mythesis.tex

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%Copyright (c) 2018 Chen Wang [https://chenwang.site]
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%SOFTWARE.

% #############################################################
% #                                                            #
% #  Modified by Junxiang (Eric) Jia @ WeberLab, NTU.          #
% #  GitHub link of this repo:                                 #
% #  https://github.com/EricJ928/NTU_SPMS_thesis_template      #
% #                                                            #
% #  - Modified to match the template for SPMS, NTU.           #
% #  - Add an option that can split Bibliography               #
% #    separately for each chapter.                            #
% #                                                            #
% #############################################################

% Disclaimer:
% ===========
% Please always check with the official template from the school's administration. I am not responsible for any mismatch, delay, or inconvenience that happens to your thesis and data while using this template.


\documentclass[12pt,a4paper]{Thesis} % Paper size, default font size and one-sided paper

\graphicspath{%
	{./Pictures/}%
	{./Figures/}%
}
\DeclareMathOperator{\Tr}{Tr}
\let\savedegree\degree
\let\degree\relax
\let\savedegree\ref
\let\rem\relax
\usepackage{adjustbox}
\usepackage{amsmath}
\usepackage[amssymb]{SIunits}
\usepackage{amssymb}
\usepackage{multirow}
\usepackage{wrapfig}
\usepackage{enumitem}
\usepackage{subcaption}
\usepackage{mathtools}
\usepackage{lipsum}
\usepackage[ruled,vlined,noresetcount]{algorithm2e}
%\usepackage{algpseudocode}
\usepackage[square, numbers, comma, sort&compress]{natbib} % Use the natbib reference package - read up on this to edit the reference style; if you want text (e.g. Smith et al., 2012) for the in-text references (instead of numbers), remove 'numbers'
% \usepackage{tocbibind}

\title{\ttitle} % Defines the thesis title - don't touch this

%extra packages
\usepackage{float}
\usepackage{color,soul}               % highlighting text
\usepackage{enumerate}
\usepackage{Styles/mydefs}
\usepackage{tabularx}           % for table
\renewcommand\tabularxcolumn[1]{m{#1}}      % vertical centering of table cell

\newcommand{\red}[1]{\textcolor{red}{#1}}
\newcommand{\blue}[1]{\textcolor{blue}{#1}}
% \newcommand{\angstrom}{\mbox{\normalfont\AA}}


\begin{document}

\frontmatter % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages

\setstretch{1.3} % Line spacing of 1.3
% Define the page headers using the Fr package and set up for one-sided printing

\pagestyle{fancy} % Finally, use the "fancy" page style to implement the FancyHdr headers
\fancyhead{}   %clear all fields
\fancyhead[LO]{\sl{\leftmark}}
\fancyhead[RE]{\sl{\rightmark}}
\fancyhead[LE,RO]{\thepage}


%----------------------------------------------------------------------------------------
%	TITLE PAGE
%----------------------------------------------------------------------------------------

%%% Use \maketitleforreview instead of \maketitle, if you want a PLAIN TITLE PAGE

\maketitle
\maketitleforreview


% ----------------------------------------------------------------------------------------
% 	DECLARATION PAGE
% ----------------------------------------------------------------------------------------

\thesisdeclareOriginality{I hereby certify that the work embodied in this thesis is the result of original research done by me except where otherwise stated in this thesis. The thesis work has not been submitted for a degree or professional qualification to any other university or institution. I declare that this thesis is written by myself and is free of plagiarism and of sufficient grammatical clarity to be examined. I confirm that the investigations were conducted in accord with the ethics policies and integrity standards of Nanyang Technological University and that the research data are presented honestly and without prejudice.}{Sep. 2022}{Styles/Signature_NTU.png}

\thesisdeclareSupervisor{I have reviewed the content and presentation style of this thesis and declare it of sufficient grammatical clarity to be examined. To the best of my knowledge, the thesis is free of plagiarism and the research and writing are those of the candidate’s except as acknowledged in the Author Attribution Statement. I confirm that the investigations were conducted in accord with the ethics policies and integrity standards of Nanyang Technological University and that the research data are presented honestly and without prejudice.}{Sep. 2022}{Styles/Signature_NTU.png}

\thesisdeclareAuthorship{Please select one of the following; *delete as appropriate:
\\
*(A) This thesis \textbf{does not} contain any materials from papers published in peer-reviewed journals or from papers accepted at conferences in which I am listed as an author.
\\
*(B) This thesis contains material from [x number] paper(s) published in the following peer-reviewed journal(s) / from papers accepted at conferences in which I am listed as an author.}
{
Please amend the typical statements below to suit your circumstances if (B) is selected.

