Lognormal Research Articles

Fitting the return period of dengue fever epidemic in Guangdong province of China

ObjectivesThe prevention and control of dengue fever (DF) has been a major public health issue in Guangdong (GD) province, China. This study aims to analyze the return period (RP) and the return level (RL) of DF epidemic in GD, to help the formulation of prevention and control plan. MethodsThree models, namely Lognormal distribution (Lognor D.), normal distribution (Norm D.), and generalized logistic distribution (GLD) were selected to fit the annual number of indigenous DF cases in GD from 1978 to 2021. The coefficient of determination (R2), the root mean squared error (RMSE), and the Akaike information criterion (AIC) were used to evaluate the goodness of fit. We predicted the RP of 45130 historical maximum cases that occurred in 2014 and the RP of 4884 peak cases that occurred in 2019 over the 5 years up to 2021. ResultsFitting through the three models, the R2 was 0.98, 0.98, and 0.96, respectively. The predicted RLs of the annual DF case number were between 297 and 43234, 297 and 43233, 362 and 41868 for the RPs of 2–45 years. The predicted RPs of DF outbreaks exceeding the historical maximum were 43, 43, and 44 years, and the RPs of DF epidemic exceeding the peak in 2019 were 7, 7, and 8 years, respectively. Therefore, we predicted that GD would experience a DF outbreak beyond the historical maximum in the next 35 or 36 years from 2022. And in the next 4 or 5 years from 2022, there would be a DF epidemic exceeding the peak in 2019. ConclusionsThe study discloses a temporal periodicity inherent to the DF epidemic in GD. The three models are applicable for forecasting and evaluating the RP and RL of DF epidemic in GD, separately.

Effect of soil spatial variability on the stability of pipelines under horizontal loading

Submarine pipeline has been utilized more and more widely in offshore oil and gas transportation engineering. Given that these pipelines frequently subject horizontal loading during operation, thus precise predicting their horizontal bearing capacity is essential. However, most previous studies employ deterministic analysis without considering soil spatialvariability. This article introduces a two-dimensional (2D) random finite element analysis to study the horizontal pullout behaviour and failure mechanisms of a pipeline in a spatial variability soil. It is observed that the effect of soil spatial variability on the horizontal bearing capacity factor and failure mechanisms is remarkably substantial, with the distribution of the former showing a close approximation to a log-normal distribution. Furthermore, the average horizontal bearing capacity typically falls below the corresponding deterministic value. Consequently, the deterministic estimation of the horizontal bearing capacity tends to be inflated. Eventually, a reliability-based approach is formulated, where a factor of safety is incorporated to account for the uncertainties arising from spatial variability and ensure a sufficient safety margin. This methodology enables engineers to determine appropriate factor of safety tailored to the specific requirements of each project.

A Fuzzy Log-Normal Distribution Model for the Rainfall level of Namakkal District

A Fuzzy Log-Normal Distribution Model for the Rainfall level of Namakkal District

A comparative study of numerical methods for reliability assessment based on semi-Markov processes

The semi-Markov process, renowned for its versatile applications, has garnered significant attention in recent years. However, deriving closed-form expressions for computing reliability metrics proves challenging when sojourn times deviate from exponential distributions. This paper investigates three numerical techniques for computing the transition function matrix of the semi-Markov process, including the algebraic method, the truncated method, and the iterative method. It delves into their truncation and discretization errors, as well as their computational complexities. Additionally, the Laplace-based method and the semi-Markov-chain-based method are discussed to contrast their effectiveness with the three devised numerical approaches. Building on the linkage between the Markov renewal equation and system reliability metrics, five computational methods are applied to the evaluation of system reliability and availability. A case study on sequential cyber-attacks is presented to illustrate the applicability of these methods, considering sojourn times that follow exponential, gamma, lognormal, and Weibull distributions respectively. The results reveal that the three proposed numerical methods not only achieve high precision and rapid speed but also address scenarios beyond the capability of the Laplace-based method.

