Presentations and Posters ⇒ How to enumerate the blocks in a poster

[BarbaraG]

Hi everybody!
As the title suggests, I am writing a poster and I want to enumerate the blocks. I am using the Jacobs Landscape Poster and I'd like to have a small number at the bottom right. I need this template because is so clear, but I was told the block in the middle make kind of confusion on the order, then I want to enumerate all the blocks and make it clear.
Thank you very much!

[Johannes_B]

Welcome,

if the order in which to read the blocks is clear depends on the layout of the blocks, little numbers will only help a little.


How is the current setup of your poster?

[BarbaraG]

Hi!
I didn't change any blocks of the original one (okay, of course I wrote down my texts instead of Lore ipsum..). I was just told the blue block in the middle is a little bit confusing. One does not know where to look exactly after that.

[Stefan Kottwitz]

Hi Barbara,

welcome to the forum!

Perhaps post your code here. I would test it to see how to enumerate.
I just did not find the time to search for the "Jacobs Landscape Poster" and to create an example myself. If you already have code, simply post it. That's easier for all.

Stefan

[BarbaraG]

Of course! Thank you!
P.s.: I am new, so I don't know exactly if there is a better way to post it. Anyway, here there is =)

Code: Select all

\documentclass[final]{beamer}

\usepackage[scale=1.24]{beamerposter} % Use the beamerposter package for laying out the poster
\usepackage{subfig}

\usetheme{confposter} % Use the confposter theme supplied with this template

\setbeamercolor{block title}{fg=ngreen,bg=white} % Colors of the block titles
\setbeamercolor{block body}{fg=black,bg=white} % Colors of the body of blocks
\setbeamercolor{block alerted title}{fg=white,bg=dblue!70} % Colors of the highlighted block titles
\setbeamercolor{block alerted body}{fg=black,bg=dblue!10} % Colors of the body of highlighted blocks
% Many more colors are available for use in beamerthemeconfposter.sty


\newlength{\sepwid}
\newlength{\onecolwid}
\newlength{\twocolwid}
\newlength{\threecolwid}
\setlength{\paperwidth}{48in} % A0 width: 46.8in
\setlength{\paperheight}{36in} % A0 height: 33.1in
\setlength{\sepwid}{0.024\paperwidth} % Separation width (white space) between columns
\setlength{\onecolwid}{0.22\paperwidth} % Width of one column
\setlength{\twocolwid}{0.464\paperwidth} % Width of two columns
\setlength{\threecolwid}{0.708\paperwidth} % Width of three columns
\setlength{\topmargin}{-0.8in} % Reduce the top margin size
%-----------------------------------------------------------

\usepackage{graphicx}  % Required for including images

\usepackage{booktabs} % Top and bottom rules for tables

%----------------------------------------------------------------------------------------
%	TITLE SECTION 
%----------------------------------------------------------------------------------------

\title{Stability and connectivity of dynamical systems on graphs} % Poster title

\author{Barbara Giunti} % Author(s)

\institute{Universit\`a degli studi di Torino} % Institution(s)

%\begin{flushright}
%\begin{figure}
%\includegraphics[width=0.4\linewidth]{Logo1.png}
%\end{figure}
%\end{flushright}

%----------------------------------------------------------------------------------------

\begin{document}

\addtobeamertemplate{block end}{}{\vspace*{0.1ex}} % White space under blocks
\addtobeamertemplate{block alerted end}{}{\vspace*{0.1ex}} % White space under highlighted (alert) blocks

\setlength{\belowcaptionskip}{0.1ex} % White space under figures
\setlength\belowdisplayshortskip{1ex} % White space under equations

\begin{frame}[t] % The whole poster is enclosed in one beamer frame

\begin{columns}[t] % The whole poster consists of three major columns, the second of which is split into two columns twice - the [t] option aligns each column's content to the top

\begin{column}{\sepwid}\end{column} % Empty spacer column

\begin{column}{\onecolwid} % The first column

%----------------------------------------------------------------------------------------
%	OBJECTIVES
%----------------------------------------------------------------------------------------

\begin{alertblock}{Objectives}

We consider a finite simple graph and assign to each vertex a scalar state variable, we described the collective dynamics with a gradient-type dynamical system. The system is linear and his matrix is closely related to the signless Laplacian of the graph. Then, its behaviour is determined by the spectral properties of its matrix: 
\begin{itemize}
\item we computed explicitly the eigenvalues and the eigenspaces for special classes of graphs
\item we collect a number of qualitative results from the literature, for more general classes of graphs
\item we then use these results to discuss the stability properties of the dynamical system on the graph
\item we perturb the deterministic system by a white noise term at each node
\end{itemize}

