21,297 research outputs found
Polynomial tuning of multiparametric combinatorial samplers
Boltzmann samplers and the recursive method are prominent algorithmic
frameworks for the approximate-size and exact-size random generation of large
combinatorial structures, such as maps, tilings, RNA sequences or various
tree-like structures. In their multiparametric variants, these samplers allow
to control the profile of expected values corresponding to multiple
combinatorial parameters. One can control, for instance, the number of leaves,
profile of node degrees in trees or the number of certain subpatterns in
strings. However, such a flexible control requires an additional non-trivial
tuning procedure. In this paper, we propose an efficient polynomial-time, with
respect to the number of tuned parameters, tuning algorithm based on convex
optimisation techniques. Finally, we illustrate the efficiency of our approach
using several applications of rational, algebraic and P\'olya structures
including polyomino tilings with prescribed tile frequencies, planar trees with
a given specific node degree distribution, and weighted partitions.Comment: Extended abstract, accepted to ANALCO2018. 20 pages, 6 figures,
colours. Implementation and examples are available at [1]
https://github.com/maciej-bendkowski/boltzmann-brain [2]
https://github.com/maciej-bendkowski/multiparametric-combinatorial-sampler
Parameter reduction in nonlinear state-space identification of hysteresis
Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of
science and engineering problems. The identification of hysteretic systems from
input-output data is a challenging task. Recent work on black-box polynomial
nonlinear state-space modeling for hysteresis identification has provided
promising results, but struggles with a large number of parameters due to the
use of multivariate polynomials. This drawback is tackled in the current paper
by applying a decoupling approach that results in a more parsimonious
representation involving univariate polynomials. This work is carried out
numerically on input-output data generated by a Bouc-Wen hysteretic model and
follows up on earlier work of the authors. The current article discusses the
polynomial decoupling approach and explores the selection of the number of
univariate polynomials with the polynomial degree, as well as the connections
with neural network modeling. We have found that the presented decoupling
approach is able to reduce the number of parameters of the full nonlinear model
up to about 50\%, while maintaining a comparable output error level.Comment: 24 pages, 8 figure
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