Continuous Distribution Research Articles

Analyzing symmetric distributions by utilizing extropy measures based on order statistics

Quantification of the uncertainty of distribution functions, by using entropy and extropy, is important in many statistical analyses. Inspired by this, our study uses extropy and several related measures (including the cumulative residual extropy, cumulative past extropy, and extropy-inaccuracy measure) of order statistics (OSs) to offer multiple characterizations of symmetric continuous distributions. We demonstrate that a defining feature of symmetric distributions is the equality of these measures of upper and lower OSs. Using concomitants of OSs based on the bivariate distributions belonging to the Farlie-Gumbel-Morgenstern (FGM) family, the same characteristic is demonstrated for these measures. Finally, a real data set is used to illustrate the applicability of the suggested test.

Genetic analysis of QTLs for lysine content in four maize DH populations

BackgroundLow levels of the essential amino acid lysine in maize endosperm is considered to be a major problem regarding the nutritional quality of food and feed. Increasing the lysine content of maize is important to improve the quality of food and feed nutrition. Although the genetic basis of quality protein maize (QPM) has been studied, the further exploration of the quantitative trait loci (QTL) underlying lysine content variation still needs more attention.ResultsEight maize inbred lines with increased lysine content were used to construct four double haploid (DH) populations for identification of QTLs related to lysine content. The lysine content in the four DH populations exhibited continuous and normal distribution. A total of 12 QTLs were identified in a range of 4.42–12.66% in term of individual phenotypic variation explained (PVE) which suggested the quantitative control of lysine content in maize. Five main genes involved in maize lysine biosynthesis pathways in the QTL regions were identified in this study.ConclusionsThe information presented will allow the exploration of candidate genes regulating lysine biosynthesis pathways and be useful for marker-assisted selection and gene pyramiding in high-lysine maize breeding programs.

Measuring strain distributions in an asphalt pavement using fibre optic sensors under static loading by test vehicles

Understanding the in-situ structural behaviour of pavements plays an important role in road engineering. Hence, various measurement methods were developed in the past to get an insight into the response of roads to traffic loading. In the present study, distributed fibre optic strain sensors were embedded into a hot mix asphalt pavement. The sensors were used for strain measurements with high spatial resolution in order to assess its feasibility to gain the continuous strain distribution in the pavement under short-term static loading. In addition, the loading process was measured with high temporal resolution, indicating that – using shorter sensor lengths – vehicle passages could also be studied. The strain distributions gathered with this type of sensor were compared to the results of a simple finite element model and the effect of applying various sensor cables. In addition, new opportunities provided by distributed fibre optic sensors in road engineering are discussed.

Extremality of factorizable copulas and implicit dependence copulas

Copulas of continuous random variables satisfying f(X)=g(Y) a.s. for some Borel functions f and g, where f(X) has continuous distribution, are called implicit dependence copulas, of which a special subclass is the class of factorizable copulas, i.e., copulas that can be written as the Markov product of a left invertible copula and a right invertible copula in that order. Implicit dependence copulas were recently shown to coincide with generalized Markov products of left and right invertible copulas, where the joining copulas are arbitrary. In this paper, we obtain characterizations of extreme factorizable copulas and prove that implicit dependence copulas whose joining copula is one of the Fréchet-Hoeffding bounds are extreme. This condition, however, is not necessary, which will be shown via some examples of extreme implicit dependence copulas.

On the Addams family of discrete frailty distributions for modeling multivariate case I interval-censored data.

Random effect models for time-to-event data, also known as frailty models, provide a conceptually appealing way of quantifying association between survival times and of representing heterogeneities resulting from factors which may be difficult or impossible to measure. In the literature, the random effect is usually assumed to have a continuous distribution. However, in some areas of application, discrete frailty distributions may be more appropriate. The present paper is about the implementation and interpretation of the Addams family of discrete frailty distributions. We propose methods of estimation for this family of densities in the context of shared frailty models for the hazard rates for case I interval-censored data. Our optimization framework allows for stratification of random effect distributions by covariates. We highlight interpretational advantages of the Addams family of discrete frailty distributions and theK-point distribution as compared to other frailty distributions. A unique feature of the Addams family and the K-point distribution is that the support of the frailty distribution depends on its parameters. This feature is best exploited by imposing a model on the distributional parameters, resulting in a model with non-homogeneous covariate effects that can be analyzed using standard measures such as the hazard ratio. Our methods are illustrated with applications to multivariate case I interval-censored infection data.