Early Detection of Chronic Kidney Disease Using Plasma Neutrophil Gelatinase-Associated Lipocalin and Kidney Injury Molecule-1 in Small-Breed Dogs: A Retrospective Pilot Study.

Multiple diagnostic modalities are urgently needed to identify early-stage kidney diseases. Various molecules have been investigated; however, most studies have focused on identifying specific biomarkers in urine. Considering that assessing the symmetrical dimethylarginine (SDMA) plasma concentration is more suitable as an early diagnostic test for chronic kidney disease (CKD) in routine veterinary practice, we aimed to investigate the clinical usefulness of plasma neutrophil gelatinase-associated lipocalin (pNGAL) and plasma kidney injury molecule-1 (pKIM-1) concentrations for CKD detection in small-breed dogs. Through a retrospective analysis, we found that numerous clinicopathological data showed a log-normal distribution, even when they satisfied normality tests. Moreover, the log-transformed pNGAL and pKIM-1 concentrations successfully identified CKD International Renal Interest Society (IRIS) stages 1-4 and the risk group with underlying CKD risk factors. Correlation analysis and group comparison of other factors confirmed the possibility of using these two biomarkers for detecting the CKD risk group and IRIS stage 1. Receiver operating characteristic curve analysis revealed that the diagnostic accuracy for discriminating the risk group was superior in the order of pKIM-1, pNGAL, SDMA, and serum creatinine levels. In conclusion, these results suggest that pKIM-1 and pNGAL are possible early or quantifiable markers of insignificant CKD or can be at least used as an adjunct with traditional indicators.

Competition among recombination pathways in single FAPbBr3 nanocrystals.

Single particle level microscopy of immobilized FAPbBr3 nanocrystals (NCs) has elucidated the involvement of different processes in their photoluminescence (PL) intermittency. Four different blinking patterns are observed in the data from more than 100 NCs. The dependence of PL decays on PL intensities brought out in fluorescence lifetime intensity distribution (FLID) plots is rationalized by the interplay of exciton- and trion-mediated recombinations along with hot carrier (HC) trapping. The high intensity-long lifetime component is attributed to neutral exciton recombination, the low intensity-short lifetime component is attributed to trion assisted recombination, and the low intensity-long lifetime component is attributed to hot carrier recombination. Change-point analysis (CPA) of the PL blinking data reveals the involvement of multiple intermediate states. Truncated power law distribution is found to be more appropriate than power law and lognormal distribution for on and off events. Probability distributions of PL trajectories of single NCs are obtained for two different excitation fluences and wavelengths (λex = 400, 440nm). Trapping rate (kT) prevails at higher power densities for both excitation wavelengths. From a careful analysis of the FLID and probability distributions, it is concluded that there is competition between the HC and trion assisted blinking pathways and that the contribution of these mechanisms varies with excitation wavelength as well as fluence.

Potential of Benchtop NMR for the Determination of Polymer Molar Masses, Molar Mass Distributions, and Chemical Composition Profiles by Means of Diffusion-Ordered Spectroscopy, DOSY.

The determination of molar masses and their distributions is crucial in polymer synthesis and design. This work presents the current performance and limitations of diffusion-ordered spectroscopy (DOSY) on a low-field (benchtop) NMR spectrometer (at 90MHz) as an alternative to size exclusion chromatography (SEC) for determining diffusion coefficient distributions (DCDs) and molar mass distributions (MMDs). After optimization for narrowly distributed homopolymers, MMDs obtained with inverse Laplace transformation (ILT) and log-normal distribution are compared with average molar masses obtained with mono- and bi-exponential fits, as well as MMDs obtained from SEC. This approach enables ILT to determine DCDs and MMDs even for bimodal homopolymers with fully spectrally overlapping signals and block copolymers with various chemical compositions, for which chemical composition profiles are determined. The feasibility of low-field diffusion NMR with samples dissolved in non-deuterated solvents is further demonstrated and methods for solvent suppression are discussed.

