On maps

How are “mobility” and trips visualized and represented? Well, the most direct, intuitive way of doing so, is using maps. Representations, converting the 3-dimensional earth (*sphere*) to a flat  2-dimensional surface. This post is about maps, map properties, map distortion and curious maps. We hope you enjoy it!

Mapping the earth, or parts of it, is a classic, well-studied problem. For hundreds / thousands of years, cartographers and mathematicians have come up with different methods to map the curved surface of the earth to a flat plane. The main problem is that you cannot do this perfectly, (Theorema Egregium). The shape, area, distances and directions of the surface cannot be represented properly at the same time on a map.


Shape: If a map preserves shape, then feature outlines (like country boundaries or the coast lines) look the same on the map as they do on the earth. A map that preserves shape is conformal. The amount of distortion, however, is regular along some lines in the map. For example, features lying on the 20th parallel are equally distorted, features on the 40th parallel are equally distorted (but differently from those on the 20th parallel), and so on. The Mercator projection is one of the most famous and well-used shape-preserving maps:


Area: If a map preserves area, then the size of a feature on a map is the same relative to its size on the earth. For example, on an equal-area world map, Spain takes up the same percentage of map space that the actual Spain takes up on the earth. In an equal-area map, the shapes of most features are distorted. No map can preserve both shape and area for the whole world, although some come close over sizeable regions. Sinusoidal projection is an area-preserving projection:


Distance: If a line from a to b on a map is the same distance (accounting for scale) that it is on the earth, then the map line has true scale. No map has true scale everywhere, but most maps have at least one or two lines of true scale. For instance, in the Casini projection, the distances perpendicular to central meridian are preserved:


Direction: Direction, or azimuth, is measured in degrees of angle from north. On the earth, this means that the direction from a to b is the angle between the meridian on which a lies and the great circle arc connecting a to b. If the azimuth value from a to b is the same on a map as on the earth, then the map preserves direction from a to b. No map has true direction everywhere.

Finding the compromise: Most of the maps used are compromise solutions, partially preserving some of the above mentioned properties. The most used one (by far) is the one you can find in Google Maps, OpenStreetMaps etc. called Web Mercator, Google Web Mercator, WGS 84 Web Mercator or WGS 84/Pseudo-Mercator. It is a variation of the Mercator projection, ignoring the ellipticity of Earth for faster computation:


The Winkel tripel projection. “Triple” stands for trying to minimize errors in three properties at the same time: area, direction, and distance. The Winkel tripel is the arithmetic mean of different projections (equi-rectangular, area and shape preserving)


There is even a whole family called Myriahedral projections. These consider the earth *sphere* to be a polyhedron with a very large number of faces, a “myriahedron”. This myriahedron is cut open into small pieces and unfolded. The resulting maps have a large number of subareas that are (almost) conformal and that (almost) conserve areas. The location of the map interruptions can be “selected” (oftenly using sea areas etc)

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Some ingenious representations mix the approach from Myriahedral projections and other property-preserving projections. e.g. the Goode Homolosineprojection:


All the previous projections provoke distorsion. There is no perfect projection. In the nineteenth century, Nicolas Auguste Tissot developed a simple method for analysing map-projection distortion. An infinitely small circle on the earth’s surface will be projected as an infinitely small ellipse on any given map projection. The resulting ellipse of distortion, or “indicatrix”, shows the amount and type of distortion at the location of the ellipse. Some examples for the most-used projections are given below.


If all the previous was not enough, it just leaves the door open to other projections that represent additional variables in maps, such as socio-demographic or technical indicators.

A map with country size proportional to population:


Proportional to number of immigrants:


Proportional to the number of tourists (Spain the biggest country in the world!):


Or even proportional to the total number of flights (this is one of my favourites!):


Some references and further reading on the topic:

INXmas greetings, 2017

We have had lots of fun innovating in 2016, so we are eager for a 2017 full of harder technical and scientific challenges, new research threads and complex innovation.

