122Is the k-NN classifier in high dimensions affected by the curse of dimensionality? - 24 pp., a revision of Oct. 2011 Dagstuhl preprint DPA-11341, to appear in Computers & Mathematics with Applications.
doi> 10.1016/j.camwa.2012.09.011.
[arXiv]
2013
121
(Edited, with Monika Ludwig, Vitali D. Milman, and Nicole Tomczak-Jaegermann)
Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program, Fields Institute Communications 68, Springer, 2013, 408 pages, ISBN-13: 978-1461464051.
The
book webpage.
120Lower bounds on performance of metric tree indexing schemes for exact similarity search in high dimensions. - Algorithmica 66 (2013), 310-328.
doi> 10.1007/s00453-012-9638-2. (A journal version of [112].)
[arXiv]
119PAC learnability under non-atomic measures: a problem by Vidyasagar.
- Theoretical Computer Science 473 (2013), 29-45. (A journal version of [110].) doi> 10.1016/j.tcs.2012.10.015.
[arXiv]
2012
118
(with Aleksandra Kwiatkowska)
An introduction to hyperlinear and sofic groups. -
"Appalachian Set Theory 2006-2012" (James Cummings and Ernest Schimmerling, eds.), London Mathematical Society Lecture
Notes Series 406, Cambridge University Press (2012), pp. 145-186.
[arXiv version]
117
(Edited, with Gonzalo Navarro)
Similarity Search and Applications: 5th International Conference, SISAP 2012, Toronto, ON, Canada, August 9-10, 2012, Proceedings, Springer Lecture Notes in Computer Science 7404, 2012, 255 pages, ISBN-13: 978-3642321528,
doi > 10.1007/978-3-642-32153-5. The
book webpage.
116
(with Brice R. Mbombo)
Subgroups of isometries of Urysohn-Katětov metric spaces of uncountable density. - Topology and its Appl. 159 (2012), 2490-2496. doi> 10.1016/j.topol.2011.06.068,
[arXiv]
114
(with Yousef Al-Gadid and Brice Rodrigue Mbombo Dempowo, jr.)
Sur les espaces test pour la moyennabilité. -
C. R. Math. Acad. Sci. Soc. R. Canada 33 (2011), No.3, pp. 65-77.
[arXiv]
113PAC learnability versus VC dimension: a footnote to a basic result of statistical learning, in: Proceedings of the 2011 International Joint Conference on Neural Networks (IJCNN'2011), San José, CA (July 31 - Aug. 5, 2011), pp. 1141 -
1145, doi> 10.1109/IJCNN.2011.6033352. [arXiv]
112 Lower bounds on performance of metric tree indexing schemes for exact similarity search in high dimensions. - Proceedings of the 4th International Conference on Similarity Search and Applications (SISAP 2011), 30 June - 1 July 2011, Lipari, Sicily, Italy. Editor: Alfredo Ferro, ACM, New York, NY, 2011, pp. 25-32. For a journal version, see [121].
2010
111A note on sample complexity of learning binary output neural networks
under fixed input distributions. - in: Proc. 2010 Eleventh Brazilian Symposium on Neural Networks (São Bernardo do Campo, SP, Brazil, 23-28 October 2010), IEEE Computer Society, Los Alamitos-Washington-Tokyo, 2010, pp. 7-12. doi> 10.1109/SBRN.2010.10
[ arXiv ]
109PAC learnability of a concept class under non-atomic measures: a problem by Vidyasagar. - in: Proc. 21st Intern. Conference on Algorithmic Learning Theory (ALT'2010), Canberra, Australia, 6-8 Oct. 2010 (M. Hutter, F. Stephan, V. Vovk, T. Zuegmann, eds.), Lect. Notes in Artificial Intelligence 6331, Springer, 2010, pp. 134-147. [arXiv version] An expanded and improved journal version is [119].
