arXiv subjects

Weerawit Horinouchi

Publications and source records attributed to Weerawit Horinouchi.

5 recordsLinked to original sources

arXiv2026

Random matrix theory of sparse neuronal networks with heterogeneous timescales

Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is attributed to emergent marginally stable equilibria [PNAS 122 (2025) e2316745122]. Yet the link between trained network characteristics and their roles in shaping desirable dynamical landscapes remains unexplored. Here, we investigate the Jacobian matrices describing the dynamics near these equilibria and show that they are sparse, non-Hermitian rectangular-block matrices modified by heterogeneous synaptic decay timescales and activation-function gains. We specify a random matrix ensemble that faithfully captures the spectra of trained Jacobian matrices, arising from the inhibitory core - excitatory periphery network motif (pruned E weights, broadly distributed I weights) observed post-training. An analytic theory of this ensemble is developed using statistical field theory methods: a Hermitized resolvent representation of the spectral density is processed with a supersymmetry-based treatment in the style of Fyodorov and Mirlin. In this manner, an analytic description of the spectral edge is obtained, relating statistical parameters of the Jacobians (sparsity, weight variances, E/I ratio, and the distributions of timescales and gains) to near-critical features of the equilibria essential for robust working memory computation.

q-bio.NC↗

arXiv2025

First return times on sparse random graphs

We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an analytic theory of the first return time probability distribution. The problem turns out closely related to finding the spectrum of the normalized graph Laplacian that controls the continuum time version of the nearest-neighbor-hopping random walk. In the infinite graph limit, where loops are highly improbable, the returns operate in a manner qualitatively similar to c-regular trees, and the expressions for probabilities resemble those on random c-regular graphs. Because the vertex degrees are not exactly constant, however, the way c enters the formulas differs from the dependence on the graph degree of first return probabilities on random regular graphs.

cond-mat.dis-nn↗

arXiv2024

Remarks on the light ring images and the optical appearance of hairy black holes in Einstein-Maxwell-dilaton gravity

The behaviors of null geodesics in the spherical symmetric black holes in Einstein-Maxwell-dilaton (EMD) theory with coupling function $f(Φ)=e^{-2αΦ}$ are meticulously analyzed. We investigate the effects of coupling constant $α$ on the effective potential of photon trajectories within three ranges, namely $0<α<1$, $α=1$ and $α>1$. We find that the thicknesses of lensing and photon rings are smaller at larger $α$ and fixed electric charge in the unit of mass $q$, whereas they are larger at fixed $α$ and larger $q$. This behavior can be described by using the angular Lyapunov exponent $γ$ in the vicinity of the critical curve. Remarkably, the behaviors of photon trajectories are found to be more interesting when $α>1$. Namely, the radius of the black hole shadow $R_\text{s}$ becomes to be smaller than the photon sphere radius $r_\text{ph}$ when $α> 1$ and $q>q^*$. Moreover, $R_\text{s}$ goes to zero as $q$ saturates the extremal limit, beyond which the photon orbit becomes absent. Furthermore, we construct the optical appearance of black holes surrounded by optically and geometrically thin accretion disk with three cases of Gralla-Lupsasca-Marrone (GLM) emission profile. Our results indicate that the observed flux originating from the lensing and photon rings exhibits suppression as $α$ increases, while it undergoes amplification with the increasing parameter $q$.

gr-qc↗

arXiv2024

Observing Black Hole Phase Transitions in Extended Phase Space and Holographic Thermodynamics Approaches from Optical Features

The phase transitions of charged Anti-de Sitter (AdS) black holes are characterized by studying null geodesics in the vicinity of the critical curve of photon trajectories around black holes as well as their optical appearance as the black hole images. In the present work, the critical parameters including the orbital half-period $τ$, the angular Lyapunov exponent $λ_L$, and the temporal Lyapunov exponent $γ_L$ are employed to characterize black hole phase transitions within both the extended phase space and holographic thermodynamics frameworks. Under certain conditions, we observe multi-valued function behaviors of these parameters as functions of bulk pressure and temperature in the respective approaches. We propose that $τ$, $λ_L$, and $γ_L$ can serve as order parameters due to their discontinuous changes at first-order phase transitions. To validate this, we provide detailed analytical calculations demonstrating that these optical critical parameters follow scaling behavior near the critical phase transition point. Notably, the critical exponents for these parameters are found to be $1/2$, consistent with those of the van der Waals fluid. Our findings suggest that static and distant observers can study black hole thermodynamics by analyzing the images of regions around the black holes.

gr-qc↗

arXiv2024

A Gaussian integral that counts regular graphs

In a recent article J. Phys. Compl. 4 (2023) 035005, Kawamoto evoked statistical physics methods for the problem of counting graphs with a prescribed degree sequence. This treatment involved truncating a particular Taylor expansion at the first two terms, which resulted in the Bender-Canfield estimate for the graph counts. This is surprisingly successful since the Bender-Canfield formula is asymptotically accurate for large graphs, while the series truncation does not a priori suggest a similar level of accuracy. We upgrade the above treatment in three directions. First, we derive an exact formula for counting d-regular graphs in terms of a d-dimensional Gaussian integral. Second, we show how to convert this formula into an integral representation for the generating function of d-regular graph counts. Third, we perform explicit saddle point analysis for large graph sizes and identify the saddle point configurations responsible for graph count estimates. In these saddle point configurations, only two of the integration variables condense to significant values, while the remaining ones approach zero for large graphs. This provides an underlying picture that justifies Kawamoto's earlier findings.

cond-mat.stat-mech↗