	Chapter 4 is published as {\color{blue}D.T. Murphy, S. Schmid, J.R. Hester, P.E.R. Blanchard, and W. Miiller.  Coordination site disorder in spinel-type LiMnTiO4.  Inorganic Chemistry 54, 4636-4643 (2015). DOI: 10.1021/ic502747p.}

	The contributions of the co-authors are as follows:
	\begin{itemize}[topsep=1pt,itemsep=1pt,partopsep=1pt, parsep=1pt]
		\item A/Prof Schmid provided the initial project direction and edited the manuscript drafts.
		\item I prepared the manuscript drafts.  The manuscript was revised by Dr Hester and Dr. Blanchard.
		\item I co-designed the study with A/Prof Siegbert Schmid and performed all the laboratory work at the School of Materials Science and Engineering and the Singapore Synchrotron Light Source.   I also analyzed the data.
		\item All microscopy, including sample preparation, was conducted by me in the Facility for Analysis, Characterization, Testing and Simulation.
		\item Dr James Hester assisted in the collection of the neutron powder diffraction data.
		\item Dr Peter Blanchard assisted in the interpretation of the X-ray absorption spectroscopy data and carried out the spectral interpretation.
		\item Dr Wojciech Miiller assisted in the collection and provide guidance in the interpretation of the magnetic measurement data.
	\end{itemize}

	Chapter 5 is published as {\color{blue}H. V Doan, B. Yao, Y. Fang, A. Sartbaeva, U. Hintermair, V. P Ting, Controlled Formation of Hierarchical Metal-Organic Frameworks using CO2 Expanded Solvent Systems. In press, ACS Sustainable Chemistry \& Engineering (2017). DOI: 10.1021/acssuschemeng.7b01429}

	The contributions of the co-authors are as follows:
	\begin{itemize}[topsep=1pt,itemsep=1pt,partopsep=1pt, parsep=1pt]
		\item Prof Ting suggested the materials area and edited the manuscript drafts.
		\item I wrote the drafts of the manuscript.  The manuscript was revised together with Dr. Sartbaeva and Dr. Yao.
		\item II performed all the materials synthesis, collected X-ray diffraction patterns and visible light spectra, carried transmission electron microscopy, and conducted data evaluation.
		\item IDr. Y. Fang conducted the Rietveld analysis of the powder X-ray diffraction data and single crystal structure determinations.
		\item IDr U. Hintermair conducted the molecular dynamics simulations.
		\item IMs. A. Sartbaeva prepared the samples for electron microscopy.
	\end{itemize}
 
}{Sep. 2022}{Styles/Signature_NTU.png}



%----------------------------------------------------------------------------------------
%	ABSTRACT PAGE
%----------------------------------------------------------------------------------------

\addtotoc{Abstract} % Add the "Abstract" page entry to the Contents

\abstract{\addtocontents{toc}{\vspace{0.8em}}}% Add a gap in the Contents, for aesthetics

% 1. The Problem 2. The Issues 3. The Approach 4. The Results 5. The Experiments 6. The Applications

My abstracts

\clearpage

% ----------------------------------------------------------------------------------------
% 	ACKNOWLEDGEMENTS
% ----------------------------------------------------------------------------------------

\setstretch{1.3} % Reset the line-spacing to 1.3 for body text (if it has changed)

\acknowledgements{\addtocontents{toc}{\vspace{0.8em}} % Add a gap in the Contents, for aesthetics

I wish to express my greatest gratitude to my advisor.

% \begin{flushright}
% \emph{Jinming Xu, December 2015}
% \end{flushright}
}

%----------------------------------------------------------------------------------------
%	QUOTATION PAGE
%----------------------------------------------------------------------------------------

\pagestyle{empty} % No headers or footers for the following pages
\emph{"If I had one hour to save the world, I would spend 55 minutes defining the problem and only five minutes finding the solution."}

\begin{flushright}
---Einstein, Albert
\end{flushright}
\null\vfill % Add some space to move the quote down the page a bit

\begin{center}
\large{To my dear family}
\end{center}
\vfill\vfill\null % Add some space at the bottom to position the quote just right
\cleardoublepage % Start a new page and make the next page a right-hand (odd-numbered) page, producing a blank page if necessary

