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8. Kolyada Inequality between Mixed Moduli of Smoothness in Metrics \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{L}_{\boldsymbol{p}}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{L}_{\boldsymbol{\infty}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{L}_{\boldsymbol{p}}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{L}_{\boldsymbol{\infty}}$$\end{document}

Author

Potapov†, M. K. and Simonov, B. V.

Published
2022
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13. Designing Robotic Groups Under Incomplete Information About the Dominance of Many Goals

Author

Misyurin, S. Yu., Nelyubin, A. P., Potapov, M. A., Ceccarelli, Marco, Series Editor, Hernandez, Alfonso, Editorial Board Member, Huang, Tian, Editorial Board Member, Takeda, Yukio, Editorial Board Member, Corves, Burkhard, Editorial Board Member, Agrawal, Sunil, Editorial Board Member, Misyurin, Sergey Yu., editor, Arakelian, Vigen, editor, and Avetisyan, Arutyun I., editor

Published
2020
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15. Refinement of Relations between Mixed Moduli of Smoothness in the Metrics of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\infty$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\infty$$\end{document}

Author

Potapov, M. K. and Simonov, B. V.

Published
2021
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16. Refinement of the Relations between Mixed Smoothness Moduli in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ L_{1} $\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ L_{q} $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ L_{1} $\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ L_{q} $\end{document} Metrics

Author

Potapov, M. K. and Simonov, B. V.

Published
2021
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17. Global fine-resolution data on springtail abundance and community structure

