scholarly journals A Tighter Bound for Graphical Models

2001 ◽  
Vol 13 (9) ◽  
pp. 2149-2171 ◽  
Author(s):  
M. A. R. Leisink ◽  
H. J. Kappen
Keyword(s):  
Graphical Models ◽  
Mean Field ◽  
Third Order ◽  
First Order ◽  
Direct Extension ◽  
Odd Order ◽  
Order Polynomial ◽  
The Mean ◽  
Mean Field Bound ◽  
Better Than

We present a method to bound the partition function of a Boltzmann machine neural network with any odd-order polynomial. This is a direct extension of the mean-field bound, which is first order. We show that the third-order bound is strictly better than mean field. Additionally, we derive a third-order bound for the likelihood of sigmoid belief networks. Numerical experiments indicate that an error reduction of a factor of two is easily reached in the region where expansion-based approximations are useful.

Calibration of pneumotachographs using a calibrated syringe

2003 ◽  
Vol 95 (2) ◽  
pp. 571-576 ◽  
Author(s):  
Yongquan Tang ◽  
Martin J. Turner ◽  
Johnny S. Yem ◽  
A. Barry Baker
Keyword(s):  
Calibration Method ◽  
Linear Range ◽  
Data Sets ◽  
Constant Flow ◽  
Calibration Constant ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Calibration Curves ◽  
Order Polynomial ◽  
Better Than

Pneumotachograph require frequent calibration. Constant-flow methods allow polynomial calibration curves to be derived but are time consuming. The iterative syringe stroke technique is moderately efficient but results in discontinuous conductance arrays. This study investigated the derivation of first-, second-, and third-order polynomial calibration curves from 6 to 50 strokes of a calibration syringe. We used multiple linear regression to derive first-, second-, and third-order polynomial coefficients from two sets of 6–50 syringe strokes. In part A, peak flows did not exceed the specified linear range of the pneumotachograph, whereas flows in part B peaked at 160% of the maximum linear range. Conductance arrays were derived from the same data sets by using a published algorithm. Volume errors of the calibration strokes and of separate sets of 70 validation strokes ( part A) and 140 validation strokes ( part B) were calculated by using the polynomials and conductance arrays. Second- and third-order polynomials derived from 10 calibration strokes achieved volume variability equal to or better than conductance arrays derived from 50 strokes. We found that evaluation of conductance arrays using the calibration syringe strokes yields falsely low volume variances. We conclude that accurate polynomial curves can be derived from as few as 10 syringe strokes, and the new polynomial calibration method is substantially more time efficient than previously published conductance methods.

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation

2011 ◽  
Vol 172-174 ◽  
pp. 608-617 ◽  
Author(s):  
William A. Soffa ◽  
David E. Laughlin ◽  
Nitin Singh
Keyword(s):  
Nearest Neighbor ◽  
Binary Solution ◽  
Mean Field ◽  
Lattice Relaxation ◽  
Two Phase ◽  
First Order ◽  
Tetragonal Lattice ◽  
Wide Range ◽  
Third Law Of Thermodynamics ◽  
The Mean

The tetragonal lattice relaxation has been included in the thermodynamics of the fcc→L10ordering to produce a first-order character of the transition within the mean field description of the binary solution energetics. In view of growing interest in such systems e.g. Fe-Pd and Co-Pt alloys, which display a wide range of applications relevant to current and futuristic technologies, the fcc→L10two-phase field is re-examined utilizing a generalized Bragg-Williams approach including first and second nearest neighbor interactions. The thermodynamic behavior is examined in the limit of T→0K and discussed in terms of the implications of the Third Law of Thermodynamics.

