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22 results on '"Pasechnik, D.V."'

2. Groups acting on necklaces and sandpile groups

Author

Duzhin, S.V. and Pasechnik, D.V.

Subjects
Jewelry, Mathematics
Abstract

We introduce a group naturally acting on aperiodic necklaces of length n with two colors using a one-to-one correspondence between such necklaces and irreducible polynomials of degree n over the field F2 of two elements. We notice that this group is isomorphic to the quotient group of nondegenerate circulant matrices of size n over that field modulo a natural cyclic subgroup. Our groups turn out to be isomorphic to the sandpile groups for a special sequence of directed graphs. Bibliography: 15 titles., UDC 515.16 1. INTRODUCTION This work originated in the research of the first author related to the Drinfeld associator (6). It is well known (e.g., see (5)) that the logarithm [...]

Published
2014

5. SciPy 1.0: fundamental algorithms for scientific computing in Python: 24 February 2020 : An amendment to this paper has been published and can be accessed via a link at the top of the paper

Author

Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, I., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., Mulbregt, P., Vijaykumar, A., Bardelli, A.P., Rothberg, A., Hilboll, A., Kloeckner, A., Scopatz, A., Lee, A., Rokem, A., Woods, C.N., Fulton, C., Masson, C., Häggström, C., Fitzgerald, C., Nicholson, D.A., Hagen, D.R., Pasechnik, D.V., Olivetti, E., Martin, E., Wieser, E., Lenders, F., Silva, Fabrice, Wilhelm, F., Young, G., Price, G.A., Ingold, G.-L., Allen, G.E., Lee, G.R., Audren, H., Probst, Irvin, Dietrich, J.P., Silterra, J., Webber, J.T., Slavič, J., Nothman, J., Buchner, J., Kulick, J., Schönberger, J.L., Miranda Cardoso, J.V., Reimer, J., Harrington, J., Rodríguez, J.L.C., Nunez-Iglesias, J., Kuczynski, J., Tritz, K., Thoma, M., Newville, M., Kümmerer, M., Bolingbroke, M., Tartre, M., Pak, M., Smith, N.J., Nowaczyk, N., Shebanov, N., Pavlyk, O., Brodtkorb, P.A., Lee, P., McGibbon, R.T., Feldbauer, R., Lewis, S., Tygier, S., Sievert, S., Vigna, S., Peterson, S., More, S., Pudlik, T., Oshima, T., Pingel, T.J., Robitaille, T.P., Spura, T., Jones, T.R., Cera, T., Leslie, T., Zito, T., Krauss, T., Upadhyay, U., Halchenko, Y.O., Vázquez-Baeza, Y., SciPy 1.0, Contributors, Low Temperature Laboratory, TKK Helsinki University of Technology (TKK), Centre Interdisciplinaire de Nanoscience de Marseille (CINaM), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne-Centre National de la Recherche Scientifique (CNRS), SNECMA Villaroche [Moissy-Cramayel], Safran Group, New Technologies Research Centre [Plzeň] (NTC), University of West Bohemia [Plzeň ], Institute of Environmental Physics [Bremen] (IUP), University of Bremen, Istituto Nazionale di Ricerca Metrologica (INRiM), Laboratoire Chrono-environnement - CNRS - UBFC (UMR 6249) (LCE), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Sons, Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), European Synchrotron Radiation Facility (ESRF), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Max Planck Institute for Solar System Research (MPS), Max-Planck-Gesellschaft, University of Chicago, Consortium of Advanced Radiation Sciences, Advanced Photon Source, GSECARS, University of Chicago, Laboratoire de physique des gaz et des plasmas (LPGP), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), The Open University [Milton Keynes] (OU), Nobeyama Radio Observatory, Gommers, Ralf [0000-0002-0300-3333], Haberland, Matt [0000-0003-4806-3601], Reddy, Tyler [0000-0003-2364-6157], van der Walt, Stéfan J. [0000-0001-9276-1891], Millman, K. Jarrod [0000-0002-5263-5070], Nelson, Andrew R. J. [0000-0002-4548-3558], Laxalde, Denis [0000-0002-5540-4825], Ribeiro, Antônio H. [0000-0003-3632-8529], van Mulbregt, Paul [0000-0002-2382-8308], Apollo - University of Cambridge Repository, van der Walt, Stéfan J [0000-0001-9276-1891], Millman, K Jarrod [0000-0002-5263-5070], Nelson, Andrew RJ [0000-0002-4548-3558], Ribeiro, Antônio H [0000-0003-3632-8529], Quansight LLC, California Polytechnic State University [San Luis Obispo] (CAL POLY), Los Alamos National Laboratory (LANL), AUTRES, National Research University Higher School of Economics [St. Petersburg], Tallinn Technical University, University of California [Berkeley] (UC Berkeley), University of California (UC), University of Birmingham [Birmingham], Skolkovo Innovation Center, Australian Nuclear Science and Technology Organisation [Australie] (ANSTO), Enthought Inc, University of Washington [Seattle], University of Massachusetts [Amherst] (UMass Amherst), University of Massachusetts System (UMASS), Bruker BioSpin Corporation, Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne (ENISE)-Centre National de la Recherche Scientifique (CNRS), University of Texas at Austin [Austin], Astronomical Institute Anton Pannekoek (AI PANNEKOEK), University of Amsterdam [Amsterdam] (UvA), Universidade Federal de Minas Gerais [Belo Horizonte] (UFMG), Google LLC, Laboratoire Chrono-environnement (UMR 6249) (LCE), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), and Max-Planck-Institut für Sonnensystemforschung = Max Planck Institute for Solar System Research (MPS)

