P.G. Demidov Yaroslavl State University
International B.N. Delaunay Laboratory
Discrete and Computational Geometry
Yaroslavl International Conference
“Geometry, Topology, and Applications”
September 23-27, 2013
ABSTRACTS
Yaroslavl 2013
UDC 514
Yaroslavl International Conference “Geometry, Topology, and Application”. <...> This is the case for spherical t-designs (i.e. finite
subsets of spheres) or for combinatorial t-designs, here a combinatorial t(v, k, λ) design means a good subset which approximates the space of all k
element subsets of a v set. <...> Euclidean t-designs are certain generalizations
of spherical designs. <...> Relative t-designs (defined by Delsarte) are certain
generalizations of combinatorial t-designs. <...> It is known that there are close similarities between ”theory of spherical
t-designs vs. theory of Euclidean t-designs” and ”theory of combinatorial
t-designs vs. theory of relative t-designs in binary Hamming schemes.” The
former theories have been studied more extensively than the latter ones,
since spherical harmonics is more transparent than the theory of harmonic
analysis on finite homogeneous spaces, i.e. on certain association schemes. <...> Ohio State University, Department Of Computer Science and Engineering,
mbelkin@cse.ohio-state.edu .
9
Spherization of 2-jet space and contact classification of second
order differential equations
Pavel Bibikov∗
Abstract
In this work we obtain an analog of symplectization for 2-jet space
J 2 Rn . <...> This analog is called spherization S(J 2 Rn ) and is used to
solve the problem of contact equivalence of second order differential
equations, which are polynomial in highest derivatives.
1
Introduction
Let J 2 Rn be the space of 2-jets of smooth functions f : Rn → R with
canonical coordinates (x, y, y1 , y2 ). <...> To
overcome this difficulty we consider spherization S(J 2 Rn ) of 2-jet space
J 2 Rn and rewrite our problem as follows: classify smooth functions on
S(J 2 Rn ), which are homogeneous in fiber coordinates of natural bundle
π : S(J 2 Rn ) → J 1 Rn , with respect to contact diffeomorphisms of J 1 Rn . <...> This problem can be solved with the help <...>
Yaroslavl_International_Conference_Geometry,_Topology,_and_Applica-_tion._September_23-27,_2013._Abstracts.pdf
P.G. Demidov Yaroslavl State University
International B.N. Delaunay Laboratory
Discrete and Computational Geometry
Yaroslavl International Conference
“Geometry, Topology, and Applications”
September 23-27, 2013
ABSTRACTS
Yaroslavl 2013
Стр.1
UDC 514
Yaroslavl International Conference “Geometry, Topology, and Application”.
September 23-27, 2013. Abstracts. —P.G. Demidov Yaroslavl State
University, 2013. — 138 p.
Funded by Russian Government Grant 220 / Contract 11.G34.31.0053
Program Commitee:
Herbert Edelsbrunner
Vladimir bondarenko
Victor Buchstaber
Vladimir Dolnikov
Sergey Glyzin
Alexander Ivanov
Roman Karasev
Oleg Musin
Sergey Novikov
Evgeny Shchepin
Mikhail Shtogrin
ISBN 978-5-8397-1003-0
- P.G. Demidov Yaroslavl
State University, 2013
c
- Authors
c
Стр.2
Contents
Eiichi Bannai
On tight relative t-designs . . . . . . . . . . . . . . . . . . . . . . 7
Mikhail Belkin
Differential Geometric Aspects of Machine Learning
and Data Analysis . . . . . . . . . . . . . . . . . . . . . . . 9
Pavel Bibikov
Spherization of 2-jet space and contact classification
of second order differential equations . . . . . . . . . . . . . 10
Andrey I. Bodrenko
Continuous AG-deformations of surfaces in Riemannian space . . 14
Irina I. Bodrenko
A characteristic feature of the surfaces with constant Gaussian
torsion in E4 . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Vladimir Bondarenko, Andrei Nikolaev
On graphs of the cone decompositions for the min-cut
and max-cut problems with nonnegative edges . . . . . . . 19
K´
aroly B¨ oczky
or¨
Full contact packings of unit balls in the Euclidean 3-space . . . 24
Florin Damian, Vitalii Makarov, Peter Makarov
Star complexes over regular maps . . . . . . . . . . . . . . . . . . 27
Nikolay P. Dolbilin, Herbert Edelsbrunner,
Alexey Glazyrin, Oleg R. Musin
Functionals on Triangulations of Delaunay Sets . . . . . . . . . . 33
O. Dunaeva, S. Kashin, R. Kuvaev, A. Lukyanov,
M. Machin, D. Malkova
Segmentation of Clinical Endoscopic Images Based