Author

Potapov, A. M., Chen, T. -W., Striuchkova, A. V., Alatalo, J. M., Alexandre, D., Arbea, J., Ashton, T., Ashwood, F., Babenko, A. B., Bandyopadhyaya, I., Baretta, C. R. D. M., Baretta, D., Barnes, A. D., Bellini, B. C., Bendjaballah, M., Berg, M. P., Bernava, V., Bokhorst, S., Bokova, A. I., Bolger, T., Bouchard, M., Brito, R. A., Buchori, D., Castano-Meneses, G., Chauvat, M., Chomel, M., Chow, Y., Chown, S. L., Classen, A. T., Cortet, J., Cuchta, P., de la Pedrosa, A. M., De Lima, E. C. A., Deharveng, L. E., Doblas Miranda, E., Drescher, J., Eisenhauer, N., Ellers, J., Ferlian, O., Ferreira, S. S. D., Ferreira, A. S., Fiera, C., Filser, J., Franken, O., Fujii, S., Koudji, E. G., Gao, M., Gendreau-Berthiaume, B., Gers, C., Greve, M., Hamra-Kroua, S., Handa, I. T., Hasegawa, M., Heiniger, C., Hishi, T., Holmstrup, M., Homet, P., Hoye, T. T., Ivask, M., Jacques, B., Janion-Scheepers, C., Jochum, M., Joimel, S., Jorge, B. C. S., Jucevica, E., Kapinga, E. M., Kovac, L., Krab, E. J., Krogh, P. H., Kuu, A., Kuznetsova, N., Lam, W. N., Lin, D., Lindo, Z., Liu, A. W. P., Lu, J. -Z., Lucianez, M. J., Marx, M. T., Mawan, A., Mccary, M. A., Minor, M. A., Mitchell, G. I., Moreno, D., Nakamori, T., Negri, Ilaria, Nielsen, U. N., Ochoa-Hueso, R., Oliveira Filho, L. C. I., Palacios-Vargas, J. G., Pollierer, M. M., Ponge, J. -F., Potapov, M. B., Querner, P., Rai, B., Raschmanova, N., Rashid, M. I., Raymond-Leonard, L. J., Reis, A. S., Ross, G. M., Rousseau, L., Russell, D. J., Saifutdinov, R. A., Salmon, S., Santonja, M., Saraeva, A. K., Sayer, E. J., Scheunemann, N., Scholz, C., Seeber, J., Shaw, P., Shveenkova, Y. B., Slade, E. M., Stebaeva, S., Sterzynska, M., Sun, X., Susanti, W. I., Taskaeva, A. A., Tay, L. S., Thakur, M. P., Treasure, A. M., Tsiafouli, M., Twala, M. N., Uvarov, A. V., Venier, L. A., Widenfalk, L. A., Widyastuti, R., Winck, B., Winkler, D., Wu, D., Xie, Z., Yin, R., Zampaulo, R. A., Zeppelini, D., Zhang, B., Zoughailech, A., Ashford, O., Klauberg-Filho, O., Scheu, S., Negri I. (ORCID:0000-0001-5188-1408), Potapov, A. M., Chen, T. -W., Striuchkova, A. V., Alatalo, J. M., Alexandre, D., Arbea, J., Ashton, T., Ashwood, F., Babenko, A. B., Bandyopadhyaya, I., Baretta, C. R. D. M., Baretta, D., Barnes, A. D., Bellini, B. C., Bendjaballah, M., Berg, M. P., Bernava, V., Bokhorst, S., Bokova, A. I., Bolger, T., Bouchard, M., Brito, R. A., Buchori, D., Castano-Meneses, G., Chauvat, M., Chomel, M., Chow, Y., Chown, S. L., Classen, A. T., Cortet, J., Cuchta, P., de la Pedrosa, A. M., De Lima, E. C. A., Deharveng, L. E., Doblas Miranda, E., Drescher, J., Eisenhauer, N., Ellers, J., Ferlian, O., Ferreira, S. S. D., Ferreira, A. S., Fiera, C., Filser, J., Franken, O., Fujii, S., Koudji, E. G., Gao, M., Gendreau-Berthiaume, B., Gers, C., Greve, M., Hamra-Kroua, S., Handa, I. T., Hasegawa, M., Heiniger, C., Hishi, T., Holmstrup, M., Homet, P., Hoye, T. T., Ivask, M., Jacques, B., Janion-Scheepers, C., Jochum, M., Joimel, S., Jorge, B. C. S., Jucevica, E., Kapinga, E. M., Kovac, L., Krab, E. J., Krogh, P. H., Kuu, A., Kuznetsova, N., Lam, W. N., Lin, D., Lindo, Z., Liu, A. W. P., Lu, J. -Z., Lucianez, M. J., Marx, M. T., Mawan, A., Mccary, M. A., Minor, M. A., Mitchell, G. I., Moreno, D., Nakamori, T., Negri, Ilaria, Nielsen, U. N., Ochoa-Hueso, R., Oliveira Filho, L. C. I., Palacios-Vargas, J. G., Pollierer, M. M., Ponge, J. -F., Potapov, M. B., Querner, P., Rai, B., Raschmanova, N., Rashid, M. I., Raymond-Leonard, L. J., Reis, A. S., Ross, G. M., Rousseau, L., Russell, D. J., Saifutdinov, R. A., Salmon, S., Santonja, M., Saraeva, A. K., Sayer, E. J., Scheunemann, N., Scholz, C., Seeber, J., Shaw, P., Shveenkova, Y. B., Slade, E. M., Stebaeva, S., Sterzynska, M., Sun, X., Susanti, W. I., Taskaeva, A. A., Tay, L. S., Thakur, M. P., Treasure, A. M., Tsiafouli, M., Twala, M. N., Uvarov, A. V., Venier, L. A., Widenfalk, L. A., Widyastuti, R., Winck, B., Winkler, D., Wu, D., Xie, Z., Yin, R., Zampaulo, R. A., Zeppelini, D., Zhang, B., Zoughailech, A., Ashford, O., Klauberg-Filho, O., Scheu, S., and Negri I. (ORCID:0000-0001-5188-1408)

Abstract

Springtails (Collembola) inhabit soils from the Arctic to the Antarctic and comprise an estimated ~32% of all terrestrial arthropods on Earth. Here, we present a global, spatially-explicit database on springtail communities that includes 249,912 occurrences from 44,999 samples and 2,990 sites. These data are mainly raw sample-level records at the species level collected predominantly from private archives of the authors that were quality-controlled and taxonomically-standardised. Despite covering all continents, most of the sample-level data come from the European continent (82.5% of all samples) and represent four habitats: woodlands (57.4%), grasslands (14.0%), agrosystems (13.7%) and scrublands (9.0%). We included sampling by soil layers, and across seasons and years, representing temporal and spatial within-site variation in springtail communities. We also provided data use and sharing guidelines and R code to facilitate the use of the database by other researchers. This data paper describes a static version of the database at the publication date, but the database will be further expanded to include underrepresented regions and linked with trait data.

