Corpus ID: 1177415

# On the thermodynamics of curves and other curlicues

@inproceedings{Moore1989OnTT,
title={On the thermodynamics of curves and other curlicues},
author={R. R. Moore and A.J. van der Poorten},
year={1989}
}
• Published 1989
• Mathematics
16 Citations
Machine learning pipeline for battery state of health estimation
• Computer Science
• ArXiv
• 2021
This work designs and evaluates a machine learning pipeline for estimation of battery capacity fade—a metric of battery health—on 179 cells cycled under various conditions, and provides insights into the design of scalable data-driven models for battery SOH estimation, emphasizing the value of confidence bounds around the prediction. Expand
Curlicues generated by circle homeomorphisms
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism.Expand
Thermodynamic analogies for the characterization of 3D human coronary arteries
• C. Bulant, +5 authors R. Feijóo
• Computer Science, Mathematics
• Biomed. Signal Process. Control.
• 2018
The thermodynamics of three-dimensional curves is explored through numerical simulations, providing room for a broader range of applications, and some of the proposed thermodynamic descriptors have different mean values for healthy/diseased left anterior descending (LAD) and left circumflex (LCx) arteries. Expand
A CHAIN OF CURLICUES
The upward-sweeping FM signal represented by eit 1.4 is sampled at nonnegative integer values of the time t starting with 0. An interesting chain of increasingly more Cornu-like spirals in theExpand
Error term improvements for van der Corput transforms
We improve the error term in the van der Corput transform for exponential sums \sum_{a \le n \le b} g(n) exp(2\pi i f(n)). For many functions g and f, we can extract the next term in theExpand
Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems
• Mathematics, Computer Science
• Entropy
• 2009
According to the proposed method all linear dynamical systems evolve at constant zero entropy, while higher asymptotic values characterise nonlinear systems, in which case it has common features with other classic approaches. Expand
Limiting curlicue measures for theta sums
We consider the ensemble of curves $\{\gamma_{\alpha,N}:\alpha\in(0,1],N\in\N\}$ obtained by linearly interpolating the values of the normalized theta sum \$N^{-1/2}\sum_{n=0}^{N'-1}\exp(\pi iExpand
A generalised entropy of curves: An approach to the analysis of dynamical systems
• Mathematics, Computer Science
• 2008 47th IEEE Conference on Decision and Control
• 2008
A generalisation of the entropy of a plane curve to ¿n space is provided and the generalised entropy is used to evaluate the nonlinear behaviour of dynamical systems. The entropy of a curve, firstExpand
Algorithmic dimensionality reduction for molecular structure analysis.
• Computer Science, Medicine
• The Journal of chemical physics
• 2008
This work investigates the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation--a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space and describes an efficient approach for a deterministic enumeration of ring conformations. Expand

#### References

Renormalisation of curlicues
• Mathematics
• 1988
The recursively spiralling patterns drawn in the complex plane by the values of SL( tau )= Sigma Ln=1 exp(i pi tau n2) as L to infinity with tau fixed in the range 0<or= tau <or=1, depend on theExpand