Growth Model Research Articles

Stochastic Models for Ontogenetic Growth

Based on allometric theory and scaling laws, numerous mathematical models have been proposed to study ontogenetic growth patterns of animals. Although deterministic models have provided valuable insight into growth dynamics, animal growth often deviates from strict deterministic patterns due to stochastic factors such as genetic variation and environmental fluctuations. In this study, we extend a general model for ontogenetic growth proposed by West et al. to stochastic models for ontogenetic growth by incorporating stochasticity using white noise. According to data variance fitting for stochasticity, we propose two stochastic models for ontogenetic growth, one is for determinate growth and one is for indeterminate growth. To develop a universal stochastic process for ontogenetic growth across diverse species, we approximate stochastic trajectories of two stochastic models, apply random time change, and obtain a geometric Brownian motion with a multiplier of an exponential time factor. We conduct detailed mathematical analysis and numerical analysis for our stochastic models. Our stochastic models not only predict average growth well but also variations in growth within species. This stochastic framework may be extended to studies of other growth phenomena.

Combustion Characterization and Kinetic Analysis of Coupled Combustion of Bio-Syngas and Bituminous Coal

The coupled combustion of bio-syngas and bituminous coal is an effective technology to reduce pollutant emissions from coal-fired power plants and improve the utilization rate of biomass energy. However, the effects of bio-syngas blending on bituminous coal combustion characteristics and reaction kinetics remain unclear, restricting the development of bio-syngas and bituminous coal combustion technology. In this study, the experimental studies on the coupled combustion of bio-syngas and bituminous coal under different bio-syngas lower-heating-value-based blending ratio (BLBR) were carried out by Micro-Fluidized Bed Reaction Analyzer (MFBRA), the coupled combustion characteristics and kinetic reaction mechanism of coupled combustion of bio-syngas and bituminous coal were analyzed. The results indicated that the nucleation and growth model (F1 Model) provided a reasonable description of the bituminous coal combustion process on the coupled combustion of bio-syngas and bituminous coal in MFBRA. The blending of bio-syngas significantly reduces the apparent activation energy and pre-exponential factor of bituminous coal combustion reaction. In particular, when the BLBR is 5, 10, 20, and 30%, the apparent activation energy is 48.70, 45.45, 46.75, and 42.35 kJ·mol−1, and the pre-exponential factor is 9.26, 7.10, 8.95, and 6.70 s−1, respectively. This research is helpful for improving the coupled combustion efficiency and ensuring the efficient operation of the coupled combustion system.

Growth models for the progress test in Italian dentistry degree programs

Growth models for the progress test in Italian dentistry degree programs

Relationship of Individual Athlete External Load, Session Rating of Perceived Exertion, and Athlete Playing Status Across a Collegiate Women’s Basketball Season

External (EL) and internal (IL) load are commonly used methods used to quantify training load in team sports. Playing time and playing position may influence the training loads for specific athletes throughout a season. The purpose of the current study was to evaluate the effect of athlete playing status and individual in-season practices on EL and IL across a collegiate women’s basketball season. Female basketball athletes were classified as high-minute (HMA; ≥15 min/game) or low-minute (LMA; <15 min/game) and wore microsensors during 53 practices for a total of 583 data points. EL was obtained via an inertial measurement unit (IMU) device that contained a triaxial accelerometer to obtain three-dimensional positioning data. IL and strength training (ST) load were determined via session rating of perceived exertion (sRPE) to create a daily summated value. Descriptive statistics indicate that athletes experienced individual differences in EL, ST, and IL throughout the season. A growth model showed that HMAs experienced higher EL than LMAs at the start of the season for practices (90.21 AU). Across all athletes, IL increased across the season (40.11 AU) and for each 1 unit of change in EL, IL increased by 1.04 AU. Repeated measures correlations identified a large relationship between IL and EL (r = 0.51, p < 0.001). A location-scale model indicated that the within-person variability of IL across all athletes was 3.29 AU but was not due to athlete playing status. It is recommended to base in-season training on individual loads and game demands to promote athlete readiness and improved sport performance.

