Seminar “Modern classification methods of single-channel ECGs. Part 2”
At the moment, there are mobile devices that can read a single-channel ECG. These devices can be used for preliminary screening of various diseases. This report will talk about various methods that allow you to classify single-channel mobile ECGs with a fairly high quality. Many of these methods and improvements to them were proposed for the first time by the author of this report. The report highlights the strengths and weaknesses of the proposed methods. It is worth noting that all the methods considered can be generalized to work with traditional ECGs.
Seminar “On Lavrentiev phenomenon”
The Lavrentiev phenomenon is the difference between the minimums/minimizers of integral functionals when minimized over "wide" and "narrow" Sobolev spaces. In particular, the "narrow" space can be understood as the closure of smooth function in the "wide" Sobolev space (the natural energy space of functions, where the integral functional is finite), and in this case the Lavrentiev phenomenon happens when smooth functions are not dense in the "wide" Sobolev space.
Scientific seminar “Normal derivative lemma for equations of divergent form”
We provide some versions of the Zaremba-Hopf-Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coefficients of equations and on the boundaries of domains.
Postgraduate Mathematical Seminar “On stationary solutions of the Vlasov-Poisson equations in a bounded domain”
A two-dimensional system of the Vlasov-Poisson equations for a two-component plasma in a bounded domain is considered. It is shown that in the neighborhood of a stationary solution of such a system with zero potential there are stationary solutions with non-zero potential of a self-consistent electric field.
Scientific seminar “On stability of steady state and time-space dependent equilibrium for chemotactic models”
The subject of the talk are biological and biomedical problems that we model using systems of chemotactic equations with cross-diffusion terms. I will present recent results related to quasi-periodic behavior of biological system arising from chemotactic framework of Keller-Segel.