Search Results (1,107)

The stability of energy demand–supply systems is often affected by delayed feedback caused by regulatory inertia, communication lags, and heterogeneous agent responses. Conventional models typically assume discrete delays, which may oversimplify real dynamics and reduce controller effectiveness. This work addresses this limitation by introducing a novel class of nonlinear energy models with distributed delay feedback governed by gamma-distributed memory kernels. Specifically, we consider both weak (exponential) and strong (Erlang-type) kernels to capture a spectrum of memory effects. Using the linear chain trick, we reformulate the resulting integro-differential model into a higher-dimensional system of ordinary differential equations. Analytical conditions for local asymptotic stability and Hopf bifurcation are derived, complemented by Lyapunov-based global stability criteria. The related numerical analysis confirms the theoretical findings and reveals a distinct stabilization regime. Compared to fixed-delay approaches, the proposed framework offers improved flexibility and robustness, with implications for delay-aware energy control and infrastructure design. Full article

We develop and analyze a distributed-delay model for nutrient–fish–mussel dynamics in multitrophic aquaculture systems. Extending the classical discrete-delay framework, we incorporate gamma-distributed kernels to capture the time-distributed nature of nutrient assimilation, yielding a more realistic and analytically tractable representation. These kernels introduce a form of temporal symmetry in the system’s memory, where past nutrient levels influence present dynamics in a balanced and structured way. Using the linear chain trick, we reformulate the integro-differential equations into ordinary differential systems for both weak and strong memory scenarios. We derive conditions for local stability and Hopf bifurcation, and establish global stability using Lyapunov-based methods. Numerical simulations confirm that increased delay can destabilize the system, leading to oscillations, while stronger memory mitigates this effect and enhances resilience. Bifurcation diagrams, time series, and phase portraits illustrate how memory strength governs the system’s dynamic response. This work highlights how symmetry in memory structures contributes to system robustness, offering theoretical insights and practical implications for the design and management of ecologically stable aquaculture systems. Full article

Modeling loss data is a crucial aspect of actuarial science. In the insurance industry, small claims occur frequently, while large claims are rare. Traditional heavy-tail distributions, such as Weibull, Log-Normal, and Inverse Gaussian distributions, are not suitable for describing insurance data, which often exhibit skewness and fat tails. The literature has explored classical and Bayesian inference methods for the parameters of composite distributions, such as the Exponential–Pareto, Weibull–Pareto, and Inverse Gamma–Pareto distributions. These models effectively separate small to moderate losses from significant losses using a threshold parameter. This research aims to introduce a new composite distribution, the Gamma–Pareto distribution with two parameters, and employ a numerical computational approach to find the maximum likelihood estimates (MLEs) of its parameters. A novel computational approach for a nonlinear regression model where the loss variable is distributed as the Gamma–Pareto and depends on multiple covariates is proposed. The maximum likelihood (ML) and Approximate Bayesian Computation (ABC) methods are used to estimate the regression parameters. The Fisher information matrix, along with a multivariate normal distribution as the prior distribution, is utilized through the ABC method. Simulation studies indicate that the ABC method outperforms the ML method in terms of accuracy. Full article

A significant portion of coal mined in Kazakhstan is mainly used for fuel energy and metallurgy. Approximately 60% of electricity is generated by coal-fired power engineering. About 19 million tons of ash and slag waste (ASW) are annually sent to dumps. After coal combustion, in ASW not only are natural radioactive nuclides NRN (U²³⁸, Th²³², K⁴⁰) concentrated, but also rare and rare earth elements (REE). In this regard, ASW that essentially turns into quasi-technogenic deposits of NRN and REE, requires systemic measures for their utilization. The possibilities of extracting REE from coal power-industry waste are estimated based on the analysis of the concentration of REE (Ce, La, Nd, Sm, etc.), NRN (U²³⁸, Th²³² and their decay products, K⁴⁰) and the established significant correlations between rare earth and radioactive elements. The purpose of this paper is to study the natural radioactivity of coals and ash and slag waste as potential raw materials for assessing the quality and extracting rare earth metals. The stated purpose involves solving the following problems: studying the features of the NRN and REE distribution in coals and ash and slag waste; assessing the possibility of using ash and slag waste as a promising source of REE extraction based on nuclear radiometric studies; and studying the spectrometry of natural gamma radiation for assessing the quality of coals. Full article

