arXiv subjects

Hiroki Suyari

Publications and source records attributed to Hiroki Suyari.

At least 19 recordsLinked to original sources

arXiv2026

Breakdown of Edgeworth Expansion in Finite-Blocklength Regime and Exact Absorption via $q$-Deformation

This paper addresses the structural breakdown of the Edgeworth expansion in the finite-blocklength (FBL) regime, where conventional asymptotic approximations yield unphysical negative probabilities in the deep-tail region. We propose a $q$-deformed framework that resolves this inconsistency by replacing additive polynomial perturbations with a geometric deformation of the information density space. Motivated by the linearization of nonlinear dynamics, we prove that dynamically scaling the $q$-logarithmic parameter exactly absorbs the third-order skewness while preserving global nonnegativity. We establish a universal asymptotic matching, demonstrating that the framework encapsulates higher-order asymptotic scales. Numerical results confirm that the proposed method matches the state-of-the-art precision of the Cornish-Fisher bound without the risk of negative probabilities. The framework offers a robust and computationally stable foundation for evaluating operational limits in ultra-reliable communications such as 6G and URLLC.

cs.IT↗

arXiv2026

Trinity of Varentropy: Finiteness, Fluctuations, and Stability in Power-Law Statistics

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 mapping the microscopic combinatorics sequentially onto the probability constraints of Type-B superstatistics, we prove that the entropic index is strictly governed by the exact identity $q-1 = 1/C$, where $C$ is the total thermodynamic heat capacity of the system and the reservoir. This deductive derivation, enforced by the uniqueness of the inverse Laplace transform, demonstrates that power-law statistics emerges as a necessary consequence of finite thermal environments, providing a first-principles description beyond the standard infinite Boltzmann-Gibbs limit ($C \to \infty$).

cond-mat.stat-mech↗

arXiv2026

Breakdown of Perturbative Expansions and Exact Algebraic Absorption of Finite-Size Fluctuations in Statistical Mechanics

In statistical mechanics, evaluating finite-size macroscopic fluctuations typically relies on Edgeworth expansions. However, these perturbative methods append additive polynomial corrections that break down in the large deviation regime, yielding unphysical negative probabilities. We propose a structural resolution: rather than relying on additive polynomials, we absorb finite-size skewness using a globally stable $q$-deformed framework. By introducing a dynamic scaling law $1-q_n = O(n^{-1})$ for the nonextensivity parameter, we prove this $q$-deformed framework captures macroscopic higher-order fluctuations in independent and identically distributed (i.i.d.) systems. Specifically, this algebraic tuning absorbs third-order skewness while guaranteeing probability density nonnegativity across the entire domain. Furthermore, the $k$-th degree term of this $q$-logarithmic expansion corresponds to the $O(n^{1-k/2})$ asymptotic order of classical $(k+1)$-th moment Edgeworth corrections. This correspondence functions as a stable resummation of divergent asymptotic expansions, establishing a mathematical bridge between finite-size i.i.d. fluctuations and the Tsallis statistics governing complex systems.

cs.IT↗

arXiv2026

Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations

Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by introducing the Linearization Principle directly at the dynamical stage. By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the $q$-deformed geometry, corresponding to Tsallis statistics, exhibits a fundamental duality between the dynamic index $q$ and the thermodynamic index $2-q$: the stationary state is a $q$-Gaussian distribution that minimizes a free energy functional defined by a generalized entropy of index $2-q$. We prove the $H$-theorem for the derived equation and demonstrate its application to the harmonic oscillator and the free particle. This framework describes anomalous diffusion without relying on ad-hoc constraints or phenomenological nonlinear drift forces.

cond-mat.stat-mech↗

arXiv2026

A Constructive Approach to $q$-Gaussian Distributions: $α$-Divergence as Rate Function and Generalized de Moivre-Laplace Theorem

The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. 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.

math.PR↗

arXiv2026

Exact Density Profiles of 1D Quantum Fluids in the Thomas-Fermi Limit: Geometric Hierarchy to the Tonks-Girardeau Gas

We present a geometric framework for 1D quantum fluids across interaction regimes in the Thomas-Fermi limit. Based on the Linearization Principle via the $q$-logarithm, macroscopic density profiles form a discrete hierarchy: the ideal Bose gas ($q=1$), the mean-field Gross-Pitaevskii condensate ($q=-1$), and the strongly correlated Tonks-Girardeau gas ($q=-3$). We further derive a universal sound velocity scaling, $c \propto ρ^{(1-q)/4}$, valid in the interacting regimes ($q \le -1$). This establishes a non-perturbative link between static geometry and dynamical excitations in many-body systems.

cond-mat.quant-gas↗

arXiv2025

Development of an Unpaired Deep Neural Network for Synthesizing X-ray Fluoroscopic Images from Digitally Reconstructed Tomography in Image Guided Radiotherapy

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.

cs.CV↗

arXiv2023

Spatiotemporal forecasting of vertical track alignment with exogenous factors

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.

cs.LG↗

arXiv2019

Advantages of $q$-logarithm representation over $q$-exponential representation from the sense of scale and shift on nonlinear systems

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts with the distinction between exponential and non-exponential family in the sense of the scale unit of measurement. In the simplest nonlinear model ${dy}/{dx}=y^{q}$, it is shown how typical effects such as rescaling and shift emerge in the nonlinear systems and affect observed data. Based on the present results, the two representations, namely the $q$-exponential and the $q$-logarithm ones, are proposed. The former is for rescaling, the latter for unified understanding with a fixed scale unit. As applications of these representations, the corresponding entropy and the general probability expression for unified understanding with a fixed scale unit are presented. For the theoretical study of nonlinear systems, $q$-logarithm representation is shown to have significant advantages over $q$-exponential representation.

