• Corpus ID: 1177415

On the thermodynamics of curves and other curlicues

  title={On the thermodynamics of curves and other curlicues},
  author={R. R. Moore and A.J. van der Poorten},

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.

Machine learning pipeline for battery state of health estimation

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.


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 the

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 the

Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems

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.

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 i

A generalised entropy of curves: An approach to the analysis of dynamical systems

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, first

Algorithmic dimensionality reduction for molecular structure analysis.

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.


Renormalisation of curlicues

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 the