When adding coprime numbers A and B, one could ask how big A, B, and A + B could be compared with the product of the prime numbers dividing these numbers. One can expect that this prime product has...Show moreWhen adding coprime numbers A and B, one could ask how big A, B, and A + B could be compared with the product of the prime numbers dividing these numbers. One can expect that this prime product has about three times as many digits as A + B, but with smart choices of A and B this prime product can be smaller than A + B. However, the so-called ABC-conjecture says that it cannot be much smaller. Several mathematicians have tried to develop algorithms creating infinitely many triples An, Bn, and An + Bn such that An + Bn is large compared to the product of the primes dividing one of the numbers An, Bn, and An + Bn. And I add a new algorithm to this list of algorithms and use the tool of elliptic curves, the zero set of a polynomial equation together with a group law, to create my triples.Show less
Gr¨obnerbases vormen een van de centrale objecten van de algebra¨ısche meetkunde, als het gaat om het expliciet uitvoeren van berekeningen. Een Gr¨obnerbasis van een ideaal in een polynoomring is...Show moreGr¨obnerbases vormen een van de centrale objecten van de algebra¨ısche meetkunde, als het gaat om het expliciet uitvoeren van berekeningen. Een Gr¨obnerbasis van een ideaal in een polynoomring is een stel voortbrengers met fijne algoritmische eigenschappen. Met behulp van een Gr¨obnerbasis kunnen veel problemen eenvoudig worden opgelost. We noemen het oplossen van een stelsel polynomiale vergelijkingen, het bepalen of een polynoom in een ideaal ligt en het bepalen of twee idealen gelijk zijn. Zie [8] of [11] voor meer toepassingen. Al deze problemen hebben een hoge algoritmische complexiteit. Bijvoorbeeld, zelfs als we ons beperken tot polynomen in 4 variabelen is het ideaallidmaatschapsprobleem (bepalen of een polynoom in een gegeven ideaal ligt) NP-moeilijk, wat betekent dat ieder NP-compleet probleem in polynomiale tijd te reduceren is tot dit probleem [24]. Het volgt meteen dat de constructie van een Gr¨obnerbasis uit een willekeurig stel voortbrengers van een ideaal niet eenvoudig kan zijn. Een algoritme dat deze constructie uitvoert is gegeven door Buchberger, en het is naar hem genoemd. Het principe van dit algoritme is om net zolang voortbrengers van het ideaal te blijven toevoegen totdat we een Gr¨obnerbasis hebben. Buchbergers algoritme termineert altijd, maar het bewijs daarvan is niet constructief. Daarom is het onbekend hoelang het algoritme bezig is, oftewel wat de complexiteit ervan is. Hier is veel onderzoek naar gedaan, maar sluitende onder- en bovengrenzen zijn er niet. Naast Buchbergers algoritme zijn er andere algoritmes die Gr¨obnerbases construeren [19, 28]. Deze zijn echter van meer theoretisch belang en in de praktijk werkt Buchbergers algoritme het beste. We gaan hier in deze scriptie niet verder op in. We beginnen deze scriptie met een behandeling van de onderliggende theorie. We defini¨eren Gr¨obnerbases, voeren Buchbergers algoritme in en formuleren de complexiteitsvragen. We eindigen dit hoofdstuk met een voorbeeld. De meeste stellingen bewijzen we niet: we verwijzen vaak naar het boek van Cox, Little en O’Shea [11]. De eerste twee hoofdstukken van dat boek zijn ook heel geschikt als een grondigere inleiding in Gr¨obnerbases dan we hier geven. In hoofdstuk 2 geven we ondergrenzen voor de complexiteit. We laten zien dat de grootte van een Gr¨obnerbasis dubbelexponentieel kan groeien in het aantal variabelen in de polynoomring. Aan de andere kant is er altijd een Gr¨obnerbasis met grootte begrensd door een vergelijkbare bovengrens: dat bewijzen we in hoofdstuk 3. Het is onbekend of deze bovengrens ook geldt voor de complexiteit van Buchbergers algoritme. In hoofdstuk 4, het belangrijkste deel van deze scriptie, leiden we een nieuwe bovengrens voor die complexiteit af, in termen van de Ackermannfunctie. We gebruiken daarbij alleen combinatorische argumenten. Tot dusver waren er vrijwel alleen bovengrenzen bekend onder beperkingen op de invoer (zoals het aantal variabelen of de gebruikte monoomordening), maar onze grens geldt algemeen. Kort geleden ontdekten we dat dit resultaat niet geheel nieuw is: vergelijkbare grenzen worden afgeleid in [13]. Toch zullen we op bladzijde 25 zien dat onze grenzen een nuttige toevoeging vormen. Het laatste hoofdstuk behandelt enkele onderwerpen uit de literatuur rond Buchbergers algoritme en de complexiteit daarvan. We bespreken aanpassingen van het algoritme die de complexiteit verlagen. Ook geven we complexiteitsgrenzen wanneer het aantal variabelen in de polynoomring klein is. Ten slotte bekijken we de invloed van monoomordeningen op het algoritme, en hoe we daar gebruik van kunnen maken. Ik wil mijn begeleiders Ronald van Luijk en Jeannette de Graaf, en ook Hendrik Lenstra, bedanken voor de tijd en moeite die ze hebben gestoken in de ondersteuning van dit bacheloronderzoek.Show less
