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Blijkt Econometrie ineens een vooropleiding. PerVectum

Een succesvolle carrièrestart is meer dan een goede cijferlijst. Het begint met karakter en inzicht in jezelf. Ontdekken wie je bent, weten waar je naartoe wilt groeien én hoe je dat voor elkaar krijgt staat altijd aan de basis. Ernst & Young Actuarissen coacht jou actief op weg naar jouw succes. Of je nu een financieel directeur van een verzekeraar wilt adviseren over een nieuwe premiestructuur of het toeslagenbeleid van een pensioenfonds wilt toetsen. Ernst & Young Actuarissen is onderdeel van een Europese organisatie waarin actuarissen uit alle financiële centra van Europa samenwerken. Volop kansen dus. Ontdek ons op ey.nl/actuarissen

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December 2011

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PerVectum

Word from the President Dear Econometricians, After four months of straight studying the year 2011 is nearing its end, leaving you with the prospect of a well-deserved Christmas holiday. This also means that the first half of the current academic year is almost over and it seems a majority of you have reached a midpoint in their study in some way or another. For me personally it does not only mark a midpoint as far as my Master studies are concerned, but it also implies that we are already entering the second half of our board year. With this in mind I would like to seize this opportunity to invite you all to our semi-annual GMA on the 17th of January.

enjoying the first few months of your study, something I hope Vectum was also able to assist you a little bit in.

For our new students the end of the semester means that you have now completed almost half of your first year, have hopefully successfully mastered your first classes in Analysis and Linear Algebra, are on track to pass the faculty’s BSA and that you are in the midst of positioning yourself well for the study abroad ranking next summer. I am convinced you will also have mastered the transition from high school to university by now and have been

For our starting year of 2010 the end of this semester marks not only the midpoint in their Bachelor degree, but it also means that they will by now know the location of your study abroad university next semester. I hope you all ended up with the place you wanted to go to, whatever place this may be, and I am sure you will all have a great time there! (Also note that due to that semester abroad, at least in terms of study load, you have actu4


December 2011 ally already passed the midpoint of your study).

Harks, who started at the Department of quantitative Economics just a few weeks ago. His research area is Operations Research and he has joined the Department from the technical University of Berlin. Also serving those interested in Operations Research, Frank’s article wraps up his recent Master thesis in the area. The Actuarial side of our study track is covered by an insight into his current work at AZL by recent graduate Gijs Cremers.

Last but not least, most of our third and fourth year students are in the middle of their final year, only a few months away from graduating on either Bachelor or Master level. For those among you who are planning to leave university next summer, there will be ample opportunities arranged during the upcoming blocks to give you a last career guidance and get you in contact with our sponsors to help you get your career started! Our Business Trips and the LED 2012 are just some of the activities to mention in this regard. Please regularly check our website for both upcoming activities and job openings!

I would like to conclude this introduction by wishing you all a pleasant Christmas holiday, and I hope to continue to see many of you around at our regular activities! Finally, on behalf of the SCOPE | Vectum Board 2011/2012, I wish you a merry Christmas and all the best for 2012.

Among others, this issue includes a report of Vectum’s former president on his current experiences on his Master exchange in Boston. Further it features an introduction on the current research of Tobias

Simon Freyaldenhoven President 2011-2012

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PerVectum

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December 2011

Table of contents PerVectum Magazine for Econometrics students at Maastricht University Year 16, issue 2 of 4 December 2011 Circulation 250 copies Print Compact Drukwerken Lanaken

Editor in Chief Suzanne de Boef Co-editor Celine Brouwers

4 Word from the President 8 Angelo's Exchange in Boston 11 Impressions of Bowling and

Ice Skating

14 Gijs' working experience at AZL 17 Skiing 18 Research article: Computing

Optimal Tolls on Subnetworks

24 Impressions of the Block Drink,

Puzzle

26 Master thesis: Localization in SCOPE|Vectum P.O. Box 616 6200 MD Maastricht +31 (0)43 388 39 40 ABN Amro 44 10 37 887 Visiting Address Tongersestraat 43 Room 1.014 6211 LM Maastricht

Ad-Hoc Sensor Networks

31 SCOPE's Winterball 2011 33 Solutions to the Puzzles 34 Upcoming Events

info@scope-vectum.nl www.scope-vectum.nl

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PerVectum

Master Exchange in Boston by Angelo Lacroix Extending your studies with an exchange semester abroad after you have fulfilled all requirements to graduate at Maastricht University is something that I can recommend to every student. Especially if you are not really sure about in which company or sector you want to pursue your first full-time position. Looking for something less technical and abstract than the theoretical econometrics courses, I decided to apply for a position as exchange student at Brandeis University in the greater Boston area. After having an interview with the International Relations Office I was one of the two privileged students that represented Maastricht University at Brandeis during the Fall 2011 semester.

