Aspects of the Facet-Edge Data Structure for the Construction of Voronoi Cells

The construction of Voronoi diagrams has two main aspects: The construction algorithm and the data structure. For the construction of planar Voronoi diagrams e.g. the well known plane sweep algorithm can be applied. Another efficient method is the incremental construction of the Delaunay triangulation by using the quad-edge data structure. Within this data structure the Delaunay triangulation is treated as a planar graph. Incremental construction implies that manipulations of the triangulation are allowed. Its Voronoi diagram is obtained simply by accessing the triangulation's dual graph. We extend this method to tree dimensions, by implementing a 3D Delaunay triangulation on the facet-edge data structure. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于倾向值匹配的干扰数据检测方法

数据中掺杂干扰数据的现象十分常见,对于随机出现的干扰数据处理,目前已有很多方法可以借鉴,但对于人为的干扰数据,若继续使用传统方法,则可能不会达到很好的效果.倾向值可以用一维数值来描述多维数据的特征,且当数据具有相近的倾向值时,其本身常常也很相似,并可能来自同一总体.因此,文章提出一种应用倾向值匹配检测干扰数据的新方法,...     

Statistical,Physical, and Computational Aspects of Massive Data Analysis and Assimilation in Atmospheric Applications

Abstract

The goals and procedures of the most data-intensive operations in atmospheric sciences, including data assimilation and fusion, are introduced. We explore specific problems that result from the expansion in observing systems from conventional to satellite borne and the corresponding transition from small, medium, and large datasets to massive datasets. The satellite data, their volumes, heterogeneity, and structure are described in specific examples. We illustrate that the atmospheric data analysis and assimilation procedures and the satellite data pose unique problems that do not exist in other applications and are not easily addressed by existing methods and tools. Existing solutions are presented and their performance with massive datasets is critically evaluated. We conclude that since the problems are interdisciplinary, a comprehensive solution must be interdisciplinary as well. We note that components of such a solution already exist in statistics, atmospheric, and computational sciences, but that in isolation they often fail to scale up to the massive data challenge. The prospects of synthesizing an interdisciplinary solution which will scale up to the massive data challenge are thus promising.     

Interference percolation

Let G be an infinite connected graph with minimum degree δ and maximum degree Δ. Let G_p be a random induced subgraph of G obtained by selecting each vertex of G independently with probability p, , and let be the induced subgraph of G_p obtained by deleting all vertices of G_p with degree greater than k in G_p. We show that if and is not too large then almost surely has no infinite component. Moreover, this result is essentially best possible since there are examples where has an infinite component (a) when , 4, or 5, and k = 3; (b) when for any δ and k = 3; and (c) when for any and . In addition, we show that if G is the d ‐dimensional lattice then almost surely has an infinite component for sufficiently large d. © 2014 Wiley Periodicals, Inc. Random Struct. Alg. 44, 399–418, 2014     

On Interference Graphs

The study of interference graphs assumes significance in the context of the study of Frequency assignment problem. By an interference graph we mean the graph whose vertices represent a transmitter and the edges denote the interference constraint between two adjacent transmitters. In this paper we probe the relationship between 2-coloring and radio labeling and the effect of its computational aspect to certain restricted class of graphs. We also indicate some possible directions for further research.     

Aspects of free analysis

We survey the analysis around the free difference quotient derivation, which is the natural derivation for variables with the highest degree of noncommutativity. The analogue of the Fourier transform is then bialgebra duality for the bialgebra with derivation-comultiplication to which the free difference quotient gives rise and which involves fully matricial analytic functions. Some of the motivation from free probability, especially free entropy and random matrices are also discussed. Dan-Virgil Voiculescu; Research supported in part by NSF Grant DMS 0501178.     

Aspects of CXXR internals

The CXXR project aims gradually to refactor the fundamental parts of the R interpreter from C into C++ whilst retaining the full functionality of the standard distribution of R. It is hoped that this will enable researchers more easily to enhance the functionality of R by allowing them to extend the interpreter’s internal C++ class hierarchy. The paper summarises progress to date and describes key aspects of the internal implementation of the CXXR where this differs from the standard interpreter. It also explains stratagems used to facilitate updating CXXR to reflect a new release of R, and examines the relative performance of CXXR and the standard interpreter.     

Aspects of Feynman Graphs

Points (vertices) and lines (edges) can be compared to the particles and waves in nature. Graphical, visual representations of objects and processes possess many properties which are quite advantageous and practically useful. Richard P. Feynman, made copious applications of the graph-theoretic language, ideas and methods for understanding the micro-world of elementary particles and their interactions. Here, we discus certain significant features of Feynman graphs or diagrams in the modern context. We make a novel observation that the CPT theorem is embedded in the space-time concepts of Feynman graphs and hence the success and precision of some the calculations of QED are in fact testament to the correctness and accuracy of this theorem.     

Computational Aspects of Irreducible Polynomials

Computational Mathematics and Mathematical Physics - We present results on testing the computation of bounds for polynomial divisors and give estimates for their heights. There are also given...     

Topological Aspects of Differential Chains

In this paper we investigate the topological properties of the space of differential chains $\,^{\prime}\mathcal{B}(U)$ defined on an open subset U of a Riemannian manifold M. We show that $\,^{\prime}\mathcal {B}(U)$ is not generally reflexive, identifying a fundamental difference between currents and differential chains. We also give several new brief (though non-constructive) definitions of the space $\,^{\prime}\mathcal{B}(U) $ , and prove that it is a separable ultrabornological (DF)-space. Differential chains are closed under dual versions of the fundamental operators of the Cartan calculus on differential forms (Harrison in Geometric Poincare lemma, Jan 2011, submitted; Operator calculus??the exterior differential complex, Jan 2011, submitted). The space has good properties, some of which are not exhibited by currents $\mathcal{B}'(U)$ or? $\mathcal{D}'(U)$ . For example, chains supported in finitely many points are dense in $\,^{\prime}\mathcal{B}(U)$ for all open U?M, but not generally in the strong dual topology of? $\mathcal{B}'(U)$ .     

Mathematical Aspects of Manpower Planning

In this paper, concepts of linear programming-in particular the Simplex algorithm and the Dual Simplex algorithm-are used within a discrete renewal model for the development of a graded population, when the transfer rates between the various grades are given, and "wastage" is replaced by suitable recruiting.The following questions are dealt with:

1. 1)
   Which population structures (i.e. partitions into grades) can be attained from a given structure, after one or more steps?
    
2. 2)
   From which structures can a given structure be attained in one or more steps?
    
3. 3)
   If the present structure as well as a desired future structure are given, can the latter be attained from the former in one or more steps? If so, how?
    
4. 4)
   The last problem is of special interest if the starting structure is identical with that to be attained and is called re-attaining after more than one step, or strictly maintaining after one step.
    

Examples are given to illustrate the procedure, and some attention is given to the possibility of alternative routes in cases (3) and (4). It is observed that if a structure is attainable (or re-attainable) after n steps, then it is not necessarily attainable (or re-attainable) after n + 1 steps.     

Algorithmic Aspects of Tree Amalgamation

The amalgamation of leaf-labeled trees into a single (super)tree that “displays” each of the input trees is an important problem in classification. We discuss various approaches to this problem and show that a simple and well-known polynomial-time algorithm can be used to solve this problem whenever the input set of trees contains a minimum size subset that uniquely determines the supertree. Our results exploit a recently established combinatorial property concerning the structure of such collections of trees.