Microstructure Evaluation for Time Dependent Nucleation Protocols in KJMA Kinetics

1999 ◽  
Vol 580 ◽  
Author(s):  
Eloi Pineda ◽  
Daniel Crespo
Keyword(s):  
Mean Field ◽  
Quantitative Agreement ◽  
Nucleation And Growth ◽  
Time Dependent ◽  
First Order ◽  
Microstructure Evaluation ◽  
The Mean ◽  
Dependent Growth ◽  
First Order Phase

AbstractThe microstructure developed in a first order phase transformation is obtained using a populational extension of the Kolmogorov, Johnson-Mehl and Avrami (KJMA) model, PKJMA. PKJMA allows one to determine the grain size distribution resulting from nucleation and growth kinetics. PKJMA is grounded on the mean field hypothesis that the free space around the growing grains is randomly distributed, independent of the grain radius. Although this approach is perfectly valid for the case of constant nucleation, a detailed analysis of the model shows that this hypothesis does not hold in the case of time dependent nucleation protocols or pre-existing nuclei. In this work, the PKJMA model has been improved by estimating the average free surface around the grains as a function of their radius and the time elapsed since nucleation. The resulting model gives quantitative determination of the microstructure developed under a variety of nucleation and growth processes: pre-existing nuclei, constant nucleation, and the combination of both mechanisms, constant and radius dependent growth rates. Comparison with Monte Carlo simulations, showing a quantitative agreement will be presented.

scholarly journals Comparative Results of Regional and Residual Anomalies with the Upward Continuation, Moving Average, and Polynomial Methods for Magnetic Data

2020 ◽  
Vol 2 (2) ◽  
pp. 90-93
Author(s):  
Luvera Deva Intan Indrawati ◽  
Rina Dwi Indriana ◽  
Irham Nurwidyanto
Keyword(s):  
Moving Average ◽  
Continuation Method ◽  
Second Order ◽  
Magnetic Data ◽  
Third Order ◽  
First Order ◽  
Upward Continuation ◽  
Order Polynomial ◽  
Matlab Programming ◽  
Polynomial Methods

Geophysics programing of regional and residual anomaly separation on Magnetic data has been carried out with the results compared with the upward continuation method in the OasisMontaj software. Separation of anomalies with moving average and polynomial methods is processed using Matlab programming. The orders used in the polynomial method are first-order, second-order and third-order. Comparison is done by calculating the match value. The chosen matching method is autocorrelation. Correlation of residual magnetic anomalies resulting from upward continuation (Magpick) to moving averages, 1st-order polynomials, 2nd-order polynomials and 3rd-order polynomials. Correlation values obtained for the moving average method are 0.9604, first order polynomial 0.9072, 2nd order polynomial 0.9482 and third order polynomial 0.6057. The moving average and second order polynomial methods can be used as a substitute method if we do not use the upward continuation method.

VEGETATIVE PROPAGATION OF CONIFERS: XI. EFFECTS OF TYPE OF CUTTING ON THE ROOTING OF NORWAY SPRUCE CUTTINGS

1942 ◽  
Vol 20c (2) ◽  
pp. 116-121 ◽  
Author(s):  
J. L. Farrar ◽  
N. H. Grace
Keyword(s):  
Norway Spruce ◽  
Vegetative Propagation ◽  
Root Length ◽  
Early Spring ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Sphagnum Peat ◽  
Growth Development ◽  
Better Than

Full length Norway spruce cuttings, with and without a heel of old wood, were collected from the lower part of the tree at semimonthly intervals from July to October and were propagated in several media in outside frames.Plain cuttings generally rooted better than cuttings with a heel of old wood, as judged by percentage rooted and the number and lengths of root. Heels, however, for'summer collections favoured survival and rooting in sand, and root length in sand–peat. In several experiments involving early spring collections propagated in sand, the presence or absence of heels had little effect on the responses of the cuttings.A late October collection involved six types of plain cuttings taken from the lower part of the tree and propagated in two different sand–peat media. In sedge peat medium there was little difference in the rooting of second order terminal, second order large lateral, second order small lateral, or third order lateral cuttings, the average rooting being 90%. Third order lateral cuttings showed an inferior development of new growth. The percentage of first order terminal cuttings rooted was 67%; these had markedly superior new growth development; when shortened, only 32% of such cuttings rooted. Irregular differences between the types of cutting occurred in the inferior sphagnum peat medium.