Disentangling drivers of mudflat intertidal DOM chemodiversity using ecological models

Microorganisms consume and transform dissolved organic matter (DOM) into various forms. However, it remains unclear whether the ecological patterns and drivers of DOM chemodiversity are analogous to those of microbial communities. Here, a large-scale investigation is conducted along the Chinese coasts to resolve the intrinsic linkages among the complex intertidal DOM pools, microbial communities and environmental heterogeneity. The abundance of DOM molecular formulae best fits log-normal distribution and follows Taylor’s Law. Distance-decay relationships are observed for labile molecular formulae, while latitudinal diversity gradients are noted for recalcitrant molecular formulae. Latitudinal patterns are also observed for DOM molecular features. Negative cohesion, bacterial diversity, and molecular traits are the main drivers of DOM chemodiversity. Stochasticity analyses demonstrate that determinism dominantly shapes the DOM compositional variations. This study unveils the intrinsic mechanisms underlying the intertidal DOM chemodiversity and microbial communities from ecological perspectives, deepening our understanding of microbially driven chemical ecology.

Understanding patient-derived tumor organoid growth through an integrated imaging and mathematical modeling framework.

Patient-derived tumor organoids (PDTOs) are novel cellular models that maintain the genetic, phenotypic and structural features of patient tumor tissue and are useful for studying tumorigenesis and drug response. When integrated with advanced 3D imaging and analysis techniques, PDTOs can be used to establish physiologically relevant high-throughput and high-content drug screening platforms that support the development of patient-specific treatment strategies. However, in order to effectively leverage high-throughput PDTO observations for clinical predictions, it is critical to establish a quantitative understanding of the basic properties and variability of organoid growth dynamics. In this work, we introduced an innovative workflow for analyzing and understanding PDTO growth dynamics, by integrating a high-throughput imaging deep learning platform with mathematical modeling, incorporating flexible growth laws and variable dormancy times. We applied the workflow to colon cancer organoids and demonstrated that organoid growth is well-described by the Gompertz model of growth. Our analysis showed significant intrapatient heterogeneity in PDTO growth dynamics, with the initial exponential growth rate of an organoid following a lognormal distribution within each dataset. The level of intrapatient heterogeneity varied between patients, as did organoid growth rates and dormancy times of single seeded cells. Our work contributes to an emerging understanding of the basic growth characteristics of PDTOs, and it highlights the heterogeneity in organoid growth both within and between patients. These results pave the way for further modeling efforts aimed at predicting treatment response dynamics and drug resistance timing.

Constraining the Selection-corrected Luminosity Function and Total Pulse Count for Radio Transients

Studying transient phenomena, such as individual pulses from pulsars, has garnered considerable attention in the era of astronomical big data. Of specific interest to this study are rotating radio transients (RRATs), nulling, and intermittent pulsars. This study introduces a new algorithm named LuNfit, tailored to correct the selection biases originating from the telescope and detection pipelines. Ultimately LuNfit estimates the intrinsic luminosity distribution and nulling fraction of the single pulses emitted by pulsars. LuNfit relies on Bayesian nested sampling so that the parameter space can be fully explored. Bayesian nested sampling also provides the additional benefit of simplifying model comparisons through the Bayes ratio. The robustness of LuNfit is shown through simulations and applying LuNfit onto pulsars with known nulling fractions. LuNfit is then applied to three RRATs, J0012+5431, J1538+1523, and J2355+1523, extracting their intrinsic luminosity distribution and burst rates. We find that their nulling fractions are 0.4(2), 0.749(5), and 0.995(2), respectively. We further find that a log-normal distribution likely describes the single pulse luminosity distribution of J0012+5431 and J1538+1523, while the Bayes ratio for J2355+1523 slightly favors an exponential distribution. We show the conventional method of correcting selection effects by “scaling up” the missed fraction of radio transients can be unreliable when the mean luminosity of the source is faint relative to the telescope sensitivity. Finally, we discuss the limitations of the current implementation of LuNfit while also delving into potential enhancements that would enable LuNfit to be applied to sources with complex pulse morphologies.

