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Data-driven reconstruction of spatiotemporal phase dynamics for traveling and oscillating patterns via Bayesian inference
Authors:
Takahiro Arai,
Toshio Aoyagi,
Yoji Kawamura
Abstract:
Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns. Spatiotemporal phase dynamics are described by spatial and temporal phases that represent the position and oscillation of the pattern, respectively. Using Baye…
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Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns. Spatiotemporal phase dynamics are described by spatial and temporal phases that represent the position and oscillation of the pattern, respectively. Using Bayesian inference, our method directly reconstructs phase equations from time-series data. When tested on simulation data from coupled Gray-Scott models exhibiting traveling breathers, the method accurately reconstructs the deterministic part of the phase equations in the weak-noise regime, in which the phase dynamics converge to a linearly stable fixed point.
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Submitted 26 April, 2026;
originally announced April 2026.
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The Super Fine-Grained Detector for the T2K neutrino oscillation experiment
Authors:
S. Abe,
H. Alarakia-Charles,
I. Alekseev,
T. Arai,
T. Arihara,
S. Arimoto,
A. M. Artikov,
Y. Awataguchi,
N. Babu,
V. Baranov,
G. Barr,
D. Barrow,
L. Bartoszek,
A. Beliakova,
L. Bernardi,
L. Berns,
S. Bhattacharjee,
A. V. Boikov,
A. Blondel,
A. Bonnemaison,
F. Cadoux,
S. Cap,
A. Cauchois,
J. Chakrani,
P. S. Chong
, et al. (147 additional authors not shown)
Abstract:
The magnetised near detector ND280 of the long-baseline neutrino experiment T2K has been upgraded to improve its detection performance and, consequently, enhance our understanding of neutrino-nucleus interactions, reducing the systematic uncertainties in measurements of the neutrino oscillation parameters. A key component of the upgrade is a novel segmented plastic scintillator detector, called th…
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The magnetised near detector ND280 of the long-baseline neutrino experiment T2K has been upgraded to improve its detection performance and, consequently, enhance our understanding of neutrino-nucleus interactions, reducing the systematic uncertainties in measurements of the neutrino oscillation parameters. A key component of the upgrade is a novel segmented plastic scintillator detector, called the Super Fine-Grained Detector (SuperFGD), made of approximately 2 million optically isolated 1 cm$^3$ cubes read out by three orthogonal wavelength-shifting (WLS) fibres. Scintillation photons are detected by 55,888 Hamamatsu Multi-Pixel Photon Counters (MPPCs). The SuperFGD provides 3D images of neutrino interactions by tracking the final-state charged particles produced isotropically, including protons down to a threshold of around 330 MeV/$c$. The high light yield of SuperFGD greatly improves particle identification and the sub-nanosecond time resolution provides an excellent identification of Michel electrons. The SuperFGD is also able to detect neutrons from neutrino interactions and, for the first time in a neutrino experiment, to reconstruct their kinetic energy using a fine detector segmentation and by measuring the time-of-flight with sub-nanosecond precision. In this article the details of the detector design, construction and performance are described. The detector was installed in ND280 and successfully commissioned with cosmic data in 2023 and, later, with the T2K neutrino beam. The detector response has been characterised with the 2023 and 2024 data and the results are reported in this article.
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Submitted 16 March, 2026;
originally announced March 2026.
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Identifiable factor analysis for mixed continuous and binary variables based on the Gaussian-Grassmann distribution
Authors:
Takashi Arai
Abstract:
We develop a factor analysis for mixed continuous and binary observed variables. To this end, we utilized a recently developed multivariate probability distribution for mixed-type random variables, the Gaussian-Grassmann distribution. In the proposed factor analysis, marginalization over latent variables can be performed analytically, yielding an analytical expression for the distribution of the o…
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We develop a factor analysis for mixed continuous and binary observed variables. To this end, we utilized a recently developed multivariate probability distribution for mixed-type random variables, the Gaussian-Grassmann distribution. In the proposed factor analysis, marginalization over latent variables can be performed analytically, yielding an analytical expression for the distribution of the observed variables. This analytical tractability allows model parameters to be estimated using standard gradient-based optimization techniques. We also address improper solutions associated with maximum likelihood factor analysis. We propose a prescription to avoid improper solutions by imposing a constraint that row vectors of the factor loading matrix have the same norm for all features. Then, we prove that the proposed factor analysis is identifiable under the norm constraint. We demonstrate the validity of this norm constraint prescription and numerically verified the model's identifiability using both real and synthetic datasets. We also compare the proposed model with quantification method and found that the proposed model achieves better reproducibility of correlations than the quantification method.
