Moscow Russian-French conference
"Foundations of Internet"
Moscow, November 15-19, 2004
The conference program included eleven one-hour talks and four free
- The talk by Senya Shlosman (CPT, Marseille) "Phase transitions in
Internet models and eternal transient dynamical systems" gave a model of
Internet as a dynamical system using methods of statistical physics.
- The talk by Alexander Rybko (IITP, Moscow) "Fluid Limit for Queueing
Networks" described his recent joint work with Senya Shlosman on
limiting behavior of the large queueing systems in some simple
("mean-field") cases. It turns out that the Poisson Hypothesis holds in
this case, and the corresponding dynamical systems, defined by the
non-linear Markov processes, have a line of fixed points which are
- The talk by Matthieu Latapy (LIAFA, Paris 7) "Complex Networks: State
of the Art and Perspectives" described his recent joint work with
Jean-Loup Guillaume on a new approach to representation of Internet
topology using exploration process.
- The talk by Kave Salamatian (LIP 6, Paris) "Internet measurements:
state of the art and challenges" gave an overview of user and
application traffic characteristics of Internet traffic, including
different aspects of user, application and backbone traffic behaviour.
The talk also
discussed different models for Internet traffic and quality of Service
- The talk by Ilya Segalovich (Yandex, Moscow) "Math problems of
practical Internet" discussed mathematical aspects of search engines
used in modern Internet technologies.
- The talk by Patrice Abry (ENS, Lyon) "Statistical analysis and
modelling of Internet traffic": Scaling, Long Memory and Multifractal"
presented several statistical models of Internet based on real
measurements in the network using different features: self-similarity
and random walks, multifractality, and cluster point process.
- The talk by Alexander Shen (IUM and IITP, Moscow) "Internet and
parallel computations" discussed mathematical aspects of Internet
- The talk by Nikolai Vereschagin (Moscow State University) "The
Kolmogorov complexity of approximate descriptions" discussed different
notions of descriptive complexity of computable sequences which can be
used in Internet measurements.
- The talk by Mati Pentus (Moscow State University) "Algorithmic
complexity of the Lambek syntactic calculus" gave an overview of modern
state of art in theory of formal languages, aimed at study of natural
languages, web query languages, or event sequences in discrete event
systems. The main tools discussed are Lambek grammars, yielding exactly
the class of context-free languages. Lambek Calculus, is a formal system
for deriving reduction laws in Lambek grammars. The author presented
his recent significant result: the derivability problem for Lambek
Calculus is NP-complete.
- The talk by Vladimir N. Krupski (Moscow State University) "On proof
theoretical interfaces" considered interfaces for construction of proofs
in formal deductive systems. The author's approach is based on
propositional logic of proofs; the expressive power of the basic
language is crucially increased by adding reference modalities.
- The talk by Gregory Kabatianski (IITP RAN, Moscow) "Superchannel
approach to networks or how to decrease delay in Internet" discussed
various algebraic codes dealing with network traffic.
Topics of free discussions:
- "Internet as an object of mathematical statistical physics"
(Moderator: Senya Shlosman)
- "What mathematics does Internet need?" (Moderator:
- "What are the main challenges of network research in the coming
years?" (Moderator: Patrice Abry)
- "Internet and mathematical logic" (Moderator: