Predicting the probability distribution of Martian rocks mechanical property based on microscale rock mechanical experiments and accurate grain-based modeling

The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.

Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Modeling load distribution for rural photovoltaic grid areas using image recognition

Expanding photovoltaic(PV)resources in rural-grid areas is an essential means to augment the share of solar energy in the energy landscape,aligning with the“carbon peaking and carbon neutrality”objectives.However,rural power grids often lack digitalization;thus,the load distribution within these areas is not fully known.This hinders the calculation of the available PV capacity and deduction of node voltages.This study proposes a load-distribution modeling approach based on remote-sensing image recognition in pursuit of a scientific framework for developing distributed PV resources in rural grid areas.First,houses in remote-sensing images are accurately recognized using deep-learning techniques based on the YOLOv5 model.The distribution of the houses is then used to estimate the load distribution in the grid area.Next,equally spaced and clustered distribution models are used to adaptively determine the location of the nodes and load power in the distribution lines.Finally,by calculating the connectivity matrix of the nodes,a minimum spanning tree is extracted,the topology of the network is constructed,and the node parameters of the load-distribution model are calculated.The proposed scheme is implemented in a software package and its efficacy is demonstrated by analyzing typical remote-sensing images of rural grid areas.The results underscore the ability of the proposed approach to effectively discern the distribution-line structure and compute the node parameters,thereby offering vital support for determining PV access capability.

Finer topographic data improves distribution modeling of Picea crassifolia in the northern Qilian Mountains

The Qilian Mountains, a national key ecological function zone in Western China, play a pivotal role in ecosystem services. However, the distribution of its dominant tree species, Picea crassifolia (Qinghai spruce), has decreased dramatically in the past decades due to climate change and human activity, which may have influenced its ecological functions. To restore its ecological functions, reasonable reforestation is the key measure. Many previous efforts have predicted the potential distribution of Picea crassifolia, which provides guidance on regional reforestation policy. However, all of them were performed at low spatial resolution, thus ignoring the natural characteristics of the patchy distribution of Picea crassifolia. Here, we modeled the distribution of Picea crassifolia with species distribution models at high spatial resolutions. For many models, the area under the receiver operating characteristic curve (AUC) is larger than 0.9, suggesting their excellent precision. The AUC of models at 30 m is higher than that of models at 90 m, and the current potential distribution of Picea crassifolia is more closely aligned with its actual distribution at 30 m, demonstrating that finer data resolution improves model performance. Besides, for models at 90 m resolution, annual precipitation (Bio12) played the paramount influence on the distribution of Picea crassifolia, while the aspect became the most important one at 30 m, indicating the crucial role of finer topographic data in modeling species with patchy distribution. The current distribution of Picea crassifolia was concentrated in the northern and central parts of the study area, and this pattern will be maintained under future scenarios, although some habitat loss in the central parts and gain in the eastern regions is expected owing to increasing temperatures and precipitation. Our findings can guide protective and restoration strategies for the Qilian Mountains, which would benefit regional ecological balance.

Application of a 2 Parameter Weibull Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.

Species abundance distribution models of Toona ciliata communities in Hubei Province,China

The study of plant species abundance distribution(SAD)in natural communities is of considerable importance to understand the processes and ecological rules of community assembly.With the distribution of tree,shrub and herb layers of eight natural communities of Toona ciliata as research targets,three diff erent ecological niche models were used:broken stick model,overlapping niche model and niche preemption model,as well as three statistical models:log-series distribution model,log-normal distribution model and Weibull distribution model,to fi t SAD of the diff erent vegetation layers based on data collected.Goodness-of-fi t was compared with Chi square test,Kolmogorov–Smirnov(K–S)test and Akaike Information Criterion(AIC).The results show:(1)based on the criteria of the lowest AIC value,Chi square value and K–S value with no signifi cant diff erence(p>0.05)between theoretic and observed SADs.The suitability and goodness-of-fi t of the broken stick model was the best of three ecological niche models.The log-series distribution model did not accept the fi tted results of most vegetation layers and had the lowest goodness-of-fi t.The Weibull distribution model had the best goodness-of-fi t for SADs.Overall,the statistical SADs performed better than the ecological ones.(2)T.ciliata was the dominant species in all the communities;species richness and diversity of herbs were the highest of the vegetation layers,while the diversities of the tree layers were slightly higher than the shrub layers;there were fewer common species and more rare species in the eight communities.The herb layers had the highest community evenness,followed by the shrub and the tree layers.Due to the complexity and habitat diversity of the diff erent T.ciliata communities,comprehensive analyses of a variety of SADs and tests for optimal models together with management,are practical steps to enhance understanding of ecological processes and mechanisms of T.ciliata communities,to detect disturbances,and to facilitate biodiversity and species conservation.