I share an apartment with two Italians, a French and a Spanish guy. Courses are taught in a different way than in Maastricht, instead of the PBL system only lectures are used. There is still quite an emphasis on interaction as participation is graded and often case studies are used as a basis for discussion. Professors are experts in their field and have next to their academic careers often impressive professional records. This makes it very interesting to talk to them about real-life examples and you can have conversations about many things which are not directly course-related. Compared to my study abroad during my BSc, which I did in Bogotรก, it did not get as crazy in terms of partying. By no ways, though, this means that my life at Brandeis is boring. First of all, Americans are very passionate about sports. Almost all students can be found on a regular basis at the athletics centre; if my schedule allows me I try to play squash every day. Brandeis also organizes intramurals to see which team performs best in their sport within Brandeis. As our origin forced us to do, our exchange

The International Business School (IBS) from Brandeis offers an extremely international environment, less than 20% of the students are native Americans. This makes it easy to get in touch with a variety of cultures and traditions. Brandeis has exchange agreements with only top European Business schools like Bocconi, ESSEC, ESADE and WHU. Generally exchange students live on campus, 8


December 2011 student team won the Intramural soccer title in October. Which was actually great as the Americans took it quite serious and they kept on running like robots. IBS also has a graduate soccer team with which I played several games against for example Harvard, MIT and Tufts. Next to actively exercising a sport, Americans are also very passionate about watching sports. They are not (yet) interested in soccer however, although it is becoming increasingly popular. The main focus is on the big four traditional sports; baseball, American football, basketball and ice hockey. Unfortunately the NBA did not start because of contractual problems between the team’s owners and the players. I went to watch a game of the Boston Red Sox (baseball) and Boston Bruins (ice hockey), which were both amazing. Especially an ice hockey match deserves a recommendation to US visitors as the ambience is unique.

and just reflects intellectuality in all senses. I was actually lucky to be in Daniel’s presence one day and to follow some lectures of the PhD program. Due to the great student body in Boston parties can be great. There are many clubs and small bars with their own characteristics and there is basically something for everyone. Clubbing can be very expensive, but once every while it is simply worth it. One of the disadvantages is however that clubs are forced to close between 1 and 2 am by law. This simply implies that you need to start pre-drinking while still cooking dinner and that you have

The Boston area is characterized by a great student population due to the numerous universities and colleges that reside in Boston, Cambridge and surroundings. The most famous one is of course Harvard. As Daniel Pollmann started his PhD in Economics in September at Harvard, he was the best possible guide you can ever have for your guided tour at the Harvard campus. The campus is beautiful 9


PerVectum same price as in Europe and the show is amazing.

to be in the club between 10 and 11. Due to the Mediterranean mentality of my housemates we often do not make it and end up throwing a last-minute house party, which is obviously also a lot of fun.

My best trip however was a one week journey in Puerto Rico. As Brandeis is a Jewish university they do not schedule classes on Jewish holidays. Due to some fortunate changes to my course schedule I was able to leave Boston for one week during the semester without having official holidays. Searching for a sunny destination I simply looked for the cheapest flight to a tropical place, which turned out to be Puerto Rico. Puerto Rico is an unincorporated territory of the United States in the Caribbean. As it is a former Spanish colony there are many colonial buildings left in the historical centre of San Juan, Puerto Rico’s capital. San Juan was of strategic importance for the Spaniards as it controlled all sea traffic between Europe and the Caribbean. The main three forts used to protect San Juan are still intact and are open for visitors. Another famous attraction in San Juan is the Bacardi plant, the biggest one in the world. Nightlife is Latin-alike and is simply crazy. Although city beaches are usually not the best ones, San Juan’s beaches are clean, white and a good alternative if you do not want to leave the mainland.

