Embedding Meshes on the Star Graph

We develop algorithms for mapping n-dimensional meshes on a star graph of degree n with expansion 1 and dilation 3. We show that an n-degree star graph can efficiently simulate an n-dimensional mesh.     

A locally sensitive method for cluster analysis

In this paper a new method of mode separation is proposed. The method is based on mapping of data points from the N-dimensional space onto a sequence so that the majority of points from each mode become successive elements of the sequence. The intervals of points in the sequence belonging to the respective modes of the p.d.f. are then determined from a function generated on this sequence. The nuclei of the modes formed by the elements of these intervals are then used to obtain separating surfaces between the modes and so to partition the data set with multimodal probability density function into unimodal subsets.     

Core zone scatterplots: A new approach to feature extraction for visual displays

This paper presents a new scheme for mapping high dimensional data onto two-dimensional viewing spaces. The mapping procedure is carried out in two stages. In the first stage, the fuzzy c-means (FCM) algorithm is applied to the N-dimensional data to find membership functions of clusters in the data. Core subsets are then selected from the original data based upon threshold values applied to the membership functions found by FCM. In the second stage feature vectors in the selected “core” subsets are submitted to various feature extraction mappings, which yield scatterplots of the image points in 2D space. The proposed approach has two significant advantages over many previous schemes. First, changes in the core structure imposed on the original data under feature extraction can be used to gauge the relative quality of competing extraction techniques. And second, the cores provide a way to generalize almost any known method, resulting in new extraction algorithms. We also discuss various ways to color the selected data that enhance the 2D display. Our approach incorporates a means for assessing the “quality” of the 2D display via parameters which provide an evaluation of (i) the validity of clusters in the original data set and (ii) the relative ability of various extraction mappings to preserve certain well-defined structural properties of the original data. The feasibility of our approach is illustrated using two sets of data: the well known Iris data; and a set of flow cytometric data. Color displays are used to visually assess scatterplot configurations in 2-space.     

Nontidal wetland mapping in South Carolina using airborne multispectral scanner data

High resolution multispectral scanner (MSS) imagery of Savannah River nontidal wetlands were analyzed to identify 1) useful spectral bands for discriminating among National Wetland Inventory classes, 2) where the classes cluster in n-dimensional feature space, and 3) what wetland classification accuracies can be expected. Spectral measurements in the green (0.55–0.60 μm), red (0.65–0.70 μm), and near-infrared wavelengths (0.70–0.79 μm and 0.92–1.10 μm) provided the most useful information. Emergent marsh (both persistent and nonpersistent), scrub-shrub, mixed deciduous swamp forest, and mixed deciduous upland forest were found to cluster in somewhat predictable regions of 2- and 3-dimensional feature space. The overall classification accuracy of the Steel Creek delta study area was 83% and was assessed by comparing the remote sensing derived thematic map with 1325 linear meters of transects sampled in situ. These results suggest that high resolution aircraft MSS data can provide detailed vegetation type information for mapping both thermally affected and rejuvenating nontidal wetland in the South Carolina Savannah River Swamp System.     

On the construction and display of a polytopal mesh for the N-dimensional hypercube and (N + 1) simplex

By considering the analytical properties of polytopes it is possible to design a general data structure, a polytopal mesh, to represent such N-dimensional objects. Further investigation of the N-dimensional hypercube leads to the construction of a ternary code for representing the hypercube and the interconnection between levels of the polytopal mesh. This technique has been extended to other convex polytopes and specific examples of the N-dimensional cross polytope and simplex are given. Various projection techniques are used to display the convex polytopes on a two dimensional viewport.     

Locating,characterizing and computing the stationary points of a function

A method for the localization, characterization and computation of the stationary points of a continuously differentiable real-valued function ofn variables is presented. It is based on the combinatorial topology concept of the degree of a mapping associated with an oriented polyhedron. The method consists of two principal steps: (i) localization (and computation if required) of a stationary point in ann-dimensional polyhedron; (ii) characterization of a stationary point as a minimum, maximum or saddle point. The method requires only the signs of gradient values to be correct and it can be successfully applied to problems with imprecise values.     

Graph-based representations of point clouds

This paper introduces a skeletal representation, called Point Cloud Graph, that generalizes the definition of the Reeb graph to arbitrary point clouds sampled from m-dimensional manifolds embedded in the d-dimensional space. The proposed algorithm is easy to implement and the graph representation yields to an effective abstraction of the data. Finally, we present experimental results on point-sampled surfaces and volumetric data that show the robustness of the Point Cloud Graph to non-uniform point distributions and its usefulness for shape comparison.     

基于四元索引结构和SQL语言的XPath优化方案

针对五元索引结构在编码上的不足,提出了更为紧凑的四元索引结构.基于该结构扩展了SQL语言,根据XML数据的底层结构实现了扩展的SQL运算符,设计了基于SQL语言的XPath优化方案.实验表明,基于四元索引结构的优化方案在性能上有了显著改善.     