109Intrinsic Dimensionality. - The SIGSPATIAL Special, Newsletter of the Association for Computer Machinery special interest group on spatial information, a
special issue on searching in metric spaces,
vol. 2, No. 2 (2010), 8-11.
108Indexability, concentration, and VC theory. - An invited paper,
Proceedings of the 3rd International Conference on Similarity Search and Applications (SISAP 2010), 18-19 September 2010, Istanbul, Turkey. Editors: Paolo Ciaccia and Marco Patella, ACM, New York, NY, 2010, pp. 3-12.
For an expanded, corrected and improved journal version, see [115].
107Predictive PAC learnability: a paradigm for learning from exchangeable input data. - In: Proc. 2010 IEEE Int. Conference on Granular Computing (San Jose, CA, 14-16 Aug. 2010), pp. 387-391, Symposium on Foundations and Practice of Data Mining. doi> 10.1109/GrC.2010.102
[arXiv]
106Concentration of measure and whirly actions of Polish groups. - Proceedings of the 1st Mathematical Society of Japan Seasonal Institute "Probabilistic Approach to Geometry" (Kyoto, July-Aug. 2008). Advanced Studies in Pure Mathematics 57, Mathematical Society of Japan, Tokyo, 2010, pp. 383-403.
[arXiv]
105 (With Lionel Nguyen Van Thé)
Fixed point-free isometric actions of topological groups on Banach spaces. - Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 29-51.
[arXiv version]
2009
104
(With Ilya Volnyansky)
Curse of dimensionality in pivot-based indexes. - Proceedings of the 2nd International Workshop on Similarity Search and Applications (SISAP 2009), Prague, Czech Republic, August 29-30, 2009, T. Skopal and P. Zezula (eds.), IEEE Computer Society, Los Alamitos--Washington--Tokyo, 2009, pp. 39-46. [arXiv version]
2008
103 Hyperlinear and sofic groups: a brief guide. - The Bulletin of Symbolic Logic 14 (2008), pp. 449-480.
[paper in postscript]
102
A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space. - Topology and its Applications 155 (2008),
special issue: Workshop on the Urysohn space (Ben-Gurion University of the Negev, Beer Sheva, Israel, 21-24 May 2006), pp. 1561-1575.
101
An axiomatic approach to intrinsic dimension of a dataset. -
Neural Networks 21, 2-3 (2008), 204-213.
(A special volume on Advances in Neural Networks Research: IJCNN ′07, 2007 International Joint Conference on Neural Networks IJCNN ′07.) [arXiv version]
2007
100 (with A. Stojmirović)
Indexing schemes for similarity search in datasets of short protein
fragments. - Information Systems 32 (2007), 1145-1165.
99Intrinsic dimension of a dataset: what properties does one expect? -
In: Proceedings of the 20th International Joint Conference on Neural Networks (IJCNN'2007), Orlando, Florida (Aug. 12--17, 2007), pp. 1775--1780.
[arXiv version]
98
The isometry group of the Urysohn space as a Lévy group. -
Proceedings of the 6-th Iberoamerican Conference on Topology and its Applications (Puebla, Mexico, 4-7 July 2005). A special issue of Topology and is Appl. 154 (2007), pp. 2173-2184.
97
Forty-plus annotated questions about large topological groups.
- in: Open Problems in Topology II (Elliott M. Pearl, ed.), Elsevier BV., Amsterdam, 2007, pp. 439-450.
96 (with Thierry Giordano)
Some extremely amenable groups related to operator algebras and ergodic theory
. - J. Inst. Math. Jussieu 6 (2007), 279-315.
2006
95 Dynamics of Infinite-Dimensional Groups: the Ramsey-Dvoretzky-Milman phenomenon.
- American Math. Society University Lecture Series 40, 2006, 192 pp.
Book page.
94
(with Vladimir V. Uspenskij)
Representations of residually finite groups by isometries of the Urysohn space.
- Journal of the Ramanujan Mathematical Society 21 (2006), 189-203.