May be one of the nicest things is that Boston is very close to the city that never sleeps, New York. It takes a bus 4 hours to go from downtown to downtown and you pay $15 for a single ticket. I had been before to NY, but I still went there two times during my study abroad due to its proximity and the fact that there is always something going on. You’ll always find new things to explore and to do and some things that you would like to repeat. The overall ambience is just amazing and especially if the winter is approaching the city is decorated with all Christmas decorations which gives it a romantic touch. I also recommend everyone to go to a Broadway musical if you are in NY as it is basically the best you can get for the

As I had time I did not stay on the mainland and went to visit an is10


December 2011 land on the east of Puerto Rico, Isla de Vieques. Vieques is a tiny island with a rural character and enables the adventurer to avoid the mass-tourism. As I travelled in the low-season period I was lucky to be basically the only tourist on the island. This allowed me to hike on beautiful deserted beaches and only coming across wild dogs and horses. Vieques is also famous for its bioluminescent bay, which is known to be one of the best in the world. The bay has large numbers of dinoflagellates, who when stimulated glow to scare off predators. So at night I went with a kayak tour and when we started paddling the water started to get a bright colour. This was an amazing phenomena. I was a little bit unfortunate to have an open sky with a full moon which did

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not allow me to see all effects, but it was still a great experience. Tourists used to be able to take a swim in the bay but as there was a shark attack some weeks before we were not allowed to refresh ourselves in the bay. While I am writing this article during Thanksgiving I realize that I just have one month left at Brandeis. I still have a small trip coming up to Chicago. After that I have my final exams and my student life will come to an end. I will probably stay on this side of the Atlantic Ocean to travel a bit more in Latin America until I run out of money. I wish you all a Merry Christmas and all the best for 2012.


PerVectum PerVectum

Impressions Impressions from from Bowling Bowling

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December 2011

Impressions from Ice Skating

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PerVectum

A Working Class Hero at AZL by Gijs Cremers Is definitely something to be. For me the working life began this summer and in this article I’ll share my experiences of the past five months.

personal financial situation since July. My tasks at AZL partially changed since my full-time employment. I still do some of the things I worked at before, but many tasks are now done by Anne (Balter) who joined AZL as a work-student in January of this year. In case you are interested in becoming a work-student at AZL, you can! There is a vacancy right now and all Dutch-speaking 2nd and 3rd year students can apply. If you have any questions, feel free to ask me (or Anne). One of the things I work on (with some help of Anne) are the intra-year reports that AZL offers clients. In these reports (the so called QuickScan and RiskMap), we provide pension funds with information on their funding ratio, the current macro-economic situation and their risk positions. As a work-student I was mainly involved with preparing these reports as well as some calculations. Now I not only calculate, but also answer questions, verify figures with asset managers, explain the numbers to pension fund board members and discuss with external actuaries and advisors. This adds a human touch to all the numbers and figures,

I started out at AZL in March of 2010 as a work-student (and actually wrote an article in PerVectum on this topic in the first issue of 2010-2011). In May of this year, when I was busy finishing my studies in Maastricht, AZL offered me to stay and in July I started as a full-time employee at the Actuarial department. Right from the beginning I was of on a busy start: trying to complete a thesis in combination with a working week is not a cakewalk. Furthermore, waking up at 6.45 am every day (opposed to the nice 11 o’clock lectures twice a week) is no bed of roses either. There are of course some advantages of being a Working Class Hero. Somehow work feels more rewarding than studying as the tasks I perform often have a direct impact on choices that pension boards make. This means my work helps pension funds to improve their financial situation, not to mention the improvement of my 14


December 2011 which makes the job a lot more interesting. Since September I also got another task: being the actuarial advisor of two pension funds. They are AMF and BFM known as the mining-funds (which means that the “mijnfondsen” are actually “mijn fondsen”). In contrast to the intra-year reports which are rather “standard” for all funds, as an advisor you serve the specific needs of your own fund. This means writing memorandums on various topics like the financial position of a fund, the funds recovery plan and the future of the fund. It also means going to board meetings (completely suited up, which is not the “normal” AZL dress code) and explaining your memorandum, giving advice to the board and answering ad hoc questions. Going to a board meeting is particularly satisfying as you can see your own advice being put to practice or as an input for discussion. Next to that it is very instructive: it shows that communicative skills are just as important as content related knowledge. As actuary you are an expert in your field, in other words, you know way more about the financial side of pensions than most of the board members. This means that the ability to communicate this knowledge in a clear way is key. Even though student-life came to an end, does not mean I don’t have 15

to study anymore. To become a fullfledged actuary (and be allowed to use the AAG-title) I am studying an Executive Master of Actuarial Science (or EMAS). This means traveling to Utrecht or Tilburg for lessons once a month often on a Friday, Saturday or both. Good thing though is that I meet people from actuarial companies throughout the country. Furthermore it is nice to mention that Econometrics & OR, followed by a master in the Actuarial Science track is the “perfect” pre-training: out of the 27 people that started in September I am the only one that was allowed to start right after the master, without having to take any extra courses. Even better, I am likely to get an exemption for one of the six courses after following “Life Insurance I” in Maastricht. The course I am following right now is called “statistical methods”, and despite the name it is not as technical as the subjects that Urbain teaches. Next to the courses there are some cases as well, meaning I know not only about pensions, but I am also acquainted with disability and health insurance (maternity and pregnancy being my particular specialty…). Of course all this studying requires time and effort and luckily AZL pays my tuition, books, 1st class traveling-costs and hotel stays to easy the study-burden. Even better, I get quite some free days (about one day a week) to facilitate my


