Mathematics, Physics & Computer Science Seminar Series

March 8, 2023 from 4:30 PM at Governor's Palace, Moravské náměstí 1a, Baroque Hall

Tomasz Łuczak

The phase transition phenomena in combinatorial structures

Abstract:

The notion of the phase transition was introduced in physics to describe a wide class of phenomena when a tiny change of parameters can significantly affect the behaviour of the physical system. In the talk we present several results when such a rapid transformation of the structure can be observed and rigorously analysed. Some of them were inspired and anticipated by actual physical phenomena, others emerged naturally in the studies of discrete combinatorial systems.

Tomasz Łuczak is a Polish mathematician working in the field of probabilistic combinatorics. He graduated at Adam Mickiewicz University, where he is now working as professor at Faculty of Mathematics and Computer Science. He has received a number of awards, including EMS Prize, the Prize of the Foundation for Polish Science, Kazimierz Kuratowski Prize, Stefan Banach Medal, and Władysław Sierpiński Medal. Since 1998 he is a member of the Polish Academy of Sciences.

Postdoc position in Mathematics - Differential and Difference Equations

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

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.