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Submitted 11 December, 2025;
originally announced December 2025.
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Identifiability and improper solutions in the probabilistic partial least squares regression with unique variance
Authors:
Takashi Arai
Abstract:
This paper addresses theoretical issues associated with probabilistic partial least squares (PLS) regression. As in the case of factor analysis, the probabilistic PLS regression with unique variance suffers from the issues of improper solutions and lack of identifiability, both of which causes difficulties in interpreting latent variables and model parameters. Using the fact that the probabilistic…
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This paper addresses theoretical issues associated with probabilistic partial least squares (PLS) regression. As in the case of factor analysis, the probabilistic PLS regression with unique variance suffers from the issues of improper solutions and lack of identifiability, both of which causes difficulties in interpreting latent variables and model parameters. Using the fact that the probabilistic PLS regression can be viewed as a special case of factor analysis, we apply a norm constraint prescription on the factor loading matrix in the probabilistic PLS regression, which was recently proposed in the context of factor analysis to avoid improper solutions. Then, we prove that the probabilistic PLS regression with this norm constraint is identifiable. We apply the probabilistic PLS regression to data on amino acid mutations in Human Immunodeficiency Virus (HIV) protease to demonstrate the validity of the norm constraint and to confirm the identifiability numerically. Utilizing the proposed constraint enables the visualization of latent variables via a biplot. We also investigate the sampling distribution of the maximum likelihood estimates (MLE) using synthetically generated data. We numerically observe that MLE is consistent and asymptotically normally distributed.
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Submitted 4 December, 2025;
originally announced December 2025.
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Introducing a Markov Chain-Based Time Calibration Procedure for Multi-Channel Particle Detectors: Application to the SuperFGD and ToF Detectors of the T2K Experiment
Authors:
S. Abe,
H. Alarakia-Charles,
I. Alekseev,
C. Alt,
T. Arai,
T. Arihara,
S. Arimoto,
A. M. Artikov,
Y. Awataguchi,
N. Babu,
V. Baranov,
G. Barr,
D. Barrow,
L. Bartoszek,
L. Bernardi,
L. Berns,
S. Bhattacharjee,
A. V. Boikov,
A. Blanchet,
A. Blondel,
A. Bonnemaison,
S. Bordoni,
M. H. Bui,
T. H. Bui,
F. Cadoux
, et al. (168 additional authors not shown)
Abstract:
Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed must be able to efficiently correct for minimal mis-synchronisation between channels and achieve the best detector performance. We present an iterative time calibr…
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Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed must be able to efficiently correct for minimal mis-synchronisation between channels and achieve the best detector performance. We present an iterative time calibration method based on Markov Chains, suitable for detector systems with multiple readout channels. Starting from correlated hit pairs alone, and without requiring an external reference time measurement, the method solves for fixed per-channel offsets, with precision limited only by the intrinsic single-channel resolution. A mathematical proof that the method is able to find the correct time offsets to be assigned to each detector channel in order to achieve inter-channel synchronisation is given, and it is shown that the number of iterations to reach convergence within the desired precision is controllable with a single parameter. Numerical studies are used to confirm unbiased recovery of true offsets. Finally, the application of the calibration method to the Super Fine-Grained Detector (SuperFGD) and the Time of Flight (TOF) detector at the upgraded T2K near detector (ND280) shows good improvement in overall timing resolution, demonstrating the effectiveness in a real-world scenario and scalability.
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Submitted 19 September, 2025; v1 submitted 11 August, 2025;
originally announced August 2025.