Two sunspot group populations and Gnevyshev-Waldmeier rule

Based on the materials of the Royal Greenwich Observatory catalog, the study of two different sunspot group populations continued: LLG – large long-lived, and SSG – small short-lived groups. The task of achieving a higher accuracy of the population separation parameter than before (Nagovitsyn & Pevtsov 2016, 2021) is being solved. A procedure for randomizing the lifetimes of sunspot groups observed once a day is proposed, which allows for statistical studies to achieve a higher time resolution. The form of the Gnevyshev-Waldmeier Rule is taken, which linearly connects the logarithm of the logS area and the lifetime of the sunspot group LT (over limited time intervals). It is shown that it has coefficients significantly different for SSG and LLG populations. The range of values of the group lifetime parameter separating the populations was found as LT∗=4.75±0.53 days, which is in agreement with the threshold values obtained earlier for the number of days of sunspot group observation: mSSG⩽5 days and mLLG>5 days. It is shown that the parameters of the bilognormal distribution of the sunspot group areas, obtained from their common grouped sample statistically by Levenberg–Marquardt method and with a preliminary division into lognormal distributions by lifetime, correspond to each other. It was clarified that, with an accuracy of up to a tenth of a day, the SSG population corresponds to the lifetimes of groups ⩽4.6 days, and the LLG population corresponds to times ⩾4.7 days. The results obtained make it possible to study various physical properties of SSG and LLG populations independently of each other in order to compare them and study their nature.

Analysis of the Tensile Properties and Probabilistic Characteristics of Large-Tow Carbon Fiber-Reinforced Polymer Composites.

Large-tow carbon fiber-reinforced polymer composites (CFRP) have great application potential in civil engineering due to their low price, but their basic mechanical properties are still unclear. The tensile properties of large-tow CFRP rods and plates were investigated in this study. First, the tensile properties of unidirectional CFRP rods and plates were studied, and the test results of the relevant mechanical properties were statistically analyzed. The tensile strength of the CFRP rod and plate are 2005.97 MPa and 2069.48 MPa. Second, the surface of the test specimens after failure was observed using a scanning electron microscope to analyze the type of failure and damage evolution process. Finally, the probabilistic characteristics of the mechanical properties were analyzed using normal, lognormal, and Weibull distributions for parameter fitting. Quasi-optimality tests were performed, and a probability distribution model was proposed for the mechanical properties of large-tow CFRP rods and plates.

Architecture characterization of orchard trees for mechanical behavior investigations

Characterizing the architecture of tree root systems is essential to advance the development of root-inspired anchorage in engineered systems. This study explores the structural root architectures of orchard trees to understand the interplays between the mechanical behavior of roots and the root architecture. Full three-dimensional (3D) models of natural tree root systems, Lovell, Marianna, and Myrobalan, that were extracted from the ground by vertical pullout are reconstructed through photogrammetry and later skeletonized as nodes and root branch segments. Combined analyses of the full 3D models and skeletonized models enable a detailed examination of basic bulk properties and quantification of architectural parameters. While the root segments are divided into three categories, trunk root, main lateral root, and remaining roots, the patterns in branching and diameter distributions show significant differences between the trunk and main laterals versus the remaining lateral roots. In general, the branching angle decreases over the sequence of bifurcations. The main lateral roots near the trunk show significant spreading while the lateral roots near the ends grow roughly parallel to the parent root. For branch length, the roots bifurcate more frequently near the trunk and later they grow longer. Local thickness analysis confirms that the root diameter decays at a higher rate near the trunk than in the remaining lateral roots, while the total cross-sectional area across a bifurcation node remains mostly conserved. The histograms of branching angle, and branch length and thickness gradient can be described using lognormal and exponential distributions, respectively. This unique study presents data to characterize mechanically important structural roots, which may help link root architecture to the mechanical behaviors of root structures.

