An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.

CURDIS:A template for incremental curve discretization algorithms and its application to conics

We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion.These two elements can be adapted for any type of curve,leading to algorithms dedicated to the shape of specific curves.While the calculation of the tangent quadrant for various curves,such as lines,conics,or cubics,is simple,it is more complex to analyze how pixels are traversed by the curve.In the case of conic arcs,we found a criterion for determining the pixel exit side.This leads us to present a new algorithm,called CURDIS-C,specific to the discretization of conics,for which we provide all the details.Surprisingly,the criterion for conics requires between one and three sign tests and four additions per pixel,making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations.Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel,achieving this generality at the cost of potentially computing up to two square roots per arc.We illustrate the use of CURDIS for the discretization of different curves,such as ellipses,hyperbolas,and parabolas,even when they degenerate into lines or corners.

Temporal-spatial Changes in Inner Mongolian Grassland Degradation during Past Three Decades

[Objective] This study aimed to analyze the temporal-spatial variation of Inner Mongolian grassland degradation during past three decades. [Method] The dis- tribution characteristics of grassland were described by land use types supervised classification with TM/ETM. Then, temporal-spatial changes of grassland coverage were quantified by the mean of maximum vegetation coverage in last 30 years. Lastly, the grassland degradation reasons were explored through statistic analysis between the grassland coverage and precipitation, temperature and grazing intensity. [Result] The grassland degradation index of Inner Mongolia was increased from 1.38 to 1.68, and the smallest was 1.28 in 2005s. Grassland degradation and improve- ment were concurrent after 1980s, but grassland degradation was the major change trend for Inner Mongolia grassland. The area of grassland degradation was enlarged from 18.08×10^4 km2 in 1980s to 22.47×10^4 km2 in 2010s on the whole and distribu- tion range was shifted from central-eastern to west in Inner Mongolia that mainly distributed on Hulun Buir and Xilin Gol grassland in 1980s and Ordos and Alax grassland in 2010s. The grassland area of degradation had a rising trend form 1980s to 1995s, then reduced to 10.8x104 km2 in 2005s, and decreased in 2010s, which mainly speared in the west of Xilin Gol grassland. [Conclusion] Inner Mongo-lian grassland degradation were become more seriously in last 30 years because that temperature, precipitation and graze intensities change, which not performance on decreasing coverage but grassland areas.

Temporal-spatial Distribution Model of Cold Chain Logistics for Vegetables

[Objective] The aim was to study on temporal-spatial distribution model of cold chain logistics for vegetables. [Method] Broccoli was taken as an example. Detailedly, time-space distribution model of cold chain logistics for broccoli was proposed from standpoints of costs and benefits based on changes of time and space, and a comprehensive evaluation was made on timeliness, efficiency, risks, added- value of products and satisfaction of information in cold-chain logistics. [Result] The efficiency of cold chain logistics for vegetable can be greatly improved by temporal- spatial distribution model of cold chain logistics. [Conclusion] Costs and benefits of vegetables in temporal-apstial distribution could be evaluated by the model.

High-resolution algorithm based on temporal-spatial extrapolation

To enhance the resolution of parameter estimation with limited samples received by a short passive array, an iterative nonparametric algorithm for estimating the frequencies and direction-of-arrivals （DOAs） of signals is proposed. The cost function is constructed using 12-norm Gaussian entropy combined with an additional constraint, 12-norm constraint or linear constraint. By minimizing the cost functions in the temporal and the spatial dimensions using corresponding iteration algorithms respectively, the sparse discrete Fourier transforms （DFTs） of temporal and spatial samples are obtained to represent the extrapolated sequences with much larger sizes than the original samples. Then frequency and angle estimates are obtained by performing the traditional simple methods on the extrapolated sequences. It is shown that the proposed algorithm offers increased resolution and significantly reduced sidelobes compared with the periodogram and beamforming based methods. And it achieves high precision compared with the high-resolution method with lower computational burden. Some numerical simulations and real data processing results are presented to verify the effectiveness of the method.

