V MODELLING WEEK UCM€¦ · Programme The event will have 4 parts: PRESENTATION OF THE PROBLEMS:...

V MODELLING WEEK UCM Master in Mathematical Engineering - UCM

Madrid, June 13-21, 2011

Welcome On behalf of the Organizing Committee, we welcome you to the V Modelling Week UCM. This event is organized, within the framework of the Master in Mathematical Engineering at Universidad Complutense de Madrid, by the Faculty of Mathema-tical Sciences and the Interdisciplinary Mathematics Institute (IMI). The aim is to promote the use of Mathematics as a tool to solve problems ari-sing from the industry. The presentations and exhibitions will take place on June 13nd and 21th and attendance is free for all interested people. The event will build on the success of the previous editions, while incorporating new features to enhance your experience. The conference venue is in the heart of Madrid, Spain. In June, Madrid weather is at its finest. Please join us at the V Modelling Week and enjoy the beauty of Madrid. We look forward to seeing old friends and meeting new ones.

Juan Tejada Facultad de Ciencias Matemáticas, UCM

Valeri Makarov Modelling Week

Coordinator

Marta Arregi Interdisciplinary

Mathematics Institute

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

Newsletter 2 June 9th, 2011 Contents 1. Welcome

2. Collaborators, programme, problems, participants

3. Participation costs

4. Practical info

V MODELLING WEEK UCM Madrid, June 13-21 , 2011

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

Programme The event will have 4 parts:

PRESENTATION OF THE PROBLEMS: by problem coordinators and by companies representa-tives, on June, 13, Monday.

WORK GROUPS: each group of students, coordinated by one or various coordinators, will work on a problem from 16:00 h. to 21:00 h. until June 20, Monday.

PRESENTATION OF RESULTS AND CONCLUSIONS: each group will deliver a report describing the results and conclusions reached and one or more of its members will make a public pre-sentation on June, 21, Tuesday.

WRITTEN REPORTS: each Working Group will write a paper setting out the results and conclu-sions reached.

Monday 13-06-2011. Opening session

16:00 h Introduction and opening of the V Modelling Week, UCM

16.10 - 16.20h Exposition of Problem 1. Luigi Barletti, Università degli Studi di Firenze, Italy.

16.25 - 16.45h Exposition of Problem 2. Iván Fernández, INDIZEN, Spain.

16.50 - 17.10h Exposition of Problem 3. Fernando Prieto, Javier Calvo, Management Solutions, Spain.

17.15 - 17.35h Exposition of Problem 4. Cameron Hall, University of Oxford, United Kingdom.

17.40 - 18.00h Exposition of Problem 5. Santiago Doblas, Neometrics, Spain.

18.05 - 18.25h Exposition of Problem 6. Andrés Ramos, Universidad Pontificia de Comillas, Spain

18.30 - 18.50h Exposition of Problem 7. Jouni Sampo, Lappeenranta University of Technology, Finland.

18.50 - 20.45h Working Groups at the laboratories. Tuesday 14-06-2011 to Monday 20-06-2011

16:00 - 20:45h Working Groups at the laboratories. Tuesday 21-06-2011

16:00 - 16:45h Preparing final details of each group at the laboratories

17:00 - 19:30h Each working Group gives a public presentation describing the main results

19:30h Closing of the V Modelling Week, UCM

V MODELLING WEEK UCM Madrid, June 13-21 , 2011 http://www.mat.ucm.es/congresos/mweek/

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PROBLEM 1:

Signal propagation in nonlinear optical fiber

Problem proposed by CNIT

Instructor Luigi Barletti (Universtità degli Studi di Firenze, Italy) Exposition of the problem The proposed problem concerns the propagation of an electromagnetic signal in an optical fiber, with dispersive, nonlinear and dissipative effects. In general, such propagation can be described by a one-dimensional Schrödinger equation with cubic nonlinearity, where the roles of space and time variables are inverted with respect to the usual Schrödinger equation of quantum mechanics. The concomitant effects of chromatic dispersion (different wavelenghts travel with different speed) and of nonlinear refraction (the refraction index depends of the field intensity) lead to a signal dis-torsion. The signal, moreover, which travels for hundreds, or even thousands, of kilometers, needs to be periodically reinforced by optical amplifiers. In this way, undesired noise is introduced into the fiber. Usually, such noise is modelled as an input gaussian white process. Then, signal and noise nonlinearly mix up during the propagation, and this contributes to the degeneration of the output. Modelling and simulation of all such phenomena is fundamental for the correct interpretation of the output signal and is, therefore, of central interest for the telecommunications industries. The proposed model, rather than using directly the Schrödinger equation, exploits the so-called Made-lung transform which leads to an Euler-like system of equations for a compressible fluid. Such sys-tem has some advantages with respect to the original formulation; in particular, a “semiclassical” approximation (which is somehow related to the geometrical optics approximation) can be perfor-med, leading to a considerable simplification of the model

Scheme of the work to be done 1) Introduction of the basic ingredients of the model: the nonlinear Schrödinger equation, the Ma-delung transform and the resulting fluid-like description. Discussion about input and boundary data which, as a first step, will be supposed to be deterministic. 2) Introduction of a suitable scaling and discussion about possible approximations, in particular the “semiclassical” one.

3) Numerical solution of the deterministic and semiclassical propagation problem

4) Discussion about possible refinements of the model, such as insertion of the stochastic input and/or dropping of the semiclassical approximation. Then, if possible, numerical implementation of the refined model.

Participants De Decker, Michelle García Roldán, José María Herterich, James Kospach, Alexander Ristori, Tommaso


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PROBLEM 2:

Forecasting Prices in Electricity Markets Problem proposed by INDIZEN Instructor Juan Tejada (Universidad Complutense de Madrid, Spain) Hugo Marrao (Indizen) Exposition of the problem Electricity is one of the most important goods for our society. Forecasting electricity prices at diffe-rent time frames is very important for all industry stakeholders for cash flow analysis, capital bud-geting and financial procurement as well as regulatory rule-making and integrated resource plan-ning, among others. All factors determining the price can be clasified as endogenous or exogenous to the market, bring about uncertainty and volatility to the electricity prices. The most important outcome of an electricity market is the formation of a price at which all power is traded, at least on a daily basis, by way of the so-called ‘Spot’ market. The daily (spot) electricity market serves as a marketplace of last resort for generators and demands to trade their remaining available not-contracted power. Almost all spot electricity markets currently under operation have implemented a mandatory day-ahead bidding framework, which may or may not be complemented with intra-day and real-time (balancing) markets. In terms of the amount of energy being traded, the day-ahead market is the most significant one among all spot (intradía or real-time) markets. As a matter of fact, the economics of the whole electricity industry depends on a great deal on the electricity prices cleared at the market. In the short- run (from three to 24 hours) electricity price forecasting is especially important in electricity markets in which participants must optimize their positions (bidding price and quantity for the various markets, namely day-ahead and intraday) ba-sed on their perception of what the future hourly prices and incremental costs will be over the bid-ding period. Moreover, some agents, especially large consumers with self power production, are able to decide which portion of their consumption is to be supplied by the market or by their own production and the corresponding timing. Nonetheless, the driving force behind the decisionmaking of all market participants is the maximization of profit. Forecasting electricity prices is a challenging task not Orly because the prices are uncertain but, most importantly, because of the particularities of how these prices are brought into being. The process of price formation in electricity markets follows in essence the basic rule of microeconomic theory (Law of Supply and Demand) by which the price of the underlying commodity in a competiti-ve market should reflect the relative scarcity of the supply for a given demand level. If the demand for a commodity is low, those suppliers with higher incremental costs must step out of competition (or make negative profits) and give way to suppliers with the lowest incremental costs. This process results in relatively low equilibrium prices. On the other hand, as the demand increases, those sup-pliers with the lowest incremental costs are the first ones to enter the market and use up their pro-duction capacity so more and more expensive suppliers have to come in to supply the increasingly scarce commodity, rising the equilibrium price. This process is observed in electricity markets on a regular basis. The market clearing prices tend to follow closely the daily and seasonal swings in consumption. If consumption and price were de-termined by a one-toone deterministic relationship, anticipating the electricity prices would boil down to forecasting accurately the demand, which is one of the most investigated problems in po-wer systems operation and planning. The influence of the demand on the electricity prices is, howe-ver, far from being deterministic. There are a series of factors that bring about uncertainty to the price formation process even if the demand is known with certainty. One of the known factors that play a special role in electricity prices are the renewable energies. For example, in Spain ,the wind power is the most important factor to know electricity prices. Electricity price forecasting techniques may be classified according to three major basic approaches, namely Production-Cost, Statistical and Heuristic or Data Mining models The aim of this work is the development of a prediction model of the hourly generation program and price of the Spanish power market . Also, is desirable to conclude the strenths and weakness of this model and a little comparison with the most used in the market.


