"Abstract: We formalize and study a generalized form of the Pareto principle or '20/80–rule' as a property of bounded cumulative processes. Modeling such processes by non-negative gain densities, we first show that any such process satisfies a generalized Pareto principle of the form 'fraction p of inputs yields fraction 1 − p of outputs'. To obtain a non-trivial and unique characterization, we define the generalized Pareto principle via the decreasing rearrangement of the gain density function. Within this framework, we analyze both constructed gain densities that exemplify the framework and its imposed restrictions, as well as distribution families commonly encountered in datasets, including power-law, exponential, and normal distributions. Finally, we predict commonly encountered ranges for the generalized Pareto principle and discuss the implications of elevating a structural property into a prescriptive role."
Abstract: "Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out."
Referenced in the paper: "Inequality Measures: The Kolkata index in comparison with other measures" - https://arxiv.org/abs/2005.08762
Abstract: "We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient."
"Abstract. The outer size of a tropical cyclone (TC) plays a pivotal role in its impact through a modulation of wind duration, rainfall extent and storm surge. While global and basin scale trends in TC size have been examined previously, whether there have been regional changes over time remains unclear. Here, using a suite of observations and reanalyses, we detect an increasing TC outer size over the western North Atlantic during 1979–2022. Over the western subtropical North Atlantic where the largest changes are found, the area-averaged increase in the radius of 17 ms<sup>-1</sup> winds is about 7.5% over this period. Analysis of the large-scale environment reveals that the air-sea thermodynamic state has become more favorable for storm intensification, and thereby expansion, over that region. Further, numerical model simulations link changes in the environment with those in storm size, and suggest a combination of natural variability and external forcing in driving them."
("TC outer size" is defined as the radius of gale-force winds.)
"Abstract. A substantial share of workers are self-employed, but there is a dearth of data on heterogeneity in these work arrangements. To address this gap, the authors identify the variety of self-employment work arrangements in novel data produced using machine learning, leveraging 2003–2019 Panel Study of Income Dynamics respondents’ narrative descriptions of their industry, type of work, and employer names. The authors examine trends in the prevalence and nature of these forms of self-employment, transitions across them, and who works in them. Findings show disparate trends in the prevalence of different work arrangements and in transitions across work arrangements that would otherwise be masked. Further results suggest that the informally self-employed are less likely to have business assets, engage in more routine and less abstract skills on their jobs, are less educated, are less likely to be male and non-Hispanic White, have less labor income, and have worse well-being."
"Abstract. The Middle Pleistocene (MP; ca. 774 to 129 ka) marks a critical period of human evolution, characterized by increasing behavioral complexity and the first unambiguous evidence of plant-based technologies. Despite this, direct evidence for early wooden tool use remains exceptionally rare. Here, we present the earliest handheld wooden tools, identified from secure contexts at the site of Marathousa 1, Greece, dated to ca. 430 ka (MIS12). Through a systematic morphological, microscopic, taphonomic, and taxonomic analysis of the sampled wood macroremains, two specimens were securely identified as modified by hominins: one small alder (Alnus sp.) trunk fragment bears clear working and use-wear traces consistent with a multifunctional stick likely used in digging at the paleolakeshore; and one very small willow/poplar (Salix sp./Populus sp.) artifact exhibits signs of shaping and potential use-wear. A third specimen, a large alder trunk segment, shows deep, nonanthropogenic striations interpreted here as claw marks from a large carnivoran. The wooden tools were excavated together with butchered elephant remains, small lithic artifacts and debitage, and worked bone, underscoring the diversity of engagement with a variety of different raw materials for technological purposes at Marathousa 1. These finds extend the temporal range of early wooden tools. They represent both the use of expedient larger handheld tools as well as a much smaller, likely finger-held wooden tool, which is uniquely small for the Pleistocene, expanding known functional purposes of early wood technologies. Moreover, they highlight the Megalopolis Basin’s exceptional preservation conditions and its role in understanding the evolution of hominin behavior."
Abstract: "In Navier–Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional (3-D) NS equations indicate that employing observational data resolved down to a specific length scale, ℓ<sup>3-D</sup><sub>∗</sub>, enables the successful reconstruction of small-scale flows. Such a length scale of ‘essential resolution of observation’ for reconstruction ℓ<sup>3-D</sup><sub>∗</sub> is close to the dissipation scale in three-dimensional NS turbulence. Here, we study the equivalent length scale in two-dimensional (2-D) NS turbulence, ℓ<sup>2-D</sup><sub>∗</sub>, and compare with the three-dimensional case. Our numerical studies using data assimilation and conditional Lyapunov exponents reveal that, for Kolmogorov flows with Ekman drag, the length scale ℓ<sup>2-D</sup><sub>∗</sub> is actually close to the forcing scale, substantially larger than the dissipation scale. Furthermore, we discuss the origin of the significant relative difference between the length scales, ℓ<sup>2-D</sup><sub>∗</sub> and ℓ<sup>3-D</sup><sub>∗</sub>, based on inter-scale interactions, ‘cascades’ and orbital instabilities in turbulence dynamics."
