Hiroki Suyari

Hiroki Suyari

In finite-blocklength information theory, evaluating the fundamental limits of channel coding typically relies on normal approximations and Edgeworth expansions, which introduce additive polynomial corrections for skewness and higher-order moments. This paper proposes an alternative approach: rather than appending external error terms to a Gaussian baseline, we absorb these finite-length penalties using a generalized $q$-algebraic framework. By introducing a dynamic scaling law $1-q_n = αn^{-1}$ for the tuning parameter, we prove that the $q$-generalized information density corresponds to macroscopic higher-order fluctuations. Specifically, by setting this scaling constant to $α= T/(3V^2)$ (where $V$ is the varentropy and $T$ is the third central moment), our framework recovers the third-order coding limit, absorbing the $O(1)$ non-Gaussian penalty without relying on Hermite polynomials. Furthermore, we demonstrate that the $k$-th degree term of our algebraic expansion matches the $O(n^{1-k/2})$ asymptotic order of the $(k+1)$-th moment Edgeworth correction. This approach unifies classical probabilistic approximations within a single algebraic structure, establishing a mathematical connection between finite-blocklength analysis and generalized logarithmic mappings.

Katsuya Kosukegawa, Yasukuni Mori, Hiroki Suyari et al.

To ensure the safety of railroad operations, it is important to monitor and forecast track geometry irregularities. A higher safety requires forecasting with higher spatiotemporal frequencies, which in turn requires capturing spatial correlations. Additionally, track geometry irregularities are influenced by multiple exogenous factors. In this study, a method is proposed to forecast one type of track geometry irregularity, vertical alignment, by incorporating spatial and exogenous factor calculations. The proposed method embeds exogenous factors and captures spatiotemporal correlations using a convolutional long short-term memory. The proposed method is also experimentally compared with other methods in terms of the forecasting performance. Additionally, an ablation study on exogenous factors is conducted to examine their individual contributions to the forecasting performance. The results reveal that spatial calculations and maintenance record data improve the forecasting of vertical alignment.

Hiroki Suyari

Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the \textit{renormalized entropy} $s_{2-q}$. Derived from the asymptotic scaling of the combinatorial $q$-factorial, this quantity yields a stable thermodynamic limit, remaining finite ($O(N^0)$) for systems with strong correlations. Furthermore, we clarify the physical origin of the nonlinearity parameter $q$ through the concept of \textit{Varentropy} (Variance of Entropy). By unifying the macroscopic variational principle with the microscopic Superstatistics framework, we derive the relation $|q-1| \simeq 1/C$, where $C$ is the heat capacity of the reservoir. This result suggests that power-law statistics provides a thermodynamic description of finite systems, where the finite heat capacity of the heat bath necessitates a generalization beyond the standard Boltzmann-Gibbs limit ($C \to \infty$).