\pagestyle{fancy} % Return the page headers back to the "fancy" style
\fancyhead{}   %clear all fields
\fancyhead[LO]{\sl{\leftmark}}
\fancyhead[RE]{\sl{\rightmark}}
\fancyhead[LE,RO]{\thepage}


%----------------------------------------------------------------------------------------
%	LIST OF CONTENTS/FIGURES/TABLES PAGES
%----------------------------------------------------------------------------------------

\pagestyle{fancy} % The page style headers have been "empty" all this time, now use the "fancy" headers as defined before to bring them back

\tableofcontents % Write out the Table of Contents

\listoffigures % Write out the List of Figures

\listoftables % Write out the List of Tables


%----------------------------------------------------------------------------------------
%	ABBREVIATIONS
%----------------------------------------------------------------------------------------

%\clearpage % Start a new page
%
%\setstretch{1.5} % Set the line spacing to 1.5, this makes the following tables easier to read
%
%\lhead{\emph{Abbreviations}} % Set the left side page header to "Abbreviations"
%\listofsymbols{ll} % Include a list of Abbreviations (a table of two columns)
%{
%\textbf{LAH} & \textbf{L}ist \textbf{A}bbreviations \textbf{H}ere \\
%%\textbf{Acronym} & \textbf{W}hat (it) \textbf{S}tands \textbf{F}or \\
%}

%----------------------------------------------------------------------------------------
%	PHYSICAL CONSTANTS/OTHER DEFINITIONS
%----------------------------------------------------------------------------------------

%\clearpage % Start a new page
%
%\lhead{\emph{Physical Constants}} % Set the left side page header to "Physical Constants"
%
%\listofconstants{lrcl} % Include a list of Physical Constants (a four column table)
%{
%Speed of Light & $c$ & $=$ & $2.997\ 924\ 58\times10^{8}\ \mbox{ms}^{-\mbox{s}}$ (exact)\\
%% Constant Name & Symbol & = & Constant Value (with units) \\
%}

%----------------------------------------------------------------------------------------
%	SYMBOLS
%----------------------------------------------------------------------------------------

% \cleardoublepage  % Start a new page (no need if the previous page is list of figures)

\listofnomenclature{ll} % Include a list of Symbols (a three column table)
{
\multicolumn{2}{l}{\LARGE{\textbf{Symbols}}}\\[0.618cm]
$\mathbb{Z}$                       &Integer\\
$\mathcal{R}^n$                    &the $n$-dimensional Euclidean space\\
$\mathcal{H}$                      &the Euclidean  space\\
$\norm{\cdot}$                     &the 2-norm of a vector or matrix in Euclidean space\\
$\norm{\cdot}_G$                   &the induced norm of a vector in G-space\\
$\norm{\cdot}_E$                   &the induced norm of a vector or matrix in probabilistic space\\


$\odot$                            &the Hadamard (component-wise) product\\
$\otimes$                          &the Kronecker product\\
$\innprod{\cdot}{\cdot}$           &the inner product of two vectors\\
$\circ$                            &the composition of functions\\ [0.618cm]


$\nabla f$                    &the gradient vector\\
$\mathcal{C}^k$               &the function with continuous partial derivatives up to $k$ orders\\
% $T_x\mathcal{M}$              &the tangent space of the set $\mathcal{M}$\\
% $x_i$                         &the $i$-th component of a vector $x$\\
$x_{i,k}$                     &the $i$-th component of a vector $x$ at time $k$\\
$\bar{x}$                     &the vector with the average of all components of $x$ as each element\\
$\ones$                       &all-ones column vector with proper dimension\\
$\mathcal{C}$                 &the average space, i.e., $span\{{\bf 1}\}$ \\
$\mathcal{C}^\perp$           &the disagreement space, i.e., $span^\perp\{{\bf 1}\}$ \\
% W                             &the weight matrix\\
% L                             &the Laplacian matrix\\
$\Pi_\parallel$               &the projection matrix to the average space $\mathcal{C}$\\
$\Pi_\perp$                   &the projection matrix to the disagreement space $\mathcal{C}^\perp$ \\
$O(\cdot)$                    &order of magnitude or ergodic convergence rate (running average)\\
$o(\cdot)$                    &non-ergodic convergence rate\\
% $O(\cdot)$                    &the ergodic convergence rate stated in terms of the running average\\
% $o(\cdot)$                    &the non-ergodic convergence rate stated in terms of $x_k$\\



