Public defence in the field of Mathematics and Statistics, M.Sc. (Tech) Timo Takala 23.5.2025
8. May 2025
Title of the thesis: Nonlocal function spaces and conformal deformations of metric measure spaces
Thesis defender: Timo Takala
Opponent: Associate Professor Matthew Badger, University of Connecticut, US
Custos: Associate Professor Riikka Korte, Aalto University School of Science
The oscillation of functions is an interesting and useful mathematical property. In particular the space of functions of bounded mean oscillation (BMO) is important for example in harmonic analysis and in the study of partial differential equations. The John-Nirenberg space (JNp) is a generalization of BMO, and the oscillation of JNp functions is also bounded in a certain sense. JNp and BMO were introduced in the literature already in the 1960s but only recently there has been more interest in studying JNp. Properties of JNp spaces are studied in this thesis.
JNp and BMO are examples of nonlocal function spaces. Another nonlocal function space studied in this thesis is the Besov space. In boundary value problems of partial differential equations, the solution gets certain values on the boundary of the domain. If the solution is a Sobolev function inside the domain, then the correct space for the boundary values is the corresponding Besov space, which is also called the fractional Sobolev space. Consequently the Besov space is relevant in the study of boundary value problems. Partial differential equations can be studied in Euclidean spaces but also in rather general metric measure spaces, where there is a distance defined between points, but for example the concept of direction does not exist.
Sphericalizations and flattenings are examples of conformal deformations of metric measure spaces. Sphericalizations transform an unbounded space into a bounded space, and flattenings transform a bounded space into an unbounded space. These deformations are useful in the study of partial differential equations, because some methods are applicable in bounded spaces but not in unbounded spaces. Similarly some methods are applicable in unbounded spaces but not in bounded spaces.
In this thesis the preservation of Besov functions in these deformations is studied, so that the deformations can be applied in the study of boundary value problems. The thesis also presents general conditions for sphericalizations that preserve other important geometric properties of metric measure spaces, which enable for example techniques in the study of partial differential equations and in harmonic analysis. Previously different sphericalizations have been constructed for different applications. Our results aim to offer a unified theory for this kind of conformal deformations.
Keywords: John-Nirenberg space, bounded mean oscillation, metric measure space, Besov space, sphericalization, flattening
Contact information: timo.i.takala@aalto.fi
Thesis available for public display 10 days prior to the defence at
Aaltodoc.
Public defence in the field of Systems and Operations Research, M.Sc. Zichan Xie 16.5.2025
30. April 2025
Title of the thesis: Dynamic Modeling of District Heating Network Based on Discrete Event Simulation
Thesis defender: Zichan Xie
Opponent: Professor Henrik Saxén, Åbo Akademi
Custos: Professor Risto Lahdelma, Aalto University School of Science
Heating and cooling are vital to our daily lives, accounting for nearly half of the EU's energy consumption. While district heating (DH) systems offer an efficient way to integrate renewable energy and reduce emissions, they currently supply only 8% of global heat demand. A major challenge is the lack of real-time monitoring and smart control, which limits system efficiency and sustainability.
In this research, we developed a fast, accurate, and flexible simulation model for DH networks. Our innovative approach uses variable time steps within a discrete event simulation (DES) framework. By dynamically adjusting calculations and focusing only on critical system changes, the model achieves both computational efficiency and reliability.
The DES model was validated using measurements from three real applications: a single pipe, a tree-shaped network, and a meshed network. Key results demonstrate that our model can simulate an 85-day operation of a meshed DH network with 186 pipes in just 0.29 seconds, while maintaining temperature deviations as low as 1.15 K across 80 substations.
This high-performance DES model provides operators with a powerful tool for:
Real-time system monitoring and operational state detection
Fault diagnosis and operational troubleshooting
Network updating and performance evaluation
Control strategy testing and improvement
Renewable energy integration planning
The model's combination of accuracy and computational efficiency enables rapid scenario analysis and system optimization, supporting smarter decision-making for DH network operations.
Key words: Discrete event simulation; Lagrangian method; Variable time step; Dynamic hydraulic-thermal simulation; District heating network
Thesis available for public display 10 days prior to the defence at
Aaltodoc.
Public defence in the field of Mathematics and Statistics, M.Sc. Antti Autio 9.5.2025
22. April 2025
Title of the thesis: Approximate solution of a parametric diffusion equation for electrical impedance tomography
Thesis defender: Antti Autio
Opponent: Docent Tomas Vejchodsky, Czech Academy of Sciences, Czech Republic
Custos: Associate Professor Antti Hannukainen, Aalto University School of Science
Electrical impedance tomography is a measurement technique where the inner conductivity distribution of some object is reconstructed from electrode measurements made on the surface of the object. In these measurements, an electric current is fed from the outside and the resulting voltage on the surface is measured. The method has applications both in medicine and in industry. Determining the inner conductivity distribution based on the current input and the measured voltage is a challenging mathematical inverse problem. It requires accurately modelling the electric field inside the object.
