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.

Hexagon-Islands Density and Size Distribution on Growing Single-Walled Carbon Nanotubes in the Kinetic 5-Vertex Model

A kinetic 5-vertex model is used to investigate hexagon-islands formation on growing single-walled carbon nanotubes (SWCNT). In the model, carbon atoms adsorption and migration processes on the SWCNT edge are considered. These two dynamic processes are assumed to be mutually independent as well as mutually dependent as far as the whole growth of the nanotube is concerned. Key physical parameters of the model are the growth time t, the diffusion length Γ defined as the ratio of the diffusion rate D to the carbon atomic flux F and the SWCNT chiral angle. The kinetic equation that describes the nanotube edge dynamics is solved using kinetic Monte Carlo simulations with the Bortz, Kalos and Lebowitz update algorithm. The behaviors of islands density and size distribution are investigated within the growth parameters’ space. Our study revealed key mechanisms that enable the formation of a new ring of hexagons at the SWCNT edge. The growth occurs either by pre-existing steps propagation or by hexagon-islands growth and coalescence on terraces located between dislocation steps, depending on values of model parameters. This should offer a road map for edge design in nanotubes production. We also found that in appropriate growth conditions, the islands density follows Gaussian and generalized Wigner distributions whereas their size distribution at a given growth time shows a decreasing exponential trend.

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.

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.

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.

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.

COMPUTER MODEL OF COPPER SMELTING PROCESS AND DISTRIBUTION BEHAVIORS OF ACCESSORY ELEMENTS

A computer model has been developed to simulate the distribution behaviors of Ni, Co. Sn. Ph,Zn, As, Sb, Bi, An and Ag in copper smelting process. The model assumes that the copper smelting furnaceis in thermodynamic equilibrium. As many as 21 elements (Cu. S, Fe. Ni, Co. Sn, As, Sb. Bi, Ph. Zn.An. Ag. O, N, C, H, Ca, Mg, Al, and St) and 73 compounds are considered. This model accounts forphysical entrainment in the melts. The predictions by the present computer model are compared with theknown commercial data from Guixi Smelter in China, Home Smelter in Canada and Naoshima Smelter inJapan. The agreements between the computer predictions and the commercial data are excellent, so that thepresent computer model can be used to monitor and optimize the actual industrial operations of copper smelting. It is applicable to simulation of almost all copper pyrometallurgical processes.

Modelling the spatial distribution of snake species in northwestern Tunisia using maximum entropy(Maxent) and Geographic Information System(GIS)

We used GIS and maximum entropy to predict the potential distribution of six snake species belong to three families in Kroumiria（Northwestern Tunisia）： Natricidae（Natrix maura and Natrix astreptophora）, Colubridae（Hemorrhois hippocrepis, Coronella girondica and Macroprotodon mauritanicus）, and Lamprophiidae（Malpolon insignitus）. The suitable habitat for each species was modelled using the maximum entropy algorithm, combining presence field data（collected during 16 years：2000–2015） with a set of seven environmental variables（mean annual precipitation, elevation, slope gradient,aspect, distance to watercourses, land surface temperature and normalized Differential Vegetation Index. The relative importance of these environmental variables was evaluated by jackknife tests and the predictive power of our models was assessed using the area under the receiver operating characteristic. The main explicative variables of the species distribution were distance from streams and elevation, with contributions ranging from 60 to 77 and from 10 to 25%,respectively. Our study provided the first habitat suitability models for snakes in Kroumiria and this information can be used by conservation biologists and land managers concerned with preserving snakes in Kroumiria.

