\subsection{Spatial and temporal analysis}

We navigate our multidimensional dataset by first analysing the spatial and temporal dimensions to answer {AQ1}. These analysis can quantify the volumes of relevant  Twitter messages based on the countries of the users and the country mentions, since these volumes are strong indicators of real-world  events \cite{weng2011event}.
Figure~\ref{fig:tweets-country} depicts the total number of tweets for the 20 most active countries.

\begin{figure}[h]
	\centering
		\includegraphics[width=0.95\columnwidth]{Number_of_tweets_per_country}
	\caption{\ensuremath{{\cal T}_{UL}}\xspace per top-20 countries in log scale.}
	\label{fig:tweets-country}
\end{figure}

\begin{figure}[h]
	\centering
		\includegraphics[width=0.95\columnwidth]{Number_of_tweets_per_day_and_news}
	\caption{\ensuremath{{\cal T}}\xspace per day and top pieces of news.}
	\label{fig:tweets-day}
\end{figure}

Since the dataset is in English most of the tweets
($56.1$\%) come from users located in United Kingdom (UK), therefore in Section~\ref{sec:uk} we focus our analysis on UK. Nevertheless, a significant fraction of the data
come from other countries, e.g., France (FR) accounts for $6.9$\% of the tweets and Germany (DE)
accounts for $5.9$\%. Without loss of generality, our methodology can be extended to other languages
by simply extending the seed hashtags used in the sentiment dimension construction.
As far as the mention location is concerned, we see that users from 51 countries mention 154 countries Europe, Asia and Africa.
This is analyzed in further detail in Section~\ref{sec:uk}.

Figure~\ref{fig:tweets-day} illustrates tweets volumes along the temporal dimension, therefore relating volumes to events, summarized in Table \ref{tab:events}.
This clearly includes all the tweets in \ensuremath{{\cal T}}\xspace and not only the geo-located ones. We observed significant volume peaks in
days August 19, September 4 and September 19. As we can see from the table, these days match the major events since the UK and France security deal signed on the 18 of August regarding Calais, the drowned Syrian boy found in a beach, Hungary takes refugees to Austrian border by bus in days 2 to 4 September,
and migrants breaking through Hungarian border on September 16.

\begin{table}
\scriptsize
\caption{Major events during the observation period as reported by UK Newspapers}\label{tab:events}
\begin{tabular}{r|p{6.8cm}}
  18.08 & UK and France to sign Calais security deal. \\
  20-21.08 & Macedonian police teargas thousands of refugees crossing from Greece and declares state of emergency over surge in migrants \& refugees.  \\
  27-28.08 & 71 dead refugees found dead in truck in Austria. \\
  31.08 & Angela Merkel: Europe as a whole must help with refugees. \\
  1.09 & Hungary closes main Budapest station to refugees. \\
  2.09 & Alan Kurdi drowned off the shores of Turkey. \\
  4-6.09 & Migrants are allowed to cross the Austro-Hungarian border; Refugees welcomed warmly in Germany. \\
  8.09 & Hungarian Journalist appears to kick and trip fleeing refugees. \\
  14.09 & Austria followed Germany's suit and instituted border controls;  Refugee boat sinking: dozens including children drown off Greek island. \\
  15.09 & Croatia started to experience the first major waves of refugees; Hungary announced it would start arresting people crossing the border illegally. \\
  16.09 & Refugee crisis escalates as people break through Hungarian border; Hungary had detained 519 people and pressed criminal charges against 46 for trespassing, leading to pursue alternative routes through Croatia from Serbia. \\
  17.09 & Croatia decided to close its border with Serbia. \\

\end{tabular}
\end{table}

\begin{figure}[b]
	\centering
		\includegraphics[width=0.95\columnwidth]{Top_migrant_crisis_EU_2}
	\caption{EU country mentions per day in log scale.}
	\label{fig:tweets-day-country-mentioned-EU}
\end{figure}

\begin{figure}[h]
	\centering
		\includegraphics[width=0.95\columnwidth]{Top_migrant_crisis_ORIENT}
	\caption{Non-EU country mentions per day in log scale.}
	\label{fig:tweets-day-mentioned-ORIENT}
\end{figure}

Next, we analyze location mention to a country related to the refugee  migration.
Figure~\ref{fig:tweets-day-country-mentioned-EU}
reports the volumes of tweets mentioning the  EU countries most impacted by the refugees route, namely Austria, Germany, Croatia, Macedonia, Hungary, Serbia, Greece. We see that there is an interesting correspondence between the peaks of mentions and the events timeline. An evident peak for Germany, Austria and Hungary is the first week of September, probably related to the issues of borders being opened to refugees. We also notice a peak of mentions of Croatia corresponding to the close of borders with Serbia.
Macedonia also sees and important increase of mentions around the 20 of August, probably in relation to the  Macedonian Police using gas towards refugees.

Similarly, Figure~\ref{fig:tweets-day-mentioned-ORIENT} focuses on the mention of relevant non European countries. The number of tweets mentioning Syria increases dramatically after the aforementioned facts of September 4, Turkey has a peak the day 4 of September due probably to the young kid found on the beach. We also observe how the mentions to other countries remains more or less stable along this period to witness the fact that they were not directly related to the events reported by the media in that period and that involved mainly the Syrian refugees.

From a content standpoint we tracked how hashtags usage is closely related to the relevant events.
We have counted the frequency of each hashtag in each day, then performed a two-pass normalization.
First we normalized the frequencies of hashtags on each day so as to avoid that days with lower recorded traffic are given less importance.
Then we normalized each hashtag over the observed period, so that the values are comparable among different hashtags.
We then measured the variance of the normalized frequencies, considering that hashtags with higher variance are those with a more unbalanced distribution among days. The hypothesis is that the unbalanced distribution is due to a close relation of the hashtag with a specific temporal event (usually one or two days).
Figure \ref{fig:hashtags} shows the resulting twenty highest-variance hashtags.
The plot shows how this simple method allowed us to quickly spot hot topic in the observed stream of tweets and to correctly place them in time.

\begin{figure}[b]
	\centering
		\includegraphics[width=0.98\columnwidth]{hashtag_refugees_edit}
	\caption{Highest-variance hashtags per day; intense red represents higher relative freq.}
	\label{fig:hashtags}
\end{figure}

\input{sentiment}

\section{Introduction}

We are recently witnessing one of the largest movement of migrants and refugees from Asian, African and Middle-east countries towards Europe. The United Nations High Commissioner for Refugees (UNHCR) estimates
one million of refugees arrived to the Mediterranean coasts in 2015 mainly from Syria (49\%), Afghanistan (21\%) and Iraq (8\%). Figure~\ref{fig:route} reports main routes to EU coasts and to northern Europe.
The largest wave of arrivals started in August 2015 following a main route through Turkey, Greece, Macedonia, Hungary and Austria to Germany, France, UK and other northern European countries. Since then, this phenomenon has been in spotlight of the media, which have reported an increasing number of events related to migrants, such as the additional border controls established by Hungary, Austria and Germany, the several incidents happened to refugees, or the touching photo of the young Syrian boy found dead on the seashore in Turkey in September 2015.

