March 4-5, 2014
The Institute of Statistical Mathematics
Tachikawa, Tokyo
Room
March 4 Seminar Room 1 (third floor)
March 5 Meeting Room 1 (second floor)
Organizers
Yukito Iba (ISM)
Hiroshi Fujisaki (Nippon Medical School)
Takashi Washio(Osaka University)
The art of realizing rare events in computer simulation and the calculation of their occurrence probabilities are important in many fields of science and engineering. The goal of this series of symposiums is to provide a coherent perspective on this subject, focusing on novel computational techniques and their applications to highly complex and nonlinear systems.
Recently, there has been interest in rare event sampling in the field of molecular simulation. Typical examples are numerical studies on the transition paths of conformational changes of a protein molecule. In this symposium, a keynote lecture by Prof. Eric Vanden-Eijnden (Courant Institute), as well as several talks by leading Japanese researchers in this field has been scheduled.
On the other hand, there are a number of other application fields of rare event sampling. Specifically, recent introduction and innovative use of Markov Chain Monte Carlo (MCMC) promotes a variety of novel applications in these fields. Some interesting examples are found in studies on chaotic dynamical systems, random graphs, random matrices, and counting combinatorial objects, as well as other hard computing problems in information theory, machine learning, meteorology, and astronomy. In this symposium, we also investigate these subjects and algorithms that have been developed for them.
Data assimilation and the design of computer experiment are subjects closely related to rare event sampling. In a nutshell, data assimilation selects a set of simulation sample paths that are compatible to observed data from the real world, whereas rare event sampling selects a set of sample paths that are compatible to target rare events. In the adaptive design of computer simulations, a most informative set of initial conditions and parameters are selected using past simulation results. We also include these subjects, aiming at cross-fertilization among these topics and rare event sampling.
MODELING OF REACTIVE EVENTS
Prof. Eric Vanden-Eijnden (Courant Institute)
Dynamics in nature often proceed in the form of reactive events. The system under study spends very long periods of time at various metastable states; only very rarely it hops from one metastable state to another. Understanding the dynamics of such systems requires us to study the ensemble of transition paths between the different metastable states.
Transition path theory (TPT) is a general mathematical framework developed for this purpose. It is also the foundation for developing modern numerical algorithms such as the string method for finding the transition pathways or milestoning to calculate the reaction rate, and it can also be used in the context of Markov State Models (MSMs).
In these lectures, I will review the basic ingredients of the transition path theory and discuss connections with transition state theory (TST) as well as approaches to metastability based on potential theory and large deviation theory. I will also discuss how the string method arises in order to find approximate solutions in the framework of the transition path theory, the connections between milestoning and TPT, and the way the theory help building MSMs.
The concepts and methods will be illustrated using examples from molecular dynamics, material science and atmosphere/ocean sciences.
10:00-10:15
Yukito Iba@
Intoroduction
10:15-11:45
Eric Vanden-Eijnden (Courant Institute)
Invited Lecture Part I
(lunch break)
12:45-13:45
Eric Vanden-Eijnden (Courant Institute)
Invited Lecture Part II
(short break)
14:00-15:00
Tadashi Tsuyuki (Meteorological Research Institute)
Deterministic Predictability of the Most Probable State
and Reformulation of Variational Data Assimilation
15:00-15:30
Takashi Washio(Osaka University)
Rare Flood Scenario Analysis Using Observed Rain Fall Data
(short break)
15:45-16:45
Norifumi Yamamoto (Chiba Institute of Technology)
Pathways of Chemical Reactions and Protein Conformational Changes
16:45-17:45
Motoyuki Shiga (Japan Atomic Energy Agency)
Quantum Statistical Analysis of Hydrogen Bonded Systems
10:00-11:00
Hiroshi Fujisaki (Nippon Medical School)
Path Search and Path Sampling Problems for Biomolecules
11:00-12:00
Yasuhiro Matsunaga (RIKEN AICS)
Finding Conformational Transition Pathways in Biomolecules with
the String Method and Sequential Data Assimilation
(lunch break)
13:00-14:00
Hiromichi Nagao (ERI Univesity of Tokyo)
Foundation of Data Assimilation and its Application to
the Solid Earth Science
(short break)
14:15-15:15
Yukito Iba (ISM)
Multicanonical Sampling of Rare Events
15:15-15:45
Nen Saito (Univesity of Tokyo)
Rare Event Sampling in Random Matrices
15:45-16:15
Kitajima Akimasa (National Diet Library)
Numerous, but Rare: Estimating the Number of Magic Squares with Multicanonical Monte Carlo Method