scholarly journals Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 143
Author(s):  
Alexis Thibault ◽  
Lénaïc Chizat ◽  
Charles Dossal ◽  
Nicolas Papadakis
Keyword(s):  
Lyapunov Function ◽  
Global Convergence ◽  
Optimal Transport ◽  
Bregman Projection ◽  
Projection Operators ◽  
Simple Method ◽  
Order Of Magnitude ◽  
Adaptive Choice ◽  
Bregman Projections ◽  
Local Convergence Analysis

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes.

Evaluation of the Service Performance of Ships

2005 ◽  
Vol 42 (04) ◽  
pp. 177-183
Author(s):  
Poul Andersen ◽  
Anne-Sophie Borrod ◽  
Hervé Blanchot
Keyword(s):  
Input Data ◽  
High Efficiency ◽  
Service Performance ◽  
The Other ◽  
Simple Method ◽  
Propulsive Efficiency ◽  
Order Of Magnitude ◽  
Time Periods

A simple method has been established for the evaluation of the service performance of ships. Input data are easily collected daily on board and transformed to a well-defined condition that makes possible the comparison between ships, for instance, sister ships, and between different time periods of voyages for the same ship. The procedure has been applied to two ships that are identical, with the only exception that one has a conventional propeller, whereas the other one is fitted with a high-efficiency propeller of the KAPPEL type. The results are obtained from a period of 2 years steaming for both vessels. They clearly confirm the increase of propulsive efficiency obtained with the KAPPEL propeller in the order of magnitude of 4%.

A Simple Method for Elastic Analysis of Grillages

1968 ◽  
Vol 12 (02) ◽  
pp. 153-159
Author(s):  
Pin-Yu Chang
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Computer Time ◽  
Design Tool ◽  
Matrix Transformations ◽  
Simple Method ◽  
Elastic Foundations ◽  
Beam Analysis ◽  
Order Of Magnitude ◽  
Desk Calculator

The theory of beams supported by elastic foundations has been shown to be particularly well-suited to the analysis of grillage beams [1, 2, 3[.2 This theory leads to a far more general formulation regarding the types of structures amenable to analysis than that offered by the orthotropic plate theory. As compared to the methods of finite element theory, the theory of beams supported by elastic foundations decreases the computer time by an order of magnitude, thus making the analysis particularly valuable as a design tool. This paper shows that the measurement of the grillage beam analysis based upon the elastic foundation concept can be further simplified by certain matrix transformations that uncouple the deflection equations. The problem has, in fact, been simplified to such an extent that many large grillages can be analyzed with the aid of a desk calculator. Whenever comparison with results obtained from finite element methods has been possible, it has been found that, for all practical purposes, complete correlation exists.

Assessment on the Collection Efficiency of an Aerosol Sampler in Micro and Nanoparticles Environment

2014 ◽  
Vol 609-610 ◽  
pp. 483-488 ◽  
Author(s):  
Yi Yang ◽  
Ping Mao ◽  
Shu Yan Feng ◽  
Jin Hua Zhang
Keyword(s):  
Collection Efficiency ◽  
Cascade Impactor ◽  
Test Results ◽  
Simple Method ◽  
Workplace Environment ◽  
Aerosol Nanoparticles ◽  
Micrometer Particle ◽  
In Series ◽  
Order Of Magnitude ◽  
Assessment Result

The collection efficiency (CE) of an aerosol sampler is usually assessed dependently by using a sampler with higher CE and higher sampling accuracy or comparing the grain size distribution, concentration and/or other characteristics of the collected dust to that of the original dust, instead of the sampler itself. To establish a simple method for the assessment on the collection efficiency (CE) of an aerosol sampler, a self-dependent method was derived to calculate the CE of an aerosol sampler, which was patented with the number of ZL200910233001.X by the State Intellectual Property Office of China. According to the patent method, two or more uniform aerosol samplers of the same model were connected in series the inlet of a sampler was connected directly with the outlet of another sampler. The CE (η) of the aerosol sampler can be calculated by a simple equation as:η=1-m2/m1, in whichm1andm2is the weight of the aerosol particles collected by sampler 1# and sampler 2# in the connection sequence, respectively. A cascade impactor sampler was used to sample in a micrometer particle (d50=2.5 μm) aerosol environment and a nanoparticle (d50=42 nm) aerosol environment which were formed artificially in a glove box, as well as a workplace environment which manufactured nanometer powders. The sampling test results indicated that the cascade impactor sampler showed relative high CE (99.51%) for micrometer aerosol but a little bit low CE (95.2%) for nanoparticle aerosol. However, a low CE (93.93%) was calculated out by the method because of low concentration aerosol nanoparticles in the workplace environment, which result to big testing errors. It was found that the assessment result on collection efficiency of a sampler is highly affected by the subsequent analytical methods and detection accuracies after the sampling process. If the precision of the electronic balance was improved to a reasonable higher order of magnitude, the cascade impactor sampler can hopefully show much higher collection efficiency on nanoparticle aerosols.

