Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.

A Cautionary Note on the Application of GIS in Spatial Optimization Modeling

Spatial optimization as part of spatial modeling has been facilitated significantly by integration with GIS techniques. However, for certain research topics, applying standard GIS techniques may create problems which require attention. This paper serves as a cautionary note to demonstrate two problems associated with applying GIS in spatial optimization, using a capacitated p-median facility location optimization problem as an example. The first problem involves errors in interpolating spatial variations of travel costs from using kriging, a common set of techniques for raster files. The second problem is inaccuracy in routing performed on a graph directly created from polyline shapefiles, a common vector file type. While revealing these problems, the paper also suggests remedies. Specifically, interpolation errors can be eliminated by using agent-based spatial modeling while the inaccuracy in routing can be improved through altering the graph topology by splitting the long edges of the shapefile. These issues suggest the need for caution in applying GIS in spatial optimization study.

Spatial Expression of Assembly Geometric Errors for Multi-axis Machine Tool Based on Kinematic Jacobian-Torsor Model

Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool.And it cannot be eliminated due to the error propagation of components in the assembly process,which is generally non-uniformly distributed in the whole working space.A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice.However,the expression ranges based on the standard quasistatic expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool.To address this issue,a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors.Firstly,an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies,respectively.Furthermore,based on the proposed kinematic Jacobian-Torsor model,a spatial expression of geometric errors for the multi-axis machine tool is given.And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools.The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors.

A novel model to evaluate spatial structure in thinned conifer-broadleaved mixed natural forests

In order to ensure the effective analysis and reconstruction of forests,it is key to ensure the quantitative description of their spatial structure.In this paper,a distance model for the optimal stand spatial structure based on weighted Voronoi diagrams is proposed.In particular,we provide a novel methodological model for the comprehensive evaluation of the spatial structure of forest stands in natural mixed conifer-broadleaved forests and the formulation of management decision plans.The applicability of the rank evaluation and the optimal solution distance model are compared and assessed for different standard sample plots of natural mixed conifer-broadleaved forests.The effect of crown width on the spatial structure unit of the trees is observed to be higher than that of the diameter at breast height.Moreover,the influence of crown length is greater than that of tree height.There are nine possible spatial structure units determined by the weighted Voronoi diagram for the number of neighboring trees in the central tree,with an average intersection of neighboring crowns reaching 80%.The rank rating of natural forest sample plots is correlated with the optimal solution distance model,and their results are generally consistent for natural forests.However,the rank rating is not able to provide a quantitative assessment.The optimal solution distance model is observed to be more comprehensive than traditional methods for the evaluation of the spatial structure of forest stands.It can effectively reflect the trends in realistic stand spatial structure factors close to or far from the ideal structure point,and accurately assesses the forest spatial structure.The proposed optimal solution distance model improves the integrated evaluation of the spatial structure of forest stands and provides solid theoretical and technical support for sustainable forest management.

Spatial Inhomogeneity of Atmospheric CO_(2) Concentration and Its Uncertainty in CMIP6 Earth System Models

This paper provides a systematic evaluation of the ability of 12 Earth System Models(ESMs)participating in the Coupled Model Intercomparison Project Phase 6(CMIP6)to simulate the spatial inhomogeneity of the atmospheric carbon dioxide(CO_(2))concentration.The multi-model ensemble mean(MME)can reasonably simulate the increasing trend of CO_(2) concentration from 1850 to 2014,compared with the observation data from the Scripps CO_(2) Program and CMIP6 prescribed data,and improves upon the CMIP5 MME CO_(2) concentration(which is overestimated after 1950).The growth rate of CO_(2) concentration in the northern hemisphere(NH)is higher than that in the southern hemisphere(SH),with the highest growth rate in the mid-latitudes of the NH.The MME can also reasonably simulate the seasonal amplitude of CO_(2) concentration,which is larger in the NH than in the SH and grows in amplitude after the 1950s(especially in the NH).Although the results of the MME are reasonable,there is a large spread among ESMs,and the difference between the ESMs increases with time.The MME results show that regions with relatively large CO_(2) concentrations(such as northern Russia,eastern China,Southeast Asia,the eastern United States,northern South America,and southern Africa)have greater seasonal variability and also exhibit a larger inter-model spread.Compared with CMIP5,the CMIP6 MME simulates an average spatial distribution of CO_(2) concentration that is much closer to the site observations,but the CMIP6-inter-model spread is larger.The inter-model differences of the annual means and seasonal cycles of atmospheric CO_(2) concentration are both attributed to the differences in natural sources and sinks of CO_(2) between the simulations.

