A General Mapping Approach and New Travelling Wave Solutions to（2＋1）-Dimensional Boussinesq Equation

A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.

Breeding design in wheat by combining the QTL information in a GWAS panel with a general genetic map and computer simulation

A large amount of genome-wide association study(GWAS)panels together with quantitative-trait locus(QTL)information associated with breeding-targeted traits have been described in wheat(Triticum aestivum L.).However,the application of mapping results from a GWAS panel to conventional wheat breeding remains a challenge.In this study,we first report a general genetic map which was constructed from 44 published linkage maps.It permits the estimation of genetic distances between any two genetic loci with physical map positions,thereby unifying the linkage relationships between QTL,genes,and genomic markers from multiple genetic populations.Second,we describe QTL mapping in a wheat GWAS panel of 688 accessions,identifying 77 QTL associated with 12 yield and grain-quality traits.Because these QTL have known physical map positions,they could be mapped onto the general map.Finally,we present a design approach to wheat breeding by using known QTL information and computer simulation.Potential crosses between parents in the GWAS panel may be evaluated by the relative frequency of the target genotype,trait correlations in simulated progeny populations,and genetic gain of selected progenies.It is possible to simultaneously improve yield and grain quality by suitable parental selection,progeny population size,and progeny selection scheme.Applying the design approach will allow identifying the most promising crosses and selection schemes in advance of the field experiment,increasing predictability and efficiency in wheat breeding.

SYSTEM FOR AUTOMATIC GENERALIZATION OF TOPOGRAPHIC MAPS

With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper describes a topographic map generalization system recently developed by the authors. The system has the following characteristics： 1） taking advantage of three levels of automation, i.e. fully automated generalization, batch generalization, and interactive generalization, to undertake two types of processes, i.e. intelligent inference process and repetitive operation process in generalization; 2） making use of two kinds of sources for generalizing rule library, i.e. written specifications and cartographers＇ experiences, to define a six-element structure to describe the rules; 3） employing a hierarchical structure for map databases, logically and physically; 4） employing a grid indexing technique and undo/redo operation to improve database retrieval and object generalization efficiency. Two examples of topographic map generalization are given to demonstrate the system. It reveals that the system works well. In fact, this system has been used for a number of projects and it has been found that a great improvement in efficiency compared with traditional map general- ization process can be achieved.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

Point Set Generalization Based on the Kohonen Net

Point set generalization is one of the essential problems in map generalization. On the demands analysis of point set generalization, this paper proposes a method to generalize point sets based on the Kohonen Net model; the standard SOM algorithm has been improved so as to preserve the spatial distribution properties of the original point set. Examples illustrate that this method suits the generalization of point sets.

Subdivision of Polygon Parcel in Land-Use Data Generalization

In land-use data generalization, the removal of insignificant parcel withsmall size is the most frequently used operator. Traditionally for the generalization method, thesmall parcel is assigned completely to one of its neighbors. This study tries to improve thegeneralization by separating the insignificant parcel into parts around the weighted skeleton andassigning these parts to different neighbors. The distribution of the weighted skeleton depends onthe compatibility between the removed object and its neighbor, which considers not only topologicalrelationship but also distance relationship and semantic similarity. This process is based on theDelaunay triangulat'on model. This paper gives the detailed geometric algorithms for this operation.

Spatial Relation Resolution and Spatial Relation Abstraction

This paper attempts toregard spatial relation transformationas an important process in map gener-alization. The spatial relation generali-zation can be divided into the compo-nents of abstraction: topology, dis-tance and orientation. The concept‘ spatial relation resolution' is intro-duced to describe the constraints ofrelative spatial relation. On the basisof nine intersection models, the cardi-nal direction models and the iso-dis-tance-relation models, this paper givesthree sorts of relation resolution repre-sentations for topological, distance andorientation relation, respectively. Twomapping implementations in map gen-eralization is discussed.

Multi-scale Representation of Building Feature in Urban GIS

This paper aims at multi_scale representation of urban GIS,presenting a model to dynamically generalize the building on the basis of Delaunay triangulation model.Considering the constraints of position accuracy,statistical area balance and orthogonal characteristics in building cluster generalization,this paper gives a progressive algorithm of building cluster aggregation,including conflict detection (where),object (who) displacement,and geometrical combination operation (how).The algorithm has been realized in an interactive generalization system and some experiment illustrations are provided.

The Spatial Characteristics of a Line and Their Application to Line Simplification

This paper discusses the spatial knowledge related to a line ,and the characteristic points of lines is detected.According to the requirements of line generalization,new algorithms for identifying characteristic line points are presented.These characteristic points are used to improve the algorithms of line generalization.An algorithm for identifying bends is shown.In this paper,improved algorithms based on those by Douglas_Peucker,Visvalingam and Whyatt are shown.In this test,the progressive process of line generalization is emphasized.

Displacement of Building Cluster Using Field Analysis Method

This paper presents a field based method to deal with the displacement of building cluster, which is driven by the street widening. The compress of street boundary results in the force to push the building moving inside and the force propagation is a decay process. To describe the phenomenon above, the field theory is introduced with the representation model of isoline. On the basis of the skeleton of Delaunay triangulation, the displacement field is built in which the propagation force is related to the adjacency degree with respect to the street boundary. The study offers the computation of displacement direction and offset distance for the building displacement. The vector operation is performed on the basis of grade and other field concepts.