Sustainable Economic Growth And Industry Insights: Nonlinear Interaction Analysis of GDP Vs FDI in Malaysia Using SCILAB Programming

Objective: To investigate the nonlinear relationship between Gross Domestic Product (GDP) and Foreign Direct Investment (FDI) in Malaysia, with the aim of providing insights into their bidirectional interactions. Theoretical Framework: The main concepts and theories that underpin the research are nonlinear regression techniques and economic growth models. These frameworks provide a solid basis on understanding the dynamic interaction between GDP and FDI in the context of Malaysia’s economic. Method: The methodology comprises writing Scilab coding to analyze nonlinear regression models. Malaysia's economic data on GDP and FDI were utilized as inputs for the analysis. The study involves modeling the dynamics between these indicators and evaluating their relationship over time. Results and Discussion: The results obtained revealed a significant nonlinear relationship between GDP and FDI in Malaysia. These results are contextualized within the theoretical framework, highlighting the bidirectional nature of the relationship. Possible discrepancies and limitations, including data constraints and assumptions of the nonlinear models, are also considered. Research Implications: This research offers valuable insights for policymakers, helping shape economic planning,and investment strategies. It highlights the importance of FDI in promoting sustainable economic growth and industrial development towards United Nation SDG 8 and SDG 9. Originality/Value: This study contributes by using nonlinear regression techniques and Scilab programming to analyze the complex relationship between GDP and FDI, an approach not widely applied to Malaysia's context. The relevance and value of this research are evidenced by its potential impact on economic policy and its contributions to a deeper understanding of Malaysia's economic development.

Shielding competitiveness: Germany’s wage policy during the inflation shock years in comparative perspective

We analyse wage developments in Germany during the inflation shock years of 2021–2023 from three perspectives: cost of living, supply-side cost pressure, and relational. With an export-led growth model, Germany is dependent on a favourable real effective exchange rate. Because of its above-average exposure to the energy crisis and low unemployment, Germany was particularly vulnerable to strong wage demands, putting at risk its cost competitiveness. In response to the inflation crisis, moderate collective bargaining outcomes have resulted from widespread use of one-off payments, longer duration of collective agreements, and ‘zero-month’ clauses, which have delayed wage increases. As in all other eurozone countries, employees have suffered real wage losses, but nominal wage increases at the lower end of the labour market fared better than average. Major competitiveness shifts have occurred in the eurozone, particularly to the detriment of Eastern European countries and the Baltics, but not Germany.

Quantifying the Influence of Cloud Seeding on Ice Particle Growth and Snowfall Through Idealized Microphysical Modeling

Cloud seeding is a weather modification technique for enhancing precipitation in arid and semi-arid regions, including the Western U.S. However, designing an optimal cloud seeding operation based on comprehensive evaluation metrics, such as seeding agent dispersion and atmospheric conditions, has yet to be thoroughly explored for this region. This study investigated the impacts of cloud seeding, particularly utilizing silver iodide, on ice particle growth within clouds through numerical modeling. By leveraging the Snow Growth Model for Rimed Snowfall (SGMR), the microphysical processes involved in cloud seeding across five distinct events were simulated. The events were in the Lake Tahoe region, nestled within the Sierra Nevada Mountain ranges in the Western U.S. This model was executed based on six primary variables, including cloud top height, cloud base height, cloud top temperature, cloud base temperature, liquid water content, and ice water content. This study incorporated datasets from the Modern-Era Retrospective Analysis for Research and Applications Version 2 and the Clouds and the Earth Radiant Energy System. The findings revealed the importance of ice nucleation, aggregation, diffusion, and riming processes and highlighted the effectiveness of cloud seeding in enhancing ice particle number concentration, ice water content, and snowfall rates. However, event-specific analyses indicated diverse precipitation responses to cloud seeding based on initial atmospheric conditions. The SGMR modeling hints at the importance of improving ice microphysical processes and provides insights for future cloud seeding research using regional and global climate models.

Heterogeneous Trajectories of Parental Psychological Aggression from Middle Childhood to Early Adolescence in China: Associations with Child- and Family-Level Predictors and Children's Developmental Outcomes.

Previous research has shown that parental psychological aggression may change with children's age, and individual differences existed in the developmental trajectories of parental psychological aggression within different families. However, most studies on the heterogeneous psychological aggression trajectories have focused solely on mothers or combined mothers' and fathers' data, with few studies separately exploring the unique trajectories of fathers and mothers and their predictors and outcomes within Chinese societies. Therefore, this study investigated the heterogeneous trajectories of paternal and maternal psychological aggression from middle childhood to early adolescence and their associations with child- and family-level predictors and outcomes in China. A total of 1137 Chinese families with children in grades 1-3 (Mage = 7.17; SDage = 0.95 at Time 1; 52.35% boys, 47.65% girls) participated in assessments at five time points, using 1-year internals in between. Latent class growth models were used to estimate the heterogeneous trajectories of paternal and maternal psychological aggression from ages 7 to 11 years. Logistic regression analyses were used to understand the child- and family-level predictors of these trajectories, and analysis of covariance was used to examine the outcomes of these trajectories. The findings revealed that three trajectories of paternal psychological aggression were identified: low-persistent (88.95%), high-decreasing (7.93%), and high-increasing-decreasing (3.12%) trajectories. Four trajectories of maternal psychological aggression were identified: low-persistent (86.17%), high-decreasing (5.94%), high-increasing-decreasing (4.08%), and low-increasing (3.81%) trajectories. Lower marital satisfaction, more psychological aggression experiences during childhood, and being a parent of a boy were risk factors for both paternal and maternal trajectories, while higher negative affectivity in children was a risk factor of maternal but not paternal trajectories. In addition, the high-increasing-decreasing trajectory for both fathers and mothers as well as the low-increasing trajectory for mothers predicted children's more internalizing and externalizing problems. These findings highlight the importance of considering heterogeneity in understanding the developmental patterns of parental psychological aggression, their predictors, and cumulative effects on child development.

Disentangling developmental trajectories of childhood anxiety and depression symptoms in the prediction of adolescent substance use.

Adolescent substance use is comorbid with internalizing problems (e.g., anxious and depressive symptoms) and externalizing problems (EPs). Developmental researchers have linked early anxious and depressive symptoms to later substance use behaviours via an "internalizing pathway". Support for this pathway exists among young adults; however, evidence from prospective studies of adolescents has been inconsistent. Given the paucity of prospective studies in this area, the current study used a developmental framework to examine childhood anxiety and depression symptom trajectories as predictors of adolescent substance use and whether these relationships depend on sex and EPs. Children with and without EPs participated annually in an ongoing longitudinal study (N = 744; Time 1 age = 6.3-10.6). Youth completed self-report measures of anxiety and depression symptoms (Times 3-6) and substance use (Times 7-8). Parents and teachers completed measures of children's EPs (Time 0). Parallel process growth models showed that changes over time in childhood depression symptoms were significantly positively associated with adolescent alcohol/cannabis use, substance-related consequences, and total score of problematic substance use. Changes over time in childhood anxiety symptoms were significantly negatively associated with adolescent alcohol/cannabis use. These results were invariant by EPs and sex. Research implications of this study emphasize the importance of isolating the respective pathways of anxious and depressive symptoms to later substance use outcomes, while clinical implications focus on targets for early identification and prevention of problematic substance use in adolescence.

A longitudinal study of healthcare workers' mental health during Western Australia's unique policy response to COVID-19.

