"DYNAMICAL CONFINEMENT" IN NEURAL NETWORKS

1995 ◽  
Vol 03 (04) ◽  
pp. 1157-1165 ◽  
Author(s):  
C. JÉZÉQUEL ◽  
O. NÉROT ◽  
J. DEMONGEOT
Keyword(s):  
Phase Transition ◽  
Neural Networks ◽  
Invariant Measure ◽  
Hopfield Model ◽  
Stability Boundaries ◽  
Contour Lines ◽  
The Stability ◽  
Unique Invariant Measure ◽  
First Time

Randomisation of a well known mathematical model is proposed (i.e. the Hopfield model for neural networks) in order to facilitate the study of its asymptotic behavior: in fact, we replace the determination of the stability basins for attractors and for stability boundaries by the study of a unique invariant measure, whose distribution function maxima (or respectively, percentile contour lines) correspond to the location of the attractors (or respectively, boundaries of their stability basins). We give the name of "confinement" to this localization of the mass of the invariant measure. We intend to show here that the study of the confinement is in certain cases easier than the study of underlying attractors, in particular if these last are numerous and possess small stability basins (for example, for the first time we calculate the invariant measure in the random Hopfield model in a case for which the deterministic version exhibits many attractors, and after in a case of phase transition).

Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework

2015 ◽  
Vol 18 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Francesco Cordoni ◽  
Luca Di Persio
Keyword(s):  
Invariant Measure ◽  
Stochastic Partial Differential Equation ◽  
Forward Rate ◽  
Infinite Dimensional ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Unique Invariant Measure

In this paper we study a particular class of forward rate problems, related to the Vasicek model, where the driving equation is a linear Gaussian stochastic partial differential equation. We first give an existence and uniqueness results of the related mild solution in infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroup with respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.

scholarly journals Improved Determination of Mercury Complex with Thiomicher’s Ketone by β-Correction Spectrophotometry

2000 ◽  
Vol 83 (1) ◽  
pp. 231-236 ◽  
Author(s):  
Hong-Wen Gao ◽  
Sheng-Yi Zhang ◽  
Su-Mei Ye
Keyword(s):  
Stability Constant ◽  
Nonionic Surfactant ◽  
Molar Absorptivity ◽  
Mercury Complex ◽  
Relative Standard ◽  
Standard Deviations ◽  
Wastewater Samples ◽  
The Stability ◽  
First Time

Abstract Determination of the mercury complex formed with Thiomicher's ketone (TMK) was improved by β-correction spectrophotometry in the presence of a nonionic surfactant at pH 5. The complex formed was Hg(TMK)2, and its true molar absorptivity is reported for the first time: εHg(TMK)2560 = 1.04 × 105 L/mol·cm. In addition, the stability constant of Hg(TMK)2 was equal to 3.64 × 1010 at an ion strength of 0.01 at 20°C. Results from analyses of wastewater samples showed that the relative standard deviations were ≤8.3%, and the recoveries of mercury ranged from 90 to 110%.

A Stability Algorithm for the General Milling Process: Contribution to Machine Tool Chatter Research—7

1968 ◽  
Vol 90 (2) ◽  
pp. 330-334 ◽  
Author(s):  
R. Sridhar ◽  
R. E. Hohn ◽  
G. W. Long
Keyword(s):  
Stability Analysis ◽  
Milling Process ◽  
Stability Boundaries ◽  
Machine Tool Chatter ◽  
Milling Operation ◽  
Cutting Operation ◽  
Differential Difference Equation ◽  
Linear Differential ◽  
The Stability

In this paper, a method of stability analysis for the general milling process is given. The milling operation is described by a linear differential-difference equation with periodic coefficients. An algorithm which can be used in conjunction with the digital computer is developed as a means of analytically determining the stability of this equation. This algorithm will permit the determination of the stability boundaries in the space of controllable parameters associated with a cutting operation and allows more realistic models for milling to be studied than have been attempted up to the present time. The technique is used to predict the stability in an example of a milling operation.

Determination of Poisson’s Ratio by Spherical Indentation Using Neural Networks—Part II: Identification Method

2000 ◽  
Vol 68 (2) ◽  
pp. 224-229 ◽  
Author(s):  
N. Huber ◽  
Ch. Tsakmakis
Keyword(s):  
Neural Networks ◽  
Poisson’S Ratio ◽  
Inverse Function ◽  
Poisson's Ratio ◽  
Spherical Indentation ◽  
Plastic Yield ◽  
Different Depths ◽  
Unloading Stiffness ◽  
First Time

In a previous paper it has been shown that the load and the unloading stiffness are, among others, explicit functions of the Poisson’s ratio, if a spherical indenter is pressed into a metal material. These functions can be inverted by using neural networks in order to determine the Poisson’s ratio as a function of the load and the unloading stiffness measured at different depths. Also, the inverse function possesses as an argument the ratio of the penetration depth and that depth, at which plastic yield occurs for the first time. The latter quantity cannot be measured easily. In the present paper some neural networks are developed in order to identify the value of Poisson’s ratio. After preparing the input data appropriately, two neural networks are trained, the first one being related to Set 2 of the previous paper. In order to avoid an explicit measurement of the yield depth, the second neural network has to be trained in such a way, that its solution intersects with that of Set 2 at the correct value of Poisson’s ratio. This allows to identify Poisson’s ratio with high accuracy within the domain of finite element data.

