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.
Public defence in the field of Mathematics and Statistics, M.Sc. David Adame Carrillo 25.2.2025
31. January 2025
Title of the thesis: Lattice models and conformal field theory
Doctoral student: David Adame Carrillo
Opponent: Professor Alessandro Giuliani, Universita degli Studi Roma Tre, Italy
Custos: Professor Kalle Kytölä, Aalto University School of Science, Department of Mathematics and Systems Analysis
Statistical mechanics is the classical branch of Physics and Mathematics that studies ensembles of a large number of microscopic entities. The purpose of statistical mechanics is the inference of macroscopic properties of a model from its microscopic degrees of freedom by conceiving the system probabilistically.
Since the 1980s, it has been known to physicists that the macroscopic properties of statistical models at a critical point can be described by quantum field theories with conformal symmetries, nowadays known as conformal field theories.
The object of this thesis is the mathematical description of the connection between statistical mechanics and conformal field theories in two dimensions. The key insight underpinning the results of this thesis is that, by carving the appropriate discrete complex analysis tools, one can conceive a critical lattice model as a discrete version of a conformal field theory.
Keywords: mathematical physics, statistical mechanics, conformal field theory
Thesis available for public display 10 days prior to the defence at:
https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/Doctoral theses at the School of Science:
https://aaltodoc.aalto.fi/handle/123456789/52
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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