Some of my recent research work has been in the following areas:

We have also started to use machine learning on the measures that we derive from the attractor for various classification problems. One example is given in [5].

A nice video explaining our method can be found
here.

[1] P.J. Aston, M. Nandi, M.I. Christie and Y.H. Huang.
Beyond HRV: Attractor reconstruction using the entire cardiovascular
waveform data for novel feature extraction.
*Phys. Meas.* **39**, 024001, 2018.

[2] M. Nandi, J. Venton and P.J. Aston.
A novel method to quantify arterial pulse waveform morphology: Attractor
reconstruction for biologists.
*Phys. Meas.* **39**, 103008, 2018.

[3] P.J. Aston, M. Nandi, M.I. Christie and Y.H. Huang.
Comparison of attractor reconstruction and HRV methods for analysing blood
pressure data.
*Computing in Cardiology* **41**, 437-440, 2014.

[4] P.H. Charlton, L. Camporota, J. Smith, M. Nandi, M.I. Christie,
P.J. Aston and R. Beale.
Measurement of cardiovascular state using attractor reconstruction
analysis.
*Proc. 23rd European Signal Processing Conference (EUSIPCO)*, Nice,
444-448, 2015.

[5] J.V. Lyle, P.H. Charlton, E. Bonet-Luz, G. Chaffey, M. Christie, M. Nandi
and P.J. Aston.
Beyond HRV: Analysis of ECG signals using attractor reconstruction.
*Computing in Cardiology* **44**, 091-096,
2017.

We have developed an interactive 'cardiomorph generator' using the pulse
oximetry signal generated by a fingertip monitor, in collaboration with
AD Instruments.
We demonstrated this at a Mathematics Festival held at
the Science Museum in November 2015. The Festival was entitled
What's Your Angle: Uncovering Maths and was one of the events organised by
the London Mathematical Society to celebrate its 150^{th}
anniversary. The many visitors to the Festival were fascinated at seeing
their own cardiomorph on the screen.

[4] P.J. Aston and N. Bristow. Alternating period-doubling cascades.

This paper was one of four papers selected in the Elementary Particles,
Fields and Nuclear Physics category of the EPL
Highlights of 2012 Collection.

[5] P.J. Aston.
Is radioactive decay really exponential?
*EPL* **97**, 52001, 2012.

[6] P.J. Aston and O. Junge. Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis.

The second problem concerned rebound, in which the receptor increases above
baseline at some point. After analysing four regions of parameter space
in detail, we concluded that rebound would occur if and only if the
elimination of the complex is slower than the elimination of both the ligand
and the receptor [8]. We have also considered a generalised model
in which the constant production rate of the receptor is replaced by
negative feedback. Many results were obtained for this more general model
[9].

[7] P.J. Aston, G. Derks, A. Raji, B.M. Agoram and P.H. van der Graaf.
Mathematical analysis of the pharmacokinetic-pharmacodynamic
(PKPD) behaviour of monoclonal antibodies: predicting *in vivo*
potency. *J. Theor. Biol.* **281**, 113-121, 2011.

[8] P.J. Aston, G. Derks, B.M. Agoram and P.H. van der Graaf.
A mathematical analysis of rebound in a target-mediated drug disposition
model. I. Without feedback.
*J. Math. Biol.* **68**, 1453-1478, 2014.

[9] P.J. Aston, G. Derks, B.M. Agoram and P.H. van der Graaf.
A mathematical analysis of rebound in a target-mediated drug disposition
model. II. With feedback.
Submitted to *J. Math. Biol.*

In [11], the earlier problem is extended to include a vertical wall.
Motion of the superball where it bounces alternately between the floor and the
wall several times is considered. Using the same model as in [10], a nonlinear
mapping is derived which relates the launch data of the
(*n*+1)^{th}
floor bounce to that of the *n*^{th}. This mapping is analysed
numerically and theoretically, and a detailed description is presented
of various possible motions. Regions of initial conditions which
result in a specified number of bounces against the wall are also considered.

[10] P.J. Aston and R. Shail.
The dynamics of a bouncing superball with spin.
*Dyn. Sys.* **22**, 291-322, 2007.

[11] P.J. Aston, P.M. Milliken and R. Shail.
The bouncing motion of a superball between a horizontal floor and a
vertical wall.
*Int. J. Nonlin. Mech.* **46**, 204-221, 2011.

P.Aston@surrey.ac.uk Updated: 15