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First measurement of neutron capture multiplicity in neutrino-oxygen neutral-current quasi-elastic-like interactions using an accelerator neutrino beam
Authors:
T2K Collaboration,
K. Abe,
S. Abe,
R. Akutsu,
H. Alarakia-Charles,
Y. I. Alj Hakim,
S. Alonso Monsalve,
L. Anthony,
M. Antonova,
S. Aoki,
K. A. Apte,
T. Arai,
T. Arihara,
S. Arimoto,
Y. Asada,
Y. Ashida,
N. Babu,
G. Barr,
D. Barrow,
P. Bates,
M. Batkiewicz-Kwasniak,
V. Berardi,
L. Berns,
S. Bordoni,
S. B. Boyd
, et al. (314 additional authors not shown)
Abstract:
We report the first measurement of neutron capture multiplicity in neutrino-oxygen neutral-current quasi-elastic-like interactions at the gadolinium-loaded Super-Kamiokande detector using the T2K neutrino beam, which has a peak energy of about 0.6 GeV. A total of 30 neutral-current quasi-elastic-like event candidates were selected from T2K data corresponding to an exposure of $1.76\times10^{20}$ p…
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We report the first measurement of neutron capture multiplicity in neutrino-oxygen neutral-current quasi-elastic-like interactions at the gadolinium-loaded Super-Kamiokande detector using the T2K neutrino beam, which has a peak energy of about 0.6 GeV. A total of 30 neutral-current quasi-elastic-like event candidates were selected from T2K data corresponding to an exposure of $1.76\times10^{20}$ protons on target. The $γ$ ray signals resulting from neutron captures were identified using a neural network. The flux-averaged mean neutron capture multiplicity was measured to be $1.37\pm0.33\text{ (stat.)}$$^{+0.17}_{-0.27}\text{ (syst.)}$, which is compatible within $2.3\,σ$ than predictions obtained using our nominal simulation. We discuss potential sources of systematic uncertainty in the prediction and demonstrate that a significant portion of this discrepancy arises from the modeling of hadron-nucleus interactions in the detector medium.
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Submitted 30 May, 2025; v1 submitted 28 May, 2025;
originally announced May 2025.
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Characterization of the optical model of the T2K 3D segmented plastic scintillator detector
Authors:
S. Abe,
I. Alekseev,
T. Arai,
T. Arihara,
S. Arimoto,
N. Babu,
V. Baranov,
L. Bartoszek,
L. Berns,
S. Bhattacharjee,
A. Blondel,
A. V. Boikov,
M. Buizza-Avanzini,
J. Capó,
J. Cayo,
J. Chakrani,
P. S. Chong,
A. Chvirova,
M. Danilov,
C. Davis,
Yu. I. Davydov,
A. Dergacheva,
N. Dokania,
D. Douqa,
T. A. Doyle
, et al. (106 additional authors not shown)
Abstract:
The magnetised near detector (ND280) of the T2K long-baseline neutrino oscillation experiment has been recently upgraded aiming to satisfy the requirement of reducing the systematic uncertainty from measuring the neutrinonucleus interaction cross section, which is the largest systematic uncertainty in the search for leptonic charge-parity symmetry violation. A key component of the upgrade is Super…
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The magnetised near detector (ND280) of the T2K long-baseline neutrino oscillation experiment has been recently upgraded aiming to satisfy the requirement of reducing the systematic uncertainty from measuring the neutrinonucleus interaction cross section, which is the largest systematic uncertainty in the search for leptonic charge-parity symmetry violation. A key component of the upgrade is SuperFGD, a 3D segmented plastic scintillator detector made of approximately 2,000,000 optically-isolated 1 cm3 cubes. It will provide a 3D image of GeV neutrino interactions by combining tracking and stopping power measurements of final state particles with sub-nanosecond time resolution. The performance of SuperFGD is characterized by the precision of its response to charged particles as well as the systematic effects that might affect the physics measurements. Hence, a detailed Geant4 based optical simulation of the SuperFGD building block, i.e. a plastic scintillating cube read out by three wavelength shifting fibers, has been developed and validated with the different datasets collected in various beam tests. In this manuscript the description of the optical model as well as the comparison with data are reported.
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Submitted 31 October, 2024;
originally announced October 2024.
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Setting of the Poincaré section for accurately calculating the phase of rhythmic spatiotemporal dynamics
Authors:
Takahiro Arai,
Yoji Kawamura,
Toshio Aoyagi
Abstract:
The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements. However, the synchronization of spatiotemporal dynamics cannot be analyzed because a standardized method for calculating the phase has not been established. The presence of spatial structure complicates…
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The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements. However, the synchronization of spatiotemporal dynamics cannot be analyzed because a standardized method for calculating the phase has not been established. The presence of spatial structure complicates the determination of which measurements should be used for accurate phase calculation. To address this, we explore a method for calculating the phase from the time series of measurements taken at a single spatial grid point. The phase is calculated to increase linearly between event times when the measurement time series intersects the Poincaré section. The difference between the calculated phase and the isochron-based phase, resulting from the discrepancy between the isochron and the Poincaré section, is evaluated using a linear approximation near the limit-cycle solution. We found that the difference is small when measurements are taken from regions that dominate the rhythms of the entire spatiotemporal dynamics. Furthermore, we investigate an alternative method where the Poincaré section is applied to the time series obtained through orthogonal decomposition of the entire spatiotemporal dynamics. We present two decomposition schemes that utilize the principal component analysis. For illustration, the phase is calculated from the measurements of spatiotemporal dynamics exhibiting target waves or oscillating spots, simulated by weakly coupled FitzHugh-Nagumo reaction-diffusion models.
