition of, e.g., new minimization algorithms and activation functions in the future. We demonstrate the power of the genetically trimmed K-NARX algorithm on a representative data set.     

Expansion of a matrix in terms of external products of configuration vectors

The paper proposes a neural-net iterative algorithm that allows us to represent any random symmetrical N×N matrix as a weighted Hebbian series of configuration vectors with a given accuracy. The iterative algorithm is shown to demonstrate the fastest convergence when the vectors of expansion are stable nods of the N-dimensional space corresponding to the extremums of the neural-net energy functional. It so proves that all conclusions about neural networks and optimization algorithms that are based on Hebbian matrices are true for any other type of matrix. The text was submitted by the author in English.     

Fuzzy wavelet neural network based on fuzzy clustering and gradient techniques for time series prediction

This paper presents the development of fuzzy wavelet neural network system for time series prediction that combines the advantages of fuzzy systems and wavelet neural network. The structure of fuzzy wavelet neural network (FWNN) is proposed, and its learning algorithm is derived. The proposed network is constructed on the base of a set of TSK fuzzy rules that includes a wavelet function in the consequent part of each rule. A fuzzy c-means clustering algorithm is implemented to generate the rules, that is the structure of FWNN prediction model, automatically, and the gradient-learning algorithm is used for parameter identification. The use of fuzzy c-means clustering algorithm with the gradient algorithm allows to improve convergence of learning algorithm. FWNN is used for modeling and prediction of complex time series and prediction of foreign-exchange rates. Exchange rates are dynamic process that changes every day and have high-order nonlinearity. The statistical data for the last 2 years are used for the development of FWNN prediction model. Effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based systems and with the comparative simulation results of previous related models.     

Morphogenetic approach to system identification

In this paper, we propose a novel approach to system identification based on morphogenetic theory (MT). Given a context H defined by a set of M objects, each described by a set of N attributes, and a vector X of desired outputs for each object, MT combines notions from formal concept analysis and tensor calculus so as to generate a morphogenetic system (MS). The MS is defined by a set of weights s¹, …, s^N, one for each attribute. Given H and X, weights are computed so as to generate the projection Y of X on the space of the attributes with the minimum distance between Y and X. An MS can be represented as a neuron, morphogenetic neuron, with a number of synapses equal to the number of attributes and synaptic weights equal to s¹, …, s^N. Unlike traditional neural network paradigm, which adopts an iterative process to determine synaptic weights, in MT, weights are computed at once. We introduce a method to generate a morphogenetic neural network (MNN) for identification problems. The method is based on extending appropriately and iteratively the attribute space so as to reduce the error between desired output and computed output. By using four well‐known datasets, we show that an MNN can identify an unknown system with a precision comparable with classical multilayer perceptron with complexity similar to the MNN but reducing drastically the time needed to generate the neural network. Furthermore, the structure of the MNN is generated automatically by the method and does not require a trial‐and‐error approach often applied in classical neural networks. © 2009 Wiley Periodicals, Inc.     

Hopfield Neural Network Based Stereo Matching Algorithm

In this paper, a neural network based optimization method is described in order to solve the problem of stereo matching for a set of primitives extracted from a stereoscopic pair of images. The neural network used is the 2D Hopfield network. The matching problem amounts to the minimization of an energy function involving specified stereoscopic constraints. This function reaches its minimum when these constraints are satisfied. The network converges to its stable state when the minimum is reached. In the initial step, the primitives to match are extracted from the stereoscopic pair of images. The primitives we use are specific points of interest. The feature extraction technique is the one developed by Moravec, and called the interest operator. Its output comprises mostly corners or feature points with high variance. The Hopfield network is represented as a N _l × N _r matrix of neurons, where N _l is the number of features in the left image and N _r the number of features in the right one. An update of the state of each neuron is done in order to perform the network evolution and then allowing it to settle down into a stable state. In the stable state, each neuron represents a possible match between a left candidate and a right one.     

The Minimum Number of Errors in the N-Parity and its Solution with an Incremental Neural Network

The N-dimensional parity problem is frequently a difficult classification task for Neural Networks. We found an expression for the minimum number of errors f as function of N for this problem, performed by a perceptron. We verified this quantity experimentally for N=1,...,15 using an optimal train perceptron. With a constructive approach we solved the full N-dimensional parity problem using a minimal feedforward neural network with a single hidden layer of h=N units.     

Realization of Dynamic Walking and Running of the Quadruped Using Neural Oscillator

In the present study we attempt to induce a quadruped robot to walk dynamically on irregular terrain and run on flat terrain by using a nervous system model. For dynamic walking on irregular terrain, we employ a control system involving a neural oscillator network, a stretch reflex and a flexor reflex. Stable dynamic walking when obstructions to swinging legs are present is made possible by the flexor reflex and the crossed extension reflex. A modification of the single driving input to the neural oscillator network makes it possible for the robot to walk up a step. For running on flat terrain, we combine a spring mechanism and the neural oscillator network. It became clear in this study that the matching of two oscillations by the spring-mass system and the neural oscillator network is important in order to keep jumping in a pronk gait. The present study also shows that entrainment between neural oscillators causes the running gait to change from pronk to bound. This finding renders running fairly easy to attain in a bound gait. It must be noticed that the flexible and robust dynamic walking on irregular terrain and the transition of the running gait are realized by the modification of a few parameters in the neural oscillator network.     