Refinements to nearest-neighbor searching ink-dimensional trees

This note presents a simplification and generalization of an algorithm for searchingk-dimensional trees for nearest neighbors reported by Friedmanet al [3]. If the distance between records is measured usingL ₂ , the Euclidean norm, the data structure used by the algorithm to determine the bounds of the search space can be simplified to a single number. Moreover, because distance measurements inL ₂ are rotationally invariant, the algorithm can be generalized to allow a partition plane to have an arbitrary orientation, rather than insisting that it be perpendicular to a coordinate axis, as in the original algorithm. When ak-dimensional tree is built, this plane can be found from the principal eigenvector of the covariance matrix of the records to be partitioned. These techniques and others yield variants ofk-dimensional trees customized for specific applications. It is wrong to assume thatk-dimensional trees guarantee that a nearest-neighbor query completes in logarithmic expected time. For smallk, logarithmic behavior is observed on all but tiny trees. However, for largerk, logarithmic behavior is achievable only with extremely large numbers of records. Fork = 16, a search of ak-dimensional tree of 76,000 records examines almost every record.     

A new approach to rectangle intersections part I

Rectangle intersections involving rectilinearly-oriented (hyper-) rectangles in d-dimensional real space are examined from two points of view. First, a data structure is developed which is efficient in time and space and allows us to report all d-dimensional rectangles stored which intersect a d-dimensional query rectangle. Second, in Part II, a slightly modified version of this new data structure is applied to report all intersecting pairs of rectangles of a given set. This approach yields a solution which is optimal in time and space for planar rectangles and reasonable in higher dimensions.     

On time mapping of uniform dependence algorithms into lowerdimensional processor arrays

Most existing methods of mapping algorithms into processor arrays are restricted to the case where n-dimensional algorithms, or algorithms with n nested loops, are mapped into (n-1)-dimensional arrays. However, in practice, it is interesting to map n-dimensional algorithms into (k-1)-dimensional arrays where k<n. A computational conflict occurs if two or more computations of an algorithm are mapped into the same execution time. Based on the Hermite normal form of the mapping matrix, necessary and sufficient conditions are derived to identify mapping without computational conflicts. These conditions are used to find time mappings of n-dimensional algorithms into (k-1)-dimensional arrays, k<n , without computational conflicts. For some applications, the mapping is time-optimal     

Tree and building detection in dense urban environments using automated processing of IKONOS image and LiDAR data

The automated detection and reconstruction of artificial structures, larger than 10 m² in area using high resolution satellite images and Light Detection and Ranging (LiDAR) data through 3-dimensional shapes and/or 2-dimensional boundaries is described here. Additionally, it is demonstrated how individual tree crowns have been detected with more than 90% accuracy in very dense urban environments from very high-resolution images and range data. Pre-existing machine vision algorithms and techniques were modified and updated for this particular application to building detection within dense urban areas. All products from such procedures have not only been demonstrated with a significant areal coverage but have also been quantitatively assessed against manually obtained and third party mapping data. Accuracies of around 85% have been achieved for building detection and almost 95% for tree crown detection.     

Scheduling Functions for Spatiotemporal Mapping of d-Dimensional Algorithms with Homogeneous Dependences on (d-2)-Dimensional Parallel Architectures

A formalized method is proposed for construction of scheduling functions for spatiotemporal mapping of d-dimensional algorithms represented by systems of homogeneous recurrence equations on (d-2)-dimensional parallel architectures. Basic operations of the algorithms are scheduled separately by means of functions with rational coefficients.     

Embeddings of Hypercubes and Grids into de Bruijn Graphs

An embedding of a graph G into a graph H is an injective mapping f from the vertices of G into the vertices of H together with a mapping P_f of edges of G into paths in H. The dilation of the embedding is tile maximum taken over all the lengths of the paths P_f(xy) associated with the edges xy of G. We show that it is possible to embed a D-dimensional hypercube into the binary de Bruijn graph of the same order and diameter with dilation at most [D/2]. Similarly a majority of planar grids can be embedded into a binary de Bruijn graph of the same or nearly the same order with dilation at most [D/2] where D is the diameter of the de Bruijn graph.     

