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The dissertation "Metric compactification of Banach spaces" contains a detailed overview of the construction of the metric compactification of arbitrary metric spaces followed by complete explicit descriptions of the metric compactification of classical Banach spaces in finite and infinite dimensions. Consequently, some ergodic and fixed point theorems are revisited.
Natural and social phenomena are often modeled by deterministic or random processes. These models can be mathematically described by a collection of mappings acting on certain spaces with a rich structure. Metric spaces are perfect environments where many mathematical models can be analyzed analytically and geometrically. In order to obtain precise knowledge of the model we also need certain topological properties. Compactness is a topological property that is needed in many areas of mathematics.
The metric compactification is the result of making a metric space into a dense subset of a compact space by adding a boundary at infinity. The elements of the metric compactification have functorial properties and, more importantly, define a weak topology on arbitrary metric spaces that gives a geometric interpretation of points escaping to infinity.
Explicit formulas for all the elements of the metric compactification of classical Banach spaces were presented in this dissertation. In addition, geometric proofs of certain ergodic and fixed point theorems were provided.
Opponent: Dr. Bas Lemmens, University of Kent, UK.
Custos: Professor Kalle Kytölä, Aalto University School of Science, Department of Mathematics and Systems Analysis.
Contact information: Armando W. Gutiérrez, Department of Mathematics and Systems Analysis, wladimir.gutierrez@aalto.fi, +593443075558
In the dissertation “On Computational modeling of Biological Development” the biological patterning and growth were investigated by means of computational simulation. The focus of the research was on understanding the patterning of taste papillae and the formation of tooth enamel.
Opponent: Professor Nicolas Goudemand, Institut de Génomifique Fonctionnelle de Lyon (IGFL), ENS Lyon, France.
Custos: Professor Antti Hannukainen, Aalto University School of Science, Department of Mathematics and Systems Analysis.
Contact information: Teemu Häkkinen, University of California, San Francisco, +1-(415)-676-0215, teemu.hakkinen@aalto.fi
The dissertation is publicly displayed 10 days before the defence at the noticeboard of the School of Science in Konemiehentie 2, Espoo.
The goal of the dissertation "On Matroid Theory and Distributed Data Storage" is to obtain tradeoffs between the main parameters of a distributed storage system with locality, as well as to analyse the repair properties of certain optimal storage codes. This is done by developing connections between storage codes and matroids.
In the last few years, the development of web services and social media content has generated an astronomical quantity of digital data. From the point of view of a single user, cloud storage allows for a constant and remote access to the data without overwhelming their own storage capacity. The same benefits apply to companies as well, on a much larger scale. Therefore, huge data storage systems were built by the big information technology companies such as Amazon and Microsoft to offer cloud storage and cloud computing. The starting point of this thesis is to study how to efficiently and reliably store data. Since the data is spread amongst multiple storage servers, a storage system has to deal with several server failures on a daily basis. To prevent from data loss, it is necessary to store redundant data alongside the initial data by using a storage code. The amount of redundant data in the system is referred to as the storage overhead. When a server fails, a new server is added to the system and nearby servers are contacted to reconstruct the lost data. The number of servers contacted for repairing a server failure is called the locality.
This thesis focuses on the notion of locality. More precisely, the main goal is to derive tradeoffs between the storage overhead, the failure tolerance, and the locality when the underlying code alphabet is fixed. Deriving a tradeoff is important in practice as it characterises the best possible codes. Furthermore, since the alphabet relates to the repair complexity and affects the different aforementioned notions, it is interesting to derive alphabet-dependent tradeoffs. To approach this problem, we use the internal structure of the storage codes and the relation between codes and matroids. Matroids are interesting mathematical objects on their own right and provide useful tools to analyse the internal structure of the storage codes. In addition to deriving tradeoffs, matroidal tools help in the design of efficient repair processes for storage codes.
Opponent: Dr. Thomas Britz, University of New South Wales, Australia
Custos: Professor Camilla Hollanti, Aalto University School of Science, Department of Mathematics and Systems Analysis
Doctoral candidate: Matthias Grezet, Department of Mathematics and Systems Analysis, matthias.grezet@aalto.fi, +358 505052525
The dissertation is publicly displayed 10 days before the defence at the noticeboard of the School of Science in Konemiehentie 2, Espoo.
Dissertation "Optimization Models for Assessing Energy Systems in Transition" presents models for assessing the ongoing transition of energy systems.
Opponent: Professor Steven Gabriel, University of Maryland, USA.
Custos: Professor Ahti Salo Aalto University School of Science, Department of Mathematics and Systems Analysis
Contact information: Vilma Virasjoki, Department of Mathematics and Systems Analysis, vilma.virasjoki@aalto.fi
Salo has also received other awards for his work. For instance, he and his collaborators Jeffrey Keisler and Alec Morton won the 2013 Publication Award of the INFORMS Decision Analysis Society for their book on portfolio decision analysis.
“Conventional methods of decision analysis help pick one good alternative from many alternatives. Our work on portfolio decision analysis extends these methods to problems in which the number of alternatives can be very high and many of them will be selected. We have successfully worked on many applications in areas such as energy, healthcare and risk management”, explains Salo.
A team of Aalto University students participated in the International Mathematics Competition for University Students 2019 in Blagoevgrad, Bulgaria at the end of July.