Ramping cells in the rodent medial prefrontal cortex encode time to past and future events via real Laplace transform

In interval reproduction tasks, animals must remember the event starting the interval and anticipate the time of the planned response to terminate the interval. The interval reproduction task thus allows for studying both memory for the past and anticipation of the future. We analyzed previously published recordings from the rodent medial prefrontal cortex [J. Henke et al., eLife10, e71612 (2021)] during an interval reproduction task and identified two cell groups by modeling their temporal receptive fields using hierarchical Bayesian models. The firing in the "past cells" group peaked at the start of the interval and relaxed exponentially back to baseline. The firing in the "future cells" group increased exponentially and peaked right before the planned action at the end of the interval. Contrary to the previous assumption that timing information in the brain has one or two time scales for a given interval, we found strong evidence for a continuous distribution of the exponential rate constants for both past and future cell populations. The real Laplace transformation of time predicts exponential firing with a continuous distribution of rate constants across the population. Therefore, the firing pattern of the past cells can be identified with the Laplace transform of time since the past event while the firing pattern of the future cells can be identified with the Laplace transform of time until the planned future event.

Targeted Broader Sharing for Liver Continuous Distribution.

In recent years, changes to US organ allocation have aimed to improve equity and accessibility across regions. The Organ Procurement and Transplantation Network plans to adopt continuous liver distribution, prioritizing candidates based on a weighted composite allocation score (CAS) incorporating proximity, ABO types, medical urgency, and pediatric priority. The Liver Committee has requested research on CAS variations that account for geographical heterogenicity. We describe a method for designing a geographically heterogeneous CAS with targeted broader sharing (CAS-TBS) to balance the highly variable geographic distributions of liver transplant listings and liver donations. CAS-TBS assigns each donor hospital to either broader sharing or nearby sharing, adjusting donor-candidate distance allocation points accordingly. We found that to reduce geographic disparity in the median Model for End-stage Liver Disease at transplant (MMaT), >75% of livers recovered in regions 2 and 10 should be distributed with broader sharing, whereas 95% of livers recovered in regions 5 and 1 should be distributed with nearby sharing. In a 3-y simulation of liver allocation, CAS-TBS decreased MMaT by 2.1 points in high-MMaT areas such as region 5 while increasing MMaT only by 0.65 points in low-MMaT areas such as region 3. CAS-TBS significantly decreased median transport distance from 202 to 167 nautical miles under acuity circles and decreased waitlist deaths. Our CAS-TBS design methodology could be applied to design geographically heterogeneous allocation scores that reflect transplant community values and priorities within the continuous distribution project of the Organ Procurement and Transplantation Network. In our simulations, the incremental benefit of CAS-TBS over CAS was modest.

Confidence bounds for compound Poisson process

AbstractThe compound Poisson process (CPP) is a common mathematical model for describing many phenomena in medicine, reliability theory and risk theory. However, in the case of low-frequency phenomena, we are often unable to collect a sufficiently large database to conduct analysis. In this article, we focused on methods for determining confidence intervals for the rate of the CPP when the sample size is small. Based on the properties of process parameter estimators, we proposed a new method for constructing such intervals and compared it with other known approaches. In numerical simulations, we used synthetic data from several continuous and discrete distributions. The case of CPP, in which rewards came from exponential distribution, was discussed separately. The recommendation of how to use each method to have a more precise confidence interval is given. All simulations were performed in R version 4.2.1.

Forced carrier perturbation opens a loophole for chip-based continuous variable quantum key distribution system

The integration of the continous-variable quantum key distribution(CVQKD) system is an important technical route with great potential value for constructing high-performance and low-cost CVQKD system. In all previous CVQKD studies, the quantum efficiency of the detector can be calibrated in advance and is considered to remain unchanged. But when the size of the system shrinks to the on-chip level, especially in the premise of non-uniform waveguide, heavy doping and other factors, effects such as free carrier absorption and scattering loss will become prominent, which will directly cause carriers undergo violent migration due to the tiny jitter of the local oscillator and further lead to dynamical variation of quantum efficiency of detection. In this paper, we propose a practical chip-based detector model, and numerous simulation results based on this model show that the practical system will face potential security threats due to the variable quantum efficiency. Moreover, two defense strategies are proposed to solve these practical security problems commonly exist in general chip-based CVQKD systems. This work breaks the inherent viewpoint that the quantum efficiency in the chip-based CVQKD system can still be calibrated in advance, and suggests a more rigorous consideration of practical security for development of chip-based CVQKD.

Direct computations of viscoelastic moduli of biomolecular condensates.