Temporal-Spatial Variability of Soil Organic Carbon Stocks in a Rehabilitating Ecosystem

In global change research, changes of soil organic carbon (SOC) reservoirs intropical and subtropical regions are still unknown. The temporal-spatial variability of SOC stockswas determined in a basin of over 579 km^2 in subtropical China from 1981to 2002. ArcGIS8.l softwarewas utilized for spatial analysis of semivariance, ordinary kriging (OK), and probability kriging(PK). Grid and hierarchical approaches were employed for the sampling scenario in 2002 with 106Global Position System (GPS) established spots sampled. Bulk topsoil samples (0—30 cm) werecollected at three random sites on each spot. The SOC content for 1981 came from the SOC map of theSecond National Soil Survey. Geostatistical results of the nugget to sill ratio (0.215-0.640)in therehabilitating ecosystem indicated a moderate spatial dependence for SOC on this large scale. Therange of SOC changed from 2.04 km in 1981 to 7.15 km in 2002. The mean topsoil SOC increased by 4.6%from 10.63 g kg^(-1) (1981) to 11.12 g kg^(-1)(2002). However, during this 21-year period 25.2% ofthe total basin area experienced a decrease in SOC. Also, the probability kriging results showedthat the geometric mean probabilities of SOC <= 6.0 g kg^(-1), <= 11.0 g kg^(-1) and > 15.0 gkg^(-1) were 0.188, 0.534 and 0.378, respectively in 2002, comparing to 0.234, 0.416 and 0.234 inthat order in 1981, respectively. The SOC storage in the topsoil increased by 17.0% during this timewith the main increase occurring in forests and cultivated land,which amounted to 82.5% and 17.0%of the total increase, respectively.

Sand-dust storms in China: temporal-spatial distribution and tracks of source lands

Sand-dust storm is a special natural disaster that frequently occurs in deserts and their surrounding areas. With the data published onSurface Meteorological Monthly Bulletin andSurface Chart during 1971–1996, the temporal-spatial distribution and annual variation of sand-dust storms are analyzed on the basis of the case study of atmospheric processes. Furthermore, the tracks and source areas of sand-dust storms are determined with the aid of GIS. The results show that except some parts of Qinghai Province and Inner Mongolia as well as Beijing, sand-dust storms decrease apparently in time and space in recent decades in China. Sand-dust storms occur most frequently in spring, especially in April. According to their source areas, sand-dust storms are classified into two types, i.e., the inner-source and outer-source sand-dust storms. Most of the outer-source sand-dust storms move along the north and west tracks. The north-track outer-source sand-dust storms always intrude into China across the Sino-Mongolian border from Hami, a city in the eastern part ofXinjiang, to Xilin Gol, a league in Inner Mongolia, while the west-track ones intrude into China from both southern and northern Xinjiang. The source lands of inner-source sand-dust storms concentrate in the Taklimakan Desert and its surrounding areas in southern Xinjiang, southern part of the Junggar Basin in north of Xinjiang, the Hexi Corridor in western Gansu Province, the dry deserts of Inner Mongolia and the Qaidam Basin in Qinghai.

New method for discretization of continuous attributes in rough set theory

A new method for discretization of continuous attributes is put forward to overcome the limitation of the traditional rough sets, which cannot deal with continuous attributes.The method is based on an improved algorithm to produce candidate cut points and an algorithm of reduction based on variable precision rough information entropy. With the guarantee of consistency of decision system, the method can reduce the number of cut points and im- prove efficiency of reduction. Adopting variable precision rough information entropy as measure criterion, it has a good tolerance to noise. Experiments show that the algorithm yields satisfying reduction results.

Temporal-spatial distribution and variability of cadmium contamination in soils in Shenyang Zhangshi irrigation area,China

Heavy metal contamination in soils has been of wide concern in China in the last several decades. The heavy metal contamination was caused by sewage irrigation, mining and inappropriate utilization of various agrochemicals and pesticides and so on. The Shenyang Zhangshi irrigation area （SZIA） in China is a representative area of heavy metal contamination of soils resulting from sewage irrigation for about 30 years duration. This study investigated the spatial distribution and temporal variation of soil cadmium contamination in the SZIA. The soil samples were collected from the SZIA in 1990 and 2004; Cd of soils was analyzed and then the spatial distribution and temporal variation of Cd in soils was modelled using kriging methods. The kriging map showed that long-term sewage irrigation had caused serious Cd contamination in topsoil and subsoil. In 2004, the Cd mean concentrations were 1.698 and 0.741 mg/kg, and the maxima 10.150 and 7.567 mg/kg in topsoils （0-20 cm） and subsoils （20-40 cm） respectively. These values are markedly more than the Cd levels in the second grade soil standard in China. In 1990, the Cd means were 1.023 and 0.331 mg/kg, and the maxima 9.400 and 3.156 mg/kg, in topsoils and subsoils respectively. The soil area in 1990 with Cd more than 1.5 mg/kg was 2701 and 206.4 hnl2 in topsoils and subsoils respectively; and in 2004, it was 7592 and 1583 hm^2, respectively. Compared with that in 1990, the mean and maximum concentration of Cd, as well as the soil area with Cd more than 1.5 mg/kg had all increased in 2004, both in topsoils and subsoils.

