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.

Biologically Inspired Spiking Neurons : Piecewise Linear Models and Digital Implementation

Abstract: There has been a strong push recently to examine biological scale simulations of neuromorphic algorithms to achieve stronger inference capabilities. This paper presents a set of piecewise linear spiking neuron models, which can reproduce different behaviors, similar to the biological neuron, both for a single neuron as well as a network of neurons. The proposed models are investigated, in terms of digital implementation feasibility and costs, targeting large scale hardware implementation. Hardware synthesis and physical implementations on FPGA show that the proposed models can produce precise neural behaviors with higher performance and considerably lower implementation costs compared with the original model. Accordingly, a compact structure of the models which can be trained with supervised and unsupervised learning algorithms has been developed. Using this structure and based on a spike rate coding, a character recognition case study has been implemented and tested.

Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization

Abstract: In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions, respectively. We then propose a methodology for the optimal design of such decision rules that have a finite number of pieces and solve the problem robustly using mixed-integer optimization. We demonstrate the effectiveness of the proposed methods in the context of two multistage inventory control problems. We provide global lower bounds and show that our approach is (i) practically tractable and (ii) provides high quality solutions that outperform alternative methods.

A global representation of multidimensional piecewise-linear functions with linear partitions

Abstract: An analytical representation is introduced for m -dimensional piecewise-linear functions which are affine over convex polyhedral regions bounded by linear partitions. Explicit formulas are presented to compute the coefficients associated with this representation along with an example.

Macroscopic urban dynamics: Analytical and numerical comparisons of existing models

Abstract: In this paper we compare a single reservoir model and a trip-based model under piecewise linear MFD and a piecewise constant demand. These assumptions allow to establish the exact solution of the accumulation-based model, and continuous approximations of the trip-based model at any order using Taylor series.