THE METHOD OF GRAPHIC SIMPLIFICATION OF AREA FEATURE BOUNDARY WITH RIGHT ANGLES

Some rules of simplification of area feature boundary and the method of acquiring spatial knowledge, such as maintaining area and shape of area feature, are discussed. This paper focuses on the progressive method of graphic simplification of area feature boundary with right angles based on its characteristics.

Measurement of Similarity for Spatial Directions Between Areal Objects

Similarity for spatial directions plays an important role in GIS. In this paper, the conventional approaches are analyzed. Based on raster data areal objects, the authors propose two new methods for measuring similarity among spatial directions. One is to measure the similarity among spatial directions based on the features of raster data and the changes of distances between spatial objects, the other is to measure the similarity among spatial directions according to the variation of each raster cell centroid angle. The two methods overcome the complexity of measuring similarity among spatial directions with direction matrix model and solve the limitation of small changes in direction. The two methods are simple and have broader applicability.

Road Density Analysis Based on Skeleton Partitioning for Road Generalization

This paper proposes an algorithm for road density analysis based on skeleton partitioning. Road density provides metric and statistical information about overall road distribution at the macro level. Existing measurements of road density based on grid method, fractal geometry and mesh density are reviewed, and a new method for computing road density based on skeleton partitioning is proposed. Experiments illustrate that road density based on skeleton partitioning may reveal the overall road distribution. The proposed measurement is further tested against road maps at 1:10k scale and their generalized version at 1:50k scale. By comparing the deletion percentage within different density interval, a road density threshold can be found, which indicate the need for further operations during generalization. Proposed road density may be used to examine the quality of road generalization, to explore the variation of road network through temporal and spatial changes, and it also has future usage in urban planning, transportation and estates evaluation practice.

On the canonical map of surfaces with q≥6

We carry out an analysis of the canonical system of a minimal complex surface S of general type with irregularity q > 0.Using this analysis,we are able to sharpen in the case q > 0 the well-known Castelnuovo inequality KS2≥3pg(S) + q(S)-7.Then we turn to the study of surfaces with pg=2q-3 and no fibration onto a curve of genus > 1.We prove that for q≥6 the canonical map is birational.Combining this result with the analysis of the canonical system,we also prove the inequality:KS2≥7χ(S) + 2.This improves an earlier result of Mendes Lopes and Pardini (2010).

A progressive method for the collapse of river representation considering geographical characteristics

During map generalization,the collapse of geometry,which is also called geometric dimension reduction,is a basic generalization operation.When the map scale decreases,rivers with long,shallow polygonal shapes,usually require their dual-line representation to be collapsed to a single line.This study presents a new algorithm called superpixel river collapse(SURC)to convert dual-line rivers to single-line rivers based on raster data.In this method,dual-line rivers are first segmented at different levels of detail using a superpixel method called simple linear iterative clustering.Then,by connecting the edge midpoints and centre of mass of each superpixel,single-line rivers are preliminarily generated from dual-line rivers.Finally,an interpolation algorithm called polynomial approximation with an exponential kernel is applied to maintain the uniform distribution of the feature points of single-line rivers at different levels of detail(LOD).The presented method can progressively collapse the river during scale transformation to support the LOD representation in a highly sensitive way.The results show that compared with three typical thinning algorithms,the SURC method can generate smooth single-line rivers from dual-line rivers considering different river widths while effectively avoiding burrs and fractured intersections.

Constraints of Progressive Transmission of Spatial Data on the Web

The progressive transmission of map data on the World Wide Web provides the user with a self-adaptive strategy to access remote data. It not only speeds up the web transfer but also offers an efficient navigation guide for information acquisition. The key technology in this transmission is the efficient multiple representation of spatial data and pre-organization on the server site. This paper aims at progressive transmission investigating some constraints from three aspects: data organization on server site, data control in the transmission process and data restore after reaching the client. Two strategies, namely on-line map generalization and off-line map generalization, are examined respectively for this kind of progressive transmission.

A raster-based typification method for multiscale visualization of building features considering distribution patterns

In map multiscale visualization,typification is the process of replacing original objects,such as buildings,using a smaller number of objects while maintaining initial geometrical and distribution characteristics.During the past few decades,many vector-based methods for building typification have been developed,whereas raster-based methods have received less attention.In this paper,a new method for the typification of buildings with different distribution patterns called superpixel building typification(SUBT)is developed based on raster data.Using this method,buildings with different distribution patterns,such as linear,grid and irregular patterns,are first grouped by image connected component detection and superpixel analysis.Then,the new positions for building typification are determined by superpixel resegmentation.Finally,a new representation of the buildings is determined through analysis of the orientation and shape of the buildings in each superpixel.To test the proposed SUBT method,buildings from both cities and countrysides in China are applied to perform typification.The experimental results show that the proposed SUBT method can realize typification for buildings with linear,grid and irregular distributions while effectively maintaining the original distribution characteristics of the buildings.

A characterization of Burniat surfaces with K^2 = 4 and of non nodal type

Let S be a minimal surface of general type with pg(S) = 0 and K_S^2= 4. Assume the bicanonical map ψ of S is a morphism of degree 4 such that the image of ψ is smooth. Then we prove that the surface S is a Burniat surface with K^2= 4 and of non nodal type.