MIMS/CMMA Lecture Series

MIMS/CMMA Lecture Series

主催 共同利用・共同研究拠点
明治大学先端数理科学インスティテュート(MIMS) 「現象数理学拠点」
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第3回MIMS/CMMA Lecture Series
日時 :
2015年9月24, 25日 14:00~16:10
場所 :
明治大学 中野キャンパス高層棟6階 研究セミナー室3
講師:
Prof. Jacques Demongeot
(Université Joseph Fourier - Grenoble)
Title:
"Mathematical approach of
the individual and collective
decision process in social networks"

-A continuous PDE modelling idealizing
the spread of the decision in discrete
social networks. Application to the alimentary
choice in obesity spread.-
9 /24
 14:00-15:00 講義1(Part 1)
 15:10-16:10 演習 (Problem session)

9 /25
 14:00-15:00 講義2(Part 2)
 15:10-16:10 演習 (Problem session)

The talk deals with the effect of the social transmission of nutrition habits in a social context on obesity, and accordingly on its main complication, the type II diabetes. The evolution of social networks and inside a network the healthy weight of a person are depending on the context in which this person has contacts and exchanges concerning his alimentation, physical activity and sedentary habits, inside the dominant social network in which the person lives (e.g., scholar for young, professional for adult, home or institution for elderly people). Three successive steps of evolution will be considered for social networks (like for neural one’s): i) initial random connectivity, ii) destruction and consolidation of links following a new transition rule of nutrition choice called homophilic until iii) an asymptotic architectural organization and configuration of states. The individual decision is modelled following a differential model and the spread of the alimentary choices is idealized by a PDE equation, and simulated on a discrete graph in concrete cases. The application of such a network dynamics concerns the sequence overweight/obesity/type II diabetes.


 
 
第2回MIMS/CMMA Lecture Series
日時 :
2015年6月23日(火) 13:00~16:10
場所 :
明治大学 中野キャンパス高層棟6階 研究セミナー室3
講師 :
永幡幸生 氏
(新潟大学工学部)

Title:
流体力学極限について
講義1:13:00-14:30 流体力学極限について(1)
講義2:14:40-16:10 流体力学極限について(2)
流体力学極限とは標語的には「空間—時間に関して適切なスケール変換を取ることにより(ランダムな)微視的運動法則から(決定論的な)巨視的方程式を得ること」です。この微視的運動法則として格子気体を取り上げ、Varadhan Yau の結果(Diffusive limit of lattice gas with mixing conditions, Varadhan S.R.S., Yau H.T., The Asian Journal of Mathematics, 1, 623-678, 1997 )を紹介します。その後最近の研究として、拡散係数が退化した多孔質媒質の方程式に関する話を紹介します。
By taking an appropriate space-time scaling limit of random microscopic dynamics, we can derive deterministic macroscopic dynamics. We call this kind of procedure hydrodynamic limit. In this lecture we pick up lattice gas model as microscopic model and give a survey on Varadhan Yau's result (Diffusive limit of lattice gas with mixing conditions, Varadhan S.R.S., Yau H.T., The Asian Journal of Mathematics, 1, 623-678, 1997). After that we give a survey on hydrodynamic limit of lattice gas with degenerate rate, from which we can derive porous medium equation.


 
 
第1回MIMS/CMMA Lecture Series
日時 :
2015年5月18日(月) 14:40~17:50
場所 :
明治大学 中野キャンパス高層棟6階 研究セミナー室3
講師:
Prof. Bernold Fiedler
(Institute of Mathematics, Free University Berlin)

Title:
"Biochemical reaction networks" 
生化学ネットワーク反応
1:14:40-16:10
"Sensitivity of equilibrium response"
For monomolecular chemical or biological reaction networks, we describe the steady state response to perturbations of reaction rates. Our function-free approach does not require numerical input, but is based on the directed graph structure of the monomolecular reaction network, only. Our results and concepts are motivated by specific metabolic networks like the tricarboxylic citric acid cycle.
2:16:20-17:50
"Dynamics of regulatory networks"
We show that the concepts of informative nodes (Mochizuki) and determining nodes (Foias, Temam) coincide with the notion of feedback vertex sets from graph theory. As a result we can determine, and control, the long-time dynamics of entire networks from observations on a feedback vertex set, only. Examples include early Ascidian embryogenesis and genetic circadian clocks in mammals.
Both talks are joint work with Atsushi Mochizuki (RIKEN Tokyo). He will kindly give an introduction to the biological background, for each talk.
See also http://dynamics.mi.fu-berlin.de/