Department of Mathematics and Systems Analysis

Current

Public defence in Mathematics and Statistics, M.Sc. (Tech) Sami Helander, 25.8.2022

12. August 2022

With the recent developments in the precision of measurement technology and storage capacity, massively large and high dimensional data sets have become commonplace over nearly all fields of science. Functional data – data arising from measuring a generating process of continuous nature over its continuum – has emerged as a prominent type of such big data due to the richness of its structural features. One does not have to search far to find an abundance of great examples of functional data sets: the growth curves of children, measurements of meteorological events such as temperature or precipitation and hourly electricity consumption over a day, are all examples of processes within the realm of functional data.

Detailed analysis of the shape features of functional data is often the key to revealing important modes of variance in functional data. For instance, recognizing structural deviancies from the typical in the growth pattern of school aged children can be one of the earliest markers warning of potential underlying problems in health and well-being. Accurately predicting the hourly electricity consumption is crucial for an electricity company to be able to match the production to the demand. Distinguishing between the silhouettes of a child and a dog can be crucial in computer vision applications for self-driving cars. In short, sensitivity of the developed methodology to variations in shape has become an important topic in the literature. However, precisely defining typicality or atypicality in shape has proven to be a difficult problem. In how fine detail should the variations in local features be considered? What precisely makes a curve ‘too curvy’ in comparison to a set of other observations? Clearly, it is time to leave the classical, location-based considerations in the offside and shift our focus towards the intricacies in shape and structure.

In the dissertation, we develop methods for assessing the shape typicality and similarity of observations and study their properties in theory and in practice. Furthermore, we study the practical implementations of the methods in some prominent, common applications such as supervised learning and outlier detection, and evaluate their performance compared to some popular modern competitors. In particular, we demonstrate the excellent properties of the proposed methods and show that in many commonly encountered settings, they are able to match or even outperform many of the leading competitors.

Opponent is Professor Thomas Verdebout, Université Libre de Bruxelles, Belgium

Custos is Professor Pauliina Ilmonen, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral student: sami.helander@aalto.fi, +358 50 5186136

The public defence will be organised on campus (Otakaari 1, lecture hall H304).

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis


Major international event in mathematics approaching in Helsinki

27. June 2022

The foremost international meeting of mathematicians, ICM 2022, was supposed to be held in Saint Petersburg in July 2022, and Vladimir Putin was supposed to have opened it. Due to the war in Ukraine, the organisers decided to move the congress online and find another venue for the opening ceremony. The International Mathematical Union (IMU) received many offers of new venues. The Finnish community of mathematicians offered to organise the event in Helsinki on 5th-6th July 2022, and IMU accepted Finland's invitation.

The opening ceremony for the ICM 2022 congress will be held in Helsinki on 5th July 2022, and at the ceremony, distinguished mathematicians will be awarded the Fields medalsthe Carl Friedrich Gauss prizethe Chern medalthe Leelavati prize, and the Abacus prize for mathematical computing. These prizes are highly esteemed among mathematicians as proof of remarkable scientific achievements in the field of mathematics. Among the medals awarded by IMU, the Fields medal is best known outside the field of mathematics as a recognition comparable to the Nobel Prize.

The opening ceremony will be held at the Töölö hall of Aalto University, and some 600 attendees are expected along with members of the international press, since the award ceremony is traditionally also a media event. President of the Republic of Finland Sauli Niinistö will open the ceremony. The event will be hosted by Professor Camilla Hollanti from Aalto University.

On the following day, July 6th, the awardees will give scientific talks on the most current breakthrough research in mathematics at the Töölö auditorium of Aalto University. Both the award ceremony and the lectures of the awardees will be streamed live to the participants of the virtual ICM conference.

The organisers of the event in Finland are the national committee of mathematics, member of the Council of Finnish Academies, chaired by professor in mathematics at the University of Helsinki, Professor Antti Kupiainen, and the Finnish Mathematical Society, chaired by professor in mathematics at the University of Helsinki, Professor Tuomo Kuusi, as well as a large number of Finnish mathematicians from these two organisations.