基于ERDAS的三维地形景观图制作——以甘肃省敦煌市鸣沙山地形为例

简单介绍了DRG数据和DEM数据的获取方法,对如何利用已有的DRG数据和DEM数据制作三维地形景观图的方法、步骤进行详细的介绍,阐述了三维地形景观图是一种由基础测绘数字产品相互组合而形成的专题地图产品,是一种新型的复合测绘产品。并对三维地形景观图的应用前景作了展望。     

Real-time recognition of two-dimensional tapes by cellular automata

We introduce an n-dimensional cellular automaton (n-BCA) which accepts (n + 1)-dimensional tapes in real time. Here we regard an (n + 1)-dimensional tape as a time sequence of n-dimensional tapes, and we say that an (n + 1)-dimensional tape is accepted by an n-BCA if a final-state configuration of the acceptor belongs to a predetermined set of n-dimensional words. We state some features of the sets of 2-dimensional tapes accepted by deterministic 1-BCA's (1-DBCA's), including closure properties. For the unary input alphabet, we obtain that 1-DBCA's can recognize every set of tapes each of which has length represented by a polynomial in its width. For an arbitrary input alphabet, we obtain that the class of languages each of which consists of all the ith rows of 2-dimensional tapes accepted by a 1-DBCA coincides with the class of context-sensitive languages. For n ? 2, we show that a language not containing the empty word is recursively enumerable if and only if it is the set of top rows of (n + 1)-dimensional tapes accepted by an n-DBCA.     

Partitioning and mapping of nested loops for linear array multicomputers

In distributed-memory multicomputers, minimizing interprocessor communication is the key to the efficient execution of parallel programs. In order to reduce the amount of communication overhead, parallel programs on multicomputers must be carefully scheduled by parallelizing compilers. This paper proposes some compilation techniques for partitioning and mapping nested loops with constant data dependences onto linear array multicomputers. First, a systematic partition strategy is proposed to project ann-dimensional computational structure, representing ann-nested loop, onto a line to form a one-dimensional projected structure with low communication overhead. Then, a mapping algorithm is proposed for mapping the partitioned loops onto linear arrays in a way that balances the workload and minimizes the communication cost among processors. Finally, parallel execution codes can be automatically generated for such linear array multicomputers.     

Discernible visualization of high dimensional data using label information

Visualization methods could significantly improve the outcome of automated knowledge discovery systems by involving human judgment. Star coordinate is a visualization technique that maps k-dimensional data onto a circle using a set of axes sharing the same origin at the center of the circle. It provides the users with the ability to adjust this mapping, through scaling and rotating of the axes, until no mapped point-clouds (clusters) overlap one another. In this state, similar groups of data are easily detectable. However an effective adjustment could be a difficult or even an impossible task for the user in high dimensions. This is specially the case when the input space dimension is about 50 or more.In this paper, we propose a novel method toward automatic axes adjustment for high dimensional data in Star Coordinate visualization method. This method finds the best two-dimensional view point that minimizes intra-cluster distances while keeping the inter-cluster distances as large as possible by using label information. We call this view point a discernible visualization, where clusters are easily detectable by human eye. The label information could be provided by the user or could be the result of performing a conventional clustering method over the input data. The proposed approach optimizes the Star Coordinate representation by formulating the problem as a maximization of a Fisher discriminant. Therefore the problem has a unique global solution and polynomial time complexity. We also prove that manipulating the scaling factor alone is effective enough for creating any given visualization mapping. Moreover it is showed that k-dimensional data visualization can be modeled as an eigenvalue problem. Using this approach, an optimal axes adjustment in the Star Coordinate method for high dimensional data can be achieved without any user intervention. The experimental results demonstrate the effectiveness of the proposed approach in terms of accuracy and performance.     

Structural and dynamic insights into the C-terminal extension of cysteine proteinase B from Leishmania amazonensis

Cysteine proteinase B (CPB) is a significant virulence factor for Leishmania infections. Upon processing from its zymogen form, it happens a release of the immunomodulatory CPB C-terminal extension (cyspep) into the cytoplasm of the macrophage. Epitopes derived from this fragment were shown to influence the proportion of lymphocytes CD8+ upon infection, favoring the parasite escaping from the host́s immune system. At present, there is no available structural data of cyspep, which impairs a proper understanding of its biological functions. Here, we attempted to build molecular models for this fragment and subsequently evaluate their stabilities in aqueous solution from molecular dynamics simulations analysis. Characterization of our models obtained with distinct techniques (comparative modeling, threading, and ab initio) indicates a prevalence of β−sheets in agreement with consensus secondary structure predictions. Simulation data supported this finding since the formation of new strands, along with a rapid disruption of helical content, were observed. Overall, this study provides a rationalization of epitope mapping data and an improved understanding of cyspep antigenicity.     

Nasseh method to visualize high-dimensional data

Today’s ever-increasing application of high-dimensional data sets makes it necessary to find a way to fully comprehend them. One of these ways is visualizing data sets. However, visualizing more than 3-dimensional data sets in a fathomable way has always been a serious challenge for researchers in this field. There are some visualizing methods already available such as parallel coordinates, scatter plot matrix, RadViz, bubble charts, heatmaps, Sammon mapping and self organizing maps. In this paper, an axis-based method (called Nasseh method) is introduced in which familiar elements of visualization of 1-, 2- and 3-dimensional data sets are used to visualize higher dimensional data sets so that it will be easier to explore the data sets in the corresponding dimensions. Nasseh method can be used in many applications from illustrating points in high-dimensional geometry to visualizing estimated Pareto-fronts for many-objective optimization problems.