PROGRAM
1330

Opening Address
Michitaka Kameyama
Dean, Graduate School of Information Sciences, Tohoku University1340-1430

Inhomogeneous Random Graph Models and Generalized
Percolation and Epidemic Processes
Philippe Blanchard
Faculty of Physics and ZiF, University of Bielefeld
1450-1540

Information Theoretic Background of Statistical Potentials ofProtein Structures
Matsuyuki Shirota
Graduate School of Information Sciences, Tohoku University
1600-1650

Learning Multiple Belief Propagation Fixed Point for Real TimeRoad Traffic Inference
Cyril Furtlehler
Institut National de Recherche en Informatique et Automatique(INRIA), Sacley, TAO Project-Term
1700Closing

CMRU The Collaborative Mathematics Research Unit was just founded in January 2011as part of the Graduate School of Information Sciences (GSIS), Tohoku University. The CMRU
aims at contributing to the development of collaborative study of mathematics and otherfields of science, particularly, information science, biological and life science, social andenvironmental science, and others.

ABSTRACTS
Inhomogeneous Random Graph Models and Generalized Percolation andEpidemic Processes
Philippe Blanchard (Faculty of Physics and ZiF, University of Bielefeld)

We review the theory of inhomogeneous random graph models, Cameo graphs(Blanchard-Krüger 2004) and BJR graphs (Bollobas-Janson-Riordan 2005) and thegeneralized epidemic process (GEP) formalism including local dynamics and global
mean field dynamics and discuss their main properties: phase transitions, connection
to threshold percolation, communication index and all that. We introduce different
GEP models to describe the spreading of different social processes and "diseases" like
corruption, knowledge, innovation, opinion, terrorism ....

Information Theoretic Background of Statistical Potentials of Protein
Structures
Matsuyuki Shirota (Graduate School of Information Sciences, Tohoku University)

The prediction of the three-dimensional structure of a protein from its amino acidsequence is a challenging task in computational biology. For this task, various model
structures are generated for a given amino acid sequence, and the quality of thesemodels must be evaluated to select the most reliable one as the prediction result. Onemajor group of such model evaluation methods is the statistical potential, which isbased on the conformational preferences observed among the known protein
structures in the Protein Data Bank (PDB). We discuss the information theoreticbackground of the statistical potentials both in terms of constructing them from PDB
and in terms of using them to evaluate model structures. In the former part, thereference state must be defined to quantify the significance of the observed
occurrence of the conformations. We demonstrate that apparently arbitrary choices of
the reference states result in the differences in the accuracy in model evaluation due
to the changes in the physical properties of the statistical potentials such ashydrophobicity and attractiveness. In the latter part, we reformulate the statisticalpotentials as the absolute quality scores, i.e. the scores of different proteins can becompared with each other. We first recast the statistical potential as the difference
between the Kullback-Leibler divergence from a model structure to the native state
and that to the reference state. We then show that statistical potentials can evaluate
the absolute quality of models of various native-likeness with respect to the nativestates and the reference states, although these potentials are developed by using only
the data set of native structures. These analyses shed light to the information
theoretic aspect of statistical potentials that the native-like state of a model structure
is evaluated with respect to the native structures in the PDB.

Learning Multiple Belief Propagation Fixed Point for Real Time Road TrafficInference
Cyril Furtlehner (Institut National de Recherche en Informatique et Automatique (INRIA),Sacley, TAO Project-Term)

We consider the generic problem of inferring present and future configurations of acomplex system, based on partial present-time observations in addition to pastobservations of its behavior. To address this question we develop a method based onthe "loopy belief propagation" algorithm, as a surrogate to an exact Markov Random
Field modelling, computationally too expensive for large scale systems. A priorinformation composed of correlations among a large set of N variables, is encoded
into a graphical model; this encoding is optimized with respect to an approximate
decoding procedure, which is used to infer hidden variables from an observed subset.
We focus on the situation where the underlying data have many different statisticalcomponents, representing a variety of independent patterns. We define a model able
to associate a belief propagation fixed point to each component of the underlying
probabilistic mixture. Asymptotic analysis reveal an exact connection with some
Hopfield model at finite temperature and steady state, when the number of mixture
components is proportional to the number of variables. We then discuss the relevanceof this results to the problem of reconstructing and predicting traffic states based on
floating car data and show some experiments based on artificial and real data.

主催：東北大学大学院情報科学研究科
支援：東北大学重点戦略支援プログラム「数学をコアとするスマート・イノベーション
融合研究共通基盤の構築と展開」
東北大学情報科学研究科重点研究プロジェクト「多様なセンサー情報を融合した道路交通流のナウキャストとフォアキャスト」
東北大学情報科学研究科重点研究プロジェクト「生命情報ビックバン時代の生命情報科学研究の基盤構築」
組織委員会：尾畑伸明・田中和之・桑原雅夫・木下賢吾