scholarly journals An analytic expression of relative approximation error for a class of evolutionary algorithms

2016 ◽  
Author(s):  
Jun He
Keyword(s):  
Evolutionary Algorithms ◽  
Approximation Error ◽  
Analytic Expression ◽  
Relative Approximation

Complexity issues for the symmetric interval eigenvalue problem

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Milan Hladík
Keyword(s):  
Computational Complexity ◽  
Eigenvalue Problem ◽  
Relative Error ◽  
Symmetric Matrix ◽  
Approximation Error ◽  
Np Hard ◽  
Approximation Errors ◽  
The Matrix ◽  
Polynomially Solvable ◽  
Relative Approximation

AbstractWe study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error. We show in which error factors the problem is polynomially solvable and in which factors it becomes NP-hard.

scholarly journals MERACLE: Constructive Layer-Wise Conversion of a Tensor Train into a MERA

2020 ◽  
Author(s):  
Kim Batselier ◽  
Andrzej Cichocki ◽  
Ngai Wong
Keyword(s):  
Approximation Error ◽  
Low Rank ◽  
Multi Scale ◽  
Crucial Component ◽  
Procrustes Problem ◽  
First Time ◽  
And Storage ◽  
Relative Approximation ◽  
Matrix Factors ◽  
New Algorithms

Abstract In this article, two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is never explicitly computed but stored as a tensor train instead, resulting in both computationally and storage efficient algorithms. Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error. In addition, an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors, which are a crucial component in the construction of a low-rank MERA. Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

Opponent Center-Surround Contrast: Colour to Grey Conversion

2020 ◽  
Vol 2020 (1) ◽  
pp. 105-108
Author(s):  
Ali Alsam
Keyword(s):  
Evolutionary Algorithms ◽  
Three Dimensional ◽  
The State ◽  
Colour Space ◽  
Vision Science ◽  
State Of Art ◽  
Over Time

Vision is the science that informs us about the biological and evolutionary algorithms that our eyes, opticnerves and brains have chosen over time to see. This article is an attempt to solve the problem of colour to grey conversion, by borrowing ideas from vision science. We introduce an algorithm that measures contrast along the opponent colour directions and use the results to combine a three dimensional colour space into a grey. The results indicate that the proposed algorithm competes with the state of art algorithms.

Applied Process Simulation-Driven Oil and Gas Separation Plant Optimization using Surrogate Modeling and Evolutionary Algorithms

2019 ◽  
Author(s):  
Anders Andreasen
Keyword(s):  
Evolutionary Algorithms ◽  
Gas Separation ◽  
Oil And Gas ◽  
Optimal Solution ◽  
Computer Experiment ◽  
Latin Hypercube Sampling ◽  
Surrogate Models ◽  
Inlet Temperature ◽  
Separation Plant ◽  
Separation Stage

In this article the optimization of a realistic oil and gas separation plant has been studied. Two different fluids are investigated and compared in terms of the optimization potential. Using Design of Computer Experiment (DACE) via Latin Hypercube Sampling (LHS) and rigorous process simulations, surrogate models using Kriging have been established for selected model responses. The surrogate models are used in combination with a variety of different evolutionary algorithms for optimizing the operating profit, mainly by maximizing the recoverable oil production. A total of 10 variables representing pressure and temperature various key places in the separation plant are optimized to maximize the operational profit. The optimization is bounded in the variables and a constraint function is included to ensure that the optimal solution allows export of oil with an RVP < 12 psia. The main finding is that, while a high pressure is preferred in the first separation stage, apparently a single optimal setting for the pressure in downstream separators does not appear to exist. In the second stage separator apparently two different, yet equally optimal, settings are revealed. In the third and final separation stage a correlation between the separator pressure and the applied inlet temperature exists, where different combinations of pressure and temperature yields equally optimal results.<br>

THE MODEL FOR MANAGING INVESTMENTS IN THE MOSCOW ENVIRONMENT BASED ON A POWER REGRESSION EQUATION

2020 ◽  
Vol 2 (7) ◽  
pp. 91-99
Author(s):  
E. V. KOSTYRIN ◽  
◽  
M. S. SINODSKAYA ◽  
Keyword(s):  
Solid Waste ◽  
Influencing Factors ◽  
Pair Correlation ◽  
Approximation Error ◽  
Regression Equation ◽  
Regression Equations ◽  
The Impact ◽  
The Relationship ◽  
Average Approximation ◽  
Average Approximation Error

The article analyzes the impact of certain factors on the volume of investments in the environment. Regression equations describing the relationship between the volume of investment in the environment and each of the influencing factors are constructed, the coefficients of the Pearson pair correlation between the dependent variable and the influencing factors, as well as pairwise between the influencing factors, are calculated. The average approximation error for each regression equation is determined. A correlation matrix is constructed and a conclusion is made. The developed econometric model is implemented in the program of separate collection of municipal solid waste (MSW) in Moscow. The efficiency of the model of investment management in the environment is evaluated on the example of the growth of planned investments in the activities of companies specializing in the export and processing of solid waste.

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