PerVectum study. Looking back it somehow feels I missed those little perks in Maastricht.

not one of the songs in the questions. All in all working life is not bad at all. And even though I sincerely miss the great fun lectures from Eichler, Urbain and Crombrugghe there is some charm to sitting in a brand new office (we just moved), listening how my colleague whistles the tunes being played on the radio (even though it is out-of-tune), and of course work.

As you can read I have plenty of things (intra-year reports, AMF/ BFM, studying, ect.) to fill my agenda with and especially when working on the intra-year reports a working week does not end after 40 hours. There is still some time for fun as well though; we recently had a music-pub-quiz. Though not actually in a pub (but at my boss’s house) there was beer and pizza so the scenery was much alike. Much to my surprise I did not win, even though I bribed the Quiz-master (turns out I was not the only one). And no‌Working Class Hero was

Should you have any questions regarding my work, working at AZL or becoming a work-student (but no questions on Time Series), feel free to mail me at Gijs.Cremers@azl.eu.

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December 2011

Snowworld by Cameron Assmann Winter is coming soon, and with a high number of people from Vectum going to the Alps during the holidays, an opportunity to practice skiing was very much appreciated. On the 15th of November our members, both experienced and inexperienced skiers, gathered at the university gate before heading off to Snowworld for a night packed with fun and adventure. Now, by adventure, of course, I am referring to the drive from Maastricht to Snowworld in Jim’s car. Apparently singing does NOT improve your driving (just kidding Jim, your driving is superb), but we needed to practice for the upcoming musical Pretty Boiiz©. Aerosmith, Ronan Keating, Westlife… only the best of the best would be sung by the best. Surely, the girls who sat in the back must have enjoyed listening to us just as much as we enjoyed singing to them. It was too bad it only took us 25 minutes to reach our destination, because, honestly, we could have gone on forever. As we did not want to miss a thing, we joined the rest of the group

inside the building. With most of the third year students being on exchange to another country, this group consisted mostly of second year students and a couple of first year students. We paid for tickets, changed into skiwear, went up the slope and mentally prepared ourselves for broken bones. Luckily, most of us got the hang of it rather quickly. Some needed to make it a little more exciting by racing each other, in which Andréas and Florentijn proved to be the ski and snowboard kings. Florentijn even proved he was the FunPark king, as he was the only one with the guts to slide down the rail. Others decided to go downhill in a more relaxed manner, so that they could enjoy the view of Snowworld or something. Whichever way was picked, we would all get down eventually just so we could do it over and over again. Even though everyone seemed to be having a blast out in the (artificial) snow, far more important matters were at hand in the restaurant downstairs: hot chocolate, croquettes and the football match against Germany (which, I believe, 17


PerVectum the Netherlands won). Some students reckoned they had been skiing for long enough and decided to head off, but most second year students stayed and chatted for a while. We came up with the idea to go down the slope with the entire group before we would leave, which proved to be a great conclusion to our night. After some time, Suzanne and Jim were the only ones who had not made it all the way down yet. Since Jim had fallen and needed to put his skis back on, everyone expected Suzanne to get down the hill first. However, the big man from Landgraaf proved to be a quick learner and was able to win the race in his hometown just in time. It looks as though several people went from beginner to pro in under 4 hours, which was most likely due to the easiness of the slopes. Clearly, most of us were ready or already experienced enough to go skiing in the Alps. However, that does not mean we will not be back in Snowworld with Vectum next time. I advise you to be there as well, as you do not want to miss out on one of the most fun activities Vectum has planned all year!

