Exact controllability for wave equation on general quantum graphs with non-smooth controls

In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a constructive proof that the wave equation on the graph is exactly controllable if $H^1(0,T)'$ Neumann controllers are placed at the active vertices and $L^2(0,T)$ Dirichlet controllers are placed at the active edges. The proofs for the shape and velocity controllability are purely dynamical, while the proof for the exact controllability utilizes both dynamical and moment method approaches. The control time for this construction is determined by the chosen orientation and path decomposition of the graph

Rational in silico design of aptamers for organophosphates based on the example of paraoxon

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Poisoning by organophosphates (OPs) takes one of the leading places in the total number of exotoxicoses. Detoxication of OPs at the first stage of the poison entering the body could be achieved with the help of DNA- or RNA-aptamers, which are able to bind poisons in the bloodstream. The aim of the research was to develop an approach to rational in silico design of aptamers for OPs based on the example of paraoxon. From the published sequence of an aptamer binding organophosphorus pesticides, its threedimensional model has been constructed. The most probable binding site for paraoxon was determined by molecular docking and molecular dynamics (MD) methods. Then the nucleotides of the binding site were mutated consequently and the values of free binding energy have been calculated using MD trajectories and MM-PBSA approach. On the basis of the energy values, two sequences that bind paraoxon most efficiently have been selected. The value of free binding energy of paraoxon with peripheral anionic site of acetylcholinesterase (AChE) has been calculated as well. It has been revealed that the aptamers found bind paraoxon more effectively than AChE. The peculiarities of paraoxon interaction with the aptamers nucleotides have been analyzed. The possibility of improving in silico approach for aptamer selection is discussed

Reconstructing the potential for the 1D Schrödinger equation from boundary measurements

International audienceWe consider the inverse problem of determining the potential in the dynamical Schrödinger equation on the interval by the measurement on the boundary. We use the Boundary Control method to recover the spectrum of the problem from the observation at either left or right end points. Using the specificity of the one-dimensional situation we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only the finite number of eigenvalues are known and prove the convergence of the method