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1. State-of-the-Art fNIRS for Clinical Scenarios: A Brief Review

Author

Mirdan, Samandari Ali, Nikolaevich, Afonin Andrey, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Rasheed, Jawad, editor, Abu-Mahfouz, Adnan M., editor, and Fahim, Muhammad, editor

Published
2024
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2. On the structure of the $6 \times 6$ copositive cone

Author

Hildebrand, Roland and Afonin, Andrey

Subjects
Mathematics - Optimization and Control, 15B48, 90C26
Abstract

In this work we complement the description of the extreme rays of the $6 \times 6$ copositive cone with some topological structure. In a previous paper we decomposed the set of extreme elements of this cone into a disjoint union of pieces of algebraic varieties of different dimension. In this paper we link this classification to the recently introduced combinatorial characteristic called extended minimal zero support set. We determine those components which are essential, i.e., which are not embedded in the boundary of other components. This allows to drastically decrease the number of cases one has to consider when investigating different properties of the $6 \times 6$ copositive cone. As an application, we construct an example of a copositive $6 \times 6$ matrix with unit diagonal which does not belong to the Parrilo inner sum of squares relaxation ${\cal K}^{(1)}_6$.

Published
2022

11. Les rayons extrêmes du cône copositif de taille 6x6

Author

Afonin, Andrey, Hildebrand, Roland, Dickinson, Peter, Moscow Institute of Physics and Technology [Moscow] (MIPT), Données, Apprentissage et Optimisation (DAO), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), University of Twente, and University of Twente [Netherlands]

Subjects
non-convex optimization, extreme ray, minimal zero, MSC 2020: 90C26, 15B48, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], copositive matrix
Abstract

International audience; We provide a complete classification of the extreme rays of the 6 × 6 copositive cone COP^6. We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix A ∈ COP^6. To each such minimal zero support set we construct a stratified semi-algebraic manifold in the space of real symmetric 6 × 6 matrices S^6 , parameterized in a semi-trigonometric way, which consists of all exceptional extremal matrices A ∈ COP^6 having this minimal zero support set. Each semi-algebraic stratum is characterized by the supports of the minimal zeros u as well as the supports of the corresponding matrix-vector products Au. The analysis uses recently and newly developed methods that are applicable also to copositive matrices of arbitrary order.

Published
2021

12. The extreme rays of the 6 × 6 copositive cone

Author

Afonin, Andrey, Hildebrand, Roland, Dickinson, Peter, Moscow Institute of Physics and Technology [Moscow] (MIPT), Données, Apprentissage et Optimisation (DAO), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and University of Twente [Netherlands]

Subjects
non-convex optimization, extreme ray, minimal zero, MSC 2020: 90C26, 15B48, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], copositive matrix
Abstract

International audience; We provide a complete classification of the extreme rays of the 6 × 6 copositive cone COP^6. We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix A ∈ COP^6. To each such minimal zero support set we construct a stratified semi-algebraic manifold in the space of real symmetric 6 × 6 matrices S^6 , parameterized in a semi-trigonometric way, which consists of all exceptional extremal matrices A ∈ COP^6 having this minimal zero support set. Each semi-algebraic stratum is characterized by the supports of the minimal zeros u as well as the supports of the corresponding matrix-vector products Au. The analysis uses recently and newly developed methods that are applicable also to copositive matrices of arbitrary order.

Published
2021

15. Essential components of extremal copositive matrices

Author

Hildebrand, Roland, Afonin, Andrey, Données, Apprentissage et Optimisation (DAO), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Moscow Institute of Physics and Technology [Moscow] (MIPT), Données, Apprentissage et Optimisation [2020-....] (DAO [2020-....]), Laboratoire Jean Kuntzmann [2020-....] (LJK [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), and Université Grenoble Alpes [2020-....] (UGA [2020-....])