Grey series time-delay predicting model in state estimation for power distribution networks

A new combined model is proposed to obtain predictive data value applied in state estimation for radial power distribution networks. The time delay part of the model is calculated by a recursive least squares algorithm of system identification, which can gradually forget past information. The grey series part of the model uses an equal dimension new information model (EDNIM) and it applies 3 points smoothing method to preprocess the original data and modify remnant difference by GM(1,1). Through the optimization of the coefficient of the model, we are able to minimize the error variance of predictive data. A case study shows that the proposed method achieved high calculation precision and speed and it can be used to obtain the predictive value in real time state estimation of power distribution networks.

Validation methodology for distribution-based degradation model

Distribution-based degradation models （or graphical approach in some literature） occur in a wide range of applications. However, few of existing methods have taken the validation of the built model into consideration. A validation methodology for distribution-based models is proposed in this paper. Since the model can be expressed as consisting of assumptions of model structures and embedded model parameters, the proposed methodology carries out the validation from these two aspects. By using appropriate statistical techniques, the rationality of degradation distributions, suitability of fitted models and validity of degradation models are validated respectively. A new statistical technique based on control limits is also proposed, which can be implemented in the validation of degradation models＇ validity. The case study on degradation modeling of an actual accelerometer shows that the proposed methodology is an effective solution to the validation problem of distribution-based de qradation models.

Dynamic vaccine distribution model based on epidemic diffusion rule and clustering approach

Due to the fact that the emergency medicine distribution is vital to the quick response to urgent demand when an epidemic occurs, the optimal vaccine distribution approach is explored according to the epidemic diffusion rule and different urgency degrees of affected areas with the background of the epidemic outbreak in a given region. First, the SIQR （susceptible, infected, quarantined,recovered） epidemic model with pulse vaccination is introduced to describe the epidemic diffusion rule and obtain the demanded vaccine in each pulse. Based on the SIQR model, the affected areas are clustered by using the self-organizing map （SOM） neutral network to qualify the results. Then, a dynamic vaccine distribution model is formulated, incorporating the results of clustering the affected areas with the goals of both reducing the transportation cost and decreasing the unsatisfied demand for the emergency logistics network. Numerical study with twenty affected areas and four distribution centers is carried out. The corresponding numerical results indicate that the proposed approach can make an outstanding contribution to controlling the affected areas with a relatively high degree of urgency, and the comparison results prove that the performance of the clustering method is superior to that of the non-clustering method on controlling epidemic diffusion.

Congregated electron phase and Wagner model applied in titanium distribution behavior in low-titanium slag

For studying the carbon thermal reduction rules of titanium in hot metal and providing a theoretical basis for the blast furnace（BF） hearth protection, the distribution behavior of titanium between low-titanium slag system of CaO-SiO2-MgO-Al2O3-TiO2 and hot metal was studied using analytical reagents in a temperature range from 1350 °C to 1600 °C. Through high temperature melting, rapid quenching, chemical analysis and thermodynamic model calculating, the results showed that the increase of reaction temperature, which improved the titanium distribution L（Ti） and lowered the system activity coefficient γsys, leads to the rise of equilibrium constant. Combined with Wagner and congregated electron phase models, the data obtained in distribution experiments were used to fit out the Gibbs free energy formula of titanium carbothermic reduction. Finally, the relations between the contents of Si and Ti in hot metal and the titanium load to reach the minimum w（Ti） for the formation of Ti C were given.

Exploring a New Lifetime Distribution for Modelling the Waiting Time of Bank Customers

The fitting of lifetime distribution in real-life data has been studied in various fields of research. With the theory of evolution still applicable, more complex data from real-world scenarios will continue to emerge. Despite this, many researchers have made commendable efforts to develop new lifetime distributions that can fit this complex data. In this paper, we utilized the KM-transformation technique to increase the flexibility of the power Lindley distribution, resulting in the Kavya-Manoharan Power Lindley (KMPL) distribution. We study the mathematical treatments of the KMPL distribution in detail and adapt the widely used method of maximum likelihood to estimate the unknown parameters of the KMPL distribution. We carry out a Monte Carlo simulation study to investigate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the KMPL distribution. To demonstrate the effectiveness of the KMPL distribution for data fitting, we use a real dataset comprising the waiting time of 100 bank customers. We compare the KMPL distribution with other models that are extensions of the power Lindley distribution. Based on some statistical model selection criteria, the summary results of the analysis were in favor of the KMPL distribution. We further investigate the density fit and probability-probability (p-p) plots to validate the superiority of the KMPL distribution over the competing distributions for fitting the waiting time dataset.