The implications of this refugee crisis are several and complex.
The whole phenomenon is nowadays object of a heated and polarized debate.
Understanding how the debate is framed between governmental organizations, media and citizens may help to better handle this emergency.
Through the analysis of the Twitter online social network, we address the following questions:
``How is the European population perceiving this phenomenon? What is the general opinion of each country? How is perception influenced by events? What is the impact on public opinion of news related to refugees? How does perception evolve in time in different European countries?"

\begin{figure}[t]
	\centering
		\includegraphics[width=1\columnwidth]{route}
	\caption{The routes to European countries (source Business Insider - Europol, Reuters, Washington Post, AFP, ICMPD).}
	\label{fig:route}
\end{figure}

Social media may help in answering these relevant questions but the volume of messages exchanged is massive and the extraction of sentiment is challenging.
Basic analyses of the phenomenon through Twitter have been already performed by media in a simplistic way, mainly through manual analysis of content, news and hashtags for small samples of tweets. For instance, the usage of terms \textit{refugees} and \textit{migrants} have been compared\footnote{https://storify.com/ImagineEurope/what-is-associated-with-europe} in offline and online media. The former indicates someone forced to leave her country to avoid war or imprisonment,  the latter is instead someone moving from his/her country searching for better living conditions. Additional basic quantitative analyses on Twitter hashtags about refugees have been performed, i.e. the \textit{\#welcome refugees} and \textit{\#germany} hashtags are used mainly from outside Germany\footnote{http://orientalreview.org/2015/09/21/who-is-twitter-luring-refugees-to-germany/}.
These are a few examples on simple analyses performed. However a more comprehensive work trying to analyze the perception of users about these events, shaped across places and time, is still missing.

In this work we propose an analytical framework to interpret social trends from large tweet collections by extracting and crossing information about the following three dimensions: time, location and sentiment. We describe the methodology to: 1) extract relevant spatial information, 2) enrich data with the sentiment of the message and of the user (retrieved in an automatic iterative way through Machine Learning), 3) perform multidimensional analyses considering content and locations in time. The approach is general and can be easily adapted to any topic of interest involving multiple dimensions. It is scalable due to the automatic enrichment procedure. For the scope of this paper we use our framework to outline the European perception of the refugee crisis.

\section{Introduction}
\label{sec:introduction}
\input{intro}

\section{Related Work}
\label{sec:related}
\input{related}

\section{The Analytical Framework}
\label{sec:methodology}
\input{methodology}

\section{Refugees Crisis Perception Analysis}
\label{sec:experiments}
\input{experiments}

\section{Conclusions and Future Work}
\label{sec:conclusions}
\enlargethispage*{1cm}
\vspace{-0.25cm}
\input{conclusions}

{\bf Acknowledgments. }
{\small This work was partially supported by the EC H2020 Program INFRAIA-1-2014-2015 {\em SoBigData: Social Mining \& Big Data Ecosystem} (654024).}

\newcommand{\setlength{\itemsep}{0.25 em}}{\setlength{\itemsep}{0.25 em}}
\bibliographystyle{IEEEtran}

\vspace{-0.25cm}

\subsection{Data Collection and Analysis Dimensions}

We used the Twitter streaming API to collect English tweets data under the \textit{Gardenhose} agreement (10\% of all tweets in Twitter) in period from mid August to mid Sept 2015, noted with \ensuremath{{\cal G}}\xspace, out of which we selected the tweets related to the refugee crisis topic, called the {\em relevant} tweets (denoted as \ensuremath{{\cal T}}\xspace). We did this by manually choosing a subset of 200 hashtags frequently used and specifically related to refugees in the period of analysis.
From \ensuremath{{\cal T}}\xspace we extracted information about three main dimensions: \textbf{ spatial, temporal, and sentiment-based}, resulting in the set of users and tweets as reported in Table~\ref{tab:notation}.

\subsection{Spatial and Temporal Dimensions}

For each tweet we extract two kinds of spatial information if present: the \textit{user location} of the person posting the message and the \textit{mentioned locations} within the tweet text.
The \textit{user location} is structured in two levels, the city (if present) and the country. The user city is identified from the \textit{GPS coordinates} or \textit{place} field when available. Since GPS and {\em place} data are quite rare (about 3.5K in all dataset) we used the free-text \textit{user location} field to enrich location metadata.
We identified locations in the user generated field
based on location data from the Geonames\footnote{http://www.geonames.org/} dictionary which fed a parsing and matching heuristic procedure.
This technique provides high-resolution, high-quality geo-location in presence of meaningful user location data \cite{onnela2011geographic}. The user country  is collected in a similar way and when not explicitly present we infer from the city.
The \textit{mentioned locations} in the text are also represented at city and country level, and they are extracted from tweets' text with the same heuristic procedure as for user location.

We limit our analysis to the perception and sentiment of European citizens.
For the mentioned locations we are also interested to the countries involved in the migration crisis.
The numbers of tweets with user location \ensuremath{{\cal T}_{UL}}\xspace and mentioned locations \ensuremath{{\cal T}_{ML}}\xspace are reported in Table \ref{tab:notation}.

Finally, we extracted the publishing time of each tweet and the period of time when each user was active. This information is necessary to study the evolution of the migrant crisis phenomenon
and users' perception over time.

\subsection{Sentiment Dimension}

We are interested in understanding if the user has a positive feeling in welcoming the migrants or if he/she mainly expresses negative feelings (fear, worry, hate).
Therefore, the dataset is enriched with information about the sentiment for both of tweets and users.