scholarly journals POVM construction: A simple recipe with applications to symmetric states

2017 ◽  
Vol 15 (06) ◽  
pp. 1750042
Author(s):  
Swarnamala Sirsi ◽  
Karthik Bharath ◽  
S. P. Shilpashree ◽  
H. S. Smitha Rao
Keyword(s):  
Orthonormal Basis ◽  
Dimensional Space ◽  
Rotation Group ◽  
Dimensional Subspace ◽  
Irreducible Representations ◽  
Projection Operators ◽  
Simple Method ◽  
Positive Operator Valued Measures ◽  
Higher Dimensional ◽  
Symmetric States

We propose a simple method for constructing positive operator-valued measures (POVMs) using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the [Formula: see text]-dimensional subspace of the [Formula: see text]-dimensional Hilbert space of [Formula: see text] qubits comprising the permutationally symmetric states. Using the notion of vectorization, the constructed POVMs are interpretable as projection operators in a higher-dimensional space. We then describe a method to physically realize the constructed POVMs for symmetric states using the Clebsch–Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones.

Population dynamics using temporal series analysis in a industrial two-stage activated sludge pilot plant

1998 ◽  
Vol 37 (4-5) ◽  
pp. 255-258
Author(s):  
Eloy Bécares ◽  
Susana Romo ◽  
Margarita Fernandez-Aláez
Keyword(s):  
Activated Sludge ◽  
Pilot Plant ◽  
General Pattern ◽  
Industrial Effluents ◽  
Oscillation Period ◽  
Two Stage ◽  
Simple Method ◽  
Density Dependent ◽  
Series Analysis ◽  
Order Of Magnitude

A time series analysis using an autocorrelation function (ACF) was used to assess the relative importance of density (DD) and non density-dependent - (NDD) factors on microfauna abundance of a two-stage activated sludge pilot plant treating industrial effluents. Although some previous work has detected a carrying capacity for the total microfauna abundance in both reactors, ACF showed a general pattern of non-density dependent abundance regulation. Stationarity due to density-dependent factors was observed for the two major species in the first reactor, the sessile Opercularia asymmetrica and the crawling Chilodonatella minuta. There was no evidence of bacterial competition and only weak evidence of floc surface competition. It is possible that the main driving factor in the first reactor was the constant wasting rate. In the second reactor, the microfauna was clearly dependent on substrate fluctuations, attaining densities one order of magnitude higher than in the first reactor. This was probably a consequence of its longer sludge age. An 8-day oscillation period was detected only in the first reactor, while a second oscillation of about 30 days was observed in both the first and second reactors. ACF was shown to be a simple method for discriminating between DD and NDD factors influencing species and total abundance dynamics.

On the demonstration of electric lines of force, and a new method of measuring the electric moment of tourmaline

1930 ◽  
Vol 26 (4) ◽  
pp. 491-495 ◽  
Author(s):  
M. E. Maurice
Keyword(s):  
Electric Field ◽  
New Method ◽  
Electric Moment ◽  
Simple Method ◽  
Charged Body ◽  
Order Of Magnitude ◽  
Lines Of Force ◽  
Liquid Surfaces

1. A description of a simple method of demonstrating electric lines of force around a charged body is given.2. The instability of liquid surfaces in an electric field is used to obtain an idea of the order of magnitude of the charge developed on tourmaline on cooling through about 140° C.3. A new method of measuring the electric moment of tourmaline is described.

scholarly journals Design and performance of a Nafion dryer for continuous operation at CO<sub>2</sub> and CH<sub>4</sub> air monitoring sites

2013 ◽  
Vol 6 (5) ◽  
pp. 1217-1226 ◽  
Author(s):  
L. R. Welp ◽  
R. F. Keeling ◽  
R. F. Weiss ◽  
W. Paplawsky ◽  
S. Heckman
Keyword(s):  
Water Vapor ◽  
Ambient Air ◽  
Gas Mixing ◽  
Inlet System ◽  
Simple Method ◽  
Mixing Ratios ◽  
Peak Broadening ◽  
Order Of Magnitude ◽  
And Performance ◽  
The Impact