Subjects
MSC: 15B48, 90C26, extreme ray, minimal zero, algebraic manifolds, Mathematics::Differential Geometry, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], copositive matrix, Mathematics::Geometric Topology, Mathematics::Symplectic Geometry
Abstract

We represent the ensemble of extremal copositive matrices A ∈ COP^n of the copositive cone as a disjoint union of a finite number of algebraic manifolds. These manifolds are strata of algebraic sets, each of which is characterized by a finite collection E of pairs of index sets. We give necessary conditions on E to correspond to an algebraic set containing exceptional extremal matrices of COP^n. A manifold of extremal matrices is essential if it is not contained in the closure of another such manifold. We compute the essential manifolds of extremal matrices of the cone COP^6.

Published
2020

24. ChemInform Abstract: N‐Vinyl‐2‐(trifluoroacetylethynyl)pyrroles and E‐2‐(1‐Bromo‐2‐trifluoroacetylethenyl)pyrroles: Cross‐Coupling vs. Addition During C—H‐Functionalization of Pyrroles with Bromotrifluoroacetylacetylene in Solid Al2O3 Medium. H‐Bonding Control.

Author

Tomilin, Denis N., primary, Gotsko, Maxim D., additional, Sobenina, Lyubov N., additional, Ushakov, Igor A., additional, Afonin, Andrey V., additional, Soshnikov, Dmitri Yu., additional, Trofimov, Alexander B., additional, Koldobsky, Andrey B., additional, and Trofimov, Boris A., additional

Published
2016
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25. N -Vinyl-2-(trifluoroacetylethynyl)pyrroles and E -2-(1-bromo-2-trifluoroacetylethenyl)pyrroles: Cross-coupling vs. addition during C H-functionalization of pyrroles with bromotrifluoroacetylacetylene in solid Al 2 O 3 medium. H-bonding control

Author

Tomilin, Denis N., primary, Gotsko, Maxim D., additional, Sobenina, Lyubov N., additional, Ushakov, Igor A., additional, Afonin, Andrey V., additional, Soshnikov, Dmitri Yu., additional, Trofimov, Alexander B., additional, Koldobsky, Andrey B., additional, and Trofimov, Boris A., additional

Published
2016
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27. Synthesis of 2-(Selenophen-2-yl)pyrroles and Their Electropolymerization to Electrochromic Nanofilms

Author

Trofimov, Boris A., primary, Schmidt, Elena Yu., additional, Mikhaleva, Albina I., additional, Pozo-Gonzalo, Cristina, additional, Pomposo, Jose A., additional, Salsamendi, Maitane, additional, Protzuk, Nadezhda I., additional, Zorina, Nadezhda V., additional, Afonin, Andrey V., additional, Vashchenko, Alexander V., additional, Levanova, Ekaterina P., additional, and Levkovskaya, Galina G., additional

Published
2009
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30. Synthesis, Structure, and Spectral Properties of Bis(pyrrol-2-yl)pyridines

Author

Trofimov, Boris A., primary, Vasil'tsov, Alexander M., additional, Schmidt, Elena Yu., additional, Zorina, Nadezhda V., additional, Afonin, Andrey V., additional, Mikhaleva, Al'bina I., additional, Petrushenko, Konstantin B., additional, Ushakov, Igor A., additional, Krivdin, Leonid B., additional, Belsky, Vitaly K., additional, and Bryukvina, Lyubov I., additional

Published
2005
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31. Expedient routes to 4,4-dialkyl- 5-methylene-1,3-oxazolines

Author

Schmidt, Elena Yu., primary, Vasil’tsov, Alexander M., additional, Mikhaleva, Al’bina I., additional, Zaitsev, Alexey B., additional, Afonin, Andrey V., additional, Toryashinova, Dar’ya-Syren D., additional, Klyba, Ludmila V., additional, Arndt, Jan-Dirk, additional, and Henkelmann, Jochem, additional

Published
2003
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40. 2-Arylazo-1-vinylpyrroles: A Novel Promising Family of Reactive Dyes

Author

Trofimov, Boris A., Schmidt, Elena Yu., Mikhaleva, Al’bina I., Vasil’tsov, Alexander M., Zaitsev, Alexey B., Smolyanina, Natalia S., Senotrusova, Elena Yu., Afonin, Andrey V., Ushakov, Igor’ A., Petrushenko, Konstantin B., Kazheva, Olga N., Dyachenko, Oleg A., Smirnov, Vladimir V., Schmidt, Alexander F., Markova, Marina V., and Morozova, Ludmila V.

