Search Results (94)

Earlier work by some of the present authors identified power-law statistical regularities across the periodic table: a near-Zipf relationship $W\propto Z^{1.09}$ between atomic weight and atomic number in neutral atoms, and a fine-structure splitting scaling $\Delta E\propto Z^{1.78}$ in the $3d^{2+}$ (Cr-like) isoelectronic sequence of highly charged ions (HCIs). The apparent tension between this superlinear empirical exponent and the linear-in-Z scaling derived analytically by Lyu, Keitel, and Harman for relativistic clock-state transitions in $n{d}^6$ ions is resolved by writing the scaling law in the form $\Delta E=A{(Z-Z^{\ast })}^{\gamma }$, which gives $\gamma =1.03$ and $Z^{\ast }=25.83$ for the $3d^{2+}$ data and restores a near-Zipf interpretation. We extend the thresholded model from the single $3d^{2+}$ sequence to fourteen isoelectronic sequences spanning C-like ($Z\ge 6$) through Mo-like ($Z\ge 42$), drawing on the NIST Atomic Spectra Database, evaluated compilations of strontium, copper, and tungsten ion data, and digitization of GRASP MCDHF Mo-like results. Comparing the fitted threshold $Z^{\ast }$ against the classical Slater shielding ${\sigma }_{\mathrm{Slater}}$ of the valence shell reveals three regimes: (i) Coulomb-LS sequences (C/N/O/Ne-like) with $Z^{\ast }$ fixed at zero by construction; (ii) a mainstream cluster of nine sequences (a mix of spin–orbit fine-structure and, for the $d^2$ Ca-/Sr-like members, Coulomb term separations) for which $Z^{\ast }$ tracks ${\sigma }_{\mathrm{Slater}}$ within $\pm 1.5$ units; (iii) a pair of $n{d}^6{}^{5}D_0$ sequences (Cr-like $3d^6$ and Mo-like $4d^6$) with $Z^{\ast }-{\sigma }_{\mathrm{Slater}}=+7.20$ and $+10.36$, scaling linearly with Z in the jj regime (after resolving a low-Z LS–jj crossover for the Mo-like member). The slope ratio $A_{\mathrm{Mo}}/A_{\mathrm{Cr}}\approx 0.48$ is of the order of the hydrogenoid radial-extent ratio $⟨r^2⟩(3d)/⟨r^2⟩(4d)\approx 0.32$, exceeding it by ∼50% as expected from relativistic $4d$ contraction. A falsifiable extrapolation for the W-like $5d^6{}^{5}D_0$ sequence is offered: $\Delta \in [+7,+11]$, $A_W\in [0.12,0.18]$ eV/Z, with explicit failure modes specified for an independent GRASP MCDHF test. Full article

Background: The global use of herbal medicines and research on plant bioactive compounds have steadily increased. In Chile, this growth is linked to ethnobotanical knowledge and advances in phytochemistry, although gaps persist in its evolution, leadership, and regulatory articulation. This study analyzes scientific production on phytochemicals and medicinal plants (1976–2025), identifying growth patterns, leading journals, authorship, and collaboration networks. Methodology: A mixed-methods approach combined bibliometric analysis of Web of Science records with inductive qualitative content analysis from researcher interviews. The quantitative phase applied performance analysis and scientific mapping, using indicators such as Price’s, Lotka’s, Bradford’s, and Zipf’s laws to evaluate evolution, productivity, and impact. The qualitative phase explored perceptions of the field’s current state, limitations, and challenges, thereby contextualizing the bibliometric findings. Results and discussion: Analysis of 2149 articles and 6878 authors shows exponential growth (11.46% annually; R² = 0.952), with 674 publications projected by 2035. Productivity is concentrated among key authors and institutions (University of Chile, Concepción, Talca). Research focuses on antioxidant activity and bioactive compounds. Despite progress, gaps persist in clinical validation, technology transfer, and health system integration, while biodiversity and omics are emerging as strategic assets. Conclusions: Phytochemistry in Chile is expanding rapidly, requiring integrated frameworks that combine clinical validation, sustainable biodiversity management, advanced analytical and computational tools, technology transfer, and adaptive public policies to translate scientific knowledge into evidence-based healthcare, biotechnology, and sustainable innovation. Full article

