Department of Mathematics and Systems Analysis


Open positon: Doctoral Researchers in Mathematics, Operations Research, and Statistics

5. December 2023

We are now looking for several

Doctoral Researchers in Mathematics, Operations Research, and Statistics

The doctoral researchers will work within one of the department’s main research areas:

  • Algebra and Discrete Mathematics
  • Analysis
  • Mathematical Physics
  • Maths & Arts
  • Numerical Analysis
  • Operations Research and Systems Analysis
  • Statistics and Mathematical Data Science

Public defence in Systems and Operations Research, M.Sc. (Tech) Juha Mäntysaari

23. October 2023

Multiobjective optimization boosts energy-smart decision making 

Have you ever had to make a decision in which you need to take into account several criteria? Such decision making situations in everyday life can be, for example, buying a new home or a car. In addition to the purchase cost, criteria such as driving comfort and safety can affect the car selection. Operations Research is a discipline that studies decision making, where multicriteria problems can be examined with multiobjective optimization. In practice, multiobjective problems often evolve over time, such as the heating of a house or the regulation of a lake-river system. In his dissertation, Juha Mäntysaari approaches these types of dynamic multiobjective optimization problems by developing suitable solution methods, such as price coordination and goal programming methods. The challenge of the owner of an electrically heated house is to find the best way to use heating when electricity price can vary strongly during the day. The goal is to identify the optimal daily heating profile in terms of heating costs and living comfort. In the lake-river regulation problem, the dynamics is created by the changing in-flow of water over time and the temporal variation in the value of the electricity produced. The multiobjective problem arises from the combined optimization of flood risks caused by the varying water levels and the value of the energy produced. In the dissertation, Juha Mäntysaari has studied the use of the house as a heat storage which allows to transfer the use of electricity for heating to cheaper hours by adjusting the desired indoor temperature, for example, during the night. This activity is a way to implement demand side management in electricity markets. Similar demand side management approaches can be implemented on a larger scale within consumer groups or in process industries. The dissertation also examines demand side management in process industry by using price coordination between production planning systems and energy management systems. The overall solution procedure is based on the exchange of energy price and consumption data signals between the systems. It is shown that this can lead to a better overall solution. The environmental management case considered in the dissertation is a multiobjective optimization model developed for the regulation of the Päijänne-Kymijoki lake-river system in Finland.

Contact details:

Puhelinnumero  +358 50 332 5247

Doctoral theses in the School of Science:

New hourly paid teachers of mathematics and systems analysis for spring 2024

10. October 2023

The Department of Mathematics and Systems Analysis is seeking

New hourly-paid teachers in Mathematics and Systems Analysis for spring term 2024.

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 6 November 2023.

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

More information: 

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) 



Postdoctoral Researcher in Mathematics: Well-rounded number-theoretic lattices

2. October 2023
Closes on: 15.11.2023

Aalto Math Camp

20. August 2023
Aalto Math Camp is back!!
6 - 8.10.2023

For lukio students.
Follow this link for more info and registration (deadline 22.9).

Public defence in Mathematics, M.Sc. Muhammad Ardiyansyah, 11.8.2023

8. August 2023

Statistical Modeling with Hidden Variables

Statistical models have been used to study real phenomena that are rather complex. If we want to build reasonably nice statistical models that could explain the complicated feature of these real phenomena, then we often need to gather a big amount of data and this process could be time-consuming, expensive, or just infeasible. We can overcome these limitations by incorporating hidden random variables corresponding to the unmeasurable variables into our models. In this thesis, we focus on two important examples of hidden variable models: phylogenetic model and factor analysis model. 

Phylogenetics is a field in biology that studies the evolutionary relationships between biological entities. From biological data such as DNA sequences, we can extract some useful information that can be used to infer evolutionary relationships that are presented in terms of networks. Hidden variables in phylogenetic models correspond to ancestors whose DNA samples are unmeasurable. 

In phylogenetics, we focus our study to the embedding and the network distinguishability problems. Roughly speaking, the embedding problem asks how restrictive it is to model the evolutionary processes which regard time as a continuous variable and assume that substitution events always occur at the same rate. On the other hand, the goal of studying the network distinguishability problems is to distinguish the set of probability distributions arising from two phylogenetic network models. 

For the embedding problem, we provide criteria of embeddability of Markov matrices belonging in some phylogenetic models that include the most common models studied in the literature. These results enable us to approximate how large the set of embeddable Markov matrices is inside the set of Markov matrices within the models. Moreover, we provide some conditions under which we can distinguish certain phylogenetic network models. 

Factor analysis models seek to reduce the number of observable variables that is often quite large in terms of fewer number of underlying hidden factors which are thought to better explain the covariance between the observable variables. Dropping the Gaussianity assumption of the classical factor analysis model, we introduce the higher order factor analysis model which takes into account higher order moment or cumulant tensors. Additionally, we compute the dimension of this model which can be used to measure the complexity of the model.

Contact details:

Mobile 0504552250

Doctoral theses in the School of Science:

Public defence in Mathematics and Statistics, M.Sc. (Tech) / M.Sc. (Econ) Olga Kuznetsova, 19.7.2023

29. June 2023

Title of the doctoral thesis: Interactions of Algebra, Statistics and Optimization

Doctoral student: Olga Kuznetsova
Opponent: Professor Serkan Hoşten, San Francisco State University, USA
Custos: Assistant Professor Kaie Kubjas, Aalto University School of Science, Department of Mathematics and Systems Analysis

The structure and complexity of optimization problems in statistics and algebra 

Consider the question: “How can we predict the duration of hospital stays in different departments based on the observations from the past year?”. Similar problems arise in medical care scheduling, traffic routing, and airline pricing. Optimization theory provides the tools to answer such questions. Its main idea is to use a criterion to identify the best solution from a set of alternatives. 

We study the structure of optimization problems, the conditions for the existence of an optimal solution, and the complexity of computing an optimum. We focus on Gaussian and log-concave maximum likelihood estimation (MLE), which is an optimization method in statistics, and polynomially-constrained optimization. 

Gaussian random variables are popular in statistics and machine learning due to their theoretical properties and the ability to represent many processes in biology and economics. We use graphs to describe the relationships between the random variables, for example, the similarity of the different departments in a hospital. We develop a package GraphicalModelsMLE for the computer algebra system Macaulay2 to study Gaussian graphical models and suggest directions for further research. 

Random variables with log-concave densities are a generalization of Gaussian random variables and have attracted significant attention in recent years. We show that the optimal solution is often transcendental. As a result, modern computers can only solve such problems imprecisely. We also study the properties of log-concave MLE under the additional constraints imposed by undirected graphs. 

The goal of polynomially-constrained optimization is to find an optimal solution among the alternatives that satisfy a system of polynomial equations. Examples of such problems in statistics are the MLE of discrete random variables and the MLE of the means of Gaussian random variables. Estimating the average duration of a hospital stay is an example of the latter. We require that the critical points, i.e., the candidate solutions to the optimization problem, satisfy an explicit formula. The precise form of this formula depends on the data. We show that there is a finite number of critical points whenever the data is sufficiently general. This quantity is a valuable indicator of the complexity of an optimization problem because one often needs to compute all critical points to identify the optimal solution.

Thesis available for public display 10 days prior to the defence at:

Summer party for newcomers and buddies was all about sharing onboarding experiences and solving escape rooms challenges

26. June 2023

An Aalto 'buddy' is a new employee’s colleague who supports them settling into Aalto. The first-ever summer party for newcomers and buddies took place on June 6 at the Trap Factory. All the newcomers of 2022 and their buddies were invited, and around 50 attended the event. They shared their experiences via informal talks and feedback stations.

According to the feedback, the buddy program can help a new employee make friends during the first months at Aalto. Among other things, the Finnish weather might be challenging for many newcomers. Ozias Hounkpatin, a postdoctoral researcherat the Department of Built Environment, was told that staff scientist Mika Jalava will show him around. 

‘It was very cold outside when I arrived, but I was feeling very warm inside’, Hounkpatin says.

Anya Siddigi, lecturer in the Language Centre, thinks that the buddy programme can make you feel like you are part of the organization. Sophia Hagolani-Albov, Coordinator of Sustainability Science Days working in leadership support services, found her buddy to be "maybe the best in the history of onboarding buddies", helping her to get to know the sometimes confusing but lovely organisational culture of AaltoAnd Minna-Kaarina Forssén, a senior manager for Unite!, got the feeling that she really belongs to the team.

Pattanun Chanpiwat, doctoral researcher at the Department of Mathematics and Systems Analysis, came to Aalto from Thailand. His buddy was Muhammad Ardiyansyah, a doctoral researcher in the same department.

‘I had a Zoom call before coming to Aalto. Everything went smoothly. I even got help with organizing daycare for our children. In addition to my onboarding buddy, Johanna Glader, our HR, was very helpful.’

Sometimes a newcomer and a buddy will become friends. This maybe happened at the School of Science, where Nicoletta Michieletto took the role of a buddy, and welcomed a newcomer, Juhani Lehtinen to the school’s own event team.

