On the Topology and Geometry of Spaces of Affine Shapes

We define the space of affine shapes of k points in R ⁿ to be the topological quotient of (R ⁿ ) ^k modulo the natural action of the affine group of R ⁿ . These spaces arise naturally in many image-processing applications, and despite having poor separation properties, have some topological and geometric properties reminiscent of the more familiar Procrustes shape spaces Σ _n ^k in which one identifies configurations related by an orientation-preserving Euclidean similarity transformation. We examine the topology of the connected, non-Hausdorff spaces Sh _n ^k in detail. Each Sh _n ^k is a disjoint union of naturally ordered strata, each of which is homeomorphic in the relative topology to a Grassmannian, and we show how the strata are attached to each other. The top stratum carries a natural Riemannian metric, which we compute explicitly for k>n, expressing the metric purely in terms of “pre-shape” data, i.e. configurations of k points in R ⁿ .     

Statistical Modeling of the 3D Geometry and Topology of Botanical Trees

We propose a framework for statistical modeling of the 3D geometry and topology of botanical trees. We treat botanical trees as points in a tree‐shape space equipped with a proper metric that captures the geometric and the topological differences between trees. Geodesics in the tree‐shape space correspond to the optimal sequence of deformations, i.e. bending, stretching, and topological changes, which align one tree onto another. In this way, the 3D tree modeling and synthesis problem becomes a problem of exploring the tree‐shape space either in a controlled fashion, using statistical regression, or randomly by sampling from probability distributions fitted to populations in the tree‐shape space. We show how to use this framework for (1) computing statistical summaries, e.g. the mean and modes of variations, of a population of botanical trees, (2) synthesizing random instances of botanical trees from probability distributions fitted to a population of botanical trees, and (3) modeling, interactively, 3D botanical trees using a simple sketching interface. The approach is fast and only requires as input 3D botanical tree models with a known upright orientation.     

Concurrency in Ada and multicomputers

Implementation of Ada's parallel tasks on a multicomputer architecture requires additional communication and naming overhead because tasks can operate on shared data via global variables and pointers. This increases the complexity of implementing Ada and has a negative impact on program understandability.     

Concurrency in programming languages: A survey

This paper surveys concurrency issues of programming languages. The evolution of these issues is analyzed in the context of the evolution of other language concepts, such as data and control abstraction.Specific concurrency concepts discussed in the paper include: granularity of parallelism, degree of parallelism, synchronization and communication, and physical distribution. The review of the problems of synchronization and communication includes semaphores, messages and mailboxes, and monitors.Concurrency aspects of ADA are also presented as a case study of a state-of-the-art programming language.     

基于博弈论的多跳无线网络拓扑结构控制

为了构建低耗能、高连通性、低干扰并具有合理路由的多跳无线网络,应用基于博弈论的网络拓扑结构控制解决方案,为节点设计了一种新颖的收益函数。理论分析表明,根据此收益函数,网络将收敛于一个理想的稳定状态（纳什均衡点）,并通过最佳响应算法可获得该稳定状态。仿真结果显示,应用此方案和收益函数进行拓扑控制能形成性能良好的网络。     

Oval Domes: History,Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word “oval” comes from the Latin ovum, egg. The present paper contains an outline of the origin and application of the oval in historical architecture; a discussion of the spatial geometry of oval domes, that is, the different methods employed to lay them out; a brief exposition of the mechanics of oval arches and domes; and a final discussion of the role of geometry in oval arch and dome design.