Topic
Piecewise linear function
About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.
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TL;DR: In this article, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated, and robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated.
46 citations
TL;DR: In this paper, an exact formula for the various measure dimensions of attractors associated with contracting similitudes is given, and an example is constructed showing that for more general affine maps the different measure dimensions are not always equal.
Abstract: An exact formula for the various measure dimensions of attractors associated with contracting similitudes is given. An example is constructed showing that for more general affine maps the various measure dimensions are not always equal.
45 citations
TL;DR: This paper investigates the exact existence and dynamical behaviors of multiple equilibrium points for delayed competitive neural networks with a class of nondecreasing piecewise linear activation functions with 2r(r>=1) corner points and shows that under some conditions, the N-neuron DCNNs can only have (2r+1)^N equilibrium points, which are locally exponentially stable.
45 citations
TL;DR: A bent line quantile regression model is proposed that is theoretically justified and its parameters are of direct biological interests and its parameter estimates are asymptotically valid given the existence of a change-point.
Abstract: Quantile regression, which models the conditional quantiles of the response variable given covariates, usually assumes a linear model. However, this kind of linearity is often unrealistic in real life. One situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates. To analyze such data, we propose a bent line quantile regression model. We derive its parameter estimates, prove that they are asymptotically valid given the existence of a change-point, and discuss several methods for testing the existence of a change-point in bent line quantile regression together with a power comparison by simulation. An example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests.
45 citations
TL;DR: This article constructs and analyzes an electronic circuit that models this class of piecewise linear equations, which combines CMOS logic and RC circuits to model the logical control of the increase and decay of protein concentrations in genetic networks.
Abstract: Ordinary differential equations are often used to model the dynamics and interactions in genetic networks. In one particularly simple class of models, the model genes control the production rates of products of other genes by a logical function, resulting in piecewise linear differential equations. In this article, we construct and analyze an electronic circuit that models this class of piecewise linear equations. This circuit combines CMOS logic and RC circuits to model the logical control of the increase and decay of protein concentrations in genetic networks. We use these electronic networks to study the evolution of limit cycle dynamics. By mutating the truth tables giving the logical functions for these networks, we evolve the networks to obtain limit cycle oscillations of desired period. We also investigate the fitness landscapes of our networks to determine the optimal mutation rate for evolution.
45 citations