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

A novel hybrid thermodynamic model for pore size distribution characterisation for shale

Scholars often see the gas adsorption technique as a straight-to-interpret technique and adopt the pore size distribution(PSD)given by the gas adsorption technique directly to interpret pore-structure-related issues.The oversimplification of interpreting shale PSD based on monogeometric thermodynamic models leads to apparent bias to the realistic pore network.This work aims at establishing a novel thermodynamic model for shale PSD interpretation.We simplified the pore space into two geometric types—cylinder-shaped and slit-shaped.Firstly,Low-temperature Nitrogen Adsorption data were analyzed utilizing two monogeometric models(cylindrical and slit)to generate PSD_(cyl).and PSD_(slit);Secondly,pore geometric segmentation was carried out using Watershed by flooding on typical SEM images to obtain the ratio of slit-shaped(∅_(s))and cylinder-shaped pores(∅_(c)).Combining the results of the two,we proposed a novel hybrid model.We performed pyrolysis,XRD,FE-SEM observation,quantitative comparison with the results obtained by the DFT model,and fractal analysis to discuss the validity of the obtained PSD_(Hybrid).The results showed that:the hybrid model proposed in this work could better reflect the real geometry of pore space and provide a more realistic PSD;compared with thermodynamic monogeometric models,PSD obtained from the hybrid model are closer to that from the DFT model,with an improvement in the deviation from the DFT model from 5.06%to 68.88%.The proposed hybrid model has essential application prospects for better interpretation of shale pore space.It is also worth noting that we suggest applying the proposed hybrid model for PSD analysis in the range of 5-100 nm.

Potential distributional shifts in North America of allelopathic invasive plant species under climate change models

Predictive studies play a crucial role in the study of biological invasions of terrestrial plants under possible climate change scenarios.Invasive species are recognized for their ability to modify soil microbial communities and influence ecosystem dynamics.Here,we focused on six species of allelopathic flowering plants-Ailanthus altissima,Casuarina equisetifolia,Centaurea stoebe ssp.micranthos,Dioscorea bulbifera,Lantana camara,and Schinus terebinthifolia-Xhat are invasive in North America and examined their potential to spread further during projected climate change.We used Species Distribution Models(SDMs)to predict future suitable areas for these species in North America under several proposed future climate models.ENMEval and Maxent were used to develop SDMs,estimate current distributions,and predict future areas of suitable climate for each species.Areas with the greatest predicted suitable climate in the future include the northeastern and the coastal northwestern regions of North America.Range size estimations demonstrate the possibility of extreme range loss for these invasives in the southeastern United States,while new areas may become suitable in the northeastern United States and southeastern Canada.These findings show an overall northward shift of suitable climate during the next few decades,given projected changes in temperature and precipitation.Our results can be utilized to analyze potential shifts in the distribution of these invasive species and may aid in the development of conservation and management plans to target and control dissemination in areas at higher risk for potential future invasion by these allelopathic species.

A modified lumped parameter model of distribution transformer winding

The modelling of the distribution transformer winding is the starting point and serves as important basis for the transformer characteristics analysis and the lightning pulse response prediction.A distributed parameters model can depict the winding characteristics accurately,but it requires complex calculations.Lumped parameter model requires less calculations,but its applicable frequency range is not wide.This paper studies the amplitude-frequency characteristics of the lightning wave,compares the transformer modelling methods and finally proposes a modified lumped parameter model,based on the above comparison.The proposed model minimizes the errors provoked by the lumped parameter approximation,and the hyperbolic functions of the distributed parameter model.By this modification it becomes possible to accurately describe the winding characteristics and rapidly obtain the node voltage response.The proposed model can provide theoretical and experimental support to lightning protection of the distribution transformer.

