Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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01 Mar 1993TL;DR: The authors describe a multinetwork, or modular, neural network architecture that learns to perform control tasks using a piecewise control strategy that is described in a probabilistic framework and learning algorithms that perform gradient ascent in a log-likelihood function are discussed.
Abstract: The authors describe a multinetwork, or modular, neural network architecture that learns to perform control tasks using a piecewise control strategy. The architecture's networks compete to learn the training patterns. As a result, a plant's parameter space is adaptively partitioned into a number of regions, and a different network learns a control law in each region. This learning process is described in a probabilistic framework and learning algorithms that perform gradient ascent in a log-likelihood function are discussed. Simulations show that the modular architecture's performance is superior to that of a single network on a multipayload robot motion control task. >
190 citations
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TL;DR: The algorithm discussed here uses only scalar Riemann solvers and Satisfaction of a set of Kruzkov-type entropy inequalities is established for the limit solution, from which geometric entropy conditions follow.
Abstract: Convergence is established for a scalar finite difference scheme, based on the Godunov or Engquist--Osher (EO) flux, for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient. Other works in this direction have established convergence for methods employing the solution of 2 × 2 Riemann problems. The algorithm discussed here uses only scalar Riemann solvers. Satisfaction of a set of Kruzkov-type entropy inequalities is established for the limit solution, from which geometric entropy conditions follow. Assuming a piecewise constant coefficient, it is shown that these conditions imply L1-contractiveness for piecewise C1 solutions, thus extending a well-known theorem.
190 citations
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TL;DR: A sufficient condition is obtained to ensure that n-neuron recurrent neural networks can have (4k-1)n equilibrium points and (2k)n of them are locally exponentially stable, which improves and extends the existing stability results in the literature.
Abstract: In this brief, stability of multiple equilibria of recurrent neural networks with time-varying delays and the piecewise linear activation function is studied. A sufficient condition is obtained to ensure that n-neuron recurrent neural networks can have (4k-1)n equilibrium points and (2k)n of them are locally exponentially stable. This condition improves and extends the existing stability results in the literature. Simulation results are also discussed in one illustrative example.
189 citations
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TL;DR: A new effective method for sequential adaptive segmentation is proposed, which is based on parallel application of two sequential parameter estimation procedures, which demonstrates the good detection properties of the algorithm and in particular an excellent ability to allocate the segment boundaries even within a sequence of short segments.
189 citations
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TL;DR: This work uses the lowest possible approximation order, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Stokes equation and Darcy's equation, applying an edge stabilization term to avoid locking.
189 citations