Abstract

New reactive dyes, 2-arylazo-1-vinylpyrroles, have been synthesized in 52–94 % yield by a modified azo coupling of readily accessible 1-vinylpyrroles with arenediazonium hydrocarbonates in aqueous ethanol (≈3:1) at 0 °C. The λmax values for the UV/Vis absorption of the dyes ranges from 377.8–480.6 nm with log ε = 4.11–4.99, and this strongly depends on the substituent structure both in the pyrrole and the benzene ring, and is indicative of highly polarizable and tunable chromophores. X-ray, 1H NMR spectroscopic and quantum chemical studies [B3LYP/6-311 (d,p)] show the E,anti,anti isomer of the dyes to be the most stable under normal conditions. The dyes are reversibly protonated and complex to BF3 with a color change. Their copolymerization across the vinyl group affords intrinsically colored copolymers. They have also been shown to act as good ligands in the Pd-catalyzed Heck alkene arylation. Thus, the properties of the novel dyes are promising for creating new molecular switches, memory and recording devices, acid-base and metal sensors, as well as transition-metal complex catalysts.(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

Published
2006
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41. ChemInform Abstract: N-Vinyl-2-(trifluoroacetylethynyl)pyrroles and E-2-(1-Bromo-2-trifluoroacetylethenyl)pyrroles: Cross-Coupling vs. Addition During C-H-Functionalization of Pyrroles with Bromotrifluoroacetylacetylene in Solid Al2O3 Medium. H-Bonding Control.

Author

Tomilin, Denis N., Gotsko, Maxim D., Sobenina, Lyubov N., Ushakov, Igor A., Afonin, Andrey V., Soshnikov, Dmitri Yu., Trofimov, Alexander B., Koldobsky, Andrey B., and Trofimov, Boris A.

Published
2016
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44. Evidence for the O-H···O=C Resonance-Assisted Hydrogen Bond in Tropolones and Quantification of its σ- and π-Components Using Molecular Tailoring Approach.

Author

Afonin AV and Rusinska-Roszak D

Abstract

For a series of tropolones, the nature of the intramolecular O-H×××O=C hydrogen bond closing the five-membered quasi-cycle was studied. Enhancement of conjugation in the hydrogen-bonded rotamer was revealed. Quantification of hydrogen bond energy in tropolones via the molecular tailoring approach yields values in the range from 15 to 20 kcal/mol suggesting that the intramolecular interaction in tropolones has nature of the resonance-assisted hydrogen bond. The total resonance-assisted hydrogen bond energy in the tropolones was divided into σ- and π-components. The magnitudes of total energy of resonance-assisted hydrogen bond in the substituted tropolones can be controlled by the electronic properties of the substituents at the tropone ring. In 3-, 4-, and 5-substituted tropolones, the resonance-assisted hydrogen bond energy is raised due to electron-donating substituents and lowered due to electron-withdrawing ones. The opposite trend is observed in 7-substituted tropolones. The size of the π-shares plays a crucial role in establishing the total energy of resonance-assisted hydrogen bond. The reason for the occurrence of a resonance-assisted hydrogen bond in the tropolones is the molecular backbone aromaticity, since, in accordance with the Hückel rule, 10 π-electrons are delocalized., (© 2024 Wiley‐VCH GmbH.)

Published
2024
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45. Cyanoquinolines and Furo[3,4- b ]quinolinones Formation via On-The-Spot 2,3-Functionalization of Quinolines with Cyanopropargylic Alcohols.

