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mxochicale committed Oct 26, 2018
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25 changes: 12 additions & 13 deletions README.md
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PhD Thesis
---

The current tamplate of the PhD thesis is based on the
[PhD thesis template for Cambridge University Engineering Department (CUED)](https://github.com/kks32/phd-thesis-template).
It is recommended to read the instructions on how to use the template
[USAGE.md](https://github.com/mxochicale/phd-thesis/blob/master/USAGE.md).


There is a README.md in each Chapter to refer to the original chapter1.tex file
and also as a logbook for any changes.


My PhD Thesis as submitted on 26th October 2018.

## Citation

If you use or adapt any of the files in this repository,
use the following BibTeX to cite [my PhD thesis](http://).
use the following BibTeX to cite [my PhD thesis](https://github.com/mxochicale/phd-thesis).

```
@phdthesis{XochicalePhDThesis2018,
author = {Xochicale Miguel},
day = {26},
month = {10},
Year = {2018},
school = {University of Birmingham},
Expand All @@ -29,5 +19,14 @@ use the following BibTeX to cite [my PhD thesis](http://).
}
```

>> **NB** I will be polishing and updating this repository
while I am wait for my viva (tentatively January 2019 or February 2019).


# Issues
If you see any errors or have any questions
please create an [issue](https://github.com/mxochicale/phd-thesis/issues)




178 changes: 106 additions & 72 deletions abstract/abstract.tex
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% ************************** Thesis Abstract *****************************
% Use `abstract' as an option in the document class to print only the titlepage and the abstract.
\begin{abstract}

%% This abstract were written folllwing the nature's template for abstracts
%% (https://twitter.com/trevorabranch/status/620699527486373888?lang=en)

% I follow the guidelines of the nature's template for abstracts (https://twitter.com/trevorabranch/status/620699527486373888?lang=en)