scholarly journals Tales of the Unexpected: The Case of Zirconium(IV) Complexes with Desferrioxamine

Molecules ◽  
2019 ◽  
Vol 24 (11) ◽  
pp. 2098 ◽  
Author(s):  
Matteo Savastano ◽  
Carla Bazzicalupi ◽  
Giovanni Ferraro ◽  
Emiliano Fratini ◽  
Paola Gratteri ◽  
...  
Keyword(s):  
Stability Constants ◽  
Density Functional ◽  
Maldi Mass Spectrometry ◽  
Binuclear Complexes ◽  
X Ray Scattering ◽  
Complex Solutions ◽  
The Stability ◽  
Ph Range ◽  
First Time

The Zr4+ complexes with desferrioxamine (H3DFO) and its derivatives are the only 89Zr-based imaging agents for proton emission tomography (PET) that have been used so far in clinical trials. Nevertheless, a complete speciation of the Zr4+/H3DFO system in solution has never been performed and the stability constants of the relevant complexes are still unknown. Here we report, for the first time, the speciation of this system in water, performed by potentiometric titrations, and the determination of the stability constants of all complexes formed in the pH range 2.5–11.5. Surprisingly, although desferrioxamine gives rise to very stable 1:1 complexes with Zr4+ (logK = 36.14 for Zr4+ + DFO3− = [ZrDFO]+), 2:2 and 2:3 ones are also formed in solution. Depending on the conditions, these binuclear complexes can be main species in solution. These results were corroborated by small-angle X-ray scattering (SAXS) and MALDI mass spectrometry analyses of complex solutions. Information on complex structures was obtained by means of density functional theory (DFT) calculations.

Investigation of Surface Phase Layers on GaAs after Selective Chemical Etching

2015 ◽  
Vol 1085 ◽  
pp. 91-94
Author(s):  
Oksana N. Zarubina ◽  
Gennady M. Mokrousov ◽  
Alexander G. Touryanski ◽  
Igor V. Pirshin ◽  
Liubov V. Maliy
Keyword(s):  
Phase Distribution ◽  
Theoretical Data ◽  
Selective Dissolution ◽  
Phase Layers ◽  
Interfacial Boundary ◽  
Combination Of Methods ◽  
Elemental Arsenic ◽  
The Stability ◽  
First Time

Normal 0 false false false RU X-NONE X-NONE The combination of methods of voltammetry, Raman spectroscopy, and X-ray reflectometry for the first time has been applied for the more comprehensive investigation of interfacial boundaries of GaAs, i.e. determination of phase distribution and thickness of the phase layers. The conditions for the formation of elemental arsenic on a GaAs surface in the process of selective dissolution are discussed. The stability of interfacial boundaries in air has also been studied. The investigations have shown that air storage lead to the oxidation of formed As0 and reorganization of GaAs interfacial boundary accompanied by the formation of Ga2O3 and As0 as a result of a reaction between As2O3 and GaAs. The results on interfacial boundaries composition were found to be correlated with the theoretical data. /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Обычная таблица"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}

scholarly journals Synthesis and properties of dehydroabietyl glycidyl ether grafted hydroxypropyl chitosan

BioResources ◽  
2020 ◽  
Vol 15 (2) ◽  
pp. 4110-4123
Author(s):  
Wei Guo ◽  
Zhaosheng Cai ◽  
Qi Xu ◽  
Kaiyong Sun ◽  
Xujuan Huang ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Nonionic Surfactant ◽  
Foam Stability ◽  
Glycidyl Ether ◽  
Surface Activities ◽  
The Stability ◽  
Stability Time ◽  
First Time ◽  
Emulsifying Ability

A nonionic surfactant based on chitosan and rosin, i.e. dehydroabietyl glycidyl ether grafted hydroxypropyl chitosan (DAGE-g-HPCS), was synthesized for the first time through reaction between hydroxypropyl chitosan (HPCS) and dehydroabietyl glycidyl ether (DAGE). The surface activities of DAGE-g-HPCS in aqueous solution were investigated via determination of surface tension, and its emulsifying ability was evaluated according to the stability time of emulsion composed of benzene-water with DAGE-g-HPCS as emulsifier; the foam stability was evaluated using the oscillation method. Through modulating the molecular weight of HPCS and the grafting degree (DG) of DAGE-g-HPCS, the emulsion stability and foam stability were surprisingly controllable. Compared to HPCS and specific emulsifier, the stability time of emulsion composed of benzene-water with DAGE-g-HPCS showed a remarkable performance with DG of 16.5% as the emulsifier was 7320 s, and the foam retention of DAGE-g-HPCS with 2.0 g·L-1 was 91.5%. Simultaneously, the critical micelle concentration (CMC) of DAGE-g-HPCS decreased with increased DG, while the emulsifying ability and foam stability exhibited opposite trend. The CMC, emulsifying ability, and foam stability of DAGE-g-HPCS increased with decreased HPCS molecular weight. These results demonstrated that the DAGE-g-HPCS was an excellent surfactant that should be considered as a promising substitute for petrochemical nonionic surfactant.

