Moscow Russian-French conference "Foundations of Internet"

Moscow, November 15-19, 2004

The conference program included eleven one-hour talks and four free discussions.

1. 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.
2. 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 global attractors.
3. 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.
4. 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 measures.
5. The talk by Ilya Segalovich (Yandex, Moscow) "Math problems of practical Internet" discussed mathematical aspects of search engines used in modern Internet technologies.
6. 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.
7. The talk by Alexander Shen (IUM and IITP, Moscow) "Internet and parallel computations" discussed mathematical aspects of Internet software.
8. 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.
9. 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.
10. 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.
11. 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:

1. "Internet as an object of mathematical statistical physics" (Moderator: Senya Shlosman)
2. "What mathematics does Internet need?" (Moderator: Kave Salamatian)
3. "What are the main challenges of network research in the coming years?" (Moderator: Patrice Abry)
4. "Internet and mathematical logic" (Moderator: Valentin Shehtman)