‘We’re a perfect match, I’m the control freak and Giovanni – as I call Juhani – is the chill person’, Michioletto says. 

The event was organized by HRD specialist Mari Kaarni, who is responsible for the buddy program, Networking Platform Manager Heidi Henrickson, and Hanna-Mari Ylinen, a communications and events. The news article was coordinator for the platform, and the .Photos for the article were taken by a newcomer, Oona Hilli, a communications trainee in the School of Science, and the news article was written by a ‘buddy’, Tiina Aulanko-Jokirinne. All the feedback gathered will be considered in the development of the program.


Public defence in Systems and Operations Research, M.Sc. Nikita Belyak, 22 June 2023

9. June 2023

Title of the doctoral thesis: Modelling and solution methods for renewables-driven energy markets

Doctoral student: Nikita Belyak
Opponent: Prof. Carlos Henggeler Antunes,University of Coimbra, Portugal
Custos: Prof. Fabricio Oliveira, Aalto University School of Science, Department of Mathematics and Systems Analysis

Pressed by climate change, many countries have paid significant attention to a sustainable transition of energy systems towards carbon neutrality. One can find numerous ongoing investigations on decarbonisation strategies ranging from advancing the existing generation technologies and proposing new ones, such as carbon capture and storage technologies. A common tool allowing one to understand the impact of the potential solution on economic and social aspects of life is energy systems modelling. One can highlight two essential parts related to energy system modelling: i) formulating the model and ii) solving the model. Formulating the model usually implies defining the set of mathematical relationships representing the real-world problem. Solving the mathematical model implies the application of some algorithm to mathematically derive the optimal solution for the problem. 

Despite being vastly used in numerous applications, energy modelling tools have been criticised for providing insufficient precision of the information for the policymakers. Among the others one can pinpoint two major points of criticism: i) a large number of simplifications is usually made when modelling real-world energy systems and ii) very few attempts are made to consider multiple energy system agents (e.g., for example, transmission system operators and generation companies) within the scope of a single energy model. 

This dissertation aims to address both aforementioned points of criticism. First, it studies the extent to which transmission system operators can impact the decisions of the private generation companies regarding their decisions on the expansion of the conventional and renewable (i.e., green) generation infrastructure. Therefore, the mathematical model proposed in the dissertation considers transmission system operators, generation companies and national policies regarding the carbon tax and renewable generation incentives in a distinct energy model. Additionally, this dissertation proposes a solution algorithm that can be applied to solve the aforementioned energy model as well as to the mathematical models from other fields that have similar structure. The solution method allows one to solve the mathematical model even in cases when the model thoroughly represents large-scale and complex energy system in detail, i.e., one does not assume a significant number of simplifications when formulating the model.

Thesis available for public display 10 days prior to the defence at:

Kurotuksia - Higher Powers student exhibition blending math and arts opens at Heureka today

6. June 2023
The Ocean’s Curtain is inspired by the way the surface of water looks when viewed from the seabed. Kurotuksia - Higher Powers exhibition. Photo: Mikko Raskinen.

The Ocean’s Curtain is inspired by the way the surface of water looks when viewed from the seabed. The group of students included Helena Hartman, Seyed Alireza Fatemi Jahromi, Meri Aho, Xiao Mou and Irmuun Tuguldur. Photo: Mikko Raskinen.

Aalto University's interdisciplinary course "Crystal Flowers in Mirror Rooms: Mathematics meets Art and Architecture" culminates in the exhibition Kurotuksia - Higher Powers, which opens today at Heureka, the Finnish Science Centre. It celebrates a decade of promoting interdisciplinary interaction in the course and is the second time the course has an exhibition at Heureka.

‘Folding, origami, kirigami, cutting, crumpling and other methods that allow for the transformation of flat material into three-dimensional space are featured in the course and in the exhibition. We also wanted to highlight harmonious colors in the exhibition, such as the Greyscale Rainbows made under the guidance of the Textile Artist of the Year, Laura Isoniemi,’ says Kirsi Peltonen, a senior lecturer in mathematics who is responsible for the course.

The students come from different schools and different stages of their studies, and students from the University of Helsinki also took part in the course. The exhibition is located near the ceiling of Heureka, at a height of about three meters.

‘The exhibition plays with geometries, symmetries and organic shapes. The previous Crystal Flowers exhibition at Heureka six years ago caused sighs of beauty in the viewers. It was precisely for the sake of beauty that we decided to extend the exhibition for a few extra months,’ says Mikko Myllykoski, director of Heureka.