\end{alertblock}

%----------------------------------------------------------------------------------------
%	INTRODUCTION
%----------------------------------------------------------------------------------------

\begin{block}{Motivation}
\textbf{Mathematical motivation:}
the signless Laplacian $Q$ matrix is square, symmetric, non negative, real and positive semi-definite. Thus his eigenvalues are real, non negative and are computed fast. Moreover, from \cite{CveSiI} we know that studying graphs by $Q$-spectra is more efficient than studying them by their (adjacency) spectra.
\begin{figure}
\includegraphics[width=0.65\linewidth]{Capsid2.jpg}
\caption{Viral capsid}
\end{figure}
\textbf{Biological motivation:}
in order to model the opening of a viral capsid, we define a potential depending on only two parameters. One governs the square of the distance from the capsid center, the other the attraction between two adjacent faces \cite{CerInZap}\cite{Tirion}.
\begin{equation*}
U\left(\pmb{x}\right)=
\frac{a}{2}\sum_{i=1}^{n}x_{i}^{2}+\frac{b}{2}\sum_{i=1}^{n}\sum_{j=1}^{n}A_{ij}\left(x_{i}+x_{j}\right)^{2}
\end{equation*}
His gradient turns out to be:
\begin{equation*}
\nabla U\left(\pmb{x}\right)=\left(a I + 2b Q\right)\pmb{x}
\end{equation*}
\end{block}

%----------------------------------------------------------------------------------------

\end{column} % End of the first column

\begin{column}{\sepwid}\end{column} % Empty spacer column

\begin{column}{\twocolwid} % Begin a column which is two columns wide (column 2)

\begin{columns}[t,totalwidth=\twocolwid] % Split up the two columns wide column

\begin{column}{\onecolwid}\vspace{-.6in} % The first column within column 2 (column 2.1)

%----------------------------------------------------------------------------------------
%	SECONDA COLONNA
%----------------------------------------------------------------------------------------

\setbeamercolor{block alerted title}{fg=black,bg=norange} % Change the alert block title colors
\setbeamercolor{block alerted body}{fg=black,bg=white} % Change the alert block body colors
\begin{alertblock}{Definition}
Given a graph $G$, with adjacency matrix $A$ and degree matrix $D$, the signless Laplacian is defined by:
$$ Q = A + D $$
\end{alertblock}
\begin{block}{Graph and signless Laplacian}
We performed the explicit calculation for eigenvalues and eigenvectors of the complete graph $K_{n}$, the complete bipartite graph $K_{n,m}$, the cycle $C_{n}$, the path $P_{n}$ and the star $S_{n}$. 
%For example, 
$K_{n,m}$ has four different eigenvalues, 
$n+m^{1}, m^{n-1}, n^{m-1}, 0^{1}$, the superscript is the multiplicity. The first eigenvector is 
\begin{center}
$\qquad \pmb{v}_{1}=\left(\frac{1}{n},\dots,\frac{1}{n}, \frac{1}{m}\dots,\frac{1}{m}\right)$
\end{center}
\end{block}

%----------------------------------------------------------------------------------------

\end{column} % End of column 2.1

\begin{column}{\onecolwid}\vspace{-.6in} % The second column within column 2 (column 2.2)

%----------------------------------------------------------------------------------------
%	METHODS
%----------------------------------------------------------------------------------------

\begin{block}{General results for $Q$}
There are a lot of interesting results for more general graphs' classes. 
\begin{itemize}
\item the smallest eigenvalue of a bipartite graph is $0^{1}$
\item the largest eigenvalue of a $r$-regular graph is $2r$ 
with eigenvector $\left(1,\dots,1\right)$
\item only $K_{n}$ has got only two distinct eigenvalues  
\end{itemize}
%For bipartite graph the Laplacian spectrum correspond to the $Q$-spectrum. 
Comparing the general results, we noticed that there is a correlation between the connection properties of a graph and the number of eigenvalues: more connected is the graph, less eigenvalues we have. For example, on all the tree graphs, only the star $S_{n}$ has three distinct eigenvalues; all the others have at least four. Moreover, if a graph has diameter $d$ then $k$, the number of distinct eigenvalues, will satisfy $ k-1 \geq d$.
\end{block}

%----------------------------------------------------------------------------------------

\end{column} % End of column 2.2

\end{columns} % End of the split of column 2 - any content after this will now take up 2 columns width