Modern healthcare and engineering both rely on robust reliability models, where handling censored data effectively translates into longer-lasting devices, improved therapies, and safer environments for society. To address this, we develop a novel inferential framework for the ZLindley (ZL) distribution under the improved adaptive progressive Type-II censoring strategy. The proposed approach unifies the flexibility of the ZL model—capable of representing monotonically increasing hazards—with the efficiency of an adaptive censoring strategy that guarantees experiment termination within pre-specified limits. Both classical and Bayesian methodologies are investigated: Maximum likelihood and log-transformed likelihood estimators are derived alongside their asymptotic confidence intervals, while Bayesian estimation is conducted via gamma priors and Markov chain Monte Carlo methods, yielding Bayes point estimates, credible intervals, and highest posterior density regions. Extensive Monte Carlo simulations are employed to evaluate estimator performance in terms of bias, efficiency, coverage probability, and interval length across diverse censoring designs. Results demonstrate the superiority of Bayesian inference, particularly under informative priors, and highlight the robustness of HPD intervals over traditional asymptotic approaches. To emphasize practical utility, the methodology is applied to real-world reliability datasets from clinical trials on leukemia patients and hydrological measurements from River Styx floods, demonstrating the model’s ability to capture heterogeneity, over-dispersion, and increasing risk profiles. The empirical investigations reveal that the ZLindley distribution consistently provides a better fit than well-known competitors—including Lindley, Weibull, and Gamma models—when applied to real-world case studies from clinical leukemia trials and hydrological systems, highlighting its unmatched flexibility, robustness, and predictive utility for practical reliability modeling. Full article

This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert-F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and tail behavior. Structural properties are derived, including the probability density function, cumulative distribution function, quantile function, hazard rate, and moments. Parameter estimation is addressed using the method of moments and maximum likelihood, and a Monte Carlo simulation study carried out to evaluate the performance of the proposed estimators. The practical applicability of the Lambert–Lindley distribution is demonstrated with two real datasets: stress rupture times of Kevlar/epoxy composites and hospital stay durations of breast cancer patients. Comparative analyses using goodness-of-fit tests and information criteria demonstrate that the proposed model can outperform classical alternatives such as the Gamma and Weibull distributions. Consequently, the Lambert–Lindley distribution emerges as a flexible alternative for modeling positive unimodal data in contexts such as material reliability studies and clinical duration analysis. Full article

Adaptor Protein-1 (AP-1) is a heterotetrameric essential for intracellular vesicular trafficking and polarized localization of somato-dendritic proteins in neurons. Variants in the AP1G1 gene, encoding the gamma-1 subunit of adaptor-related protein complex 1 (AP1γ1), have recently been associated with Usmani–Riazuddin syndrome (USRISD, MIM#619467), a very rare human genetic disorder characterized by intellectual disability (ID), speech and neurodevelopmental delays. Here we report a novel variant (c.196G>A; p.Gly66Arg) identified by exome sequencing analysis in a young girl showing overlapping clinical features with USRIS, such as motor and speech delay, intellectual disability and abnormal aggressive behavior. In silico analysis of the missense de novo variant suggested an alteration in AP1G1 protein folding. Patient’s fibroblasts have been studied with immunofluorescence techniques to analyze the intracellular distribution of AP-1. Zebrafish are widely regarded as an excellent vertebrate model for studying human disease pathogenesis, given their transparent embryonic development, ease of breeding, high genetic similarity to humans, and straightforward genetic manipulation. Leveraging these advantages, we investigated the phenotype, locomotor behavior, and CNS development in zebrafish embryos following the microinjection of human wild-type and mutated AP1G1 mRNAs at the one-cell stage. Knockout (KO) of the AP1G1 gene in zebrafish led to death at the gastrula stage. Lethality in the KO AP1G1 fish model was significantly rescued by injection of the human wild-type AP1G1 mRNA, but not by transcripts encoded by the Gly66Arg missense allele. The phenotype was also not rescued when ap1g1−/− zebrafish embryos were co-injected with both human wild-type and mutated mRNAs, supporting the dominant-negative effect of the new variant. In this study, we defined the effects of a new AP1G1 variant in cellular and animal models of Usmani–Riazzudin syndrome for future therapeutic approaches. Full article

Background: Long COVID can lead to a considerable economic burden because of ongoing care for persistent symptoms such as fatigue, dyspnea, or cognitive dysfunction. However, systematic research quantifying healthcare expenditures associated with long COVID remains limited. Objective: This study estimated the excess total, payer, and out-of-pocket healthcare expenditures associated with long COVID among adults in the United States (US). Methods: This was a cross-sectional analysis on adults ≥18 years using 2022 Medical Expenditure Panel Survey (MEPS) data (N = 17,119; representing approximately 254 million adults). Economic burden was measured with (1) total, (2) payer, and (3) out-of-pocket expenditures by individuals and their families. Generalized linear models (GLMs) with gamma distribution and log link were utilized to estimate excess expenditures associated with long COVID after adjusting for age, sex, race and ethnicity, social determinants of health, health status, and lifestyle factors. Results: Overall, 7.0% of the population reported long COVID. Adults with long COVID exhibited higher total (USD 11,305 vs. USD 7162) and payer (USD 9983 vs. USD 6097) expenditures compared to those with no COVID. In a fully adjusted analysis, long COVID was associated with an excess of USD 4098 in total healthcare expenditures and USD 3705 in payer expenditures. We did not observe significant differences in out-of-pocket expenditures between those with long COVID and no COVID. Conclusions: Adults with long COVID had 1.5 times higher total healthcare costs compared to those without COVID. This study highlights the need for comprehensive strategies and policies to reduce the economic burden associated with long COVID. Full article

