Search Results (83)

Brain lateralization is a biological asymmetry in which a bilaterally organized nervous system develops direction-specific functional organization. This hypothesis distinguishes gravity-driven physical symmetry reduction from informational symmetry breaking. Gravity provides a stable vertical reference, yet matched leftward and rightward tilts become biologically relevant only when noisy vestibular population responses carry decodable tilt-sign information. At fixed unsigned tilt magnitude, the criterion is nonzero conditional mutual information between binary tilt sign and vestibular population response; for equal sign priors, this is equivalent to Jensen–Shannon divergence between sign-conditioned response distributions. Shannon entropy describes within-condition response spread, Fisher information describes local continuous-angle precision, and noise-aware representational distance describes PIVC-centered state separation. The otolith-to-perceptual pathway is formulated as a constrained effective state-space transformation from vestibular population responses through an intermediate brainstem–cerebellar state to distributed parieto-insular vestibular cortex (PIVC)-centered cortical states and perceived self-orientation. The framework predicts sign-specific vestibular and PIVC information for matched tilts, reduced or reorganized sign information in bilateral vestibulopathy, and covariance among cortical geometry, orientation-estimation reliability, and orientation-dependent behavior. Auditory and visual spatial transformations provide computational precedents rather than anatomical homology. The model offers a testable sensorimotor scaffold without determining a fixed hemispheric sign. Full article

This paper investigates statistical inference for the Shannon entropy of the Transmuted Weibull Distribution under progressively Type-II censored samples. The Transmuted Weibull Distribution is obtained by applying the quadratic rank transmutation map to the cumulative distribution function of the two-parameter Weibull distribution, thereby substantially enhancing its modeling flexibility while preserving the analytical tractability of the baseline distribution. Consequently, it provides greater flexibility for modeling lifetime data exhibiting pronounced skewness and complex hazard rate behaviors. First, a closed-form expression for the Shannon entropy of the Transmuted Weibull Distribution is derived. From a frequentist perspective, the maximum likelihood estimators of the model parameters are obtained numerically using the Newton–Raphson algorithm, and the corresponding maximum likelihood estimator of Shannon entropy is derived through the invariance property of maximum likelihood estimation. To quantify estimation uncertainty, asymptotic confidence intervals are constructed using the Delta method together with the observed Fisher information matrix, while Bootstrap confidence intervals are also developed to improve finite-sample inference. From a Bayesian perspective, posterior inference is conducted using a hybrid Gibbs sampling algorithm within the Markov chain Monte Carlo framework. Bayesian point estimators of Shannon entropy are obtained under the squared error loss function, the absolute error loss function, and the 0–1 loss function, corresponding to the posterior mean, posterior median, and posterior mode, respectively. In addition, highest posterior density credible intervals are constructed for the Shannon entropy. The proposed methods are evaluated through an extensive Monte Carlo simulation study under three representative progressively Type-II censoring schemes. Estimation performance is assessed in terms of bias, mean squared error, interval coverage probability, and average interval length. The simulation results demonstrate that the Bayesian estimators consistently outperform the maximum likelihood estimator, particularly for small sample sizes and heavy censoring, while the highest posterior density credible intervals achieve more accurate coverage probabilities and shorter interval lengths. Finally, the proposed inferential procedures are illustrated using a real dataset consisting of remission times from 128 bladder cancer patients, demonstrating their practical applicability and robustness. Full article

Graph-based narrative extraction relies on a coherence function to score transitions between events, but the coherence metrics in current use are defined operationally and lack an information-theoretic foundation. We study the composite metric $C=\sqrt{A·T}$, where A is the angular similarity of document embeddings and $T=1-d_{\mathrm{JS}}$ is the topic proximity through the Jensen–Shannon distance of soft cluster memberships, and we provide an information-geometric reading of this metric together with an axiomatic characterization of the geometric-mean combinator. On the product manifold ${\mathbb{S}}^{d-1}\times {\Delta }_{+}^{K-1}$, the negative log-coherence decomposes additively into an angular and a topic cost. Because the Riemannian metric tensor induced by the Jensen–Shannon distance on the simplex is proportional to the Fisher information matrix, the topic component is locally consistent with the Fisher–Rao metric singled out by Chentsov’s theorem. Within a parametric family of combinators (the compensability spectrum), the geometric mean is the unique combinator consistent with four natural axioms (a boundary/veto condition, symmetry, log-additivity, normalization), and the construction also motivates a proper product metric $d_{\times }$ that we use as a reference distance. Experiments on four corpora spanning news and academic domains (40 to 6000 documents), three general-purpose embedding families (GPT-4/ada-002, MPNet, MiniLM-L6) plus citation-aware SPECTER2, and three alternative topic models (LDA, soft k-means, GMM) are consistent with the framework: the Fisher identity holds with $R\ge 0.99$, the geometric mean tracks $d_{\times }$ closely ($\rho =0.999$), and a downstream LLM-as-judge consistency check shows that the geometric mean is not empirically dominated by any alternative combinator or single-channel baseline. Sweeping the compensability spectrum, the bottleneck-coherence gap between extracted storylines and random sequences splits into a symmetric component—maximized at the geometric mean on the four corpora above and a fifth, human-navigation corpus—and a displacement term; a cross-modal case study on a human-curated image narrative reproduces the same effect in a second modality. Together, these results provide an information-geometric justification for the composite coherence metric and articulate the conditions under which the geometric mean is the natural choice. Full article