%----------------------------------------------------------------------------------------
%	IMPORTANT RESULT
%----------------------------------------------------------------------------------------

\begin{alertblock}%{Linked eigenvalues}

Labelling with $\lambda_{i}$ the eigenvalues of the dynamical system on the graph and with $q_{i}$ the $Q$-eigenvalues of the graph, we have the following relations:
$\lambda_{i}=-a-2b q_{n-i+1}$, for $a \in \mathbb{R}$ and $b \in \mathbb{R}^{+}$.
If  the largest eigenvalue of the system is negative, the system is stable. Then we can find a simple stability condition depending on the smallest $Q$-eigenvalue: 
if $q_{n}>-\dfrac{a}{2b}$ the system is stable, 
%if $q_{n}<-\dfrac{a}{2b}$ 
otherwise
the system is unstable.
\end{alertblock} 

%----------------------------------------------------------------------------------------

\begin{columns}[t,totalwidth=\twocolwid] % Split up the two columns wide column again

\begin{column}{\onecolwid} % The first column within column 2 (column 2.1)

%----------------------------------------------------------------------------------------
%	MATHEMATICAL SECTION
%----------------------------------------------------------------------------------------
\begin{block}{Dynamical systems on the graph}
Given a graph $G$ of order $n$, consider a vector field $\pmb{x}\in \mathbb{R}^{n}$ whose components $\left(x_{1},\dots,x_{n}\right)$ are scalar fields associated to the vertices of $G$. Using the potential we defined before $U: \mathbb{R}^{n}\rightarrow \mathbb{R}$, the system becomes:
\begin{equation}
\dot{\pmb{x}}=- \left(aI+2bQ\right) \pmb{x}
\label{eqn:Einstein}
\end{equation}
$Q$ is a non negative, positive semidefinite, symmetric matrix. Thus $\exists R \in SO\left(n\right)$ that diagonalizes $Q$. We put $\pmb{\xi}=R^{-1}\pmb{x}$ and $\mathcal{D}=R^{-1}QR$ the diagonal matrix of all eigenvalues. 
\begin{align*}
R^{-1}\dot{\pmb{x}}&=-R^{-1}\left(a I+2 b Q\right) R R^{-1}\pmb{x} 
\\
\Rightarrow \dot{\pmb{\xi}}&=-\left(a I+2 b \mathcal{D}\right)\pmb{\xi}
\end{align*} 
%Making explicit the individual equations, which are decoupled, we find:
%\begin{equation*}
%\dot{\xi}_{i}=-\left(a +2 b q_{i}\right)\xi_{i}, \qquad i=1,\dots, n .
%\end{equation*}
%The solutions of these equations are:
%\begin{equation*}
%\xi_{i}\left(t\right)=\xi_{i}\left(0\right)exp\left[-\left(a+2 b q_{i}\right)t\right] \qquad i=1,\dots, n
%\end{equation*}
and then the general solution is given by
\begin{equation}
\pmb{\xi}\left(t\right)=\sum_{i=1}^{n} e^{-\left(a+2bq_{i}\right)t}\pmb{c}_{i}
\end{equation}
where $\pmb{c}_{i}$ belongs to the $Q$-eigenspace. The system is unstable in $\pmb{x}=\pmb{0}$ if the largest eigenvalue is positive, and it is stable otherwise.
\end{block}

%----------------------------------------------------------------------------------------

\end{column} % End of column 2.1

\begin{column}{\onecolwid} % The second column within column 2 (column 2.2)

%----------------------------------------------------------------------------------------
%	RESULTS
%----------------------------------------------------------------------------------------

\begin{block}{System's eigenvalues}
\begin{figure}[tb]
\subfloat
{\includegraphics[width=.45\columnwidth]{StarGraph}} \quad
\subfloat
{\includegraphics[width=.45\columnwidth]{index}}
\caption{Simulation for the system on $S_{5}$ and $C_{9}$}
%\label{fig:subfig}
\end{figure}
We combine the previous results. The $K_{n}$ system has smallest eigenvalue $\lambda_{n}=-a-4b\left(n-1\right)$ with eigenvector $\left(1,\dots,1\right)$. The perturbation spreads along all direction. It is needed a strong force to disrupt all the connection. 
Then, a high connected graph like a complete graph $K_{n}$ goes in a very stable system.    
On the other hand, the eigenspaces of the $P_{n}$ system have all dimension equal to one and a perturbation goes along just one vector. 
That means that first it is easier to disconnect the system, because the perturbation can act on only one vector, and second the perturbation acts really specifically, leaving the other vertices untouched.

