A Note of Perfect Nonlinear Functions

2006 ◽  
pp. 259-269 ◽  
Author(s):  
Xiyong Zhang ◽  
Hua Guo ◽  
Jinjiang Yuan
Keyword(s):  
Nonlinear Functions

Multiplicative vs. arbitrary gene action in heterosis.

Genetics ◽  
1992 ◽  
Vol 131 (2) ◽  
pp. 461-469 ◽  
Author(s):  
F W Schnell ◽  
C C Cockerham
Keyword(s):  
Gene Action ◽  
Extensive Literature ◽  
Additive Effects ◽  
Nonlinear Functions ◽  
Epistatic Effects ◽  
Genetic Significance ◽  
The Mean ◽  
The Difference ◽  
Multiplicative Models ◽  
Multiplicative Effects

Abstract In this article we investigate multiplicative effects between genes in relation to heterosis. The extensive literature on heterosis due to multiplicative effects between characters is reviewed, as is earlier work on the genetic description of heterosis. A two-locus diallelic model of arbitrary gene action is used to derive linear parameters for two multiplicative models. With multiplicative action between loci, epistatic effects are nonlinear functions of one-locus effects and the mean. With completely multiplicative action, the mean and additive effects form similar restrictions for all the rest of the effects. Extensions to more than two loci are indicated. The linear parameters of various models are then used to describe heterosis, which is taken as the difference between respective averages of a cross (F1) and its two parent populations (P). The difference (F2 - P) is also discussed. Two parts of heterosis are distinguished: part I arising from dominance, and part II due to additive x additive (a x a)-epistasis. Heterosis with multiplicative action between loci implies multiplicative accumulation of heterosis present at individual loci in part I, in addition to multiplicative (a x a)-interaction in part II. Heterosis with completely multiplicative action can only be negative (i.e., the F1 values must be less than the midparent), but the difference (F2 - P) can be positive under certain conditions. Heterosis without dominance can arise from multiplicative as well as any other nonadditive action between loci, as is exemplified by diminishing return interaction. The discussion enlarges the scope in various directions: the genetic significance of multiplicative models is considered.(ABSTRACT TRUNCATED AT 250 WORDS)

scholarly journals Photonic Reservoir Computer with Output Expansion for Unsupervized Parameter Drift Compensation

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 955
Author(s):  
Jaël Pauwels ◽  
Guy Van der Sande ◽  
Guy Verschaffelt ◽  
Serge Massar
Keyword(s):  
Electronic System ◽  
Nonlinear Functions ◽  
System Complexity ◽  
Trade Off ◽  
Parameter Drift ◽  
Output Layer ◽  
Drift Compensation ◽  
Output Neurons ◽  
Performance Gains

We present a method to improve the performance of a reservoir computer by keeping the reservoir fixed and increasing the number of output neurons. The additional neurons are nonlinear functions, typically chosen randomly, of the reservoir neurons. We demonstrate the interest of this expanded output layer on an experimental opto-electronic system subject to slow parameter drift which results in loss of performance. We can partially recover the lost performance by using the output layer expansion. The proposed scheme allows for a trade-off between performance gains and system complexity.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

An efficient class of fourth-order derivative-free method for multiple-roots

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sunil Kumar ◽  
Deepak Kumar ◽  
Janak Raj Sharma ◽  
Ioannis K. Argyros
Keyword(s):  
Multiple Root ◽  
Second Step ◽  
Optimal Order ◽  
Multiple Roots ◽  
Nonlinear Functions ◽  
New Methods ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Derivative Free Method ◽  
Good Number

Abstract Many optimal order multiple root techniques, which use derivatives in the algorithm, have been proposed in literature. Many researchers tried to construct an optimal family of derivative-free methods for multiple roots, but they did not get success in this direction. With this as a motivation factor, here, we present a new optimal class of derivative-free methods for obtaining multiple roots of nonlinear functions. This procedure involves Traub–Steffensen iteration in the first step and Traub–Steffensen-like iteration in the second step. Efficacy is checked on a good number of relevant numerical problems that verifies the efficient convergent nature of the new methods. Moreover, we find that the new derivative-free methods are just as competent as the other existing robust methods that use derivatives.

Riesz–McNaughton functions and Riesz MV-algebras of nonlinear functions

2017 ◽  
Vol 311 ◽  
pp. 1-14 ◽  
Author(s):  
Antonio Di Nola ◽  
Giacomo Lenzi ◽  
Gaetano Vitale
Keyword(s):  
Nonlinear Functions ◽  
Mv Algebras ◽  
Mcnaughton Functions
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