In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schrödinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel–Duke ordering to obtain exact analytical solutions for the energy spectrum and wave functions. The interplay between the fractal parameter $\alpha$, the effective lattice scale $l_0$, and the harmonic confinement strength $\omega$ is explored. We perform a comprehensive analysis of the Shannon entropy, Fisher information, and Fisher–Shannon complexity in both coordinate and momentum spaces. Our results demonstrate that these parameters directly control the localization–delocalization transition and the informational architecture of the quantum states, while satisfying the entropic and Fisher uncertainty relations. Furthermore, we derive the exact partition function and the corresponding thermodynamic properties (free energy, internal energy, entropy, and specific heat) of the system. The analytical framework presented offers valuable insights into the spectral, information-theoretic, and thermodynamic behavior of quantum systems in fractal semiconductor-like environments. Full article

To characterize finite-velocity propagation in a finite system, we use the lattice telegrapher equation, which is equivalent to a non-local-in-time master equation with generic jumping models. We studied the solution of this finite-velocity transport equation on a ring. Our analysis focused on finding the phase-space parameters where the probability $P_s\left(t\right)$ shows wave-like behavior. We introduced a novel criterion based on the absolute value of the solution to find the phase-space region where $P_s\left(t\right)⩾0$ for all the sites and times. This criterion helped us to create a diagram illustrating the wave-like nature of the probability distribution for various Markov matrix jump models. Additionally, the Shannon and Fisher measures reveal an oscillatory pattern across the ring for all the jump models studied, implying a time-dependent wavy Cramér–Rao bound. Full article

Background: Metabolic syndrome (MetS) is a cluster of cardiometabolic abnormalities linked to increased risk of type 2 diabetes and cardiovascular disease. Emerging evidence implicates gut microbiota dysbiosis in MetS pathophysiology; however, human clinical data on seaweed-based dietary interventions remain scarce. Methods: Twenty-four older women were stratified into a MetS group (n = 13) and a control group (n = 11) per NCEP-ATP III criteria with Korean-specific waist circumference cutoffs. All participants consumed 4 g of dried laver (Porphyra tenera) per day for 12 weeks. Fecal DNA was subjected to 16S rRNA gene amplicon sequencing (V4 region; Illumina iSeq 100). Bioinformatic processing used QIIME2 and MicrobiomeAnalyst; alpha diversity was quantified by Chao1 and Fisher indices; beta diversity by Bray–Curtis, Jensen–Shannon, and UniFrac metrics; and differential abundance by LEfSe. Results: The Firmicutes/Bacteroidetes ratio declined 0.81-fold in the control group and 0.54-fold in the MetS group. Alpha diversity (Chao1 and Fisher indices) increased significantly in both groups (p < 0.001 and p < 0.05, respectively). Unweighted UniFrac distance showed significant compositional differences (R² = 0.141, p = 0.001). LEfSe identified four FDR-significant genera: CAG_873 in the control group and Muribaculaceae, Paraprevotella, and Tyzzerella in the MetS group. Conclusions: Twelve-week dried laver supplementation produced measurable shifts in gut microbial diversity and community composition in older women, with potentially greater responsiveness in those with MetS. These preliminary findings justify adequately powered randomized controlled trials to evaluate laver as a gut-microbiome-targeted dietary strategy for MetS. Full article

We investigate a two-component Bose–Einstein condensate as a platform for quantum metrology and characterize the dynamical evolution of the quantum state using two complementary metrics: the quantum Fisher information and the normalized Shannon entropy. With time-dependent control, metrological resources can be prepared and stabilized over a finite time window. These schemes provide a comprehensive assessment of the quantum dynamics of these resources in terms of phase sensitivity and the concentration of the state distribution, thereby offering a theoretical basis for designing robust quantum metrology protocols. Full article

