S Association magazine of W.S.G. Abacus
Interview
Tariq Bontekoe Classic:
Christmas Dinner recipes Jorn de Jong
Balanced Matrices
New Leaf 2022
INDEX 4 6 7
Columns Chairman's Thoughts Your Story Staff says Mathematical Balanced Matrices 11
5, 10 6 12 14 15 16
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Fun Interview Review Christmas Dinner recipes Puzzles Puzzles Solutions Meme page
Editorial Dear reader, At the time of writing, it is 27 April, so that means it’s King's day, with the red-white-blue flag sticking out next to my window. When I think about how I remember my King- or Queen's days in the past, I see myself helping at the athletics clubhouse in my village. We were close to the field with all the carpets, where lots of people try to sell the stuff they collected. Because it was that close to that field, we had an attractive place with electricity and water. From 7:00 onwards, people started to come by at our place for a visit to the toilet, a cup coffee or tea, or homemade waffles. It was quite a busy day when you’re that young. That is what I also experience at this moment: being busy makes your life more fun. After the last two years I, and probably more people, could conclude that an approximately empty agenda isn’t that good for your working spirit. Today being 27 April also means that the study-year is already way closer to the end of this year than to the start of it. Before we know it, we are already in our summer holidays. It is definitely not the period of the year to be bored, with the lots of activities happening in May and June at Abacus or other places. That
sometimes makes it harder to keep the concentration at some useful level, but also more fun. I hope that everyone, including me, can be proud of their study results of this quartile when they go into their holiday weeks. In this Ideaal!, one can find the recipes of the Christmas dinner (in March :)), a piece about an algorithm with balanced matrices, and two interviews: with an Advanced Technology-student and an old Abacus board member. In this edition you will also find two puzzles, one of which being a word search. Talking about puzzles: at the end of year we want to publish an Ideaal! puzzle booklet just like last year! But, of course, before this booklet can be made, we need the help of as much members as possible. If you would like to contribute to this puzzle booklet, send us an email via ideaal@abacus.utwente.nl or tell one of the Ideaal!members in person! I hope you will all enjoy reading this Ideaal! and have a nice continuation of your spring, or even already the beginning of your summer!
Editors: Jorg Gortemaker Tim Hut Daan van Kats Eva van Laar Lavinia Lanting Fia Nase Timon Veurink
• 19 May 17:45 Study evening • 20 May 12:00 Active Members Weekend • 23 May 20:00 Prom • 25 May 16:00 Marbelympics • 25 May 20:00 Wiivening • 30 May 12:45 Master track case AI for Health
Daan
Colophon Editorial address: W.S.G. Abacus Postbus 217, 7500 AE Enschede Phone: 053 - 489 3435 ideaal@abacus.utwente.nl www.abacus.utwente.nl
AGENDA
Guest writers: Niels Apeldoorn (Chairman's thoughts), Sophie Buurman (Your Story), Mengwu Guo (Staff Says), Diana Dalenoord (Interview: Tariq Bontekoe), Jorn de Jong (Balanced Matrices, Puzzle)
Ideaal! is the magazine issue of Wiskundig Studiegenootschap Abacus and the department of Applied Mathematics. The responsibility for the articles published in this magazine lies with the original author(s). The period of notice of Abacus is four weeks before the end of the association year (August 1st). That means that you must cancel your membership before July 4th. If you have forgotten to cancel your membership before that time, you will pay contribution for another college year. Would you like to cancel your membership? Send an email to board@abacus.utwente.nl.
