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Kohei Noda

Publications and source records attributed to Kohei Noda.

16 recordsLinked to original sources
arXiv2026

Two-dimensional Coulomb gases with multiple outposts

We study two-dimensional Coulomb gases in the presence of $m\in\mathbb{N}_{>0}$ outposts. An outpost is a connected component of the coincidence set that lies outside the droplet. The case $m=1$ was previously investigated by Ameur, Charlier, and Cronvall. They showed that, as the total number of particles in the Coulomb gas tends to infinity, the number of particles accumulating near the outpost remains of order one and converges in distribution to the Heine distribution. In this work, we extend this analysis to the case of an arbitrary but fixed number $m$ of outposts. We prove that the joint distribution of the numbers of particles near the outposts converges to a multidimensional Heine distribution. Our results reveal a interesting phenomenon: although the outposts are geometrically disconnected, the particle count near each outpost is strongly correlated with the particle counts near all other outposts, not only the nearest ones (provided the outposts are not separated by a component of the droplet).

math.PR↗
arXiv2025

Omics-scale polymer computational database transferable to real-world artificial intelligence applications

Developing large-scale foundational datasets is a critical milestone in advancing artificial intelligence (AI)-driven scientific innovation. However, unlike AI-mature fields such as natural language processing, materials science, particularly polymer research, has significantly lagged in developing extensive open datasets. This lag is primarily due to the high costs of polymer synthesis and property measurements, along with the vastness and complexity of the chemical space. This study presents PolyOmics, an omics-scale computational database generated through fully automated molecular dynamics simulation pipelines that provide diverse physical properties for over $10^5$ polymeric materials. The PolyOmics database is collaboratively developed by approximately 260 researchers from 48 institutions to bridge the gap between academia and industry. Machine learning models pretrained on PolyOmics can be efficiently fine-tuned for a wide range of real-world downstream tasks, even when only limited experimental data are available. Notably, the generalisation capability of these simulation-to-real transfer models improve significantly as the size of the PolyOmics database increases, exhibiting power-law scaling. The emergence of scaling laws supports the "more is better" principle, highlighting the significance of ultralarge-scale computational materials data for improving real-world prediction performance. This unprecedented omics-scale database reveals vast unexplored regions of polymer materials, providing a foundation for AI-driven polymer science.

physics.chem-ph↗
arXiv2025

Partition functions of two-dimensional Coulomb gases with circular root- and jump-type singularities

In this paper, we study the random polynomial $p_n(\rho):=\prod_{j=1}^n (|z_j|-\rho)$, where the points $\{z_j\}_{j=1}^n$ are the eigenvalue moduli of random normal matrices with a radially symmetric potential. We establish precise large $n$ asymptotic expansions for the moment generating function \[ \mathbb{E}\!\left[e^{\tfrac{u}{\pi}\mathrm{Im}\log p_n(\rho)}\, e^{a\,\mathrm{Re}\log p_n(\rho)}\right], \qquad u\in\mathbb{R}, \; a>-1, \] where $\rho>0$ lies in the bulk of the spectral droplet. The asymptotic expansion is expressed in terms of parabolic cylinder functions, which confirms a conjecture of Byun and Charlier. This also provides the first free energy expansion of two-dimensional Coulomb gases with general circular root- and jump-type singularities. While the $a=0$ case has already been widely studied in the literature due to its relation to counting statistics, we also obtain new results for this special case.

math-ph↗
arXiv2025

Real Eigenvalues of Asymmetric Wishart Matrices: Expected Number, Global Density and Integrable Structure

We investigate the real eigenvalues of asymmetric Wishart matrices of size $N$, indexed by the rectangular parameter $ν\in \mathbb{N}$ and the non-Hermiticity parameter $τ\in [0,1]$. The rectangular parameter $ν$ is either fixed or proportional to $N$. The non-Hermiticity parameter $τ$ is either fixed or $τ= 1 - O(1/N)$, corresponding to the strongly and weakly non-Hermitian regimes, respectively. We establish a decomposition structure for the finite-$N$ correlation kernel of the real eigenvalues, which form Pfaffian point processes. Taking the symmetric limit $τ= 1$, where the model reduces to the Laguerre orthogonal ensemble, this decomposition structure reduces to the known rank-one perturbation structure established by Adler, Forrester, Nagao, and van Moerbeke, as well as by Widom. Using the decomposition structure, we show that the expected number of real eigenvalues is proportional to $\sqrt{N}$ in the strongly non-Hermitian regime and to $N$ in the weakly non-Hermitian regime, providing explicit leading coefficients in both cases. Furthermore, we derive the limiting real eigenvalue densities, which recovers the Marchenko-Pastur distribution in the symmetric limit.