Published
2024

18. A Stable Solution of a Nonuniformly Perturbed Quadratic Minimization Problem by the Extragradient Method with Step Size Separated from Zero.

Author

Artem'eva, L. A., Dryazhenkov, A. A., and Potapov, M. M.

Abstract

A quadratic minimization problem is considered in Hilbert spaces under constraints given by a linear operator equation and a convex quadratic inequality. The main feature of the problem statement is that the practically available approximations to the exact linear operators specifying the criterion and the constraints converge to them only strongly pointwise rather than in the uniform operator norm, which makes it impossible to justify the use of the classical regularization methods. We propose a regularization method that is applicable in the presence of error estimates for approximate operators in pairs of other operator norms, which are weaker than the original ones. For each of the operators, the pair of corresponding weakened operator norms is obtained by strengthening the norm in the domain of the operator and weakening the norm in its range. The weakening of operator norms usually makes it possible to estimate errors in operators where this was fundamentally impossible in the original norms, for example, in the finite-dimensional approximation of a noncompact operator. From the original optimization formulation, a transition is made to the problem of finding a saddle point of the Lagrange function. The proposed numerical method for finding a saddle point is an iterative regularized extragradient two-stage procedure. At the first stage of each iteration, an approximation to the optimal value of the criterion is refined; at the second stage, the approximate solution with respect to the main variable is refined. Compared to the methods previously developed by the authors and working under similar information conditions, this method is preferable for practical implementation, since it does not require the gradient step size to converge to zero. The main result of the work is the proof of the strong convergence of the approximations generated by the method to one of the exact solutions to the original problem in the norm of the original space. [ABSTRACT FROM AUTHOR]

Published
2024
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22. Mixed Moduli of Smoothness in $L_p$, $1<p<\infty$

Author

Potapov, M. K., Simonov, B. V., and Tikhonov, S. Yu.

Subjects
Mathematics - Classical Analysis and ODEs, 26A15, 26A33, 42A10, 41A25, 41A30, 42B05, 26B05
Abstract

In this paper we survey recent developments over the last 25 years on the mixed fractional moduli of smoothness of periodic functions from $L_p$, $1