Temporal and spatial distribution characteristics of water resources in Guangdong Province based on a cloud model

With a focus on the difficulty of quantitatively describing the degree of nonuniformity of temporal and spatial distributions of water resources, quantitative research was carried out on the temporal and spatial distribution characteristics of water resources in Guangdong Province from 1956 to 2000 based on a cloud model. The spatial variation of the temporal distribution characteristics and the temporal variation of the spatial distribution characteristics were both analyzed. In addition, the relationships between the numerical characteristics of the cloud model of temporal and spatial distributions of water resources and precipitation were also studied. The results show that, using a cloud model, it is possible to intuitively describe the temporal and spatial distribution characteristics of water resources in cloud images. Water resources in Guangdong Province and their temporal and spatial distribution characteristics are differentiated by their geographic locations. Downstream and coastal areas have a larger amount of water resources with greater uniformity and stronger stability in terms of temporal distribution. Regions with more precipitation possess larger amounts of water resources, and years with more precipitation show greater nonuniformity in the spatial distribution of water resources. The correlation between the nonuniformity of the temporal distribution and local precipitation is small, and no correlation is found between the stability of the nonuniformity of the temporal and spatial distributions of water resources and precipitation. The amount of water resources in Guangdong Province shows an increasing trend from 1956 to 2000, the nonuniformity of the spatial distribution of water resources declines, and the stability of the nonuniformity of the spatial distribution of water resources is enhanced.

A modified multi-group model of angular and momentum distribution of cosmic ray muons for thickness measurement and material discrimination of slabs

Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.

Vegetation NPP Distribution Based on MODIS Data and CASA Model——A Case Study of Northern Hebei Province

Net Primary Productivity （NPP） is one of the important biophysical variables of vegetation activity, and it plays an important role in studying global carbon cycle, carbon source and sink of ecosystem, and spatial and temporal distribution of CO2. Remote sensing can provide broad view quickly, timely and multi-temporally, which makes it an attractive and powerful tool for studying ecosystem primary productivity, at scales ranging from local to global. This paper aims to use Moderate Resolution Imaging Spectroradiometer （MODIS） data to estimate and analyze spatial and temporal distribution of NPP of the northern Hebei Province in 2001 based on Carnegie-Ames-Stanford Approach （CASA） model. The spatial distribution of Absorbed Photosynthetically Active Radiation （APAR） of vegetation and light use efficiency in three geographical subregions, that is, Bashang Plateau Region, Basin Region in the northwestern Hebei Province and Yanshan Mountainous Region in the Northern Hebei Province were analyzed, and total NPP spatial distribution of the study area in 2001 was discussed. Based on 16-day MODIS Fraction of Photosynthetically Active Radiation absorbed by vegetation （FPAR） product, 16-day composite NPP dynamics were calculated using CASA model; the seasonal dynamics of vegetation NPP in three subreglons were also analyzed. Result reveals that the total NPP of the study area in 2001 was 25.1877 × 10^6gC/（m^2.a）, and NPP in 2001 ranged from 2 to 608gC/（m^2-a）, with an average of 337.516gC/（m^2.a）. NPP of the study area in 2001 accumulated mainly from May to September （DOY 129-272）, high NIP values appeared from June to August （DOY 177-204）, and the maximum NPP appeared from late July to mid-August （DOY 209-224）.

Distribution Prediction Model of a Rare Orchid Species (<i>Vanda bicolor</i>Griff.) Using Small Sample Size

Advancement in field of GIS and Information Technology has taken conservation works and strategies a step further as most conservation works are now dependent on these technologies. The present study explores the prediction ability of MAXENT using a very low sample size by applying jackknife analysis over a well defined smaller region and using only climate data. Vanda bicolor is a horticulture important orchid grown in certain patches of North Eastern region of India and the species considered to be “Vulnerable”. Present study reports a distribution prediction model using different geo-climatic parameters for a small area. Model validation by ground truthing gives a significant successful result which clearly defines the ability of MAXENT prediction model to give high success rate (71%) with low training samples. Use of the low sample size over a larger area results in unstable models however application of these samples in smaller radius around the occurrence points could provide good working models.

Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination

Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a statistical damage evolution equation was established based on the property that strength of micro-cells is consistent with normal distribution function, through discussing the characteristics of random distributions for strength of micro-cells, then a statistical damage constitutive model that can simulate the full process of rock strain softening under specific confining pressure was set up. Secondly, a new method to determine the model parameters which can be applied to the situations under different confining pressures was proposed, by deeply studying the relations between the model parameters and characteristic parameters of the full stress-strain curve under different confining pressures. Therefore, a unified statistical damage constitutive model for rock softening which can reflect the effect of different confining pressures was set up. This model makes the physical property of model parameters explicit, contains only conventional mechanical parameters, and leads its application more convenient. Finally, the rationality of this model and its parameters-determining method were identified via comparative analyses between theoretical and experimental curves.

Analytical model and application of stress distribution on mining coal floor

Given the analysis of underground pressure, a stress calculation model of coal floor stress has been established based on a theory of elasticity. The model presents the law of stress distribution on the relatively fixed position of the mining coal floor： the extent of stress variation in a fixed floor position decreases gradually along with depth, the decreasing rate of the vertical stress is clearly larger than that of the horizontal stress at a specific depth. The direction of the maximum principal stress changes gradually from a vertical direction to a horizontal direction with the advance of the working face. The deformation and permeability of the rock mass of the coal floor are obtained by contrasting the difference of the principal stress established from theoretical calculations with curves of stress-strain and permeability-strain from tests, which is an important mechanical basis for preventing water inrush from confined aauifers.

A New Function for Modelling Diameter Frequency Distribution in the Tropical Rain Forest of Xishuangbanna,Southwest of China

Permanent plots in the montane tropical rain forests in Xishuangbanna, southwest China, were established, and different empirical models, based on observation data of these plots in 1992, were built to model diameter frequency distributions. The focus of this study is on predicting accuracy of stem number in the larger diameter classes, which is much more important than that of the smaller trees, from the view of forest management, and must be adequately considered in the modelling and estimate. There exist 3 traditional ways of modelling the diameter frequency distribution: the negative exponential function model, limiting line function model, and Weibull distribution model. In this study, a new model, named as the logarithmic J-shape function, together with the others, was experimented and was found as a more suitable model for modelling works in the tropical forests.

Analysis of substrate eddy effects and distribution effects in silicon-based inductor model

The concepts of substrate eddy influence factor and distribution-effects-occurring frequency are presented. The effects of substrate resistivity and inductor spiral length on the substrate eddy and distribution effects are captured. The substrate eddy influence factors of an inductor （6 turn, 3 060 μm in length） fabricated on low （ 1 Ω. cm） and high resistivity（ 1 000 Ω.cm） silicon substrates are 0. 3 and 0. 04, and the distribution-effects- occurring frequencies are 1.8 GHz and 14. 5 GHz, respectively. The measurement results show that the equivalent circuit model of the inductor on low resistivity silicon must take into consideration substrate eddy effects and distribution effects. However, the circuit model of the inductor on high resistivity silicon cannot take into account the substrate eddy effects and the distribution effects at the frequencies of interest. Its simple model shows agreement with the measurements, and the contrast is within 7%.

Sulfur Distribution and Transport Studies in East Asia Using Eulerian Model

A three-dimensional regional Eulenan model of sulfur deposition and transport is developed.Processes treated in the model include emission,transport,diffusion,gas-phase and aqueous-phase chemical process,dry deposition,ramout and washout of sulfur.A 'looking up table' method is provided to deal with the gas-phase chemical process including sulfur transfer Dry-depositon velocity considers the influence of underlying surface,wind,degree of stability by parameterization Model calculated values reasonably agrees with observation.Distribution of sulfur deposition and transport in East Asia are also analyzed in this paper Some amount of sulfur emission of different countries transport across boundaries,but the main origin of sulfur deposition in each country in East Asia is from itself.Furthermore.some transport paths on different layers and outlet or inlet zones are found.According to sulfur balance and budget we concluded that sulfur outlets are bigger than inlets across boundary and emissions are more than deposition in most places of East Asia