math.PR↗
arXiv2024

Determinantal structure of the overlaps for induced spherical unitary ensemble

In this note, we study the determinantal structure of the $k$-th conditional expectation of the overlap for induced spherical unitary ensemble. We will show the universality for the scaling limits of the $k$-the conditional expectation of the overlap in the three regimes, strongly non-unitary, weakly non-unitary, and the singular origin regimes. As a consequence, we will confirm the universality for the overlap.

math-ph↗
arXiv2024

Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble

We study the integrable structure and scaling limits of the conditioned eigenvector overlap of the symplectic Ginibre ensemble of Gaussian non-Hermitian random matrices with independent quaternion elements. The average of the overlap matrix elements constructed from left and right eigenvectors, conditioned to $x$, are derived in terms of a Pfaffian determinant. Regarded as a two-dimensional Coulomb gas with the Neumann boundary condition along the real axis, it contains a kernel of skew-orthogonal polynomials with respect to the weight function $\omega^{(\mathrm{over})}(z)=|z-\overline{x}|^2(1+|z-x|^2)e^{-2|z|^2}$, including a non-trivial insertion of a point charge. The mean off-diagonal overlap is related to the diagonal (self-)overlap by a transposition, in analogy to the complex Ginibre ensemble. For $x$ conditioned to the real line, extending previous results at $x=0$, we determine the skew-orthogonal polynomials and their skew-kernel with respect to $\omega^{(\mathrm{over})}(z)$. This is done in two steps and involves a Christoffel perturbation of the weight $\omega^{(\mathrm{over})}(z)=|z-\overline{x}|^2\omega^{(\mathrm{pre})}(z)$, by computing first the corresponding quantities for the unperturbed weight $\omega^{(\mathrm{pre})}(z)$. Its kernel is shown to satisfy a differential equation at finite matrix size $N$. This allows us to take different large-$N$ limits, where we distinguish bulk and edge regime along the real axis. The limiting mean diagonal overlaps and corresponding eigenvalue correlation functions of the point processes with respect to $\omega^{(\mathrm{over})}(z)$ are determined. We also examine the effect on the planar orthogonal polynomials when changing the variance in $\omega^{(\mathrm{pre})}(z)$, as this appears in the eigenvector statistics of the complex Ginibre ensemble.

math-ph↗
arXiv2024

Advancing Extrapolative Predictions of Material Properties through Learning to Learn

Recent advancements in machine learning have showcased its potential to significantly accelerate the discovery of new materials. Central to this progress is the development of rapidly computable property predictors, enabling the identification of novel materials with desired properties from vast material spaces. However, the limited availability of data resources poses a significant challenge in data-driven materials research, particularly hindering the exploration of innovative materials beyond the boundaries of existing data. While machine learning predictors are inherently interpolative, establishing a general methodology to create an extrapolative predictor remains a fundamental challenge, limiting the search for innovative materials beyond existing data boundaries. In this study, we leverage an attention-based architecture of neural networks and meta-learning algorithms to acquire extrapolative generalization capability. The meta-learners, experienced repeatedly with arbitrarily generated extrapolative tasks, can acquire outstanding generalization capability in unexplored material spaces. Through the tasks of predicting the physical properties of polymeric materials and hybrid organic--inorganic perovskites, we highlight the potential of such extrapolatively trained models, particularly with their ability to rapidly adapt to unseen material domains in transfer learning scenarios.