This thesis is about transport of solutes across a biological membrane, a ‘lipid bilayer’. The goal is to create a template of differential equations, which is applicable to many types of molecules...Show moreThis thesis is about transport of solutes across a biological membrane, a ‘lipid bilayer’. The goal is to create a template of differential equations, which is applicable to many types of molecules and ways of transport. The approach aims to be abstract but aplicable and built up entirely from biophysics and clearly stated, reasonable assumptions. Free diffusion over the membrane will be considered explicitely, from which Ficks law will be derived. An ion-trap mechanism will also be specifically considered.Show less
This thesis describes the result and the process of a research to determine an optimal trading strategy for storage systems in the low voltage grid. To give a clear insight in the problem and in...Show moreThis thesis describes the result and the process of a research to determine an optimal trading strategy for storage systems in the low voltage grid. To give a clear insight in the problem and in the algorithms to solve the problem, a phased approach is used. First a simple model of a storage system is described, that is extended in three steps to the final model that is a realistic model of a storage system. All four models are described and for each of these models an algorithm is developed to determine an optimal trading strategy. In these models the energy prices per quarter of an hour are given in advance for 24 hours, the model is discrete in time. We use n intervals of a quarter of an hour in which the storage system can charge energy, discharge energy or do nothing. We assume that there is no residual value of energy. Though the problem solved is a normal LP problem, the phased approach and the description of the problem and the algorithm give insight in the solution that is required. In the first model, Model A, the state of charge of the storage system of interval i, SOC(i), is either full or empty, this can be naturally modeled as a binary integer problem. Algorithm 1 is developed to determine an optimal trading strategy as described above. Algorithm 1 has complexity O(n). In Model B the charge capacity, the discharge capacity and the capacity of the storage system can have different values. With three different values for these physical constrains, the SOC cannot be modeled as a discrete model and thus the SOC is modeled as a continuous model. Algorithm 2 is developed to determine an optimal trading strategy for Model B as described above, Algorithm 2 has complexity O(n 2 ). As an extension to Model B, in Model C energy losses from using the storage system are taken into account. There is energy required for charging and for discharging the storage system. This is energy that cannot be used for trading. Also, in time the energy in the storage system decreases, this is energy that cannot be sold. The energy that cannot be sold constitutes a loss from using the storage system. To take the losses into account, there are two virtual energy prices developed, the virtual charge price and the virtual discharge price. Similar to the previous model, the maximum amount of energy to trade can be determined, using the new determined SOC(i). Algorithm 3 is developed to determine an optimal trading strategy for Model C, as described above. This Algorithm has complexity O(n 2 ). In the final model, Model D, there are bounds included in the model. With these bounds it is possible to use the storage system for trading as well as for solving problems in the low voltage grid. To solve problems in the low voltage grid, space to store too much energy that is in the low voltage grid is required. It is also possible that not all the energy demanded can be transported, for instance because of the capacity of the network. If there is a storage system nearby the problem it is possible that the energy available in the storage system can help to overcome the problem. For such a problem, the storage system is used to supply energy. To be able to help overcome both types of problems, there is a lower and an upper bound required. With these bounds, there is less storage space available for trading. To be able to solve problems in the low voltage grid, every interval must have a SOC within the bounds. Algorithm 4 is developed to determine an optimal trading strategy for Model D. While the complexity of Algorithm 2 and 3 is O(n 2 ), the complexity of Algorithm 4 is O(n 3 ). To reduce the complexity, a greedy algorithm is developed. For every iteration i, interval i is first used to discharge the maximum amount of energy that is possible with respect to the discharge capacity. After this, the minimum amount of energy must be charged to get the SOC(i) equal to the LB. The absolute local minimum before interval i is used to charge energy for minimum cost. This is done for all intervals, and gives an optimal trading strategy. Algorithm 5 determines an optimal trading strategy for Model D with complexity O(n 2 ). For KEMA the program ATMP1 is developed. The code of the algorithms that are used in ATMP are written in Visual Basic Application of Excel. Therefore these algorithms can be used by KEMA for the overal program PLATOS2 . ATMP is used to give clear insight in the algorithms developed and the output of the algorithms is processed graphically. The user can even try to develop a trading strategy that is better than the trading strategy developed by ATMP. This helps the user to get a good insight in the problem and trust in the solution. In the Appendices the algorithms used are described.Show less