A Hybrid Spatial Dependence Model Based on Radial Basis Function Neural Networks (RBFNN) and Random Forest (RF)

The majority of spatial data reveal some degree of spatial dependence. The term “spatial dependence” refers to the tendency for phenomena to be more similar when they occur close together than when they occur far apart in space. This property is ignored in machine learning (ML) for spatial domains of application. Most classical machine learning algorithms are generally inappropriate unless modified in some way to account for it. In this study, we proposed an approach that aimed to improve a ML model to detect the dependence without incorporating any spatial features in the learning process. To detect this dependence while also improving performance, a hybrid model was used based on two representative algorithms. In addition, cross-validation method was used to make the model stable. Furthermore, global moran’s I and local moran were used to capture the spatial dependence in the residuals. The results show that the HM has significant with a R2 of 99.91% performance compared to RBFNN and RF that have 74.22% and 82.26% as R2 respectively. With lower errors, the HM was able to achieve an average test error of 0.033% and a positive global moran’s of 0.12. We concluded that as the R2 value increases, the models become weaker in terms of capturing the dependence.

Understanding the spatial interaction of ultrasounds based on three-dimensional dual-frequency ultrasonic field numerical simulation

A transient 3D model was established to investigate the effect of spatial interaction of ultrasounds on the dual-frequency ultrasonic field in magnesium alloy melt.The effects of insertion depth and tip shape of the ultrasonic rods,input pressures and their ratio on the acoustic field distribution were discussed in detail.Additionally,the spacing,angle,and insertion depth of two ultrasonic rods significantly affect the interaction between distinct ultrasounds.As a result,various acoustic pressure distributions and cavitation regions are obtained.The spherical rods mitigate the longitudinal and transversal attenuation of acoustic pressure and expand the cavitation volume by 53.7%and 31.7%,respectively,compared to the plate and conical rods.Increasing the input pressure will enlarge the cavitation region but has no effect on the acoustic pressure distribution pattern.The acoustic pressure ratio significantly affects the pressure distribution and the cavitation region,and the best cavitation effect is obtained at the ratio of 2:1(P15:P20).

Statistical Channel Modeling for Indoor VLC Communications Based on Channel Measurements

Visible light communication(VLC)has attracted much attention in the research of sixthgeneration(6G)systems.Furthermore,channel modeling is the foundation for designing efficient and robust VLC systems.In this paper,we present extensive VLC channel measurement campaigns in indoor environments,i.e.,an office and a corridor.Based on the measured data,the large-scale fading characteristics and multipath-related characteristics,including omnidirectional optical path loss(OPL),K-factor,power angular spectrum(PAS),angle spread(AS),and clustering characteristics,are analyzed and modeled through a statistical method.Based on the extracted statistics of the above-mentioned channel characteristics,we propose a statistical spatial channel model(SSCM)capable of modeling multipath in the spatial domain.Furthermore,the simulated statistics of the proposed model are compared with the measured statistics.For instance,in the office,the simulated path loss exponent(PLE)and the measured PLE are 1.96and 1.97,respectively.And,the simulated medians of AS and measured medians of AS are 25.94°and 24.84°,respectively.Generally,the fact that the simulated results fit well with measured results has demonstrated the accuracy of our SSCM.

Drivers of spatial structure in thinned forests

Background:As is widely known,an increasing number of forest areas were managed to preserve and enhance the health of forest ecosystems.However,previous research on forest management has often overlooked the importance of structure-based.Aims:Our objectives were to define the direction of structure-based forest management.Subsequently,we investigated the relationships between forest structure and the regeneration,growth,and mortality of trees under different thinning treatments.Ultimately,the drivers of forest structural change were explored.Methods:On the basis of 92 sites selected from northeastern China,with different recovery time (from 1 to 15years) and different thinning intensities (0–59.9%) since the last thinning.Principal component analysis (PCA)identified relationships among factors determining forest spatial structure.The structural equation model (SEM)was used to analyze the driving factors behind the changes in forest spatial structure after thinning.Results:Light thinning (0–20%trees removed) promoted forest regeneration,and heavy thinning (over 35% of trees removed) facilitated forest growth.However,only moderate thinning (20%–35%trees removed) created a reasonable spatial structure.While dead trees were clustered,and they were hardly affected by thinning intensity.Additionally,thinning intensity,recovery time,and altitude indirectly improve the spatial structure of the forest by influencing diameter at breast height (DBH) and canopy area.Conclusion:Creating larger DBH and canopy area through thinning will promote the formation of complex forest structures,which cultivates healthy and stable forests.

