arXiv subjects

Takashi Ichinomiya

Publications and source records attributed to Takashi Ichinomiya.

10 recordsLinked to original sources

arXiv2023

Time series analysis using persistent homology of distance matrix

The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the distance matrix. Using this method, we can obtain the topological features embedded in the trajectories. We apply this method to the logistic map, Rössler system, and electrocardiogram data. The results reveal that our method can effectively identify nonlocal characteristics of the attractor and can classify data based on the amount of noise.

physics.data-an↗

arXiv2020

Protein folding analysis using features obtained by persistent homology

Understanding the protein folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the understanding of this process. In this study, we applied persistent homology, an emerging methods to analyze topological features in a dataset, to reveal protein folding dynamics. We developed a new method to characterize protein structure based on persistent homology and applied this method to molecular dynamics simulations of chignolin. Using principle component analysis or non-negative matrix factorization, our analysis method revealed two stable states and one saddle state, corresponding to the native, misfolded, and transition states, respectively. We also identified an unfolded state with slow dynamics in the reduced space. Our method serves as a promising tool to understand the protein folding process.

physics.comp-ph↗

arXiv2014

Thermodynamic Characterization of Synchronization-Optimized Oscillator-Networks

We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo (MCMC) simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1,000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.

nlin.AO↗

arXiv2013

Power-law exponent of the Bouchaud-Mézard model on regular random network

We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as $x\rightarrow \infty$. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be good agreement with those of the numerical simulations.

nlin.AO↗

arXiv2012

Wealth distribution on complex networks

We study the wealth distribution of the Bouchaud--Mézard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theorem, we derive equations that determine the probability distribution function. The results are compared to those of simulations for various networks. We find good agreement between our theory and the simulations, except the case of Watts--Strogatz networks with a low rewiring rate, due to the breakdown of independent assumption.

nlin.AO↗

arXiv2012

Bouchaud-Mézard model on a random network

We studied the Bouchaud-Mézard(BM) model, which was introduced to explain Pareto's law in a real economy, on a random network. Using "adiabatic and independent" assumptions, we analytically obtained the stationary probability distribution function of wealth. The results shows that wealth-condensation, indicated by the divergence of the variance of wealth, occurs at a larger $J$ than that obtained by the mean-field theory, where $J$ represents the strength of interaction between agents. We compared our results with numerical simulation results and found that they were in good agreement.

nlin.AO↗

arXiv2006

Power-law distribution in Japanese racetrack betting

Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds $P_o(x)$ indicates a clear power law $P_o(x)\propto 1/x$, where $x$ represents the final odds. This power law can be explained on the basis of the assumption that that every bettor bets his money on the horse that appears to be the strongest in a race.

physics.soc-ph↗

arXiv2005

Path-integral approach to the dynamics in sparse random network

We study the dynamics involved in a sparse random network model. We extend the standard mean-field approximation for the dynamics of a random network by employing the path-integral approach. The result indicates that the distribution of the variable is essentially identical to that obtained from globally coupled oscillators with random Gaussian interaction. We present the results of a numerical simulation of the Kuramoto transition in a random network, which is found to be consistent with this analysis.

cond-mat.dis-nn↗

arXiv2004

Frequency synchronization in random oscillator network

We study the frequency-synchronization of randomly coupled oscillators. By analyzing the continuum limit, we obtain the sufficient condition for the mean-field type synchronization. We especially find that the critical coupling constant $K$ becomes 0 in the random scale free network, $P(k)\propto k^{-γ}$, if $2 < γ\le 3$. Numerical simulations in finite networks are consistent with these analysis.

cond-mat.dis-nn↗

arXiv2000

Impurity-induced Ferromagnetism in Doped Triplet Excitonic Insulator

The theory of impurities in excitonic insulator is investigated in the light of the recent experiments on hexaborides. First, we study the bound state around the impurity and find that the bound state emerges when ${Re}Δ$ is positive. Second, we study the continuum state using Abrikosov-Gor'kov's approach. We find that the energy gap is reduced strongly when ${Im}Δ=0$. Finally, we solve Bogoliubov-de Gennes equations for excitonic insulator numerically. We get the results consistent with the analytic ones. We also find that incomplete ferromagnetism appears in doped triplet excitonic insulator with impurity. We make a short qualitative discussion on the ferromagnetism of doped hexaborides using our result.

cond-mat.str-el↗