Low-Complexity Equalizer based on Volterra Series and Piecewise Linear Function for DML-based IM/DD System

2020 ◽  
Author(s):  
Yukui Yu ◽  
Tianwai Bo ◽  
Yi Che ◽  
Daeho Kim ◽  
Hoon Kim
Keyword(s):  
Linear Function ◽  
Volterra Series ◽  
Piecewise Linear ◽  
Low Complexity ◽  
Piecewise Linear Function

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

Recognition of handwritten digits using a neural network based on the piecewise linear function

1994 ◽  
Author(s):  
Hongyu Liu ◽  
Yialei Wang ◽  
Peimao Sun ◽  
Tianyun Zhang ◽  
Rong Jiang
Keyword(s):  
Neural Network ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function

MAXIMUM DYNAMIC RANGE OF BIFURCATION OF CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 471-481 ◽  
Author(s):  
A. A. A. NASSER ◽  
E. E. HOSNY ◽  
M. I. SOBHY
Keyword(s):  
Linear Function ◽  
Dynamic Range ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Bifurcation Parameter ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Simulation Results

This paper includes a method for detecting the maximum possible range of bifurcations based upon the multilevel oscillation technique. An application of the method to Chua's circuit, and new simulation results using the slope of the piecewise-linear function as a bifurcation parameter are presented.

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