A vector model of associative memory with clipped synapses

The influence of a clipping procedure on the properties of vector associative memory is investigated. The analysis is performed for the particular case of a phase model of a parametric neural network with 2q-state neurons. The critical network size N _c is found. It is shown that, for small network sizes (N < N _c ), the clipping leads to an increase of the storage capacity and enhances the network ability to retrieve strongly distorted patterns. Clipping of bigger networks (N > N _c ) leads to a deterioration of the recognition ability and reduces the storage capacity. Boris Vladimirovich Kryzhanovsky was born in 1950 in Yasnaya Polyana in the Tula region of Russia and graduated (with an M.Sc.) from Yerevan State University in 1971. He received his Ph.D. (Optics) in 1981 and his D.Sc. (Laser Physics) in 1991. At the present time, he is the director of the Center for Optical Neural Technologies of the Scientific Research Institute for Systems Analysis of the Russian Academy of Sciences. His research interests include neural networks. He is a corresponding member of the Russian Academy of Sciences and the author of over 200 research publications. Vladimir Mikhailovich Kryzhanovsky was born in 1984 in Kirovakan, Armenia and graduated (with an M.Sc.) from the Moscow Engineering Physics Institute in 2007. At the present time, he is a junior research assistant at the Center for Optical Neural Technologies of the Scientific Research Institute for Systems Analysis of the Russian Academy of Sciences. His research interests include Neural Networks, and he is the author of over 20 research publications. Dina Igorevna Simkina was born 1981 in Buinaksk in Dagestan, Russia and graduated (with an M.Sc.) from Dagestan State University in 2003. At the present time, she is a junior research assistant at the Center for Optical Neural Technologies of the Scientific Research Institute for Systems Analysis of the Russian Academy of Sciences. Her research interests include neural networks, and she is the author of over 20 research publications.     

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.     

Learning as a nonlinear line of attraction in a recurrent neural network

A method to embed N dimensional, multi-valued patterns into an auto-associative memory represented as a nonlinear line of attraction in a fully connected recurrent neural network is presented in this paper. The curvature of the nonlinear attractor is defined by the Kth degree polynomial line which best fits the training data in N dimensional state space. The width of the nonlinear line is then characterized by the statistical characteristics of the training patterns. Stability of the recurrent network is verified by analyzing the trajectory of the points in the state space during convergence. The performance of the network is benchmarked through the reconstruction of original gray-scale images from their corrupted versions. It is observed that the proposed method can quickly and successfully reconstruct each image with an average convergence rate of 3.10 iterations.     

区间时间序列的混合预测模型

提出一种基于自回归求和移动平均(ARIMA) 与人工神经网络(ANN) 的区间时间序列混合模型, 并用混合模型分别对区间中值序列和区间半径序列建模. 采用Monte Carlo 方法生成模拟区间序列, 分别用ARIMA、ANN和混合模型3 种方法进行建模和预测实验, 并用统计学方法检验模型误差. 最后分别采用3 种方法对H市轨道交通某号线牵引能耗区间序列进行了建模和预测, 实验结果表明混合模型的建模精度和预测性能均优于单一模型.

     

Development of neurofuzzy architecture for solving the N-Queens problem

Neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents an architecture of recurrent neural networks for solving the N-Queens problem. More specifically, a modified Hopfield network is developed and its internal parameters are explicitly computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points, which represent a solution of the considered problem. The network is shown to be completely stable and globally convergent to the solutions of the N-Queens problem. A fuzzy logic controller is also incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.     

Nonlinear Short-term Prediction of Aluminum Foil Thickness via Global Regressor Combination

In this study, short-term prediction of aluminum foil thickness time-series data recorded during cold-rolling process was investigated. The locally projective nonlinear noise reduction was applied in order to improve the predictability of the time series. The higher-order statistics methods (bispectrum and bicoherence) were used to detect the nonlinearity. The embedding vectors with appropriate embedding dimension and time delay were obtained via the false nearest neighbors and mutual information methods, respectively. The maximum prediction horizon was determined depending on the maximal Lyapunov exponent. For various prediction horizons, the embedding vector and corresponding thickness value pairs were used as the dataset to assess the prediction performance of various machine learning algorithms (i.e., multilayer perceptron neural network, support vector machines with Pearson VII function-based kernel, and radial basis function network). The n-step ahead prediction outputs of the machine learning algorithms were globally combined with simple voting in favor of the one having minimum absolute error. The accuracy of our proposed method was compared with nonlinear autoregressive exogenous model for various thickness time-series data using mean absolute percentage error measure.     

A Bell inequality for a class of multilocal ring networks

Quantum networks with independent sources of entanglement (hidden variables) and nodes that execute joint quantum measurements can create strong quantum correlations spanning the breadth of the network. Understanding of these correlations has to the present been limited to standard Bell experiments with one source of shared randomness, bilocal arrangements having two local sources of shared randomness, and multilocal networks with tree topologies. We introduce here a class of quantum networks with ring topologies comprised of subsystems each with its own internally shared source of randomness. We prove a Bell inequality for these networks, and to demonstrate violations of this inequality, we focus on ring networks with three-qubit subsystems. Three qubits are capable of two non-equivalent types of entanglement, GHZ and W-type. For rings of any number N of three-qubit subsystems, our inequality is violated when the subsystems are each internally GHZ-entangled. This violation is consistently stronger when N is even. This quantitative even-odd difference for GHZ entanglement becomes extreme in the case of W-type entanglement. When the ring size N is even, the presence of W-type entanglement is successfully detected; when N is odd, the inequality consistently fails to detect its presence.