Existence and learning of oscillations in recurrent neural networks

We study a particular class of n-node recurrent neural networks (RNNs). In the 3-node case we use monotone dynamical systems theory to show, for a well-defined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. We then investigate whether RNNs of this class can adapt their internal parameters so as to ?learn? and then replicate autonomously (in feedback) certain external periodic signals. Our learning algorithm is similar to the identification algorithms in adaptive control theory. The main feature of the algorithm is that global exponential convergence of parameters is guaranteed. We also obtain partial convergence results in the n-node cas

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov–Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.This work was supported in part by the National Natural Science Foundation of China under Grant 50608072, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany

Robust identification of Parkinson\u27s disease subtypes using radiomics and hybrid machine learning

OBJECTIVES: It is important to subdivide Parkinson\u27s disease (PD) into subtypes, enabling potentially earlier disease recognition and tailored treatment strategies. We aimed to identify reproducible PD subtypes robust to variations in the number of patients and features. METHODS: We applied multiple feature-reduction and cluster-analysis methods to cross-sectional and timeless data, extracted from longitudinal datasets (years 0, 1, 2 & 4; Parkinson\u27s Progressive Marker Initiative; 885 PD/163 healthy-control visits; 35 datasets with combinations of non-imaging, conventional-imaging, and radiomics features from DAT-SPECT images). Hybrid machine-learning systems were constructed invoking 16 feature-reduction algorithms, 8 clustering algorithms, and 16 classifiers (C-index clustering evaluation used on each trajectory). We subsequently performed: i) identification of optimal subtypes, ii) multiple independent tests to assess reproducibility, iii) further confirmation by a statistical approach, iv) test of reproducibility to the size of the samples. RESULTS: When using no radiomics features, the clusters were not robust to variations in features, whereas, utilizing radiomics information enabled consistent generation of clusters through ensemble analysis of trajectories. We arrived at 3 distinct subtypes, confirmed using the training and testing process of k-means, as well as Hotelling\u27s T2 test. The 3 identified PD subtypes were 1) mild; 2) intermediate; and 3) severe, especially in terms of dopaminergic deficit (imaging), with some escalating motor and non-motor manifestations. CONCLUSION: Appropriate hybrid systems and independent statistical tests enable robust identification of 3 distinct PD subtypes. This was assisted by utilizing radiomics features from SPECT images (segmented using MRI). The PD subtypes provided were robust to the number of the subjects, and features

Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics

Adaptive Natural Oscillator to Exploit Natural Dynamics for Energy Efficiency

We present a novel adaptive oscillator, called Adaptive Natural Oscillator (ANO), to exploit the natural dynamics of a given robotic system. This tool is built upon the Adaptive Frequency Oscillator (AFO), and it can be used as a pattern generator in robotic applications such as locomotion systems. In contrast to AFO, that adapts to the frequency of an external signal, ANO adapts the frequency of reference trajectory to the natural dynamics of the given system. In this work, we prove that, in linear systems, ANO converges to the system's natural frequency. Furthermore, we show that this tool exploits the natural dynamics for energy efficiency through minimization of actuator effort. This property makes ANO an appealing tool for energy consumption reduction in cyclic tasks; especially in legged systems. We also extend the proposed adaptation mechanism to high dimensional and general cases; such as n-DOF manipulators. In addition, by investigating a hopper leg in simulation, we show the efficacy of ANO in face of dynamical discontinuities; such as those inherent in legged locomotion. Furthermore, we apply ANO to a simulated compliant robotic manipulator performing a periodic task where the energy consumption is drastically reduced. Finally, the experimental results on a 1-DOF compliant joint show that our adaptive oscillator, despite all practical uncertainties and deviations from theoretical models, exploits the natural dynamics and reduces the energy consumption

Développement d'outils d’analyse de la motricité fine pour l’investigation de troubles neuromusculaires : théorie, prototype et mise en application dans le contexte des accidents vasculaires cérébraux

RÉSUMÉ Cette thèse examine la possibilité d’évaluer la susceptibilité à un accident vasculaire cérébral (AVC) à partir des attributs des mouvements humains. Ces travaux reposent sur l’hypothèse selon laquelle l’existence d’un état pré-AVC peut, dans certains cas, être détecté par l’évaluation de la santé neuromotrice du patient. À défaut de disposer de données longitudinales permettant d’étudier directement cette conjecture, nos résultats démontrent que le diagnostic des principaux facteurs de risque d’AVC est effectivement réalisable à partir des propriétés des mouvements. Ces conclusions sont tirées à la suite de l’analyse transversale des réponses de 120 sujets à neuf tests neuromoteurs. Par cette étude des liens entre la motricité et la présence de conditions menant potentiellement à l’AVC, on espère stimuler l’intérêt des chercheurs en santé pour l’hypothèse – rapportée de façon anecdotique par plusieurs cliniciens – de l’existence d’un état pré-AVC. Les investigations nécessaires à cette démonstration ont été menées dans le cadre de la Théorie Cinématique et suivent principalement trois axes directeurs, soit l’étude fondamentale du mouvement humain, le développement d’outils d’extraction permettant la modélisation lognormale des mouvements et l’analyse statistique des paramètres lognormaux dans le but du diagnostic des principaux facteurs de risque d’AVC (diabète, obésité, tabagisme, problèmes cardiaques, alcoolisme, hypertension et hypercholestérolémie). En introduction de la première partie de cette thèse sont répertoriés les différents indices disséminés dans la littérature scientifique étayant l’existence de liens entre les mouvements humains et les principaux facteurs de risque d’AVC. Observant que la présence de tels liens est supportée par l’état des connaissances actuelles, le paradigme offert par la Théorie Cinématique ainsi que la modélisation lognormale qui en découle sont adoptés, puis présentés. L’apparition de profils de forme lognormale au niveau des primitives du mouvement est ensuite expliquée d’un point de vue original. Une fois ces bases établies, il a été possible de procéder à l’analyse des données dont nous disposions, ce qui a mis en lumière un certain nombre de phénomènes fondamentaux relatifs à l’étude du contrôle moteur, dont trois sont particulièrement importants. En premier lieu, il a été relevé que la nature des mouvements est intrinsèquement proportionnelle.----------ABSTRACT This Ph. D. thesis investigates the brain stroke susceptibility assessment based on the movement analysis of data acquired using neuromuscular tests. This work is rooted in the hypothesis of the existence of a pre-stroke state which can sometimes be detected by looking at the properties of a patient’s neuromuscular system. As the study of this hypothesis would require longitudinal data that were unavailable, our analysis concentrates on the demonstration that the brain stroke risk factors can be diagnose from a human movement analysis. This conclusion derives from a transversal study of 120 subject’s responses to nine neuromuscular tests. It is hoped that this investigation on the links between fine motor control and brain stroke risk factors can stimulate the interest of the medical community for the anecdotic report, by some clinicians, of the possible existence of a pre-stroke state. The work presented herein was made under the Kinematic Theory and it follows three main axes which are 1) the fundamental study of human movements, 2) the design of extraction algorithms allowing the lognormal modeling of human motion, and 3) the statistical analysis of the kinematic parameters of human movements for the diagnosis of principal brain stroke risk factors. In the first part of this thesis, an overview is presented of the many observations scattered in the scientific literature concerning the link between the human movements and the main brain stroke risk factors (diabetes, obesity, cigarette smoking, cardiac problems, alcoholism, hypertension and hypercholesterolemia). Building on the observation that the existence of such a link is supported, a modeling framework is chosen and the lognormal models forming its foundations are reported from an original point of view. The application of this methodology to our database allowed the investigation of some fundamental phenomena concerning the study of motor control. Notably, the proportional nature of human motion is examined and compared to the serial representation of psychophysical processes. The delta-lognormal modeling of speed-accuracy tradeoffs (Fitts’ task) has also allowed the discovery of some fundamental aspects related to the control of this kind of movements, such as the increase of the coupling between the motor commands as the task becomes more difficult and the enhancement of the temporal coordination of the neuromuscular action as the geometrical properties of the task are scaled up

Existence and Learning of Oscillations in Recurrent Neural Networks

In this paper we study a particular class of $n$-node recurrent neural networks (RNNs).In the $3$-node case we use monotone dynamical systems theory to show,for a well-defined set of parameters, that,generically, every orbit of the RNN is asymptotic to a periodic orbit.Then, within the usual 'learning' context of NeuralNetworks, we investigate whether RNNs of this class can adapt their internal parameters soas to 'learn' and then replicate autonomously certain external periodic signals.Our learning algorithm is similar to identification algorithms in adaptivecontrol theory. The main feature of the adaptation algorithm is that global exponential convergenceof parameters is guaranteed. We also obtain partial convergence results in the $n$-node case

Existence and Learning of Oscillations in Recurrent Neural Networks

In this paper we study a particular class of $n$-node recurrent neural networks (RNNs).In the $3$-node case we use monotone dynamical systems theory to show,for a well-defined set of parameters, that,generically, every orbit of the RNN is asymptotic to a periodic orbit.Then, within the usual 'learning' context of NeuralNetworks, we investigate whether RNNs of this class can adapt their internal parameters soas to 'learn' and then replicate autonomously certain external periodic signals.Our learning algorithm is similar to identification algorithms in adaptivecontrol theory. The main feature of the adaptation algorithm is that global exponential convergenceof parameters is guaranteed. We also obtain partial convergence results in the $n$-node case