Welcome to Mathematical Kaleidoscope II
Description: The five subjects to be covered by the course are described below.
Jakob Gulddahl Rasmussen: Temporal point processes and the conditional intensity function
Horia Cornean: On some fundamental spectral properties of finite dimensional stochastic matrices
Olav Geil: Applications of Gröbner basis theory to problems in information theory
Anton Evgrafov: Finite element analysis of elliptic problems
Poul Svante Eriksen: Introduction to genetic algorithms
1. Times of events, such as earthquakes, can be modelled by temporal point processes. When modelling temporal point processes, the so-called conditional intensity function is a particularly useful tool. Roughly speaking, the conditional intensity function tells us if an event is going to happen now given we know the times of events in the past. Likelihood functions, simulation algorithms and model checking procedures can be constructed from the conditional intensity function. We will look at some of the theory behind temporal point processes and conditional intensity functions, and apply this theory to data.
2. We will start by investigating the Jordan normal form of any square matrix by using elementary methods from complex function theory. We will then focus on left stochastic matrices (square matrices with non-negative entries whose columns sum to one), by proving classical spectral results like the Gershgorin and Perron-Frobenius Theorems. As an application we will study the approach to equilibrium of non-homogeneous Markov chains in finite state spaces.
3. Algebraic methods play a fundamental role in the theory of error-correcting codes. Different languages are applied such as algebraic geometry, function field theory, pure algebraic methods, and recently also Gröbner basis theory. This course gives an introduction to the use of Gröbner basis theory in algebraic coding theory and other information theoretical applications.
4. Finite Element Method (FEM) is objectively the most widely used numerical approach for finding approximate solutions of partial differential equations.
Starting from the simplest case of conforming approximations to problems defined by symmetric, coercive, and bounded bilinear forms we will explore the rich theory and practice of FEM arising, when the underlying assumptions are successively relaxed.
5. Genetic algorithms are designed to seek for solutions of a given optimality problem. The basic idea is inspired by population biology, where we consider a population of potential solutions. We randomly create new generations and adapt the darwinistic principle: survival of the fittest. Concepts like mutation, recombination and migration are included to allow drift against different solutions.
Prerequisites: Basic knowledge in mathematics and statistics.
Learning objectives:
Form of evaluation:
Active participation is required (including a show up of minimum 80% corresponding to 4 topics) together with a successful evaluation of the solutions for a selected part of the exercises (as agreed with the lecturer) for at least 3 topics (selected by each student).
Organizer: Jesper Møller, e-mail: jm@math.aau.dk
Lecturers: Associate Professor Jakob Gulddahl Rasmussen, Professor Horia Cornean, Professor Olav Geil, Associate Professor Anton Evgrafov, Associate Professor Poul Svante Eriksen.
ECTS: 5
Time: January 30 2025, 8:15-16:15 (Jakob Gulddahl Rasmussen);
February 3 2025, 8.15-16.15 (Horia Cornean);
February 6 2025, 8:15-16:15 (Olav Geil);
February 10 2025, 8:15-16:15 (Anton Evgrafov);
February 13 2025, 8:15-16:15 (Poul Svante Eriksen).
Place: Thomas Manns Vej 23, Room: 1.344Zip code: 9220
City: Aalborg
Maximal number of participants: XX
Deadline: 9. januar 2025
Important information concerning PhD courses:
There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.
We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.
To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.
For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at aauphd@adm.aau.dk When contacting us please state the course title and course period. Thank you.
- Teacher: Horia Cornean
- Teacher: Anton Evgrafov
- Teacher: Olav Geil
- Teacher: Jesper Møller
- Teacher: Jakob Gulddahl Rasmussen
- Teacher: Søren Byg Vilsen
Description:
The aim of this course is to equip PhD students with a comprehensive understanding of cutting-edge natural language processing (NLP) technologies and their application in real-world industrial settings. Solid understanding of these vital NLP techniques equips business and engineering PhD students with the necessary skills to leverage textual data effectively to solve the real-world problems, e.g., improving customer satisfaction, developing intelligent systems, and making data-driven decisions. This leads to success in today's data-driven and language-driven industrial landscape. The topics covered here are text classification, sentiment analysis, speech recognition, conversational AI and applications of large language model (e.g. ChatGPT). In addition to theoretical knowledge, this course places a strong emphasis on practical implementation and problem-solving. Participants will engage in hands-on exercises, working with industry-standard tools and libraries. Participants will develop the ability to identify and solve NLP challenges specific to their respective fields. By the end of the course, participants will possess the skills necessary to navigate the rapidly evolving landscape of NLP technologies. They will have the ability to develop and deploy advanced NLP models to tackle complex language-related problems faced by businesses and industries.