Published
2013

36. Globally invariant metabolism but density-diversity mismatch in springtails

Author

Potapov, A. M., Guerra, C. A., van den Hoogen, J., Babenko, A., Bellini, B. C., Berg, M. P., Chown, S. L., Deharveng, L., Kováč, Ľ., Kuznetsova, N. A., Ponge, J. F., Potapov, M. B., Russell, D. J., Alexandre, D., Alatalo, J. M., Arbea, J. I., Bandyopadhyaya, I., Bernava, V., Bokhorst, S., Bolger, T., Castaño-Meneses, G., Chauvat, M., Chen, T. W., Chomel, M., Classen, A. T., Cortet, J., Čuchta, P., Manuela de la Pedrosa, A., Ferreira, S. S. D., Fiera, C., Filser, J., Franken, O., Fujii, S., Koudji, E. G., Gao, M., Gendreau-Berthiaume, B., Gomez-Pamies, D. F., Greve, M., Tanya Handa, I., Heiniger, C., Holmstrup, M., Homet, P., Ivask, M., Janion-Scheepers, C., Jochum, M., Joimel, S., Claudia, S. Jorge B., Jucevica, E., Ferlian, O., Iuñes de Oliveira Filho, L. C., Klauberg-Filho, O., Baretta, D., Krab, E. J., Kuu, A., de Lima, E. C. A., Lin, D., Lindo, Z., Liu, A., Lu, J. Z., Luciañez, M. J., Marx, M. T., Mccary, M. A., Minor, M. A., Nakamori, T., Negri, Ilaria, Ochoa-Hueso, R., Palacios-Vargas, J. G., Pollierer, M. M., Querner, P., Raschmanová, N., Rashid, M. I., Raymond-Léonard, L. J., Rousseau, L., Saifutdinov, R. A., Salmon, S., Sayer, E. J., Scheunemann, N., Scholz, C., Seeber, J., Shveenkova, Y. B., Stebaeva, S. K., Sterzynska, M., Sun, X., Susanti, W. I., Taskaeva, A. A., Thakur, M. P., Tsiafouli, M. A., Turnbull, M. S., Twala, M. N., Uvarov, A. V., Venier, L. A., Widenfalk, L. A., Winck, B. R., Winkler, D., Wu, D., Xie, Z., Yin, R., Zeppelini, D., Crowther, T. W., Eisenhauer, N., Negri I. (ORCID:0000-0001-5188-1408), Potapov, A. M., Guerra, C. A., van den Hoogen, J., Babenko, A., Bellini, B. C., Berg, M. P., Chown, S. L., Deharveng, L., Kováč, Ľ., Kuznetsova, N. A., Ponge, J. F., Potapov, M. B., Russell, D. J., Alexandre, D., Alatalo, J. M., Arbea, J. I., Bandyopadhyaya, I., Bernava, V., Bokhorst, S., Bolger, T., Castaño-Meneses, G., Chauvat, M., Chen, T. W., Chomel, M., Classen, A. T., Cortet, J., Čuchta, P., Manuela de la Pedrosa, A., Ferreira, S. S. D., Fiera, C., Filser, J., Franken, O., Fujii, S., Koudji, E. G., Gao, M., Gendreau-Berthiaume, B., Gomez-Pamies, D. F., Greve, M., Tanya Handa, I., Heiniger, C., Holmstrup, M., Homet, P., Ivask, M., Janion-Scheepers, C., Jochum, M., Joimel, S., Claudia, S. Jorge B., Jucevica, E., Ferlian, O., Iuñes de Oliveira Filho, L. C., Klauberg-Filho, O., Baretta, D., Krab, E. J., Kuu, A., de Lima, E. C. A., Lin, D., Lindo, Z., Liu, A., Lu, J. Z., Luciañez, M. J., Marx, M. T., Mccary, M. A., Minor, M. A., Nakamori, T., Negri, Ilaria, Ochoa-Hueso, R., Palacios-Vargas, J. G., Pollierer, M. M., Querner, P., Raschmanová, N., Rashid, M. I., Raymond-Léonard, L. J., Rousseau, L., Saifutdinov, R. A., Salmon, S., Sayer, E. J., Scheunemann, N., Scholz, C., Seeber, J., Shveenkova, Y. B., Stebaeva, S. K., Sterzynska, M., Sun, X., Susanti, W. I., Taskaeva, A. A., Thakur, M. P., Tsiafouli, M. A., Turnbull, M. S., Twala, M. N., Uvarov, A. V., Venier, L. A., Widenfalk, L. A., Winck, B. R., Winkler, D., Wu, D., Xie, Z., Yin, R., Zeppelini, D., Crowther, T. W., Eisenhauer, N., and Negri I. (ORCID:0000-0001-5188-1408)

Abstract

Soil life supports the functioning and biodiversity of terrestrial ecosystems. Springtails (Collembola) are among the most abundant soil arthropods regulating soil fertility and flow of energy through above- and belowground food webs. However, the global distribution of springtail diversity and density, and how these relate to energy fluxes remains unknown. Here, using a global dataset representing 2470 sites, we estimate the total soil springtail biomass at 27.5 megatons carbon, which is threefold higher than wild terrestrial vertebrates, and record peak densities up to 2 million individuals per square meter in the tundra. Despite a 20-fold biomass difference between the tundra and the tropics, springtail energy use (community metabolism) remains similar across the latitudinal gradient, owing to the changes in temperature with latitude. Neither springtail density nor community metabolism is predicted by local species richness, which is high in the tropics, but comparably high in some temperate forests and even tundra. Changes in springtail activity may emerge from latitudinal gradients in temperature, predation and resource limitation in soil communities. Contrasting relationships of biomass, diversity and activity of springtail communities with temperature suggest that climate warming will alter fundamental soil biodiversity metrics in different directions, potentially restructuring terrestrial food webs and affecting soil functioning.

Published
2023

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