All the Innaxis team wish you a Merry Xmas break -including some fun and rest-  and a superb 2017!

ho ho ho!!!


ComplexityCosts holds Close-Out Meeting

After more than four years of intensive research the SESAR WP-E project ComplexityCosts has finally concluded. Project partners from the University of Westminster and Innaxis gathered with experts at the EUROCONTROL Experimental Centre in Brétigny-sur-Orge, France in early October to discuss the project results and close the research activities.

The ComplexityCosts study focused on the trade-offs between several disturbances and mechanisms from a passenger and stakeholder’s costs perspective. A major highlight of the project was the concept of resilience costs and further identifying a metric to effectively measure it.

The research continues on within the Horizon2020 DATASET2050 and SESAR LTER Vista projects, so stay tuned for further developments on mobility research.

EU Door-to-Door Mobility Workshop: 12th July 2016

We’re pleased to host and coordinate the first workshop examining EU door-to-door mobility.
An outline of sessions can be found below (abstracts are here).

Date: 12th July 2016. 10:30 – 17:00 (approx)

Location: 309 Regent Street, London W1B 2HW University of Westminster, UK

10:00 refreshments on arrival

Welcome and introduction – University of Westminster (PDF)

  • Session 1. Challenges of a data-driven model

The DATASET2050 model

The current state of mobility in EuropeUniversity of Westminster (PDF)
Which journeys are in scope when measuring the 4-hour door-to-door target?
What data sources are available for the current and future models?
Meeting the passenger’s demand: current and futureBauhaus Luftfahrt (PDF)
Challenges ahead: how will we model 2035 and 2050?
Assessing current supply and demand profiles.
Developing a new model for European mobility Innaxis (PDF)
What new metrics (and segmentations) do we need, apart from simply measuring average journey times?
Analytical approach – what metrics are needed?
What is the current status of such journeys – latest progress with the model.

  • Session 2. Further exploring the journey process phase by phase – where are the efficiency gains?

Door-to-kerbKai Nagel, Technical University of Berlin (PDF)
Improved airport accessibility: intermodal mobility; efficiencies of different modes (e.g. better utilisation of road-based modes – fuller cars/taxis; prioritisation schemes); modal shift; integration and passenger confidence.
Kerb-to-gateGenovefa Kefalidou, Horizon 2020 PASSME project (PDF)
Reducing door-to-door airport travel time for passengers in Europe.
Providing passengers with real-time information on predicted demand for airport services.
Improving the airport experience for passengers.
Gate-to-gateSteve Williams, NATS (PDF)
The impact of new SESAR solutions aimed at improving gate-to-gate operations, including free-routing, business trajectories, functional airspace blocks and ATM performance targets.
The role of wider EU policies such as Regulation 261/2004.

  • Session 3. Looking ahead to 2035 and 2050

Futures near and farChristoph Schneider, Munich Airport (PDF)
Evolution of demand – market maturities, new technologies and travel patterns.
From where will the key performance improvements come? – panel discussion (PDF)
Major improvements and barriers. Is the 4-hour target achievable – at what price? What should be the role of regulation and policy?
Close and wrap-upUniversity of Westminster (PDF)

Registration: Attendance is free of charge, however the number of places are limited.
Dynamic conversations and exchanges of views are encouraged at the workshop.

EU Door-to-Door Mobility Workshop – Abstracts

  • Session 1. Challenges of a data-driven model

The current state of mobility in Europe – University of Westminster
The foundations of the DATASET2050 model are described in this presentation, along with some of the corresponding data sources used in its construction. Using mobility, we show roughly how far from the target we are currently in Europe, with optimistic and less optimistic scenarios. We present the order of magnitude of the trip segments and introduce the main problematic. Finally, we have a brief look at how uncertainty is playing a key role right now in transportation with the creation of buffers – pure interplay between supply and demand.