Area-law entropy appears in local quantum ground states, low-temperature Gibbs states, and gravitational physics, whereas classical thermodynamics is formulated with volume-extensive entropy. We propose a coarse-grained information-theoretic framework, based on an effective free-energy functional combining Fisher information, a potential term, and Shannon entropy, that organises these different scalings within a single thermodynamic picture. Comparing localisation costs, external stabilisation, and gravitational self-interaction at the level of scaling reveals three regimes. At microscopic scales, locality and low-temperature coherence enforce area-type entropy scaling. At intermediate scales, volume-law entropy emerges as an effective regime sustained by non-gravitational confinement or external support; in the absence of such support, volume-extensive entropy does not by itself define an intrinsically stable equilibrium. At large scales dominated by gravitational self-interaction, a reduced scaling analysis identifies area-type behaviour as the distinguished infrared scaling, consistent with black-hole thermodynamics and with macroscopic universality requirements. The framework clarifies the limited domain of classical extensivity and offers a unified coarse-grained perspective on the recurrence of area-law scaling across quantum and gravitational settings. Full article

We study information-theoretic and complexity measures for the Dunkl-supersymmetric harmonic oscillator to identify the effect of supersymmetry on these quantities. Using the Rakhmanov probability density of the Dunkl-SUSY functions, we analyze the Shannon entropy, spreading measures (Heller, Rényi, and Fisher lengths), and several statistical and dynamical complexities. The Shannon entropy is obtained both asymptotically and in closed analytic form, showing that supersymmetry does not affect the leading large-n scaling. In contrast, spreading measures reveal enhanced localization of the SUSY eigenstates relative to the standard harmonic oscillator. Finally, we find that LMC and Fisher–Shannon complexities are higher in the supersymmetric case. Full article

Here we perform a detailed information-theoretic (IT) analysis of atomic electron densities in the periodic table, from hydrogen (Z = 1) to lawrencium (Z = 103). By use of the Shannon entropy, the Fisher information and the disequilibrium functionals in both position and momentum spaces as fundamental descriptors of the atomic densities, the periodic table can be represented in a three-dimensional information space as a continuous, highly ordered manifold. The analysis shows that chemical periodicity naturally emerges as a helicoidal manifold (reminiscent of a helix) at the coordinates of a 3D theoretic-information space (Shannon, Fisher, Disequilibrium), with each period forming one segment within the continuous global trajectory. We find information-theoretic signatures of shell structure, sub-shell filling, and electron-configuration anomalies, such as the familiar irregularities seen in chromium and copper. Therefore, the helicoidal character emerges naturally and is not imposed a priori. Further, through the uncertainty principle of the complementary analysis in momentum space, more insights are gained by exposing maximal information-theoretic differentiation for lighter atoms and compression among heavy elements. Notably, momentum-space analysis reveals that hydrogen occupies a natural intermediate position between helium and lithium based on kinetic energy distribution—contrasting with IT position-space results that emphasize hydrogen’s unique delocalized electron density. Indeed, the 3D IT representation of the elements in position space aligns with the view that H does not belong to either the alkali metals or the halogens, but rather stands as a unique, standalone element. This complementary perspective provides new quantitative support for understanding hydrogen’s dual chemical nature, providing new quantitative insight into ongoing debates about hydrogen’s optimal periodic table position. Furthermore, by considering triadic relationships and complexity properties in relation to the López–Mancini–Ruiz (LMC) and Fisher–Shannon (FS) functionals, we show that atomic complexity increases monotonically along with nuclear charge, and we provide a quantitative measure of how organized atomic electron densities are distributed throughout the periodic system. Based on our IT analyses, the fundamental character of periodicity could be addressed by employing helicoidal representations that highlight the characteristics of hydrogen, while simultaneously preserving the autonomy of the blocks of elements. Full article

Background: Kawasaki disease (KD) is a systemic vasculitis of unknown origin, though recent evidence implicates viral pathogens in its pathogenesis. Given the central role of T cell receptors (TCRs) in antigen recognition and immune response, this study investigated the association between KD and viral infection through comparative analysis of TCR repertoires. Methods: TCR repertoires from KD patients, healthy children, and individuals with viral infections were comparatively analyzed. TCR diversity and V(D)J usage were assessed using Shannon’s entropy, the Mann–Whitney U test, and Fisher’s exact test. Positional motif enrichment analysis within CDR3 regions was performed based on paratope hotspot classification. Results: Relatively reduced TCR clonal abundance and diversity were observed in KD patients compared to healthy controls. While substantial overlap in VJ gene segment usage was detected between KD and cytomegalovirus (CMV) infection, limited overlap in clonal TCRαβ chains was found between KD and viral infection groups. A predominant TCR combination, TRAV14DV4-J13-TRBV20-1-J2-5, enriched with characteristic amino acid motifs (EET, YNE, LAG, GQG, and AYE), was frequently identified in KD. Conclusions: These observations suggest potential differences in TCR repertoire features between KD patients and both healthy and virus-infected groups. However, the relationship between KD pathogenesis and the viruses examined requires further investigation with larger cohorts. Full article