Professor Antti Kupiainen and Professor Tuomo Kuusi consider it a great honour for Finland and Finnish mathematics to have the ceremony here. It has been held in Finland only once before, in 1978.

Many get-togethers and satellite conferences will be organised in connection with the event for mathematicians from different fields, such as the conference World Meeting for Women in Mathematics, which will award the prize for mathematical physics, named after Olga Aleksandrovna Ladyzhenskaya, who was born a hundred years ago. The Probability and Mathematical Physics Satellite Conference, which is organized in Helsinki between 28 June - 7 July, will feature several previous Fields medalists as speakers.

The IMU Award Ceremony 2022 will be streamed on 5 July

Program

Original media release

Professor Antti Kupiainen, University of Helsinki, antti.kupiainen@helsinki.fi, phone +358 50 4480305   

Professor Tuomo Kuusi, University of Helsinki, tuomo.kuusi@helsinki.fi, phone +358 50 5560814 

Professor Camilla Hollanti, Aalto University, camilla.hollanti, phone +358 50 5628987

World Meeting for Women in Mathematics:
Senior University Lecturer Kirsi Peltonen, kirsi.peltonen@aalto.fi, phone: +358 50 5747006


How to build an inclusive research group: interview with Camilla Hollanti

27. June 2022
Camilla Hollanti, photo: Lasse Lecklin.

Camilla Hollanti is head of the research group “Algebra, Number Theory and Applications” at Aalto University, which has a very striking gender balance. Read the interview (European Women in Mathematics)

Public defence in Mathematics, M.Sc. (Tech) Kristian Moring, 6.7.2022

27. June 2022

This thesis studies two different prototypes of nonlinear partial differential equations with porous medium type and p-growth structure. These equations can be interpreted as nonlinear generalizations of the heat equation modeling various physical phenomena such as gas flow in porous medium, heat conduction or water movement in soil. The thesis focuses on regularity properties of solutions as well as their gradients to these equations. Boundary regularity for the gradient is shown in terms of higher integrability for porous medium type equations. Moreover, we demonstrate that both solutions and their gradients are stable with respect to the parameter characterizing the equation. If there is an obstacle restricting the behavior of the solution, we show that the solution is continuous provided that the obstacle is sufficiently regular. The obstacle problem is closely connected to the concept of supersolutions, which we define in the thesis as functions obeying a comparison principle. We show that supersolutions according to this definition are divided into two mutually exclusive classes for which we give several characterizations. The results in the thesis show that both solutions and their gradients possess properties that are mathematically relevant. The proofs of our results require new mathematical techniques and their implementations, which could be expected to be useful in other contexts as well.

Opponent is Professor José Miguel Urbano, University of Coimbra, Portugal

Custos is Professor Juha Kinnunen, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral candidate: kristian.moring@aalto.fi

The public defence will be organised on campus (Otakaari 4, lecture hall 216).

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis


Public defence in Systems and Operations Research, M.Sc. (Tech) Pekka Laitila, 25.5.2022

13. May 2022

Risk management and decision-making under uncertainty are common challenges in business and public administration. Often the framework of a decision-making problem consists of various types of factors and variables whose mutual probabilistic dependencies may be difficult to know or perceive exactly. For instance, there might not be suitable historical data available, or the relevant data may be difficult to identify. These problems are typical in situations where risks are novel or unprecedented. Among such instances are, e.g., unique projects, ecological and economical disasters, and governmental conflicts.

Even though there might be a lack of suitable historical data, there is often an abundance of expert insight available, along with diverse information on indirectly related factors. In these situations, analysis of risks and decision-making under uncertainty can effectively be supported by Bayesian networks (BNs). A BN represents a system of linked components both visually and numerically enabling a rigorous quantification of risks and a clear communication of the components’ interaction. BNs can be constructed based on various information sources such as experimental data, historical data, and expert knowledge. The applications of BNs are numerous and cover a wide range of domains, such as medical decision support, risk analysis concerning epidemics, ecosystems, and industry, as well as policy and military planning.

