Hiroki Suyari

Hiroki Suyari, Antonio M. Scarfone

The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are concepts of information theory and probability. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law distributions has primarily evolved through descriptive models or variational principles, rather than a constructive derivation comparable to the classical binomial process. This paper establishes a constructive probabilistic framework for power-law distributions, proceeding from the nonlinear differential equation $dy/dx = y^q$ without assuming a specific distribution a priori. We build the algebraic and combinatorial foundations, which lead to a generalized binomial distribution based on finite counting. We prove the LDP for this generalized binomial distribution in the regime $0 < q < 1$, demonstrating that the $α$-divergence is identified as the rate function, and clarify the breakdown of this macroscopic scaling for heavier tails ($q > 1$). This result connects our constructive framework to the structures of information geometry. Furthermore, we prove a generalized de Moivre-Laplace theorem, showing that the generalized binomial distribution converges to a heavy-tailed limit distribution (the $q$-Gaussian distribution). We derive that the scaling law follows the order of $n^{q/2}$ as a consequence of the underlying nonlinearity. These analytical results are numerically verified for distinct values of $q \in (0, 2)$. This framework provides a constructive basis that unifies the shift-invariant exponential family and the rescaling-invariant power-law family.

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 ($C \to \infty$).

Chisako Hayashi, Shinichiro Mori, Yasukuni Mori et al.

Purpose The purpose of this study was to develop and evaluate a deep neural network (DNN) capable of generating flat-panel detector (FPD) images from digitally reconstructed radiography (DRR) images in lung cancer treatment, with the aim of improving clinical workflows in image-guided radiotherapy. Methods A modified CycleGAN architecture was trained on paired DRR-FPD image data obtained from patients with lung tumors. The training dataset consisted of over 400 DRR-FPD image pairs, and the final model was evaluated on an independent set of 100 FPD images. Mean absolute error (MAE), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and Kernel Inception Distance (KID) were used to quantify the similarity between synthetic and ground-truth FPD images. Computation time for generating synthetic images was also measured. Results Despite some positional mismatches in the DRR-FPD pairs, the synthetic FPD images closely resembled the ground-truth FPD images. The proposed DNN achieved notable improvements over both input DRR images and a U-Net-based method in terms of MAE, PSNR, SSIM, and KID. The average image generation time was on the order of milliseconds per image, indicating its potential for real-time application. Qualitative evaluations showed that the DNN successfully reproduced image noise patterns akin to real FPD images, reducing the need for manual noise adjustments. Conclusions The proposed DNN effectively converted DRR images into realistic FPD images for thoracic cases, offering a fast and practical method that could streamline patient setup verification and enhance overall clinical workflow. Future work should validate the model across different imaging systems and address remaining challenges in marker visualization, thereby fostering broader clinical adoption.