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December 2011

Computing Optimal Tolls on Subnetworks by Tobias Harks Have you been in a traffic jam lately? How much time of your life do you spend in traffic jams? At least for daily commuters this question may produce devastating answers. In fact, today’s traffic situations in large cities are still far from being satisfactory. Traffic jams at rush hour or at special events (sport or music events) occur frequently and drivers suffer from increased total travel times. Moreover, traffic congestion significantly increases exhaust gas pollution. The situation is particularly dramatic in the rising mega-cities in Asia and SouthAmerica. The traffic volume in China, for instance, has increased in 2005 by 15% and is expected to grow faster in the next years [2], making good network planing and traffic control indispensable. It is a well known fact that selfish behavior of traffic participants is one of the main reasons that leads to inefficient traffic situations. Since every traffic participant solely aims at minimizing her individual travel time, the overall outcome is less efficient, e.g., in terms of the total average travel time, than when everybody would have been routed 19

according to a centrally coordinated scheme. Modeling selfish behavior in traffic networks has been a central topic in the operations research and transportation literature for decades. The classical theory of selfish behavior in traffic networks started with the traffic model of Wardrop [11]. The basic idea is to model the interaction among the selfish network users as a non-cooperative game. The traffic network is modeled as a directed graph with latency functions on the edges modeling the travel time needed to traverse the edge. The commuters are modeled by a set of origin-destination pairs, called commodities. Every commodity is associated with a demand, which specifies the rate of flow that needs to be sent from the respective origin to the destination. Every demand represents a continuum of agents, each controlling an negligible amount of flow. The latency that an agent experiences when traversing an edge is given by a (non-decreasing) function of the total flow on that edge. Agents are assumed to act selfishly and route


PerVectum their flow along a minimum-latency path from their origin to their destination. A solution in which no agent can switch to a path with smaller travel time corresponds to a Wardrop equilibrium [11]. It is well known that a Wardrop flow in general does not minimize the total travel time; or said differently, selfish behavior may cause a severe performance degradation in the network (compared to the optimum). It is known that this performance degradation can be dramatic (unbounded) even on networks of parallel edges. Due to this large efficiency loss, researchers have proposed congestion pricing strategies for over 80 years, see Pigou [6] and Beckmann et al. [1]. The basic idea is to impose tolls on network edges that guarantee that the selfish outcome corresponds to a predetermined routing scheme, e.g., one that minimizes the total average travel time. Assuming that one can possibly collect tolls on every edge of the network and that the value of time is the same for all users, it is a classical result in the economic theory of transportation that tolls equal to the marginal edge cost of the system optimal solution (marginal cost pricing) induce a socially optimal equilibrium flow [1]. Over the last decades, congestion pricing strategies have been 20

implemented in various cities. Examples include London [9] (London congestion charge), Stockholm [8], Bergen [10], and Singapore [7] (Electronic Road Pricing). All these applications have in common that only designated areas of the transport network are amenable to tolls. In London [9] and Stockholm [8], a congestion fee is charged only for access to the center of the city. Bergen [10] implemented a toll ring where congestion fees are charged. These features makes the application of classical marginal cost pricing impossible. Since in practice it may not be feasible to impose tolls on every edge of a given traffic network, Harks, Kleinert, Klimm and Mรถhring [3] studied the resulting mathematical problem of computing tolls on a predefined subset of edges of the network so as to minimize the travel time of the induced equilibrium flow. They present an analytical study for the special case of networks consisting of parallel edges that highlights the intrinsic complexity and non-convexity of the resulting optimization problem. The setting of parallel edges describes situations in which access roads to the central district of a city are the bottlenecks for the inbound or outbound traffic. These roads may be either tollable (bridges or highways) or non-tollable and the goal


December 2011

(a) Modeling of outbound traffic as flow on a parallel edge graph. Edges with bridges are assumed to be tollable.

(b) Highway with four lanes, two of which are with tolls.

Figure 1: Two applications of parallel edge graphs in traffic models.

is to devise tolls so as to minimize congestion on the bottleneck edges. Another application arises when a highway is divided into tollable and non-tollable lanes (as in Tel Aviv [5]), see Fig. 1 for an illustration. Harks et al. [3] devise an algorithm that approximates an optimal solution within an additive error of ε > 0. The algorithm runs in poly(m, K, κ, d, 1/ε)-time, where m denotes the number of edges, K is an upper bound on the latency functions, κ is a common Lipschitz constant of the latency functions, their derivatives, and inverse functions, d is the flow demand, and ε is the precision. Previously, a polynomial algorithm was known only for affine latencies [4].

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For general networks they present a series of algorithms that are inspired by the gradient descent method. The idea is to iteratively increase the toll on those feasible edges on which the edge flow of the current Wardrop flow exceeds the system optimal edge flow, and to decrease the tolls otherwise. The rationale behind this iterative process is to follow a solution trajectory along a gradient descent direction of the objective function. A computational study is provided evaluating the quality and convergence behavior of the algorithms on large-scale network instances. It turns out that for all test instances, already a small number of tollable edges suffices to significantly reduce the total travel time (only 25


PerVectum edges have been tolled for the results obtained in Table 1). An overview about the instances, including network parameters and actual values of the total travel time of the system optimum, Wardrop equilibrium, and the resulting inefficiency with and without tolls are depicted in Table 1. The study of [3] suggest that even if only subnetworks are amenable to tolls, computing the right tolls bears significant potential in reducing the overall travel time.