%The largest eigenvalue is $\lambda_{1}=-a$, with eigenvector $\pmb{v}\left(q_{n}\right)=\left(1,\dots,1\right)$

\end{block}

%----------------------------------------------------------------------------------------

\end{column} % End of column 2.2

\end{columns} % End of the split of column 2

\end{column} % End of the second column

\begin{column}{\sepwid}\end{column} % Empty spacer column

\begin{column}{\onecolwid} % The third column

%----------------------------------------------------------------------------------------
%	CONCLUSION
%----------------------------------------------------------------------------------------

\begin{block}{Stochastic system}
We want now to add a stochastic noise to our differential equation. 
We consider a stochastic vector, i.e., a vector of random variables defined on a probability space $\left(\Omega, \mathcal{F}, \mu\right)$, whose components are associated to the vertices of the graph. The equation becomes:
\begin{equation}
dX_{t}=-\left(a I+2 b Q\right) X_{t}dt+\beta\sum_{i=1}^{n}dW_{t}^{i} \label{stocheq}
\end{equation}
%$X_{t}:\Omega \rightarrow \mathbb{R}^{n}$,
where $\beta \in \mathbb{R}^{+}$ and $W_{t}=\left(W_{t}^{1},\dots,W_{t}^{n}\right)$ is a $n$-dimensional Brownian motion.
The equation has a solution in the form:
\begin{equation}
X_{t}=e^{-Ht}\left(c+\beta\int_{0}^{t}e^{Hs}dW_{s}\right) \label{solstoch}
\end{equation}
If we have an asymptotically stable solution, $H$ is positive definite and then $X_{t}$ converges in distribution to a normal distribution $\mathcal{N}\left(\mathbf{0},\frac{1}{2} \beta^2 H^{-1}\right)$.
\end{block}

%----------------------------------------------------------------------------------------
%	ADDITIONAL INFORMATION
%----------------------------------------------------------------------------------------

\begin{block}{Conclusion}
\begin{itemize}
\item More connected is the graph, less distinct eigenvalues there are, bigger is the dimension of the relative eigenspaces
\item the smallest eigenvalue of the graph system, is simple and his eigenvector is positive
\item for bipartite graphs the largest eigenvalue is $\lambda_{1}=-a$, i.e., the system is unstable for all $a<0$
\end{itemize}

\end{block}

%----------------------------------------------------------------------------------------
%	REFERENCES
%----------------------------------------------------------------------------------------

\begin{block}{References}

\nocite{*} % Insert publications even if they are not cited in the poster
\small{\bibliographystyle{unsrt}
%\bibliography{}\vspace{0.75in}
\begin{thebibliography}{1}
\bibitem{Arnold} L. Arnold, {\em Stochastic differential equations: theory and applications}, Krieger Publishing Company 1992
\bibitem{CerInZap} P. Cermelli, G. Indelicato, E. Zappa, {\em A stochastic model for the destabilization of viral capsids},  to appear
\bibitem{CveSiI} D. Cvetkovi\'c, S.K. Simi\'{c}, {\em Towards a spectral theory of graphs based on the signless Laplacian I}, Linear Algebra Appl. 432 (2010) 2257-2272
\bibitem{KazShre} I. Karatzas, S.E. Shreve, {\em Brownian motion and stochastic calculus}, Springer-Verlag New York (1991)
\bibitem{Tirion} M. M. Tirion, {\em Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis}, PRL, 99-7 (1996)
\end{thebibliography}
}
\end{block}

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

\setbeamercolor{block title}{fg=red,bg=white} % Change the block title color

%\begin{block}{Acknowledgements}
%
%\small{\rmfamily{Nam mollis tristique neque eu luctus. Suspendisse rutrum congue nisi sed convallis. Aenean id neque dolor. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.}} \\
%
%\end{block}

%----------------------------------------------------------------------------------------
%	CONTACT INFORMATION
%----------------------------------------------------------------------------------------

\setbeamercolor{block alerted title}{fg=black,bg=norange} % Change the alert block title colors
\setbeamercolor{block alerted body}{fg=black,bg=white} % Change the alert block body colors

\begin{alertblock}{Contact Information}

\begin{itemize}
\item Email: \href{mailto:}{}
\item Skype: 
\item Phone: 
\end{itemize}

\end{alertblock}

%\begin{center}
%\begin{tabular}{ccc}
%\includegraphics[width=0.4\linewidth]{Logo1.png} %& \hfill & \includegraphics[width=0.4\linewidth]{logo.png}
%\end{tabular}
%\end{center}

%----------------------------------------------------------------------------------------

\end{column} % End of the third column

\end{columns} % End of all the columns in the poster

\end{frame} % End of the enclosing frame

\end{document}