Western Australia's response to the COVID-19 pandemic was swift and effective in implementing public health protections and preventing the spread of the virus for the first 2 years. However, healthcare staff continued to be at increased risk of mental health concerns. To investigate the longitudinal patterns of post-traumatic stress symptoms (PTSS), depression and anxiety among healthcare workers in Western Australia, and the risk and protective factors associated with changes in status during the first wave. Participants comprised 183 healthcare staff working at tertiary hospitals and major clinics across Perth, for whom longitudinal data were available. Questionnaire data were collected before Western Australia's first major COVID-19 community wave in early 2022 and following the first wave in late 2022. Online surveys comprised validated measures assessing psychological symptoms, risk and protective factors, and original measures of workplace factors. Overall rates of PTSS, depression and anxiety remained stable across the two assessment points. However, latent growth models revealed that those with lower PTSS, depression or anxiety symptoms at baseline reported a larger increase in symptoms over time, and those with higher symptoms at baseline had a smaller decline over time, indicating a 'catch-up' effect. Workplace stressors, sleep difficulties and trauma exposure were key risk factors for changes in psychological symptoms from baseline, and workplace and social supports played protective roles. Improvements in systemic workplace factors are needed to support healthcare workers' mental health during periods of acute stress, even in settings with high levels of emergency preparedness.

Financial development and economic growth: Current issues of theory and practice of research

The article contains an analysis of theoretical and empirical research on the relationship between financial and economic development, that have been accumulated since the beginning of the 20th century. The diversity of concepts in the absence of a recognized theory of economic growth, and the rapid evolution of financial market make this issue still relevant. The empirical research is based on the theories which were developed at least 30 years ago and they don’t include a number of modern trends (a multiple increase in financial innovation, the dominance of global markets, sectoral polarization of economies and contraction of the real sector in a number of countries). This leaves gaps in understanding the mechanisms of financial market impact on economic growth, increases the diversity of results. The purpose of this work is to systemize the ideas around financial market influence on economic growth that have been established in theory and practice to form an objective picture of what was happening, as well as to identify the actual ways of theoretical concepts renewal, to prepare recommendations for improving analytical approaches. Using the methods of analytical grouping, meaningful and evolutionary analysis: databases of theoretical (25 for 1911—2000s) and empirical (71 for 1993—2023) works have been formed (by groups of financial market influence); the evolution of theoretical concepts and endogenous economic-mathematical models of economic growth based on financial development has been considered; a factor analysis of empirical studies by 11 essential parameters has been carried out. According to the results, the influence of financial market on economic growth is not universal and varies across countries. The increased diversity of research results is associated with a decrease in their accuracy due to: emergence of new mechanisms of the financial market influence on economic growth; failure to take into account differences in sectoral structures of economies; dependence of empirical research on external factors not related to the hypothesis being tested (9 out of 11 reviewed). Conclusions and recommendations are provided: on the need to rethink of the theoretical concepts, on improving the quality of empirical studies; on the importance of accumulating a new body of empirical data around the impact of the financial market on economic growth at the present stage.

Modelling icing growth on overhead transmission lines: Current advances and future directions

AbstractThe increasing impact of climate change raises concerns regarding the vulnerability of overhead transmission lines to ice disasters. To address this issue, this study reviews icing growth modelling in two categories: physical‐driven models (PDMs) and data‐driven models (DDMs), covering current advances and future directions. First, PDMs are summarised, focusing on the thermodynamic and fluid mechanics mechanisms. Existing PDMs are compared based on principles, analysing their advantages, disadvantages, and challenges faced. Second, the summarisation of DDMs involves four aspects: data preparation, algorithm selection, model training, and model evaluation. In data preparation, techniques such as preprocessing methods are reviewed to handle multisource data. In algorithm selection, various modelling algorithms are compared and analysed, from basic to deep learning approaches. In model training, processes are summarised to enhance practical applicability, including data partitioning, hyperparameter adjustment, generalisation capability, and model interpretability. In model evaluation, the predictive capabilities are analysed, covering both regression and classification tasks. Subsequently, based on the analyses, a comparison of PDMs and DDMs across various aspects is presented. Finally, future directions in icing growth modelling are outlined. The aim is to enhance icing assessment by understanding the underlying mechanism in attempt to reduce vulnerability and ensure reliability against adverse weather conditions.

