A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called $\mathcal{B}$-projection functions. Broadly speaking, a $\mathcal{B}$-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras

Complex Neural Networks for Audio

Audio is represented in two mathematically equivalent ways: the real-valued time domain (i.e., waveform) and the complex-valued frequency domain (i.e., spectrum). There are advantages to the frequency-domain representation, e.g., the human auditory system is known to process sound in the frequency-domain. Furthermore, linear time-invariant systems are convolved with sources in the time-domain, whereas they may be factorized in the frequency-domain. Neural networks have become rather useful when applied to audio tasks such as machine listening and audio synthesis, which are related by their dependencies on high quality acoustic models. They ideally encapsulate fine-scale temporal structure, such as that encoded in the phase of frequency-domain audio, yet there are no authoritative deep learning methods for complex audio. This manuscript is dedicated to addressing the shortcoming. Chapter 2 motivates complex networks by their affinity with complex-domain audio, while Chapter 3 contributes methods for building and optimizing complex networks. We show that the naive implementation of Adam optimization is incorrect for complex random variables and show that selection of input and output representation has a significant impact on the performance of a complex network. Experimental results with novel complex neural architectures are provided in the second half of this manuscript. Chapter 4 introduces a complex model for binaural audio source localization. We show that, like humans, the complex model can generalize to different anatomical filters, which is important in the context of machine listening. The complex model\u27s performance is better than that of the real-valued models, as well as real- and complex-valued baselines. Chapter 5 proposes a two-stage method for speech enhancement. In the first stage, a complex-valued stochastic autoencoder projects complex vectors to a discrete space. In the second stage, long-term temporal dependencies are modeled in the discrete space. The autoencoder raises the performance ceiling for state of the art speech enhancement, but the dynamic enhancement model does not outperform other baselines. We discuss areas for improvement and note that the complex Adam optimizer improves training convergence over the naive implementation

Learning Schemes for Recurrent Neural Networks

兵庫県立大学大学院202

Computational aspects of electromagnetic NDE phenomena

The development of theoretical models that characterize various physical phenomena is extremely crucial in all engineering disciplines. In nondestructive evaluation (NDE), theoretical models are used extensively to understand the physics of material/energy interaction, optimize experimental design parameters and solve the inverse problem of defect characterization. This dissertation describes methods for developing computational models for electromagnetic NDE applications. Two broad classes of issues that are addressed in this dissertation are related to (i) problem formulation and (ii) implementation of computers;The two main approaches for solving physical problems in NDE are the differential and integral equations. The relative advantages and disadvantages of the two approaches are illustrated and models are developed to simulate electromagnetic scattering from objects or inhomogeneities embedded in multilayered media which is applicable in many NDE problems. The low storage advantage of the differential approach and the finite solution domain feature of the integral approach are exploited. Hybrid techniques and other efficient modeling techniques are presented to minimize the storage requirements for both approaches;The second issue of computational models is the computational resources required for implementation. Implementations on conventional sequential computers, parallel architecture machines and more recent neural computers are presented. An example which requires the use of massive parallel computing is given where a probability of detection model is built for eddy current testing of 3D objects. The POD model based on the finite element formulation is implemented on an NCUBE parallel computer. The linear system of equations is solved using direct and iterative methods. The implementations are designed to minimize the interprocessor communication and optimize the number of simultaneous model runs to obtain a maximum effective speedup;Another form of parallel computing is the more recent neurocomputer which depends on building an artificial neural network composed of numerous simple neurons. Two classes of neural networks have been used to solve electromagnetic NDE inverse problems. The first approach depends on a direct solution of the governing integral equation and is done using a Hopfield type neural network. Design of the network structure and parameters is presented. The second approach depends on developing a mathematical transform between the input and output space of the problem. A multilayered perceptron type neural network is invoked for this implementation. The network is augmented to build an incremental learning network which is motivated by the dynamic and modular features of the human brain

ECG analysis and classification using CSVM, MSVM and SIMCA classifiers

Reliable ECG classification can potentially lead to better detection methods and increase accurate diagnosis of arrhythmia, thus improving quality of care. This thesis investigated the use of two novel classification algorithms: CSVM and SIMCA, and assessed their performance in classifying ECG beats. The project aimed to introduce a new way to interactively support patient care in and out of the hospital and develop new classification algorithms for arrhythmia detection and diagnosis. Wave (P-QRS-T) detection was performed using the WFDB Software Package and multiresolution wavelets. Fourier and PCs were selected as time-frequency features in the ECG signal; these provided the input to the classifiers in the form of DFT and PCA coefficients. ECG beat classification was performed using binary SVM. MSVM, CSVM, and SIMCA; these were subsequently used for simultaneously classifying either four or six types of cardiac conditions. Binary SVM classification with 100% accuracy was achieved when applied on feature-reduced ECG signals from well-established databases using PCA. The CSVM algorithm and MSVM were used to classify four ECG beat types: NORMAL, PVC, APC, and FUSION or PFUS; these were from the MIT-BIH arrhythmia database (precordial lead group and limb lead II). Different numbers of Fourier coefficients were considered in order to identify the optimal number of features to be presented to the classifier. SMO was used to compute hyper-plane parameters and threshold values for both MSVM and CSVM during the classifier training phase. The best classification accuracy was achieved using fifty Fourier coefficients. With the new CSVM classifier framework, accuracies of 99%, 100%, 98%, and 99% were obtained using datasets from one, two, three, and four precordial leads, respectively. In addition, using CSVM it was possible to successfully classify four types of ECG beat signals extracted from limb lead simultaneously with 97% accuracy, a significant improvement on the 83% accuracy achieved using the MSVM classification model. In addition, further analysis of the following four beat types was made: NORMAL, PVC, SVPB, and FUSION. These signals were obtained from the European ST-T Database. Accuracies between 86% and 94% were obtained for MSVM and CSVM classification, respectively, using 100 Fourier coefficients for reconstructing individual ECG beats. Further analysis presented an effective ECG arrhythmia classification scheme consisting of PCA as a feature reduction method and a SIMCA classifier to differentiate between either four or six different types of arrhythmia. In separate studies, six and four types of beats (including NORMAL, PVC, APC, RBBB, LBBB, and FUSION beats) with time domain features were extracted from the MIT-BIH arrhythmia database and the St Petersburg INCART 12-lead Arrhythmia Database (incartdb) respectively. Between 10 and 30 PCs, coefficients were selected for reconstructing individual ECG beats in the feature selection phase. The average classification accuracy of the proposed scheme was 98.61% and 97.78 % using the limb lead and precordial lead datasets, respectively. In addition, using MSVM and SIMCA classifiers with four ECG beat types achieved an average classification accuracy of 76.83% and 98.33% respectively. The effectiveness of the proposed algorithms was finally confirmed by successfully classifying both the six beat and four beat types of signal respectively with a high accuracy ratio

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement

Particle Physics Reference Library

This second open access volume of the handbook series deals with detectors, large experimental facilities and data handling, both for accelerator and non-accelerator based experiments. It also covers applications in medicine and life sciences. A joint CERN-Springer initiative, the “Particle Physics Reference Library” provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A,B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access