The paper features a textual analysis of the UN speeches made by the US President Donald Trump and by France’s President Macron. President Trump’s speech was made in the absence of a teleprompter and lasted almost an hour. President Macron’s speech was representative of a more standard diplomatic speech. Both speeches are analyzed using a variety of models and techniques. The analysis incorporates an exploration of Manin’s link of Zipf’s law to concepts from information theory and algorithmic complexity, Tao’s concepts applied to power laws, ‘E pluribus unum’, out of many, one, plus a completely new application of Villermaux’s universal law of fragmentation, applied in a lexical context. All theories are found to be supported. The comparative study shows that a ‘rhetorical physics’ approach can capture the “universality” of the Zipf–Mandelbrot law while simultaneously identifying “speaker-specific” rhetorical fingerprints. Macron uses “high-complexity” signaling for elite diplomatic audiences, while Trump uses “low-complexity” fragmentation for broader impact. Full article

Background: The purpose of this preliminary study was to evaluate the use of the Zipf–Mandelbrot (ZM) law to mathematically model the percentage occurrence of adverse drug reactions (ADRs), as a function of rank, reported to the United States Food and Drug Administration Adverse Event Monitoring System (US FDA AEMS). Methods: Six commonly used but pharmacologically different hospital-based medications were examined. Nonlinear curve fitting of the two ZM coefficients was utilized to model the percentage occurrence of ADRs in a hierarchical or rank order for each drug examined. Results: The reported complications and their associated occurrence rates for all six medications were accurately modeled using the ZM law. Those medications that have a greater percentage of reported ADRs within their first ten ranks were also found to have a greater negative slope. Furthermore, a natural logarithmic transformation of both the reported FDA data and the ZM law-derived predicted values demonstrated a consistent near-linear relationship, which was statistically significant. The ratio of the coefficients of the ZM law, $a·b^{-1}$, was also found to be a potentially useful index that allows for describing and comparing the overall shape of the medication-specific distributions. Conclusions: Based upon this preliminary examination, the ZM law appears to be applicable to the mathematical modeling of US FDA-reported ADRs. Additional research to assess and utilize this law for the analysis, economic management, and possible improvement in patient outcomes may be warranted. Full article

Background: Alzheimer’s disease (AD) is a complex neurodegenerative disorder and a major global health challenge. The traditional “one drug–one target” paradigm has shown limitations in addressing its multifactorial nature. Multitarget-directed ligands (MTDLs), designed to modulate multiple pathological pathways, have emerged as a promising therapeutic strategy. Objectives: To examine the structural, thematic, and temporal evolution of multitarget strategies for AD treatment between 2006 and 2025. Methods: A total of 1184 Web of Science-indexed articles were analyzed. Publication growth, h-index, author productivity, institutional and national contributions, and keyword co-occurrence networks were evaluated using VOSviewer. Bibliometric laws (Price, Bradford, Zipf, and Lotka) were applied to characterize productivity patterns and thematic organization. Results: Multitarget research shows exponential growth, suggesting a consolidation of the MTDL paradigm. China, India, the United States, Italy, and Spain were the most productive countries. Early studies focused on cholinesterase inhibition, particularly acetylcholinesterase-based hybrids. The field expanded to include β-amyloid aggregation, oxidative stress, metal chelation, and blood–brain barrier permeability. Recent trends emphasize integration of computational approaches, including molecular docking, molecular dynamics, virtual screening, and network pharmacology, alongside targets such as BACE1 and GSK-3β. Conclusions: Multitarget strategies have evolved toward a systems-oriented framework. Despite advances, challenges remain in reducing cholinesterase dependency and improving translational validation. This study provides a framework to interpret therapeutic evolution and guide future network-based drug design. Full article

This paper develops a scenario-based population modelling framework for the 847 mahalle (smallest administrative unit) of Istanbul, Türkiye, extending an empirical baseline for 2007–2025 into prospective scenarios to 2035. The baseline combines rank-size (Zipf) analysis, density quintile trajectories, trajectory classification, and phase-diagram analysis of early versus late-period growth. It reveals a persistent U-shaped deviation from the Zipf benchmark: both the most and least populous mahalle grew strongly through suburban mega-development and peri-urban expansion, respectively, while the established inner-city middle tier remained essentially unchanged. Density followed an inverted gradient, rising sharply on the low-density suburban fringe and contracting in the hyper-dense core. Building on this baseline, the paper defines a baseline continuation (S0) and four alternative scenarios: moderate economic stress (S1), a major North Anatolian Fault earthquake (S2), a combined shock (S3), and policy-led urban renewal (S4). The baseline trajectory amplifies existing inequalities; seismic and economic shocks compress upper-tail growth while generating displacement demand in outer-ring mahalle; and only S4 partially reverses the density-gradient inversion, by stimulating inner-city regeneration under Türkiye’s risky-area programme. The findings link intra-urban population redistribution to seismic-risk exposure and inform spatially targeted planning. Full article

We investigate the linguistic complexity and emotional valence of popular song lyrics across English ($n=1491$), Spanish ($n=307$), and German ($n=225$), using an analytical corpus of 2023 tracks drawn from 2113 deduplicated tracks on Spotify’s weekly Top 200 charts (2019–2021). Transformer-based sentiment analysis is combined with complexity-science tools to characterize both the affective content and the structural organization of commercially successful lyrics. A multilingual BERT model reveals a mild negative skew across all three languages (63.7% negative overall); the 1.003-point English–German gap observed under the English-centric VADER lexicon collapses to 0.127 points under BERT, indicating that earlier cross-linguistic sentiment differences are largely measurement artifacts. Word frequency distributions follow Zipf’s law in all three languages ($R^2>0.96$), with English steepest ($\alpha =1.409$) and German shallowest ($\alpha =1.181$). Detrended fluctuation analysis indicates persistent long-range correlations ($H\approx 0.66$–$0.76$; none of the 50 shuffled surrogates exceeded the observed values), and multifractal singularity spectra are statistically indistinguishable across languages once corpus size is controlled (all pairwise Mann–Whitney $p>0.13$). Streaming counts within the Top 200 are concentrated (German Gini $=0.556$) but, given the truncated single-snapshot sample, are reported as within-chart descriptors rather than population-level scaling. Full article

Handgrip strength (HGS) has been considered as an indicator of muscle strength and overall physical fitness, with increasing relevance in sports science for talent identification and performance monitoring. However, no bibliometric study has been conducted to map the HGS research landscape in athletic contexts. A bibliometric analysis was conducted in the Web of Science Core Collection database, retrieving 229 publications. Typical bibliometric laws (i.e., Price’s, Bradford’s, Lotka’s, and Zipf’s) were employed to analyze publication trends, core journals, influential authors, country contributions, and keyword co-occurrences. Annual publications increased exponentially, especially after 2019, reaching 37 documents in 2024. The Journal of Strength and Conditioning Research and Journal of Sports Medicine and Physical Fitness were the most prominent journals. The United States and Spain led in productivity and impact. Key research themes included strength, performance, body composition, and physical fitness, with HGS demonstrating significant associations with sport tasks such as throwing, racquet sports, and weightlifting. HGS constitutes an accessible and valuable tool for assessing and predicting athletic performance, especially in sports requiring upper body strength and coordination. Future research should aim to expand database inclusion and address identified gaps, such as the relationship between HGS training and sport-specific outcomes. Full article