Biomolecular condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model that leverages information regarding intra- and inter-chain contacts, which we extract from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations of phase separation. The key ingredient of the generalized Rouse model is a graph Laplacian that we compute from equilibrium MMC simulations. We compute two flavors of graph Laplacians, one based on a single-chain graph that accounts only for intra-chain contacts, and the other referred to as a collective graph that accounts for inter-chain interactions. Calculations based on the single-chain graph systematically overestimate the storage and loss moduli, whereas calculations based on the collective graph reproduce the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two graphs proves to be most accurate. In line with the theory of Rouse and contrary to recent assertions, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic vs dominantly viscous behaviors does not imply a single relaxation time. Instead, it is influenced by the totality of the relaxation modes. Hence, our analysis affirms that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain the relaxation time spectra that underlie the dynamics within condensates. This is of practical importance given advancements in passive and active microrheology measurements of condensate viscoelasticity.

Spatial evolution and influencing factors of water-town settlements in Southern China: evidence from 942 villages in Zhongshan City

ABSTRACT Zhongshan, a city characterized by its profound historical heritage and distinctive rural civilization, has been consistently influenced by traditional agricultural practices throughout its history. This research conducts an in-depth exploration of Zhongshan’s unique rural spaces, systematically examining the evolutionary trends and determinants of Zhongshan’s water-town settlements across different historical epochs through the application of multidimensional spatial analysis techniques. The results indicate that these settlements exhibited cohesive spatial distribution characteristics across five historical periods. Notably, there was a significant clustering effect during the Ming and Qing dynasties, while Before the Qing dynasty, the spatial distribution of the settlements presented a pattern with multiple core areas coexisting. After the Qing dynasty, the spatial layout of these principal core areas stabilized and gradually diffused to surrounding areas, forming a balanced and continuous distribution pattern. Throughout the study period, the spatial pattern of the water-town settlements exhibited characteristics of five primary core areas and several secondary core areas. Concurrently, the centroid of the water-town settlements consistently shifted southeastward. When examining the intensity of influence on spatial evolution, the study found that socio-economic (q = 0.345) and accessibility factors (q = 0.356) exert a greater impact on the spatial distribution of rural settlements than do natural environmental factors (q = 0.136). However, the interaction between natural environmental factors and socio-economic and accessibility factors provides greater explanatory power than the interactions within natural factors alone. This suggests that in a specific socio-economic context, the impact of the natural environment on water-town settlements is enhanced. Furthermore, multivariate linear regression analysis demonstrates that the rural population, regional economic status, proximity to urban centers, and the distribution of water bodies positively influence the spatial evolution of water-town settlements.

Adsorption and retention of fracturing fluid and its impact on gas transport in tight sandstone with different clay minerals

To elucidate the adsorption characteristics and retention mechanisms of fracturing fluids in diverse clay minerals, we conducted on-line nuclear magnetic resonance (NMR) and atomic force microscopy (AFM) experiments. The depth and extent of solid phase damage are determined by the ratio between the size of fine fractions in fracturing fluid residue and the pore-throat size in experiments. Poor physical properties (K < 0.5 mD) result in a more preferential flow pathway effect during flowback, and the stepwise incremental pressure differential proves to be more effective for the discharge of fracturing fluid in submicron pore throats. The permeability is significantly influenced by the differential distribution of retained fracturing fluid, as supported by direct experimental evidence. The presence of good physical properties (K > 0.5 mD) combined with a scattered distribution of retained fracturing fluid is associated with high gas phase recovery permeability, whereas a continuous sheet-like distribution results in low recovery permeability. The expansive surface area and presence of filamentous illite minerals facilitate the multiple winding and adsorption of fracturing fluids, demonstrating strong hydrogen-bonding, multi-layering and multiple adsorption properties. The geological characteristics of the main gas formations exhibit significant variation, and the severity of damage caused by fracturing fluids occurs in diverse sequences. To address this issue, a differentiated strategy for optimizing fracturing fluids has been proposed.