Prerequisites: The course will target PhD students in the fields of business and engineering from all the Danish universities and ideally from the universities all over the world. Industry professionals are also encouraged to participate
Learning objectives: TBA
Organizer:
Chen Li, cl@mp.aau.dk
Lecturers:
Associate Professor, Chen Li, Department of Materials and Production
Associate Professor, Dimitris Chrysostomou, Department of Materials and Production
Associate Professor, Elizabeth Jochum, Department of Communication and Psychology
Postdoc, David Andres Figueroa Salvador, Department of Materials and Production
ECTS: 3
Time: 24 - 28 November 2025
Place: Aalborg University
Zip code: 9220
City: Aalborg
Maximal number of participants: 20
Deadline: 3 November 2025
Important information concerning PhD courses:
There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.
We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.
To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.
For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at aauphd@adm.aau.dk When contacting us please state the course title and course period. Thank you.
- Teacher: Dimitris Chrysostomou
- Teacher: Elizabeth Jochum
- Teacher: Chen LI
Description:
Proper choice of characterization methods is crucial in most experimental projects. This course addresses theory and application of several microscopy and spectroscopy techniques important in studies of bulk materials, surfaces as well as bio- and nanoscale objects. Essential part of the course is hands-on training in selected microscopy and spectroscopy techniques. The participants can prioritize up to 3 methods of interest for hands-on training.
The course covers six topics:
• Electron and X-ray diffraction (L. Diekhöner);
• Scanning electron microscopy (SEM) and X-ray microanalysis (L. Gurevich and M. Larsen);
• Scanning probe microscopy (SPM) (L. Gurevich and P. Fojan);
• Raman spectroscopy (L.R. Jensen);
• Terahertz (THz) spectroscopy (E. Skovsen);
• Sum frequency spectroscopy (K. Pedersen)
• Nuclear Magnetic Resonance (NMR) (R. Wimmer).
Prerequisites: The course is suitable for participants with different background (physics, chemistry, biology, medicine, mechanical/materials/electronic engineering and similar).
Learning objectives:
Form of evaluation:
Description of course assignment
The course entitles PhD students to 3 ECTS which requires active preparation in lectures, hands-on training as well as submission of a report of sufficient quality. The report should focus on one of the experimental methods applied during the course and, if possible, should be based on the measurements on student’s own samples. If a student is not able to bring his/her own samples, the data from demo samples provided by us can be used.
The report has to include:
- Theoretical background of the experimental method used;
- Description of the material(s) examined;
- Goal of the study;
- Description of the experimental procedure;
- Presentation of the results obtained and description of data processing (if necessary);
- Data analysis correlating the material structure/properties with the obtained experimental results;
- Conclusion;
- List of references.
The report is expected to be about 10 pages. Note that all report will be checked with anti-plagiarism software Urkund prior to assessment. Reports with substantial plagiarism level will be rejected.
The report should be uploaded as pdf file into the below folder by December 15th.
Organizer:
Dr. Leonid Gurevich, lg@mp.aau.dk
Lecturers:
Kjeld Pedersen, MP, Peter Fojan, MP; Lars Diekhöner, MP; Mikael Larsen, MP; Lars Rosgaard Jensen, MP; Esben Skovsen, MP; Leonid Gurevich, MP; Reinhard Wimmer, BIO.
ECTS: 3
Time: 24 - 28 November 2025
Place: Aalborg University
Zip code: 9220
City: Aalborg
Maximal number of participants: 18
Deadline: 3 November 2025
Important information concerning PhD courses:
There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.
We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.
To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.
For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at aauphd@adm.aau.dk When contacting us please state the course title and course period. Thank you.
- Teacher: Lars Diekhöner
- Teacher: Peter Fojan
- Teacher: Leonid Gurevich
- Teacher: Lars Rosgaard Jensen
- Teacher: Mikael Larsen
- Teacher: Kjeld Pedersen
- Teacher: Esben Skovsen
- Teacher: Reinhard Wimmer
Description:
There is an increase in the popularity of exoskeletons worldwide, demonstrating the relevance of creating assistive technologies for daily life, ergonomics, and rehabilitation among others. Moreover, the research field related to exoskeletons has grown in the last decade, increasing the demand for appropriate instruction of graduate students that work on the topic. Therefore, this PhD course targets researchers that either design exoskeletons or test current exoskeleton technologies.