We consider two polarized classes $c \in \ensuremath{{\cal C}}\xspace$: \textit{pro refugees} ($c_+$) and \textit{against refugees} ($c_-$).
We implemented and modified the algorithm $PTR$~\cite{coletto2016} to assign a class to each polarized tweet and to each polarized user in an iterative way by considering his/her tweets and the hashtags contained.
The approach proposed in \cite{coletto2016} is suitable to track polarized users according to a specific topic which is in our case the ``refugees phenomenon''.

\begin{algorithm}[t!]
\small
\caption{\label{alg:iterative} $PTR$\xspace Algorithm}
\begin{algorithmic}[1]
\Require a set of users \ensuremath{{\cal U}}\xspace, their tweets \ensuremath{{\cal T}}\xspace with hashtags \ensuremath{{\cal H}}\xspace,
\Statex \hspace{2em} a set of hashtags $H_c^{0}$ for each class $c \in \ensuremath{{\cal C}}\xspace$
\Ensure Classification of users $U_c$ and hashtags $H_c$
\Procedure{$PTR$\xspace}{\; $\{H_c^{0}\}_{c \in \ensuremath{{\cal C}}\xspace}$\; }
\State $\tau \gets 0$
\Repeat
\Statex \Comment{Classify tweets on the basis of the used hashtags}
\State $\left\{T_{c}^{\tau} \right\}_{c \in \ensuremath{{\cal C}}\xspace} \gets \mbox{\sc TwClass}\left(  \left\{ H_{c}^{\tau} \right\}_{c \in \ensuremath{{\cal C}}\xspace}, \cal{T} \right)$
\Statex \Comment{Classify users on the basis of the written tweets}
\State $\left\{U_{c}^{\tau} \right\}_{c \in \ensuremath{{\cal C}}\xspace} \gets \mbox{\sc UsClass}\left(\left\{T_{c}^{\tau}\right\}_{c \in \ensuremath{{\cal C}}\xspace}, \cal{U}   \right)$
\Statex \Comment{Find better hashtags on the basis of $U_c^{\tau}$}
\State $\{H_c^{\tau+1}\}_{c \in \ensuremath{{\cal C}}\xspace} \gets \mbox{\sc HtClass}(\{U_c^{\tau}\}_{c \in \ensuremath{{\cal C}}\xspace})$
\State $\tau \gets \tau+1$
\Until{ {\em convergence} }
\State \textbf{return} $\{{\cal{U}}_c^{\tau}\}_{c \in \ensuremath{{\cal C}}\xspace}, \{{\cal{T}}_c^{\tau}\}_{c \in \ensuremath{{\cal C}}\xspace}, \{H_c^{\tau}\}_{c \in \ensuremath{{\cal C}}\xspace}$
\EndProcedure
\end{algorithmic}
\end{algorithm}

The Alg.~\ref{alg:iterative} illustrates the procedure. As  input the algorithm receives an initial set of polarized hastags $\left\{ H_{c}^{0} \right\}$ (initial \textit{seed}) for each class $c$ and the collection of relevant tweets \ensuremath{{\cal T}}\xspace.
The initial seeds have been selected by analyzing the most frequent among about 95 K unique hashtags:

{\small $H_{c_+}^{0}=$} {\footnotesize \texttt{\#refugeeswelcome \#refugeesnotmigrants \#welcomerefugees}}

{\small $H_{c_-}^{0}=$} {\footnotesize \texttt{\#refugeesnotwelcome \#migrantsnotwelcome \#norefugees}}

The initial seed $H_{c_+}^{0}$ is used in 36K tweets, whereas hashtags in class $c_-$ are used in only 2K tweets. One of the benefits of $PTR$ is that after only a few iterations the results are less dependent on the size of the original seed, correcting the unbalanced number of occurrences of the seed by class $c$ in the data.

The internal functions of Alg.~\ref{alg:iterative} are defined as follows:

\begin{itemize}[leftmargin=*]
\item $\mbox{\sc TwClass}$: a tweet is polarized to one class $c$ only if it contains only hashtags of one
class $\left\{ H_{c} \right\}_{c \in \ensuremath{{\cal C}}\xspace}$.

\item $\mbox{\sc UsClass}$: a user is polarized to one class $c$ only if
his polarized tweets of class $c$ are at least twice the number of his polarized
tweets of any other class.

\item $\mbox{\sc HtClass}$: an hashtag $h$ is assigned to one class $c$ if $S_c(h)> \beta \cdot S_{c'}(h) \quad \forall c'\neq c$, where
$S_c(h)$ is the conjunct probability of observing $h$ in tweets polarized to class $c$, and
not observing $h$ in the tweets polarized to other classes.
(For our experiments $\beta=0.005$ was chosen after empirical evaluation.)

\end{itemize}

The procedure adds information about polarization of the users by polarized hashtags extension through the analysis of all the tweets written by an already polarized users and not only the polarized tweets.
The iterative procedure has been run 4 times until convergence has been reached. We excluded from the hashtags retrieved by $PTR$ all the hashtags which directly mention a city or a country. This is to keep the sentiment value independent by the location in computing of the polarization. The combination of location and sentiment is done by crossing the space and sentiment.

Alg.~\ref{alg:iterative} extracts new hashtags at each iteration. We report the most relevant retrieved hashtags in addition to seed ones after the final iteration of the algorithm for
each class $c$:

{\small $H_{c_+}^{\tau=final}$} : {{\footnotesize \texttt{\#campliberty
\#health
\#humanrights
\#marchofhope
\#migrantmarch
\#refugee
\#refugeecrisis
\#refugeemarch
\#refugeescrisis
\#sharehumanity
\#solidarity
\#syriacrisis
\#trainofhope}}

{\small $H_{c_-}^{\tau=final}$} : {\footnotesize \texttt{
\#alqaeda
\#guns
\#illegalimmigration
\#illegals
\#invasion
\#isis
\#islamicstate
\#justice
\#migrant
\#migrantcrisis
\#muslimcrimes
\#muslims
\#no2eu
\#noamnesty
\#nomoremigrants
\#nomorerefugees
\#patriot
\#quran
\#stoptheeu
\#taliban
\#terrorism}}

From the analysis of the extracted hashtags we can see that people with a positive sentiment prefer to use the term \textit{refugees}, while people with a negative sentiment refer to them as \textit{migrants}, thus minimizing the fact that they are escaping war and persecution.  Users with a negative sentiment frequently use \textit{refugees} and the Islamic religion together, somehow correlating, in a prejudicial way, refugees with Islam and terrorism. Finally, we observe that individuals with negative sentiment are often patriotic and not pro Europe.

Note that the algorithm, may classify both users and tweets as non polarized, thus
favoring accuracy of truly polarized content.
The polarization algorithm was able to assign the sentiment to 68\% of the tweets and to 66\% of the users in our dataset.
Regarding EU-geolocated tweets and users,
the algorithm assigned the sentiment to 73\% of tweets and to 71\% of the users.

\subsection{Sentiment Analysis}
\label{subsec:paruserlco}

To answer the analytical question AQ2, we analyze the perception of the refugee crisis phenomenon by the European countries
by exploiting the sentiment and location dimensions of the Twitter users
in our dataset.
To simplify the notation in the following we refer to \ensuremath{{\cal U}_L}\xspace simply by \ensuremath{{\cal U}}\xspace.