93 (with Aleksandar Stojmirović)
Indexing schemes for similarity search: an illustrated paradigm.
- Fundamenta Informaticae 70 (2006), 367-385.
2005
92
Dynamics of Infinite-Dimensional Groups and Ramsey-Type Phenomena,
Publicações dos Colóquios de Matemática, IMPA,
Rio de Janeiro, 2005, iv + 241 pp. [pdf file at Jussieu.]
91 (with A.S. Kechris and S. Todorcevic)
Fraïssé limits, Ramsey theory, and topological dynamics
of automorphism groups
.
- Geom. Funct. Anal. 15 (2005), 106-189.
2004
90 (with Markus Hegland)
Additive models in high dimensions.
- In: Proc. of 12th Computational Techniques and Applications
Conference, CTAC-2004 (Rob May and A.J. Roberts, eds.), ANZIAM J.
46 (2004/2005), C1205--C1221 [electronic].
2003
89 (with A.S. Kechris and S. Todorcevic)
Universal minimal flows of automorphism groups.
- Bull. Acad. Serb. Sci. Arts 77 (2003), Nr. 28,
93-106.
88 (with Su Gao)
On a universality property of some abelian Polish groups.
- Fundamenta Mathematicae 179 (2003), 1-15.
87
On some
questions of Eymard and Bekka concerning amenability of homogeneous
spaces and induced representations. - C.R. Math. Rep. Acad. Sci.
Canada 25 (2003), 76-81.
2002
86 MM-spaces and group actions. -
L'Enseignement Mathématique 48 (2002), 209-236.
85
Remarks on actions on compacta by some infinite-dimensional groups.
- in:
Infinite-Dimensional Lie Groups in Geometry and
Representation Theory (Washington, D.C., 2000),
World Sci. Publishing, River Edge, NJ, 2002, pp. 145-163.
84
(with Thierry Giordano)
Some extremely amenable groups. -
C.r. Acad. Sci. Paris, Sér. I 334 (2002), No. 4,
273-278.
83
Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely
amenable groups.
- Israel Journal of Mathematics 127 (2002), 317-358.
Corrigendum, ibid., 145 (2005), 375-379.
2001
82 (with M.G. Megrelishvili and V.V. Uspenskij)
A note on the precompactness of weakly almost periodic groups.
In: Nuclear groups and Lie groups,
E. Martin Peinador, J. Nunez Garcia (eds.),
Heldermann Verlag, 2001 (Research and Exposition in Mathematics,
Volume 24), pp. 209-216.
2000
81
Topological groups: where to from here?
- in:
Proceedings, 14th Summer Conf. on General
Topology and its Appl. (C.W. Post Campus
of Long Island University, August 1999),
Topology Proceedings 24 (1999), 421--502.
80
Amenable representations and dynamics of the unit sphere in an
infinite-dimensional Hilbert space.
- Geom. Funct. Anal. 10 (2000), 1171-1201.
79 (with S.A. Morris)
Subgroups of monothetic groups.
- Journal of Group Theory 3 (2000), 407-417.
78
Two 1935 questions of Mazur about polynomials in Banach spaces:
counter-examples. - Quaestiones Mathematicae
23 (2000), 235-240.
77
(with Ugo Bruzzo)
On the notion of compactness in supergeometry.
- Bull. Austral. Math. Soc. 61 (2000),
473--488.
76On the geometry of similarity search: dimensionality curse
and concentration of measure.
- Information Processing Letters 73 (2000), 47-51.
75 (With S.A. Morris and P. Nickolas)
Limit laws for wide varieties of topological groups II. -
Houston J. Math. 26 (2000), 17-27.
74 The concentration phenomenon and topological groups. -
Topology Atlas Invited Contributions 5 (2000), 5-10 (online).
1999
73 (with Kohzo Yamada)
Free topological groups on metrizable spaces and inductive limits. -
Topology and its Applications 98 (1999), 291-301.