Factors Influencing the Spatial Variability of Air Temperature Urban Heat Island Intensity in Chinese Cities

Few studies have investigated the spatial patterns of the air temperature urban heat island(AUHI)and its controlling factors.In this study,the data generated by an urban climate model were used to investigate the spatial variations of the AUHI across China and the underlying climate and ecological drivers.A total of 355 urban clusters were used.We performed an attribution analysis of the AUHI to elucidate the mechanisms underlying its formation.The results show that the midday AUHI is negatively correlated with climate wetness(humid:0.34 K;semi-humid:0.50 K;semi-arid:0.73 K).The annual mean midnight AUHI does not show discernible spatial patterns,but is generally stronger than the midday AUHI.The urban–rural difference in convection efficiency is the largest contributor to the midday AUHI in the humid(0.32±0.09 K)and the semi-arid(0.36±0.11 K)climate zones.The release of anthropogenic heat from urban land is the dominant contributor to the midnight AUHI in all three climate zones.The rural vegetation density is the most important driver of the daytime and nighttime AUHI spatial variations.A spatial covariance analysis revealed that this vegetation influence is manifested mainly through its regulation of heat storage in rural land.

Geospatial Analysis of Urban Heat Island Effects and Tree Equity

In recent decades, Urban Heat Island Effects have become more pronounced and more widely examined. Despite great technological advances, our current societies still experience great spatial disparity in urban forest access. Urban Heat Island Effects are measurable phenomenon that are being experienced by the world’s most urbanized areas, including increased summer high temperatures and lower evapotranspiration from having impervious surfaces instead of vegetation and trees. Tree canopy cover is our natural mitigation tool that absorbs sunlight for photosynthesis, protects humans from incoming radiation, and releases cooling moisture into the air. Unfortunately, urban areas typically have low levels of vegetation. Vulnerable urban communities are lower-income areas of inner cities with less access to heat protection like air conditioners. This study uses mean evapotranspiration levels to assess the variability of urban heat island effects across the state of Tennessee. Results show that increased developed land surface cover in Tennessee creates measurable changes in atmospheric evapotranspiration. As a result, the mean evapotranspiration levels in areas with less tree vegetation are significantly lower than the surrounding forested areas. Central areas of urban cities in Tennessee had lower mean evapotranspiration recordings than surrounding areas with less development. This work demonstrates the need for increased tree canopy coverage.

Using autologistic spatial models to simulate the distribution of land-use patterns in Zhangjiajie, Hunan Province

Nowadays, spatial simulation on land use patterns is one of the key contents of LUCC. Modeling is an important tool for simulating land use patterns due to its ability to integrate measurements of changes in land cover and the associated drivers. The conventional regression model can only analyze the correlation between land use types and driving factors but cannot depict the spatial autocorrelation characteristics. Land uses in Yongding County, which is located in the typical karst mountain areas in northwestern Hunan province, were investigated by means of modeling the spatial autocorrelation of land use types with the purpose of deriving better spatial land use patterns on the basis of terrain characteristics and infrastructural conditions. Through incorporating components describing the spatial autocorrelation into a conventional logistic model, we constructed a regression model （Autologistic model）, and used this model to simulate and analyze the spatial land use patterns in Yongding County. According to the comparison with the conventional logistic model without considering the spatial autocorrelation, this model showed better goodness and higher accuracy of fitting. The distribution of arable land, wood land, built-up land and unused land yielded areas under the ROC curves （AUC） was improved to 0.893, 0.940, 0.907 and 0.863 respectively with the autologistic model. It is argued that the improved model based on autologistic method was reasonable to a certain extent. Meanwhile, these analysis results could provide valuable information for modeling future land use change scenarios with actual conditions of local and regional land use, and the probability maps of land use types obtained from this study could also support government decision-making on land use management for Yongding County and other similar areas.

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.

Anomaly Models of Spatial Structures for Copper-Molybdenum Ore Deposits and their Application

This paper discusses the enrichment and depletion regularities for porphyry coppermolybdenum ore deposits in different regions and varied deposit genetic types in the same area, taking three porphyry copper-molybdenum ore deposits （i.e., the Chengmenshan in Jiangxi, Wunugetushan in Inner Mongolia, Baishantang in Gansu） and two copper deposits in Gansu Province （the Huitongshan skarn deposit and Gongpoquan composite deposit） as case studies. The results show that porphyry Cu-Mo deposits or skarn copper deposits include both enrichment of the ore-forming elements and associated elements, and depletion of some lithophile dispersed elements, rare earth elements （REE） and some major elements. And the depleted elements vary with deposits, having generality and their own features. On a deposit scale, the positive anomalies of enriched elements and negative anomalies of depleted elements follow in a sequence to comprise regular anomaly models of spatial structures. The exploration in the Tongchang deposit in Jiangxi and Huitongshan deposit in Gansu suggests that anomaly models play a key role in the identification of mineral occurrences and deposits compared to one single enriched element anomaly. And the anomaly models exert a critical effect on the optimization of prospecting targets and their potential evaluation.