The team was very successful, receiving three medals and an honorary mention. Selim Virtanen received a silver medal and bronze medals went to Alvar Kallio and Iiro Kumpulainen, whereas Aman Sher Agha obtained an honorary mention.
As in the International Math Olympiad for high school students, several medals of each color are given. This year the requirement for a silver medal was a position within the best 50% out of a total of 360 participants. The best competitors (Grand First Prize) came from the universities of Göttingen and Saint Petersburg.
Participation in the competition was funded by Emil Aaltonen Foundation.
Further information:
Pekka Alestalo, team leader
pekka.alestalo@aalto.fi
IMC website (results and problems with solutions from all years)
Alex Karrila, M.Sc. (Tech.), will defend the dissertation “Conformally invariant scaling limits of random curves and correlations” on Friday 26 July 2019 at 12 noon at the Aalto University School of Science, lecture hall M1, Otakaari 1, Espoo. The dissertation studies mathematically the highly symmetric emergent structures in continuum limits of critical statistical-physics models. The results are formulated in terms of random curves and correlations.
Dr. Vincent Beffara, Université Grenoble Alpes, will act as the opponent. Custos is Professor Kalle Kytölä, Department of Mathematics and Systems Analysis.
Dissertation press release (in Finnish) is available at: https://www.aalto.fi/en/events/defence-of-dissertation-in-the-field-of-mathematics-alex-karrila-msctech
Physicists and mathematicians have long used the so-called Stefan problem to explain how crystals such as snowflakes take their shape. Now, researchers from Aalto University and the University of Helsinki have adapted the same principle to explain how enamel is distributed over teeth. The newly published work helps to explain why even closely-related species – such as humans and orangutans – have very different looking teeth.
Tooth enamel matrix is soft at first, but quickly hardens into the most mineralized and toughest part of the mammalian body. As enamel cannot be repaired or remodelled, its growth is a critical step in tooth formation. It's the durability of enamel that makes teeth capable of lasting for such a long time and why they are so plentiful in the fossil record.
The researchers propose that differences in enamel thickness are regulated by the nutrient diffusion rate, i.e. the rate that individual regions on a crown receive the required nutrients and substances needed to make the enamel.
Starting with a model that is used to simulate snowflake formation – the Stefan problem – the researchers built a new model that mimics the formation of the enamel matrix.
"Whereas enamel is not obviously as intriguingly shaped as snowflakes, it is interesting that the same physical principles can account for the increase in complexity in both systems," says Teemu Häkkinen from Aalto University.
Enamel has a long history in paleontological and medical research, and the new model can be used to investigate both evolutionary differences between species, and medical defects in enamel formation.
Starting with CT-images of real teeth from which enamel was digitally removed, the enamel matrix was applied to underlying dentin surfaces using a computer simulation. Only when simulating the matrix secretion as a diffusion-limited process were the researchers able to make the subtle enamel features found on a human molar.
In contrast to humans, orangutan molar teeth have complex ridges and grooves that could be simulated by lowering the diffusion rate of enamel-forming nutrients even further. Thus, orangutans, which eat hard foods such as unripe fruits and bark, may have evolved their wrinkly enamel with a relatively simple developmental change.
In addition to human and orangutan teeth, the researchers investigated enamel matrix growth in images of pig molars at the European Synchrotron Radiation Facility (ESRF). Synchrotron images reveal growth lines that provide a record of enamel matrix growth, much like tree rings show the growth of the tree. In addition to the final enamel surface, the diffusion-limited simulations reproduced these enamel growth lines.
"There are huge amounts of different data available on enamel, and now we have the tools of physicists to make testable predictions," says Academy Professor Jukka Jernvall from the Institute of Biotechnology, University of Helsinki.
The research was a collaboration between Aalto University and the University of Helsinki.
Bibliographical information:
Häkkinen TJ, Sova SS, Corfe IJ, Tjäderhane L, Hannukainen A, Jernvall J (2019) Modeling enamel matrix secretion in mammalian teeth. PLoS Comput Biol 15(5): e1007058. https:// doi.org/10.1371/journal.pcbi.1007058
Contact information:
Teemu Häkkinen
Doctoral student
Aalto University
hakkinen@fastmail.com
Jukka Jernvall
jernvall@fastmail.fm
Tel. +358 40 740 3478
The exhibition opening of IN TRANSITION Mathematics and Art will take place at Espoo Cultural Centre on 21. May, 17.00. The exhibition showcases student work from the Crystal Flowers in Halls of Mirrors course. The exhibition will be opened by Aalto University Provost Kristiina Mäkelä.
The exhibition will be open for visitors until the end of August 2019.
The final exhibition of the cross-disciplinary Crystal Flowers in Halls of Mirrors course is a concrete starting point for the promotion of interaction between art and science. It places deep phenomena on the level of human interaction. Open-minded and ground-breaking collaboration opens up opportunities for the pursuance of shared objectives. Authentic and real interaction challenges conventional beliefs and creates an exciting example of new possibilities.
Ranging from first-year undergraduates to postgraduate students, the course participants represent different schools of Aalto University. The diverse groups have designed and implemented their own interpretations in the fields of low-dimension geometry and topology under the guidance of a multidisciplinary team of teachers.
Together with EMMA – Espoo Museum of Modern Art, the work has been curated into a coherent art exhibition taking place at the Espoo Cultural Centre for the duration of summer 2019.
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