In this PhD course, we will firstly establish the basics on the ergonomic interactions that define the need for mechanical assistance on shoulder, back and lower limbs. The course then evolves to introduce the need for specific exoskeleton design, covering actuation, sensing and control issues. Finally, the course will introduce different techniques for the evaluation of exoskeleton technologies considering human-machine interaction and its challenges/limitations. Hands-on experience on the use of motion capture and surface electromyography (EMG) as tools for evaluation will be proposed. Moreover, we will introduce and practice the use of computational models as an alternative method to evaluate the effectiveness of exoskeleton assistance.
Prerequisites:
Basic understanding of mechanics, actuation and control is required. A basic background within Anatomy, human biomechanics are desirable. Moreover, basic skills in signal processing using Matlab or Python are also desired. Students will have an opportunity to install and try biomechanical analysis software on their computers. This requires the Windows operating system.
Learning objectives:
Form of evaluation:
A final assignment consisting of performing data processing using experimental data recorded during the course should be submitted up to 3 weeks after the course. The analysis can be carried using the experimental data, computer simulations or a combination of both. Further instructions will be announced prior to the course start.
Key literature:
Preparatory reading materials will be specified depending on the qualification of the enrolled students, to accommodate all necessary knowledge to attend the course.
Organizer: Anderson S. Oliveira, Associate Professor (Aalborg University), oliveira@mp.aau.dk
Lecturers:
Anderson S. Oliveira, Associate Professor (Aalborg University)
Shaoping Bai, Professor (Aalborg University)
John Rasmussen, Professor (Aalborg University)
ECTS: 3
Time: 4 - 6 June 2025
Place: Aalborg University
Zip code: 9220
City: Aalborg
Maximal number of participants: TBA
Deadline: 14 May 2025
Important information concerning PhD courses:
There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.
We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.
To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.
For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at aauphd@adm.aau.dk When contacting us please state the course title and course period. Thank you.
- Teacher: Shaoping Bai
- Teacher: Anderson de Souza Castelo Oliveira
- Teacher: Anderson de Souza Castelo Oliveira
- Teacher: John Rasmussen
Description:
This Ph.D. course introduces techniques for modeling of musculoskeletal systems based on multibody dynamics. Unlike most courses in the field, this one takes a bottom-up approach beginning multibody kinematics and ending with analysis of complex and anatomically realistic models.
The first day of the course contains a general introduction to musculoskeletal modeling, but participants must be prepared to study the subject in preparation for the course.
The remainder focuses on advanced topics on the forefront of research.
The participants must install the AnyBody Modeling System and familiarize themselves with the system prior to the course. Software licenses will be provided.
The course contents are the following:
1. Monday: Introduction to musculoskeletal modeling (MSA)
- Kinematics
- Kinetics
- The AnyBody Modeling System
2. Tuesday: Model structure and AMMR (JR)
- Introduction to the model repository and ecosystem
- Model parts and structure
- Scaling and morphing
- Adding and removing body parts
- How things are connected
3. Wednesday: The thoracic spine model (JR)
- Anatomy and biomechanics of the spine and thorax including breathing
- Review of thorax models
- The role of kinematic determinacy
- The current thorax model and the averaging measure
- Use of the thorax model for breathing and scoliosis models
4. Thursday: Modeling of shoulder biomechanics (MdZ)
- Anatomy and biomechanics of the shoulder
- The shoulder model in AMMR
- Review of research based on computational shoulder models.
- The shoulder rhythm
- Modeling stability, instability, rotator cuff deficiency and impingement
5. Friday: Exercises and assignment (MSA)
- Modeling workshop: develop your own model of the shoulder or thoracic spine
- Introduction of assignment
Learning objectives:
Key literature: TBA
Organizer: Professor John Rasmussen, email: jr@mp.aau.dk
Lecturers: John Rasmussen, Mark de Zee, Michael Skipper Andersen
ECTS: 4.0
Time: Date Month Year 28 April - 2 May 2025
Place: Aalborg University, Department of Materials and Production, Fibigerstræde 16, 9220 Aalborg Ø
OBS: The course will run in a hybrid format with teachers and students with physical presence in Fibigerstræde 16 and an option to follow the course remotely via the Teams platform.
Zip code: 9220
City: Aalborg
Maximal number of participants: 30
Each participant must bring a reasonably modern Windows laptop on which software can be installed.
The course will run in a hybrid format with teachers and students with physical presence in Fibigerstræde 16 and an option to follow the course remotely via the Teams platform.
Deadline: 7 April 2025
Price:
- For students with physical presence, 500 DKK will be requested for refreshments during the course.
- For students from industry, we charge DKK 4000 for participation.
Important information concerning PhD courses:
There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.
We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.
To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.
For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at aauphd@adm.aau.dk When contacting us please state the course title and course period. Thank you.
- Teacher: Michael Skipper Andersen
- Teacher: John Rasmussen
- Teacher: Mark de Zee