Calculation of the thermodynamic quantities of perovskite metal organics DMAKCr and perovskite HyFe close to the weakly first-order relaxor-like structural transformation using the mean field theory

2019 ◽  
Vol 33 (11) ◽  
pp. 1950103 ◽  
Author(s):  
H. Yurtseven ◽  
Ö. Tarı
Keyword(s):  
Field Theory ◽  
Field Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Excess Heat Capacity ◽  
Mean Field Model ◽  
First Order ◽  
Entropy Formula ◽  
Inverse Susceptibility ◽  
The Mean

Weakly first-order or nearly second-order phase transitions occurring in metal–organic frameworks (MOFs), particularly in DMAKCr and perovskite HyFe, are studied under the mean field model by using the observed data from the literature. In this work, mainly thermal and magnetic properties among various physical properties which have been reported in the literature for those MOFs are studied by the mean field theory. By expanding the free energy in terms of the magnetization (order parameter), the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S), latent heat (L), magnetization (M) and the inverse susceptibility ([Formula: see text]) are calculated as a function of temperature close to the weakly first-order phase transition within the Landau phenomenological model which is fitted to the experimental data from the literature for C[Formula: see text] (DMAKCr and perovskite HyFe) and for magnetization M (HyFe). Our predictions of the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S) agree below T[Formula: see text] with the observed data within the temperature intervals studied for DMAKCr and perovskite HyFe. From our predictions, we find that magnetization decreases continuously whereas the inverse susceptibility decreases linearly with increasing temperature toward the transition temperature in those MOFs as expected for a weakly first-order transition from the mean field model.

scholarly journals Relation of the average interaction field with the coercive and interaction field distributions in First order reversal curve diagrams of nanowire arrays

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Y. G. Velázquez ◽  
A. Lobo Guerrero ◽  
J. M. Martínez ◽  
E. Araujo ◽  
M. R. Tabasum ◽  
...  
Keyword(s):  
Field Distribution ◽  
Coercive Field ◽  
Mean Field ◽  
Full Width ◽  
Switching Field ◽  
Distribution Profile ◽  
First Order ◽  
Interaction Field ◽  
The Mean ◽  
Switching Field Distribution

AbstractFirst-order reversal curve diagrams, or FORC diagrams, have been studied to determine if the widths of their distributions along the interaction and coercivity axes can be related to the mean-field magnetization dependent interaction field (MDIF). Arrays of nanowires with diameters ranging from 18 up to 100 nm and packing fractions varying from 0.4 to 12% have been analyzed. The mean-field MDIF has been measured using the remanence curves and used as a measuring scale on the FORC diagrams. Based on these measurements, the full width of the interaction field distribution and the full width at half maximum (FWHM) of the FORC distribution profile along the interaction field direction are shown to be proportional to the MDIF, and the relation between them is found. Moreover, by interpreting the full width of the coercive field distribution in terms of the dipolar induced shearing, a simple relation is found between the width of this distribution and the MDIF. Furthermore, we show that the width of the FORC distribution along the coercive field axis is equal to the width of the switching field distribution obtained by the derivation of the DC remanence curve. This was further verified with the switching field distribution determined using in-field magnetic force microscopy (MFM) for very low density nanowires. The results are further supported by the good agreement found between the experiments and the values calculated using the mean-field model, which provides analytical expressions for both FORC distributions.

A FIRST ORDER PHASE TRANSITION IN ISING FERRIMAGNETS

1995 ◽  
Vol 09 (21) ◽  
pp. 1347-1351 ◽  
Author(s):  
HASAN M. AL MUKADAM ◽  
DIMO I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
First Order ◽  
First Order Phase Transition ◽  
Exchange Constants ◽  
The Mean ◽  
First Order Phase ◽  
Ising Spins

The mean field theory is used for the analysis of a two-sublattice system of Ising spins, which describes ferro-, antiferro-, and ferrimagnetic orderings. It is proven that the phase transition in these systems is of a first order when the exchange constants of the sublattices are different. The free energy, the order parameter profiles and the latent heat of the phase transition are calculated for almost equivalent sublattices.

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