After finishing my BA-Thesis on the burials of Anse à la Gourde in 2008 and excavating burials in 2009 on St. Lucia I knew I wanted to do more with burials, mortuary practices and taphonomy....Show moreAfter finishing my BA-Thesis on the burials of Anse à la Gourde in 2008 and excavating burials in 2009 on St. Lucia I knew I wanted to do more with burials, mortuary practices and taphonomy. Instead of doing another casestudy of just one assemblage, the idea came to compare samples from three assemblages in the Caribbean. These three sites are Kelbey’s Ridge 2 on Saba, Anse à la Gourde on Guadeloupe and Anse Lavoutte (Cas-en-Bas) on St. Lucia. The goal was to see if the burial customs from these three islands were the same. From each assemblage, a sample from seven burials were taken, mostly random. To make the comparison as valid as possible, all burials were described according to a uniform approach. The cultural context and ancestry was also extensively examined in order to make sure that a comparison could be made and that the ancestry was the resembling or at least had the same common history in terms of origin. When the origin turned out to be alike, the 21 burials were analysed upon their single or multiple deposit, their primary or secondary state and if they were filled or empty during the time of decomposition. In the end it turns out that the all three samples showed correspondence on multiple levels and it is concluded that they share the same burial customs.Show less
Context. To get fully acquainted with Voronoi diagrams, Delaunay triangulations and the relationship between the two. To investigate a computational side of these tessellations and an application...Show moreContext. To get fully acquainted with Voronoi diagrams, Delaunay triangulations and the relationship between the two. To investigate a computational side of these tessellations and an application in astronomy in the form of modeling the Cosmic Web. Aims. First of all, to present and understand Brown’s algorithm, its tools, benefits and drawbacks. Secondly, to familiarize ourselves with modern views on and models of the Cosmic Web, and one of the new interesting tools used, namely the Delaunay Tessellation Field Estimator (DTFE). In particular, we are interested in accessing the quality of its reconstructions quantitatively. Methods. Obvious key concepts are Voronoi diagrams and Delaunay triangulations. For the computational component inversion and complexity analysis are of importance. For the astronomical component, various sampling methods and Fourier transforms come into play. Results. It seems that Brown’s algorithm has clear benefits in higher dimensional computations, but for two and three dimensions there may be better alternatives. Even though the DTFE reconstructions of the Cosmic Web appear to be visually satisfying, it appears that it is actually very sensitive to Poisson noise in the point distribution and in principle, minor effects may seriously distort the actual underlying continuous distribution. Greater care needs to be taken to access this further. There are many further research topics open here.Show less
In de deze doctoraalscriptie wordt ingegaan op de theorie dat ronde gebouwen zijn gewijd aan de windgod Quetzalcoatl-Ehecatl in Mesoamerika. In hoofdstuk 1 wordt de volgorde van de onderwerpen van...Show moreIn de deze doctoraalscriptie wordt ingegaan op de theorie dat ronde gebouwen zijn gewijd aan de windgod Quetzalcoatl-Ehecatl in Mesoamerika. In hoofdstuk 1 wordt de volgorde van de onderwerpen van de scriptie besproken en de probleemstelling uiteengezet. Hoofdstuk 2 gaat in op hoe deze theorie tot stand is gekomen. Er wordt onderzocht op welke manier en in welke mate de verschillende wetenschappers met de theorie omgaan. Op welke regio’s, culturen en gebouwen zij deze toepassen. Deze theorie wordt al in de 16e eeuw gebruikt. De moderne wetenschappers houden zich op de vlakte bij het noemen van deze theorie. In hoofdstuk 3 wordt aangegeven wat er op basis van historische en recente publicaties bekend is over de goden Quetzalcoatl en Ehecatl. Welke plaats namen deze goden in, in de religie en in het dagelijks leven. Met name van Quetzalcoatl-Ehecatl worden de verschillende aspecten besproken. Zoals Quetzalcoatl als