Pseudo-static/dynamic solutions of required reinforcement force for steep slopes using discretization-based kinematic analysis

This paper presents a procedure for assessing the reinforcement force of geosynthetics required for maintaining dynamic stability of a steep soil slope. Such a procedure is achieved with the use of the discretization technique and kinematic analysis of plasticity theory, i.e. discretization-based kinematic analysis. The discretization technique allows discretization of the analyzed slope into various components and generation of a kinematically admissible failure mechanism based on an associated flow rule.Accordingly, variations in soil properties including soil cohesion, internal friction angle and unit weight are accounted for with ease, while the conventional kinematic analysis fails to consider the changes in soil properties. The spatialetemporal effects of dynamic accelerations represented by primary and shear seismic waves are considered using the pseudo-dynamic approach. In the presence of geosynthetic reinforcement, tensile failure is discussed providing that the geosynthetics are installed with sufficient length. Equating the total rates of work done by external forces to the internal rates of work yields the upper bound solution of required reinforcement force, below which slopes fail. The reinforcement force is sought by optimizing the objective function with regard to independent variables, and presented in a normalized form. Pseudo-static analysis is a special case and hence readily transformed from pseudodynamic analysis. Comparisons of the pseudo-static/dynamic solutions calculated in this study are highlighted. Although the pseudo-static approach yields a conservative solution, its ability to give a reasonable result is substantiated for steep slopes. In order to provide a more meaningful solution to a stability analysis, the pseudo-dynamic approach is recommended due to considerations of spatial etemporal effect of earthquake input.

Impact of Holocene environmental change on temporal-spatial distribution of Neolithic sites in Huaihe River Basin, Anhui Province

The Huaihe River basin of Anhui is not only a transitional zone of physical geography, but also a convergent area of many cultures in China. It is one of the sensitive ecotones to global changes and the birthplace of Chinese civilization. Using the field archaeological data and the sporo-pollens and the age data of the drilling cores, we analysed Neolithic cultural development and environmental evolution in the Huaihe River basin of Anhui. According to the combination of some research results in archaeology with environmental evolution research, this paper discusses the relationship between culture and environment in the Huaihe River basin of Anhui. The Neolithic cultural development was strongly impacted by the environmental change. The primitive culture （Shishanzi） was developed in the beginning of the Holocene Megathermal Period with distinct regional feature of the culture. From 6.5 kaBP to 5.5 kaBP, the climate changed warmer and wetter. The frequent occurrence of flood and waterlog due to such a climate regime and high sea level caused the earth＇s surface environment deteriorated in the Huaihe River basin of Anhui and the interruption of the Neolithic cultural development, hence a lack of archaeological sites. From 5.5 kaBP to 4.0 kaBP, the climate changed from wet to dry, the natural environment was propitious to human survival. Dawenkou Culture and Longshan Culture flourished in this period. The Neolithic cultural development, the number of the sites and their distribution characteristics of the sites in the study area differed apparently from those in Central China and Shandong Province.

Long-term temporal-spatial dynamics of marine coastal water quality in the Tolo Harbor,Hong Kong,China

The long-term temporal and spatial dynamics of marine coastal water quality in Tolo Harbor, Hong Kong were explored. The Harbor is divided into three zones represented as Harbor, Buffer, and Channel Subzones. The time range for the study covers the period from the 1970s to the 1990s. The selected indicators for the comprehensive assessment of water quality consist of physical, chemical and biological aspects, including suspended solids(SS), Secchi disk depth(SD), 5-day biochemical oxygen demand(BOD\-5), total nitrogen(TN), total phosphorus(TP), faecal coliform, chlorophyll-a(Chl-a), and the number of red tide occurrences. The results indicated the presence of obvious temporal and spatial trends with regard to changes in water quality. Spatially, water quality in the Channel Subzone is the best, while that in the Harbor Subzone is the worst. On a temporal basis, the average trend from bad to good was 1980s>1990s>1970s as indicated by most of the selected water quality indicators. Water quality during the late 1980s reached its worst level with the lowest SD, the highest BOD\-5, TN, TP, Chl-a concentrations, and the number of red tide occurrences. These long-term temporal-spatial water quality trends were also found in other studies of the Tolo Harbor. The large quantity of pollutants produced as a result of increasing population, industrial and commercial actives, and urbanization and industrialization trends in both Shatin and Tai Po seem to be primarily responsible for the changes in marine coastal water quality.