$\mathcal{N}_i$               &the index set of the neighbors of agent $i$ \\ [1cm]

\multicolumn{2}{l}{\LARGE{\textbf{Acronyms}}}\\[0.618cm]
DOP                      & Distributed Optimization Problem\\
EDOP                     & Equivalent Distributed Optimization Problem\\
SDOP                     & Stochastic Distributed Optimization Problem\\
OEP                      & Optimal Exchange Problem\\
OCP                      & Optimal Consensus Problem\\
DOCP                     & Dynamic Optimal Consensus Problem\\[0.618cm]
AugDGM           & Augmented Distributed Gradient Methods\\
AsynDGM          & Asynchronous Distributed Gradient Methods\\
D-ESC            & Distributed Extremum Seeking Control\\
D-SPA            & Distributed Simultaneous Perturbation Approach\\
% D-PDSPA & Distributed Primal-Dual Simultaneous Perturbation Approach\\
D-FBBS           & Distributed Forward-Backward Bregman Splitting\\
ADMM             & Alternating Direction Method of Multipliers\\
DSM              & Distributed (Sub)gradient Method\\[0.618cm]

GAS                      & Globally Asymptotically Stable \\
UGAS                     & Uniformly Globally Asymptotically Stable \\
SPAS                     & Semi-globally Practically Asymptotically Stable\\
USPAS                    & Uniformly Semi-globally Practically Asymptotically Stable\\[0.618cm]
HoS                      & Heterogeneity of Stepsize\\
FPR                      & Fixed Point Residual\\
OBE                      & Objective Error\\[0.618cm]
i.i.d.           & independent and identically distributed\\
$a.s.$           & almost sure convergence of a random sequence\\
}

%----------------------------------------------------------------------------------------
%	THESIS CONTENT - CHAPTERS
%----------------------------------------------------------------------------------------

\mainmatter       % Begin numeric (1,2,3...) page numbering
\pagenumbering{arabic}
\setstretch{1.3}  % Return the line spacing back to 1.3

% define the headings for the body of the thesis
\fancyhead{}   %clear all fields
\fancyhead[LO]{\sl{\leftmark}}
\fancyhead[RE]{\sl{\rightmark}}
\fancyhead[LE,RO]{\thepage}


% Include the chapters of the thesis as separate files from the Chapters folder
% Uncomment the lines as you write the chapters

\input{./Chapters/Chapter1}
% \part{Part Name: Use it when there are many chapters}
\input{./Chapters/Chapter2}
\input{./Chapters/Chapter3}
% \part{Again for Second Part}
\input{./Chapters/Chapter4}
\input{./Chapters/Chapter5}
\input{./Chapters/Chapter6}


%----------------------------------------------------------------------------------------
%	THESIS CONTENT - APPENDICES
%----------------------------------------------------------------------------------------

\addtocontents{toc}{\vspace{0.8em}} % Add a gap in the Contents, for aesthetics

\appendix % Cue to tell LaTeX that the following 'chapters' are Appendices

% Include the appendices of the thesis as separate files from the Appendices folder
% Uncomment the lines as you write the Appendices

\input{./Appendices/AppendixA}
%\input{./Appendices/AppendixB}

% \cleardoublepage    % start a new page
\clearpage

%----------------------------------------------------------------------------------------
%	AUTHOR'S PUBLICATIONS
%----------------------------------------------------------------------------------------

% \cleardoublepage
% \authorpublications{

% \section*{Awards}

% \begin{itemize}
% 	\item \textbf{Best Paper Awards}, ``A Great Thesis,'' \emph{Nature}.
% \end{itemize}

% \section*{Patents}
% \begin{itemize}
% 	\item \textbf{A Great System}, ``A Great Thesis,'' \emph{Nature}.
% \end{itemize}

% \section*{Journal Articles}

% \begin{itemize}
%     \item \textbf{My name} and My colleague, ``A Great Thesis,'' \emph{Nature}.
% \end{itemize}

% \section*{Conference Proceedings}

% \begin{itemize}
%   \item \textbf{My name}, My colleague 1, My colleague 2 and My colleague 3, ``Greater Thesis,'' in \emph{Conference of Vision, 2018}.
% \end{itemize}

% }

\backmatter

%----------------------------------------------------------------------------------------
%	BIBLIOGRAPHY
%----------------------------------------------------------------------------------------

\label{Bibliography}
\setstretch{1}
\bibliographystyle{unsrtnat}
\bibliography{References/References}

\end{document}