We detail a procedure to transform the current empirical stage in the study of complex systems into a predictive phenomenological one. Our approach starts with the statistical-mechanical Landau-Ginzburg equation for dissipative processes, such as kinetics of phase change. Then, it imposes discrete time evolution to explicit back feeding, and adopts a power-law driving force to incorporate the onset of chaos, or, alternatively, criticality, the guiding principles of complexity. One obtains, in closed analytical form, a nonlinear renormalization-group (RG) fixed-point map descriptive of any of the three known (one-dimensional) transitions to or out of chaos. Furthermore, its Lyapunov function is shown to be the thermodynamic potential in q-statistics, because the regular or multifractal attractors at the transitions to chaos impose a severe impediment to access the system’s built-in configurations, leaving only a subset of vanishing measure available. To test the pertinence of our approach, we refer to the following complex systems issues: (i) Basic questions, such as demonstration of paradigms equivalence, illustration of self-organization, thermodynamic viewpoint of diversity, biological or other. (ii) Derivation of empirical laws, e.g., ranked data distributions (Zipf law), biological regularities (Kleiber law), river and cosmological structures (Hack law). (iii) Complex systems methods, for example, evolutionary game theory, self-similar networks, central-limit theorem questions. (iv) Condensed-matter physics complex problems (and their analogs in other disciplines), like, critical fluctuations (catastrophes), glass formation (traffic jams), localization transition (foraging, collective motion). Full article

Background: Autism spectrum disorder (ASD) represents a major challenge in neurological development research and is receiving increasing attention from the pharmacological and pharmaceutical sciences. Despite this constant growth, there is no document that provides a comprehensive overview integrating publication trends, key contributors, and thematic developments, allowing efforts to be focused on specific areas. Objective: To conduct a comprehensive bibliometric analysis of pharmacological research related to ASD published between 2001 and 2025. Methods: The database obtained contains 1170 articles indexed in the Web of Science (WoS) database in the JCR Pharmacy and Pharmacology category. Bibliometric indicators such as publication growth, h-index, authorship, institutional and national productivity, and keyword co-occurrence were analyzed using VOSviewer and the laws of Price, Bradford, Zipf, and Lotka. Results: A total of 1170 documents were analyzed, showing an exponential increase in pharmacological research related to ASD over the last two decades. The United States, China, and Italy emerged as the most productive countries, while King Saud University, Harvard Medical School, and The Ohio State University were among the leading institutions. The most frequently cited keywords, such as “autism spectrum disorder,” “valproic acid,” “oxidative stress,” and “flavonoids,” revealed a translational approach linking neurobiological mechanisms, redox imbalance, and therapeutic interventions. Contemporary research emphasizes immuno–synaptic interactions, microbiota, and biomarker-guided approaches. Conclusions: This study highlights the global expansion and diversification of pharmacological research in ASD. The results underscore a shift toward integrated biological frameworks and precision-oriented strategies, reinforcing the need for interdisciplinary collaboration to advance translational outcomes in ASD therapy. Full article

Smart farming integrates digital technologies to optimize agricultural production and promote sustainability. Its impact depends both on technological development and adoption by farmers. Research shows significant progress, but technical and socio-behavioral gaps remain, requiring integrated approaches to strengthen its contribution to the SDGs. In this context, scientific research on smart farming has grown significantly, becoming a key axis for the fulfillment of the Sustainable Development Goals (SDGs). The aim of this study was to analyze the evolution, structure, and impact of scientific production in smart farming, identifying its main trends, authors, journals, and contributions to the SDGs. To this end, a bibliometric analysis was applied to 1580 articles indexed in the Web of Science (WoS) database, using productivity, citation, and impact indicators based on Price’s, Lotka’s, Bradford’s, and Zipf’s laws, as well as the Hirsch index. The results reveal important growth in scientific production between 2014 and 2024, with a strong concentration in high-impact journals and international collaboration networks. In conclusion, smart farming represents an engine of innovation and sustainability, integrating science, technology, and digital management to address the global challenges of food security, climate change, and sustainable development. Full article