The dissertation elaborates the construction of BNs by expert elicitation which involves subjective assessments of a domain expert and is often required in practical applications. The main contribution is the development of new elicitation approaches that help the expert to establish required numerical dependencies between BN components. The approaches improve an existing elicitation method commonly used in BN applications. They reduce the elicitation effort of the expert and also extend the application scope of the underlying method. Their practical execution is supported by thorough guidelines and online implementations. Consequently, the new approaches facilitate and promote the effective and diverse utilization of BNs in various applications.

Opponent is Professor Norman Fenton, Queen Mary University of London, UK

Custos is Professor Kai Virtanen, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral student: pekka.laitila@aalto.fi

The public defence will be organised on campus and via Zoom. Link to the event

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis


Department's Biitsi Party 2022

5. April 2022
Perhaps the date (April Fool's Day) had an effect on the slightly low amount of the participants..
nevertheless Biitsi was super nice, food delicious and we had great fun!

Thanks for the participants! Here are some photos.

New hourly paid teachers of mathematics and systems analysis for fall 2022

4. April 2022

The Department of Mathematics and Systems Analysis is seeking

New hourly-paid teachers in Mathematics and Systems Analysis for fall term 2022.

Your tasks include teaching in exercise groups and grading exercises and exams.

Regarding teaching in mathematics, we expect the applicants to have completed at least 20 credits of mathematical studies at university level with good grades. Regarding teaching in systems analysis (courses MS-C/E2xxx), we expect the applicants to have completed the course they would like to teach. If you have previous experience in teaching, it is considered as an advantage, but is not necessary. This is a part-time job (2-4 hours/week). The salary is 30-40 euros/teaching hour based on your education level.

Grading exercises and exams will be (typically) compensated separately (300-400 euros depending on your education and the course level).

Read carefully! If you are not working for Aalto at the moment you apply, fill in the application form here. If you are working for Aalto at the moment you apply, you have to apply as an internal candidate via Workday, see instructions Sisäisen työpaikan hakeminen | Aalto-yliopisto.

Attach an open motivation letter, a cv and a transcript of records as one PDF file.

Deadline for the applications is Monday 9 May 2022.

Based on the applications, we will invite some of the applicants for a web interview.

More information: johanna.glader@aalto.fi 

Note: if you have previously worked as an hourly-based teacher at the MS Department, you have received a separate link from johanna.glader(at)aalto.fi. 

 

 


Defence of doctoral thesis in the field of mathematics, MSc Milo Orlich, 25.2.2022

11. February 2022

This thesis is in abstract algebra, more specifically in the theory of monomial ideals. The main algebraic objects considered here are polynomials, and all polynomials can be built by summing together monomials, which are products of variables. A monomial ideal is the set of polynomials that one can obtain starting from some fixed monomials. The key idea in this subject is to associate to any monomial ideal a combinatorial object, for instance a graph (also called a network), consisting of nodes and edges. Such a graph is a finite structure that can be easily "counted", and many algebraic properties of the monomial ideal are encapsulated in this graph. Vice versa, starting from a graph one can suitably define a monomial ideal, and tackle graph-theoretic problems from an algebraic point of view.

Some of the main concepts in this subject were defined in the 70's and 90's. However, many fundamental problems remain open. In order to tell graphs apart and understand their behaviour, one can associate numbers to them, like the number of nodes, the number of edges, the number of connected components, etc. There is in fact an infinite family of such numbers, called Betti numbers, that one can associate to a given graph. Starting from some specific basic information about the graph, there are algorithms to determine all the Betti numbers, but one does not know what to expect a priori. One of the main open problems is to give closed formulas that describe the Betti numbers in essentially one line, without going through a long algorithm. The main results of this thesis are in this direction.

