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\begin{document}
\title{Citychrone Platforms: quantities description, open data and algorithms.}
\author[1]{Bernardo Monechi}%
\affil[1]{Affiliation not available}%
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\date{\today}
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\section{CityChrone platform - Science for City, Citizen for Science.}
The CityChrone Platform has two principal objectives: the first one is to contribute to base on quantitative studies the science of city. The second one is to allow users and citizen to participate in finding new and creative solution to public transport problems in city.
\subsection{Science for City}
The CityChrone project study the quality of the services of the public transport in cities. The CityChrone platform shows simple and meaningful quantities to measure the quality and the performance of public transport in cities. It allow to answer questions like: "Which zone of the city is well served by pubic transport?". "How much the public transport of Paris differ with those of Rome?".
The CityChrone Project aims to give quantitative measure of cities, it is intended as a theoretical as well as "experimental" work to help in basing the emergent field of the "New Science of City"\ref{batty2013new}. Moreover the measures will be presented in a interactive and user-friendly platform that allows the more vast audience to understand and reuse the results. The data produced as well as the code used will be freely downloadable from open-source platform, allowing scientist, institution and citizen use it.
\subsection{Citizen for Science}
The second part of the project calls users of the platform to play in order to solve very difficult scientific and society issue. The problem which users will face off is finding new public transport scenario in order to optimize the quality measure described above. For specific cities there is a section called "new Scenario" where it is possible, constraint to a limited budget, add new metro lines to the city and see, in nearly real time, how change the public transport services in the city. The platform uses the intellectual ability of users to explore the huge space of possible new subways scenario, impossible to explore by brute-force algorithms. At the end of each new configuration tested the position in the ranking of the scenario is shown enhancing the gamification aspect of the platform.
\section{Quantities definition:}
In the next subsections we define the quantities that measure the quality of public transport services in cities shown in \href{www.citychrone.org}{citychrone.org}. We start from the isochrone layers, prerequisite to understand the other quantities: {\bf Velocity Score} and the {\bf Sociality Score}.
\subsection{Isochrone}
An isochrone at time $t$ is the surface at equal time distance from a starting points. In the layer "isochrones" in \href{www.citychrone.org}{citychrone.org} the isochrones, computed by public transports are shown. In fig.1 is shown the public transport isochrones in New York city, every $15m$ from a starting point in Manhattan. On the \href{www.citychrone.org}{citychrone.org} is possible to explores the isochrones of the cities, clicking on the map so to change the starting point.\selectlanguage{english}
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\includegraphics[width=0.70\columnwidth]{figures/newyorkIso1/newyorkIso1}
\caption{{Replace this text with your caption%
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\subsection{Velocity Score}
{\bf The Velocity Score of point in the city can be interpret as the velocity that a person has from the considered point, chosen a random directions, in a typical daily trip with public transport}. Larger it is, better the point is server by public transports.
The details how it is computed is explained in the following. \newline
For each point in the cities it is possible to compute the isochrones. The isochrone at different times represent an expansion process starting from a point. The more efficient is the public transport in a considered area, the more fast will grow the surface within the isochrone. This information is summarized by the {\bf Velocity Score}, which quantifies how fast this area is growing (i.e. the speed of growth of the ``average radius'' of the area). The precise definition is the following, consider the area $A(t, P)$ of the isochrone at time $t$, starting from the point $P$. If we consider this area as circular we can compute its ray $r(t,P)$:
\begin{equation}
r(t,P) = \sqrt{\frac{A(t, P)}{\pi}}
\end{equation}
and if we divide by time, we have a quantity that is a velocity:
\begin{equation}
v(t,P) = \frac{r(t,P)}{t}
\end{equation}
Now we have a velocity that depend on the time of the isochrone that we are considering. We have to average on the time in order to have for each point on the map a quantity not depending on time. For this purpose we use the ''time-budged distribution'' of the individuals moving in a city $f(t)$, i.e. the distribution of the maximum amount of time a person typically spend travelling during its daily activities. Hence, we defined the \emph{Velocity Score} of an point $P$ as:
\begin{equation}
v(P) = \int_0^{\infty} v(t, P) f(2t) dt,
\end{equation}
$f(t)$ is evaluated at $2t$ since we suppose that each individual performs the longer trip possible in order to be able to come back to their starting point. The choice of $f(t)$ is in principle arbitrary, but many examples can be found in literature that have been extrapolated from empirical data. Here, we will use the functional form derived in \cite{kolbl2003energy} for different means of transportation, using those one indicated for public transport in cities. In fig.2 is shown the {\bf Velocity Score} of Rome.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/velocityRome/velocityRome}
\caption{{\label{fig:velocity}{\bf Velocity Score} of the city of Rome. Larger is the value better the point is served by public transport. The center is better served than the suburbs. There are large part of of Rome that as very low values. Go to \href{http://www.citychrone.org}{CityChrone} to explore interactively the map and compare different cities.%
}}
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\end{figure}
\subsection{Sociality Score}
{\bf {\bf Sociality Score} quantifies how many citizens it is possible to reach with a ``typical trip'' starting from somewhere in the city}.
An expanding Isochrone not only covers larger and larger areas as the time increases, but also larger and larger parts of the population living within the urban area. {\bf Sociality Score} helps crossing the information coming from public transport data to the way in which the population is distributed in the city. Alternatively, this can be seen as a quantification of the amount of people a person living there can potentially meat with a typical working day trip with public transport.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/sociality/sociality}
\caption{{\label{fig:sociality}{\bf Sociality Score} of the city of Rome. Larger is the value more people potentially you can meet by public transport services. This quantity incorporate the data of the population distribution in cities in the measure of the quality of public transport service. Go to \href{http://www.citychrone.org}{CityChrone} to explore interactively the map and compare different cities.%
}}
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\end{figure}
\section{Data} The core of Citychrone is a database with the collections of \emph{General Transit Feed Specification} (\href{https://developers.google.com/transit/gtfs/reference/}{GTFS}) public transport data. GTFS is a data format developed by Google, in order to incorporate transit data about public transport into the Google Maps service\footnote{https://www.google.it/maps}. GTFS data can be often freely downloadable from the web pages of the public transport company, or from some web site that collect them, like \href{https://transitfeeds.com/}{transitfeeds}. These data with the street graphs downloadable from \{https://www.openstreetmap.org}{OpenStreetMap} allow for the computation of the time needed to reach each point in a city from all the other point in the same city using public transports. The Populations data has been gathered through the \href{http://ec.europa.eu/eurostat/web/gisco/geodata/reference-data/population-distribution-demography/geostat}{Eurostat Population Grid} for the European cities and the Gridded Population of the world made by the Center for International Earth Science Information Network \cite{sedacV4}.
\section{Algorithms}
For the routing computations we use a modified version of the \emph{Connection Scan Algorithm} (CSA) \cite{dibbelt2013intriguingly}. We compute the footpaths by a \href{https://github.com/Project-OSRM/osrm-backend}{OSRM} server.
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