228 research outputs found

    Farm Animals and Their Welfare in 2000

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    Farm animals have been a traditional concern of the modern animal protection movement. In the early 1800s, when the movement emerged as a significant sociopolitical force in the United Kingdom, its first priority was protection of farm animals, with particular emphasis on cattle and horses. Subsequently priorities changed, and throughout most of the 1900s, animal protectionism in Europe and the English-speaking world focused more strongly on the use of animals for scientific research and on the rescue of abandoned or ill-treated companion animals. Today, however, with vigorous public debate over animal agriculture and its effects, farm animals are re-emerging as a major subject of humane concern

    Farm Animals and Their Welfare in 2000

    Get PDF
    Farm animals have been a traditional concern of the modern animal protection movement. In the early 1800s, when the movement emerged as a significant sociopolitical force in the United Kingdom, its first priority was protection of farm animals, with particular emphasis on cattle and horses. Subsequently priorities changed, and throughout most of the 1900s, animal protectionism in Europe and the English-speaking world focused more strongly on the use of animals for scientific research and on the rescue of abandoned or ill-treated companion animals. Today, however, with vigorous public debate over animal agriculture and its effects, farm animals are re-emerging as a major subject of humane concern

    Degree-Driven Design of Geometric Algorithms for Point Location, Proximity, and Volume Calculation

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    Correct implementation of published geometric algorithms is surprisingly difficult. Geometric algorithms are often designed for Real-RAM, a computational model that provides arbitrary precision arithmetic operations at unit cost. Actual commodity hardware provides only finite precision and may result in arithmetic errors. While the errors may seem small, if ignored, they may cause incorrect branching, which may cause an implementation to reach an undefined state, produce erroneous output, or crash. In 1999 Liotta, Preparata and Tamassia proposed that in addition to considering the resources of time and space, an algorithm designer should also consider the arithmetic precision necessary to guarantee a correct implementation. They called this design technique degree-driven algorithm design. Designers who consider the time, space, and precision for a problem up-front arrive at new solutions, gain further insight, and find simpler representations. In this thesis, I show that degree-driven design supports the development of new and robust geometric algorithms. I demonstrate this claim via several new algorithms. For n point sites on a UxU grid I consider three problems. First, I show how to compute the nearest neighbor transform in O(U^2) expected time, O(U^2) space, and double precision. Second, I show how to create a data structure in O(n log Un) expected time, O(n) expected space, and triple precision that supports O(log n) time and double precision post-office queries. Third, I show how to compute the Gabriel graph in O(n^2) time, O(n^2) space and double precision. For computing volumes of CSG models, I describe a framework that uses a minimal set of predicates that use at most five-fold precision. The framework is over 500x faster and two orders of magnitude more accurate than a Monte Carlo volume calculation algorithm.Doctor of Philosoph

    A Faithful Discretization of the Augmented Persistent Homology Transform

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    The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT such that it faithfully represents the underlying shape. We provide a discretization that is exponential in the dimension of the shape (making it Furthermore, we provide an output-sensitive algorithm; that is, the algorithm reports the discretization in time proportional to the size of the discretization. Finally, our approach relies only on knowing the heights and dimensions of topological events, meaning that it can be adapted to provide discretizations of other dimension-returning topological transforms, including the Betti curve transform

    Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams

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    Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in Rd\mathbb{R}^d, the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph -- and, more generally one-skeleton -- reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs.Comment: This work originally appeared in the 2022 proceedings of the Canadian Conference on Computational Geometry (CCCG). We have updated the proof of Theorem 2 in Appendix A for clarity and correctness. We have also corrected and clarified Section 3.2, as previously, it used slightly stricter general position assumptions than those given in Assumption

    From Curves to Words and Back Again: Geometric Computation of Minimum-Area Homotopy

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    Let γ\gamma be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if γ\gamma is self-overlapping by geometrically constructing a combinatorial word from γ\gamma. More recently, Zipei Nie, in an unpublished manuscript, computed the minimum homotopy area of γ\gamma by constructing a combinatorial word algebraically. We provide a unified framework for working with both words and determine the settings under which Blank's word and Nie's word are equivalent. Using this equivalence, we give a new geometric proof for the correctness of Nie's algorithm. Unlike previous work, our proof is constructive which allows us to naturally compute the actual homotopy that realizes the minimum area. Furthermore, we contribute to the theory of self-overlapping curves by providing the first polynomial-time algorithm to compute a self-overlapping decomposition of any closed curve γ\gamma with minimum area.Comment: 27 pages, 16 figure
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