vii modelling week ucm · 2013. 6. 4. · vii modelling week ucm master in mathematical engineering...

VII MODELLING WEEK UCM Master in Mathematical Engineering - UCM

Madrid, June 10-14, 2013

Welcome We are delighted to announce the seventh Modelling Week, which will be held from June 10 to June 14, 2013 at the Faculty of Mathematics of Universidad Complutense de Madrid, Spain. The VII Modelling Week is organized within the Master Program of the Faculty of Mathematics of UCM in cooperation with the Institute of Interdisciplinary Mathematics (IMI). The main purpose of the VII Modelling Week is to promote the use of mathematical methods and models in research, industry, innovation, and management in the knowledge economy. The Modelling Week is open to the students of the Master in Mathematical Engineering at UCM and to participants from other mathematically oriented master programs worldwide. Students will work in small groups on real industrial problems proposed by companies under supervision of one or two qualified instructors. The official language of the event is English.

José A. Villacorta Facultad de Ciencias Matemáticas, UCM

Valeri Makarov Modelling Week

Coordinator

Marta Arregi Institute of Interdisciplinary

Mathematics

http://www.mat.ucm.es/congresos/mweek/

Newsletter June, 2013 Contents 1. Welcome

2. Collaborators, programme, problems, participants

3. Participation costs

4. Practical info

VII MODELLING WEEK UCM Madrid, June 10-14, 2013

Supported by:

Attendants and instructors from:

Problems proposed by:

http://www.mat.ucm.es/congresos/mweek/ 2.

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Università degli Studi di Firenze

Univ. Complutense de Madrid

Faculty of Mathematics, UCM

MTM2011 - 26119

MONDAY 10-06-2013. Opening session (open to the public)

Room: Miguel de Guzmán (S118A, floor -1)

16:00 - 16:20. Introduction and opening of the VII Modelling Week, UCM

16:20 - 16:40. Exposition of Problem 1. Angiolo Farina, University of Florence, Italy.

16:40 - 17:00. Exposition of Problem 2. Fernando Prieto, Management Solutions, Spain.

17:00 - 17:20. Exposition of Problem 3. Christopher Bell, University of Oxford, United Kingdom.

17:20 - 17:40. Exposition of Problem 4. Fátima Drubi Vega, Goal Systems, Spain.

17:40 - 18:00. Exposition of Problem 5. Francisco Ortegón Gallego, University of Cádiz, Spain.

18:00 - 18:20. Exposition of Problem 6. Jorge Sueiras, Accenture Analytics, Spain

18:30 - 20:30. Working Groups at laboratories.

TUESDAY 11-06-2013 TO THURSDAY 13-06-2013. Working in groups

Labs distribution:

Problem 1: Room B08-B (ground floor)

Problem 2: Room Informática 0 (S217A, floor -2)

Problem 3: Room Informática 3 (S115, floor -1)

Problem 4: Room Informática 1 (S217A, floor -2)

Problem 5: Room B08-A (ground floor)

Problem 6: Room Informática 2 (S218, Floor -2) Working hours:

Tuesday 11/06 and Thusday 13/06: 9:00 - 14:00 and 16:00 - 20:30

Wednesday 12/06: 16:00 - 20:30

FRIDAY 14-06-2013. Closing session (open to the public)

Room: Miguel de Guzmán (S118A, floor -1)

Morning. Groups at laboratories. Preparing final reports and presentations

17:00 - 19:30. Each working group gives a public presentation describing main results

19:30. Closing of the VII Modelling Week

VII MODELLING WEEK UCM Madrid, June 10-14, 2013 http://www.mat.ucm.es/congresos/mweek/

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PROBLEM 1:

Modelling flow in pipes with semi-permeable walls

Problem proposed by University of Florence

Instructor Angiolo Farina (Universtità degli Studi di Firenze, Italy) Exposition of the problem Motivations 1) INDUSTRIAL APPLICATIONS – WATER FILTERS Modern water depuration modules consist of a container housing a large number of hollow fibers whose lateral membranes is permeable to water, but not to “large” particles. 2) MEDICAL APPLICATIONS – DYALISIS In medicine, dialysis is a method for removing waste products such as urea, as well as excess water from the blood and is used primarily to provide an artificial replacement for lost kidney function in people with renal failure. 3) AGRICULTURE APPLICATIONS A widely used irrigation technique consists in delivering water by letting it filtrate through permeable pipes laid down or suspended over the ground. Several types of plants are used, according to the size of the fields to be irrigated. The above mentioned applications have a common characteristic: the ratio between the pipe length and the pipe radius is small. The radial length scale and the longitudinal length scale are well separated. Hence, the so-called upscaling (or double scale) procedure can be used. Problem description 1) To model the dynamics of a solution whose components are a Newtonian liquid (water) and a single solute within a tube whose wall (membrane) prevents to the solute molecules to be transported across it. 2) To simulate the process considering different working conditions. AN IMPORTANT EFFECT TO CONSIDER: OSMOSIS Modelling steps 1. Definition of the geometrical setting 2. Definition of the dependent variables 3. Possible simplifications 4. Fundamental equations 5. Scalings and characteristic parameters 6. Asymptotic expansion - upscaling 7. Qualitative properties of the model 8. Simulations 9. Physical interpretation of the results Scheme of the work to be done 1. Define a mathematical model aimed at describing the process. 2. Introduce a double scale procedure. 3. Define the corresponding mathematical problem (BVP problem). 4. Possible qualitative properties. 5. Perform numerical simulations.


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PROBLEM 2:

Impact of the Spanish real estate boom & crash on the mortgages recovery indicators Problem proposed by MANAGEMENT SOLUTIONS Instructor Ignacio Villanueva (Complutense University, Spain) Exposition of the problem 1. Introduction A bank, like others activities, operates in a framework in which the risk is present. Managing different kinds of risks is a key activity in the banking business. The objective of a bank entity is to maximize revenues and to minimize the risks which are assumed by it. The banking entities must be able to measure and to manage their risks. Therefore, the risk is positive because it means profitability, but it is necessary to quantify it, as it can cause losses or even lead to bankruptcy. One of the main risks a bank faces is the Credit Risk. The Credit Risk is the loss to which the Entity is exposed in the event the counterpart doesn’t make the payments it is obligated to do. Given a portfolio of contracts, the uncertainty of potential losses associated with it in a time horizon (normally 1 year) is represented by a probability distribution. Every entity should have sufficient resources to absorb the losses of its activity. These resources are reflected in: expected losses and unexpected losses. For the modeling of such credit losses three main parameters are needed: ·- PD: Probability of default of a transaction or customer. ·- EAD (Exposure at Default): Volume risk at the time of default. ·- LGD (Loss Given Default): Severity. The percentage of debt that the bank is unable to recover eventually. Focusing our attention on the LGD parameter, this is equal to 1 minus the recovery rate. This rate is the percentage of the amount recovered on the EAD. The entity must calculate its own estimated recovery rates internally. Historical data recovery will be necessary to determine the recovery capacity. In this sense we can use either to external or internal data. As it could be expected, collaterals play an important role during the recovery process. Their initial acquisition and subsequent sale are the main ways to follow in order to mitigate the loss associated to a portfolio. In this sense, there is a natural link between the LGD and the value of financial guarantees. Particularly, in mortgage portfolios, LGD strictly and directly depends on the value of the property that serves as security (by means of LTV). Thus, in periods characterized by a devaluation of housing prices, LGD increases substantially. Currently, housing price is the variable that has reflected in a better way the spread of the financial crisis to the real economy, and has been used to explain the depth of the Spanish current crisis. Our main goal regarding this issue is to calculate the LGD of a mortgage portfolio and to evaluate, through rigorous mathematical modeling, its relationship with the evolution of the housing prices and the future impact of the current crisis in the parameter. 2. Problem to be solved The tasks to be completed are: · Calculating the value of the loss-given-default (LGD) parameter for each one of the different segmentation buckets of LTV. The appropriate discount curves to calculate the present flows of data will be used. · Searching in a public context past historical data and projected housing prices. · Recalculating the LGD parameter after including this sudden rise and devaluation of the housing prices. · After that, the differences between first and second LGD values could be discussed. · Calculating associated capital requirements for Spanish financial institutions.