Table 1: Number of nodes n, number of edges m, number of commodities k, sum of the commodities’ demand, total travel time of system optimal flow f*, total travel time of Wardrop equilibrium flow f, measure of inefficiency ρ = (C( f )−C( f*))/C( f*). The value ρ* denotes the inefficiency after setting tolls on 25 edges.

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December 2011 References [1] M. Beckmann, C. McGuire, and C. Winsten. Studies in the Economics and Transportation. Yale University Press, 1956.

[8] Swedish Road Administration. Congestion tax in Stockholm. Technical report, Swedish Road Administration, 2007.

[2] Green Choice Beijing. Urban growth and its pressure on traffic, 2010. http://www.fon.org.cn/ greenchoice.

[9] Transport for London. Central london congestion charging. Technical report, Transport for London, 2008. http://www.tfl.gov. uk/assets/downloads/sixthannual-impacts-monitoringreport-2008-07.pdf.

[3] T. Harks, I. Kleinert, M. Klimm, and R. H. Möhring. Computing network tolls with support constraints. Technical report, TU Berlin, 2011. [4] M. Hoefer, L. Olbrich, and A. Skopalik. Taxing subnetworks. In C. Papadimitriou and S. Zhang, editors, Proc. 4th Internat.Workshop on Internet and Network Econom., number 5385 in LNCS, pages 286 – 294, 2008. [5] N. Nisan. Speed-price equilibrium. http://agtb.wordpress. com/2011/01/20/speed-priceequilibrium/. [6] A. Pigou. The Economics of Welfare. Macmillan, 1920. [7] Singapur Government. Electronic road pricing, 2010. http:// www.lta.gov.sg/motoring_ matters/index_motoring_erp. htm.

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[10] A. Vingan, L. Fridstrom, and K. Johansen. Congestion charging in Bergen and Trondheim - an alternative 20 years ahead? Technical report, Norwegian Transportation Institute, 2007. [11] J. Wardrop. Some theoretical aspects of road traffic research. Proc. of the Institution of Civil Engineers, 1(Part II):325–378, 1952.


PerVectum

Impressions from the Block Drink

Puzzle Magic Star It is possible in this six-pointed star to place the numbers 1 to 12 in the circles, using one of each, so that each line of four numbers has the same total. (As a hint, the total has to be 26.) And, just to make the puzzle harder, the six outermost numbers should add up to 26 as well. Where do the numbers go?

Solution to the puzzle will be provided in the next issue of the PerVectum.

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December 2011

O OVER 1,000 ,000 STUDENTS S WILL READ THIS AD. LESS THAN 10% WILL PASS OUR TEST. WE ARE SCOUTING FOR BRILLIANT MINDS ONLY START YOUR CAREER IN TRADING

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APPLY AT WWW.OPTIVER.COM


PerVectum

Localization in Ad-Hoc Sensor Networks by Frank Borggreve The topic of my Master Thesis was “Localization of Ad-Hoc Sensor Networksâ€? and my supervisor was AndrĂŠ Berger. In this article I would like to give you an impression of the work that I did.

Recent advances in wireless communications and electronics have introduced sensor nodes which are smaller and more energy efficient than ever before. These developments give rise to numerous new applications. From monitoring enemy movements on the battlefield to temperature fluctuations in the human body; the possibilities are limitless.

A wireless sensor network is a network of wireless nodes which are able to communicate with each other. A sensor node is a node that is capable of measuring some information in its vicinity (temperature, movement, etc.), process this information and communicate it to other sensor nodes within a certain radius. By communicating with each other these sensor nodes are able to transport around all the information that they gather. This information is normally transported to socalled anchor nodes. Anchor nodes are similar to normal sensor nodes, with the only difference that these nodes do know their own locations whilst the other sensor nodes do not. For most applications it is necessary that we do not only know from which sensor certain information is coming, but also where this sensor was located at that time. This is the localization problem.