Prior work has demonstrated that higher surprisal, a measure quantifying the unexpectedness of a trigger exposure, predicts headache onset over 12 to 24 h. However, these analyses relied on retrospective expectations of trigger exposure formed after extended data collection. To operationalize surprisal prospectively, Bayesian methods could update expectations dynamically over time. The objective of this study was to extend the application of surprisal theory for predicting migraine attack risk by developing methods to estimate trigger variable likelihood in real time, under conditions of limited personal observation. In a prospective daily diary study of individuals with migraine (N = 104), data were collected over 28 days, including stress, sleep, and exercise exposures. Bayesian models were applied to estimate daily expectations for each variable under uninformative and empirical priors derived from the sample. Stress was modeled using a hurdle-Gamma distribution, sleep using discrete outcomes from a Normal distribution, and exercise using a Bernoulli distribution. Surprisal was calculated based on the predictive distribution at each time point and compared to static empirical surprisal values obtained after full data collection. Dynamic Bayesian surprisal values systematically differed from retrospective empirical estimates, particularly early in the observation period. Divergence was larger and more variable under uninformative priors but attenuated over time. Empirically informed priors produced more stable, lower-bias surprisal trajectories. Substantial individual variability was observed across exposure types, especially for exercise behavior. Prospective surprisal modeling is feasible but highly sensitive to prior specification, especially in sparse data contexts (e.g., a binary exposure). Incorporating empirical or individually informed priors may improve early model calibration, though individual learning remains essential. These methods offer a foundation for real-time headache forecasting and dynamic modeling of brain–environment interactions. Full article

This study investigates the ${\mathbb{B}}_t$-transformation of probability measures within the framework of free probability. A primary focus is the invariance under this transformation of two fundamental families: the free Meixner family and the free analog of the Letac–Mora class. In addition, we introduce novel characteristics associated with the ${\mathbb{B}}_t$-transformation, offering refined analytical tools to probe its structural and functional properties. These tools allow us to uncover new and significant properties of several distributions in free probability, including the semicircle, the Marchenko–Pastur, and the free Gamma laws, yielding explicit invariance results and stability conditions. Our findings extend the theoretical understanding of the ${\mathbb{B}}_t$-transformation and provide practical methods for analyzing the dynamics and stability of classical free distributions under this operator. Full article

This paper presents a comprehensive study on the estimation of multicomponent stress–strength reliability under progressively censored data, assuming the inverse Rayleigh distribution. Both maximum likelihood estimation and Bayesian estimation methods are considered. The loss function and prior distribution play crucial roles in Bayesian inference. Therefore, Bayes estimators of the unknown model parameters are obtained under symmetric (squared error loss function) and asymmetric (linear exponential and general entropy) loss functions using gamma priors. Lindley and MCMC approximation methods are used for Bayesian calculations. Additionally, asymptotic confidence intervals based on maximum likelihood estimators and Bayesian credible intervals constructed via Markov Chain Monte Carlo methods are presented. An extensive Monte Carlo simulation study compares the efficiencies of classical and Bayesian estimators, revealing that Bayesian estimators outperform classical ones. Finally, a real-life data example is provided to illustrate the practical applicability of the proposed methods. Full article

This paper introduces a novel three-parameter probability model, the unit-Gompertz–Makeham (UGM) distribution, designed for modeling bounded data on the unit interval (0,1). By transforming the classical Gompertz–Makeham distribution, we derive a unit-support distribution that flexibly accommodates a wide range of shapes in both the density and hazard rate functions, including increasing, decreasing, bathtub, and inverted-bathtub forms. The UGM density exhibits rich patterns such as symmetric, unimodal, U-shaped, J-shaped, and uniform-like forms, enhancing its ability to fit real-world bounded data more effectively than many existing models. We provide a thorough mathematical treatment of the UGM distribution, deriving explicit expressions for its quantile function, mode, central and non-central moments, mean residual life, moment-generating function, and order statistics. To facilitate parameter estimation, eight classical techniques, including maximum likelihood, least squares, and Cramér–von Mises methods, are developed and compared via a detailed simulation study assessing their accuracy and robustness under varying sample sizes and parameter settings. The practical relevance and superior performance of the UGM distribution are demonstrated using two real-world engineering datasets, where it outperforms existing bounded models, such as beta, Kumaraswamy, unit-Weibull, unit-gamma, and unit-Birnbaum–Saunders. These results highlight the UGM distribution’s potential as a versatile and powerful tool for modeling bounded data in reliability engineering, quality control, and related fields. Full article