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Chairman's Thoughts Text: Niels Apeldoorn The month of March in 2022 was one of the sunniest months ever. With temperatures rising, the trees were ready to get out their leaves and spring was in the air. Every year after I have been disappointed by a cold and wet winter without much ice or snow, I look forward to the spring sun to finally show up. The main reason for this is that this signals the start of the road cycling season. In the winter I still make the occasional ride, but the weather is less than Ideaal! and the darkness of night arrives early on the day. This means that I can basically only ride in weekends with ten layers of clothing to fend off the cold and the wetness. Worst of all, the road is almost permanently wet. This causes my precious bikes to become extremely filthy after every ride. The task of cleaning my bike is something that I do not look forward to and something that takes up a lot of time. However, if the drivetrain is not properly cleaned, the chain and cassette wear extremely fast. All these factors added up make that, in winter, I swap my cycling shoes for ice skates or running shoes
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most of the time. However, when the sun peeks out in early spring I jump on my bike, as soon as I get the chance. This year this was on February 23rd, during the spring break. The sun shone the whole day, the roads were dry and I was happily on my bike the whole day. After that the month of March began and I believe that there was not a single moment when the sun was not shining during the day. Perfect weather for cycling. This was also when the cycling races were starting up again. These races are some of the best parts of cycling. Maybe you have seen it in the Tour de France or some other cycling race. At the start it is kind of scary to cycle in such a large group, going around tight corners, picking up speed as you go. In such a group the air resistance is much lower, compared to cycling on your own. This means that speeds can get pretty high in a peloton, going as high as 50 km/h. The key to racing is to spend as little energy as possible, but finishing first. So, it’s not just about who can cycle the fastest; there is an entirely separate discipline for that: time trials. To optimise efficiency a racer should avoid air drag as much as possible, this is achieved best
in the centre of the peloton. However, when you are in the middle of the peloton, you are locked up and can’t follow when other riders ride away at the front of the peloton. Cycling is a team sport as well, contrary to popular belief. Teammates can keep each other out of the wind and try to close gaps for each other. Usually, there is one strong rider appointed captain of the team. The rest of the team then does all the work and tries to shelter the captain as much as possible, such that he can save his energy for the final part of the race, which will either be a mass sprint or an attack to ride away from the peloton. All of these details and factors that affect a race make the sport of road cycling very interesting to participate in, and to watch as well. It takes a combination of strength and endurance, as well as bike handling skills, teamwork and tactics. Due to the corona lockdowns, many races were cancelled in the past two years, but this year I hope to be able to ride many races and hopefully also improve my performance in them. I am certain that I will enjoy it at least, because cycling is what I love to do above anything else. Good thing that spring has finally begun.
Interview Text: Eva van Laar & Lavinia Lanting Would you like to introduce yourself? Hello, I'm Christopher and I’m Fia’s brother, I’m a first-year in advanced tech and the chairman of the show committee. What is the show committee in charge of? 2 We are in charge of arranging concerts, decorating the venue, and most importantly coming up with (spicy) dance moves. What is your favorite dance move? My favorite dance move 2 is the 3 shimmy with a head tilt. I enjoy What is the theme of the choir show this year? the balance between masculinity and femininity the move proThe songs are chosen before vides. we can choose a theme. So we puzzle things together in order What is your choir experience? to create a story. With how crazy the song selection this year, the Over the years I’ve been a part of only theme that could fit was 6 different choirs. Ranging 4 from dreams. beginner stuff to self-guided jazz acapella. What is your favorite song from this concert and why? When you are not doing choir activities what are your other Ignoring all religious connotations “Near my God to Thee” is a hobbies? bop. It is powerful and a fun time For fun, I enjoy completing side to belt. projects such as designing mascots for merch and home autoWhat is the most challenging matization projects. part about being in a choir?
What was the most difficult task or decision you had to make as chairman? The biggest challenge is picking dance moves that match the skill level of the choir. You typically have to assume the worse in terms of dancing skill level.
4 What would you say to prospective choir members? If singing means anything to you then you should visit. Everyone is weird… but in a friendly way.