71
(with U. Bruzzo)
On the structure of DeWitt supermanifolds.
- Journal of Geometry and Physics 30 (1999), 169-186.
70
Amenable groups and measure concentration on spheres.
- C.r. Acad. Sc. Paris, Sér. I
328 (1999), 669--674.
1998
69
Independence of almost periodicity upon the topology of the
acting group. - Topology and its Applications,
90 (1998), pp. 223-225.
68 (with S.A. Morris)
On Lie groups in varieties of topological groups.
- Colloq. Math. 78 (1998), 39-47.
67
On free actions, minimal flows, and a problem by Ellis.
-
Trans. Amer. Math. Soc. 350 (1998), pp. 4149-4165. Article is available free of charge.
66 Abelian topological groups without irreducible
Banach representations. - In: Abelian Groups, Module Theory,
and Topology (D. Dikranjan and L. Salce, eds.), Lecture Notes in
Pure and Appl. Math. vol. 201, Marcel Dekker, 1998, 343-349.
65
(with C. Bartocci, U. Bruzzo, and D. Hernández Ruipérez)
Quotient supermanifolds.
- Bull. Austral. Math. Soc. 58 (1998), 107--120.
64 (with D.B. Shakhmatov)
A relatively free topological group that is not varietal free -
Colloq. Math. 77 (1998), 1-8.
63 (with S.A. Morris)
A topological generalization of the
Higman--Neumann--Neumann
theorem. - Journal of Group Theory 2 (1998), 181--187.
62
Some universal constructions in abstract topological dynamics.
-
In: Topological Dynamics and its Applications.
A Volume in Honor of Robert Ellis, Contemp. Math. 215 (1998), 83--99.
1997
61 (With A.G. Leiderman and S.A. Morris.)
The free abelian topological group and the free
locally convex space on the unit interval. -
Journal of the London Mathematical Society 56 (1997), 529--538.
60Epimorphisms of Hausdorff groups by way of topological dynamics. -
New Zealand Journal of Mathematics 26 (1997), 257--262.
59 (with A. Leiderman and M. Levin)
On linear continuous open surjections of the
spaces Cp(X). -
Topology and its Applications 81 (1997), 269--279.
58 (With M. Megrelishvili and P. Nickolas.)
Uniformities and uniform structures on locally connected groups. -
Bull. Australian Math. Society 56 (1997), 279--283.
57 (With
K.H. Hofmann, S.A. Morris and P. Nickolas.)
Small large subgroups of a topological group. -
Note di Matematica 14 (1997), 161--165.
1996
56 (With C. Bartocci, U. Bruzzo, and D. Hernández
Ruipèrez.)
Supermanifold theory: towards a unifying approach. -
WOGDA '95 --- Proceedings of the 4th Fall Workshop `Differential Geometry
and its applications' (Santiago de Compostela, Spain, September 18-20,
1996; M. Salgado, E. Vázques, eds.),
Anales de Fisica, Monografias 3 --- CIEMAT, Madrid 1996,
pp. 1--16.
55 (With R.D. Kopperman, M.W. Mislove, S.A. Morris, P. Nickolas,
and S. Svetlichny.)
Limit laws for wide varieties of topological groups. -
Houston Journal of Mathematics 22 (1996), no. 2, 307--328.
1995
54 Regular Lie groups and a theorem of Lie-Palais. -
Journal of Lie Theory 5 (1995), no. 2, 173--178.
53 Analytic subsets of Hilbert spaces. -
Actes du Colloque Trajectorien (A. Fruchard & A. Troesch, eds.),
Publ. IRMA (Strasbourg) 1995-13 (1995), 75--80.
52 Free abelian topological groups and the Pontryagin--van Kampen
duality. -
Bull. Austral. Math. Soc. 52 (1995), 297--311.
1994
51 On even collective effects in purely odd superspaces. -
Proceedings of the XXIInd Intern. Conf. on Differential Geometric
Methods in Theoretical Physics
(Ixtapa-Zihuatanejo, México, Sept 20--25, 1993).