In this work, electric potential is modeled by a so-called parametric diffusion equation where the parameter describes the conductivity distribution inside the object. The inverse problem can be solved iteratively. I this case the electric field is modeled with different conductivity parameter values until a value that corresponds to the measurement is found. This thesis primarily focuses on making this step faster and computationally lighter. The diffusion equation is numerically solved using the finite element method. In my work, I study reduced basis methods where the solution is sought from a specific subspace, in other words only certain possible solutions are considered. The method works since the solutions to the equation with different parameters, i.e. the potential fields, have a lot of common structure. This limits the shape of possible solutions and thus can be utilized.
In my thesis, a new method for computing the reduced basis is presented. Additionally, the structure of the solutions in a simple geometry is studied theoretically for understanding the effectiveness of these methods. I also apply the methods to electrical impedance tomography using simulated data. It turns out that the modeling can be considerably sped up without sacrificing quality significantly. Finally, a certain approximate linearized model for impedance tomography is considered. There the solution can be determined from the measurement directly without an iteration.
Keywords: electrical impedance tomography, finite element method, reduced basis method
Thesis available for public display 10 days prior to the defence at
Aaltodoc
Public defence in the field of Systems and Operations Research, M.Sc. (Tech) Tuomas Rintamäki 25.4.2025
8. April 2025
Thesis defender: Tuomas Rintamäki
Opponent: Professor Ramteen Sioshansi, Carnegie Mellon University, US
Custos: Professor Ahti Salo, Aalto University School of Science, Department of Mathematics and Systems Analysis
Traditionally, power systems have consisted of predictable loads and controllable generation sources. Global goals to reduce emissions have motivated the large-scale introduction of variable renewable energy sources (VRES) in these systems. VRES such as wind and solar power are less predictable, controllable, and have low marginal costs. Consequently, the large-scale deployment of VRES affects the adequacy and flexibility requirements of power systems and the pricing of electricity in day-ahead and intraday markets.
This Dissertation develops optimization and time-series models to answer research questions related to the large-scale integration of VRES in power markets. We build on power system data to implement time-series models to estimate the impact of wind and solar power on power prices in the Nordic and Northwestern European regions. Moreover, we develop three mathematical optimization models: (i) a model to optimize capacity payments to flexible conventional generation to reduce balancing costs due to the variability of VRES; (ii) a model to optimize the day-ahead and intraday offerings of a flexible generator in the presence of VRES; (iii) a model for long-term generation and transmission expansion to meet emission-reduction targets while considering uncertain demand and VRES.
The main contributions of this Dissertation are as follows. First, the time-series and optimization models expand on the state-of-the-art by accounting for new features, such as intraday market dispatch. Second, we develop methods to solve the optimization problems efficiently and accurately. Third, we gain insights into a long-term transmission and generation expansion plans that help meet emission-reduction goals and estimates about the impact of wind and solar power on day-ahead prices, for instance. Such insights support the design of more effective policies for VRES integration and inform producers and consumers alike on the impact of VRES. The results of the Dissertation have been exploited by other researchers in estimating the impact of VRES in other regions, for example.
Keywords: optimization, time-series models, game theory, renewable energy, power systems
Thesis available for public display 10 days prior to the defence at
Aaltodoc.
Contact information: tuomas.rintamaki@aalto.fi
Public defence in the field of Mathematics and Statistics, M.Sc. Ryan Wood 11.4.2025
3. April 2025
Title of the thesis: Non-backtracking Centrality Measures and Beyond
Thesis defender: Ryan Wood
Opponent: Senior Lecturer Philip Knight, University of Strathclyde, United Kingdom
Custos: Associate Professor Vanni Noferini, Aalto University School of Science
Networks are fundamental mathematical structures that appear in a range of fields and applications. One of the most fundamental questions one can ask about a network is which nodes are most influential. Centrality measures are functions which assign to each node a non-negative value indicative of their importance within the network and are ubiquitous in many areas of study
Centrality measures based on non-backtracking walks have been shown to yield concrete benefits over popular walk-based centralities, such as Katz centrality. However, the computational cost of such non-backtracking centralities can be prohibitively high and the classes of graphs to which they can be applied is limited.
The research presented in this doctoral thesis seeks to overcome these challenges and facilitate the use of non-backtracking centrality measures as a tool for analyzing time-evolving and/or weighted networks.
Thesis available for public display 10 days prior to the defence at
Aaltodoc
New hourly paid teachers of mathematics and systems analysis for fall 2025
26. March 2025
The Department of Mathematics and Systems Analysis is seeking
New hourly-paid teachers in Mathematics and Systems Analysis for fall term 2025.
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. Five credits may also be substituted with a math intensive course from another field of study. 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 5 May 2025.
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.
Summer internships at the department in 2025
10. January 2025
The summer internship application period has started and you will find the job ad
here.
The deadline is on 26 January at 23:59 EET (UTC+2).
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