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Our first preference to develop a new method is use WNN (Weighted Nearest Neighbor methods) after the processing of historical data prices adding the correlations found due to endogenous and exogenous conditions to the electricity prices. Work To Be Done 1) Find the correlations between data set factors and electricity prices 2) Transform the data according to this correlations 3) Compare results with other methods Participants González Salcedo, Carlos Guere Lettich, Diana Edith Keating, Natalie Martínez Calvo, Ignacio Panchal, Charmi Devendra Puente García, Víctor


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PROBLEM 3:

Obtanining an analytical approximation for the calculation of capital for credit risk Problem proposed by Management Solutions Instructor Begoña Vitoriano (Universidad Complutense de Madrid, Spain) Exposition of the problem The credit risk of an institution is its risk of loss arising from the failure of third parties to repay loans.Every financial institution must have enough resources to absorb credit losses. In the legisla-tion, such losses are broken down into: - Provisions: the average value of losses (expected loss). - Capital: the loss volatility (unexpected loss). The progress of statistical and computational techniques has permitted the development of models that can be used to calculate losses based on internal information of each financial institution. In this sense, the legislation also allows, and has encouraged, the use of internal models1 for the cal-culation of provisions and capital2. The variables used in the legislation on capital for the measurement of credit risk (hereafter labe-lled “risk parameters”) are the following: - Probability of default (PD) ·- Exposure at default (EAD) - Loss given default (LGD) % - Maturity (M) - Asset correlation (R) These variables must be estimated based on internal information and should agree with the princi-ples and hypotheses established in the legislation (New Basel Capital Accord, June 2006). The esti-mation of risk parameters is performed for the different risk segments so that all crédito portfolio operations have related risk parameters. Thus, an expression is established for the different seg-ments, from which the capital requirement over a one-year time horizon and with a confidence level of 99.9% is obtained for each operation. For example, for companies with a turnover of less than 50 million euros and an EAD above 1 million euros, the capital is given by the following expression: Correlation (R) = 0.12 × (1 – EXP (-50 × PD)) / (1 – EXP (-50)) + 0.24 × [1 - (1 - EXP(-50 × PD))/(1 - EXP(-50))] Maturity adjustment (b) = (0.11852 – 0.05478 × ln (PD))^2 Capital requirement (K) = [LGD × N [(1 - R)^-0.5 × G (PD) + (R / (1 - R))^0.5 × G (0.999)] -PD x LGD] x (1 – 1.5 x b)^ -1 × (1 + (M – 2.5) × b) Note that the allocation of capital for a given operation3 is an analytical approach at the 99.9th percentile of the loss distribution to a one-year horizon. Problem to be solved The objective is to define an analytical expression, for the portfolio of companies4, which allows the estimation of capital based not only on internal estimation of parameters, but also on the internal estimation of the loss distribution of each institution. Phases 1. Definition of the problem and clarification of doubts In this first phase, Management Solutions will present the problem in greater detail, providing the ideas that have been developed so far, and will clarify any doubts raised concerning the understan-ding of the problem5. Management Solutions will also provide a fictitious loan sample, with real characteristics, in a polis-hed and ready-to-use Excel file, so that as little time as possible will be spent on data processing.


