Yukito Iba

MULTI-SELF-OVERLAP ENSEMBLE FOR PROTEIN FOLDING : GROUND STATE SEARCH AND THERMODYNAMICS

Long chains of the HP lattice protein model are studied by the Multi-Self-Overlap Ensemble(MSOE) Monte Carlo method, which was developed recently by the authors. MSOE successfully finds the lowest energy states reported before for sequences of the chain length

Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble

N=42\sim 100

Testing Error Correcting Codes by Multicanonical Sampling of Rare Events

in two and three dimensions. Moreover, MSOE realizes the lowest energy state that ever found in a case of N=100. Finite-temperature properties of these sequences are also investigated by MSOE. Two successive transitions are observed between the native and random coil states. Thermodynamic analysis suggests that the ground state degeneracy is relevant to the order of the transitions in the HP model.

Detecting generalized synchronization between chaotic signals: a kernel-based approach

A novel family of dynamical Monte Carlo algorithms for lattice polymers is proposed. Our central idea is to simulate an extended ensemble in which the self-avoiding condition is systematically weakened. The degree of self-overlap is controlled in a similar manner as the multicanonical ensemble. As a consequence, the ensemble – the multi-self-overlap ensemble – contains adequate portions of self-overlapping conformations as well as higher energy ones. It is shown that the multi-self-overlap ensemble algorithm correctly reproduces the canonical averages at finite temperatures of the HP model of lattice proteins. Moreover, it is superior in performance to the standard multicanonical algorithm when applied to a complicated problem of a polymer with eight-stickers. An alternative algorithm based on the exchange Monte Carlo method is also discussed.

Multicanonical sampling of rare events in random matrices

The idea of rare-event sampling by the multicanonical Monte Carlo is applied to the estimation of the performance of error correcting codes. The essence of the idea is importance sampling of the pattern of noise in the channel by the multicanonical Monte Carlo, which enables efficient estimation of the tails of the distribution of bit errors. The proposed method is successfully tested with a convolutional code.

Exploration of order in chaos using the replica exchange Monte Carlo method

A unified framework for analysing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization, and dynamical change of the coupling strength between two chaotic systems can be captured by the proposed approach. It is also discussed how the kernel parameter is suitably chosen from data.

Multicanonical MCMC for sampling rare events: an illustrative review

A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble, sparse random matrices, and matrices whose components are subject to uniform density. Specifically, the probability that all eigenvalues of a matrix are negative is estimated in these cases down to the values of ∼10(-200), a region where simple random sampling is ineffective. The method can be applied to any ensemble of matrices and used for sampling rare events characterized by any statistics.

Probability of graphs with large spectral gap by multicanonical Monte Carlo

A method for exploring unstable structures generated by non-linear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters using the replica exchange Monte Carlo method, and it is efficient in searching for rare initial conditions and in the combined search for rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and searching for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.

Design Equation: A Novel Approach to Heteropolymer Design

Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or Metropolis-coupled MCMC) is also explained as an alternative to multicanonical MCMC. In the last section, multicanonical MCMC is applied to data surrogation; a successful implementation in surrogating time series is shown. In the appendix, calculation of averages and normalizing constant in an exponential family, phase coexistence, simulated tempering, parallelization, and multivariate extensions are discussed.

Multicanonical sampling of rare trajectories in chaotic dynamical systems

Graphs with large spectral gap are important in various fields such as biology, sociology and computer science. In designing such graphs, an important question is how the probability of graphs with large spectral gap behaves. A method based on multicanonical Monte Carlo is introduced to quantify the behavior of this probability, which enables us to calculate extreme tails of the distribution. The proposed method is successfully applied to random 3-regular graphs and large deviation probability is estimated.