Let us define $\rho$ the ratio between the number of polarized users pro \textit{refugees} and the number of users against \textit{refugees}:
\begin{equation}
\nonumber
\rho = \frac{ |\ensuremath{{\cal U}}\xspace_{c_+}| }{ |\ensuremath{{\cal U}}\xspace_{c_-}|  }
\end{equation}
The index $\rho$ gives a compact indication of the sentiment of a group of users.

We first analyze the sentiment across the various countries, and we then differentiate
between discussion about internal and external locations.

\subsubsection{Sentiment by country}

Figure~\ref{fig:sentiment_us}(a) shows the value of $\rho$ for users belonging
to the different European countries.
We observe that Eastern countries in general are less positive than Western countries. In particular, Russia and Turkey have a low sentiment index probably because they are highly affected by the flow of arrivals.
On the contrary, countries like Germany and Austria are more positive and this can be confirmed by the news  reporting their decision of opening borders to migrants.
Among western countries, France, UK, Italy and Netherlands have a low $\rho$ index. In Italy the large amount of refugees arrived mainly through the sea directly from Lybia or Tunisia and the tone of the discussion is  often characterized by negative notes.  In France the sentiment confirms all worries about, probably,  the situation of the Calais jungle.
The situation in Greece appears very different. The sentiment is positive even though this country remains by far the largest single entry point for new sea arrivals in the Mediterranean, followed by Italy. Greece
captured the attention of humanitarian organizations.
Countries like Ireland, Norway or Portugal are less interested by the phenomenon and therefore their perception might result more positive. Even for Spain $\rho$ is not particularly low since the problem of refugees coming from Western Mediterranean was limited in number of people compared to central and eastern countries.

\subsubsection{Internal and external country perception of the refugees crisis}

In the following we study the perceived sentiment in relation to the user country.
We denote as {\em internal perception} the sentiment of a user when mentioning his/her own country (or a city in his/her country). {\em External perception} refers to polarized tweets with no internal references.

Figure~\ref{fig:sentiment_us}(b) shows the sentiment ratio $\rho$ by country considering the internal perception, thus tweets mentioning the country itself. The $\rho$ computation is this case refers to the users of a country who mentioned in their tweets the country itself (or indirectly a city in the country).
We report only the countries for which we have a minimum amount of data.
We can see that Russia, France and Turkey have a really low $\rho$ index. We conjecture that the sentiment of a person, when the problem involves directly his/her own country, could be more negative since we are generally more critical when issues are closer to ourselves.

The external perception ratio is depicted in Figure~\ref{fig:sentiment_us}(b). Comparing the two maps, we see that internal and external perception is stable for UK and Sweden. Other countries have a much lower internal sentiment $\rho$ than external, and this is the case of France, Russia and Turkey. All these countries were indeed facing many critical problems due to the arrival of refugees to their borders. The case of \textit{Calais} is one of the most significant examples which could explain the case of the low ratio in France.
Germany, Hungary and Greece, on the contrary, have a better internal perception which might be due to the decision of Germany to open borders to allow many people to transit from Hungary to Germany, releasing the extremely difficult situation at the national borders.

\begin{figure*}[t]
	\centering
		\includegraphics[width=0.93\textwidth]{uk_bef_aft}
	\caption{Positive and negative users for different cities in UK in all period (left) before (center) and after (right) September 4. In the infographic the pies/bars show the number of polarized positive and negative users by city and the heat map in background indicates the value of $\rho$ for the cities considered in the legend. For some cities the tweets are not sufficient to compute polarization, therefore when the heat degrades to 0 it indicates no data.}
	\label{fig:uk_bef_aft}
\end{figure*}

\subsubsection{Sentiment Analysis: the UK case}
\label{sec:uk}

In this section we focus on  the sentiment analysis of UK citizens,
as UK is the most represented country in our dataset
and therefore a more detailed sentiment analyses can be done.
Indeed, for UK we detail the results at the granularity of the city level.

\inote{aiuto non capisco userloc non erano gli utenti georefereniati?? sono tutti polarizzati }

Figure~\ref{fig:uk_bef_aft} (left) shows the number of polarized users \ensuremath{{\cal U}_L}\xspace in the most represented cities of the country, with at least 100 polarized users in the dataset. We can see from the heatmap that there is a gradient of polarization from south to north in the sentiment. This could be due to the fact that the cities in the south, and London in particular, were more involved in the welcoming process of refugees and this might have generated more discontent even though the general perception is quite positive.
From the time series of $\rho$ for UK users we see an increase in the general sentiment ratio of the country after September 4.
We find news\footnote{Sept, 04: \url{http://www.bbc.com/news/uk-34148913} -- Sept, 16: \url{http://www.bbc.com/news/uk-34268604}} regarding that period from BBC and we think that the increase in the sentiment polarization could be be due mainly to the decision of the Prime Minister Cameron of acting with ``head and heart'' to help refugees. He allocated substantial amounts of money to humanitarian aid becoming, at that time, the second largest bilateral donor of aid to the Syrian conflict (after the US).
Figure~\ref{fig:uk_bef_aft} (middle) and (right), shows the comparison of the opinion in UK before and after September 4, respectively. We highlight again a gradient of polarization from north to south in both cases even though the sentiment ratio $\rho$ before and after that day is completely overturned. After September 4 the spreading of positive news in UK increases the sentiment and the volume of relevant tweets in all the country and probably government position reflects the sentiment of a vast majority of users which show support to refugees in their digital statements.

\enlargethispage*{1cm}

\subsection{Mentioned Location Analysis}
The last analysis we conducted aims at answering AQ3 by studying the sentiment of the tweets when mentioning specific countries.
We show how events impact differently the volume of tweets with positive or negative
sentiment. Furthermore, we relate the sentiment changes to events.

\begin{figure*}[t]
\centering
\subfloat[Tweet sentiment for Hungary]{\label{fig:mentionHUsenti}\includegraphics[width=0.32\textwidth]{Hungary_sentiment_per_Day.pdf}}
\subfloat[Tweet sentiment for Austria]{\label{fig:mentionATsenti}\includegraphics[width=0.32\textwidth]{Austria_sentiment_per_Day.pdf}}
\subfloat[Tweet sentiment for Croatia]{\label{fig:mentionCRsenti}\includegraphics[width=0.32\textwidth]{Croatia_sentiment_per_Day.pdf}} \\
\subfloat[Tweet sentiment for UK]{\label{fig:mentionUKsenti}\includegraphics[width=0.32\textwidth]{United_kingdom_sentiment_per_Day.pdf}}
\subfloat[Tweet sentiment for France]{\label{fig:mentionFRsenti}\includegraphics[width=0.32\textwidth]{France_sentiment_per_Day.pdf}}
\subfloat[Tweet sentiment for Germany]{\label{fig:mentionDEsenti}\includegraphics[width=0.32\textwidth]{Germany_sentiment_per_Day.pdf}}
\caption{Tweet sentiment for country mentions per day.}
\label{fig:featureAnalysis}
\end{figure*}