Myllykoski’s comments are echoed by Eija Myötyri, who works at Heureka and says that mathematics is the underlying structure of everything.

‘Mathematics is shapes, among other things. You can visualise it, and it's very beautiful to look at.’

Slime moulds and fraqility

The exhibition consists of eight showpieces. Ballad of Two Automata is a sculpture that includes two model simulations of slime moulds. It was designed and created by Poonam Chawda, Petri Juntunen, Emma Kamutta and Jonas Tjepkema. They were inspired by the slime mould Physarum polycephalus, which has also been used to model the Tokyo railway network.

According to Kamutta, the team was interested in the interaction between the two creatures in a perpetual motion space.

In the Ballad of the two automata, there are two strange creatures that you don't know whether they are friends or enemies, sad or happy,’ says Tjepkema, who thinks that teamwork was the main takeaway from the course. He says that producing the sculpture felt at times like working on an assembly line in a factory, along with the other team members.

‘It was interesting to learn how to communicate with other students from different disciplines in an understandable way,’ says Kamutta, who was a student at the University of Helsinki when she took the course. It was through the course that she found a summer job at Aalto and, at the same time, a topic and a supervisor for her final thesis.

Olio, a work by Hitomi Asaka, Nina Jokiaho, Jason Selvarajan and Henrik Kankaanpää, was also inspired by slime mould.

Olio is built on horror, otherness, and indeterminacy. We reflected on strangeness, alienation, and disgust – as decomposers are easily associated with decay, disintegration, and death,’ says Jokiaho, who explored interdisciplinary collaboration from a visual arts education perspective during the course.

The Ocean’s Curtain is inspired by the way the surface of water looks when viewed from the seabed. The group of students included Helena Hartman, Seyed Alireza Fatemi Jahromi, Meri Aho, Xiao Mou and Irmuun Tuguldur.

‘The process of material selection and working with the materials was new to me. It’s a different approach. I’ve done the whole math and arts minor, and for me, a science student, it felt like a gateway to arts,’ says Seyed Alireza Fatemi Jahromi.

‘I applied to Aalto to study mathematics precisely because of the arts courses. During the course, I learned to trust the creative process and to think in a new way: for example, we went to Oodi to sew without a plan. It was very inspiring,’ says Aho.

See also behind the scenes photos and blog post of building the Curves through folding paper art origami by Susanna Oksanen. Other team members are Joel KnippareOkko Riekki and Venja Salminiitty.

Kurotuksia - Higher Powers exhibition is open from 6 June to 31 August during Heureka's opening hours.




Public defence in Systems and Operations Research, M.Sc. (Tech) Juho Roponen, 9 June 2023

25. May 2023

Managing risks and uncertainties using probabilities 

Opponent: Professor Ali Abbas,University of Southern California, USA
Custos: Professor Ahti Salo, Aalto University School of Science, Department of Mathematics and Systems Analysis

Especially in crisis and conflict situations, decisions inevitably must be made in the face of uncertainty. In public administration and business operations, significant decisions involve not only uncertainty but also costs, work, and far-reaching consequences. Therefore, finding a good decision option, or at least avoiding the worst ones, is crucial. 

The basic principles behind methods supporting decision-making under uncertainty have remained the same for a long time. If the achievement goals can be described with a clear metric such as monetary gain, and the uncertainties associated with the decision options can be represented by probability distributions, the best decision alternative can be found only using high school mathematics. However, often in reality, determining both the benefits and probability estimates is very challenging. This dissertation develops mathematical methods for handling uncertainties related to human behavior and future developments. 

When modeling the decisions of multiple individuals in a conflict setting such as war, game theory is utilized. Adversarial risk analysis, for which methods are developed in this dissertation, applies solution concepts from game theory without strong assumptions about the information available to different parties or about decision-making logic. This allows for the assessment of uncertainties and the associated probabilities based on the limited information available. 

Future uncertainties are addressed in the dissertation using probability-based scenario analysis. Probabilistic cross-impact analysis is employed to assess the probabilities of scenarios. When examining complex future phenomena, such as technological development, the number of significant uncertainty factors becomes high. Furthermore, uncertainty factors, such as the cost, technical performance, and adoption rate of a new technology, are not independent of one another. If a new technology is faster and cheaper than older competitors, it will quickly become widespread. Therefore, forecast models must also consider such interdependencies. To address this, the dissertation presents cross-impact analysis methods that incorporate the probabilities and pairwise dependencies of uncertainty factors based on expert knowledge. These methods can be used to assess both risks and scenario probabilities, thereby supporting decision-making.

Page content by: webmaster-math [at] list [dot] aalto [dot] fi