Mapping Variable Wildfire Source Areas Through Inverse Modeling

Global climate change is leading to increased wildfire activity in many parts of the world, and with increasing development, a heightened threat to communities in the wildland urban interface. Evaluating the potential for fire to affect communities and critical infrastructure is essential for effective response decision-making and resource prioritization, including evacuation planning, with changing weather conditions during the fire season. Using a receptor–pathway–source assessment framework, we estimate the potential source area from which a wildfire could spread to a community in British Columbia by projecting fire growth outward from the community’s perimeter. The outer perimeter of the source area is effectively an evacuation trigger line for the forecast period. The novel aspects of our method are inverting fire growth in both space and time by reversing the wind direction, the time course of hourly weather, and slope and aspect inputs to a time-evolving fire growth simulation model Prometheus. We also ran a forward simulation from the perimeter of a large fire that was threatening the community to the community edge and back. In addition, we conducted a series of experiments to examine the influence of varying environmental conditions and ignition patterns on the invertibility of fire growth simulations. These cases demonstrate that time-evolving fire growth simulations can be inverted for practical purposes, although caution is needed when interpreting results in areas with extensive non-fuel cover or complex community perimeters. The advantages of this method over conventional simulation from a fire source are that it can be used for pre-attack planning before fire arrival, and following fire arrival, it does not require having an up-to-the-minute map of the fire location. The advantage over the use of minimum travel time methods for inverse modeling is that it allows for changing weather during the forecast period. This procedure provides a practical tool to inform real-time wildfire response decisions around communities, including resource allocation and evacuation planning, that could be implemented with several time-evolving fire growth models.

Predictors of frailty trajectories among people with HIV.

This study aimed to estimate the latent frailty trajectories and identify corresponding predictors (socio-demographic, HIV-related, comorbidities, and behavioral) among a cohort of PWH. Longitudinal observational study using latent class growth modeling. Nine hundred seventy-six PWH aged 40 years and older with frailty measured from at least two visits within the ACTG HAILO cohort were included. Frailty components included weakness, physical activity, weight loss, exhaustion, and slowness. Latent class growth models were estimated to capture change in frailty over time; multinomial logistic regression was used to estimate associations between predictors and frailty trajectory class. At baseline, participants were M = 51.5 years old (SD = 7.5), 81% male (n = 783), 48% White non-Hispanic (n = 461), and 20% Hispanic (n = 195). Latent class growth models identified three frailty trajectories: Sustained robustness (n = 811; 83%), Worsening frailty (n = 79; 8%), and Frailty improvement (n = 86; 9%). Older age, race, sex at birth, select comorbidities (cardiovascular disease, depression, type 2 diabetes), and behavioral characteristics (physical activity, smoking, and alcohol) were associated with fluctuations in frailty trajectories over time (p < 0.05). Modifiable factors such as managing comorbidities and promoting physical activity present ideal opportunities for future interventions to prevent or slow the progression of frailty.

Enhancing hospital protection measures reduces frontline medical workers’ stress during the pandemic

Frontline medical workers (FMWs) faced high stress levels in frontline clinics during the COVID-19 pandemic. This study aims to alleviate FMWs’ psychological stress by enhancing protection measures, which includes refining the selection process, improving protective measures for their work in frontline clinics, and determining the appropriate time for evacuation. A Chinese-language-version stress questionnaire, covering stress-related issues and sociodemographic characteristics, was administered to FMWs in Shanghai during the COVID-19 pandemic in 2022, yielding 107 valid responses. The questionnaire’s reliability and validity were subsequently confirmed. Exploratory factor analysis (EFA) was applied to the stress-related questions, with the KMO and Bartlett’s test values of 0.886, 877.8522 (df = 120, p < 0.0001), respectively. Structure equation modeling (SEM) was used to confirm the factors and measure the relationships among the stress-related questions, factors and sociodemographic characteristics. The parameters of SEM named SOFAIDC were significant with SRMSR, RMSEA, AGFI, NFI, and PNFI being 0.0422, 0.0507, 0.9946, 0.9958, and 0.7615, respectively. Paired sample t-tests revealed the significant decrease in FMWs’ stress score of the current week and the previous week, with all t-values being negative and significant (p < 0.01). A latent growth model (LGM) named LGM30 verified the overall decreasing stress trend over the weeks, with high R-squares (> 0.80), significant positive linear and negative quadratic time parameters. Based on the trajectory analysis, a stress scorecard with an AUC of 0.856 was developed. This study found that there are four factors for FMWs’ psychological stress (anxiety about infection, exhaustion, lack of cognition for infection, and hesitant feeling), and improving targeted hospital protection could alleviate FMWs’ psychological stress through SOFAIDC, as all the total effect of factors or items from the feeling of being protected by hospital were negative. Meanwhile, although overall FMWs’ stress trend has decreased, 22.43% of FMWs have maintained or experienced a high stress trend, and the stress might increase over weeks in frontline clinics. To perfect hospital protection to alleviate FMWs’ psychological stress, the scorecard could be used to select FMWs with low-stress trends, LGM30 could be used to determine the withdrawal time (such as week 8), and targeted hospital protections could be designed based on the relationships between feeling of being protected by the hospital and factors in SOFAIDC, such as providing adequate protective equipment, improving the rationality of FMWs’ work schedules, recruiting personnel with higher education levels, and paying adequate monetary compensation.