cond-mat.mtrl-sci↗
arXiv2024

Scaling limits of complex and symplectic non-Hermitian Wishart ensembles

Non-Hermitian Wishart matrices were introduced in the context of quantum chromodynamics with a baryon chemical potential. These provide chiral extensions of the elliptic Ginibre ensembles as well as non-Hermitian extensions of the classical Wishart/Laguerre ensembles. In this work, we investigate eigenvalues of non-Hermitian Wishart matrices in the symmetry classes of complex and symplectic Ginibre ensembles. We introduce a generalised Christoffel-Darboux formula in the form of a certain second-order differential equation, offering a unified and robust method for analyzing correlation functions across all scaling regimes in the model. By employing this method, we derive universal bulk and edge scaling limits for eigenvalue correlations at both strong and weak non-Hermiticity.

math.PR↗
arXiv2023

Determinantal structure of the conditional expectation of the overlaps for the induced Ginibre unitary ensemble

As is widely known, a non-Hermitian matrix exhibits distinct left and right eigenvectors, which form a bi-orthogonal system. Chalker and Mehling initiated the study of the joint statistics of the eigenvalues and the overlaps defined by the left and right eigenvectors of the Ginibre unitary ensemble. Later, Akemann et al. continued their investigation by studying the $k$-th correlation function weighted by the on- and off-overlaps of the Ginibre unitary ensemble. In this paper, as a natural extension of their work, we investigate the $k$-th correlation function weighted by the on- and off-diagonal overlaps of the induced Ginibre unitary ensemble. Similar to the Ginibre unitary ensemble case, we will demonstrate the determinantal structure. As a result, we will confirm the universality of the $k$-th correlation function weighted by the on- and off-diagonal overlaps in both the bulk and edge scaling limits in the strongly non-unitary regime. Furthermore, in the weakly non-unitary regime and at the singular origin, we will report new relationships between the overlap and such spectral regimes.

math-ph↗
arXiv2023

Observation of Rayleigh scattering by simplified optical correlation-domain reflectometry without frequency shifter

We present a method for measuring the transmission loss of an optical fiber using simplified optical correlation-domain reflectometry. By intentionally lowering the spatial resolution of the system, we observe the Rayleigh scattered signal for the first time without the need for a frequency shifter. Using this method, we simultaneously measure the transmission loss, location, and loss of faulty connections along a 10-km-long fiber under test by performing distributed reflected-power measurements of Rayleigh scattering and Fresnel reflection.

physics.optics↗
arXiv2022

High-speed high-resolution optical correlation-domain reflectometry without using electrical spectrum analyzer

We propose a newly configured optical correlation-domain reflectometry (OCDR) without the use of an electrical spectrum analyzer (ESA) for high-speed distributed reflectivity measurement with an enhanced spatial resolution. First, the operation of ESA-free OCDR is analyzed by numerical simulation, the results of which show the potential of the configuration to perform distributed reflectivity measurement with an improved spatial resolution. Subsequently, the simulation results are verified by comparison experiments, where distributed reflectivity measurements along a 32-m-long single-mode fiber joint with multiple connectors are performed using both conventional (with averaging) and ESA-free OCDR configurations (without averaging) at a repetition rate of 100 Hz. The widths of the reflectivity peaks experimentally obtained by the conventional and ESA-free OCDR configurations are 22.9 cm and 7.0 cm, respectively. Finally, we experimentally evaluated the performance of the ESA-free OCDR at higher repetition rates, achieving 6.3-cm spatial resolution at a repetition rate of 1 kHz. This result indicates that the ESA-free OCDR can perform a distributed reflectivity measurement with an improved spatial resolution at a higher operation speed than ever.

physics.optics↗
arXiv2021

Expected number of zeros of random power series with finitely dependent Gaussian coefficients

We are concerned with zeros of random power series with coefficients being a stationary, centered, complex Gaussian process. We show that the expected number of zeros in every smooth domain in the disk of convergence is less than that of the hyperbolic GAF with i.i.d. coefficients. When coefficients are finitely dependent, i.e., the spectral density is a trigonometric polynomial, we derive precise asymptotics of the expected number of zeros inside the disk of radius $r$ centered at the origin as $r$ tends to the radius of convergence, in the proof of which we clarify that the negative contribution to the number of zeros stems from the zeros of the spectral density.

math.PR↗