Author

Belyaeva KV, Nikitina LP, Afonin AV, Grishchenko LA, and Trofimov BA

Abstract

A convenient approach to 2-(1-ethoxyalkoxy)-3-cyanoquinolines (in up to 50% yields) has been developed. The approach comprises functionalization of quinolines with acetals of cyanopropargylic alcohols (KOH/H 2 O/MeCN, 55-60 °C) followed by their transformation to furo[3,4- b ]quinolinones (in up to 98% yields) via the sequential removal of acetal protection and intramolecular cyclization/hydration (7% aqueous HCl, acetone, 20-25 °C).

Published
2021
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46. 2 H -Indazole Tautomers Stabilized by Intra- and Intermolecular Hydrogen Bonds.

Author

Sigalov MV, Afonin AV, Sterkhova IV, and Shainyan BA

Abstract

2-[(2 H -Indazol-3-yl)methylene]-1 H -indene-1,3(2 H )-dione 6 and ( E )-2-[(2 H -indazol-3-yl)methylene]-2,3-dihydro-1 H -inden-1-one 7 have been synthesized. In the crystal, the NH hydrogen atom of 6 is disordered between the N(1) and N(2) atoms with the population ratio of 0.69:0.31. Molecule 7 crystallizes in two tautomeric polymorphs: 7 -1 H tautomer (yellow) and 7 -2 H tautomer (red). Both 6 and 7 form centrosymmetric dimers in the crystal with the monomeric units linked by C═O···H···N bifurcated hydrogen bonds in 6 and N-H···N hydrogen bonds in 7 . According to 1 H and 13 C NMR data, in DMSO- d 6 solution, the 6 -1 H tautomer predominates, whereas in less polar CDCl 3 or CD 2 Cl 2 , the 6 -2 H tautomer is stabilized by a strong N-H···O═C intramolecular hydrogen bond. Compound 7 in dimethyl sulfoxide (DMSO) or ethanol solutions exists in the form of 7 -1 H and 7 -2 H tautomers. On the example of the 7 -2 H tautomer, it was shown for the first time that the 2 H tautomers of 3-substituted indazoles can be stabilized by an intermolecular hydrogen bond and may remain in aprotic solvents almost indefinitely. However, in the open air or in water, fast 2 H → 1 H tautomerization occurs. As follows from density functional theory calculations, the high stability of the 2 H form in solution is due to the formation of centrosymmetric dimers, which are more stable than the corresponding dimers of the 1 H tautomer.

Published
2019
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47. Synthesis of 2-(selenophen-2-yl)pyrroles and their electropolymerization to electrochromic nanofilms.

Author

Trofimov BA, Schmidt EY, Mikhaleva AI, Pozo-Gonzalo C, Pomposo JA, Salsamendi M, Protzuk NI, Zorina NV, Afonin AV, Vashchenko AV, Levanova EP, and Levkovskaya GG

Subjects
Molecular Structure, Nanotechnology, Organoselenium Compounds chemistry, Polymers chemistry, Pyrroles chemistry, Vinyl Compounds chemistry, Alkynes chemistry, Organoselenium Compounds chemical synthesis, Pyrroles chemical synthesis, Vinyl Compounds chemical synthesis
Abstract

Bridging pyrrole and selenophene chemistries: Molecular assemblies have been developed that allow scrutiny of the electronic communication between pyrrole and selenophene nuclei. Divergent syntheses of 2-(selenophen-2-yl)pyrroles and their N-vinyl derivatives from available 2-acylselenophenes and acetylenes in a one-pot procedure have been devised (see scheme), which provide access to these exotic heterocyclic ensembles.The divergent syntheses of 2-(selenophen-2-yl)pyrroles and their N-vinyl derivatives from available 2-acylselenophenes and acetylenes in a one-pot procedure make these exotic heterocyclic ensembles accessible. Now we face a potentially vast area for exploration with a great diversity of far-reaching consequences including conducting electrochromic polymers with repeating of pyrrole and selenophene units (emerging rivalry for polypyrroles and polyselenophenes), the synthesis of functionalized pyrrole-selenophene assembles for advanced materials, biochemistry and medicine, exciting models for theory of polymer conductivity.

Published
2009
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