Mapping the potential distribution suitability of 16 tree species under climate change in northeastern China using Maxent modelling

Knowledge on the potential suitability of tree species to the site is very important for forest management planning.Natural forest distribution provides a good reference for afforestation and forest restoration.In this study,we developed species distribution model(SDM)for 16 major tree species with 2,825 permanent sample plots with natural origin from Chinese National Forest Inventory data collected in Jilin Province using the Maxent model.Three types of environmental factors including bioclimate,soil and topography with a total of 33 variables were tested as the input.The values of area under the curve(AUC,one of the receiver operating characteristics of the Maxent model)in the training and test datasets were between 0.784 and 0.968,indicating that the prediction results were quite reliable.The environmental factors affecting the distribution of species were ranked in terms of their importance to the species distribution.Generally,the climatic factors had the greatest contribution,which included mean diurnal range,annual mean temperature,temperature annual range,and iosthermality.But the main environmental factors varied with tree species.Distribution suitability maps under current(1950-2000)and future climate scenarios(CCSM4-RCP 2.6 and RCP 6.0 during 2050)were produced for 16 major tree species in Jilin Province using the model developed.The predicted current and future ranges of habitat suitability of the 16 tree species are likely to be positively and negatively affected by future climate.Seven tree species were found to benefit from future climate including B etula costata,Fraxinus mandshurica,Juglans mandshurica,Phellodendron amurense,Populus ussuriensis,Quercus mongolica and Ulmus pumila;five tree species will experience decline in their suitable habitat including B.platyphylla,Tilia mongolica,Picea asperata,Pinus sylvestris,Pinus koraiensis;and four(Salix koreensis,Abies fabri,Pinus densiflora and Larix olgensis)showed the inconsistency under RCP 2.6 and RCP 6.0 scenarios.The maps of the habitat suitability can be used as a basis for afforestation and forest restoration in northeastern China.The SDMs could be a potential tool for forest management planning.

Examining spatiotemporal distribution and CPUE-environment relationships for the jumbo flying squid Dosidicus gigas offshore Peru based on spatial autoregressive model

The spatiotemporal distribution and relationship between nominal catch-per-unit-ef fort(CPUE) and environment for the jumbo flying squid( Dosidicus gigas) were examined in of fshore Peruvian waters during 2009–2013. Three typical oceanographic factors aff ecting the squid habitat were investigated in this research, including sea surface temperature(SST), sea surface salinity(SSS) and sea surface height(SSH). We studied the CPUE-environment relationships for D. gigas using a spatially-lagged version of spatial autoregressive(SAR) model and a generalized additive model(GAM), with the latter for auxiliary and comparative purposes. The annual fishery centroids were distributed broadly in an area bounded by 79.5°–82.7°W and 11.9°–17.1°S, while the monthly fishery centroids were spatially close and lay in a smaller area bounded by 81.0°–81.2°W and 14.3°–15.4°S. Our results show that the preferred environmental ranges for D. gigas offshore Peru were 20.9°–21.9°C for SST, 35.16–35.32 for SSS and 27.2–31.5 cm for SSH in the areas bounded by 78°–80°W/82–84°W and 15°–18°S. Monthly spatial distributions during October to December were predicted using the calibrated GAM and SAR models and general similarities were found between the observed and predicted patterns for the nominal CPUE of D. gigas. The overall accuracies for the hotspots generated by the SAR model were much higher than those produced by the GAM model for all three months. Our results contribute to a better understanding of the spatiotemporal distributions of D. gigas off shore Peru, and off er a new SAR modeling method for advancing fishery science.

A Novel Statistical Delay Model Based on the Birnbaum-Saunders Distribution for RLC Interconnects in 90nm Technologies

For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.

Prediction of Potential Sorghum Suitability Distribution in China Based on Maxent Model

It is increasingly relevant to study the effects of climate change on species habitats. Using a maximum entropy model, 22 environmental factors with significant effects on sorghum habitat distribution in China were selected to predict the potential habitat distribution of sorghum in China. The potential distribution of sorghum under baseline climate conditions and future climate conditions (2050s and 2070s) under two climate change scenarios, RCP4.5 and RCP8.5, were simulated, and the receiver operating curve under the accuracy of the model was evaluated using the area under the receiver operating curve (AUC). The results showed that the maximum entropy model predicted the potential sorghum habitat distribution with high accuracy, with Bio2 (monthly mean diurnal temperature difference), Bio6 (minimum temperature in the coldest month), and Bio13 (rainfall in the wettest month) as the main climatic factors affecting sorghum distribution among the 22 environmental factors. Under the baseline climate conditions, potential sorghum habitats are mainly distributed in the southwest, central, and east China. Over time, the potential sorghum habitat expanded into northern and southern China, with significant additions and negligible decreases in potential sorghum habitat in the study area, and a significant increase in total area, with the RCP8.5 scenario adding much more area than the RCP4.5 scenario.

The Cox-Aalen Models as Framework for Construction of Bivariate Probability Distributions, Universal Representation

Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.