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.
Assistant Professor Eveliina Peltola tackles challenges of mathematical physics in her new research project. Peltola's research has been inspired by the study of mathematical models that describe very large systems – for example, transport of particles in matter, spread of infectious diseases in populations, or connections between information networks.
‘Models that examine a huge number of atoms, or the entire population of the world, must be examined as a whole, and we must be able to describe their properties in different scales,’ Peltola describes the challenge.
The research project has received an ERC Starting grant of almost 1.4 million euros from the European Research Council. The goal is to create connections between different areas of mathematics and bring new tools to the research of random geometry and mathematical physics models.
In the field of mathematical physics, mathematical tools on the one hand build the foundations for theories of physics, and on the other hand create new areas of mathematics that can be applied to classical mathematical questions.
"Physicists have models for natural phenomena, which they have tested experimentally or observationally. Mathematics, in turn, provides a solid basis for the applicability of the models in desired situations,’ says Peltola.
Peltola is particularly interested in symmetries in random geometry. A symmetry can be observed concretely, for example, when a cluster of atoms in a substance is rotated or scaled. If such a transformation changes the system itself, but its macroscopic statistical properties remain unchanged, one speaks of a statistical – or random – symmetry.
‘Symmetries help to construct mathematical structures that allow for the exploration of other properties. In other words, the importance of symmetries primarily comes from the fact that they give mathematicians additional tools," says Peltola.
Peltola is particularly concerned with Schramm-Loewner evolution curves and their connection to conformal field theory and random geometry. Her project is called Interplay of Structures in Conformal and Universal Random Geometry (ISCoURaGe). The five-year project started early this year.
The Department of Mathematics and Systems Analysis is seeking
New hourly-paid teachers in Mathematics and Systems Analysis for fall term 2023.
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 8 May 2023.
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.
From a background I’m a mathematician, but I do optimization research that is connected to mathematics, computer science and economics. The application areas are public transport planning and last mile logistics – the final step of the delivery process.
My research is mainly theoretical, but we also have a software project LinTim that moved to Aalto with me. The project was launched 15 years ago in Göttingen by Anita Schöbel and I started working in the project in 2013. In 2017, we made it open source.
In the project, we are collecting both algorithms and data sets related to public transport planning. This software project allows us to consider the planning process as a whole: if we change something in an early planning stage, how does that affect the outcome of later planning stages? For example, we can evaluate the impact of changing a line plan on the travel times of passengers by creating a corresponding timetable automatically. It is quite unique that one software is evaluating multiple planning stages in an integrated manner.
Since the project has been made available as open source, we gained multiple new collaborators and users. In Leipzig, a public transport company is testing the project and using algorithms to get new ideas for line planning. Usually, the lines that are operated by busses or trains are chosen from a predefined set, the so-called line pool. This pool is often created manually by planner. We introduced a new algorithm to generate these line pools automatically. Thus, we can get lines that differ from the ones planners would create manually and generate a larger solution space. Depending on the objective of the planner, this can either reduce the cost of the system or is beneficial for the customer by reducing the travel time or the number of transfers.
As LinTim is a research project, the algorithms contain some abstractions. To apply them to specific cities, they might need to be adapted slightly. This is currently tested in collaboration with researchers in Stuttgart and Winterthur.
The example of public transport shows that solving sequential problems in an integrated manner improves the solution quality but at the same time makes the problem more complicated to solve. As sequential problems are not limited to transportation and logistics applications, I am also considering the integration of sequential processes in a more general and abstract way. Here, it is important to understand when it is beneficial to look at the problem in an integrated manner.
I really liked the topic of my PhD; therefore, it was easy to stay with it. And when I found the call for this professorship, I really liked the idea of a department with both areas of research, mathematics, and operations research.
There are national operations research societies both in Finland and Germany. I got the opportunity to work as an assistant to the board in Germany for two years. There I was able to see more computer science and business-related operations research. It is a very large society in Germany and very nice networking opportunity. I am looking forward to getting to know the Finnish OR society as well and gain new perspectives this way.