In the first paper of the thesis we determine exactly this kind of formulas for a specific class of graphs. In the second paper we generalize this to a larger class of monomial ideals, not necessarily associated to graphs. The third paper introduces a new approach to this subject, using critical graphs, which allow to control the Betti numbers asymptotically.

Opponent: Doctor Emil Sköldberg, National University of Ireland, Ireland

Custos: Professor Alexander Engström, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral student: milo.orlich@aalto.fi

The public defence will be organised on campus and via Zoom. Link to the event

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis


Multidisciplinary research project based on origami seeks solutions for industrial needs

26. January 2022

A joint projectcovering the fields of mathematics, engineering and arts is about to start at Aalto, where the aim is to study and develop folding technology for the needs of industry. In addition to Aalto, the project includes VTT as coordinator, and several companies from the forest industry to the machine design and cosmetics brands, such as Stora Enso, Metsä Group, Lumene, Mirka, Elomatic, Anpap, Orfer and Soften. Business Finland granted funding for the Co-Innovation project.

Folding originates from the origami culture, and the Miura fold and other periodically repeated forms are at the centre of the project. The end products of the project can take a variety of concrete forms, such as packaging, acoustic boards, other room dividers and abrasive products.

Jarkko Niiranen, Associate Professor in Computational Structural Engineering at the School of Engineering, will bring engineer-like knowledge and methods to the project table, for example in the form of quantitative structural analysis.

‘Origami is interesting from the structural point of view. It contains fairly rigid and flat structures, hinges through folds and folding patterns that can produce various shapes and properties. Computer-aided concept and product design, simulation of deformation and structural analysis are all required in folding-based structures. The same methods are used in the design of structural solutions in mechanical and structural engineering, the material, size scale and application are just different.’

According to Niiranen, origami structures have previously been used in biomedicine, where a DNA origami structure folds into a small stack that later opens inside the body. Soft robotics, which aims to mimic organic movement, can also be based on origami. For instance, it is common for aircrafts to have so-called sandwich structures, which typically include a honeycomb core between the skin plates, and the core can be based on origami folding.

‘The project that is about to start will focus on the origami structure as it is, because it is not always necessary, and perhaps not even appropriate, to reinforce the folded structure with skin plates commonly used in sandwich structures. Carefully planned folds can be used to adjust the folding patterns and thus the rigidity as well as the paths and directions of movement, among other things.’

Associate Professor Masood Masoodian and Design Researcher Markus Joutsela, a packaging expert who will solve various challenges related to the functionalities of packages, for example, are both involved in the project from the School of Arts, Design and Architecture. They will also investigate the wider potential of folded structures for effective visual communication in different application areas.

‘It is important to consider how the business world will use the folded structure and how these new solutions could be supported’, Joutsela explains.

‘The project is technology-driven, and we are exploring the possibility of industrial production of different Miura folding structures. While the focus of the research project is on a general level, several of the involved companies share an interest in e-commerce packaging applications and reducing the use of fossil-based packaging materials. The project will create prototypes for different applications. Folding can be used to make truly impressive structures.’

Peltonen approaches the folding properties through mathematical models.

‘The thickness of the material prevents you to fold it infinitely, which would be possible for an extremely thin material that is in line with the ideal mathematical model. On the other hand, the material can have elasticity that allows the folding to succeed in practice, even if the mathematical forecast deems it impossible. Mathematics alone cannot answer these questions, and that is why we need genuine multidisciplinary cooperation.’

The project saw the light of day already in 2017 when VTT developed an interest in folding and launching an industrial project. In 2018–2021 the FinnCERES flagship of Aalto and VTT (funded by the Academy of Finland) that focused on the bioeconomy of materials had a Co-Innovation project focusing on folding, which laid the foundation for this soon-to-begin Co-Innovation project.

 

 

 


Summer 2022 Bridges conference

5. August 2021
In 2022 we are planning to hold an in-person Bridges conference! Join us for invited and contributed talks, hands-on workshops, art galleries and live performance events, and an excursion.

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