Probably matching the enthusiasm of the other members. It's difficult to be a casual choir member. 5
Your Story Text: Sophie Buurman For my minor I participated in the ERASMUS+ study abroad programme offered by the UT. I especially wanted to go to Spain, because I had been practicing Spanish for some years and wanted to be able to talk to some actual Spanish people, learn more about the culture and meet new people! However, after one year of careful and thorough planning it was still uncertain if I could travel there, because of the COVID-restrictions. The UT only lets people travel to countries with a green or yellow colour code, and the code had been orange for some time. Luckily, one month before departure, the colour code changed to yellow and I was finally able to go!
dam, so I was living with a host family outside of the city. The faculty I was studying was the faculty of Industrial, Aerospace and Audiovisual Engineering, and it was also rather far outside the city. It was situated in a town called Terrassa, which has roughly the same number of inhabitants as Enschede.
House prices in Barcelona city are even worse than those in Amster-
The level of the courses was almost a joke: most of the subjects did not
In Terrassa there was a great community of international students, and we met for lunch every day at the same restaurant (in Spain they eat warm for lunch, and usually three courses). Since there was only a limited number of English courses available (and almost no Spanish courses), you meet the other internationals in class every day. This way, I made lots of new friends from many different countries!
even have an exam, just a small project to hand in. This meant I had a lot of free time in the weekends, which I spent exploring Barcelona and the surroundings together with my newly made friends. Unfortunately, in Catalunya (the province of Spain that contains Barcelona) they speak mostly Catalan, so it was difficult to connect with the local people and I did not get to practice my Spanish as much as I had hoped. Still, I got to practice Spanish with the host family I was living with, since their English was not too good. At the end of the semester, the covid situation in Spain got worse and it was time for me to return to the Netherlands. But I still cherish the experience and would love to go again during my master!
Review: D.R.V. Hippocampus Text: Eva van Laar On March 13th members of D.R.V Hippocampus traveled to the Mill Ranch, a westernstyle horseback riding facility in Ede. The event was arranged by the PKcie, or the committee in charge of teaching the members about different aspects of horseback riding.
galloping for safety reasons only experienced riders were in this group. The beginner riders were in another group with horses that were easier to control and only trotted for the duration of their ride. Both groups experience a beautiful two-hour ride around the sandy planes and forests of Ede. Members noted after their ride that the horses had very entertaining names. Two sister horses were named “Coco” and “Chanel”, another pony was named “Eeny meeny” and an enthusiastic horse was named “Skittles”.
Upon arrival, the members of Hippo were greeted with a spread of snacks and drinks. Then they were split into two groups. The first group consisted of riders who were going to gallop during Typically the riders at Hippo ride their trail ride. Since horses are in dressage saddles however the more difficult to control while Mill Ranch specialized in wes6
tern saddles on sturdier breeds of horses. A dressage saddle is smaller and less heavy than a western staddle and requires an upright posterior. Western saddles however include a swell and horn at the front of the saddle, once used to hold tied up cattle, and cantle which allows the rider to slouch in the saddle and makes longer rides much more comfortable. Overall it was a fun and insightful trip on how different horseback riding styles result in different riding experiences. Many members seemed excited about the chance to come back next year.
