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@@ -1,2 +1,2 @@ build -images/*.psd +sources/*.psd @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/> + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. 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If the +Program specifies that a certain numbered version of the GNU General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + <one line to give the program's name and a brief idea of what it does.> + Copyright (C) <year> <name of author> + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <https://www.gnu.org/licenses/>. + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + <program> Copyright (C) <year> <name of author> + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +<https://www.gnu.org/licenses/>. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +<https://www.gnu.org/licenses/why-not-lgpl.html>. diff --git a/build/main.aux b/build/main.aux deleted file mode 100644 index 2df4e00..0000000 --- a/build/main.aux +++ /dev/null @@ -1,90 +0,0 @@ -\relax -\providecommand\hyper@newdestlabel[2]{} -\providecommand\HyField@AuxAddToFields[1]{} -\providecommand\HyField@AuxAddToCoFields[2]{} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}} -\citation{DBLP:conf/date/MilojicicFDR21} -\citation{DBLP:journals/computer/AthavaleBBMMPS24} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {2}{2}}} -\citation{DBLP:journals/computer/AthavaleBBMMPS24} -\citation{DBLP:usdoe/report/AP26894} -\citation{DBLP:conf/acsos/TalluriOVTI21} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{3}{3/3}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {3}{3}}} -\@writefile{nav}{\headcommand 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April 25-29, 2022}, pages 1--6. {IEEE}, 2022. -\newblock \ifshowURL {\showURL \path|https://doi.org/10.1109/NOMS54207.2022.9789853|}\fi. - -\end{thebibliography} diff --git a/build/main.blg b/build/main.blg deleted file mode 100644 index 0a294db..0000000 --- a/build/main.blg +++ /dev/null @@ -1,48 +0,0 @@ -This is BibTeX, Version 0.99e (TeX Live 2026/Arch Linux) -Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 -The top-level auxiliary file: main.aux -The style file: is-plain.bst -Database file #1: main.bib -Warning--empty booktitle in DBLP:usdoe/report/AP26894 -You've used 17 entries, - 2588 wiz_defined-function locations, - 709 strings with 12438 characters, -and the built_in function-call counts, 11785 in all, are: -= -- 1108 -> -- 690 -< -- 11 -+ -- 269 -- -- 250 -* -- 838 -:= -- 1839 -add.period$ -- 80 -call.type$ -- 17 -change.case$ -- 167 -chr.to.int$ -- 0 -cite$ -- 18 -duplicate$ -- 473 -empty$ -- 893 -format.name$ -- 250 -if$ -- 2627 -int.to.chr$ -- 0 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differdeleted file mode 100644 index dfe9111..0000000 --- a/images/unused/datacenter_complexity.psd +++ /dev/null @@ -1,6 +1,6 @@ INFO: latexindent version 3.24.7, 2025-08-15, a script to indent .tex files latexindent lives here: /usr/share/texmf-dist/scripts/latexindent/ - Fri Jun 26 13:51:47 2026 + Sat Jun 27 11:56:46 2026 Reading input from STDIN INFO: Processing switches: INFO: Directory for backup files and log file indent.log: @@ -23,16 +23,14 @@ \begin{tcolorbox}[title=DCDT's lack predictive analytics] We need Datacenter Digital Twins (DCDT) to be better able to detect and solve issues in critical ICT infrastructure~\cite{DBLP:journals/computer/AthavaleBBMMPS24}. However, DCDT's are still actively developed and lack crucial features such as predictive analytics~\cite{DBLP:usdoe/report/AP26894} to \emph{e.g.,} prevent unexpected failures. - With predictive analysis (\emph{e.g.,} simulation) DCDT's could save millions of lost \$USD~\cite{DBLP:conf/acsos/TalluriOVTI21}. \end{tcolorbox} \begin{center} \includegraphics[width=0.9\linewidth]{images/predictive_analytics.pdf} \end{center} \tiny - \textbf{Figure 1.2:} Where does our work fit within the field of datacenter digital twinning? - There are 5 core elements to any Digital Twin: \myCircled{A} The Digital $\rightarrow$ Physical Twin link, \myCircled{B} the Physical Twin (\emph{e.g.,} the datacenter), \myCircled{C} the Physical $\rightarrow$ Digital Twin link, \myCircled{D} the Digital Twin, \myCircled{E} the features necessary to any Digital Twin. - \textcolor{Green}{\faHighlighter~Highlighted areas are the contributions from this thesis, which include the autonomous actions resulting from predictive insights \myCircledGreen{A} and the predictive analysis itself within \myCircledGreen{E}.} + \textbf{Figure 1.2:} Datacenter Digital Twin Diagram. There are 5 core elements to any Digital Twin: \myCircled{A} The Digital $\rightarrow$ Physical Twin link, \myCircled{B} the Physical Twin (\emph{e.g.,} the datacenter), \myCircled{C} the Physical $\rightarrow$ Digital Twin link, \myCircled{D} the Digital Twin, \myCircled{E} the features necessary to any Digital Twin. + \textcolor{Green}{\faHighlighter~Highlighted areas are the contributions from this thesis, which include the autonomous actions resulting from predictive insights \myCircledGreen{A} and the predictive analysis framework (including simple storage capabilities) within \myCircledGreen{E}.} \end{frame} \begin{frame}\frametitle{Research Questions} @@ -56,13 +54,13 @@ \begin{frame}\frametitle{\textbf{RQ1}: Literature Review I} \begin{tcolorbox}[title=Main Finding I] - The literature on DCDTs is scarce. + The literature on DCDTs is sparse. Some systems barely classify as DTs (\emph{e.g.,} Kalibre~\cite{DBLP:conf/sensys/WangZD0TCWZ20}, ChatTwin~\cite{DBLP:conf/sensys/LiW0Z0T23}). Existing deployments specialize in \textcolor{Red}{Cooling and Heat Modelling}, together with \textcolor{Red}{3D visualizations}. Most lack predictive modelling of DC operations. \end{tcolorbox} \vspace{-0.1cm} - \input{images/table.tex} + \input{sources/table.tex} % Research on DTs for datacenters have been separate, siloed efforts focused on either datacenter cooling, network performance, power consumption or visualization efforts. % CFD usually means Navier-Stokes equations. % CFD models take ages to compute. @@ -72,11 +70,11 @@ % Mandatory: split the figure into 2: top and bottom, and that way you can fill in the entire slide nicely. \begin{tcolorbox}[title=A holistic DCDT system model] - We propose a generic model of datacenter digital twinning that can be mapped to each system from \textbf{Table 1.1}. Within this model (see \textbf{Fig. 1.3}) we introduce a concept of the \emph{Digital Thread}: a bridge between the DCDT and the physical DC equipment. + We propose a holistic model of datacenter digital twinning that can be mapped to each system from \textbf{Table 1.1}. Within this model (see \textbf{Fig. 1.3}) we introduce a concept of the \emph{Digital Thread}: a bridge between the DCDT and the physical DC equipment. \end{tcolorbox} \begin{center} \vspace{-0.1cm} - \includegraphics[width=0.8\textwidth]{images/system_model2.pdf} + \includegraphics[width=0.8\textwidth]{images/system_model.pdf} \end{center} % The reason why the cooling system is in the graph is because of the fact that 40\% of total energy consumed in DCs comes from cooling~\cite{DBLP:conf/noms/ZhangZLZWC22}. % It has come to the point where datacenters are being build in the Pan-Arctic region, such as Finland,Russia,Sweden etc. with Iceland leading in number of DCs https://www.datacentermap.com/iceland/ @@ -142,7 +140,7 @@ \begin{minipage}[b]{0.45\linewidth} \vspace{-0.2cm} \begin{center} - \includegraphics[width=1.2\linewidth]{images/predictive_analyticsv3.pdf} + \includegraphics[width=1.2\linewidth]{images/novel_eval_method.pdf} \end{center} \tiny \vspace{-0.2cm} @@ -169,7 +167,7 @@ \hspace{-0.2cm} \begin{minipage}[b]{0.45\linewidth} \begin{center} - \includegraphics[width=1.1\textwidth]{images/25_Jun_2026_152341.pdf} + \includegraphics[width=1.1\textwidth]{images/red_yellow_alarms.pdf} \end{center} \vspace{-0.3cm} \tiny @@ -179,7 +177,7 @@ \hspace{0.6cm} \begin{minipage}[b]{0.45\linewidth} \begin{center} - \includegraphics[width=1.1\textwidth]{images/25_Jun_2026_161052.pdf} + \includegraphics[width=1.1\textwidth]{images/failure_detecton_rate.pdf} \end{center} \vspace{-0.3cm} \tiny @@ -190,55 +188,65 @@ % Give more reliable results than just numbers -- do statistical testing, i.e., standard deviation, confidence intervals. \end{frame} -\begin{frame}\frametitle{\textbf{RQ3}: Experimental Results II} +\begin{frame}\frametitle{\textbf{RQ3}: Experimental Results II} % Let's say we have some knowledge about the kind of workload we are going to run, e.g., Skype video calls. + % We can then estimate on previous Skype node failures and one of statistical distributions when are failures likely to happen. + % During the experiment, we unfortunately do not know what kind of distribution will the failures follow, so we constantly check to see which one fits best, and dynamically adjust the scheduling policy based on that. + %---% + % Step 1: We know we are going to soon run a workload coming in from Skype. Let's try to predict the failure pattern we might encounter. + % Run the OpenDC simulator 5 times to estimate the possible failure patterns. Save the results inside the Digital Twin. + % Step 2: Run the Digital Twin. Each time a new metric comes in, update the similarity score of each possible distribution. + % If the distribution with the similarity score that is the highest is about to match timestamps with the running workload AND according to the distribution we are going to experience failures in hosts A,B,C,D, % We decide to stop scheduling tasks on hosts A,B,C and D (we send a message to the running datacenter). \begin{tcolorbox}[title=Main Finding III] - \emph{Sunfish} is capable of dynamic adjustments to the physical twin at runtime, and can lower the mean number of failed tasks. + Predicting failures in advance is really difficult. \emph{Sunfish} is capable of dynamic adjustments to the physical twin at runtime, and can slightly lower the number of failed tasks. \end{tcolorbox} - \hspace{0.2cm} + \hspace{-0.2cm} \begin{minipage}[b]{0.45\linewidth} \begin{center} - \includegraphics[width=1.1\textwidth]{images/23_Jun_2026_102028.pdf} + \includegraphics[width=1.1\textwidth]{images/failure_likelihood.pdf} \end{center} \vspace{-0.3cm} \tiny - \textbf{Figure 1.8a:} Experiment 2a. + \textbf{Figure 1.8a:} Experiment 2a. The figure shows which failure distribution is the most likely to be the true failure distribution while the simulation is running. + This figure shows the difficulty of predictive analytics. \end{minipage} + \hspace{0.5cm} \begin{minipage}[b]{0.45\linewidth} + \vspace{-0.1cm} \begin{center} - \includegraphics[width=1.1\textwidth]{images/23_Jun_2026_102028.pdf} + \includegraphics[width=1.1\textwidth]{images/conceptual_experiment.pdf} \end{center} \vspace{-0.3cm} \tiny - \textbf{Figure 1.8b:} Experiment 2b. + \textbf{Figure 1.8b:} Experiment 2b. With perfect precognition (\emph{i.e.,} knowing on which day, what failures might happen) we could lower the mean number of failures. + This experiment is a proof of concept (results are indication-only). \end{minipage} \end{frame} \begin{frame}\frametitle{Key Takeaways} - \begin{tcolorbox}[title=What is the societal context?] + \begin{tcolorbox}[title=Societal Context] Datacenter manageability is a top-priority for the digital society. Over 3 million jobs in the Netherlands directly depend on cloud services, which are hosted in datacenters~\cite{DBLP:journals/corr/IosupKLVG22}. \end{tcolorbox} - \begin{tcolorbox}[title=What problem did we