Subjects
FOS: Computer and information sciences, Computer science, 01 natural sciences, Biochemistry, Computer Science - Software Engineering, 631/45/56, Data Structures and Algorithms (cs.DS), 010303 astronomy & astrophysics, computer.programming_language, 0303 health sciences, Signal processing, Signal Processing, Computer-Assisted, Computational Physics (physics.comp-ph), ddc, Linear algebra, Perspective, Minification, Physics - Computational Physics, Algorithm, Algorithms, Biotechnology, De facto standard, FOS: Physical sciences, Image processing, History, 21st Century, Models, Biological, 706/703/559, Python (Computer program language), Computational science, 03 medical and health sciences, Computer Science - Data Structures and Algorithms, 0103 physical sciences, Computer Simulation, [INFO]Computer Science [cs], ddc:530, Cluster analysis, Molecular Biology, Scientific computing, 030304 developmental biology, Sparse matrix, software, Computational Biology, Cell Biology, Python (programming language), History, 20th Century, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], Software Engineering (cs.SE), Nonlinear Dynamics, Linear Models, Computer Science - Mathematical Software, Programming Languages, 631/114, computer, Mathematical Software (cs.MS), Python
Abstract

SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging scientific algorithms in the Python programming language, with more than 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories, and millions of downloads per year. This includes usage of SciPy in almost half of all machine learning projects on GitHub, and usage by high profile projects including LIGO gravitational wave analysis and creation of the first-ever image of a black hole (M87). The library includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics. In this work, we provide an overview of the capabilities and development practices of the SciPy library and highlight some recent technical developments., Comment: Article source data is available here: https://github.com/scipy/scipy-articles

Published
2020

15. Solving SDP's in Non-commutative Algebras Part I: The Dual-Scaling Algorithm

Author

de Klerk, E., Pasechnik, D.V., Research Group: Operations Research, and Econometrics and Operations Research

Subjects
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, exploiting data structure, MathematicsofComputing_NUMERICALANALYSIS, dual scaling algorithm, semidefinite programming, matrix algebras
Abstract

Semidefinite programming (SDP) may be viewed as an extension of linear programming (LP), and most interior point methods (IPM s) for LP can be extended to solve SDP problems.However, it is far more difficult to exploit data structures (especially sparsity) in the SDP case.In this paper we will look at the data structure where the SDP data matrices lie in a low dimensional matrix algebra.This data structure occurs in several applications, including the lower bounding of the stability number in certain graphs and the crossing number in complete bipartite graphs.We will show that one can reduce the linear algebra involved in an iteration of an IPM to involve matrices of the size of the dimension of the matrix algebra only.In other words, the original sizes of the data matrices do not appear in the computational complexity bound.In particular, we will work out the details for the dual scaling algorithm, since a dual method is most suitable for the types of applications we have in mind.