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The fundamental information which the sample will contain is: - Operation identifier. - Client identifier. - PD of the operation. - EAD of the operation. - LGD of the operation. - Maturity of the operation. - Correlation of the operation with the systemic risk (asset correlation). For simplicity, it will be assumed that all operations have a maturity of one year so that the impact of the maturity on the risk losses will not be considered in the calculation. Furthermore, there will only be one operation per client in order to simplify the calculations. 2. Phase 1: Loss distribution Firstly, the portfolio loss distribution will be generated. In order to do this, Monte Carlo techniques can be used. The objectives of this phase are the following: - Delve into the nature and significance of different risk parameters. - Estimate the sensitivity to changes of the credit risk loss distribution, or the hypothesis of different parameters. - Estimate the capital of the portfolio being studied. 3. Phase 2: Capital distribution Once the loss distribution has been estimated and the capital requirement for the portfolio being studied has been calculated, a stable method must be proposed for the distribution of capital bet-ween the different operations. Once the capital consumption has been assigned to each client, this estimate must be compared to that obtained by the regulatory method. The differences must be quantified and analysed, providing a conclusion on the different aspects which could be producing them. 4. Phase 3: Proposal of an analytical estimate From the results obtained in the previous two phases, an alternative analytical expression to that established in the legislation should be proposed for the allocation of minimum capital require-ments, which should also depend on the parameters characterising the sample (PD, EAD, LGD, co-rrelation, concentration and maturity7). 5. Phase 4: Exposure and discussion of results The study will conclude with the students’ presentation of the selected expression and the results obtained. Participants Andrés Andrés, Marta Batanero Akerman, Ana María Cedrola Carvalho, Vitor Gallego Casilda, Jonathan Hilario Díaz, Álvaro Mardomingo Alonso, Pedro Ismael

PROBLEM 4:

Biological control of rabbits Problem proposed by Oxford Centre for Collaborative Applied Mathematics Instructor Cameron Hall (University of Oxford, United Kingdom) Exposition of the problem After rabbits were introduced into the wild in Australia in 1859, their population rapidly increased and they quickly became a pest species. Rabbits continue to be a problem throughout southern and eastern Australia, where they eat large quantities of vegetation, depriving livestock and native animals of food. Furthermore, this loss of vegetation leads to severe erosion, causing long-term damage to the Australian ecology. Several techniques have been used to try and control the rabbit population. Most notably, the deli-berate introduction of the myxoma virus to Australia in 1950 and the release of Rabbit calicivirus in 1995 led to signi cant decreases in the rabbit population. The most effective and promising met-hod for controlling rabbits in Australia, or perhaps even for eradicating them, appears to be biologi-cal control using viruses. In order to understand why some viruses are more success at controlling the rabbit population than others, we would like to explore the relationship between different properties of an infective agent (lethality, communicability, incubation time, etc.) and its effect on the rabbit population. Hopefully, our results can be used to determine the desirable properties of a biological control agent, and should also indicate the relative importance of contagiousness, deadliness and other viral proper-ties. Scheme of the work to be done 1. Introduction to the general problem. 2. Construction of mathematical models for healthy and infected rabbit populations. 3. Analysis of model using phase portraits and related techniques for dynamical systems. 4. Development and analysis of more complicated models (e.g. incorporating incubation time). Participants Aguirre Bueno, Juan Bani, Federica Biddle, Harry González de la Cruz, Ana Maffia, Andrea Massi, Emma Moro, Eduardo


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PROBLEM 5:

Forecasting the demand for bread Problem proposed by Neometrics Instructor Conrado Manuel, Enrique González, Javier Castro (Universidad Complutense de Madrid, Spain) Exposition of the problem The determination of the daily demand for bread in stores is a very complex mathematical problem, for wich a more or less accurate solution can have a significant economic impact on the income of distribution companies The ability to forecast the number of units that will be sold in each point of sale gives a way to con-trol the two major costs involved: – “Returns” factor: The number of returns for point of sale (due to the expiration of the product) – “Out of stock” factor: The lack of supply in the event that stocks are exhausted Addressing the problem by modelling the time series of bread daily demand for point of sale has several characteristics that must be taken into account when building the mathematical models: – The outlets are too many to build a different model for point of sale. It is therefore necessary to construct a model with a common structure and then adjusting the model for point of sale, estima-ting the parameters of the model from the data associated to each point of sale – The best fitting is not necessarily the one that minimizes the error or other statistical metrics, because it must be taken into account the loss associated to underestimate the demand and the cost of returns – The factor “out of stock” skews the number of units sold: when all existing units in shop have been sold, no one knows for sure how many units could have been sold – The data for “returns” is not immediately known but is provided once the product has expired. To simplify the problem, we will assume the following hypothesis: “if a unit is not sold one day, the re-turn is done that very same day” Mathematical treatment: The aim of this analysis is to design a basic model for the treatment of this kind of series. Some examples will be provided in order to test whether the model fits well enough to data: - In this model trend and weekly seasonality should be collected at least - As the prediction horizon that arises is 7 days, it is not necessary to add to the model a cycle com-ponent which reflects the annual periodicity Some other considerations that should be reflected in the model are: - Outliers detection: calendar consideration is essential - For shop closing dates, when there is no data, the use of interpolation is allowed - It is also available a variable which shows daily advertising pressure that measures the intensity of the campaigns carried out to improve sales (transfer function models) Problem resolution information: The following information will be provided to help solve the problem: Historical data by point of sale – Point of sale code – Date: day – Number of units shipped every day by point of sale – Number of units returned daily (due to out-of-date) in each outlet Notes about point of sales – Data of several randomly chosen points of sale will be provided – In case of no sales (products sold equals to zero) it will be because of shop closing dates: “Information on whether the point of sale is closed or not, will be known at the time of the predic-tion”


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Calendar data and marketing campaigns – To assist in the prediction, you will be provided with several calendar variables for each day that may be useful in building the model, as well as a daily advertising campaign variable that measures the intensity of advertising to improve sales made that day - These data are also known at the time of the prediction ROI Analysis The prediction desired is that of knowing how many units should be sent to every point of sale in every day for the next 7 days Alternatively it is proposed that the final determination of the demand is adjusted by optimizing a cost function that takes into account the concepts “out of stock” and “returned product” To do so, it will be provided the cost of a return and the profitability of each unit not sold. Participants Baladrón Herrera, Fernando Barrigón Montañés, Laura Garrido Berenguel, Ángeles González Salcedo, Alejandro Hernández Negrín, Veronica

PROBLEM 6:

Direct Load Control Decision Model Applied to Electric Vehicle Charging Points Problem proposed by Universidad Pontificia de Comillas Instructor Andrés Ramos, Sánchez, Pedro (Universidad Pontificia de Comillas, Spain) Context ELECTRIC vehicles are becoming an alternative to combustión engines due to their low emissions, high energy efficiency and competitive autonomy range. Electric Vehicles (EV) and Plug-in Hybrid Electric Vehicle (PHEV) are two current available Technolo-gies. Coming 5-10 years PHEV/EV will be part of the urban vehicle market. Challenges One of the main difficulties of this kind of vehicles is related to its long battery charging process. – Fixed charging stations at parking garages provide a possible solution when the plug-in vehicles number is reduced. – However, to cope with an increasing number of plug-in vehicles is necessary to reinforce the elec-tric cable installation providing individual electric infrastructure per plug-in vehicle at parking gara-ges. – Charging management policies should be designed and implemented to deal with simultaneous vehicle loadings at high concentrated charging points. Work to be done. First part Use mathematical programming to design electric vehicle charging policies subject to different ob-jectives: – Complying with technical constraints of: • time schedules (arrival and departures) • vehicles (energy, power, discharging rates,)2011 • charging Point Capacities (power and number of vehicles) – Optimizing charging costs based on hourly energy prices. – Analyzing possible energy interchange among vehicles (Vehicle to Vehicle - V2V) with Electricity Retailer (Vehicle to Grid - V2G) Work to be done. Second part – Obtain optimal electric vehicle charging policies using a mathematical programming language GAMS [2] – Analyze charging policies obtained varying parameters: Discharging rates Energy price variations PHEV/EV percentages – Analyze different electric vehicle uses: Residential Business Mixed References [1] http://www.idae.es/index.php/mod.pags/mem.detalle/id.407/lang.uk [2] http://www.gams.com/docs/intro.htm 6