solve?] + \begin{tcolorbox}[title=Problem Statement] DCDT's, still under development, lack crucial features such as predictive analytics to manage datacenters well. The entire DCDT design space remains largely unexplored. \end{tcolorbox} - \begin{tcolorbox}[title=How did we solve this problem?] - Our contributions are: a thorough literature survey with a system model, a DCDT reference architecture, and prototype-based experiments via a novel evaluation method. + \begin{tcolorbox}[title=Contributions] + (1) A thorough literature survey with a system model, (2) a DCDT reference architecture, and (3) prototype-based experiments via a novel evaluation method. \end{tcolorbox} - \begin{tcolorbox}[title=What did we find?] - \emph{Sunfish} can reliably detect unexpected failures based on discrete-event predictions, and can serve as a foundation for additional research and future work. + \begin{tcolorbox}[title=Main Findings] + \emph{Sunfish} can reliably detect unexpected failures based on discrete-event predictions, and can serve as a foundation for research and future work in predictive analytics. \end{tcolorbox} % Mandatory to mention here the future work that you see happening. % Not enough space for another tcolorbox. \end{frame} -\setcounter{framenumber}{3} +\setcounter{framenumber}{4} \setbeamertemplate{footline}[page number]{} - % Unfortunately this must remain here. \setbeamercolor{frametitle}{fg=Brown,bg=Brown!20} \setbeamertemplate{frametitle}{ diff --git a/images/indent.log b/script/indent.log index 3853ba9..10fa7f0 100644 --- a/images/indent.log +++ b/script/indent.log @@ -1,6 +1,6 @@ INFO: latexindent version 3.24.7, 2025-08-15, a script to indent .tex files latexindent lives here: /usr/share/texmf-dist/scripts/latexindent/ - Sun Jun 21 16:37:44 2026 + Sat Jun 27 13:49:57 2026 Reading input from STDIN INFO: Processing switches: INFO: Directory for backup files and log file indent.log: diff --git a/script/main.tex b/script/main.tex new file mode 100644 index 0000000..a524e96 --- /dev/null +++ b/script/main.tex @@ -0,0 +1,78 @@ +\documentclass[12pt, a4paper]{article} +\usepackage{palatino, enumitem, parskip, xspace} +\usepackage[dvipsnames]{xcolor} +\newcommand{\eg}{\emph{e.g.,}\xspace} +\newcommand{\todo}[1]{\textcolor{Blue}{\textbf{TODO(#1)}}} +\newcommand{\etal}{\emph{et~al.}\xspace} +\begin{document} +\begin{center} + \Large My BSc Defence Script +\end{center} +\begin{enumerate}[label=\textbf{Slide \arabic*.}] + \item \textbf{Introduction}\\ + Good morning everyone, my name is Mateusz and today I will present to you my project \emph{Sunfish: Enabling Predictive Analytics For Datacenters Through Digital Twinning}. + + At a top level, my project is about trying to ease datacenter management by trying to pave the way to predicting unexpected events. + + \item \textbf{Societal Impact}\\ + As you know and as you will likely see in the upcoming presentations today, datacenters are important. + But, I would like to shortly mention this myself. + + + + A single GPU is already very complex. + Within a Google Datacenter, there are hundreds of server racks, with tens of such GPUs. + This begs the question: How are we going to manage this large of a datacenter, that has so many \emph{layers of complexity}? + + We cannot let these systems go down or experience big failures, because \eg in Netherlands over 3 million professionals depend daily on the cloud. + \todo{Read the slide box.} + As such, we must do something to manage datacenters well. + + + \item \textbf{Problem Statement}\\ + Digital Twinning pairs complex objects (like datacenters) via a two-way connection with their virtual representation. + \todo{Give example about the airplane from aviation.} + \emph{It a method to manage complex systems.