Published
2005

17. Solving SDP's in Non-commutative Algebras Part I: The Dual-Scaling Algorithm

Author

Klerk, E. de and Pasechnik, D.V.

Subjects
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, jel:C61, MathematicsofComputing_NUMERICALANALYSIS, semidefinite programming, matrix algebras, dual scaling algorithm, exploiting data structure
Abstract

Semidefinite programming (SDP) may be viewed as an extension of linear programming (LP), and most interior point methods (IPM s) for LP can be extended to solve SDP problems.However, it is far more difficult to exploit data structures (especially sparsity) in the SDP case.In this paper we will look at the data structure where the SDP data matrices lie in a low dimensional matrix algebra.This data structure occurs in several applications, including the lower bounding of the stability number in certain graphs and the crossing number in complete bipartite graphs.We will show that one can reduce the linear algebra involved in an iteration of an IPM to involve matrices of the size of the dimension of the matrix algebra only.In other words, the original sizes of the data matrices do not appear in the computational complexity bound.In particular, we will work out the details for the dual scaling algorithm, since a dual method is most suitable for the types of applications we have in mind.

Published
2005

18. On equicut graphs

Author

Deza, M., Pasechnik, D.V., and School of Physical and Mathematical Sciences

Subjects
Mathematics - Metric Geometry, FOS: Mathematics, Mathematics - Combinatorics, Metric Geometry (math.MG), Science::Mathematics::Geometry [DRNTU], Combinatorics (math.CO), 05C12, 52B12, Wiskunde en Informatica
Abstract

The size sz(G) of an l_1-graph G=(V,E) is the minimum of n_f/t_f over all its possible l_1-embeddings f into n_f-dimensional hypercube with scale t_f. In terms of v=|V|, the sum of distances between all the pairs of vertices of G is at most sz(G) v^2/4 for v even, (resp. sz(G)(v-1)(v+1)/4 for v odd). This bound is reached if and only if G is an equicut graph, that is, G admits an l_1-embedding with column sums v/2, v even (resp. (v-1)/2 for v odd). Basic properties of equicut graphs are investigated. A construction of equicut graphs from l_1-graphs via a natural doubling construction is given. It generalizes several well-known constructions of polytopes and distance-regular graphs. Large families of examples, mostly related to polytopes and distance-regular graphs, are presented., 13 pages

Published
1999

21. <f>c</f>-Extensions of the <f>F4(2)</f>-building

Author

Ivanov, A.A. and Pasechnik, D.V.

Subjects
*GEOMETRY, *AUTOMORPHISMS
Abstract

We construct four geometries E1,…,E4 with the diagramsuch that any two elements of type 1 are incident to at most one common element of type 2 and three elements of type 1 are pairwise incident to common elements of type 2 if and only if they are incident to a common element of type 5. The automorphism group Ei of Ei is flag-transitive, isomorphic to 2E6(2) : 2, 3·2E6(2) : 2, 226 : F4(2) and E6(2) : 2, for i=1,2,3 and 4. We calculate the suborbit diagram of the collinearity graph of Ei with respect to the action of Ei. By considering the elements in Ei fixed by a subgroup Ti of order 3 in Ei we obtain four geometries T1,…,T4 with the diagramon which CEi(Ti) induces flag-transitive action, isomorphic to U6(2) : 2, 3·U6(2) : 2, 214 : Sp6(2) and L6(2) : 2 for i=1,2,3 and 4. Next, by considering the elements fixed by a subgroup Si of order 7 in Ei we obtain four geometries with the diagramon which CEi(Si) induces flag-transitive action isomorphic to L3(4) : 2, 3·L3(4) : 2, 28 : L3(2) and (L3(2) × L3(2)) : 2, for i=1,2,3 and 4. [Copyright &y& Elsevier]

Published
2003
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22. APPROXIMATION OF THE STABILITY NUMBER OF A GRAPH VIA COPOSITIVE PROGRAMMING*.

Author

De Klerk, E. and Pasechnik, D.V.

Subjects
CONVEX programming, CONIC sections, MATRICES (Mathematics), CONVEX domains
Abstract

Examines how the stability number can be computed as the solution of a conic linear program over the cone of copositive matrices. Equations for conic programming of convex cones; Analysis of stability via copositive programming; Approximation of copositive cone.

Published
2002
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