Effect of water level fluctuations on temporal-spatial patterns of foraging activities by the wintering Hooded Crane(Grus monacha)

Background:The Yangtze River floodplain provides important wintering habitats for Hooded Cranes(Grus monacha) in China.Fluctuations in the water level change foraging habitat and food availability,affecting their temporal-spatial patterns of foraging activities.It is of considerable importance to investigate the effect of these fluctuations on food availability for wintering Hooded Cranes and their foraging response to these changes.Understanding their behavior patterns is beneficial in protecting the wintering crane population and restoring their wintering habitats.Methods:A field survey of the winter behavior of cranes was carried out at Shengjin Lake from November in 2013 to April in 2014.Habitat variables,as well as the spatial distribution and behavior patterns of wintering cranes at their foraging sites during five stages of water level fluctuation were collected.Based on this data we analyzed the relationship of foraging behavior relative to water level fluctuations and habitat types.Results:The foraging habitats used by Hooded Cranes varied at the different water level stages.As the water level decreased,the use of meadows and mudflats increased.When the water dropped to its lowest level,the use by the Hooded Crane in the mudflats reached a peak.There were statistically significant differences in time budget in the three types of habitats over the five stages of the water level.In the mudflats,the foraging behavior and maintenance behavior varied significantly with the water level,while the alert behavior showed little variation.Analysis of a generalized linear model showed that the five water level stages and three habitat types had a significant effect on foraging behavior,while the combined effect of these two variables was significant on the foraging time budget and the length of foraging activity of the Hooded Crane.Conclusions:With the decrease in the water level,the use of mudflats by Hooded Cranes increased correspondingly.Food availability in different habitats was affected by changes in the water level.The Hooded Crane adjusted its foraging patterns and made full use of the three available types of habitat in order to acquire enough food in response to fluctuations in the water level.

Half-global discretization algorithm based on rough set theory

It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithras for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.

Immune algorithm for discretization of decision systems in rough set theory

Rough set theory plays an important role in knowledge discovery, but cannot deal with continuous attributes, thus discretization is a problem which we cannot neglect. And discretization of decision systems in rough set theory has some particular characteristics. Consistency must be satisfied and cuts for discretization is expected to be as small as possible. Consistent and minimal discretization problem is NP-complete. In this paper, an immune algorithm for the problem is proposed. The correctness and effectiveness were shown in experiments. The discretization method presented in this paper can also be used as a data pre- treating step for other symbolic knowledge discovery or machine learning methods other than rough set theory.

Quantitative method for evaluating detailed volatility of wind power at multiple temporal-spatial scales

With the increasing proportion of wind power integration, the volatility of wind power brings huge challenges to the safe and stable operation of the electric power system. At present, the indexes commonly used to evaluate the volatility of wind power only consider its overall characteristics, such as the standard deviation of wind power, the average of power variables, etc., while ignoring the detailed volatility of wind power, that is, the features of the frequency distribution of power variables. However, how to accurately describe the detailed volatility of wind power is the key foundation to reduce its adverse influences. To address this, a quantitative method for evaluating the detailed volatility of wind power at multiple temporal-spatial scales is proposed. First, the volatility indexes which can evaluate the detailed fluctuation characteristics of wind power are presented, including the upper confidence limit, lower confidence limit and confidence interval of power variables under the certain confidence level. Then, the actual wind power data from a location in northern China is used to illustrate the application of the proposed indexes at multiple temporal(year–season–month–day) and spatial scales(wind turbine–wind turbines–wind farm–wind farms) using the calculation time windows of 10 min, 30 min, 1 h, and 4 h. Finally, the relationships between wind power forecasting accuracy and its corresponding detailed volatility are analyzed to further verify the effectiveness of the proposed indexes. The results show that the proposed volatility indexes can effectively characterize the detailed fluctuations of wind power at multiple temporal-spatial scales. It is anticipated that the results of this study will serve as an important reference for the reserve capacity planning and optimization dispatch in the electric power system which with a high proportion of renewable energy.