Staff Says Text: Mengwu Guo A brief, perhaps biased introduction to digital twins I would like to use this valuable opportunity at Staff Says to talk about my understanding of the digital twin technologies, from the perspective of a computational mathematician. First, I quote the definition of a digital twin from the AIAA and AIA Position Paper in 2020: “A Digital Twin is a set of virtual information constructs that mimics the structure, context, and behavior of an individual/unique physical asset, is dynamically updated with data from its physical twin throughout its lifecycle, and informs decisions that realize value.” For an actual asset in the real world, referred to as the physical twin, a mathematical and/or statistical model is constructed to be the digital twin that acts as the physical asset’s real-time replica and dynamical virtual representation. During the life cycle, the digital twin is synchronized to the physical twin in real time, so that the users can just monitor and assess the realworld asset through its digital twin. Currently, the critical importance of digital twin technologies has been recognized all over the world. For example, it was listed as one of the top 10 frontier scientific questions by the China Association for Science and Technology, Singapore launched the Virtual Singapore project to build a digital twin for the whole country, the U.S. Department of Energy provided major funding opportunities on AI and Decision Support for Complex Systems – key ingredients in digital twinning, and the EU’s Horizon 2020 program dis-
tributed more than 20 million euros to fund digital twinning research. Technically speaking, the success of realizing digital twinning relies on the synergistic integration of physics-based modeling, machine learning & data-driven modeling, and real-world sensing systems all together. It would ask for a lot of effort from applied mathematicians to lay the computational foundation of digital twin technologies. From the viewpoint of numerical simulation and computational modeling, in my opinion, three major pillars support the research of digital twinning. First off, it’s critical for a digital twin to ensure assessment, monitoring, and decision support all in a real-time manner. Thus, one of the very basic demands is for fast and reliable simulations in a multi-query, real-time fashion. This requires the further development of robust and scalable parametric model reduction, which compresses a complex physical model governed by a high-dimensional, nonlinear, parametric dynamical system into a substantially reduced dimensionality, yet without significantly compromising the accuracy. The research question is to find a low-dimensional latent space that can well represent the high-dimensional solution manifold, and subsequently recover the dynamics in the latent space. Second, to enable real-time observational data integration for digital twin synchronization, high-dimensional Bayesian calibration and updating, as well as rapid data assimilation, need to be investigated. However, the highdimensional sampling space may cause the curse of dimensionality, which has been a major issue in computational statistics and machine learning that is yet to be fully resolved. Last but not least, the ultimate utilization of digital twins is
for decision making. Towards reliable decision support in real time, effective uncertainty quantification and risk assessment would be essential, aiming at an accurate analysis of system failures often defined as rare events. Additionally, the machine learning algorithmic methods for decision support must involve domain knowledge of the application problem and feature good robustness and interpretability. In our era of big data, digital twinning will provide key technologies to Industry 4.0, and its research and development desires a comprehensive, interdisciplinary knowledge base of all scientific computing, numerical simulation, machine learning, and data science, in cooperation with the domain knowledge of science and/or engineering in the application context. I sincerely hope that some of our talented math students at UT, our future generation of applied mathematicians, will find their interests in the research and development of digital twins, and build up a T-shaped, interdisciplinary skill set to get prepared. The digital twin community welcomes you!
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Just Abacus
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Things...
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Interview: Tariq Bontekoe Text: Diana Dalenoord
Not just working on science for the sake of science, but also for society!
then 'in real life'. My TNO projects are related to the research topics of the Master’s I completed in Computer Science (track Cyber Security), in addiTariq has always tion to my Master’s in Aploved mathematics plied Mathematics. because it can describe anything - even with the Keeping data a secret simplest formulas. He decided My combined graduation to study Applied Mathematics at project was about the the University of Twente, which balance between privacy was not a surprise. During open and auditability of digital anonydays, he liked the atmosphere, mous payment transactions. I the Twents Education Model, developed a secure protocol for the pleasant chats with students anonymous payments. Only the and teachers, plus he liked the successful completion of the transaction is known to the parfamous croquettes. ties. I also looked at how scalable it is (can the system grow Studying in modules I enjoyed following the types along with the increase in use) of courses which gave me the and could it be implemented knowledge I needed for work- practically. I used a combination ing on module assignments. In of the blockchain (way of storfact, you can already work on ing and verifying data) and zerothe mathematics assignments knowledge proofs, which is a in the first module. This is defi- method by which one party (the nitely good preparation for when prover) can prove to another paryou enter the working world and ty (the verifier) that a given stateyou need to work on various ment is true while the prover avoids conveying any additional projects. information apart from the fact Working on projects at TNO that the statement is indeed I work as a Junior Scientist in true. For example in healthcare, Cyber Security at TNO. I choose you could prove that you have a my own projects, which are a bit valid health insurance, without like module assignments, but disclosing its details. Another example is where zero-knowledge proofs can help you obtain a loan by proving that you have a good credit score without disclosing it. TNO keeps track of how such new developments are used to increase the privacy of, for example, cryptocurrencies. This is just one of my tasks as a Junior Scientist at TNO. Privacy is an important aspect of Cyber Security. Via Secure Multi-Party Communication, different parties can, together, perform computation on their private data, without sharing, which is vital in the healthcare domain. GPs, hospitals and 10
insurance companies all need to work together, but they do not need to know the data that is being used. They do need to ensure that patient records are secure and private.