One might argue that there already is a working solution for the localization problem; the Global Positioning System (GPS). GPS is able to give location and time information anywhere on the earth. Unfortunately though, GPS receivers are relatively expensive and they are not really energy efficient. If we thus have a problem where we want to distribute a lot of sensors to cover a certain area, then using the GPS system is not viable. Next to that, the new sensors have the possibility to work on microscopic scale and even underground, both of which are impossible using GPS. Therefore solving the localization problem mentioned before can be of real significance. 26


December 2011 To be able to really tackle the localization problem, I will first clarify it a bit. Again, in this problem we are given a set of sensor nodes which are able to communicate with each other within a certain radius. Whenever two sensors are within this communication radius they can determine the distance between them. Also, the locations of all the sensors are unknown, except for some so-called anchors. The objective is to find the location of every sensor. In my thesis I only focused on the 2D-case, so this leads to the following formal definition: INPUT: The distances d{ij} between every pair of sensors (i,j), including anchors, which are within communication range r of each other. The locations px, where x is in R2, of every anchor. OUTPUT: The locations in R2 of the sensors. Before we are able to solve the localization problem we need to determine its computational complexity. Unfortunately it turns out that the problem is NP-hard. In simple words this means that the problem is difficult to solve and thus there is no polynomial algorithm which can solve it to optimality. But this does not mean that we cannot say anything about any possible solutions. We can use so-called heuristics, 27

algorithms which are able to find a solution reasonably fast, but there are no guarantees on their accuracy. Nonetheless, if these heuristics are well-constructed we can often find good solutions.

In my thesis I chose to compare three different heuristics with each other; the N-Hop multilateration heuristic introduced by Saviddes et al., the Robust Positioning System introduced by Savarese et al. and the MDS-MAP(P) heuristic introduced by Shang and Ruml. These three heuristics work in the following way. N-Hop multilateration The N-Hop multilateration heuristic works in two steps. In the first step it finds initial estimates for every unknown node. It does this by creating a so-called bounding box for every unknown node, in which the


PerVectum actual location of the node must lie. To create such a box, let us imagine an anchor node with a given location (xa, ya) and which has a distance X from our unknown node (if the unknown node is outside the communication range of the anchor node, we can use multiple hops to determine their distance, hence the term N-hop). Now we know that the x-coordinate for the unknown node must be in the range of (xa – X, xa + X) and the y-coordinate in the range of (ya – X, ya + X). If we do this for every anchor node we can construct all these bounds and thus the bounding box. Our initial estimate is the centre of this bounding box. In the next step we refine these initial estimates. First we calculate the difference between the distances given in the problem set and the corresponding distances calculated by using the estimated locations. Now a least-squares optimization on these differences will further refine our locations. Whenever this optimization terminates we have our locations. Robust Positioning System With the RPS algorithm we first construct all the unknown distances between every sensor, i.e. construct distances between sensors which are outside each other’s communication range. This is done by constructing shortest paths between 28

every sensor. When this full distance matrix is created, we have an over-determined system and can therefore solve it by using a system of linear equations. These initial estimates are still pretty rough, so we refine them a bit further. We do this by using weighted triangulation. Initially we award every anchor with a confidence level of 1 and unknown nodes with a confidence level of 0.1. In this iterative procedure every node is given the estimated locations of its neighbors and the corresponding distances to these neighbors and uses triangulation to refine its own position. Whenever their own position changes, it transmits this change to its neighbors and updates its own confidence level to the average of its neighbors. Whenever the position updates become sufficiently small, the algorithm terminates. MDS-MAP(P) The last heuristic that is examined in this paper is an extension to the multidimensional scaling mapping (MDS-MAP). Multidimensional scaling is a statistical technique which can be used to find the locations of the unknown sensors whenever all inter-sensor distances are given. This extension is a distributed version of the MDS-MAP algorithm, the so-called MDS-MAP(P) algorithm. The MDS-MAP(P) algo-


December 2011 rithm finds a local map for every node and then tries to merge these maps. The range for these local maps is set at two-hop distance for every node. To construct such a local map we first compute all the shortest paths between nodes within the two-hop distance of the considered node. Then we use MDS to construct the local map of this node and refine this map a bit further by using leastsquares optimization. Now we end up with a local map for every unknown sensor and every anchor.

Estimations RPS

The next step is to merge all these local maps into one big map. We do this by starting with one local map of an anchor, and one-for-one adding other local maps. The coordinates of the local maps that are added are transformed such that they 'fit' into the big map. When all the local maps have been merged into the big map, the algorithm terminates.