%%%% 200 words %%%%
\begin{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% One or two sentences proving a basic introduction to the field,
%%%%% comprehensible to a scientist in any discipline.
Movement variability is defined as the variations that occur in motor
performance across multiple repetitions of a task and such behaviour is an
inherent feature within and between each persons' movement.
In the previous four decades, research on measurement and understanding of
movement variability with methodologies of nonlinear dynamics has been well established
in areas such as biomechanics, sport science, psychology, cognitive science,
neuroscience and robotics.
Nonlinear analyses investigate the dynamics of observed time-ordered data.
Such dynamics, for this thesis, are complex systems of sensorimotor
variables of movement variability (MV) in the context of
human-humanoid interaction.
%31 words
%movement variability (MV) and also in the mechanical
%limitations of a humanoid robot (robot with the general structure of a human).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Two to three sentences of more detailed background,
%%%%% comprehensible to scientist in related disciplines.
Given that traditional methods in time-domain and frequency domain fail to
detect tiny modulations in frequency or phase of time series,
we consider a methodology from nonlinear dynamics called uniform reconstructed state space
to quantify movement variability which essentially the dynamics of
an unknown system can be reconstructed using one dimensional time series.
As pointed out by Bradley et al. uniform reconstructed state space,
if done right, can guarantee to be topologically identical to the true dynamics
and determine dynamics invariants such as fractal dimension, Kolmogorov-Sinai
entropy or Lyaponov exponents.
These algorithms, however, require time series measured with costly sensors
that provide well sampled data with little noise.
Such requirement is generally a common problem when doing precise
characterisation of time series using dynamic invariants,
to which Bradley et al. proposed additional tools of
nonlinear time series analysis for practitioners such as surrogate data,
permutation entropy, recurrence plots and network characteristics for time series.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% One sentence clearly stating the general problem being addressed by this
%%%%% particular study.
For this study, we are thefore interested in the use of uniform reconstructed
state space and the analysis of recurrence plots and metrics of recurence
quantification analysis so as to understand the quantification of movement variability.
Particularly, we are interested in the analysis of data collected through
cheap wearable inertial sensors and its effects on the
reconstructed state space, recurrence plots and metrics for recurrence
quantification analysis for different window lengths and preprocessing techniques
(like smoothing and normalisation) of the time series.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% One sentence summarising the main result (with the words "here we show"
%%%%% or their equivalent)
So, here we show the characterisation for time series to understand human movement variability in the
context of human-humanoid imitation activities and demostrate the potential
of nonlinear techniques to quantify human movement varialibity.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Two or three sentences explaining what the main results reveals in direct
%%%%% comparison to what was thought to be the case previously, or how the main
%%%%% results adds to previous knowledge.
Specifically, we explore the reconstruction of state spaces, its recurrence plots
and metrics of recurrence quantification analysis for
20 participants performing repetitions of simple vertical and horizontal arm
movements in normal and faster speed.
We also explore the differences between wearable inertial sensors attached
to the person and to the humanoid robot and between different axes of inertial sensors.
With that in mind, our contribution to knowledge is in regard to the
reliability of data from cheap wearable inertial sensors
to analyse human movement variability in the context of human-humanoid imitation activities
using methodologies of nonlinear dynamics.
Hence, this dissertation not only explores questions such as what to quantify in MV?,
or which nonlinear tools are appropriate to quantify MV?, but also how
nonlinear analyses are affected with real-world time series data
(e.g. nonstationary, data length limitations, sampling rate changes or noisiness).
%46 words
%We conducted two experiment in human-humanoid interaction where participants
%imitate simple horizontal and vertical arm movements of a humanoid robot.
%to test the
%Given that traditional methods in time-domain and frequency domain fail to
%detect tiny modulations in frequency or phase of time series,
%we consider a methodology from nonlinear dynamics called uniform reconstructed state space
%to quantify movement variability which essentially the dynamics of
%an unknown system can be reconstructed using one dimensional time series.
%As pointed out by Bradley et al. uniform reconstructed state space,
%if done right, can guarantee to be topologically identical to the true dynamics
%and determine dynamics invariants such as fractal dimension, Kolmogorov-Sinai
%entropy or Lyaponov exponents.
%These algorithms, however, require time series measured with costly sensors
%that provide well sampled data with little noise.
%Such requirement is generally a common problem when doing precise
%characterisation of time series using dynamic invariants,
%to which Bradley et al. proposed additional tools of
%nonlinear time series analysis for practitioners such as surrogate data,
%permutation entropy, recurrence plots and
%network characteristics for time series
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% One sentence clearly stating the general problem being addressed by this
%%%%%% particular study.
Particularly, I review nonlinear tools such as methods
to determine embedding parameters, Reconstructed State Spaces (RSSs),
Recurrence Plots (RPs) and Recurrence Quantification Analyses (RQA).
%25 words
%(window size length) and
%preprocessing techniques (e.g. smoothing and normalisation)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% One or two sentences to put the results into a more general context.
Such understanding and measurement of movement variability using
cheap wearable inertial sensors lead us to have a more intuitive selection of parameters
to reconstruct the state spaces and to create meaningful interpretations
of the recurrence plots and the results of the metrics with recurrence quantification
analysis. Additionally, having a better understanding of
nonlinear dynamics tools with the use of cheap inertial sensors
can enhance the development of better diagnostic tools for various pathologies
which can be applied in areas of rehabilitation, entertainment or sport science.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Two or three sentences to provide a broader perspective, readily comprehensible
%%%%% to a scientist in any discipline, may be included in the first paragraph
%%%%% if the editor considers that the accessibility of the paper is significantly
%%%%% enhanced by their inclusion. Under this circumstances, the length of the
%%%%% paragraph can be up to 300 words
%%%%%% One sentence summarising the main result (with the words "here we show"
%%%%%% or their equivalent)
%such as window size length, participants, sensors and levels of smoothness
%(see weaknesses and strengths of RQA in Chapters \ref{chapter5} and
%\ref{chapter6}).
%So, here we show the characterisation for time series to understand
%human movement variability in the
%context of human-humanoid imitation activities and demonstrate the potential
%of nonlinear techniques to quantify human movement variability.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Two or three sentences explaining what the main results reveals in direct
%%%%%% comparison to what was thought to be the case previously, or how the main
%%%%%% results adds to previous knowledge.
To my knowledge, I can conclude that, no scientific work has been reported
regarding nonlinear analyses (e.g. RSSs with UTDE, RPs and RQAs) to
quantify movement variability in the context of human-humanoid interaction.
%34 words
%thorough experimentation and exploration to test
%the weaknesses and robustness of such tools,
Also, we created 3D surfaces of RQA
values considering the variation of embedded parameters and
recurrence thresholds to show that 3D surfaces of RQA ENTR might be a
better approach to provide understanding on the dynamics of different
characteristic of real-world time series data.
%44 words
%Specifically, we explore the reconstruction of state spaces, its recurrence plots
%and metrics of recurrence quantification analysis for
%20 participants performing repetitions of simple vertical and horizontal arm
%movements in normal and faster speed.
%We also explore the differences between wearable inertial sensors attached
%to the person and to the humanoid robot and between different axes of inertial sensors.
%With that in mind, our contribution to knowledge is in regard to the
%reliability of data from cheap wearable inertial sensors
%to analyse human movement variability in the context of human-humanoid imitation activities
%using methodologies of nonlinear dynamics.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% One or two sentences to put the results into a more general context.
%Such understanding and measurement of movement variability using
%cheap wearable inertial sensors lead us to have a more intuitive selection of parameters
%to reconstruct the state spaces and to create meaningful interpretations
%of the recurrence plots and the results of the metrics with recurrence quantification
%analysis. Additionally, having a better understanding of
%nonlinear dynamics tools with the use of cheap inertial sensors
%can enhance the development of better diagnostic tools for various pathologies
%which can be applied in areas of rehabilitation, entertainment or sport science.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Two or three sentences to provide a broader perspective,
%%%%%% readily comprehensible to a scientist in any discipline,
%%%%%% may be included in the first paragraph
%%%%%% if the editor considers that the accessibility of the paper is
%%%%%% significantly enhanced by their inclusion. Under this circumstances,
%%%%%% the length of the paragraph can be up to 300 words
I can foresee many areas of applications where humanoids robots
can be pre-programmed with nonlinear analyses algorithms
to evaluate the improvement of movement performances,
to quantify and provide feedback of skill learning
or to quantify movement adaptations and pathologies.
%38 words