Fast calculations on quantum computers
I also work on quantum computers. These are computers in which the processor uses the principles of quantum mechanics. Such a processor can perform the same calculations in one go (in parallel) over multiple, different datapoints. At TNO we are investigating how these computers can be used to improve computation times for real-world problems. Many problems could benefit from the use of quantum computers, with potentially exponential speed-up in computation times. This means that we could solve problems, that would otherwise take years of computation time!
I really feel at home at TNO
I do a lot of research involving mathematics, physics and computer science. Because of my background as a mathematician and cyber security expert, I can solve practical problems. Due to my analytical skills, I understand my colleagues from other departments and I can translate the problems we need to work on and how we can find the solutions. During my time as a student, I acquired the study programme knowledge and was able to develop personally as well. I think this is just as im-
portant as obtaining a diploma. Throughout my studies, I was chairman of the board of WSG Abacus and was an education commissioner at the same time. As an education commissioner, I had regular contact with the programme director to talk about educational matters. In the time of my student assistantship, I helped younger students with maths. I was also involved in the organisation of several editions of the Twentse Wiskunde Estafette. It was really great to introduce VWO students to Ap-
plied Mathematics in a creative and fun way.
TNO internship
Are you interested in doing a cryptography or cyber security internship at TNO after reading this story? Please contact Erieke Weitenberg, internship coordinator, at erieke.weitenberg@tno.nl for more information about internships or graduation projects.
Tariq was one of the organisers of the TWE 2018 – Stef Kleinluchtenbeld (alumni Applied Mathematics) visited TWE, as a VWO teacher, with his students and…..they won first prize.
Balanced Matrices Text: Jorn de Jong Introduction I did my bachelor assignment on balanced matrices, a matrix with all entries in {−1, 0, 1} is balanced if the sum of the entries in each submatrix with exactly 2 nonzero entries per row and per column is a multiple of 4. The goal of my assignment was to improve the best known algorithm to create such a balanced matrix from another matrix by multiplying some entries with −1 (if possible). The main idea of the original algorithm was to look at the bipartite graph instead of the matrix. For any matrix A with all entries in {−1, 0, 1}, we can look at the bipartite graph with the following weighted adjacency matrix:
For example, when A is:
The corresponding bipartite graph is:
Now, instead of looking at each submatrix with exactly 2 nonzero entries per row and per column, we can look at each chordless cycle, a cycle such that no two vertices of the cycle are connected by an edge that does not belong to the cycle itself. There is a chordless cycle in the graph if and only if the corresponding entries in the matrix form a submatrix with exactly 2 nonzero entries per row and per column. Hence we can create a balanced matrix by simply making sure the sum of the entries used in each chordless cycle is a multiple of 4, which we can do using BFS.