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Work to be done 1. Definition of the problem and clarification of doubts In this first phase, Management Solutions will present the problem in greater detail, providing those ideas that have been developed so far, and will clarify any raising doubts about the understanding of the problem. Management Solutions will also provide a polished and ready-to-use Excel file, so that the smallest amount of time will be spent on data processing: - For each of the recovery processes the main information will be: · Data about the recovery process (start date, end date, amount spent, amount recovered, etc.) - Additional information will be used: · Discount curves to update the values of the recovery flows 2. Phase 1: Calculating LGD parameter Firstly, given data as the exposure, the amount spent and the amount recovered at the date of the recovery process will be calculated and should be analyzed. Finally, the value of the loss-given-default (LGD) parameter for each one of the different segmentation buckets of LTV will be calculated. Some discount curves to calculate the present data flows could be used. 3. Phase 2: Considering a projected scenario and rebuilding LGD parameter Using public historical data for housing prices, a new LTV value will be recalculated. To this purpose, students will rebuild a new LGD parameter considering these new scenarios. The results obtained in the previous phases could be discussed. Finally, the capital requirements associated could be calculated. 4. Phase 3: Exposition and discussion of results The case study will conclude with the students’ presentation of the used methods and obtained results.


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PROBLEM 3:

Neurotramsmitter release in the brain Problem proposed by Oxford Centre for Collaborative Applied Mathematics Instructor Christopher Bell (University of Oxford, United Kingdom) Exposition of the problem Introduction: The human brain consists of around 100 billion neurons each making 1000-10,000 synaptic connections. The activity of the brain is electrical but the connections between neurons are primarily chemical, across a specialised structure called the synapse. At the synapse, vesicles containing neurotransmitter fuse with the cell membrane and release their contents into the synaptic cleft. The transmitter molecules (typically 10,000-100,000 molecules per vesicle in our systems) diffuse across the synaptic cleft, where some of them engage with receptors triggering another wave of electrical activity in the post synaptic cell, while the remainder are taken back up by membrane- bound transporter proteins so they can be broken down or re-packaged. It is of interest experimentally to measure how this process changes with age or drugs. For example, do aging or drugs affect the concentration of neurotransmitter released from the vesicles and the rate of re-uptake? Experimental measurements: This release of the neurotransmitter can be detected using microelectrodes, with a typical experimental set-up as shown in Figure 1. The neurotransmitter molecules are oxidised electrochemically at the surface of the electrode, which results in an electric current. A typical current profile detected from the brain of a snail (Lymnaea stagnalis) is shown in Figure 2, from data provided by Dr. O’Hare (Imperial College London). The spikes correspond to neurotransmitter-release events. (See website for figures) Problem to be solved Mathematical modelling: We would like to be able to relate the size of the spikes in current reponse back to key parameters of the process, such as the total concentration released from the vesicle and the rate of re-uptake. This requires a theoretical model. Scheme of work • Introduction of the problem. • Partial differential equation model of vesicle release, re-uptake and oxidation at the electrode. • Analytical and numerical solution of the model. • Comparison to experimental results. • Further investigations into the effect of discrete re-uptake sites.

PROBLEM 4:

A case of study of school bus routing problem Problem proposed by Goal Systems Instructors Gregorio Tirado Domínguez (Complutense University, Spain) Javier Martín Campo (Complutense University, Spain) Exposition of the problem 1. Introduction The school bus routing problem (SBRP) seeks to plan an efficient schedule for a fleet of school buses that pick up students from various bus stops and deliver them to the school by satisfying various constraints: maximum capacity of the bus, maximum riding time of students, and time window to arrive at school. SBRP has two separate but interrelated routing issues: assigning students to their respective bus stops and routing the buses to the bus stops. SBRP is a special case of the vehicle routing problem (VRP). In a VRP, a set of n clients (the students) has to be serviced by a fleet of vehicles (the buses). Since the buses have limited capacity, the problem becomes the capacitated vehicle routing problem, which is known to be NP-hard. 2. Problem description We can initially assume that the location and number of students assigned to each bus stop is also known. Once this simplified problem is solved, the original problem can be solved by two steps: first, finding the optimal assignment of students to the bus stops, and then using the solution of the simplified problem. However, the original problem needs to find the optimal assignment of students to each bus stop as well as the optimal bus routes. In most existing approaches in literature, those steps are considered separately and sequentially, although they are highly interrelated. Could it be possible to define a method that look simultaneously for the optimal assignment of student and the bus route? Motivation for mathematical modeling Vehicle routing problem is a well-known problem in operational research area. VRP can be formulated easily; however, it turns to be a relatively difficult problem when the number of inputs increases. Mathematical models and different solution methods have been investigated in the literature to apply them for many cases in daily life. Most interesting real-world optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a near-optimal solution to large-scale optimization problem may require computational resources far beyond what is practically available. Heuristic local research methods, such as tabu search and simulated annealing, are often quite effective at finding near-optimal solutions with high probability.