The Crystal Structure of WC Type ZrTe. Advantages in Chemical Bonding as Contrasted to NiAs Type ZrTe

1999 ◽  
Vol 54 (9) ◽  
pp. 1125-1128 ◽  
Author(s):  
Gissur Örlygsson ◽  
Bernd Harbrecht
Keyword(s):  
Crystal Structure ◽  
Local Minimum ◽  
Structure Type ◽  
Metal Deficiency ◽  
Nias Type Structure ◽  
The Stability ◽  
Nias Type ◽  
First Time ◽  
Extended Hückel Calculations

Single crystals of WC type ZrTe were prepared from the elements. A single crystal structure determination of this structure type was performed for the first time: ZrTe (WC) crystallizes in the hexagonal space group P6̄m2 (No. 187), hP2, Z - 1, a - 377.06(5), c = 386.05(8) pm; 84 reflections, 5 variables, R(F) = 0.037. The distinctions in bonding for ZrTe (WC) and a hypothetical stoichiometric ZrTe crystallizing in the NiAs type structure were analyzed on the basis of extended Hückel calculations. Heteronuclear interactions contribute most strongly to the stability of both structures. Attractive Zr-Zr interactions energetically favour ZrTe (WC) relative to ZrTe (NiAs). The Fermi level of ZrTe (WC) resides in a local minimum of the DOS, whereas that of ZrTe (NiAs) intersects a local DOS maximum, and is pushed up by about 0.5 eV, expressing the decisive destabilization of NiAs type ZrTe. As a consequence, metal deficiency is observed for ZrTe (NiAs), in contrast to ZrTe (WC).

scholarly journals The α–β phase transition in volcanic cristobalite

2014 ◽  
Vol 47 (4) ◽  
pp. 1205-1215 ◽  
Author(s):  
David E. Damby ◽  
Edward W. Llewellin ◽  
Claire J. Horwell ◽  
Ben J. Williamson ◽  
Jens Najorka ◽  
...  
Keyword(s):  
Phase Transition ◽  
Ambient Temperature ◽  
Volcanic Ash ◽  
Phase Identification ◽  
Scanning Calorimetry ◽  
X Ray ◽  
Β Phase ◽  
The Stability ◽  
First Time

Cristobalite is a common mineral in volcanic ash produced from dome-forming eruptions. Assessment of the respiratory hazard posed by volcanic ash requires understanding the nature of the cristobalite it contains. Volcanic cristobalite contains coupled substitutions of Al3+ and Na+ for Si4+; similar co-substitutions in synthetic cristobalite are known to modify the crystal structure, affecting the stability of the α and β forms and the observed transition between them. Here, for the first time, the dynamics and energy changes associated with the α–β phase transition in volcanic cristobalite are investigated using X-ray powder diffraction with simultaneous in situ heating and differential scanning calorimetry. At ambient temperature, volcanic cristobalite exists in the α form and has a larger cell volume than synthetic α-cristobalite; as a result, its diffraction pattern sits between ICDD α- and β-cristobalite library patterns, which could cause ambiguity in phase identification. On heating from ambient temperature, volcanic cristobalite exhibits a lower degree of thermal expansion than synthetic cristobalite, and it also has a lower α–β transition temperature (∼473 K) compared with synthetic cristobalite (upwards of 543 K); these observations are discussed in relation to the presence of Al3+ and Na+ defects. The transition shows a stable and reproducible hysteresis loop with α and β phases coexisting through the transition, suggesting that discrete crystals in the sample have different transition temperatures.

Effect of Heating Treatment of Fresh Rice Bran on Stabilization

2012 ◽  
Vol 602-604 ◽  
pp. 1200-1205
Author(s):  
Zhu Gong ◽  
Guo Ping Yu ◽  
Chao Ran Dou ◽  
Man Xu Xu
Keyword(s):  
Heat Treatment ◽  
Rice Bran ◽  
Peroxidase Activity ◽  
Direct Determination ◽  
Material Resources ◽  
Total Antioxidant ◽  
Heating Treatment ◽  
The Stability ◽  
First Time

In the research of rice bran stabilization, most of the literature only study the lipase which is explained by the changes in free fatty acids in the storage experiment or peroxidase activity. It leads results not comprehensive, extends the experiment time, increases the experimental difficulty and wastes of manpower and material resources. For the first time, the effect of heat treatment on fresh rice bran stability is examined in terms of direct determination of water content, lipase activity, peroxidase activity and total antioxidant capacity. The optimal condition is that 120 degrees for 22 min. The results show that the heat treatment can reduce the enzyme activity of rice bran to improve the stability of rice bran.

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