Advances in Applied Clifford Algebras (Proc. Suppl.) 4
(S1) (1994), 157--164.
50 Douady's conjecture on Banach analytic spaces. -
C.R. Acad. Sci. Paris, Sér. 1, t. 319 (1994), 1043--1048.
49 Operator spaces and residually finite-dimensional C*-algebras. -
Journal of Functional Analysis 123 (1994), 308--317.
48 Analysis on superspace: an overview. -
Bull. Austral. Math. Soc. 50 (1994), 135--165.
47 A remark on embedding topological groups into products. -
Bull. Austral. Math. Soc. 49 (1994), 519--521.
1993
46 (With S. A. Morris)
Open subgroups of free abelian topological groups. -
Math. Proc. Camb. Phil. Soc. 114 (1993), part 3,
439--442.
45 An analytic structure emerging in the presence of
infinitely many odd coordinates. -
New Zealand Journal of Mathematics 22 (1993), 75--84.
44 (With C. Bartocci, U. Bruzzo, and
D. Hernández Ruipèrez).
Foundations of supermanifold theory: the axiomatic approach.-
Diff. Geometry and its Applications 3 (1993), 135-155.
43 Soul expansion of $G^\infty$ superfunctions.-
Journal of Math. Physics 34 (1993), 3316--3323.
42 Universal arrows to forgetful functors from
categories of topological algebra.-
Bull. Austral. Math. Soc. 48 (1993), 209--249.
41 On enlargability of infinite-dimensional Lie superalgebras. -
Journal of Geometry and Physics 10 (1993), 295--314.
39 Free Banach-Lie algebras, couniversal
Banach-Lie groups, and more. -
Pacific J. Math. 157 (1993), 137--144. Erratum: -
ibid., 171 (1995), 585--588.
1992
38 A correspondence between finite-dimensional Lie
superalgebras and supergroups. -
Extracta Mathematicae 7 (1992), 119--125.
37 Nonstandard hulls of Banach-Lie groups
and algebras. -
Nova Journal of Algebra and Geom. 1 (1992),
371--384.
36 General construction of Banach-Grassmann algebras. -
Atti Acad. Naz. Lincei Rend. (9) 3 (1992), no. 3, 223--231.
35 A contribution to nonstandard superanalysis. -
Journal of Math. Physics 33 (1992), 3263--3273.
34 (With C. Bartocci, U. Bruzzo, and
D. Hernández Ruipèrez.)
On an axiomatic approach to supermanifolds.-
Soviet Math. Dokl. 44 (1992), 744-748.
1991
33 Ground algebras for superanalysis. -
Reports on Math. Physics 29 (1991), 275--287.
32 On a valuation field invented by A. Robinson and
certain structures connected with it. -
Israel J. Math. 74 (1991), 65-79.
31 Nonstandard hulls of normed Grassmann algebras and
their application in superanalysis.-
Soviet Math. Dokl. 43 (1992), 456--460.
30 Even sectors of Lie superalgebras as locally convex
Lie algebras. -
Journal of Math. Physics 32 (1991), 24-32.
1990
29 On a valuation field invented by A. Robinson and
structures connected with it. -
Soviet Math. Dokl. 40 (1990), 482-485.
1989
28 (with A.V. Arhangel'skii and O.G. Okunev).
Free topological groups over metrizable spaces. -
Topology and its Appl. 33 (1989), 63-76.
27 Interpreting superanalyticity in terms of convergent
series. -
Class. Quantum Gravity 6 (1989), L145-L149.
26 On a `super' version of Lie's third fundamental theorem.-
Letters in Math. Physics 18 (1989), 27-33.
1988
25 Fermeture non standard des groupes
et algèbres de Lie
banachiques.-
C.R. Acad. Sci. Paris, Sér. 1, t. 306 (1988), no 15, 643-645.