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Participants Armero Huertas, Ismael Barcenilla Torres, María Dmitrieva, Ekaterina Naya, Jorge Peñamil Alcázar, Marcos Donner, Christian

PROBLEM 7:

Estimation of Orientation Distribution of Fibers Problem proposed by Metso Instructor Jouni Sampo (Lappeenranta University of Technology, Finland) Exposition of the problem In the paper making process wood fibers, mineral fillers, and other additives, together form the ba-sic structure of paper. The properties of paper depend essentially on how fibers are distributed. For example, orientation difference between surface and middle layers affects bending stiffness of the paper sheet, and the orientation difference between opposite surfaces causes curvature of the paper sheet. Because of this, companies like Metso are interested about methods to image and analyze fibres in paper. Fibers in the paper can be imaged in many different ways. With proper placement of light sources, the normal reflectance images taken from paper surface can reveal information about fibers on the surface. Second approach is to illuminate the paper from one side and take image from the anot-her side. This kind of transmittance images can give information not only about fibers on surface, but also a bit deeper inside the paper. If trae 3D-image of fibers in the paper is needed, X-ray tomo-graphy devices can provide that. If imaging of paper is made off-line, very high resolution can be used with all three method descri-bed above. If on-line solution for running paper web in paper mill is needed, then resolution is much lower, although imaging techniques are rapidly developing. However, question remains the same: how to estimate orientation of fibers from the images? Scheme of the work to be done 1) Explore theoretical possibilities and limitations of different type of imaging techniques discussed above. 2) Describe a method(s) to estimate (planar) orientation distribution of fibres. Some references will be given, but students are encouraged also to develop their own method(s) and algorithm(s). 3) Compare time-complexity of method(s) described in 2). 4) Test algorithm(s) with i) simulated fibre network ii) transmittace images and iii) images taken by electron microscope. Data will be provided. Participants Davidovic, Andjela Gargallo, Abel Llontop García, Marta Muñoz Ortega, Francisco Javier Toledo Carrasco, Daniel Wang, Chang


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Instructors:

Dr. Luigi Barletti Università degli Studi di Firenze

Dipartimento di Matematica Italy

Dr. Conrado Manuel Universidad Complutense de Madrid

Spain

Dr. Cameron Hall University of Oxford United Kingdom

Dr. Jouni Sampo Lappeeranta University of Technology

Finland

Dr. Juan Tejada Universidad Complutense de Madrid Facultad de Ciencias Matemáticas Spain

Dr. Begoña Vitoriano Universidad Complutense de Madrid

Facultad de Ciencias Matemáticas Spain

Dr. Andrés Ramos Universidad Pontificia de Comillas Spain


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Dr. Enrique González Universidad Complutense de Madrid Spain

Dr. Javier Castro Universidad Complutense de Madrid

Spain

Dr. Pedro Sánchez Universidad Pontificia de Comillas Spain

Hugo Marrao Indizen Spain

Confirmed Participants:

NAME NATIONALITY INSTITUTION

Juan Aguirre Bueno Spain Universidad Complutense de Madrid

Marta Andrés Andrés Spain Universidad Complutense de Madrid

Ismael Armero Huertas Spain Universidad Complutense de Madrid

Fernando Baladrón Herrera Spain Universidad Complutense de Madrid

Federica Bani Italy Università degli Studi di Firenze

María Barcenilla Torres Spain Universidad Complutense de Madrid

Laura Barrigón Montañes Spain Universidad Complutense de Madrid

Ana María Batanero Akerman Spain Universidad Complutense de Madrid

Harry Biddle United Kindom University of Oxford

Vitor Cedrola Carvalho Spain Universidad Complutense de Madrid

Michelle de Decker Belgium Universidad Politécnica de Cataluña

Ekaterina Dmitrieva Russia Lappeenranta University of Technology

Christian Donner Spain Universidad Complutense de Madrid

Jonathan Gallego Casilda Illescas Spain Universidad Complutense de Madrid

José María García Roldán Spain Universidad Complutense de Madrid

Abel Gargallo Spain Universidad Politécnica de Cataluña

Ángeles Garrido Berenguel Spain Universidad Complutense de Madrid

Ana González de la Cruz Spain Universidad Complutense de Madrid

Alejandro González Salcedo Spain Universidad Complutense de Madrid

Carlos González Salcedo Spain Universidad Complutense de Madrid

Andjela Davidovic Montenegro Universidad Autónoma de Barcelona

Diana Edith Guere Lettich Spain Universidad Complutense de Madrid

Veronica Hernández Negrín Spain Universidad Complutense de Madrid

James Herterich Ireland University of Oxford

Alvaro Hilario Diaz Spain Universidad Complutense de Madrid

Natalie Keating United Kindom University of Oxford

Alexander Kospach Spain Universidad Complutense de Madrid

Marta Llontop García Spain Universidad Complutense de Madrid

Andrea Maffia Italy Università degli Studi di Firenze

Manuel Marchito Renedo Spain Universidad Complutense de Madrid

Pedro Ismael Mardomingo Alonso Spain Universidad Complutense de Madrid

Ignacio Martínez Calvo Spain Universidad Complutense de Madrid

Emma Massi Italy Università degli Studi di Firenze

Eduardo Moro Spain Universidad de Vigo

Francisco Javier Muñoz Ortega Spain Universidad Complutense de Madrid

Jorge Naya Spain Universidad de Santiago de Compostela


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Charmi Devendra Panchal India Lappeenranta University of Technology

Marcos Peñamil Alcázar Spain Universidad Complutense de Madrid

Víctor Puente García Spain Universidad Complutense de Madrid

Tommaso Ristori Italy Università degli Studi di Firenze

Daniel Toledo Carrasco Spain Universidad Complutense de Madrid

Chang Wang. China University of Oxford

NAME NATIONALITY INSTITUTION

Confirmed Participants:


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The organization will cover, for agreed participants Travel. For non UCM participants whose costs are covered by UCM, flight / train ticket has been bought by the organization and sent to the participant by e-mail. Accomodation. For non UCM participants whose costs are covered by UCM: in shared double rooms for students and single room for instructors, at Residencia Galdós (see below). Meals: Meals: For non UCM participants whose costs are covered by UCM: at Residencia Gal-dós, breakfast included all days, lunch included from Monday to Friday (June 13, 14, 15, 16, 17) and then next Monday and Tuesday (20,21). Residencia Galdós The residence is located at the campus of the University. The address is Ramiro de Maeztu, number 2, and telephone number is (+34) 912062900. The closest underground stop is Metropolitano. Buses connect the residence with Moncloa (132 and C), many points in the Uni-versity campus (132 and F), Cuatro Caminos and Guzmán el Bueno metro stops (C and F), ... The webpage of the residence is www.residenciagaldos.com


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Campus Map Facultad de Ciencias Matemáticas and Residencia Galdós 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. A single trip costs 2 euro from the airport to the city:

A taxi would cost around 25 euro from the airport to the residence. Tipically the taxi driver will not know how to find the street, so you could print the map to show them. Handicapped people should not use Metropolitano metro stop since it’s not very accessible. They can use Guzmán el Bueno metro stop instead, and then take bus F or bus C (map in the next page):


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Bus stops near Residencia Galdós:


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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/index.html?lang=eng Cercanías (regional train): http://www.renfe.es/cercanias/madrid/ Tourism Madrid City: http://www.esmadrid.com/en/portal.do Madrid City and Region: http://www.turismomadrid.es/index_INGL.aspx 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/IMI_english.htm

Communication Tower and Cua-tro Torres Busi-ness Area, Ma-drid

Mountains, Madrid


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V MODELLING WEEK UCM€¦ · Programme The event will have 4 parts: PRESENTATION OF THE PROBLEMS:...

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Transcript of V MODELLING WEEK UCM€¦ · Programme The event will have 4 parts: PRESENTATION OF THE PROBLEMS:...