Figure~\ref{fig:featureAnalysis}~(a-c) shows the sentiment of tweets when mentioning three of the countries most impacted
by the refugees routes: Hungary, Austria and Croatia. We highlight an overall low number of mentions to these countries until the beginning of September. In the case of Hungary  and Austria there is a sudden increase at the beginning of September in the overall number of mentions, predominantly for $c_+$ with a relative increase in $c_-$. This is mostly due to the overall positive sentiment towards the events from the previous days (the death of Alan Kurdi, the young boy found he drowned), but also due to the good news of migrants being allowed to cross the Austro-Hungarian border. The negative sentiment starts to appear, and continues to grow, until the middle of September when the negative class tends to increase more than the positive one. Here we have tweets expressing negative feelings towards border controls on behalf of Austria (13-15 Sept) and Hungary arresting refugees crossing the border illegally (15-17 Sept). Croatia comes into play towards the end of our observation period when on the September 16th becomes a valid alternative to Hungary which closed its borders with Serbia. A similar analysis has been done for Greece, Macedonia and Serbia, all countries facing critical moments, but due to lack of space we are omitting here.

In Figure \ref{fig:featureAnalysis} (d-f) we look at the sentiment in relation to the mentions of UK, France and Germany. Both UK and Germany are rather balanced between positive and negative tweets. Germany presents exceptions on certain days when a positive feeling arises in support to the sad incidents related to refugees. We notice that the official media news at the end of August reported that Germany was welcoming refugees, while UK started showing a positive sentiment after the dramatic facts of Alan Kurdi and the announcement of taking in 20,000 refugees by 2020. France seems to have more negative feelings, probably due to the difficult situation in Calais and news about victims trying to across to UK while a positive peak appears in correspondence to the young victim found.


\section{Introduction}

The ternary rare-earth compound CeRu$_2$Al$_{10}$ has attracted much attention because of the mysterious transition at $T_0$=27 K.\cite{Strydom,Nishioka,Matsumura}
As for the long-range order (LRO) below $T_0$, Strydom proposed magnetic ordering.\cite{Strydom}
However, Nishioka $et~al$. pointed out that $T_0$=27 K is too high for RRu$_2$Al$_{10}$ with R=Ce because, even in GdRu$_2$Al$_{10}$, $T_{\rm N}$=16 K; they insisted that the origin of the LRO below $T_0$ is nonmagnetic and proposed charge density wave (CDW) formation.\cite{Nishioka}
Matsumura $et~al$. showed no evidence of magnetic ordering below $T_0$ from the results of $^{27}$Al-NQR measurement and proposed the occurrence of structural phase transition below $T_0$.\cite{Matsumura}
In our previous paper,\cite{Tanida} we studied the La substitution effect on CeRu$_2$Al$_{10}$ and the magnetic field effect on $T_0$ in order to clarify the nature of the LRO \cite{Tanida}, and found that $T_0$ is reduced by La substitution and disappears at $x\sim$0.45 in Ce$_x$La$_{1-x}$Ru$_2$Al$_{10}$.
The suppression of $T_0$ by a magnetic field along the easy magnetization axis was also observed.
From these results, we concluded that the origin of the LRO below $T_0$ is magnetic.
Considering the above points and a large magnetic entropy at $T_0$, a decrease in the magnetic susceptibility below $T_0$ along all the crystal axes, the existence of a gap in many physical quantities, and a positive pressure effect on $T_0$, we proposed that the LRO with a singlet ground state is formed below $T_0$.\cite{Tanida}
However, many physical properties remain to be explained from this standpoint, as mentioned in our previous paper.\cite{Tanida}
In the present study, we measured the transport properties of CeRu$_2$Al$_{10}$ single crystal, focusing on their anisotropy to clarify the unusual nature in the LRO below $T_0$.

Single crystals of Ce$_x$La$_{1-x}$Ru$_2$Al$_{10}$($x$=1 and 0.1) and CeFe$_2$Al$_{10}$ were prepared by the Al self-flux method.
Hall resistivity was measured by the conventional four probe method below $\sim$50 K.
Thermal conductivity was measured by the conventional steady state method below $\sim$ 50 K.
Thermoelectric power was measured by the conventional differential method between 1.8 and 300 K.

Figure 1 shows the temperature ($T$) dependence of the Hall resistivity $\rho_{\rm H}$ of CeRu$_2$Al$_{10}$ measured at $H$=5 T, which is applied along the $a$-, $b$-, and $c$-axes.
$\rho_{\rm H}$ shows a roughly $H$ linear dependence up to 5 T and the sign of $\rho_{\rm H}$ is positive in the entire temperature range studied here.
$\rho_{\rm H}$ shows a large anisotropy depending on the applied magnetic field direction.
$\rho_{\rm H}$ for $H\parallel b$ is the largest and that for $H\parallel a$ is the smallest.
$\rho_{\rm H}$ for $H\parallel b$ increases with decreasing temperature in a paramagnetic region and increases largely after showing a kink at $T_0$.
$\rho_{\rm H}$ below $T_0$ shows no convex $T$ dependence, which is expected when the gap is opened on the Fermi surface but shows a concave one.
For $H\parallel c$, the $T$ dependence of $\rho_{\rm H}$ in the entire temperature range is similar to that for $H\parallel b$, although its magnitude is much smaller than that for $H\parallel b$.
The magnitude at the lowest temperature is about one third of that for $H\parallel b$.
Noted that the anomaly at $T_0$ is much less pronounced than that for $H\parallel b$ and a small hump is seen at approximately $T$$\sim$17 K.
For $H\parallel a$, $\rho_{\rm H}$ is the smallest and the $T$ dependence above $\sim$ 20 K is very different from those for $H\parallel b$ and $c$.
No anomaly is recognized at $T_0$ and a concave $T$ dependence is seen down to $\sim$17 K below $\sim$25 K; in a paramagnetic region, its $T$ dependence is very small and its magnitude is also much smaller than those for $H\parallel b$ and $c$.
We emphasize that $\rho_{\rm H}$ below $T_0$ for $H{\parallel}b$ where the electrical current flows in the $ac$-plane shows very different behaviors from those for $H{\parallel}c$ and $a$.
$\rho_{\rm H}$ for $H{\parallel}c$ is largest and that for $H{\parallel}a$ is smallest in the whole temperature range studied here.
Although $\rho_{\rm H}$ for $H{\parallel}b$ and $c$ show a kink at $T_0$, that for $H{\parallel}a$ shows no anomaly.
Although the $T$ dependence is seen for $H{\parallel}b$ and $c$ in a paramagnetic region, $\rho_{\rm H}$ for $H{\parallel}a$ is independent of temperature.
If we estimate carrier concentration assuming a single carrier, we will obtain values of $\sim$0.1, $\sim$0.02, and $\sim$0.06/unit cell at $T$=1.5 K for $H\parallel a$, $b$, and $c$, respectively.
At $T$=35 K, they are $\sim$6.3, $\sim$1.2, and $\sim$2.0/unit cell for $H\parallel a$, $b$, and $c$, respectively.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.55\linewidth]{16112Fig1.eps}
\end{center}
\caption{
(Color Online) Temperature dependence of Hall resistivity of CeRu$_2$Al$_{10}$ measured at $H$=5 T, where data were obtained by following the configurations of (i) $H{\parallel}a$, $I{\parallel}c$, $V_{\rm H}{\parallel}b$, (ii) $H{\parallel}b$, $I{\parallel}a$, $V_{\rm H}{\parallel}c$, and (iii) $H{\parallel}c$, $I{\parallel}a$, $V_{\rm H}{\parallel}b$, respectively. Here, $V_{\rm H}$ is the Hall voltage.
}
\label{f1}
\end{figure}

