2,450 research outputs found
Finite Connectivity Attractor Neural Networks
We study a family of diluted attractor neural networks with a finite average
number of (symmetric) connections per neuron. As in finite connectivity spin
glasses, their equilibrium properties are described by order parameter
functions, for which we derive an integral equation in replica symmetric (RS)
approximation. A bifurcation analysis of this equation reveals the locations of
the paramagnetic to recall and paramagnetic to spin-glass transition lines in
the phase diagram. The line separating the retrieval phase from the spin-glass
phase is calculated at zero temperature. All phase transitions are found to be
continuous.Comment: 17 pages, 4 figure
Neural network based architectures for aerospace applications
A brief history of the field of neural networks research is given and some simple concepts are described. In addition, some neural network based avionics research and development programs are reviewed. The need for the United States Air Force and NASA to assume a leadership role in supporting this technology is stressed
The Hopfield model and its role in the development of synthetic biology
Neural network models make extensive use of
concepts coming from physics and engineering. How do scientists
justify the use of these concepts in the representation of
biological systems? How is evidence for or against the use of
these concepts produced in the application and manipulation
of the models? It will be shown in this article that neural
network models are evaluated differently depending on the
scientific context and its modeling practice. In the case of
the Hopfield model, the different modeling practices related to
theoretical physics and neurobiology played a central role for
how the model was received and used in the different scientific
communities. In theoretical physics, where the Hopfield model
has its roots, mathematical modeling is much more common and
established than in neurobiology which is strongly experiment
driven. These differences in modeling practice contributed to
the development of the new field of synthetic biology which
introduced a third type of model which combines mathematical
modeling and experimenting on biological systems and by doing
so mediates between the different modeling practices
Model reduction for the dynamics and control of large structural systems via neutral network processing direct numerical optimization
Three neural network processing approaches in a direct numerical optimization model reduction scheme are proposed and investigated. Large structural systems, such as large space structures, offer new challenges to both structural dynamicists and control engineers. One such challenge is that of dimensionality. Indeed these distributed parameter systems can be modeled either by infinite dimensional mathematical models (typically partial differential equations) or by high dimensional discrete models (typically finite element models) often exhibiting thousands of vibrational modes usually closely spaced and with little, if any, damping. Clearly, some form of model reduction is in order, especially for the control engineer who can actively control but a few of the modes using system identification based on a limited number of sensors. Inasmuch as the amount of 'control spillover' (in which the control inputs excite the neglected dynamics) and/or 'observation spillover' (where neglected dynamics affect system identification) is to a large extent determined by the choice of particular reduced model (RM), the way in which this model reduction is carried out is often critical
Neural networks in geophysical applications
Neural networks are increasingly popular in geophysics.
Because they are universal approximators, these
tools can approximate any continuous function with an
arbitrary precision. Hence, they may yield important
contributions to finding solutions to a variety of geophysical applications.
However, knowledge of many methods and techniques
recently developed to increase the performance
and to facilitate the use of neural networks does not seem
to be widespread in the geophysical community. Therefore,
the power of these tools has not yet been explored to
their full extent. In this paper, techniques are described
for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size
and architecture
Statistical Mechanics of Recurrent Neural Networks I. Statics
A lecture notes style review of the equilibrium statistical mechanics of
recurrent neural networks with discrete and continuous neurons (e.g. Ising,
coupled-oscillators). To be published in the Handbook of Biological Physics
(North-Holland). Accompanied by a similar review (part II) dealing with the
dynamics.Comment: 49 pages, LaTe
Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier LtdThis Letter is concerned with the analysis problem of exponential stability for a class of discrete-time recurrent neural networks (DRNNs) with time delays. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strict monotonic. Furthermore, the description of the activation functions is more general than the recently commonly used Lipschitz conditions. Under such mild conditions, we first prove the existence of the equilibrium point. Then, by employing a Lyapunov–Krasovskii functional, a unified linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the DRNNs to be globally exponentially stable. It is shown that the delayed DRNNs are globally exponentially stable if a certain LMI is solvable, where the feasibility of such an LMI can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China (05KJB110154), the NSF of Jiangsu Province of China (BK2006064), and the National Natural Science Foundation of China (10471119)
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