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33 changes: 23 additions & 10 deletions acknowledgement/acknowledgement.tex
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\begin{acknowledgements}

I would like to acknowledge to Mexican National Council of Science and Technology (CONACyT)
that funded my PhD degree at The University of Birmingham, UK.
To my supervisor Chris Baber (CB) and my cosupervisor Martin J Russell (MR)
who helped with their acute comments and critics to make a stronger contribution to
knowledge.

I would also like to thank to Dr. Dolores Columba Perez Flores for her helpful
comments to polish the use of the language of mathematics and to
Constantino Antonio Garcia Martinez et al. for developing the nonlinearTseries R package
that significantly help to accelerate the analysis of the nonlinear time series in this work.
I would like to acknowledge to the Mexican National Council of Science and
Technology (CONACyT) that funded my curiosity-driven research which
allow me to quench this endless thirst for new knowledge during my
PhD degree at The University of Birmingham, UK.
To Professor Chris Baber for supervising my scientific endeavours
and who wisely looses the leash in any of my explorations
so as to take me back at the right time to write up this thesis.
To Professor Martin J Russell who, in the first year
of my PhD, helped with his acute comments and critics to make a
better use of the language or mathematics.
To Mourad Oussalah who kindly dedicate his time to discuss
my research interest and our collaboration which were published
in three peer-reiview confereces.
I would also like to thank to Dr. Dolores Columba Perez Flores for
her valuable comments that help me to have a better insight on
nonlinear analyses, and to Constantino Antonio Garcia Martinez
for developing the \texttt{nonlinearTseries} R package that was of
significant help to accelerate the results of this thesis.

\begin{flushright}
\textbf{Miguel Xochicale}\\
\textbf{Birmingham, UK}\\
\textbf{October 2018}
\end{flushright}

\end{acknowledgements}
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