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PROBLEM 5:

Some mathematical models and numerical simulation of heat treatment of steel Problem proposed by University of Cadiz Instructor Francisco Ortegón Gallego (University of Cadiz, Spain) Exposition of the problem Steel is an alloy of iron and carbon. Steel used for industrial purposes, has a carbon content up to about 2 wt%. Other alloying elements may be present, such as Cr and V in tools steels, or Si, Mn, Ni and Cr in stainless steels. Most structural components in mechanical engineering are made of steel. Certain of these components, such as toothed wheels, bevel gears, pinions and so on, engaged each others in order to transmit some kind of (rotational or longitudinal) movement. As a result the contact surfaces of these components are particularly stressed. The goal of heat treating of steel is to attain a satisfactory hardness. Prior to heat treating, steel is a soft and ductile material. Without a hardening treatment, and due to the surface stresses, the gear teeth will soon get damaged and they will no longer engage correctly. Solid steel may be present at different phases, namely austenite, martensite, bainite, pearlite and ferrite. For a given wt% of carbon content up to 2.11, all steel phases are transformed into austenite provided the temperature has been raised up to a certain range. The minimum austenization temperature (727º) is attained for a carbon content of 0.77 wt% (eutectoid steel). Upon cooling, the austenite is transformed back into the other phases, but its distribution depends strongly on the cooling strategy. Martensite is the hardest constituent in steel, but at the same time is the most brittle, whereas pearlite is the softest and more ductile phase. Martensite derives from austenite and can be obtained only if the cooling rate is high enough. Otherwise, the rest of the steel phases will appear. The hardness of the martensite phase is due to a strong supersaturation of carbon atoms in the iron lattice and to a high density of crystal defects. From the industrial standpoint, heat treating of steel has a collateral problem: hardening is usually accompanied by distortions of the workpiece. The main reasons of these distortions are due to (1) thermal strains, since steel phases undergo different volumetric changes during the heating and cooling processes, and (2) experiments with steel workpieces under applied loading show an irreversible deformation even when the equivalent stress corresponding to the load is in the elastic range. This effect is called transformation induced plasticity. The heating stage is accomplished by an induction-conduction procedure. This technique has been successfully used in industry since the last century. During a time interval, a high frequency current passes through a coil generating an alternating magnetic field which induces eddy currents in the workpiece, which is placed close to the coil. The eddy currents dissipate energy in the workpiece producing the necessary heating. Work to be done We will be interested in the mathematical description and the numerical simulation of the hardening procedure of a certain workpieces, for instante a car steering rack. This particular situation is one of the major concerns in the automotive industry. In this case, the goal is to increase the hardness of the steel along the tooth line and at the same time maintain the rest of the workpiece soft and ductile in order to reduce fatigue.


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PROBLEM 6:

Propagation models Problem proposed by Accenture Instructor To be confirmed José Antonio Villacorta-Atienza (Complutense University, Spain) Exposition of the problem Introduction • Social media play a central role within the customer relationship Management (CRM) • The emergence of negative buzz about a brand might turn into non-negligible reputational problems if spreading of information is significant • Viral communication, ensuring fast and massive propagation, allows high performance marketing actions at very low cost • Predictive models of content propagation within social networks enable risk anticipation and opportunities identification that might have a significant impact in a company’s activity. Problem description • General goal: to develop models of content propagation within social networks. The general problem is rather complex and must have into account multiple factors. • We will restrict ourselves to Twitter (wwww.twitter.com). The proposed problem is to identify whether a given content will be send by a user (retweet) as a function of how messages have been resent before. • To perform this task the following data will be available: – A table with the directed graph of (a part of) the twitter network, including all followers and followees connections – A master table of users, with a user per record including her attributes, including all users within the previous table – A table of messages. This table includes messages received by the users in the users table. The table incluyes details of the message: message ID, ID of the user who received the message (recipient), ID of the user who retweeted the message (sender) and date-hour in which the message was received – Target table. This table contains records including user ID, message ID, and the target variable: 1 if the user retweets the message, 0 if not. · For every record in this table, there is an incoming message. This message indeed is contained in the previous table and can be matched through the message ID. · This table cannot be used to create explicative variables. · This table will be delivered in two parts: a first part to train the model and a second to test it. Work to be done Guidelines to solve the problem • Given the detail of the available information, the problem may be tackle by different means. A possible schema is described below, though it is highly encouraged to explore alternative methodologies. – To build a modelling table for the potential messages to be sent, by crossing the table of events to predict, enhancing it with aggregated information on how the user has resent messages before and how propagation has taken place between the origin and end users, using information from the graph, users, and messages tables. – Use the previous table (the train data) to develop a model to predict whether an user will or will not send a message. Assess the goodness of the model with the test data. Note: the final evaluation will be computed in terms of the roc area of the test data. • As building the training table is very time consuming and the available time is short, a SAS code is delivered to build an initial version of the table with Basic variables pre-computed. The code may be edited to include improved variables that might enhance the predictive capacity of the model.


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Mathematical treatment—data transformation • Predicting the retweet of a message M by a user U depends on several factors: – User profile U: Number of followers and followees, number of messages, number of previous RTs, etc. – Message profile M: number of times that the message has been sent, whether it has been sent by users with many or rather a few followers. – How the message has been resent by the users followeed by U. – Whether the user U uses to retweet messages retweeted by the users she follows or not. Whether this action takes place with more or less intensity depending on the type of followees who retweet the message. – Other factors to be defined(one of the objectives of the problems is finding out these additional factors and integrate them within the predictive model). • As indicated before, a SAS code will be delivered to build some of the above listed factors. Mathematical treatment—modelling • The desired model predicts a binary target variable (0 if the user DOES NOT resend the message / 1 if the user DO resend the message). • To model the propagation starting with the proposed table, the models should allow capturing non-lineal effects as well as interactions between the explicative factors defined before. • We propose to use logistic models with cross effects, neural networks or decision trees.

Instructors:


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Problem 1: Modelling flow in pipes with semi-permeable walls Angiolo Farina, University of Florence, Italy

Problem 2: Impact of the Spanish real estate boom & crash on the mortgages recovery indicators Ignacio Villanueva, Complutense University, Spain

Problem 3: Neurotransmitter release in the brain Christopher Bell, University of Oxford, United Kingdom

Problem 4: A case of study of school bus routing problem Gregorio Tirado Domínguez, Complutense University, Spain Javier Martín Campo, Complutense University, Spain

Problem 5: Some mathematical models and numerical simulation of heat treatment of steel Francisco Ortegón Gallego, University of Cadiz, Spain

Instructors:


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Problem 6: Propagation models María del Carmen Pardo Llorente, Complutense University, Spain

José Miguel García-Santesmases Martín-Tesorero, Complutense University, Spain

José Antonio Villacorta-Atienza, Complutense University, Spain

Participants:


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Problem 1: Modelling flow in pipes with semi-permeable walls Alonso Gómez, Inés Univ. Complutense de Madrid, Spain Civelli, Stella Univ. of Florence, Italy Cuesta Martín Palanco, Cristina Univ. Complutense de Madrid, Spain Popescu Diana, Roxana Univ. Complutense de Madrid, Spain Rosado Poveda, María Teresa Univ. Complutense de Madrid, Spain Problem 2: Impact of the Spanish real estate boom & crash on the mortgages recovery indicators Blázquez Esquinas, Patricia Univ. Complutense de Madrid, Spain Gilbert, Mark Univ. of Oxford, United Kingdom López Caamaño, Marta Univ. Complutense de Madrid, Spain Quintas Rodríguez, Nair Univ. Complutense de Madrid, Spain Rodríguez Rodríguez, Víctor Darío Univ. Complutense de Madrid, Spain Torres Hansa, Leonardo Univ. Complutense de Madrid, Spain Problem 3: Neurotransmitter release in the brain Alonso López, María Univ. Complutense de Madrid, Spain Anguiano Jiménez, Sandra Univ. Complutense de Madrid, Spain Hidalgo García, Blanca Univ. Complutense de Madrid, Spain Mucherino, Sonia Univ. of Florence, Italy Radillo del Fresno, Guillermo Univ. Complutense de Madrid, Spain Vizcaíno López, Israel Univ. Complutense de Madrid, Spain Problem 4: A case of study of school bus routing problem Artalejo Álvarez, Marta Univ. Complutense de Madrid, Spain Gómez Roldán, Javier Univ. Complutense de Madrid, Spain Leguey Vitoriano, Ignacio Univ. Complutense de Madrid, Spain Mateos Jaime, Ana Univ. Complutense de Madrid, Spain Palagi, Giulia Univ. of Florence, Italy Rodríguez Vallejo, Miguel Ángel Univ. Complutense de Madrid, Spain Problem 5: Some mathematical models and numerical simulation of heat treatment of steel Casannez, Laura Univ. Complutense de Madrid, Spain Díaz Bravo, Irene Univ. Complutense de Madrid, Spain Kotzagiannidis, Madeleine Sophia Univ. of Oxford, United Kingdom Rotondi Florencia, Micaela Univ. Complutense de Madrid, Spain Tejada Torres, Alicia Univ. Complutense de Madrid, Spain Problem 6: Propagation models Borrego Capitán, Silvia Univ. Complutense de Madrid, Spain García de la Mora Díaz, Sara Univ. Complutense de Madrid, Spain González Martínez, Daniel Univ. Complutense de Madrid, Spain Ignacio Mateos, Daniel Univ. Complutense de Madrid, Spain Pascual Campoy, Lourdes Univ. Complutense de Madrid, Spain Taylor-King, Jake Patrick Univ. of Oxford, United Kingdom

For non UCM participants the following costs will be covered: Travel. Flight tickets have been bought by the organizing committee and sent to the participants by e-mail. Accomodation. Shared double rooms for students and single room for instructors at Colegio Mayor Diego de Covarrubias (see information below). Meals: At Colegio Mayor Diego de Covarrubias: breakfast, lunch and dinner are included in the accomodation from Sunday night (June 9th) to Saturday morning (June 15th). Colegio Mayor Diego de Covarrubias It is located in the University Campus. The address is Avenida Séneca, 10. Phone number: (+34) 91 550 46 00. The closest underground stop is Moncloa. Buses connect the residence with Moncloa (160, 161 and A) and many locations at the University campus (U). The webpage of the residence: www.cmucovarrubias.es


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Campus Map Facultad de Ciencias Matemáticas and Colegio Mayor Diego de Covarrubias at Moncloa Campus: (Attention: this map is not north oriented)


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How to arrive from the airport There are two underground (Metro) stops at the airport, depending on the terminal you arrive. A single trip costs 5 euros from the airport to the University.

A taxi cost may vary between 40 and 60 euros from the airport to the Colegio Mayor. Tipically a taxi driver will not know how to find the place, so you better print out the map before the trip.


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Bus stops near Colegio Mayor Diego de Covarrubias


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Moving around You can find some information at: Transport Information System: http://www.ctm-madrid.es/ Metro de Madrid (underground): www.metromadrid.es/en/index.html EMT (local buses): http://www.emtmadrid.es/ Cercanías (regional trains): http://www.renfe.com/EN/viajeros/index.html Tourism Madrid City: http://www.esmadrid.com/en/portal.do Madrid City and Region: http://www.turismomadrid.es/en/ The University Universidad Complutense de Madrid: www.ucm.es Faculty of Mathematics: www.mat.ucm.es Instituto de Matemática Interdisciplinar: www.mat.ucm.es/imi/

Cibeles Square, Madrid


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Puerta de Alcalá, Madrid

vii modelling week ucm · 2013. 6. 4. · vii modelling week ucm master in mathematical engineering...

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