News archive


Small informal gathering Tuesday, 10 January, 2023, 4 pm, in our meeting room PDF Print

A small informal gathering Tuesday, 10 January, 2023, 4 pm, in our meeting room. Looking forward to chat there.

 
Public defence of the thesis - Temesgen Tsegaye Bihonegn PDF Print

Geometric Approach to Tractography in Brain Imaging (specialization Geometry, Topology, and Geometric Analysis)


by Temesgen Tsegaye Bihonegn (guarantor of the specialization Jan Slovák)


Tuesday, January 10, 2pm, meeting room at our department


Abstract:

Magnetic resonance imaging (MRI) is the non-invasive way of examining the micro-structure of biological tissue. Understanding the mechanisms of brain function is essential to better diagnose neurological disorders. However, data complexity makes this imaging method mathematically and computationally difficult. We use Riemannian geometric tools to tackle Tractography and Segmentation problems. This work discussed geometric analysis for fiber tracking and segmentation in medical tensor imaging. A systematic approach is proposed to improve fiber tracking algorithms and identify scalar quantities that could be used as biomarkers. On the basis of numerical solutions to the geodesic equations, a Riemannian geometry approach was applied to improve fiber tracking using appropriate activation functions and anisotropy data from the voxels. We present a method to choose the appropriate conformal class of metrics where the metric gets scaled according to tensor anisotropy. We use the idea that rotational information is related to the anisotropy of the tensor, and logistic functions can be exploited to capture it. In particular, the rotational information is misleading in nearly isotropic regions in the presence of noise, and the metric tensor is rescaled appropriately. In addition, we provide a framework for exploiting higher-order tensors (HOTs) appearing in high-angular resolution diffusion imaging (HARDI). These can potentially serve as biomarkers. It involves flattening of HOTs and extraction of the diagonal components.

 

See https://is.muni.cz/auth/th/l9ko0/?fakulta=1431;obdobi=8903 for the full text as well as the reports.

Last Updated on Monday, 09 January 2023 08:35
 
39th mathematical hike - 17th of December 2022 PDF Print

Dear Friends of Hikes and Mathematics,

you are cordially invited to the 39th mathematical hike planned on Saturday 17th of December. Start at 9:37 at the "Kořískova" tram stop.

The hike is about 10 km long, we will go through forests near Brno towards Obřany. We invite you also to our traditional mathematical carol-singing. (lyrics in czech, though)

All information and photos can be found at https://conference.math.muni.cz/vylety/index.php?id=kronika. (in CZ)

Looking forward to see you soon!

Pavel Francírek and Jonatan Kolegar, organizers
Jan Slovák, Director of the Department of Mathematics and Statistics

If you have questions, send them to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Last Updated on Monday, 12 December 2022 16:39
 
MUNI Seminar series - Menachem Magidor - Taming the Monster of Independence PDF Print

Mathematics, Physics & Computer Science Seminar Series

November 23, 2022 from 4:30 PM at Governor's Palace, Moravské náměstí 1a, Baroque Hall

Menachem Magidor

Taming the Monster of Independence

Abstract:

Mathematicians feel that every genuine mathematical problem has a solution. Gödel's incompleteness theorem is a major challenge to this feeling, because it claims that every rich enough mathematical theory contains a statement that can not be proved or disproved by this theory. Namely: the problem is independent of present theory. The result of the last half a century showed that many problems in many subfields of Mathematics are independent of the usual axiom system mostly used by mathematicians: ZFC. The most famous one is the Continuum Hypothesis, CH. Discovering that a problem you spent a lot of time and effort with, is independent, is very frustrating for the working mathematician. This is the source of the expression ” the monster of independence” . Can the ” ugly monster of independence” be tamed? Can we still find ways of settling problems that seem to be independent? In the talk we shall explore several approaches to this challenge.


Menachem Magidor is an Israeli mathematician who specializes in mathematical logic, in particular, set theory at the Hebrew University's Einstein Institute of Mathematics. He served as President of the Hebrew University of Jerusalem, was President of the Association for Symbolic Logic from 1996 to 1998, and is currently the President of the Division for Logic, Methodology and Philosophy of Science and Technology of the International Union for History and Philosophy of Science (DLMPST/IUHPS; 2016-2019). In 2016 he was elected an honorary foreign member of the American Academy of Arts and Sciences. In 2018 he received the Solomon Bublick Award.

Last Updated on Wednesday, 16 November 2022 15:16
 
MUNI Seminar series - Hans Munthe-Kaas - Computational Mathematics between Dynamics, Geometry and Algebra PDF Print

Mathematics, Physics & Computer Science Seminar Series

December 7, 2022 from 4:30 PM at Governor's Palace, Moravské náměstí 1a, Baroque Hall

Hans Munthe-Kaas

Computational Mathematics between Dynamics, Geometry and Algebra

Abstract:

Simulation of dynamical systems evolving in time is a central subject of numerical analysis. Traditionally, the main goals in designing a numerical integrator were high accuracy, numerical stability and computational efficiency.


In the last decades it has, however, become increasingly clear that not all errors are equally bad. For example in the simulation of a conservative mechanical system it may be crucial to preserve the Hamiltonian structure of the equations, or to preserve conserved quantities such as energy, angular momenta and other first integrals. In robotics and control, there may be geometric constraints which are important to obey exactly.

The lesson learnt is that the most important goal should be to ‘make errors in the right way’, rather than just minimising the error over a single time step. For long time simulations, the quality of the error is more important than its magnitude in each step. This gave birth to the research field Geometric Numerical Integration, or structure preserving discretisation of differential equations.

The analysis of geometric integration algorithms has evolved into a rich area of research in the borderland between computational dynamics, differential geometry and combinatorial algebra, where the interplay between these three fields is enriching all of them.

In this talk we will survey recent results in these areas, and illustrate by computational examples. The talk is aimed at scientists with a general background in computational engineering problems.

 

HANS ZANNA MUNTHE - KAAS is professor of mathematics at the University of Bergen and leader of the new Lie-Størmer Center in Tromsø. In the last four years he has been the leader of the Abelprize committee. He is editor-in-chief of the journal “Foundations of Computational Mathematics” and President of the Norwegian Mathematical Society.

 

Last Updated on Wednesday, 30 November 2022 18:44
 
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