Meeting the passenger’s demand: current and future – Bauhaus Luftfahrt
This presentation illustrates the passenger-centric approach taken within the DATASET2050 project by developing current demand profiles. It elaborates different aspects influencing passenger demand such as age, income, household structure, or technological affinity. Based on the analysis of European data, a range of passenger profiles and respective characteristics are derived. These determine the requirements passengers have during their journey and hence the time spent in different processes. Furthermore, data on European mobility behaviour yields different archetype journeys for these passengers.

Developing a new model for European mobility – Innaxis
The DATASET2050 mobility model is a mathematical framework aiming to represent the European door-to-door transportation network. The model has a stochastic approach inherited from complex networks theory, but is ultimately implemented using data science tools. This presentation will address how journey lengths are estimated as an aggregation of multiple random sub-processes and how decision networks are driven by stochastic supply and demand profiles. Several candidate mobility metrics will also be discussed and how the model can be used, to some extent, to analyse future scenarios.

  • Session 2. Further exploring the journey process phase by phase – where are the efficiency gains?

Door-to-kerb – Prof. Dr. Kai Nagel, Technical University of Berlin
The MATSim (Multi Agent Transport Simulation) project is involved with the microscopic simulation of individual travellers at the regional or even national scale. The approach starts from a synthetic population where real humans are replaced by statistical equivalents, builds full daily schedules for them, and follows them through their day with a special focus on the transport system. The system also allows us to run detailed analysis tasks; for example, investigating the accessibility of households to all kinds of services by all means of transport. Clearly, it would also be possible to follow synthetic persons from home or workplace to an airport, or from airport to workplace or home. This presentation will demonstrate current capabilities and discuss possible extensions to MATSim.

Kerb-to-gate – Dr. Genovefa Kefalidou, Horizon 2020 PASSME project
Understanding passenger, airports and airlines’ needs promptly, transforming them into intelligence and adjusting services based on this intelligence is now even more demanding. PASSME is an EU-Horizon 2020-funded project in which we aim to provide innovations to modern journey challenges while at airports. We work on innovations to enhance passengers’ experiences (including reducing stress), providing real-time personalised information, improving interiors and luggage flow and forecasting passenger flow. We identify that passenger needs intertwine strongly with airport and airline needs, manifesting opportunities to build a relationshipamongst all these stakeholders through the use of mobile, back-end and situated innovations. This relationship demands to be maintained throughout the different airport touch points (e.g. kerb-to-gate) to facilitate and optimise the journey process as knock-on effects are transferred between phases, often causing further delays and dissatisfaction.

Gate-to-gate – Steve Williams, NATS
This presentation considers a selection of SESAR concepts, considering changes from flight plans to business trajectories and from distance-based to time-based spacing, also including extended arrival management horizons and system-wide information management (SWIM). It considers the relevance of SESAR to future transport goals: what could SESAR provide to other transport modes, what are the limitations, and why are the limitations unlikely to change? The importance of air traffic management data accuracy is also discussed, and why data are much more precise once an aircraft has left the ground.

  • Session 3. Looking ahead to 2035 and 2050

Futures near and far – Christoph Schneider, Munich Airport
There are many potentially disrupting developments that add a lot of uncertainty when it comes to predicting mobility in 2035. The ACARE mobility vision does not contradict any of these trends. The European aviation market may appear to mature wrt growth rates, but absolute growth will most likely still be huge. Airport capacity is set to be the limiting factor with little hope of being coped with. Munich Airport is very actively engaged in activities to increase capacity, improve intermodality and enhance passenger experience by innovative digital products – these areas are common denominators for mobility in 2035.

Resilience2050. Workshop 2015, Bologne (SIDS)

The final project workshop took place in Bologna, Italy, 30th November 2015 in the afternoon, (14:00-18:00) attached to the SESAR Innovation Days, that officially started the following day in the morning.
You can now download the presentations of the workshop by just clicking on the links below.