on Classification of Geometrical Features . . . . . . . . . . . 38
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Robert Erdahl
Parity centers and commensurate lattice polytopes
for parallelohedra . . . . . . . . . . . . . . . . . . . . . . . . 42
Nickolai Erokhovets
Buchstaber invariant and matroids . . . . . . . . . . . . . . . . . 43
Brittany Terese Fasy
Statistical Inference For Persistent Homology . . . . . . . . . . . 47
Dirk Frettl¨
oh
Tilings with tiles in infinitely many orientations . . . . . . . . . . 48
Alexander A. Gaifullin
Flexible polyhedra and places of fields . . . . . . . . . . . . . . . 53
Alexey Garber, Andrey Gavrilyuk, Alexander Magazinov
Voronoi conjecture on parallelohedra for new special case . . . . 54
Oleg N. German
Oppenheim and Littlewood conjectures from the point of view
of multidimensional continued fractions . . . . . . . . . . . 55
Sergey Glyzin
Multimode Diffusion Chaos in Reaction-diffusion boundary
problem in the dumbbell domain . . . . . . . . . . . . . . . 56
Mikhail Gorsky
Geometry and combinatorics of subword complexes
and dual polytopes . . . . . . . . . . . . . . . . . . . . . . . 60
Peter M. Gruber
Normal Bundles of Convex Bodies . . . . . . . . . . . . . . . . . 65
Leonidas Guibas, Quentin M´
erigot, Dmitriy Morozov
Witnessed k-Distance . . . . . . . . . . . . . . . . . . . . . . . . 66
Alex Gurin
Stoker’s theorem for the Delaunay graph . . . . . . . . . . . . . . 69
Yoshiaki Itoh
Random Sequential Packing of Cubes . . . . . . . . . . . . . . . 70
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Roman Karasev, Boris Bukh
Suborbits in Knaster’s problem . . . . . . . . . . . . . . . . . . . 72
Sergey Krivovichev
Local approach and self-assembly in modern crystallography . . . 78
Robert MacPherson, Amit Patel
The Quillen 2-Category in Persistent Homology . . . . . . . . . . 80
Vladimir Makeev, Nikita Netsvetaev
Universally inscribed polyhedra and equipartitioning
by convex fans . . . . . . . . . . . . . . . . . . . . . . . . . 81
Nikolai Mnev, Georgy Sharygin
Combinatorics of circle bundles . . . . . . . . . . . . . . . . . . . 83
Jerzy Mogilski
Free topological vectors spaces over compacta . . . . . . . . . . . 84
Luis Montejano, Tudor Zamfirescu
When is a disk trapped by four lines? . . . . . . . . . . . . . . . 85
Pavel Nesterov
Geometry of parametric resonances in adiabatic oscillators . . . . 88
Mikhail Nevskii
On a longest segment of given direction in a simplex . . . . . . . 92
Gaiane Panina
Moduli space of planar polygonal linkage:
a combinatorial description . . . . . . . . . . . . . . . . . . 96
Andrei M. Raigorodskii
Graphs of diameters . . . . . . . . . . . . . . . . . . . . . . . . . 97
Idzhad Sabitov
On an approach to the calculation of volumes in spaces
of constant curvature . . . . . . . . . . . . . . . . . . . . . . 98
Marjorie Senechal
What’s New in the Aperiodic Zoo? . . . . . . . . . . . . . . . . . 101
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Georgy Sharygin, Nikolai Mnev
Characteristic classes of combinatorial bundles
and higher Reidemeister torsion . . . . . . . . . . . . . . . . 102
A.V. Shutov, E.V. Kolomeykina
On the number of a lattice plane tilings
by a given area polyominoes . . . . . . . . . . . . . . . . . . 103
Mikhail Shtogrin
Flexible surfaces with active handles . . . . . . . . . . . . . . . . 105
Iskander Taimanov
Transformations of surfaces and their applications
to spectral theory . . . . . . . . . . . . . . . . . . . . . . . . 107
Masaharu Tanemura
On the areal random packing . . . . . . . . . . . . . . . . . . . . 108
Tarasov Alexey Sergeyevich
Edge unfoldings of polyhedral surfaces with acute angle faces . . 114
Evgeniy A. Timofeev
Algorithm for Efficient Entropy Estimation . . . . . . . . . . . . 117
Andrei Vesnin
From Right-angled Hyperbolic Polyhedra . . . . . . . . . . . . . 122
Yaokun Wu
Combinatorics of the lit-only σ-game . . . . . . . . . . . . . . . . 124
Svetlana Yablokova
On homology groups of one CW-space . . . . . . . . . . . . . . . 125
Olga Yakimova, Victoriya Bogaevskaya, Andrey Gorohov,
Vladislav Alexeev, Vladimir Knyazev,
Margarita Preobrazhenskaya, Alexey Ukhalov,
Herbert Edelsbrunner
A Topology Preserving Algorithm
for Cartographic Generalization . . . . . . . . . . . . . . . . 131
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