A New Goodness of Fit Test for Complete or Type II Right Censored Samples

This study proposes a new goodness-of-fit test based on the empirical distribution function for complete or type II right-censored random samples, which are drawn from either the exponential or log-normal distributions. Some simulation studies were conducted to compare the newly proposed test with some of the well-known goodness-of-fit tests, such as Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling, in terms of power over various sample sizes and censoring rates. The simulation results show that the newly proposed goodness of fit test generally seems to perform well compared to the other goodness of fit tests considered. In addition, the newly proposed test and the other goodness of fit tests are illustrated by applying them to some real data sets obtained from the relevant literature.

Change point detection in length-biased lognormal distribution

In this paper, we develop two procedures for identifying the dynamic trends in the parameters of length-biased lognormal distribution based on likelihood ratio and modified information criterion. These methods mainly consider the test of the existence of the change point and provide the maximum likelihood estimation of the change point when the change point exists. In addition, the asymptotic distribution of test statistic based on likelihood ratio is derived as an extreme value distribution, while the asymptotic distribution of test statistic based on modified information criterion is derived as a chi-square distribution. And the consistency of parameter estimation is proved. Simulations are conducted to study the performance of the proposed method in terms of power, coverage probabilities and average sizes of confidence sets. The proposed methods are applied to a real data to illustrate the detecting procedures.

The magnetic properties of packings of cylinders

Powders of magnetic particles are used e.g. in additive manufacturing of magnets, necessitating an investigation of the properties of such powders. In this work we consider hard magnetic particles modeled as infinitely long cylinders in 2D and randomly packed in a square container. The particles have a nonlinear magnetization curve with defined remanence and coercivity and their radii follow a lognormal distribution with the standard deviation distinguishing different packings. Using a finite element approach we calculate the average and standard deviation of the magnetization of the individual particles in the packings and from these subtract the value of the corresponding regions in a solid square box to remove the shape demagnetization effect of the overall packing. We find that at applied fields close to the coercivity the average magnetization of the individual particles have the highest probability to deviate 5% from the average magnetization in the corresponding regions in the box. Away from the coercivity the packings have an near-identical magnetization to the solid box. Considering the magnetization internally in each particle, near the coercivity the standard deviation of the magnetization has the highest probability to deviate 10% from the standard deviation in magnetization in the corresponding region in the box. Thus while the overall magnetization in a packing appear to be the same as in a solid box, near the coercivity there is a larger variation of magnetization both between and within the magnetic particles, compared to a solid box.

Towards Direct Numerical Simulations of Reactivity-Controlled Compression Ignition Engine Using n-Octanol/Ethanol Fuel Blends

AbstractThe results of a two-dimensional direct numerical simulation of a lean n-octanol-ethanol fuel blend under Reactivity Controlled Compression Ignition (RCCI) conditions are presented in this paper. Stratified temperature and high reactivity fuel fields of Gaussian, bi-modal, and log-normal distributions are studied for uncorrelated and correlated scenarios. The pimple loop is made to run twice to achieve compression heating. A chemical mechanism with 171 species and 734 reactions was developed to capture autoignition characteristics and flame propagation reasonably well. Diagnosing techniques published in the literature are used to determine whether the flame fronts are spontaneously propagating or not. As reported previously for other fuel blends under RCCI conditions, both deflagration and spontaneous ignition flame fronts are observed to co-exist. Gaussian, bi-modal, and log-normal fields respectively move towards a spontaneously igniting mode. Correlating temperature and high reactivity fuel fields not only makes combustion more spontaneously igniting but also more premixed. The analysis reveals the sensitivity of the DNS results with respect to the initial conditions which accordingly should be chosen with care.