24 On unconditionally closed sets and a conjecture
of A.A. Markov. -
Siberian Math. J. 29 (1988), no 2, 260-266.
23 A criterion for the balancity of a locally compact group. -
Ukrainian Math. J. 40 (1988), 109-111.
1987
22 The category of Tychonoff spaces embeds into the
category of topological groups as a subcategory. -
Bull. Acad. Sci. Georgian SSR 128 (1987), no 2, 257-259
(in Russian).
21 Thin sets in topological groups and a new
precompactness criterion. -
Soviet Math. (Iz.VUZ) 31 (1987), no 11, 81-84.
20 A note on group topologizations. -
`Topol. structures and their mappings,' Riga,
Latvian U. Press, 1987, pp. 93-95 (in Russian).
19 Homomorphisms of topological groups cannot be
factorized with respect to their weight and dimension. -
Math. Notes 41 (1987), no 3-4, 226-228.
1986
18 On a theorem of M.M. Choban on extension of pseudometrics
to free universal algebras.
- In: Continuous Functions on Topol. Spaces,
Riga, Latvian U. Press, 1986, pp. 142-146 (in Russian).
17 On compactly generated topological groups. -
Math. Notes 40 (1986), no 5-6, 880-882.
16 (with D.B. Shakhmatov)
Continuous homomorphic images
of groups with countable base do not exhaust all groups with
countable network. - Mosc. Univ. Math. Bull. 41 (1986), 92-95.
15 Free Banach spaces and representations of
topological groups. - Funct. Anal. Appl. 20 (1986), 70-72.
14 Free topological abelian groups and the Pontryagin
duality. -
Mosc. Univ. Math. Bull. 41 (1986), no 1, 1-4.
13 An example of a nonmetrizable minimal topological
group whose unity has a type Gδ. -
Ukrainian Math. J. 37 (1986), no 6, 655-656.
1985
12 An example of a stratifiable topological group. - In:
Topol. Spaces and Their Mappings, Riga, Latvian U. Press,
1985, pp. 105-107 (in Russian).
11 The class of almost metrizable topological groups
is not closed under extensions. -
Mosc. Univ. Math. Bull. 40 (1985), no 4, 74-76.
10 Neighbourhoods of unity in free topological groups. -
Mosc. Univ. Math. Bull. 40 (1985), no 3, 8-12.
9 To the theory of free topological groups: free groups, extensions, and compact coverability,
Manuscript deposited at VINITI (Moscow) on April 1, 1985, No. 2207-85Dep. (in Russian).
1984
8 Some topological properties
preserved by the relation of M-equivalence. -
Russ. Math. Surveys 39 (1984), no 6, 223-224.
7 (with N.G. Okromeshko)
On a construction of A.S. Mishchenko in the theory of
homogenuos spaces. - Mosc. Univ. Math. Bull. 39
(1984), no 3, 33-37.
1983
6 Топологические группы и алгебраические оболочки топологических пространств.
[Topological groups and algebraic envelopes of topological spaces]. -
Ph.D. thesis, Moscow State University, Faculty of Mechanics and Mathematics, submitted May 1983, defended Dec. 16, 1983, 78 pp. (in Russian).
5 Relations between classes of almost metrizable,
projectively metrizable, and $\aleph_0$-representable
topological groups. - `Topol. spaces and their mappings,'
Riga, Latvian U. Press, 1983, 80-86 (in Russian).
1982
4 The coincidence of the dimensions dim of
l-equivalent topological spaces .-
Soviet Math. Dokl. 26 (1982), 380-382.
3 On embeddings and condensations of
topological groups. - Math. Notes 31 (1982), no 3-4, 228-230.
2 Some properties of free topological groups. -
Moscow Univ. Math. Bull. 37 (1982), no 1, 46-49.
1981
1 On the structure and embeddings of topological groups. -
Manuscript deposited at VINITI (Moscow) on April 13, 1981, No. 1495-81 Dep, 41 pp. (in Russian).