Electrochemical nucleation and growth model of MoS2 for hydrogen evolution reaction

The electrochemical nucleation of MoS2 from a mixture of sodium molybdate dihydrate (Na2MoO4·2H2O) and sodium sulphide (Na2S·xH2O) aqueous solution on Cu substrate has been investigated. The nucleation and formation of molybdenum sulphide were investigated employing cyclic voltammetry and chronoamperometry studies. The experimental i–t curves observed at various overpotentials were compared to theoretical curves derived for the two limiting situations of the 3D instantaneous/progressive nucleation and growth model, as reported by Scharifker and Hills. The outcome of electrodeposition potential on nucleation rate (A) and nucleation density (N) was calculated from the current–time transients and SEM morphology obtained at − 1.1 V (5.75 × 1014 and 1.86 × 1015) was compared with − 0.9 V, − 1.0 V, and − 1.2 V, respectively. The investigation of the initial stages of the transient current–time relationships developed for MoS2 electrodeposition specified that film formation occurred progressively initially and instantaneous nucleation during the course of time. A HPMoS2 with an average size of 5–65 nm was obtained at -1.1 V and exhibited superior performance towards the hydrogen evolution reaction compared to samples obtained at − 0.9 V, − 1.0 V, and − 1.2 V.

Hybrid model of tumor growth, angiogenesis and immune response yields strategies to improve antiangiogenic therapy

Solid tumors harbor a complex and dynamic microenvironment that hinders the delivery and efficacy of therapeutic interventions. In this study, we developed and utilized a hybrid, discrete-continuous mathematical model to explore the interplay between solid tumor growth, immune response, tumor-induced angiogenesis, and antiangiogenic drugs. By integrating published data with anti-angiogenic drugs, we elucidate three primary mechanisms by which anti-angiogenesis influences tumor progression and treatment outcomes: reduction in tumor growth rate by mitigating and temporally delaying angiogenesis, normalization of blood vessel structure and function, and improving immune cell extravasation and activation. Our results indicate a significant increase in functional blood vessels and perfusion following anti-angiogenic treatment, which in turn improves the intratumoral distribution of immune cells. The normalization window, or optimal time frame for anti-angiogenic drug administration, and the dose of the drug arise naturally in the model and are highlighted as crucial factors in maximizing treatment benefits. Prolonged anti-angiogenic treatment triggers cancer cell migration into healthy tissue and induces immunosuppression due to hypoxia, potentially leading to negative effects because these cancer cells will rapidly proliferate upon treatment termination. In conclusion, the positive contribution of anti-angiogenic treatment must balance the possible negative effects by choosing a proper treatment protocol as well as combining it with proper anti-cancer treatment. Our findings provide valuable insights and a framework for the design of protocols with anti-angiogenic treatment, targeted immunotherapy, and non-targeted anti-cancer therapies.