ON GALERKIN DISCRETIZATION OF AXIALLY MOVING NONLINEAR STRINGS

A computational technique is proposed for the Galerkin discretization of axially moving strings with geometric nonlinearity. The Galerkin discretization is based on the eigenfunctions of stationary strings. The discretized equations are simplified by regrouping nonlinear terms to reduce the computation work. The scheme can be easily implemented in the practical programming. Numerical results show the effectiveness of the technique. The results also highlight the feature of Galerkin＇s discretization of gyroscopic continua that the term number in Galerkin＇s discretization should be even. The technique is generalized from elastic strings to viscoelastic strings.

Temporal-spatial cross-correlation analysis of non-stationary near-surface wind speed time series

Temporal-spatial cross-correlation analysis of non-stationary wind speed time series plays a crucial role in wind field reconstruction as well as in wind pattern recognition.Firstly,the near-surface wind speed time series recorded at different locations are studied using the detrended fluctuation analysis(DFA),and the corresponding scaling exponents are larger than 1.This indicates that all these wind speed time series have non-stationary characteristics.Secondly,concerning this special feature( i.e.,non-stationarity)of wind signals,a cross-correlation analysis method,namely detrended cross-correlation analysis(DCCA) coefficient,is employed to evaluate the temporal-spatial cross-correlations between non-stationary time series of different anemometer pairs.Finally,experiments on ten wind speed data synchronously collected by the ten anemometers with equidistant arrangement illustrate that the method of DCCA cross-correlation coefficient can accurately analyze full-scale temporal-spatial cross-correlation between non-stationary time series and also can easily identify the seasonal component,while three traditional cross-correlation techniques(i.e.,Pearson coefficient,cross-correlation function,and DCCA method) cannot give us these information directly.

Temporal-spatial change and driving mechanism for regional difference of domestic tourism in China

By using the variation coefficient,Gini coefficient and Theil coefficient,this paper makes preliminary exploration of temporalspatial change features and driving mechanism for regional differences of domestic tourism in China from 1995 to 2009.According to the results,we drew the following conclusions:(1)The regional difference of domestic tourism in China tends to be narrowing generally,and is less than that of inbound tourism,playing an important role in narrowing the overall gap of regional tourism in China.(2)The regional internal difference features:inter-provincial difference in the eastern region and difference among the eastern,central and western regions are comparatively obvious and demonstrate a significantly shrinking tendency,the change tendency is consistent with the change tendency of overall difference and exercises a decisive role in overall difference,whereas the inter-provincial difference in the central and western regions is small and relatively stable,having less influence on the overall difference.(3)The temporal-spatial change in regional difference is featured by:low-level provinces occupy a majority and are concentrated in the central and western regions,showing a tendency of narrowing difference;high-level provinces are concentrated in the eastern region,showing a tendency of spreading to the central and western regions;spatial pattern of regional difference demonstrates 4 types,i.e."proliferation type","polarization type","quiescence type"and"collapse type."(4)The driving force for regional difference of domestic tourism in China comes down to 3 aspects:regional socio-economic attribute,regional transport accessibility level and regional development policy.

Discretization Approach in Integrated Hydrologic Model for Surface and Groundwater Interaction

The commonly used discretization approaches for distributed hydrological models can be broadly categorized into four types,based on the nature of the discrete components:Regular Mesh,Triangular Irregular Networks(TINs),Representative Elementary Watershed(REWs) and Hydrologic Response Units(HRUs).In this paper,a new discretization approach for landforms that have similar hydrologic properties is developed and discussed here for the Integrated Hydrologic Model(IHM),a combining simulation of surface and groundwater processes,accounting for the interaction between the systems.The approach used in the IHM is to disaggregate basin parameters into discrete landforms that have similar hydrologic properties.These landforms may be impervious areas,related areas,areas with high or low clay or organic fractions,areas with significantly different depths-to-water-table,and areas with different types of land cover or different land uses.Incorporating discrete landforms within basins allows significant distributed parameter analysis,but requires an efficient computational structure.The IHM integration represents a new approach interpreting fluxes across the model interface and storages near the interface for transfer to the appropriate model component,accounting for the disparate discretization while rigidly maintaining mass conservation.The discretization approaches employed in IHM will provide some ideas and insights which are helpful to those researchers who have been working on the integrated models for surface-groundwater interaction.