scheppingsgod, als de windgod, als de Messias en als de historische held. Speciale aandacht wordt gegeven aan de god Kukulcan. Deze God zou in het Maya gebied het equivalent zijn van de god Quetzalcoatl in Centraal Mexico. Kukulcan heeft echter geen windaspect. Deze verschillende aspecten Quetzalcoatl, Ehecatl en Kukulcan, zijn van belang voor het wel of niet voorkomen van ronde gebouwen in de verschillende regio’s van Mesoamerika. In hoofdstuk 4 wordt ingegaan op de verschillen van diverse nog bestaande ronde gebouwen, bij de verschillende culturen en regio’s in chronologische volgorde. Speciale aandacht is er voor de Olmeken, Teotihuacan, de Huasteken, de Zapoteken, de Mixteken en uiteindelijk bij de Tarasken, de Azteken en de Maya. De typisch Azteekse piramidetempel van Ehecatl vormt het uitgangspunt en komt bijna alleen in het centrumgebied van de Azteken voor. Hoofdstuk 5 gaat over de continuering van het inheemse geloof in de koloniale tijd en bij de huidige inheemsen. Over het syncretisme van het christelijke en inheemse geloof, en de huidige beleving van de godsdienst. Quetzalcoatl wordt mogelijk gezien als een Messias die zich achter de apostel Thomas verschuilt. In Hoofdstuk 6 volgen afsluitend conclusies, die een antwoord zullen geven op de vraag of alle ronde gebouwen inderdaad gewijd zijn aan Quetzalcoatl-Ehecatl in alle regio’s in Mesoamerika. Dit is niet het geval.Show less
This thesis deals with the Mesolithic barbed points which were found by amateur archaeologists at the area of Europoort in the Netherlands. The main goal of the thesis was to find out the possible...Show moreThis thesis deals with the Mesolithic barbed points which were found by amateur archaeologists at the area of Europoort in the Netherlands. The main goal of the thesis was to find out the possible ways of production and use of the barbed points by producing and using copies via experiments. Overall fifteen artifacts were loaned out from the Archaeological Museum of Leiden in order to be studied for the purposes of the thesis. They were made of antler and bone (mostly metapodia). The original barbed points were checked for possible traces under stereo microscope and metallographic analysis took place as well. The next step was to produce five experimental barbed points based on the information which their analyses gave. Hence, the groove and splinter technique was used for the two antler barbed points and the metapodial technique for the two barbed points made of bone. The fifth experimental tool was made out of a rib bone, which was cut in pieces in order to take the proper piece needed for the manufacture. All of them were grinded on a sand stone in order to take the proper shape and a flint blade was used to make the barbs. After that they were hafted on spears and arrows, depending on their size, and the shooting experiments took place near the city of Arnhem in the Netherlands. The experimental tools proved to be really effective. The used barbed points were analyzed and documented photographically the same way as the original artifacts. When the Mesolithic and the experimental barbed points were compared, it came out that they bear in a considerable amount the same kind of traces. Most of them were caused during the production process (grinding or scratches due to the flint tool which was used), while there is a few amount of impact scars and use wear traces. The only exception, as far as the scratches are concerned, is that the original artifacts bear a lot of randomly directed scratches, while the experimental barbed points barely have any. Therefore, it was assumed that they were a result of depositional modifications. Finally, in the discussion part of the thesis a variety of ways is suggested on how the experimental tools can be used to benefit the public, in the context of heritage management.Show less
The region of Southeast Asia is known as an epicenter for a diversity of maritime communities. The complex scatter of islands that comprise the whole region has patterned the lives of generations...Show moreThe region of Southeast Asia is known as an epicenter for a diversity of maritime communities. The complex scatter of islands that comprise the whole region has patterned the lives of generations of maritime communities. As a result, the cultural characteristics and social diversity of the local communities of people in this region is as notable as the sea that surrounds them. This geographic and cultural characteristic has given the boat a central role in the cultural history of many ethnic groups in the Southeast Asian islands. In general, for people in this region, the boat has always been more than just a seagoing vessel. Its presence in various representations has created a symbolic complex to which expressions of the group identity and communal unity can be related. This thesis presents the research of boat symbolism by focusing on the Southeast Moluccas as the case study. Two main issues will be discussed here. The first is related to the material representations of this symbolism and the second concerns the meaning and cultural-historical background of the practice of representing boat symbolism. Furthermore, this thesis analyzed how these practices have been adopted in an early stage and how these practices can be attached to special meanings and identities due to their associations with places, events, and lineage groups. As the representations of boat symbolism has served as the cultural-mark for people in this region, it will be discussed how this practice has been actively involved in the construction of cultural identity for the people in this region.Show less
