Strategic Games and Networks

Luca Dall'Asta

The framework of non-cooperative game theory has been recently extended to study the strategic behavior of players organized in complex socio- economic networks. However, the existence of a large number of (very different) Nash equilibria makes standard game theoretic analysis cumbersome and quantitatively less effective. On the other hand, it opens to the application of advanced theoretical and algorithmic techniques from the statistical mechanics of disordered systems. I will review some recent results on the problem of free-riding in public goods games and on the emergence of collaborative equilibria. Finally, I will discuss some open problems concerning dynamical aspects in repeated games and games with incomplete information.

Protein Sectors: Evolutionary Units of 3-D structure

Andrea Procaccini

How does the amino acid sequence of a protein specify its biological properties? Single site position conservation and pairwise correlation are standard measures which permit to study protein properties by amino acid sequence analysis. In the present paper Leibler, Ranganathan and co-workers carry out an approach called Statistical Coupling Analysis (SCA) to compute a conservation weighted correlation matrix between all sequence positions in the S1A serine protease family. The study of the normal modes of such matrix leads to a decomposition of the protein into groups of coevolving amino acids called Sectors. Such Sectors differ from the usual hierarchy of primary, secondary and tertiary structure but represent sets of sites which are statistically and functionally independent, physically connected in the 3-D structure and which have diverged independently in the evolution of the family.

Automated brain image segmentation with convolutional networks: a review

Carlo Baldassi

The image segmentation problem, applied to neural tissues, consists in identifying the individual structures (cell bodies, dendrites and axons) in a 3-dimensional scannerized image of a brain portion. Having a good automatic procedure for performing this task (i.e. as good as a human expert is) with good scaling properties would be useful to be able to reconstruct the connection structure of large portions of the brain (the so called "connectome"), which is supposedly a crucial part of the information needed to understand the brain functioning.
In this talk I will present the problem and review the work of Sebastian Seung and coworkers, whose approach consists in using a relatively small set of hand-made segmentations as a training set for a convolutional network (a special case of a multilayer neural network) which is subsequently used to perform the task automatically.
The learning is achieved using the back-propagation algorithm. This approach seems to work fine with relatively small image sizes (~1500 cubic micrometers, corresponding to ~50 megavoxels), but computational efficiency must be improved to process larger images (at least in the order of tens of teravoxels) in reasonable time.

[1] Supervised Learning of Image Restoration with Convolutional Networks, V. Jain et al., ICVV 2007.
[2] Convolutional networks can learn to generate affinity graphs for image segmentation, S. C. Turaga et al, NC 2008.

Griffiths inequalities

Abolfazl Ramezanpour

Correlations play an important role in statistical physics. In 1967 Griffiths derived some simple inequalities between correlations in a ferromagnetic system where interacting elements tend to have the same position in the configuration space. I will introduce these inequalities along with some generalizations to see how one can apply them to other interacting systems. References: [1] R. B. Griffiths, 1967. [2] C. M. Fortuin, P. W. Kasteleyn and J. Ginibre, 1971.

Fermi-Dirac and Bose-Einstein distributions characterize typical path length in opportunistic mobile networks

Marco Pretti

Communication engineers hope that, in a near future, portable devices will be able to exploit human mobility and so-called "opportunistic" contacts to communicate. Therefore, it is interesting to analyze the features of such opportunistic forwarding paths. A convenient model framework may be that of a random network of contacts (random graph), which randomly evolves with time (temporal random network). Here, we reformulate a recent analysis of an extremely simplified model, noting that the constraints imposed by limited local bandwidth (local latency) affect the properties of opportunistic paths, via a kind of "exclusion principle". Due to its generality, we argue that such a principle should also be at work in more realistic models of opportunistic mobile networks.

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