Settlements and settlement systems are key arenas of human–environment interaction, and reconstructing their spatial patterns is essential for understanding historical socio-environmental dynamics. Using the Complete Map of the Great Qing Empire (1905), this study employs digital extraction and spatial-statistical analysis to examine the nationwide settlement system of late Qing China. The results reveal that: (1) The system features dispersed high-level settlements and highly clustered low-level ones; provincial and prefectural cities follow administrative divisions, while counties, towns, and villages display strong spatial self-organization. (2) Mid-to high-level systems exhibit hierarchical fractures, whereas low-level settlements conform to Zipf’s law, highlighting the regularity and universality of grassroots networks. (3) Road accessibility, slope, and elevation significantly influence settlement hierarchy, whereas river proximity plays a limited role—indicating greater dependence on transportation and terrain adaptability. Overall, the study elucidates the spatial structure and formative mechanisms of the Qing settlement system and provides empirical insights into the evolution of surface patterns and regional resilience since the modern era. Full article

An in-depth analysis of land use dynamics during the evolution of regional urban systems is crucial for understanding developmental trajectories and promoting coordinated urban growth. This study adopts a land-use perspective, examining the expansion of urban construction land while identifying its source areas. By integrating Zipf’s law and using urban construction land area as an indicator of urban scale, this research analyzes transformations within the urban system. The findings reveal the following: (1) The total area of urban construction land in the Yangtze River Delta has continued to expand over time, exhibiting an inverted U-shaped curve, with high concentration observed in riverine and coastal zones. (2) Cultivated land serves as the primary source for construction land, contributing on average 77.70% over the past 25 years, amounting to a conversion of 5664.51 square kilometers. Rural residential areas rank second, contributing an average of 11.90%. (3) The rank-size distribution of cities based on urban land area largely aligns with Zipf’s law, albeit with deviations at both ends. The Pareto index increased from 0.803 to 0.897, indicating a trend toward weaker dispersion and greater concentration in urban size distribution. In conclusion, future urban development should emphasize rational expansion grounded in sustainable practices, strengthen farmland protection to ensure food security, and effectively manage rural land transformation to promote efficient land use and ecological balance. These measures will support the balanced and coordinated development of large, medium, and small cities within the urban system. Full article

Since 2000, antioxidant research in Chile has shown steady growth, from the chemical sciences to their application in biomedical sciences, functional foods, reproduction, and environmental studies. This study presents a bibliometric analysis of Chilean scientific output in the field of antioxidants from 2000 to 2024, organized into five-year intervals. A total of 3190 research articles indexed in the Web of Science (WoS) database were analyzed. Bibliometric indicators—including Price’s, Bradford’s, and Zipf’s laws—were applied to assess literature growth, authorship concentration, journal dispersion, and keyword evolution. Key findings include (i) high productivity from institutions such as the Universidad de Chile, Pontificia Universidad Católica de Chile, Universidad de Santiago de Chile, and Universidad de Concepción; (ii) the identification of leading authors such as Dr. Antonio Vega-Gálvez, Dr. Guillermo Schmeda-Hirschman, and Dr. Mario J. Simirgiotis; and (iii) the consolidation of three main research areas: biomedical applications (e.g., cancer, cardiovascular, and neurodegenerative diseases), food science and technology (e.g., antioxidant properties, and agro-industrial waste revalorization), and ethnopharmacology (e.g., native plant use). This study made it possible to map the state of the art of antioxidant research in Chile and identify key players and research lines, consolidating a comprehensive vision of scientific development in this field. Full article

Advances in technology and changes in the way people entertain themselves have made video games a cultural agent on a par with more traditional games, including language learning. In addition, the use of video games in education is becoming increasingly common and numerous benefits associated with their use have been discovered. The aim of this article is to analyze the search trends in studies dealing with the use of video games in language learning. To this end, a bibliometric analysis was carried out by applying the traditional laws of bibliometrics (Price’s law, Bradford’s law of concentration, Lotka’s law, Zipf’s law and h-index) to documents published in journals indexed in the Core Collection of the Web of Science (WoS). Annual publications between 2009 and 2022 show an exponential growth R2 = 86%. The journals with the most publications are Computer assisted language learning (Taylor & Francis) and Computers and Education (Elsevier). Jie Chi-Yang and Gwo Jen-Hwan were the most cited authors. The United States and Taiwan were the countries with the highest scientific output. The use of video games in language learning has been of particular interest in recent years, with benefits found for students who use them in their classes, although more research is needed to establish criteria and requirements for each video game for its intended purpose. Full article