Estimations N-Hop Multilation

So now we know which heuristics to use. But now we need to compare the three and this is where the nasty stuff comes in. And that is the programming. First I needed to create numerous data sets on which I could test my three heuristics. I wrote a C++ program to do this. Actually, I decided to create three different kinds of data sets;

Estimations MDS-MAP(P)

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PerVectum data without noise terms, data with noise terms and data with noise terms and some randomly missing distances (the idea for the latter one comes from the possibility of blocked signals in real life). Why keep things easy if you can make them difficult, right? After my data sets were generated I started to work on the major issue of my thesis. I needed to write a program with the three heuristics incorporated in it. Damn, that was hard. Many hours and hours went into programming the three heuristics and many, many more in finding small errors in the program. Don’t I love C++. Nothing feels better than spending a few days trying to find a simple typo. After a while my program started working though and I was able to compare the given data with the actual locations. The way I did this was to compare the found locations to the actual locations and the distances computed by the found locations to the actual distances. Both measures were used on several data sets with different size, density of the unknown nodes and anchor density. It turned out that the MDS-MAP(P) heuristic had a very long running time and was not able to solve any of the larger problems. The N-Hop and RPS heuristics performed quite similar for smaller data sets, but for 30

the larger data sets the RPS heuristic performed significantly better in both running time and accuracy. I therefore concluded that for practical applications, where we expect to use a large number of sensors, the RPS heuristic is more viable.


December 2011

SCOPE's Winterball

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PerVectum

by Kaya Verbooy There are a few things December just cannot go without; “Sinterklaas”, exam stress, Christmas break, getting wasted New Years and a fancy gala. Last of these events took place on the first day of the specified month. The evening took of spectacularly with turning “arriving fashionably late” into “arriving not so fashionably – read half a hour - to late with wet hair” at the Italian restaurant “Donatello’s” nearby our faculty. There, fifteen of the second years were gathered, and the main topic of our evening was of course the assignment of the places for our semester abroad, which were published only a few hours earlier. While waiting for and eating the pizza’s and pasta’s this lively conversation took place. Also, bow ties were fought with, a certain Casanova had to give his two dates roses – and thus with that a little speech – and Suzanne started capturing the night on camera. Around nine, the girls put on their high heels – respect goes out to Suzanne’s impossible high and Celine’s very uncomfortable, but awesome shoes - , guys put on their jackets and we made way to the ‘La Bonbonnière’ were we got only-in-black-light-visible marked on our wrists and our very pretty 32

tickets were enthusiastically ripped into two. I have to admit our year cleans up very nicely - and as some people wanted to take two pictures per fifteen minutes I think my opinion was shared. The Bonbonnière on its own is a characteristic building in the center of Maastricht, but decorated it looked even more beautiful. You could see it was professional organized; there was no usual ‘fight to hang your coat’, bodyguards guarded the door and 10 euro’s worth of drank were included in the price of the ticket. Soon we conquered a table and met some alumni’s, fourth years and even a few first years – keep up the good work! Vectum’s personal entertainment group and delegation to Troy, ‘the pretty boys’, had to open the party with some song and dancing, as it was early in the evening and the room was not even half full. Luckily, people started to show up and with them the feeling of a sold out party. It was a great night that ended around 2.30, and I think everyone agrees.


December 2011

Solution to the Puzzles PerVectum issue 1 2011-2012

Crossing the river A, B and C represent the husbands and a, b and c their wives. This side A C a c A C a A B C A B C A a A a a b a b b b -

In the boat B b B a c a B C B b A B c a c B B b

Direction → ← → ← → ← → ← → ← →

The other side b b bc bc Cc Cc ABC ABC ACac ACac

How to make a square from a cross

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PerVectum

Upcoming Events BLOCK 3 January 17th Semi-Annual GMA

During this general member assembly, we will talk about what has been going on in Vectum so far, and give a general overview of the current state of the association.

January 23th Kleynen Consultants' Pub Quiz

After the success of the first activity sponsored by Kleynen Consultant’s (Poker Tournament), we decided to organize another event similar to the first one. This time, we will have a Pub Quiz with prizes for the winning teams!

BLOCK 4 February 7th Research Lecture

This will be SCOPE Vectum’s third research lecture. The topic of the lecture will be announced soon.

February 14th YER avtivity

The first event we will have that will be a CV training by YER. We will post the actual activity on the website shortly.

February 28th and 29th Landelijke Ecometristendag (LED) This year the LED will take place in Amsterdam.

Dates may be subject to changes. Please check www.scope-vectum.nl for updated information and subscription forms.

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December 2011

D e av o n D v o o r h e t a f r o n D e n va n het fUsierapport voor een i n t e r n at i o n a l e b i e r b r o U w e r

au d i t J ta x J a dv i s o ry

35

w w w.g a a a n . n U


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