Figure 2 shows the $T$ dependence of the thermal conductivity $\kappa$ along the $a$-, $b$-, and $c$-axes.
The $T$ dependences and magnitudes of $\kappa_a$ and $\kappa_c$ are similar to each other but different from those of $\kappa_b$.
$\kappa_a$ and $\kappa_c$ show a sharp dip at $T_0$ and a clear enhancement below $T_0$.
After showing a broad maximum at approximately $T{\sim}$24 K, $\kappa_a$ and $\kappa_c$ decrease with decreasing temperature.
Although $\kappa_b$ also shows a dip at $T_0$, it is much less pronounced than in $\kappa_a$ and $\kappa_c$ and no enhancement below $T_0$ is seen.
$\kappa$ along the three crystal axes is roughly proportional to the temperature below $\sim$ 12 K down to 2 K.
A negative intersect is obtained if it is extrapolated down to $T$=0.
At low temperatures below 2 K, $\kappa$ is expected to show a $T^3$ dependence, which originates from the specific heat of phonon because the sound velocity and phonon mean free path are expected to be independent of temperature at low temperatures.
Since the magnitude of the electrical resistivity $\rho$ is large, the electronic contribution to $\kappa$ is small.
Even in the case with the smallest $\rho$ along the $a$-axis, the electronic contribution is estimated to be $\sim$2\% at $T$=20 K assuming the Wiedemann-Franz law.
Thus, thermal current is mainly carried by phonon.
Then, the observed anisotropy of $\kappa$ is considered to be dominated by the anisotropy of the phonon contribution.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.55\linewidth]{16112Fig2.eps}
\end{center}
\caption{
(Color Online) Temperature dependence of thermal conductivity of CeRu$_2$Al$_{10}$ along the $a$-, $b$-, and $c$-axes.
}
\label{f1}
\end{figure}

Figure 3 shows the $T$ dependence of the thermoelectric power $S$ of Ce$_{0.1}$La$_{0.9}$Ru$_2$Al$_{10}$ along the $a$-, $b$-, and $c$-axes.
$S$ is negative at high temperatures and is positive at low temperatures.
All the results show similar $T$ dependences and their magnitudes are also close to each other.
At high temperatures, $S$ shows a roughly $T$-linear dependence with a negative slope.
At $T\sim$ 10 K, a distinct positive peak is observed.
Considering the results of $\rho$ and specific heat of this sample, this positive peak is expected to originate from the Kondo effect.
A very broad hump at $\sim$150 K may result from the crystalline-electric-field (CEF) effect. \cite{Fulde,Maekawa}

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.55\linewidth]{16112Fig3.eps}
\end{center}
\caption{
(Color Online) Temperature dependence of thermoelectric power of Ce$_{0.1}$La$_{0.9}$Ru$_2$Al$_{10}$ along the $a$-, $b$-, and $c$-axes.
}
\label{f1}
\end{figure}

Figure 4 shows the $T$ dependence of $S$ of CeRu$_2$Al$_{10}$ along the $a$-, $b$-, and $c$-axes.
All the results show a broad maximum at $T\sim$150 K, which is much more pronounced than those of Ce$_{0.1}$La$_{0.9}$Ru$_2$Al$_{10}$.
This maximum may reflect the CEF splitting, which is expected to be larger than $\sim$ 300 K.
Although a change of sign is observed in $S_c$ between $\sim$25 K and $\sim$100 K, and the magnitude of maximum differs between $S_a$, $S_c$, and $S_b$, the overall $T$ dependences are similar to each other along three crystal axes in a paramagnetic region.
Namely, a broad maximum at high temperatures of approximately ${\sim}$150 K, a decrease down to $\sim$50 K, and an increase down to $T_0$.
The increase in $S$ below 50 K down to $T_0$ seems to be associated with the large increase in $\rho$ in the same temperature region.
$S$ below $T_0$ shows a very anisotropic and anomalous $T$ dependence as is shown in the inset of Fig. 4.
The most characteristic feature is that although $S_a$ and $S_c$ show a steep increase below $T_0$, $S_b$ shows a steep decrease below $T_0$.
This again suggests that the nature in the $ac$-plane is different from that along the $b$-axis.
Below $T_0$, $S_a$ shows a pronounced maximum at $T\sim$22 K and decreases with decreasing temperature.
A pronounced shoulder is seen at $T\sim$8 K.
$S_c$ also shows a steep increase below $T_0$.
After showing a very small concave curvature at ${\sim}$14 K, it shows a maximum at $T{\sim}$6 K.
On the other hand, $S_b$ shows a steep decrease below $T_0$ and after exhibiting a broad minimum at $T\sim$18 K, it shows a maximum at $T\sim$ 6 K.
Thus, $S$ shows two characteristic behaviors.
One is a steep increase in $S_a$ and $S_c$ and a steep decrease in $S_b$ below $T_0$.
Another is the existence of a broad maximum at 6$\sim$8 K along all the crystal axes.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.55\linewidth]{16112Fig4.eps}
\end{center}
\caption{
(Color Online) Temperature dependence of thermoelectric power of CeRu$_2$Al$_{10}$ along the $a$-, $b$-, and $c$-axes.
}
\label{f1}
\end{figure}