Sex-mismatching in isolated heart transplantation confers no postoperative risk

BackgroundFor heart transplantation, optimal donor-recipient matching is an important factor in the ongoing development of the United Network for Organ Sharing (UNOS) continuous distribution framework. Donor-recipient sex-mismatch has decreased since the 1990s, but this may be related to the risk posed by size mismatching, particularly when donor hearts are undersized. Thus, the impact of sex-mismatching, controlling for other factors including size mismatch, is uncertain. MethodsAdult first-time, isolated heart transplant patients from the UNOS database between October 1, 1987 and December 31, 2022 were analyzed. Cohorts were separated into male and female recipients. Propensity score matching on known preoperative risk factors was performed. Equivalence testing via Two One-Sided Testing (TOST) was performed to assess between-arm equivalence in postoperative outcomes. Survival differences were measured by the between-arm ratio of Restricted Mean Survival Time and binary outcome differences by the Odds Ratio (OR). ResultsIn the propensity matched cohort, we found significant equivalence between arms in both male (TOST P<0.001) and female (TOST P<0.001) recipients for overall survival at all temporal endpoints, postoperative treatment for rejection within one year, and pre-discharge dialysis. ConclusionsSex-mismatch in isolated heart transplantation confers no additional risk to postoperative outcomes when controlling for other factors, including size mismatch. Consequently, sex-mismatch should not factor into individual assessments of organ acceptance or be incorporated into any national organ allocation policy. Increasing the acceptance of sex-mismatched donors has the potential to expand the donor pool and increase female donor utilization.

Minimizing distance between distribution functions: discrete counterparts to continuous random variables with applications in non-life insurance and stochastic reliability

In this work, we propose a novel family of procedures for deriving a discrete counterpart to a continuous probability distribution. They are based on a class of distances between cumulative distribution functions, including the Cramér, the Cramér-von Mises, and the Anderson-Darling distances as particular cases. The discrete counterpart is defined and derived as the random variable which minimizes its distance to the assigned continuous probability distribution among all the discrete random variables supported on the set of integers (or positive integers). Applications are provided with reference to the exponential and the normal distributions, among others; the discrete counterparts are derived, and their main properties are discussed, also in comparison with the one obtained through an existing discretization technique based on the preservation of the cumulative distribution function at integer values. Parameter estimation for these discrete analogs is discussed, along with an analysis of two real datasets, where they are compared in terms of goodness-of-fit with some popular discrete distributions. Furthermore, in order to highlight the effectiveness and the benefits derived from the proposed discretization procedures, we illustrate two practical applications in actuarial science and in reliability engineering. In the former case, the problem of determining the distribution of the total claims amount for a non-life insurance portfolio is considered, where the claim sizes can be modelled as iid random variables, and the number of claims is random as well. Actuaries use a recursive calculation method based on Panjer's formula, which requires an appropriate discretization of the individual claim distribution, and therefore the proposed procedures can be used. Since we consider two simple cases where the distribution of the total claims amount is analytically acquirable, the efficacy of the discretization procedures in the final approximation can be easily assessed and turns out to be satisfactory, especially when compared to the existing discretization. The latter case considers the determination of the reliability parameter for a complex stress-strength model. Here, the approximation by discretization is compared to Monte Carlo simulation and shown to be relevant: with a comparable if not smaller computational effort, discretization leads to similar results as simulation. Such discretizations can also naturally be applied to more complex problems such as scenario generation in stochastic programming. R code for this article is provided as supplementary material.

First-passage and first-arrival problems in continuous-time random walks: Beyond the diffusion approximation.

Some exact solutions of the first-passage and first-arrival problems for the continuous-time random-walk model are obtained. On the basis of these exact solutions, the following has been revealed. First, for some jump-length distributions with a finite variance, the approximate solutions obtained in the diffusion approximation can differ significantly from the exact solutions. Second, for some waiting time distributions with a finite mean, the times of first passage and the times of first arrival can significantly depend on the ensemble under consideration. In particular, the mean first-passage time corresponding to the stationary ensemble can be significantly greater than the mean first-passage time corresponding to the nonaged ensemble. Third, for any continuous distribution of jump lengths, the probability of first arrival is zero for a point-like target. This last result is contrary to existing opinion, but it is consistent with the fact that a single point has a probability measure equal to zero in the probability space defined by a continuous distribution of jump lengths.

Enthalpy-based cascaded lattice Boltzmann method for conjugate heat transfer

Lattice Boltzmann (LB) methods for conjugate heat transfer are widely studied because of the simplicity and efficiency in dealing with complex boundary conditions. Recently, cascaded (or central-moments-based) LB (CLB) method has shown the potential to improve the stability of LB method. For conventional CLB method which is constructed through the continuous equilibrium distribution function, the temperature-based energy equation is recovered and solved. The continuity of temperature and heat flux at conjugate interface is unable to be accurately enforced without special treatment. To circumvent this deficiency, an enthalpy-based CLB method for conjugate heat transfer is developed in this work. In the proposed method, the enthalpy-based formulation of equilibrium moments is directly designed in the central-moment space, and the macroscopic quantity solved is converted from temperature to enthalpy. As demonstrated by the Chapman-Enskog multiscale analysis, the enthalpy-based energy equation can be recovered by the CLB equation. Compared with the conventional CLB method, the continuity condition for temperature and heat flux on the conjugate interface can be enforced automatically without special treatment. In addition, the proposed CLB method provides a new way to develop a CLB equation that can recover to a general convection-diffusion equation. Finally, the accuracy and stability of the temperature field are validated by benchmarks for the proposed enthalpy-based CLB method.