Frustration is an intrinsic feature of molecular complexes, arising when individual constituents must distort from their optimal isolated geometries to achieve collective stabilization. Although energetic frustration can be defined as the average distortion energy associated with complex formation, its quantitative origin and its connection to other molecular descriptors remain insufficiently understood. In this work, we systematically investigate frustration in four representative molecular complexes—two homogeneous clusters, (H₂O)_n and (HF)_n, and two charged clusters, H₃O⁺(H₂O)_n and F⁻(H₂O)_n (n = 1–20)—using three complementary density-based frameworks: (i) total-energy decomposition, (ii) global conceptual DFT (CDFT) descriptors, and (iii) information-theoretic approach (ITA) quantities. Strong linear correlations between the total frustration energy and most energy components, as well as CDFT indices, are revealed, enabling a quantitative interpretation of frustration from energetic and electronic-structure perspectives. Among ITA measures, only a subset, including Shannon entropy, Ghosh–Berkowitz–Parr entropy, Rényi entropy, and the relative Fisher information, exhibits robust and consistent correlations with frustration across all systems, indicating their suitability as ITA-based frustration descriptors. Particularly, the (HF)_n clusters show uniformly excellent correlations for all descriptors due to their structurally simple and homogeneous hydrogen-bonding environment. Overall, this work provides a comprehensive density-based understanding of frustration and clarifies which descriptors reliably track its behavior. These insights establish a foundation for applying ITA and CDFT analyses to frustrated phenomena in broader chemical contexts, which could be applied to other systems, including molecular recognition, conformational dynamics, and catalysis. Full article

This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability R, moments, Rényi entropy, Shannon entropy, Fisher information matrix, and partial ordering associated with this distribution, have been derived. Distributions of the sum and quotient of two independent inverted Topp–Leone variables have also been obtained. Full article

Milk microbiota is a complex microbial ecosystem with implications for product quality, safety, and animal health. However, limited data exist on goat milk microbiota, particularly in local breeds. This study provides the first detailed characterization of the milk microbiota of Girgentana goats, a resilient Sicilian breed valued for high-quality dairy products. Illumina NovaSeq sequencing was used to analyze the 16S rRNA V3–V4 regions of 44 individual and 3 bulk milk samples. Briefly, 16S rRNA-gene sequencing produced a total of 8,135,944 high-quality reads, identifying 1134 operational taxonomic units (OTUs) across all individual samples. On average, each sample showed 864 OTUs with counts > 0. Alpha diversity metrics, based on richness estimators (Chao1: 948.1; ACE: 936.3) and diversity indices (Shannon: 4.06; Simpson: 0.95; Fisher: 118.5), indicated a heterogeneous community with both common and low-abundance taxa. Firmicutes (51%) and Proteobacteria (27%) were the predominant phyla, with Lactobacillaceae (54%) and Bifidobacteriaceae (22%) dominating at the family level. Notably, farm bulk milk profiles closely mirrored individual samples. These results establish a milk microbiota baseline for the Girgentana breed and offer valuable insights into microbial ecology in traditional dairy systems, supporting future comparisons across breeds and farming practices. Full article

We present a comprehensive information-theoretic evaluation of three widely used rigid water models (TIP3P, SPC, and SPC/$\epsilon$) through systematic analysis of water clusters ranging from single molecules to 11-molecule aggregates. Five fundamental descriptors—Shannon entropy, Fisher information, disequilibrium, LMC complexity, and Fisher–Shannon complexity—were calculated in both position and momentum spaces to quantify electronic delocalizability, localization, uniformity, and structural sophistication. Clusters containing 1, 3, 5, 7, 9, and 11 molecules (denoted 1 M, 3 M, 5 M, 7 M, 9 M, and 11 M) were selected to balance computational tractability with representative scaling behavior. Molecular dynamics simulations validated the force fields against experimental bulk properties (density, dielectric constant, self-diffusion coefficient), while statistical analysis using Shapiro–Wilk normality tests and Student’s t-tests ensured robust discrimination between models. Our results reveal distinct scaling behaviors that correlate with experimental accuracy: SPC/$\epsilon$ demonstrates superior electronic structure representation with optimal entropy–information balance and enhanced complexity measures, while TIP3P shows excessive localization and reduced complexity that worsen with increasing cluster size. The transferability from clusters to bulk properties is established through systematic convergence of information-theoretic measures toward bulk-like behavior. The methodology establishes information-theoretic analysis as a useful tool for comprehensive force field evaluation. Full article