The present results of $\rho_{\rm H}$, $\kappa$, and $S$ strongly suggest that the origin of the mysterious LRO below $T_0$ exists in the $ac$-plane.
First, we consider the nature of LRO below $T_0$ from the standpoint of the crystal structures.
The powder X-ray diffraction was examined by BL02B2 in SPring-8.
The lattice constants of CeRu$_2$Al$_{10}$ are $a$=9.12233(4), $b$=10.27486(4), and $c$=9.18353(4)${\rm {\AA}}$ and those of CeFe$_2$Al$_{10}$ are $a$=9.00628(6), $b$=10.23105(7), and $c$=9.07838(6)${\rm {\AA}}$ at room temperature.
These values are obtained by Rietveld analysis.
Although the valence of the Ce ion in CeRu$_2$Al$_{10}$ is considered to be +3, the Ce ion in CeFe$_2$Al$_{10}$ is considered to be situated in a valence fluctuation regime from the magnetic susceptibility.\cite{Muro,Nishioka}
In our previous study,\cite{Nishioka} we showed that the $\rho$ of CeRu$_2$Al$_{10}$ becomes closer to that of CeFe$_2$Al$_{10}$ with increasing pressure.
This suggests that some hint on the LRO in CeRu$_2$Al$_{10}$ could be obtained from the difference of the lattice constants between these two compounds.
Here, we consider the ratio (Ru/Fe) of each lattice constant of CeRu$_2$Al$_{10}$ to that of CeFe$_2$Al$_{10}$.
The ratios are 1.01289, 1.00428, and 1.01147 for the $a$-, $b$-, and $c$-axes, respectively.
The magnitude of shrinkage in the $ac$-plane is more than twice as large as that along the $b$-axis.
In the $ac$-plane, the magnitude of shrinkage for the $a$-axis is nearly the same as that for the $c$-axis.
Considering these results, we conjecture that the LRO below $T_0$ mainly originates from the $ac$-plane.

Here, we describe the characteristics of the crystal structure in detail.
Figures 5(a) and 5(b) show the crystal structures of CeRu$_2$Al$_{10}$, which are viewed from the $c$- and $a$-axes, respectively.
In these figures, Ru-Al 1$\sim$Al 5 are connected by lines.
By considering the present results showing that the transport properties in the $ac$-plane are different from those along the $b$-axis, the above-mentioned anisotropy of lattice constants and the fact that the Al 5 site is a specific site from the NQR measurement, we consider that a layer formed by Ce, Ru, and Al 1$\sim$Al 4 is separated by Al 5 ions along the $b$-axis.
Although Al 5 ions lie on a straight line along the $b$-axis, as shown in Fig. 5(b), when viewed from the $a$-axis, the ions form a zigzag structure along the $b$-axis when viewed from the $c$-axis, as shown in Fig. 5(a).
In the upper and lower planes of this layer, there exist Ce and Al 1$\sim$Al 4 ions.
Ru ions are situated in a middle of this layer along the $b$-axis.
Although Ce ions in the upper and lower planes are equivalent, here, we distinguish them using different colors (black and gray) to see the physical meaning easily in the present discussion.
It should be noted that Ce and Al 1$\sim$Al 4 ions do not lie on the same plane.
Figure 5(c) shows the crystal structure viewed from the $b$-axis.
The Ce ions on the upper plane are surrounded by a large square formed by Al 2 and Al 3 ions.
A small square formed by Al 1 and Al 4 ions which are situated just above Ce ion in a lower plane, is situated just in the middle of four large squares.
Large and small squares are connected by two kinds of rhombuses formed by Al 1-Al 3 and Al 2-Al 4 ions.
Here, the two kind of squares are slightly distorted and the two kinds of rhombuses are not equivalent, which leads to a small difference between the lattice constants $a$ and $c$.
Figure 5(d) shows a schematic picture of the crystal viewed from the [10$\overline{1}$] direction.
In this figure, it is seen that a layer formed by Ce, Ru, and Al 1$\sim$Al 5 ions is constructed by a trapezoid with the staggered arrangement along the [101] direction.
Ce ions are situated in the middle of the base of a trapezoid.
Thus, the crystal structure of CeRu$_2$Al$_{10}$ could be viewed as a two-dimensional system.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.6\linewidth]{16112Fig5.eps}
\end{center}
\caption{
(Color Online) Crystal structure of CeRu$_2$Al$_{10}$ viewed from (a) $c$-axis, (b) $a$-axis, (c) $b$-axis, and (d) [10$\overline{1}$] direction. Although all the Ce ions are equivalent, here, we distinguish Ce ions in the upper plane (black circle) from those in the lower plane (gray circle) of the layer formed by Ce, Ru, and Al 1$\sim$ Al 4.
The upper and lower planes are drawn by a solid and dotted lines, respectively.

}
\label{f1}
\end{figure}

Now, we discuss the present results.
First, we discuss thermal conductivity.
As mentioned above, the contribution of the charge carrier can be neglected and thermal current is mainly carried by phonons.
Then, $\kappa$ is expressed as $C_{ph}v_sl_{ph}/3$.
Here, $C_{ph}$, $v_s$, and $l_{ph}$ are the specific heat of phonon, sound velocity, and mean free path of phonon, respectively.
Since $C_{ph}$ does not depend on the crystal axis, the anisotropy of $\kappa$ originates from that of $v_s$ or $l_{ph}$.
At high temperatures, $\kappa_b$ is the smallest.
This could be explained by considering the existence of the zigzag alignment of the Al 5 site along the $b$-axis, which is shown in Fig. 5(a).
At around $T_0$, although a clear dip at $T_0$ and a clear enhancement below $T_0$ are observed in $\kappa_a$ and $\kappa_c$, the anomalies at $T_0$ in $\kappa_b$ are much less pronounced.
These suggest that the origin of the LRO lies in the $ac$-plane, and a small anomaly along the $b$-axis seems to appear as a secondary effect.
In our previous paper,\cite{Tanida} we proposed that the enhancement of $\kappa$ below $T_0$ could be explained as follows.
The absolute value of $\rho$ is large and so $\kappa$ is dominated by phonons.
Below $T_0$, by forming a singlet pair between Ce ions, the vibration of Ce ions is expected to be suppressed more than when each Ce ion vibrates independently above $T_0$.
As a result, the mean free path of phonons could be enhanced below $T_0$.
This causes the enhancement of $\kappa$ below $T_0$.
At present, we do not know how $v_s$ behaves at around $T_0$.
The above should be confirmed in the future studies.