I improved this algorithm to also work for matrices with more than one component, here the components correspond to the components of the corresponding bipartite graph. Furthermore I found a linear time algorithm for graphic matrices, which are a special class of matrices. Now you may wonder why this would be useful, it all sounds pretty random. Creating a balanced matrix plays an important part in checking if a matrix is totally unimodular (TU). A matrix is TU if each square submatrix has a determinant of −1, 0 or 1. TU matrices are important in the field of combinatorial optimization. When A ∈ ℝm×n is TU and b ∈ ℤn, {max x | Ax ≤ b} has integer solutions. If you want to know more about TU matrices and their beauty, make sure to follow the course Mixed Integer Optimization in your master ;)
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Christmas dinner recipes! Text: Christmas dinner committee
Beetroot salad (4 portions) Ingredients: ● 250 g beets ● 3 tbsp olive oil ● ½ cucumber ● 1 tbsp sherry vinegar/red wine vinegar ● ½ tbsp roasted sesame oil ● 25 g roasted salted pistachios ● ⅛ tsp salt ● ⅛ tsp black pepper
Hungarian mushroom soup (4 portons)
Recipe: 1. Cut the parsley. 2. Cut the onions into small pieces and slice the mushrooms … 3. In a heavy pot, sauté the onions and mushrooms in butter over medium heat until the onions are soft and translucent, for about 15 minutes. 4. Add the dill (first only a bit), thyme, paprika powder, mushroom broth, soy sauce and white wine. 5. Bring the soup to a simmer and cook until the liquid reduces by half, for max. 20 minutes 6. Meanwhile, in a small bowl, whisk the flour into the milk until smooth. 7. Add the flour-milk mixture to the soup and cook until the soup begins to thicken, about 10 more minutes. 8. Taste the soup and maybe add more dill. 9. Turn the heat down to low and slowly stir in the sour cream and lemon juice in the evening, before serving the soup. 10. Garnish the soup with parsley.
Ingredients: ● 40 gram butter
Spinach rotolo with blue cheese, tomatoes, and lemon sauce (4
Recipe: 1. Slice the beets very thinly. 2. Slice the cucumber very thinly. 3. Preheat the oven to 230 ºC. 4. Toss the beets with the olive oil. 5. Spread the beets out on a baking sheet in a single layer. 6. Roast for 30 minutes. 7. While the beets are in the oven, toss the cucumber with the salt. 8. Drain the cucumber in a strainer. 9. Toss the cucumber with the vinegar, sesame oil, and pepper until evenly coated. 10. Fold in the beets. 11. Transfer to serving plates. 12. Top with the pistachios.
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● 1 big onion/ 2 small onions ● 500 gram white mushrooms ● 5 gram paprika powder ● 5 gram dried dill ● 250 ml full milk ● 30 ml lemon juice ● 30 gram flour ● 60 ml sour cream ● 30 ml soy sauce ● 2 tsp fresh thyme ● 2 tbsp fresh parsley ● ½ cup dry white wine ● 2 cups mushroom broth
portions) Ingredients: ● 200g 00 (double zero) flour ● 3 eggs ● 500g spinach ● 1 lemon zest ● 100g bleu d’Auvergne (blue cheese) ● 160g ricotta ● panko ● ½ package fresh flat parsley ( package ~ 14g) ● 250g cherry tomatoes ● salt Ingredients for sauce: ● 66g salted butter ● 2/3 fresh sage leaf ● Juice of 2/3 lemon ● 1.5 tablespoons of flour
Recipe pasta dough: 1. Knead the flour, 2 eggs, 5g salt together until it is a smooth dough 2. Let it rest for at least 30 minutes. Recipe pasta filling: 1. Sautee the spinach in batches for 5 minutes per batch 2. Drain the spinach of as much water as possible 3. Cut the spinach into pieces. 4. Cut the blue cheese into 1x1cm chunks and mix it with the ricotta, lemon zest, spinach, and remaining egg(s). 5. Add the panko until the consistency is satisfactory. Recipe pasta: 1. Roll out the pasta to setting 5 (so setting 1, 3, 5). 2. Pick the parsley leaves off the stems. Make sure no stem is included.