Research master thesis | Developmental Psychopathology in Education and Child Studies (research) (MSc)
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Objective: In this study we addressed the questions (1) whether there is a relation between the specialization of the brain and psychopathology, and (2) if there is a relationship between the...Show moreObjective: In this study we addressed the questions (1) whether there is a relation between the specialization of the brain and psychopathology, and (2) if there is a relationship between the specialization of the brain and performance on different academic measures. Method: We used the Finger Tapping Task (FTT) to assess maturation of the brain as measured by fine motor speed, and lateralization of the brain as measured by the difference in speed between both hands. Both maturation and lateralization are used as a measure of specialization of the brain. The participants were children in the age of 5 to 18 years old and were assigned to five distinct diagnostic groups: Mood problems (n=178), Behavior problems (n=82), Autism spectrum Disorders (n=106), Attention Deficit Hyperactivity Disorder (n=190) and Learning problems (n=44). The diagnostic groups differ with regard to age and gender. Results: We found that children with an autism spectrum disorder show delayed fine motor lateralization. We were also able to determine that the differences in fine motor speed between the different diagnostic groups get larger with age indicating that delayed maturation gets more evident while children get older. Looking at the academic measures, we found that a more matured brain, as measured with fine motor speed, is associated with better academic performance, even when controlled for age. Conclusion: Autism spectrum disorders can be differentiated from other disorders when looking at lateralization of the brain. A more matured brain is associated with a significant higher level of academic performance for math, reading and Writing.Show less
In this research I will study the phenomenon of ritualized burial practices in the Middle Bronze IIA period in Northern Palestine .My main focus will be the theoretical controversies that surround...Show moreIn this research I will study the phenomenon of ritualized burial practices in the Middle Bronze IIA period in Northern Palestine .My main focus will be the theoretical controversies that surround the study of burials. Since the past century has the evolutionary theory by Darwin inspired many researchers but in my opinion have they not all applied his work correctly. There is also no clear criterion by which cultural anthropologists and archaeologists determine that a particular type of behaviour is or not is an instance of ritual. On the base of evolutionary biology and neuropsychology new definitions entered the discussion and I will explore the possibilities to apply them on the archaeological record. Interestingly the research on obsessive compulsive behaviour showed that ritualized behaviour is not different in non-clinical contexts and cultural ceremonies.Show less
Sanger based sequencing of mammoth and mastodon dung samples were performed. The mammoth samples, from permafrost regions in Alaska and Siberia, were successfully amplified and sequenced. The...Show moreSanger based sequencing of mammoth and mastodon dung samples were performed. The mammoth samples, from permafrost regions in Alaska and Siberia, were successfully amplified and sequenced. The mastodon samples, preserved in a continuously wet, cool, low-pH, anoxic environment, on the other hand, could not be amplified; possibly because they still contained living bacteria. Innovative procedures were used to establish an optimal functioning protocol and process the sequences. The obtained results are compared with each other, based on the target gene region, as well as with conventional morphological paleoecological methods of diet reconstruction. It is concluded that it is advantageous to use Sanger based sequencing with multiple target regions for diet analysis with ancient DNA. The additional value of ancient DNA analysis is relatively large for diet analysis, as 30-50% of the obtained identifications refined the morphological analyses, and the remaining identifications supported the morphological analyses completely.Show less
