Events

What is the origin of the high brain complexity that explains the deep intricacies and refined levels of cognitive integration in the brain to form, for example, memory and consciousness?

We consider a periodic parabolic singularly perturbed boundary value problem for the Tikhonov system: a singularly perturbed system with fast and slow equations. An asymptotic approximation of the solution to the problem is constructed, conditions for the existence of a solution and its asymptotic stability according to Lyapunov are obtained for these solutions as solutions to the corresponding initial-boundary value problems for this system, both in the case of various types of quasi-monotonicity and in the case of its violation.

A finite additive measure will be constructed on a separable Hilbert space, invariant with respect to a shift to any vector. Invariance will allow us to construct smoothed functions differentiable along any coordinate direction, embedded in quadratically integrable functions, as well as tightly defined Laplace operator and Hamiltonian of an infinite-dimensional quantum oscillator. By analogy with the finite-dimensional case (Yu.N.Orlov, V.Zh.Sakbaev, D.V.Zavadsky), an approximation of the evolution of a quantum oscillator will be proved by averaging random shifts in the coordinate and pulse representations.

The uncontrollable proliferation of human papillomavirus (HPV) can cause severe cervical cancer. The objective of this work is to study the optimal control of HPV viral replication and its consequence in reducing cervical cancer cells. For this purpose, the dynamics involving healthy cells, HPV and cervical cancer cells will be modelled by a system of five differential equations.

The talk will address the question of control, by distributed source, of scalar conservation laws and of abstract evolution equations. Questions of attainability and backward constructions are also studied. For the case of scalar conservation laws with strictly convex flux (like the Hopf equation), an almost optimal result on subdomain control is established.

The talk is devoted to the theory of matrix quasi-elliptic operators. For some classes of quasi-elliptic operators, isomorphism theorems in special weighted Sobolev spaces are formulated. The results obtained are applied to the study of solvability of equations and systems of Sobolev type.

Sanofi is the world leader in human vaccines, suppling of over 2.5 million doses of vaccines every day allowing immunize more than half a billion people per year against 20 diseases. Mathematical modelling efforts applied to vaccine production aim to accelerate innovation, optimize process design and operation, provide better control and reduce experimentation. Here we will present some examples of mathematical models of different production stages as well as different techniques which are used in Marcy l'Etoile Site of Sanofi, the world's largest vaccine research, development and production site.

The challenges of examining random partitions of space are a significant class of problems in the theory of geometric transformations. Richard Miles calculated moments of areas and perimeters of any order (including expectation) of the random division of space in 1972.

Turing instability of coexistence homogeneous steady-state for reaction-diffusion systems in population biology often leads to stationary patterns.

The talk will cover topics related to Boyarsky-Meyers estimates of gradients of solutions of boundary value problems for elliptic equations.