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Submitted 22 July, 2024;
originally announced July 2024.
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SHDB-AF: a Japanese Holter ECG database of atrial fibrillation
Authors:
Kenta Tsutsui,
Shany Biton Brimer,
Noam Ben-Moshe,
Jean Marc Sellal,
Julien Oster,
Hitoshi Mori,
Yoshifumi Ikeda,
Takahide Arai,
Shintaro Nakano,
Ritsushi Kato,
Joachim A. Behar
Abstract:
Atrial fibrillation (AF) is a common atrial arrhythmia that impairs quality of life and causes embolic stroke, heart failure and other complications. Recent advancements in machine learning (ML) and deep learning (DL) have shown potential for enhancing diagnostic accuracy. It is essential for DL models to be robust and generalizable across variations in ethnicity, age, sex, and other factors. Alth…
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Atrial fibrillation (AF) is a common atrial arrhythmia that impairs quality of life and causes embolic stroke, heart failure and other complications. Recent advancements in machine learning (ML) and deep learning (DL) have shown potential for enhancing diagnostic accuracy. It is essential for DL models to be robust and generalizable across variations in ethnicity, age, sex, and other factors. Although a number of ECG database have been made available to the research community, none includes a Japanese population sample. Saitama Heart Database Atrial Fibrillation (SHDB-AF) is a novel open-sourced Holter ECG database from Japan, containing data from 100 unique patients with paroxysmal AF. Each record in SHDB-AF is 24 hours long and sampled at 200 Hz, totaling 24 million seconds of ECG data.
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Submitted 22 June, 2024;
originally announced June 2024.
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Multivariate probability distribution for categorical and ordinal random variables
Authors:
Takashi Arai
Abstract:
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the co-occurrence probabilities of dummy variables required for categorical and ordinal variables, we propose a parsimonious parameterization for the Grassmann distribution…
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We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the co-occurrence probabilities of dummy variables required for categorical and ordinal variables, we propose a parsimonious parameterization for the Grassmann distribution that ensures the positivity of probability distribution. As an application of the proposed distribution, we develop a factor analysis for categorical and ordinal variables and show the validity of the model using a real dataset.
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Submitted 2 April, 2023;
originally announced April 2023.
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Factor analysis for a mixture of continuous and binary random variables
Authors:
Takashi Arai
Abstract:
We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As an application of the proposed distribution, we develop a factor analysis for a mixture of continuous and binary variables. We also discuss improper solutions as…
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We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As an application of the proposed distribution, we develop a factor analysis for a mixture of continuous and binary variables. We also discuss improper solutions associated with factor analysis. As a prescription to avoid improper solutions, we propose a constraint that each row vector of factor loading matrix has the same norm. We numerically validated the proposed factor analysis and norm constraint prescription by analyzing real datasets.
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Submitted 12 February, 2023; v1 submitted 25 September, 2022;
originally announced September 2022.
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Extracting phase coupling functions between collectively oscillating networks directly from time-series data
Authors:
Takahiro Arai,
Yoji Kawamura,
Toshio Aoyagi
Abstract:
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical methods for investigating the synchronization properties of such a rhythmic system is to statistically extract phase coupling functions between limit-cycle oscillato…
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Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical methods for investigating the synchronization properties of such a rhythmic system is to statistically extract phase coupling functions between limit-cycle oscillators directly from observed time-series data. In Particular, using a method that combines phase reduction theory and Bayesian inference, the phase coupling functions can be extracted from the time-series data of even just one variable in each oscillatory dynamical system with many degrees of freedom. However, it remains unclear how the choice of the observed variables affects the statistical inference for the phase coupling functions. In this study, we examine the influence of observed variable types on the extraction of phase coupling functions using some typical dynamical elements under various conditions. We demonstrate that our method can consistently extract the macroscopic phase coupling functions between two phases representing collective oscillations in a fully locked state, regardless of the observed variable types; for example, even using one variable of any element in one system and the mean-field value over all the elements in another system. We also study the case of globally coupled phase oscillators in a partially locked state. Our results reveal directional asymmetry in the robustness of extracting the macroscopic phase coupling function between two networks. For instance, when an asynchronous oscillator in network $A$ and the macroscopic collective oscillation of network $B$ is observed, the macroscopic phase coupling function from network $A$ to network $B$ can be extracted more robustly than in the opposite direction.
