The Stability of the Generalized Hopfield Networks in Randomly Asynchronous Mode

1997 ◽  
Vol 10 (6) ◽  
pp. 1109-1116 ◽  
Author(s):  
Jinwen Ma
Keyword(s):  
Asynchronous Mode ◽  
Hopfield Networks ◽  
The Stability

Hyperbolic-Valued Hopfield Neural Networks in Synchronous Mode

2020 ◽  
Vol 32 (9) ◽  
pp. 1685-1696
Author(s):  
Masaki Kobayashi
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Stability Conditions ◽  
Noise Tolerance ◽  
Asynchronous Mode ◽  
High Noise ◽  
Synchronous Mode ◽  
The Stability ◽  
Complex Valued ◽  
Projection Rule

For most multistate Hopfield neural networks, the stability conditions in asynchronous mode are known, whereas those in synchronous mode are not. If they were to converge in synchronous mode, recall would be accelerated by parallel processing. Complex-valued Hopfield neural networks (CHNNs) with a projection rule do not converge in synchronous mode. In this work, we provide stability conditions for hyperbolic Hopfield neural networks (HHNNs) in synchronous mode instead of CHNNs. HHNNs provide better noise tolerance than CHNNs. In addition, the stability conditions are applied to the projection rule, and HHNNs with a projection rule converge in synchronous mode. By computer simulations, we find that the projection rule for HHNNs in synchronous mode maintains a high noise tolerance.

Dynamical Analysis of Continuous Higher-Order Hopfield Networks for Combinatorial Optimization

2005 ◽  
Vol 17 (8) ◽  
pp. 1802-1819 ◽  
Author(s):  
Miguel Atencia ◽  
Gonzalo Joya ◽  
Francisco Sandoval
Keyword(s):  
Combinatorial Optimization ◽  
Fixed Points ◽  
Optimization Problems ◽  
Target Function ◽  
Higher Order ◽  
Dynamical Analysis ◽  
Hopfield Networks ◽  
Combinatorial Optimization Problems ◽  
Continuous Equation ◽  
The Stability

In this letter, the ability of higher-order Hopfield networks to solve combinatorial optimization problems is assessed by means of a rigorous analysis of their properties. The stability of the continuous network is almost completely clarified: (1) hyperbolic interior equilibria, which are unfeasible, are unstable; (2) the state cannot escape from the unitary hypercube; and (3) a Lyapunov function exists. Numerical methods used to implement the continuous equation on a computer should be designed with the aim of preserving these favorable properties. The case of nonhyperbolic fixed points, which occur when the Hessian of the target function is the null matrix, requires further study. We prove that these nonhyperbolic interior fixed points are unstable in networks with three neurons and order two. The conjecture that interior equilibria are unstable in the general case is left open.

Method for Excitation Control of Synchronous Motor in Start and Resynchronization Modes

2021 ◽  
Vol 64 (2) ◽  
pp. 39-43
Author(s):  
Vitalii Syvokobylenko ◽  
◽  
Sergey Derkachev ◽  
Keyword(s):  
Synchronous Motor ◽  
Power Ratio ◽  
Excitation Control ◽  
Asynchronous Mode ◽  
Synchronous Motors ◽  
Additional Resistance ◽  
Instantaneous Values ◽  
The Stability ◽  
Excitation Winding ◽  
Forced Excitation

In the article proposed a method for excitation control of synchronous motor in the starting, self-starting and resynchronization modes, which makes it possible to increase the stability or facilitate the pulling into synchronism of heavily loaded synchronous motors due to the alternating connection of the excitation winding to an additional active resistance or to an exciter with a forced excitation voltage. For this, on the basis of the instantaneous values measurements of the phase currents and stator voltages, the reactive and active powers are determined, and using a criterion equal to the power polynomial from the power ratio, the asynchronous mode is revealed. The control of switching the excitation winding to an additional resistance or to the exciter is car-ried out using another criterion, defined as a derivative of the asynchronous mode criterion. The results of mathematical modeling are presented, which confirm that the proposed method for controlling the excitation of a synchronous motor allows one to identify the asynchronous mode of both excited and non-excited synchronous motors and provide easier resynchronization conditions by increasing the torque of the synchronous motor at low slip values, as well as to ensure successful start and retraction in synchronism loaded synchronous motor.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

1970 ◽  
Vol 28 ◽  
pp. 444-445
Author(s):  
E. R. Kimmel ◽  
H. L. Anthony ◽  
W. Scheithauer
Keyword(s):  
High Temperature ◽  
Metal Matrix ◽  
Oxide Particle ◽  
Oxide Phase ◽  
Dislocation Motion ◽  
Particle Dispersion ◽  
High Temperature Strength ◽  
Strengthening Effect ◽  
Oxide Particles ◽  
The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

Formation and Structure of Casein Micelles in Lactating Mammary Tissue

1970 ◽  
Vol 28 ◽  
pp. 150-151
Author(s):  
Robert J. Carroll ◽  
Marvin P. Thompson ◽  
Harold M. Farrell
Keyword(s):  
Size Distribution ◽  
G Protein ◽  
Milk Proteins ◽  
Mammary Tissue ◽  
Colloidal System ◽  
Casein Micelles ◽  
The Stability

Milk is an unusually stable colloidal system; the stability of this system is due primarily to the formation of micelles by the major milk proteins, the caseins. Numerous models for the structure of casein micelles have been proposed; these models have been formulated on the basis of in vitro studies. Synthetic casein micelles (i.e., those formed by mixing the purified αsl- and k-caseins with Ca2+ in appropriate ratios) are dissimilar to those from freshly-drawn milks in (i) size distribution, (ii) ratio of Ca/P, and (iii) solvation (g. water/g. protein). Evidently, in vivo organization of the caseins into the micellar form occurs in-a manner which is not identical to the in vitro mode of formation.

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