Abstract. In preparation for routine deployment in a network of greenhouse gas monitoring stations, we have designed and tested a simple method for drying ambient air to near or below 0.2% (2000 ppm) mole fraction H2O using a Nafion dryer. The inlet system was designed for use with cavity ring-down spectrometer (CRDS) analyzers such as the Picarro model G2301 that measure H2O in addition to their principal analytes, in this case CO2 and CH4. These analyzers report dry-gas mixing ratios without drying the sample by measuring H2O mixing ratio at the same frequency as the main analytes, and then correcting for the dilution and peak broadening effects of H2O on the mixing ratios of the other analytes measured in moist air. However, it is difficult to accurately validate the water vapor correction in the field. By substantially lowering the amount of H2O in the sample, uncertainties in the applied water vapor corrections can be reduced by an order of magnitude or more, thus eliminating the need to determine instrument-specific water vapor correction coefficients and to verify the stability over time. Our Nafion drying inlet system takes advantage of the extra capacity of the analyzer pump to redirect 30% of the dry gas exiting the Nafion to the outer shell side of the dryer and has no consumables. We tested the Nafion dryer against a cryotrap (−97 °C) method for removing H2O and found that in wet-air tests, the Nafion reduces the CO2 dry-gas mixing ratios of the sample gas by as much as 0.1 ± 0.01 ppm due to leakage across the membrane. The effect on CH4 was smaller and varied within ± 0.2 ppb, with an approximate uncertainty of 0.1 ppb. The Nafion-induced CO2 bias is partially offset by sending the dry reference gases through the Nafion dryer as well. The residual bias due to the impact of moisture differences between sample and reference gas on the permeation through the Nafion was approximately −0.05 ppm for CO2 and varied within ± 0.2 ppb for CH4. The uncertainty of this partial drying method is within the WMO compatibility guidelines for the Northern Hemisphere, 0.1 ppm for CO2 and 2 ppb for CH4, and is comparable to experimentally determining water vapor corrections for each instrument but less subject to concerns of possible drift in these corrections.

scholarly journals Ordered Array of Metal Particles on Semishell Separated with Ultrathin Oxide: Fabrication and SERS Properties

Coatings ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 20
Author(s):  
Xianglin Li ◽  
Zhiwei Wang ◽  
Chiew Tan ◽  
Zexiang Shen ◽  
Alfred Tok
Keyword(s):  
Self Assembly ◽  
Field Enhancement ◽  
Atomic Layer ◽  
Metal Particles ◽  
Simple Method ◽  
Solar Water Splitting ◽  
Plasmonic Structure ◽  
Ordered Array ◽  
Order Of Magnitude ◽  
Local Electric Field Enhancement

Metal particles in gap cavities provide an interesting system to achieve hybrid local surface plasmon modes for local field enhancement. Here, we demonstrate a relatively simple method to fabricate Ag nanoparticles positioned on Ag semishells separated by a thin (~5 nm) dielectric layer. The obtained structure can provide strong local electric field enhancement for surface-enhanced Raman scattering (SERS). The fabrication of the ordered array structure was realized by nanosphere self-assembly, atomic layer deposition, and metal thin-film dewetting. Numerical simulation proved that, compared to the conventional metal semishell arrays, the additional Ag particles introduce extra hot spots particularly in the valley regions between adjacent Ag semishells. As a result, the SERS enhancement factor of the metal semishell-based plasmonic structure could be further improved by an order of magnitude. The developed novel plasmonic structure also shows good potential for application in plasmon-enhanced solar water-splitting devices.

A simple method to fabricate poly(aniline-co-pyrrole) with highly improved electrical conductivity via pre-polymerization

RSC Advances ◽  
2016 ◽  
Vol 6 (17) ◽  
pp. 13780-13785 ◽  
Author(s):  
Xianghui Ou ◽  
Xuecheng Xu
Keyword(s):  
Electrical Conductivity ◽  
Molar Ratio ◽  
Simple Method ◽  
Order Of Magnitude ◽  
Poly Aniline

The electrical conductivity of poly(aniline-co-pyrrole) by proper pre-polymerization achieved the same order of magnitude (10−1 S cm−1) with their homopolymers, or even slightly higher, which was not affected by the molar ratio of two monomers.

The Quadratic Curve and the Trajectory in the Shear Zone in Metal Cutting

1975 ◽  
Vol 97 (3) ◽  
pp. 1105-1111 ◽  
Author(s):  
J. H. L. The
Keyword(s):  
Shear Zone ◽  
Metal Cutting ◽  
Fine Grid ◽  
Simple Method ◽  
Quadratic Curve ◽  
Parallel Lines ◽  
Order Of Magnitude ◽  
Experimental Errors ◽  
Best Fit ◽  
Cutting Speeds

The quadratic curve was investigated as an approximation of the streamline in the steady-state shear zone during metal cutting. Experimentally, a very fine grid of parallel lines (spacing 25 μ, depth 6 μ) was inscribed on the work face through a simple method which eliminates the problems associated with the photographic and etching techniques. Quick stops were taken using an explosive device for cutting speeds of 50, 150, and 250 m/min. Next, several quadratic curves were fitted to the experimental streamline, which was measured at six points along its path. The two tangents at the start and end of the shear zone were also measured. Of the three types (ellipse, hyperbola, and parabola) studied, the hyperbola and, specifically, the rectangular hyperbola (x2 − y2 = c2) gave the best fit with experiment. Trajectory deviation in these cases is &lt;1 percent and the strain-rate deviation is &lt;6 percent. These are in the order of magnitude of the experimental errors.

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