Shift-share Analysis on International Tourism Competitiveness——A Case of Jiangsu Province

Shift-share analysis has been confirmed a useful approach in the study of regional economics and many kinds of extended shift-share models have been advanced and put into practice in economic studies, but few have hitherto been introduced and applied to the tourism research in China. Moreover understanding the spatially competitive relationship is of paramount importance for marketers, developers, and planners involved in tourism strategy development. Based on international tourism receipts from 1995 to 2004, this study aims at probing into the spatial competitiveness of interna- tional tourism in Jiangsu Province in comparison with its neighbors by applying a spatially extended shift-share model and a modified dynamic shift-share model. The empirical results illustrate that exceptional years may exist in the ap- plication of dynamic shift-share models. To solve this issue, modifications to dynamic shift-share model are put forward. The analytical results are not only presented but also explained by the comparison of background conditions of tourism development between Jiangsu and its key competitors. The conclusions can be drawn that the growth of international tourism receipts in Jiangsu mainly attributes to the national component and the competitive component and Zhejiang is the most important rival to Jiangsu during the period of 1995-2004. In order to upgrade the tourism competitiveness, it is indispensable for Jiangsu to take proper positioning, promoting and marketing strategies and to cooperate and integrate with its main rivals.

Spatial-temporal Evolution and Determinants of the Belt and Road Initiative: A Maximum Entropy Gravity Model Approach

The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.

Spatial structure optimization of mountainous abandoned mine land reuse based on system dynamics model and CLUE-S model

The mountainous abandoned mine land is often distributed in the fomi of fragmented patches. Therefore, it can greatly promote the reuse value of abandoned mine land and relieve the pressure of land demand to realize the rational reuse of abandoned mine land based on the future land use structure and spatial layout of mountainous area. In this paper, optimization of the spatial structure of mountainous abandoned mine land reuse is realized through the system dynamics model and CLUE-S model. Mentougou district, Beijing, China is selected as the research area. System dynamics model with feedback functions is constructed to simulate land use structure from 2011 to 2025, which is taken as the quanfiiative constraint on spatial structure optimization. CLUE-S model with neighborhood analysis function is applied to simulate future land use spatial structure. The simulation result layer is superimposed with the abandoned mine land distribution layer and the optimized spatial structure of abandoned mine land reuse then is determined, checked by reuse suitability evaluation. The result shows that abandoned mine land can be fully optimized as other land use types according to demand, and the reuse directions are water conservancy facilities land, urban land, rural residential land, tourism land, garden land, woodland and grassland. The trend of abandoned mine land reuse tend to be consistent with land use types of neighboring patches. This study can provide theoretical reference for the practices of mountainous abandoned mine land reuse.

Distributed hydrological models for addressing effects of spatial variability of roughness on overland flow

In this study, we investigated the origin of the overland flow roughness problem and divided the current overland flow roughness research into three types, as follows: the first type of research takes into account the effects of roughness on the volume and velocity of surface runoff, flood peaks, and the scouring capability of flows, but has not addressed the spatial variability of roughness in detail; the second type of research considers that surface roughness varies spatially with different land usage types, land-cover conditions, and different tillage forms, but lacks a quantitative study of the spatial variability; and the third type of research simply deals with the spatial variability of roughness in each grid cell or land type. We present three shortcomings of the current overland flow roughness research, including(1) the neglect of roughness in distributed hydrological models when simulating the overland flow direction and distribution,(2) the lack of consideration of spatial variability of roughness in hydrological models, and(3) the failure to distinguish the roughness formulas in different overland flow regimes. To solve these problems,distributed hydrological model research should focus on four aspects in regard to overland flow: velocity field observations, flow regime mechanisms, a basic roughness theory, and scale problems.

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.

A new spatial coherence model and analytical coeffi cients for multi-support response spectrum combination

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination （correlation） coefficients of structural response are developed for multi-support seismic excitations. The coefficients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coefficients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coefficients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational efficiency of the analytical solutions of the modal combination coefficients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coefficients is less than 1/20 of that using numerical integral methods.