This paper proposes a method for assessing societal risk along a traffic link by integrating a stochastic formulation of the fundamental diagram. The approach accounts for uncertainty in vehicle speed due to user heterogeneity, vehicle characteristics, and environmental conditions. The risk index is decomposed into occurrence, vulnerability, and exposure components, with the occurrence probability modeled as a function of stochastic speed. The inverse gamma distribution is adopted to represent speed variability, enabling analytical tractability and control over dispersion. Numerical results show that urban and suburban environments exhibit distinct sensitivity to model parameters, particularly the gamma shape parameter η and the composite parameter c = β · v₀ obtained by the product of the occurrence parameter β and the free speed flow v₀. Graphical representations illustrate the impact of uncertainty on risk estimation. The proposed framework enhances existing deterministic methods by incorporating probabilistic elements, offering a foundation for future applications in traffic safety management and infrastructure design. Full article

Fluid flow prediction in clastic heterogeneous reservoirs is a universal issue, especially when diagenetic development supplants structural and depositional controls. We consider this issue in the Middle Miocene Belayim Formation of the Gulf of Suez, a principal syn-rift reservoir where extreme, diagenetically induced pore system heterogeneity thwarts production. Although fault compartmentalization is understood as creating first-order traps, sub-seismic diagenetic controls on permeability anisotropy and reservoir within these traps are not restricted. This study uses a comprehensive set of petrophysical logs (ray gamma, resistivity, density, neutrons, sonic) of four key wells in the western field of Tawila (Tw-1, Tw-3, TW-4, TN-1). We apply an integrated workflow that explicitly derives permeability from petrophysical logs and populates it within a seismically defined structural framework. This study assesses diagenetic controls over reservoir permeability and fluid flow. It has the following primary objectives: (1) to characterize complicated diagenetic assemblage utilizing sophisticated petrophysical crossplots; (2) to quantify the role of shale distribution morphologies in affecting porosity effectiveness utilizing the Thomas–Stieber model; (3) to define hydraulic flow units (HFUs) based on pore throat geometry; and (4) to synthesize these observations within a predictive 3D reservoir model. This multiparadigm methodology, involving M-N crossplotting, Thomas–Stieber modeling, and saturation analysis, deconstructs Tawila West field reservoir complexity. Diagenesis that has the potential to destroy or create reservoir quality, namely the general occlusion of pore throats by dispersed, authigenic clays (e.g., illite) and anhydrite cement filling pores, is discovered to be the dominant control of fluid flow, defining seven unique hydraulic flow units (HFUs) bisecting the individual stratigraphic units. We show that reservoir units with comparable depositional porosity display order-of-magnitude permeability variation (e.g., >100 mD versus <1 mD) because of this diagenetic alteration, primarily via pore throat clogging resulting from widespread authigenic illite and pore occupation anhydrite cement, as quantitatively exemplified by our HFU characterization. A 3D model depicts a definitive NW-SE trend towards greater shale volume and degrading reservoir quality, explaining mysterious dry holes on structurally valid highs. Critically, these diagenetic superimpressions can replace the influence of structural geometry on reservoir performance. Therefore, we determine that a paradigm shift from a highly structured control model to an integrated petrophysical and mineralogical approach is needed. Sweet spot prediction relies upon predicting diagenetic facies distribution as a control over permeability anisotropy. Full article

Clustered time-to-event data are quite common in survival analysis and finding a suitable model to account for dispersion as well as censoring is an important issue. In this article, we present a flexible model for repeated, overdispersed time-to-event data with right-censoring. We present here a general model by incorporating generalized gamma and normal random effects in a Weibull distribution to accommodate overdispersion and data hierarchies, respectively. The normal random effect has the property of being symmetrical, which means its probability density function is symmetric around its mean. While the random effects are symmetrically distributed, the resulting frailty model is asymmetric in its survival function because the random effects enter the model multiplicatively via the hazard function, and the exponentiation of a symmetric normal variable leads to lognormal distribution, which is right-skewed. Due to the intractable integrals involved in the likelihood function and its derivatives, the Monte Carlo approach is used to approximate the involved integrals. The maximum likelihood estimates of the parameters in the model are then numerically determined. An extensive simulation study is then conducted to evaluate the performance of the proposed model and the method of inference developed here. Finally, the usefulness of the model is demonstrated by analyzing a data on recurrent asthma attacks in children and a recurrent bladder data set known in the survival analysis literature. Full article