Next, we discuss the Hall effect.
Before discussing the Hall effect, we mention the results of $\rho$.
$\rho$ shows a steep increase below $T_0$ along all the crystal axes.\cite{Nishioka}
This simply suggests that the gap is opened on the Fermi surface rather isotropically.
However, such a situation could occur only when the almost complete nesting of the Fermi surface takes place.
However, this is quite difficult to expect in the present three-dimensional complex sample.
Furthermore, if such a complete isotropic nesting takes place below $T_0$, $\rho_{\rm H}$ should increase below $T_0$ in all the applied field directions.
However, no such behavior is observed.
No anomaly is seen in $\rho_{\rm H}$ for $H\parallel a$ at $T_0$.
This denies the gap opening at least for $H\parallel a$ and suggests that it is better to find other origins of the anomalous transport properties below $T_0$, except the gap opening on the Fermi surface.
$\rho_{\rm H}$ shows the clearest anomaly at $T_0$ for $H\parallel b$ and the largest magnitude.
Here, current flows in the $ac$-plane.
This suggests that the transport property in the $ac$-plane is most largely affected by the LRO at $T_0$.
In a paramagnetic region, although $\rho_{\rm H}$ shows an increase with decreasing temperature down to $T_0$ for $H\parallel a$ and $c$, that for $H\parallel b$ is temperature-independent in the temperature range studied here.
The former could be ascribed to a decrease in carrier concentration with decreasing temperature, which seems to be consistent with the $T$ dependence of $\rho$, or to the anomalous Hall effect.
However, no $T$ dependence of $\rho_{\rm H}$ for $H\parallel a$ where current flows in the $bc$-plane is observed, and its magnitude is much smaller than those for $H\parallel b$ and $c$ above $T_0$.
Thus, both below and above $T_0$, it is difficult to estimate the real carrier concentration in CeRu$_2$Al$_{10}$.
Further studies are necessary to clarify the origin of the anisotropic behavior of $\rho_{\rm H}$.

Next, we discuss thermoelectric power, which shows the most anisotropic behavior below $T_0$ among the three transport properties studied here.
$S$ is expressed as

\begin{equation}
\displaystyle S=\frac{1}{eT}\frac{\int\sigma(\varepsilon)(\varepsilon-\zeta)\frac{\partial f(\varepsilon)}{\partial \varepsilon}d\varepsilon}{\int \sigma(\varepsilon)\frac{\partial f(\varepsilon)}{\partial \varepsilon}d\varepsilon},
\end{equation}

\noindent
where, $f(\varepsilon)$ is the Fermi distribution function and $\zeta$ is the Fermi energy.
$S$ is expressed by Mott formulation as

\begin{equation}
\displaystyle S=\frac{\pi^2 k_{\rm B}^2 T}{3e}\left[\frac{1}{N(\varepsilon)v^2}\frac{\partial N(\varepsilon)v^2}{\partial \varepsilon}+\frac{1}{\tau(\varepsilon)}\frac{\partial \tau(\varepsilon)}{\partial \varepsilon}\right]_{\varepsilon=\zeta},
\end{equation}

\noindent
where $N(\varepsilon)$, $v$, and $\tau(\varepsilon)$ are the density of states, Fermi velocity, and relaxation time of conduction electrons, respectively.
In order to obtain a large magnitude of $S$, a large energy dependence of $\tau(\varepsilon)$ at around $\varepsilon=\zeta$ as a function of energy is necessary.
$\rho$ is determined by the magnitude of $\tau(\varepsilon)$ at $\varepsilon=\zeta$ itself.
In $S$, its magnitude is important but the energy dependence of $\tau(\varepsilon)$, $\partial \tau(\varepsilon)/\partial \varepsilon$ is more important.
Namely, the inelastic scattering of charge carriers associated with the term $(\varepsilon-\zeta)$ in eq. (1) is essentially important to understand the anomalous behavior in $S$.
When the gap is opened on the Fermi surface, the first term in eq. (2) originating from $N(\varepsilon)$, which is affected by the gap opening, is also important.
However, as mentioned above, it is expected that the gap is not opened at least isotropically on the Fermi surface.
Thus, we ascribe the anomalous $T$ dependence of $S$ below $T_0$ to the energy dependence of $\tau(\varepsilon)$ at around $\varepsilon=\zeta$.
It is known that the Kondo impurity induces a large anomalous $T$ dependence in $S$ at low temperatures.
Kondo explained this unusual behavior of $S$ by considering the fourth-order perturbation $J^3 V$.\cite{Kondo}
The potential scattering term $V$ is introduced for $\tau(\varepsilon)$ to be an odd function of energy.
Peshcel and Fulde calculated $S$ for a compound with a singlet ground state by considering the third-order perturbation $J^2 V$.\cite{Fulde}
The existence of CEF splitting with a singlet ground state reduces the perturbation from the fourth order to the third order.
They showed that $S$ exhibits a Schottky-type anomaly in its $T$ dependence.
This originates from the inelastic scattering of charge carriers by a spin-flip scattering between the CEF ground state and the excited state.
Namely, in such a CEF level scheme, the higher the energy, the larger the spin-flip scattering probability because the magnetic excited state is situated on the higher energy side.
In our previous paper,\cite{Tanida} we proposed that the singlet ground state is formed below $T_0$.
The present anomalous $T$ dependence of $S$ below $T_0$ could be explained using the above mechanism proposed by Peschel and Fulde.
In the model by Peschel and Fulde, the energy splitting between two levels is temperature-independent and so a Schottky-type anomaly is obtained.
However, in the present case, the singlet-triplet splitting is induced below $T_0$, which leads to a discontinuous enhancement below $T_0$.
The difference in the sign of $dS/dT$ between the $ac$-plane and the $b$-axis just below $T_0$ could be ascribed to a difference in the sign of $V$, although its microscopic mechanism is as yet unknown.
A maximum of $S$ together with a shoulder of $\rho$ at $T\sim$8 K suggests a change in the energy dependence of $\tau(\varepsilon)$ at around this temperature.
This suggests the existence of some kind of structure within a spin gap.

To conclude, we studied the thermal transport properties in CeRu$_2$Al$_{10}$ single crystal.
All the transport properties show very anisotropic behaviors below $T_0$.
Those in the $ac$-plane are very different from those along the $b$-axis, which suggests that the system could be viewed as a two-dimensional system.
The results of $\rho_{\rm H}$ deny a gap opening on the Fermi surface at least for $H\parallel a$ and suggest the existence of other mechanisms of the anomalous transport properties except the gap opening on the Fermi surface.
The results of $\kappa$ and $S$ below $T_0$ could be explained by assuming the LRO with a singlet ground state.
However, the ground state is not simple but has a structure within a spin gap.