Resilience2050 Final Workshop

13:30-14:00 Registration
14:00-14:15 Welcome and introduction Marc Bourgois, Eurocontrol, and David Perez, Innaxis
14:15-14:30 Resilience concepts and approach Hector Ureta, Innaxis
14:30-15:10 Resilience in the ATM socio-technical system: Key roles of humans balancing ATM KPA’s while dealing with disturbances Sybert Stroeve, NLR
15:10-15:30 Data-driven techniques to improve ATM resilience understanding Ernestina Menasalvas, UPM
15:30-16:00 Break
16:00-16:30 The resilience metric and efficiency model Samuel Cristobal, Innaxis
16:30-16:50 Future air traffic in Resilience2050, an operational view Cengiz Pasaoglu, DHMI
16:50-17:20 Data Driven Stochastic Modelling of European Air Traffic for Efficiency Assessment and Resilience N. Kemal Ure, ITU
17:20-17:30 Future applications and opportunities David Perez, Innaxis
17:30-18:00 Open debate All
18:00 Closure


Madrid, 25th to 27th of November, 2013

SESAR Long-term and Innovative Research, Work Package E, supports research activities that are not currently part of the ‘mainstream’ SESAR development work packages. The SESAR Innovation Days are the main forums for dissemination of WP-E results and for interaction with the wider ATM research community and industry representatives.

The fourth SESAR Innovation Days will take place in Madrid, Spain, from 25th to 27th November 2014. The event will be hosted by the Universidad Politécnica de Madrid.

Unlike any other scientific event in ATM research, the SESAR Innovation Days focus explicitly on long-term and innovative research. As well as presenting results of WP-E Networks, Projects and PhDs, the event also seeks contributions from the ATM research community through an open call. The submission deadline is 22nd September and notification of acceptance will be made by 23rd October. Download the Call for Contributions here

Further information on the event will be progressively available at: www.sesarinnovationdays.eu

For all enquiries please contact sesarinnovationdays@eurocontrol.int

Resilience2050. Workshop 24 Nov 2014

The workshop on Resilience opened the debate around the state-of-art in the context of resilience in the Air Transport System and its operations. Both the new discoveries made in the field by the FP7 project consortium, together with inputs from other teams researching in the field were welcome in this event attached to the SIDs in Madrid. The icing on the cake was asocial-networking event to discover historical Madrid city-centre, and its “resilience” to time, wars and many other disturbances.

Date: 24th November 2014, afternoon Full agenda below

Location: UPM university- ETSIAeronauticos building (detailed explanation on logistics here). Room: “Emilio Herrera”:

Attendees: Almost 50 people from operational field (airlines, airports, ANSPs) and research entities&institutions (Universities, SJU, European Commission, EUROCONTROL) attended this interesting event! Thank you all for the smart questions & comments raised and the inputs given, both during the event and the posterior talks


  • 14:00 Welcome (Paula Lopez, Innaxis).
  • Introduction to ATM Resilience and the project. (Hector Ureta, Innaxis,presentation)
  • The Resilience concept – Performance based definition of resilience. (Peter Foerster, DLR, presentation)
  • Analysis of the human role in the resilience of air traffic management. (Sybert Stroeve, NLR, presentation)
  • 6th Resilience Engineering Association Symposium teaser (full info here)
  • Description of the ATM patterns and insights discovered in search of Resilience Metrics. (Santiago Muelas, UPM,presentation and Samuel Cristobal, Innaxis, presentation)
  • Modelling – Approaches to investigate resilience in an ATM system. (Peter Foerster, DLR, presentation)
  • Macro Modeling of the European Air Traffic Network – A data analytic perspective. (Gokhan Inalhan ITU and DHMI,presentation)
  • Wrap-up,  finishing at 18:00. (Carlos Álvarez, Innaxis)
  • Social event: “Madrid’s resilience” 19:00 at Plaza España.

