1,284 research outputs found

    Zipf's law, 1/f noise, and fractal hierarchy

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    Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within the specific scientific domains. All these observations are associated with scaling laws and have caused a broad research interest in the scientific circle. However, the inherent relationships between these scaling phenomena are still pending questions remaining to be researched. In this paper, theoretical derivation and mathematical experiments are employed to reveal the analogy between fractal patterns, 1/f noise, and the Zipf distribution. First, the multifractal process follows the generalized Zipf's law empirically. Second, a 1/f spectrum is identical in mathematical form to Zipf's law. Third, both 1/f spectra and Zipf's law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf's law, and the occurrence of large catastrophic events can be described with similar exponential laws and power laws. The self-similar hierarchy is a more general framework or structure which can be used to encompass or unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws on the hierarchical structure can provide us with a holistic perspective of looking at complexity such as self-organized criticality (SOC).Comment: 20 pages, 9 figures, 3 table

    Pre-pandemic cognitive function and COVID-19 mortality:Prospective cohort study

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    Poorer performance on standard tests of pre-morbid cognitive function is related to an elevated risk of death from lower respiratory tract infections but the link with coronavirus (COVID‑19) mortality is untested. Participants in UK Biobank, aged 40 to 69 years at study induction (2006–10), were administered a reaction time test, an indicator of information processing speed, and also had their verbal-numeric reasoning assessed. Between April 1st and September 23rd 2020 there were 388 registry-confirmed deaths (138 women) ascribed to COVID-19 in 494,932 individuals (269,602 women) with a reaction time test result, and 125 such deaths (38 women) in the subgroup of 180,198 people (97,794 women) with data on verbal-numeric reasoning. In analyses adjusted for age, sex, and ethnicity, a one standard deviation slower reaction time was related to a higher rate of death from COVID-19 (hazard ratio; 95% confidence interval: 1.18; 1.09, 1.28), as was a one standard deviation disadvantage on the verbal-numeric reasoning test (1.32; 1.09, 1.59). While there was some attenuation in these relationships after adjustment for additional covariates which included socio-economic status and lifestyle factors, the two pre-pandemic indicators of cognitive function continued to be related to COVID-19 mortality

    Room temperature midinfrared electroluminescence from GaInAsSbP light emitting diodes. .

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    Room temperature electroluminescence in the midinfrared near 4 µm is reported from GaInAsSbP light emitting diodes grown on GaSb by liquid phase epitaxy. Comparison of the electro- and photoluminescence revealed that light is generated on the p side of the diode. The energy shift (24 meV) is consistent with band gap narrowing and recombination via band tail states due to the Zn doping (1×1018 cm−3) in the p layer of the structure. The temperature dependent behavior of the luminescence and the improved emission intensity was attributed to recombination from localized states arising from electrostatic potential fluctuations due to compositional inhomogeneities in these alloys

    Modeling urban street patterns

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    Urban streets patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and details-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggests that in the absence of a global design strategy, the evolution of many different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR

    Geospatial analysis and living urban geometry

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    This essay outlines how to incorporate morphological rules within the exigencies of our technological age. We propose using the current evolution of GIS (Geographical Information Systems) technologies beyond their original representational domain, towards predictive and dynamic spatial models that help in constructing the new discipline of "urban seeding". We condemn the high-rise tower block as an unsuitable typology for a living city, and propose to re-establish human-scale urban fabric that resembles the traditional city. Pedestrian presence, density, and movement all reveal that open space between modernist buildings is not urban at all, but neither is the open space found in today's sprawling suburbs. True urban space contains and encourages pedestrian interactions, and has to be designed and built according to specific rules. The opposition between traditional self-organized versus modernist planned cities challenges the very core of the urban planning discipline. Planning has to be re-framed from being a tool creating a fixed future to become a visionary adaptive tool of dynamic states in evolution

    Childhood Body Weight in Relation to Cause-Specific Mortality: 67 Year Follow-up of Participants in the 1947 Scottish Mental Survey

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    The association between childhood body weight and adult health has been little-examined, and findings are inconsistent. In a representative sample of the Scottish nation (the Scottish Mental Survey of 1947), we examined the association between body mass index measured at 11 years of age and future cause-specific mortality by age 77 years. In this cohort study, a maximum of 67 years of follow-up of 3839 study members gave rise to 1568 deaths (758 from cardiovascular disease, 610 from any malignancy). After adjustment for covariates, there was some evidence of a relation between elevated childhood body mass index and rates of mortality ascribed to all-causes (hazard ratio per 1 SD increase in body mass index; 95% confidence interval: 1.09; 1.03, 1.14), cardiovascular disease (1.09; 1.01, 1.17), all cancers combined (1.12; 1.03, 1.21), smoking-related cancers (1.13; 1.03, 1.25), and breast cancer in women (1.27; 1.04, 1.56). In conclusion, we provide further observational evidence for the need for weight control measures in youth

    The application of graph theory and percolation analysis for assessing change in the spatial configuration of pond networks

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    Pond networks support high levels of biodiversity when compared to other freshwater ecosystems such as rivers, lakes and streams. The persistence of species in these small, sometimes ephemeral, aquatic habitats depends on the dispersal of individuals among ponds in the landscape. However, the number of ponds across the landscape is at a historical low as urbanisation and intensified agricultural practices have led to a substantial loss of ponds (nodes in the pond network) over more than a century. Here, we examine the extent and drivers of pond loss in a heavily urbanised landscape (Birmingham, UK) over 105 years and determine how pond loss influences key structural properties of the pond network using graph theoretic approaches. Specifically, we calculated minimum spanning trees (MST) and performed percolation analyses to determine changes in both the spatial configuration and resilience of the pond network through time. Pond numbers declined by 82% between ca1904 and 2009, such that pond density decreased from 7.1 km-2 to 1.3 km-2. The MST analyses revealed increased distance between ponds in the network (i.e. edge length increased) by up to 49% over the 105-year period, indicating that ponds in the modern landscape (2009) were considerably more isolated, with fewer neighbours. This study demonstrates that graph theory has an excellent potential to inform the management of pond networks in order to support ecological communities that are less vulnerable to environmental change

    The Mathematical Relationship between Zipf's Law and the Hierarchical Scaling Law

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    The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf's distribution of cities is abstracted as a q-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf's law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2^n principle and Pareto's law can be associated with one another by the hierarchical organization.Comment: 30 pages, 5 figures, 5 tables, Physica A: Statistical Mechanics and its Applications, 201

    When Is Higher Neuroticism Protective Against Death? Findings From UK Biobank

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    We examined the association between neuroticism and mortality in a sample of 321,456 people from UK Biobank and explored the influence of self-rated health on this relationship. After adjustment for age and sex, a 1- SD increment in neuroticism was associated with a 6% increase in all-cause mortality (hazard ratio = 1.06, 95% confidence interval = [1.03, 1.09]). After adjustment for other covariates, and, in particular, self-rated health, higher neuroticism was associated with an 8% reduction in all-cause mortality (hazard ratio = 0.92, 95% confidence interval = [0.89, 0.95]), as well as with reductions in mortality from cancer, cardiovascular disease, and respiratory disease, but not external causes. Further analyses revealed that higher neuroticism was associated with lower mortality only in those people with fair or poor self-rated health, and that higher scores on a facet of neuroticism related to worry and vulnerability were associated with lower mortality. Research into associations between personality facets and mortality may elucidate mechanisms underlying neuroticism's covert protection against death
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