3. Add the parsley to half the pasta sheet, fold it double and roll again on setting 5. 4. Roll the pasta on setting 6. 5. Stick 2 pasta sheets together to make one sheet of equal length (but double breadth) with moist fingers. 6. Spread a thin layer of filling on the whole sheet, except for 3cm on one side. 7. Start rolling the pasta from the opposite side. Once almost finished, wet the 3cm with moist fingers and finish rolling the pasta. 8. Place 2 pasta rolls into 1 towel. Tightly roll up the towel, and tie the ends closed with some string. (make a bow in the string so it’s easy to remove) 9. Cook the rolls for 20 minutes. 10. Each portion is half a roll. Recipe sauce: 1. Melt the butter in a small pan. 2. Cut up the sage and add it to the butter. 3. Add the flour and mix with a wooden spoon for ~2 minutes. 4. Squeeze the lemon(s) and add the juice to the pan. Add water until the sauce has a suitable consistency. Note that the sauce will thicken a bit more after boiling. 5. Note of the committee: be very careful with the sauce, the lemon and sage can be very intense Forest fruit bavarois with white chocolate cream (8 portions) Ingredients bavarois: ● 250mL heavy whipping cream ● 280g forest fruits ● 5 gelatin sheets ● 2 packages of vanilla sugar ● 2 eggs ● 180mL milk ● 30g granulated sugar Ingredients white chocolate cream: ● 50mL heavy whipping cream ● 100g mascarpone
● 80g white chocolate Recipe for bavarois: 1. Boil the fruit with a bit of water. Blend it with a blender once everything has softened. 2. Heat the milk on medium heat, stir frequently. 3. Split the eggs: keep the egg yolks in a big bowl and set the egg whites aside. 4. Add the sugar and vanilla sugar to the yolks and stir until it thickens and lightens in color. 5. Once the milk is close to boiling, carefully stir it into the egg and then place the mixture back on the stove. 6. Heat until it thickens slightly (it is a crème anglaise) 7. Soak the gelatin leaves in cold water for 5-10 minutes. 8.Combine the crème anglaise with the fruit and add in the gelatin. 9. Whip the cream and carefully fold in the fruit mixture. 10. Pour it into the cups, cover with cling film touching the bavarois and place in the fridge to set. Recipe for white chocolate cream: 1. Melt the white chocolate. 2. Stir in the whipping cream. 3. Whip in the mascarpone with a whisk. 4. After the bavarois has set, pipe a single rosette on top and place the decoration diagonally on it. Stewed pears chocolate cake (8 portions) Ingredients: ● 200 gram butter ● 150 gram dark chocolate (at least 72 percent cocoa) ● 4 eggs ● 250 gram brown sugar ● 60 gram almond flour ● salt
● 1 kg Doyenne du Comice or Gieser Wildeman pears ● 1 liter pear juice ● 1 package of bay leaves Recipe: 1. Peel the pears and cut them in halves (for the shorter pears) or quarters (for the bigger pears). 2. Put the pears on with the cider and bay leaf. 3. As soon as it boils, turn the fire on the cider for a while. This will take about 35 minutes, depending on the size of the pears and the pan. 4. Remove them out of the cider and let them cool. 5. Preheat the oven to 175 ºC. 6. Grease a 24 cm baking tin and cover the bottom with parchment paper cut to size. Grease that too. 7. Melt the butter with the chocolate in a heatproof bowl over a pan of hot water (au bain-marie). 8. In a mixing bowl, beat the eggs with the brown sugar, almond flour and a pinch of salt and pour in the melted butter and chocolate. 9. Pour the batter into the baking pan. 10. Place the slices of pears on top of the cake, and push them (a little bit) into the chocolate mixture. 11. Bake the pie for about 40-45 minutes in the oven (longer is possible, it will get less fudgy but more cuttable). 12. Let the cake cool completely before slicing it. 13. Cut the cake in pieces and serve it with whipped cream, if you like.
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Puzzle: Word Search Text: Eva van Laar
Puzzle: Grid frog Text: Jorn de Jong A frog jumps around on the grid all n > 0 such that the frog can be points in the plane, from one grid back in (0, 0) after n jumps. point to another. The frog starts at the point (0, 0). Then it makes, successively, a jump of one step horizontally, a jump of 2 steps vertically, a jump of 3 steps horizontally, a jump of 4 steps vertically, et cetera. Determine
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Puzzle solution: Sudoku Text: Thomas Kanger
Puzzle solution: Cutting Pi(e) Text: Jorn de Jong The pie can be cut into 16 pieces after 5 slices.
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Meme page
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