math-ph↗

arXiv2015

Large deviation estimates involving deformed exponential functions

We study large deviation properties of probability distributions with either a compact support or a fat tail by comparing them with q-deformed exponential distributions. Our main result is a large deviation property for probability distributions with a fat tail.

math-ph↗

arXiv2014

$α$-divergence derived as the generalized rate function in a power-law system

The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise $q$-Stirling's formula. The $α$-divergence (or $q$-divergence) is uniquely derived from the generalized binomial distribution in the sense that when $α\rightarrow-1$ (i.e., $q\rightarrow1$) it recovers KL divergence obtained from the standard binomial distribution. Based on these combinatorial considerations, it is shown that $α$-divergence (or $q$-divergence) is appeared as the generalized rate function in the large deviation estimate in Tsallis statistics.

math-ph↗

arXiv2007

Multiplicative duality, q-triplet and (mu,nu,q)-relation derived from the one-to-one correspondence between the (mu,nu)-multinomial coefficient and Tsallis entropy Sq

We derive the multiplicative duality "q<->1/q" and other typical mathematical structures as the special cases of the (mu,nu,q)-relation behind Tsallis statistics by means of the (mu,nu)-multinomial coefficient. Recently the additive duality "q<->2-q" in Tsallis statistics is derived in the form of the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy. A slight generalization of this correspondence for the multiplicative duality requires the (mu,nu)-multinomial coefficient as a generalization of the q-multinomial coefficient. This combinatorial formalism provides us with the one-to-one correspondence between the (mu,nu)-multinomial coefficient and Tsallis entropy Sq, which determines a concrete relation among three parameters mu, nu and q, i.e., nu(1-mu)+1=q which is called "(mu,nu,q)-relation" in this paper. As special cases of the (mu,nu,q)-relation, the additive duality and the multiplicative duality are recovered when nu=1 and nu=q, respectively. As other special cases, when nu=2-q, a set of three parameters (mu,nu,q) is identified with the q-triplet (q_{sen},q_{rel},q_{stat}) recently conjectured by Tsallis. Moreover, when nu=1/q, the relation 1/(1-q_{sen})=1/alpha_{min}-1/alpha_{max} in the multifractal singularity spectrum f(alpha) is recovered by means of the (mu,nu,q)-relation.

cond-mat.stat-mech↗

arXiv2006

Scaling property and the generalized entropy uniquely determined by a fundamental nonlinear differential equation

We derive a scaling property from a fundamental nonlinear differential equation whose solution is the so-called q-exponential function. A scaling property has been believed to be given by a power function only, but actually more general expression for the scaling property is found to be a solution of the above fundamental nonlinear differential equation. In fact, any power function is obtained by restricting the domain of the q-exponential function appropriately. As similarly as the correspondence between the exponential function and Shannon entropy, an appropriate generalization of Shannon entropy is expected for the scaling property. Although the q-exponential function is often appeared in the optimal distributions of some one-parameter generalized entropies such as Renyi entropy, only Tsallis entropy is uniquely derived from the algebra of the q-exponential function, whose uniqueness is shown in the two ways in this paper.

cond-mat.stat-mech↗

arXiv2006

A two-parameter generalization of Shannon-Khinchin Axioms and the uniqueness theorem

Based on the one-parameter generalization of Shannon-Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have further developed the SK Axioms in accordance with the two-parameter entropy introduced by Sharma-Taneja, Mittal, Borges-Roditi, and Kaniadakis-Lissia-Scarfone. The corresponding unique theorem is proved. It is shown that the obtained two-parameter Shannon additivity is a natural consequence from the Leibniz rule of the two-parameter Chakrabarti-Jagannathan difference operator.

cond-mat.stat-mech↗

arXiv2005

The unique non self-referential q-canonical distribution and the physical temperature derived from the maximum entropy principle in Tsallis statistics

The maximum entropy principle in Tsallis statistics is reformulated in the mathematical framework of the q-product, which results in the unique non self-referential q-canonical distribution. As one of the applications of the present formalism, we theoretically derive the physical temperature which coincides with that already obtained in accordance with the generalized zeroth law of thermodynamics.

cond-mat.stat-mech↗

arXiv2004

Law of Error in Tsallis Statistics

Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined by the q-logarithm and the q-exponential functions to the definition of the likelihood function in Gauss' law of error. The maximum likelihood principle leads us to finding Tsallis distribution as nonextensively generalization of Gaussian distribution.

cond-mat.stat-mech↗

arXiv2004

q-Stirling's formula in Tsallis statistics

We present the q-Stirling's formula using the q-product determined by Tsallis entropy as nonextensive generalization of the usual Stirling's formula. The numerical computations and the proof are also shown. Moreover, we derive and prove some inequalities and equalities concerning the q-Stirling's formula. Applying the q-Stirling's formula, the mathematical foundations of Tsallis statistics can be obtained as similarly as those of Boltzmann-Gibbs statistics.

cond-mat.stat-mech↗

arXiv2004

Mathematical structure derived from the q-multinomial coefficient in Tsallis statistics

We present the conclusive mathematical structure behind Tsallis statistics. We obtain mainly the following five theoretical results: (i) the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy, (ii) symmetry behind Tsallis statistics, (iii) the numerical computations revealing the existence of the central limit theorem in Tsallis statistics, (iv) Pascal's triangle in Tsallis statistics and its properties, (v) the self-similarity of the q-product $\otimes_{q}$ leading to successful applications in Tsallis statistics. In particular, the third result (iii) provides us with a mathematical representation of a convincible answer to the physical problem: "Why so many power-law behaviors exist in nature universally ?"

cond-mat.stat-mech↗