A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing

The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 * 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.Comment: 26 pages, 24 figure

Method of increasing the information capacity of associative memory of oscillator neural networks using high-order synchronization effect

Computational modelling of two- and three-oscillator schemes with thermally coupled $VO_2$-switches is used to demonstrate a novel method of pattern storage and recognition in an impulse oscillator neural network (ONN) based on the high-order synchronization effect. The method ensures high information capacity of associative memory, i.e. a large number of synchronous states $N_s$. Each state in the system is characterized by the synchronization order determined as the ratio of harmonics number at the common synchronization frequency. The modelling demonstrates attainment of $N_s$ of several orders both for a three-oscillator scheme $N_s$~650 and for a two-oscillator scheme $N_s$~260. A number of regularities are obtained, in particular, an optimal strength of oscillator coupling is revealed when $N_s$ has a maximum. A general tendency toward information capacity decrease is shown when the coupling strength and switch inner noise amplitude increase. An algorithm of pattern storage and test vector recognition is suggested. It is also shown that the coordinate number in each vector should be one less than the switch number to reduce recognition ambiguity. The demonstrated method of associative memory realization is a general one and it may be applied in ONNs with various mechanisms and oscillator coupling topology.Comment: 18 pages, 8 figure

A Bio-Inspired Chaos Sensor Based on the Perceptron Neural Network: Concept and Application for Computational Neuro-science

The study presents a bio-inspired chaos sensor based on the perceptron neural network. After training, the sensor on perceptron, having 50 neurons in the hidden layer and 1 neuron at the output, approximates the fuzzy entropy of short time series with high accuracy with a determination coefficient R2 ~ 0.9. The Hindmarsh-Rose spike model was used to generate time series of spike intervals, and datasets for training and testing the perceptron. The selection of the hyperparameters of the perceptron model and the estimation of the sensor accuracy were performed using the K-block cross-validation method. Even for a hidden layer with 1 neuron, the model approximates the fuzzy entropy with good results and the metric R2 ~ 0.5-0.8. In a simplified model with 1 neuron and equal weights in the first layer, the principle of approximation is based on the linear transformation of the average value of the time series into the entropy value. The bio-inspired chaos sensor model based on an ensemble of neurons is able to dynamically track the chaotic behavior of a spiked biosystem and transmit this information to other parts of the bio-system for further processing. The study will be useful for specialists in the field of computational neuroscience.Comment: 12 pages, 22 figures, 4 table

Entropy-based machine learning model for diagnosis and monitoring of Parkinson's Disease in smart IoT environment

The study presents the concept of a computationally efficient machine learning (ML) model for diagnosing and monitoring Parkinson's disease (PD) in an Internet of Things (IoT) environment using rest-state EEG signals (rs-EEG). We computed different types of entropy from EEG signals and found that Fuzzy Entropy performed the best in diagnosing and monitoring PD using rs-EEG. We also investigated different combinations of signal frequency ranges and EEG channels to accurately diagnose PD. Finally, with a fewer number of features (11 features), we achieved a maximum classification accuracy (ARKF) of ~99.9%. The most prominent frequency range of EEG signals has been identified, and we have found that high classification accuracy depends on low-frequency signal components (0-4 Hz). Moreover, the most informative signals were mainly received from the right hemisphere of the head (F8, P8, T8, FC6). Furthermore, we assessed the accuracy of the diagnosis of PD using three different lengths of EEG data (150-1000 samples). Because the computational complexity is reduced by reducing the input data. As a result, we have achieved a maximum mean accuracy of 99.9% for a sample length (LEEG) of 1000 (~7.8 seconds), 98.2% with a LEEG of 800 (~6.2 seconds), and 79.3% for LEEG = 150 (~1.2 seconds). By reducing the number of features and segment lengths, the computational cost of classification can be reduced. Lower-performance smart ML sensors can be used in IoT environments for enhances human resilience to PD.Comment: 19 pages, 10 figures, 2 table

Neural Network Entropy (NNetEn): EEG Signals and Chaotic Time Series Separation by Entropy Features, Python Package for NNetEn Calculation

Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy estimation methods are required to characterize the chaotic dynamic of the system. Our concept of Neural Network Entropy (NNetEn) is based on the classification of special datasets (MNIST-10 and SARS-CoV-2-RBV1) in relation to the entropy of the time series recorded in the reservoir of the LogNNet neural network. NNetEn estimates the chaotic dynamics of time series in an original way. Based on the NNetEn algorithm, we propose two new classification metrics: R2 Efficiency and Pearson Efficiency. The efficiency of NNetEn is verified on separation of two chaotic time series of sine mapping using dispersion analysis (ANOVA). For two close dynamic time series (r = 1.1918 and r = 1.2243), the F-ratio has reached the value of 124 and reflects high efficiency of the introduced method in classification problems. The EEG signal classification for healthy persons and patients with Alzheimer disease illustrates the practical application of the NNetEn features. Our computations demonstrate the synergistic effect of increasing classification accuracy when applying traditional entropy measures and the NNetEn concept conjointly. An implementation of the algorithms in Python is presented.Comment: 24 pages, 18 figures, 2 table

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio