1,721,503 research outputs found
On global asymptotic stability of a class of nonlinear systems arising in neural network theory
No full textOn complete stability of linear and quadratic programming neural networks
No full textThe paper addresses complete stability (CS) of the important class of neural networks to solve linear and quadratic programming problems introduced by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35:554). By CS it is meant that each trajectory converges to a stationary state, i.e. an equilibrium point of the neural network. It is shown that the neural networks in (IEEE Trans. Circuits Syst., 1988; 35:554) enjoy the property of CS even in the most general case where there are infinite non-isolated equilibrium points. This result, which is proved by exploiting a new method to analyse CS (Int. J Bifurcation Chaos 2001; 11:655), extends the stability analysis by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35:554) to situations of interest where the optimization problems have infinite solutions. Copyright (C) 2002 John Wiley Sons, Ltd
Some extensions of a new method to analyze complete stability of neural networks
No full textIn a recent work, a new method has been introduced to analyze complete stability of the standard symmetric cellular neural networks (CNNs), which are characterized by local interconnections and neuron activations modeled by a three-segment piecewise-linear (PWL) function. By complete stability it is meant that each trajectory of the neural network converges toward an equilibrium point. The goal of this paper is to extend that method in order to address complete stability of the much wider class of symmetric neural networks with an additive interconnecting structure where the neuron activations are general PWL functions with an arbitrary number of straight segments. The main result obtained is that complete stability holds for any choice of the parameters within the class of symmetric additive neural networks with PWL neuron activations, i.e., such a class of neural networks enjoys the important property of absolute stability of global pattern formation. It is worth pointing out that complete stability is proved for generic situations where the neural network has finitely many (isolated) equilibrium points, as well as for degenerate situations where there are infinite (nonisolated) equilibrium points. The extension in this paper is of practical importance since it includes neural networks useful to solve significant signal processing tasks (e.g., neural networks with multilevel neuron activations). It is of theoretical interest too, due to the possibility of approximating any continuous function (e.g., a sigmoidal function), using PWL functions. The results in this paper confirm the advantages of the method of Ford and Tesi, with respect to LaSalle approach, to address complete stability of PWL neural networks
A note on neural networks with multiple equilibrium points
No full textWe give a condition which is necessary and sufficient for the injectivity (i.e., for the global invertibility) of vector fields defining a class of piece-wise-linear neural networks which include the Cellular Neural Networks as a special case. It is shown that this is the sharpest obtainable condition for injectivity, since it enables one to ascertain such property for each specific nonlinear piece-wise-linear function modeling the neuron activations. This result establishes an exact bound between neural circuits possessing a unique equilibrium point (which are tailor made, e.g., for solving global optimization problems) and those possessing multiple equilibrium points (which are suitable, e.g., for implementing a Content Addressable Memory or a Cellular Neural Network for image processing). We also prove conceptually similar results on injectivity in case of continuously differentiable neuron activations. The proof of the main results exploits topological concepts from degree theory, such as the concept of homotopy of odd vector fields. © 1996 IEEE
M-matrices and global convergence of discontinuous neural networks
No full textThe paper considers a general class of neural networks possessing discontinuous neuron activations and neuron interconnection matrices belonging to the class of M-matrices or H-matrices. A number of results are established on global exponential convergence of the state and output solutions towards a unique equilibrium point. Moreover, by exploiting the presence of sliding modes, conditions are given under which convergence in finite time is guaranteed. In all cases, the exponential convergence rate, or the finite convergence time, can be quantitatively estimated on the basis of the parameters defining the neural network. As a by-product, it is proved that the considered neural networks, although they are described by a system of differential equations with discontinuous right-hand side, enjoy the property of uniqueness of the solution starting at a given initial condition. The results are proved by a generalized Lyapunov-like approach and by using tools from the theory of differential equations with discontinuous right-hand side. At the core of the approach is a basic lemma, which holds under the assumption of M-matrices or H-matrices, and enables to study the limiting behaviour of a suitably defined distance between any pair of solutions to the neural network
AI-driven migration management procedures: fundamental rights issues and regulatory answers
No full textBlockchain-driven identification procedures in the migration context: regulatory challenges and fundamental rights issues
No full textConvergence of a subclass of Cohen-Grossberg neural networks via the Lojasiewicz inequality
No full textThis correspondence proves a convergence result for the Lotka-Volterra dynamical systems with symmetric interaction parameters between different species. These can be considered as a subclass of the competitive neural networks introduced by Cohen and Grossberg in 1983. The theorem guarantees that each forward trajectory has finite length and converges toward a single equilibrium point, even for those parameters for which there are infinitely many nonisolated equilibrium points. The convergence result in this correspondence, which is proved by means of a new method based on the Lojasiewicz inequality for gradient systems of analytic functions, is stronger than the previous. result established by Cohen and Grossberg via LaSalle's invariance principle, which requires, for convergence, the additional assumption that the equilibrium points be isolated
The deployment of artificial intelligence tools in the health sector : privacy concerns and regulatory answers within the regulation (EU) 2016/679
No full textPublished online: 09 June 2021This article examines the privacy and data protection implications of the deployment of machine learning algorithms in the medical sector. Researchers and physicians are developing advanced algorithms to forecast possible developments of illnesses or disease statuses, basing their analysis on the processing of a wide range of data sets. Predictive medicine aims to maximize the effectiveness of disease treatment by taking into account individual variability in genes, environment, and lifestyle. These kinds of predictions could eventually anticipate a patient's possible health conditions years, and potentially decades, into the future and become a vital instrument in the future development of diagnostic medicine. However, the current European data protection legal framework may be incompatible with inherent features of artificial intelligence algorithms and their constant need for data and information. This article proposes possible new approaches and normative solutions to this dilemma
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