The odyssey of women in university education: stochastic growth models for studying access and graduation process

This research aims to explore the evolution of statistics related to the proportion of women in university student populations (focusing on bachelor’s or equivalent degree programs) over an extensive period, spanning from the founding of the first university until recent times. This is done by utilizing empirical insights derived from comprehensive data series, presented here for the first time and primarily encompassing Greece, UK, Canada and USA. Motivated by the distinctive properties of these series and their sigmoid pattern, we delve into a general family of stochastic growth models for data analysis. A notable contribution of this paper lies in offering a novel interpretation of this family within a competing cause scenario, similar to those used in the theory of event history analysis. We emphasize on key common elements within the two statistical domains of research, thereby highlighting potential future research directions; besides, the interpretability of model parameters stands out as an advantage compared to other approaches such as those based on regression model theory. For assessing the proposed parameter estimation methodology under realistic conditions a simulation study is also conducted. The application and results are aimed at making a significant contribution to research in higher and university education by presenting comprehensive sets of consistent data and statistical tools to capture their fundamental characteristics and trends. Additionally, they can serve as valuable resources for education policy-makers and human resources planners alike.

Unravelling the Universal Spatial Properties of Coral Reefs

ABSTRACTAimTo characterise the size and geometry of coral reefs on a global scale.LocationGlobal.Time PeriodPresent.Major Taxa StudiedCoral reefs.MethodsWe process the Allen Coral Atlas database of shallow‐water tropical reefs to obtain a comprehensive and unprecedented inventory of coral reefs worldwide. We analyse different macroecological and morphological patterns, including size distribution, the area‐perimeter relationship, inter‐reef distance distribution, and the fractal dimension of individual reefs and coral provinces.ResultsWe identified a total of 1,579,772 individual reefs worldwide (&gt; 1000 m2), extending over a total of 52,423 km2 of ocean area with mean and median sizes of 3.32 and 0.3 ha, respectively. We unravelled three universal laws that are common to all coral reef provinces: the size‐frequency distribution and the inter‐reef distance distribution follow power laws with an exponent of 1.8 and 2.33, respectively. At the same time, the area‐perimeter relationship conforms to a power‐law with an exponent of 1.26. Furthermore, we demonstrate that coral reefs develop fractal patterns characterised by a perimeter fractal dimension of and a surface fractal dimension of . Our analysis suggests that coral reefs tend to evolve from simple rounded filled shapes to more complex, elongated and less compact forms, developing into fractal structures with a consistent surface fractal dimension and an increasing perimeter fractal dimension as they grow.Main ConclusionsCoral reefs display intricate fractal‐like geometries and exhibit universal macroecological patterns, largely independent of their geographical location. The universality of the observed patterns suggests that these features possibly stem from the highly conserved interactions of biological, physical and chemical processes. Over geological scales, these processes lead to reef landscape patterns common among all provinces, providing new information relevant to reef growth modelling.

Longitudinal association between social participation and trajectories of life satisfaction in late middle-aged Korean adults with physical disabilities

Late middle-aged adults (50–64 years of age) who have physical disabilities often experience a decline in life satisfaction due to those bodily limitations. It is crucial to understand how their life satisfaction can be enhanced to support the social participation, health and wellbeing of this age group. This study examined the association between social participation and life satisfaction over time in Korean adults 50–64 years of age with physical disabilities. Data on 545 adults with physical disabilities aged 50–64 years from the 2016–2021 Korea Panel Survey of Employment for the Disabled (PSED) were extracted. The dependent variable was self-reported life satisfaction while social participation was the time-varying independent variable which was measured with a single question. The latent growth model (LGM) was used to examine the association between social participation and life satisfaction at each time point. The sample was composed of 313 (57.43 per cent) males and 232 (42.57 per cent) females from Korea having an average age of 57.42 years. A piecewise LGM demonstrated good model fit. Social participation was positively associated with life satisfaction at each time point for over the course of six years, with standardised coefficients ranging from 0.154 to 0.275 (p&lt;0.001). Social participation contributed significantly to life satisfaction in Korean adults 50–64 years of age with physical disabilities. The findings indicate the need for social participation that could improve the life satisfaction of those with physical disabilities.