‘Partition of Unity’ RBF Networks are Universal Function Approximators

ICANN ’94 ◽  
1994 ◽  
pp. 459-462 ◽  
Author(s):  
J. Hakala ◽  
C. Koslowski ◽  
R. Eckmiller
2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Giulio Tononi ◽  
Chiara Cirelli

Sleep must serve an essential, universal function, one that offsets the risk of being disconnected from the environment. The synaptic homeostasis hypothesis (SHY) is an attempt to identify this essential function. Its core claim is that sleep is needed to reestablish synaptic homeostasis, which is challenged by the remarkable plasticity of the brain. In other words, sleep is “the price we pay for plasticity.” In this issue, M. G. Frank reviewed several aspects of the hypothesis and raised several issues. The comments below provide a brief summary of the motivations underlying SHY and clarify that SHY is a hypothesis not about specific mechanisms, but about a universal, essential function of sleep. This function is the preservation of synaptic homeostasis in the face of a systematic bias toward a net increase in synaptic strength—a challenge that is posed by learning during adult wake, and by massive synaptogenesis during development.


Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.


Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 948
Author(s):  
Jenn-Kaie Lain ◽  
Yan-He Chen

By modulating the optical power of the light-emitting diode (LED) in accordance with the electrical source and using a photodetector to convert the corresponding optical variation back into electrical signals, visible light communication (VLC) has been developed to achieve lighting and communications simultaneously, and is now considered one of the promising technologies for handling the continuing increases in data demands, especially indoors, for next generation wireless broadband systems. During the process of electrical-to-optical conversion using LEDs in VLC, however, signal distortion occurs due to LED nonlinearity, resulting in VLC system performance degradation. Artificial neural networks (ANNs) are thought to be capable of achieving universal function approximation, which was the motivation for introducing ANN predistortion to compensate for LED nonlinearity in this paper. Without using additional training sequences, the related parameters in the proposed ANN predistorter can be adaptively updated, using a feedback replica of the original electrical source, to track the LED time-variant characteristics due to temperature variation and aging. Computer simulations and experimental implementation were carried out to evaluate and validate the performance of the proposed ANN predistorter against existing adaptive predistorter schemes, such as the normalized least mean square predistorter and the Chebyshev polynomial predistorter.


2018 ◽  
Vol 171 ◽  
pp. 02005
Author(s):  
Helmut Satz

The relative multiplicities for hadron production in different high energy collisions are in general well described by an ideal gas of all hadronic resonances, except that under certain conditions, strange particle rates are systematically reduced. We show that the suppression factor γs, accounting for reduced strange particle rates in pp, pA and AA collisions at different collision energies, becomes a universal function when expressed in terms of the initial entropy density s0 or the initial temperature T of the produced thermal medium. It is found that γs increases from about 0.5 to 1.0 in a narrow temperature range around the quark-hadron transition temperature Tc ≃ 160 MeV. Strangeness suppression thus disappears with the onset of color deconfinement; subsequently, full equilibrium resonance gas behavior is attained.


2005 ◽  
Vol 64 ◽  
pp. 537-541 ◽  
Author(s):  
Adriano L.I. Oliveira ◽  
Bruno J.M. Melo ◽  
Silvio R.L. Meira
Keyword(s):  

2005 ◽  
Vol 02 (04) ◽  
pp. 601-626 ◽  
Author(s):  
JEOUNG-HEUM YEON ◽  
SUNG-KIE YOUN

A meshfree multiscale method is presented for efficient analysis of solids with strain gradient plastic effects. In the analysis of strain gradient plastic solids, localization due to increased hardening of strain gradient effect appears. Chen-Wang theory is adopted, as a strain gradient plasticity theory. It represents strain gradient effects as an internal variable and retains the essential structure of classical plasticity theory. In this work, the scale decomposition is carried out based on variational form of the problem. Coarse scale is designed to represent global behavior and fine scale to represent local behavior and gradient effect by using the intrinsic length scale. From the detection of high strain gradient region, fine scale region is adopted. Each scale variable is approximated using meshfree method. Meshfree approximation is well suited for adaptivity. As a method of increasing resolution, partition of unity based extrinsic enrichment is used. Each scale problem is solved iteratively. The proposed method is applied to bending of a thin beam and bimaterial shear layer and micro-indentation problems. Size effects can be effectively captured in the results of the analysis.


Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.


Author(s):  
Dazi Li ◽  
Haitao Zhang ◽  
Qibing Jin ◽  
Yanrui Geng
Keyword(s):  

1991 ◽  
Vol 3 (2) ◽  
pp. 246-257 ◽  
Author(s):  
J. Park ◽  
I. W. Sandberg

There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.


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