Recording of the full event available here. We are sorry for the low-mid quality

Accommodation and logistics details available here,

Some pictures of the workshop available here

ECCS’14 Satellite Event

ECCS’14 will be a major international conference and event in the area of complex systems and interdisciplinary science in general. It will offer unique opportunities to study novel scientific approaches in a multitude of application areas.

The ComplexWorld Network ECCS Satellite Meeting: Complexity Science and Transport Systems

[success] PROGRAMME NOW AVAILABLE [/success]

Following the events organised at the ECCS ’11 in Vienna, ECCS ’12 in Brussels and ECCS ’13 in Barcelona, we’re announcing the Call for Papers for a half-day Satellite Meeting in Lucca. The aim of this Satellite Meeting is to create a space for exchanging state-of-the-art results and ideas about (i) how different Complex Systems tools such as complex networks, percolation theory, self-organized criticality or agent based modeling can be used to understand the internal dynamics of transportation systems, (ii) how to model the relationships between different transportation modes, and (iii) how to improve efficiency and performance of such systems.

The intended audience of this Satellite Meeting is twofold. On one hand, it consists of researchers from the field of Complexity Science, which are expected give insight on the application of complex system tools and concepts to transportation systems. On the other hand, researchers specialised in Transportation systems will be encouraged to attend in order to give their contribution and see how such systems can be investigated with methodologies which are not currently recognized as mainstream. The main success of the meeting will be to foster an interdisciplinary forum of discussion between the two research communities.

A non-exhaustive list of topics includes:

– Topological properties of transportation systems, and the relations between topology and efficiency / resilience / propagation of disturbances.

– Dynamics of and on transportation systems: from movements of persons and goods, up to diseases and information spreading mechanisms.

– Emerging behaviors and critical phase transitions in transportation systems.

– Applications of multi-layer and time-varying network representations, statistically validated networks and community detection algorithms.

The Call for Papers

Information regarding the Call for Papers can be found here.

The Programme and Venue

The full programme and short abstracts can be downloaded here. It will take place on Thursday, the 25th of September, at SALA DEI SERVI (SAN MICHELETTO)

The Organisers

This Satellite Meeting is organized by the following researchers, who also serve as contact points for anyone interested in knowing more about the meeting:

Fabrizio Lillo
Scuola Normale Superiore
Piazza dei Cavalieri 7
56126 Pisa 
Phone: +39 050509159

Salvatore Miccichè
Dipartimento di Fisica e Chimica
Universita degli Studi di Palermo

Viale delle Scienze, Ed. 18
I-90128 Palermo Italia
Phone: +39 091 23899145

Massimiliano Zanin
The INNAXIS Foundation & Research Institute
José Ortega y Gasset 20, planta 6.
28006 Madrid (Spain)
Phone: +34 902 955 527

The Programme Committee

The Program Committee is composed of 4 persons well known and respected in either or both Complex Systems research and transport industry, as follows:

  • Marc Barthelemy, CEA, France
  • Rosario Mantegna, Università di Palermo, Italy
  • David Pérez, The INNAXIS Foundation & Research Institute, Spain.
  • Aura Reggiani, Universita’ di Bologna, Italy.

3rd SESAR Innovation Days

Stockholm, 26th to 28th of November, 2013.

SESAR Long-term and Innovative Research, Work Package E, supports research activities that are not currently part of the ‘mainstream’ SESAR development work packages. The SESAR Innovation Days are the main forums for dissemination of WP-E results and for interaction with the wider ATM research community and industry representatives.
The Third SESAR Innovation Days will take place in Stockholm, Sweden, from 26th to 28th November 2013. The event will be hosted by the KTH Royal Institute of Technology.
Unlike any other scientific event in ATM research, the SESAR Innovation Days focus explicitly on long-term and innovative research. As well as presenting results of WP-E Networks, Projects and PhDs, the event also seeks contributions from the ATM research community through an open call which can be downloaded here.
Further information on the event will be progressively available at: www.sesarinnovationdays.eu
For all enquiries please contact sesarinnovationdays@eurocontrol.int

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