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Submitted 11 May, 2022; v1 submitted 29 October, 2021;
originally announced October 2021.
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Peculiar atomic bond nature in platinum monatomic chains
Authors:
Jiaqi Zhang,
Keisuke Ishizuka,
Masahiko Tomitori,
Toyoko Arai,
Kenta Hongo,
Ryo Maezono,
Erio Tosatti,
Yoshifumi Oshima
Abstract:
Metal atomic chains have been reported to change their electronic or magnetic properties by slight mechanical stimulus. However, the mechanical response has been veiled because of lack of information on the bond nature. Here, we clarify the bond nature in platinum (Pt) monatomic chains by our developed in-situ transmission electron microscope method. The stiffness is measured with sub N/m precisio…
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Metal atomic chains have been reported to change their electronic or magnetic properties by slight mechanical stimulus. However, the mechanical response has been veiled because of lack of information on the bond nature. Here, we clarify the bond nature in platinum (Pt) monatomic chains by our developed in-situ transmission electron microscope method. The stiffness is measured with sub N/m precision by quartz length-extension resonator. The bond stiffnesses at the middle of the chain and at the connecting to the base are estimated to be 25 and 23 N/m, respectively, which are higher than the bulk counterpart. Interestingly, the bond length of 0.25 nm is found to be elastically stretched to 0.31 nm, corresponding to 24% in strain. Such peculiar bond nature could be explained by a novel concept of "string tension". This study is a milestone that will significantly change the way we think about atomic bonds in one-dimensional substance.
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Submitted 30 April, 2021;
originally announced April 2021.
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A new Granger causality measure for eliminating the confounding influence of latent common inputs
Authors:
Takashi Arai
Abstract:
In this paper, we propose a new Granger causality measure which is robust against the confounding influence of latent common inputs. This measure is inspired by partial Granger causality in the literature, and its variant. Using numerical experiments we first show that the test statistics for detecting directed interactions between time series approximately obey the $F$-distributions when there ar…
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In this paper, we propose a new Granger causality measure which is robust against the confounding influence of latent common inputs. This measure is inspired by partial Granger causality in the literature, and its variant. Using numerical experiments we first show that the test statistics for detecting directed interactions between time series approximately obey the $F$-distributions when there are no interactions. Then, we propose a practical procedure for inferring directed interactions, which is based on the idea of multiple statistical test in situations where the confounding influence of latent common inputs may exist. The results of numerical experiments demonstrate that the proposed method successfully eliminates the influence of latent common inputs while the normal Granger causality method detects spurious interactions due to the influence of the confounder.
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Submitted 11 August, 2019;
originally announced August 2019.
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The atmospheric transparency measured with a LIDAR system at the Telescope Array experiment
Authors:
Takayuki Tomida,
Yusuke Tsuyuguchi,
Takahito Arai,
Takuya Benno,
Michiyuki Chikawa,
Koji Doura,
Masaki Fukushima,
Kazunori Hiyama,
Ken Honda,
Daisuke Ikeda,
John N. Matthews,
Toru Nakamura,
Daisuke Oku,
Hiroyuki Sagawa,
Hisao Tokuno,
Yuichiro Tameda,
Gordon B. Thomson,
Yoshiki Tsunesada,
Shigeharu Udo,
Hisashi Ukai
Abstract:
An atmospheric transparency was measured using a LIDAR with a pulsed UV laser (355nm) at the observation site of Telescope Array in Utah, USA. The measurement at night for two years in $2007\sim 2009$ revealed that the extinction coefficient by aerosol at the ground level is $0.033^{+0.016}_{-0.012} \rm km^{-1}$ and the vertical aerosol optical depth at 5km above the ground is…
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An atmospheric transparency was measured using a LIDAR with a pulsed UV laser (355nm) at the observation site of Telescope Array in Utah, USA. The measurement at night for two years in $2007\sim 2009$ revealed that the extinction coefficient by aerosol at the ground level is $0.033^{+0.016}_{-0.012} \rm km^{-1}$ and the vertical aerosol optical depth at 5km above the ground is $0.035^{+0.019}_{-0.013}$. A model of the altitudinal aerosol distribution was built based on these measurements for the analysis of atmospheric attenuation of the fluorescence light generated by ultra high energy cosmic rays.
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Submitted 5 September, 2011;
originally announced September 2011.