Variation of segment joint opening of underwater shield tunnel during long operational period

Segment joint is the main water leakage channel in underwater shield tunnels, and joint deformation influences tunnel waterproof capacity greatly. Real-time structure health monitoring is a great way to investigate the joint opening and to offer early warnings for abnormality, such as data outlier and joint properties degradation. This study investigated the variation of joint opening, provided early warning indexes and evaluated the joint mechanical properties degradation using the field monitoring data of an underwater shield tunnel over 10 years, which is rarely seen in the literature. Study results show that: (1) Field monitoring data reveals that the distribution of joint opening increments obeys a heavy-tailed distribution rather than the normal distribution. The exponential distribution model and the log normal distribution model can fit the longitudinal joint increments and circumferential joint increments much better. (2) The early warning index is determined based on the statistic theory and 0.999 quantile is set as the warning value. The obtained warning values of the studied underwater tunnel are 0.005 mm and 0.08 mm for the longitudinal and circumferential joint respectively. The small warning value means that small abnormality can be identified and the early warning would be more efficient. (3) A mechanical model is proposed to evaluate the joint mechanical properties degradation based on monitoring data. Results show that normal stiffness of circumferential joint decreases from 18.3 GPa/m to 14.7 GPa/m. Results of this study provides valuable reference for early-warning and joint degradation evaluation of under water shield tunnel.

Solute transport characteristics of columnar volumetric contraction networks with mega column structure and aperture variability

Numerical simulations explore for the first time the role of mega columns and aperture variability on particle transport through mature volumetric contraction networks as informed by a unique synthesis of network propagation and maturity. Columnar fracture patterns are generated by updating a series of Voronoi centers to the midpoint of a generated polygon over many iterations, creating 250 network realizations. A DFN simulator solves for fluid flow and tracks conservative particle trajectories within each network. Dominant fracture attributes impacting fluid flow and solute transport in volumetric contraction networks are fracture orientation, density, and aperture/transmissivity. Ensemble plume snapshots generated by networks with equal fracture transmissivity define a baseline-level of dispersion that is solely attributed to network structure and connectivity. Longitudinal and transverse dispersion increase and the center of plume mass becomes delayed relative to the baseline case when fracture transmissivity is varied according to a lognormal distribution. The incorporation of highly-transmissive, large-aperture mega column fractures leads to plume snapshots with a more pronounced leading edge and an order of magnitude faster average breakthrough times. The breakthrough curves contain three peaks reflecting contrasting transport pathways in which particles are: (i) initially placed in mega column fractures and remain in these features until exiting the model domain, (ii) initially placed into small column fractures, incur additional time to migrate and enter a mega column fracture, and remain within those mega columns, and (iii) initially placed in small column fractures and remain in these fractures. Incorporating variability in fracture transmissivity for both small column and mega column fractures disrupts the binary distinction between small column and mega column fracture velocities and leads to dispersed breakthroughs over long time scales with a single peak. These results demonstrate that preferential flow paths emerge in volumetric contraction networks due to contracts in fracture transmissivity, not fracture connectivity as observed in tectonic networks.

A model for the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution

Nanocrystalline materials are a popular metamaterial used to control heat transport in semiconductor industrial applications. An accurate and reliable theoretical model is urgently needed but challenging for elucidating detailed microscopic heat transfer phenomena. In this study, we develop a mathematical model to predict the lattice thermal conductivity of nanocrystalline materials with arbitrary grain size distribution. The model first obtains the effective scattering rate of grain boundaries in single-grain-size materials, and then integrates the Landauer’s system transmission concept and series transmission concept to become applicable to multiple grain sizes. It takes into account not only intrinsic and grain boundary scattering effects, but also the effects of finite system size and grain size distribution. Numerical samples of silicon nanocrystals with single grain size, dual size, constant grain size distribution, and logarithmic normal grain size distribution are constructed and full-spectrum Monte Carlo simulations are performed for comparison. The excellent agreement observed between model predictions and simulation results validates the accuracy of the proposed theoretical model. This model will be very helpful in designing micron-scale thermal manipulation systems using nanostructures.