} + + However, in digital twinning, specifically datacenter digital twinning a lot of elements are still shifting about and there are a lot of ways to create the virtual models and there seems to not be a fully functioning DCDT out there (\emph{that meets the official NASM definition}). + + DCDT's lack mandatory features one of which is predictive analytics. + Predictive Analytics is a type of ODA that draws insights into the future based on current data, \eg telling when a host failure might happen before it does (\emph{and yet it is NOT present in existing DCDTs}). + + \item \textbf{Research Questions}\\ + We wish to enable the development of predictive analysis components for DCDT's by designing a predictive DCDT. + We ask the following research questions. \todo{Read from slide boxes.} + + \item \textbf{Literature Survey}\\ + \item \textbf{System Model}\\ + + \item \textbf{Reference Architecture and Prototype}\\ + A reference architecture. + The design is more specific than the reference architecture. + + \item \textbf{Novel Evaluation Method}\\ + In order to evaluate a prototype, we propose a novel approach. + Many researchers do not have a real facility to experiment with. + We propose to use a second simulator to act as the real datacenter. + + \todo{Say in order to not cram content into the presentation, we omit the technical setup, and include it in extra slides.} + + + \item \textbf{Experiment 1: Red and Yellow Alarms}\\ + For Experiment 1 we copy the idea of Milojicic \etal for different ways a DCDT can notify the datacenter. + + Imagine a scenario: a datacenter will soon run a workload. + We want to detect and differentiate between failures that are big and unexpected and failures we anticipated would occur. + + To achieve this: the DCDT runs the workload using the simulator. + We cannot know what kind of failures we can expect, so we use a statistical distribution to approximate what might occur in practice. + In result, we get a picture of what kind of problems we might expect. + + We now use the real-time feedback loop to notify the DC operators that what is happening in reality is different from simulation. + If we get within 80\% of the predicted threshold for number of failures we send a yellow alarm. + If we get within 90\% we send a red alarm. + \item \textbf{Experiment 2: Conceptual Experiment}\\ + \item \textbf{Key Takeaways}\\ + \todo{Read from the slide.} +\end{enumerate} +\end{document} diff --git a/images/implementation.drawio b/sources/implementation.drawio index c67a323..c67a323 100644 --- a/images/implementation.drawio +++ b/sources/implementation.drawio diff --git a/images/predictive_analyticsv2.drawio b/sources/novel_eval_method.drawio index 174f008..174f008 100644 --- a/images/predictive_analyticsv2.drawio +++ b/sources/novel_eval_method.drawio diff --git a/images/predictive_analytics.drawio b/sources/predictive_analytics.drawio index c8ff618..c8ff618 100644 --- a/images/predictive_analytics.drawio +++ b/sources/predictive_analytics.drawio diff --git a/images/ref_architecture.drawio b/sources/ref_architecture.drawio index 2506675..2506675 100644 --- a/images/ref_architecture.drawio +++ b/sources/ref_architecture.drawio diff --git a/images/system_model.drawio b/sources/system_model.drawio index cf5995c..cf5995c 100644 --- a/images/system_model.drawio +++ b/sources/system_model.drawio diff --git a/images/table.tex b/sources/table.tex index 630763d..630763d 100644 --- a/images/table.tex +++ b/sources/table.tex diff --git a/style/style.tex b/style/style.tex index d7e4e72..9f2647c 100644 --- a/style/style.tex +++ b/style/style.tex @@ -60,7 +60,7 @@ \includegraphics[height=1cm]{images/vu-logo.png} \end{textblock*}} -\author{M. Kwiatkowski \and Drs. D. Niewenhuis\inst{1} \and Prof. A. Iosup\inst{2}} +\author{M. Kwiatkowski \and drs. D. Niewenhuis\inst{1} \and Prof. A. Iosup\inst{2}} \institute{Overleaf} \date{Vrije Universiteit Amsterdam\\\vspace{0.5em}\small \today} |