Abstract: "When the species composition of ecological communities changes over time, environmental drivers are often invoked as the most plausible explanation. Several lines of reasoning, however, suggest that such compositional change, called temporal species turnover, can similarly result from intrinsic ecosystem dynamics, even in a constant environment. The degree to which these two drivers contribute to observed turnover remains unclear. To address this conundrum, we analyse the well-established BioTIME database of surveys. We expect either an acceleration of turnover with accelerating climate change or constant turnover if intrinsic mechanisms dominate. Surprisingly we find instead that species turnover over short time intervals (1-5 years) has decelerated in significantly more communities during the last 100 years than it has accelerated, typically by one third. The observed slowing of turnover, we argue, could be understood—when intrinsic dynamics dominate—as resulting because anthropogenic environmental degradation or declines of regional species pools reduce the number of potential colonisers driving turnover. Our results suggest that observed past changes in species composition were often manifestations of natural, intrinsic ecosystem dynamics. Although one can expect environmental drivers to dominate species turnover eventually as climate change accelerates further, for now such attribution should be done with caution."
Abstract: "Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models."
"Methods: The mindful endoscopy team, consisting of an endoscopist and endoscopy support practitioners (ESPs) was created. Nurse-led mindfulness comprised patient education on a range of relaxation methods just before the start of the procedure, and holistic and proactive patient support within a clear structure during it. Patient experience of awake oral and pharyngolaryngeal endoscopy (180 procedures) and transnasal panendoscopy (70 procedures) were recorded using the Gastrointestinal Endoscopy Satisfaction Questionnaire.
Results: Overall, 92.4% of patients were satisfied or very satisfied with their awake endoscopies and 96.4% indicated that they would be happy or very happy to undergo the same procedure undertaken by the same team again. At a mean follow-up of 14 months, 12 cancers had been detected and no cancers had been missed."
"Abstract. Atlantic Meridional Overturning Circulation (AMOC) is suggested to be in a bi-stable regime and might already be at the brink of a irreversible trajectory towards a complete shutdown–a so called tipping point. Such a tipping point requires a self-reinforcing feedback, for example one related to the upper ocean salt transport convergence to the North Atlantic subpolar gyre. We show that in Earth System Model simulations under abrupt high CO$_2$ forcing ($>$1.8 times the pre-industrial conditions), salt transport convergence is highly correlated with AMOC, indicating an active role for salinity in reinforcing AMOC decline. However, at weak or transiently increasing CO$_2$ forcing the relation is masked by internal variability in our model simulations and observationally constrained products. Our results suggest that with the present forcing levels, salinity reinforced AMOC decline is unlikely, and consequently, it is unlikely that AMOC would be close to a salt transport convergence induced tipping point."
Abstract: "Understanding the cold atomic hydrogen gas (H i) within cosmic filaments has the potential to pin down the relationship between the low density gas in the cosmic web and how the galaxies that lie within it grow using this material. We report the discovery of a cosmic filament using 14 H i-selected galaxies that form a very thin elongated structure of 1.7 Mpc. These galaxies are embedded within a much larger cosmic web filament, traced by optical galaxies, that spans at least $\sim 15$ Mpc. We find that the spin axes of the H i galaxies are significantly more strongly aligned with the cosmic web filament ( $\langle |\cos \psi|\rangle = 0.64 \pm 0.05$) than cosmological simulations predict, with the optically selected galaxies showing alignment to a lesser degree ( $\langle |\cos \psi|\rangle = 0.55 \pm 0.05$). This structure demonstrates that within the cosmic filament, the angular momentum of galaxies is closely connected to the large-scale filamentary structure. We also find strong evidence that the galaxies are orbiting around the spine of the filament, making this one of the largest rotating structures discovered thus far, and from which we can infer that there is transfer of angular momentum from the filament to the individual galaxies. The abundance of H i galaxies along the filament and the low dynamical temperature of the galaxies within the filament indicates that this filament is at an early evolutionary stage where the imprint of cosmic matter flow on galaxies has been preserved over cosmic time."
Abstract: "Simone Weil is one of the most prominent 20th century French philosophers. She is the sister of Andr{é} Weil, the renowned mathematician, the father of modern algebraic geometry and the initiator of the Bourbaki group. Simone and Andr{é} Weil shared a love for literature, mathematics, science and philosophy. My aim in this article is to convey, based on their writings and their correspondence, the idea that Pythagoreanism was a central element of their thought. I will put this into context, talking first about the life and work of each of them, showing how much they were linked by essential common ideas, even though their life paths were very different, and how, ultimately, Pythagorean mathematics and philosophy became naturally part of their respective intellectual worlds. The article is the written version of a lecture I gave in October 2025, at the conference ``The Life and Contribution of Pythagoras to Mathematics, Sciences, and Philosophy'' that took place on October 3-4, 2025 at the Cyprus University of Technology in Limassol"
Referenced in the paper: "Power-law distributions in empirical data" - https://arxiv.org/abs/0706.1062
Abstract: "Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out."
Referenced in the paper: "Inequality Measures: The Kolkata index in comparison with other measures" - https://arxiv.org/abs/2005.08762
Abstract: "We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient."
[edited: added two references]
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