Example of two different potentials which have practically the same fixed-energy phase shifts

It is shown that the Newton-Sabatier procedure for inverting the fixed-energy phase shifts for a potential is not an inversion method but a parameter-fitting procedure. Theoretically there is no guarantee that this procedure is applicable to the given set of the phase shifts, if it is applicable, there is no guaran- tee that the potential it produces generates the phase shifts from which it was reconstructed. Moreover, no generic potential, specifically, no potential which is not analytic in a neighborhood of the positive real semiaxis can be reconstructed by the Newton-Sabatier procedure. A numerical method is given for finding spherically symmetric compactly supported potentials which produce practically the same set of fixed-energy phase shifts for all values of angular momentum. Concrete example of such potentials is given

On deconvolution problems: numerical aspects

An optimal algorithm is described for solving the deconvolution problem of the form ${\bf k}u:=\int_0^tk(t-s)u(s)ds=f(t)$ given the noisy data $f_\delta$, $||f-f_\delta||\leq \delta.$ The idea of the method consists of the representation ${\bf k}=A(I+S)$, where $S$ is a compact operator, $I+S$ is injective, $I$ is the identity operator, $A$ is not boundedly invertible, and an optimal regularizer is constructed for $A$. The optimal regularizer is constructed using the results of the paper MR 40#5130.Comment: 7 figure

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

EPMA-World Congress 2015: Bonn, Germany. 3-5 September 2015

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Ivanova, Michail V. Eremin, Maria V. Rostovtseva A23 Сentral aortic pressure and indexes of augmentation in young persons in view of risk factors Maria E. Evsevyeva, Michail V. Eremin, Vladimir I. Koshel, Oksana V. Sergeeva, Nadesgda M. Konovalova A24 Breast cancer prediction and prevention: Are reliable biomarkers in horizon? Shantanu Girotra, Olga Golubnitschaja A25 Flammer Syndrome and potential formation of pre-metastatic niches: A multi-centred study on phenotyping, patient stratification, prediction and potential prevention of aggressive breast cancer and metastatic disease Olga Golubnitschaja, Manuel Debald, Walther Kuhn, Kristina Yeghiazaryan, Rostyslav V. Bubnov, Vadym M. 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Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)