I enjoy being at conferences. Recently I’ve presented my research for instance at the ALGO conference, the major European event for researchers, students, and practitioners in algorithms.
I think being a researcher means being perseverant – even a bit stubborn – to look at problems and find solutions. One must also be able to collaborate with others especially from different fields to get new ideas and to get different viewpoints to the problems.
I’m very much looking forward to my own research group. There is an open call for PhD students at the Department of Mathematics and Systems analysis. I also wish to build connections to the system analysis lab and applied mathematics.
LinTim, Integrated Optimization in Public Transportation
MS-E1000 Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture is open to all students, from undergraduates to PhD students, from mathematics and engineering to art, design, architecture and chemistry to business.
A maximum of 50 students are expected at the course, and the application period ends 10 January 2023. The course is worth 15 credits and it is held once every two years.
An exhibition of the course will take place in spring 2023 at the Finnish Science Centre Heureka. A similar exhibition was also held at the Heureka in 2017, and as a result the exhibition received a lot of visibility for a period of six months.
‘It's great that after the pandemic we have this opportunity again. Remote teaching and learning were very challenging, although in the end, thanks to the perseverance of the students, we were able to create a great exhibition in the courtyard of the main lobby of the Undergraduate Centre. We are looking forward to positive interaction between students, teachers and Heureka's designers,’ says Kirsi Peltonen, Senior Lecturer in Mathematics and responsible for the course.
As in previous years, the course will feature several guest lecturers in addition to the participating teachers Taneli Luotoniemi and Laura Isoniemi. For example, origami artist Paul Jackson from Tel Aviv will give a folding workshop for the students. Professor Marcelo Dias from the University of Edinburgh will shed light on the physics of the subject. Pirjo Kääriäinen, Professor of Design and Material Science, will bring her strong expertise in multidisciplinary collaboration to the course. University lecturer Luka Piškorec will bring an architectural perspective to the course and the exhibition will be produced by Markus Holste and Marco Rodriguez.
‘This course is group work, and it requires more commitment than participating in a theoretical course,’ says Peltonen.
The students can have a background in intermediate mathematics, but the course opens new perspectives also for example for the students with a major in physics or mathematics. Each group will be made up of students with as many different talents as possible. The course is therefore a unique opportunity to see the reality of people from other disciplines and to get hands-on. Previous courses have included students from all of Aalto's schools, from freshmen to graduate students.
Read more and apply now!
Title of the doctoral thesis: Weight theory on bounded domains and metric measure spaces
Public defence announcement:
A weight function describes an unequal distribution of mass. Muckenhoupt weights are a class of weight functions that are well-behaved in the sense that their oscillation is limited. Muckenhoupt weights are an indispensable part of the toolkit of modern harmonic analysis, and have important applications to neighboring fields of mathematics. One example is studying the regularity of solutions to partial differential equations, which in turn are the quasi-universal language of physics and mathematical modelling.
The present thesis develops the theory of locally defined weight functions on bounded domains of the Euclidean space, as well as weights on more general metric spaces where the facts of classical geometry are not necessarily true. A cohesive treatment of these cases has been lacking since the introduction of Muckenhoupt weights 50 years ago. One benefit of working in abstract metric spaces is that the structure of the problem is laid bare, ideally allowing us to determine the minimal conditions for a statement to hold true. Furthermore, the methods developed are useful in mathematical analysis in nonlinear environments such as groups and graphs.
On certain domains of the Euclidean space, we show a Poincaré inequality involving a different weight on each side. Poincaré inequalities are essential in the regularity theory of partial differential equations. The proof applies dyadic techniques that have lately been influential in the field of harmonic analysis. On metric measure spaces, we show that a Muckenhoupt weight defined on a measurable subset can be extended into the whole space under certain conditions. Furthermore, we investigate other possible ways to characterize Muckenhoupt-type weights.
Contact details of the doctoral student: emma-karoliina.kurki@aalto.fi
Opponent: Professor Sheldy Ombrosi, Universidad Nacional der Sur, Argentina
Custos: Professori Juha Kinnunen, Aalto University School of Science, Department of Mathematics and Systems Analysis
The public defence will be organised on campus.
The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.
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