Topology optimization with a finite strain nonlocal damage model using the continuous adjoint method

This study presents a unified formulation of topology optimization with a finite strain nonlocal damage model using the continuous adjoint method. For the primal problem to describe the material response including deterioration, we consider the standard Neo–Hookean constitutive model and incorporate crack phase-field theory for brittle fracture within the finite strain framework. For the optimization problem, the objective function is set to accommodate multiple objectives by weighting each sub-function, and the continuous adjoint method is employed to derive the sensitivity. Thus, both the governing equations for primal and adjoint problems are written as strong forms and hold at any moment and at any location in the continuum body or on its boundary. Accordingly, the proposed formulation is independent of the requirements from numerical implementation, such as element type or discretization method. In addition, the reaction–diffusion equation is used to update the design variable in an optimizing process, by which the continuous distribution of the design variable, as well as material properties, are realized. After the basic performance of the proposed formulation is demonstrated with a simple numerical setup, two-material (matrix and inclusion materials) and single-material (material and null) topology optimizations are presented, and discussions are made.

Modeling insurance loss data using novel approach of moment exponential model: Inference, actuarial measures and application

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution’s shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses.

Encouraging cycling through the improvement of streetscape perception: A bottom-up investigation into the relationship between street greening and bicycling volume

Enhancing neighborhood greenery quality proves to be an effective tactic in encouraging active travel among residents. From a cyclist's perspective, this study quantitatively evaluates street greening quality and its association with cycling behaviors. Utilizing shared bicycle usage data and SegNet-analyzed Baidu Street Views on Xiamen Island, we quantified comprehensive street greening quality. We then employed Spatial Design Network Analysis and a street greening quality rating scale to assess accessibility and aesthetics. Subsequently, models were developed using OLS, spatial autocorrelation, and Moran's I statistical methods, complemented by a spatial heterogeneity analysis of factors influencing shared bicycle riding behaviors through the Geographically Weighted Regression (GWR) model. Our study reveals that in arterial and commercial districts, the appeal and variety of street greening elements are more crucial than their quantity. These quality indicators exhibit a polycentric, continuous spatial distribution, aligning with the overall street layout. Beyond the visual impact of greenery on cycling behavior, factors like richness, openness, and safety of streets, along with diverse facilities, significantly influence cycling route preferences. In contrast, uniform street elements can disrupt or even discourage cycling. This research, by analyzing the relationship between street greening quality and cycling intensity, offers valuable insights for policymakers in prioritizing the transformation of streets into bike-friendly zones. Additionally, we propose a pragmatic, bottom-up approach to developing bicycle-friendly urban environments, indirectly fostering healthier travel habits among urban residents.

Species pool and local assembly processes drive β diversity of ammonia-oxidizing and denitrifying microbial communities in rivers along a latitudinal gradient.

Both regional species pool and local community assembly mechanism drive the microbial diversity patterns across geographical gradients. However, little has been done to separate their effects on the β diversity patterns of microbial communities involved in nitrogen (N) cycling in river ecosystems. Here, we use high-throughput sequencing of the archaeal amoA, bacterial amoA, nirK, and nirS genes, null model, and neutral community model to distinguish the relative importance of species pool and local assembly processes for ammonia-oxidizing and denitrifying communities in river wetlands along a latitudinal gradient in eastern China. Results indicated that the β diversity of the nirS-type denitrifying community co-varied with γ diversity and environmental heterogeneity, implying that regional species pool and heterogeneous selection explained variation in β diversity. However, the β diversity of ammonia-oxidizing and nirK-type denitrifying communities did not correlate with γ diversity and environmental heterogeneity. The continuous hump distribution of β deviation along the latitudinal gradient and the lower species dispersal rate indicated that the dispersal limitation shaped the variation in β diversity of ammonia-oxidizing and nirK-type denitrifying communities. Additionally, biotic interactions drove ammonia-oxidizing and nirS-type denitrifying communities by influencing species co-occurrence patterns. Our study highlights the importance of regional species pool and local community assembly processes in shaping geographical patterns of N-cycling microorganisms and extends knowledge of their adaptability to a continuously changing environment on a large scale.