There is a prevalent myth in Computer Vision that the gradient weighted algebraic distance, the so-called “Sampson Error,” is a first order approximation of the distance from a point to a curve or surface. In truth, however, it is the exact geometric distance to the first order approximation of the curve. The linguistic difference is subtle, but mathematically, the two statements are at odds. I...

We explore the relationship between R. W. Shephard's input distance function (``Cost and Production Functions,'' Princeton Univ. Press, Princeton, 1953) and D. G. Luenberger's benefit function (J. Math. Econ. 21 (1992a), 461 481). We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize technologies in bo...

Algorithms for computing similarity joins in MapReduce were offered in [2]. Similarity joins ask to find input pairs that are within a certain distance d according to some distance measure. Here we explore the “anchor-points algorithm” of [2]. We continue looking at Hamming distance, and show that the method of that paper can be improved; in particular, if we want to find strings within Hamming...

Algorithms for computing similarity joins in MapReduce were offered in [2]. Similarity joins ask to find input pairs that are within a certain distance d according to some distance measure. Here we explore the “anchor-points algorithm” of [2]. We continue looking at Hamming distance, and show that the method of that paper can be improved; in particular, if we want to find strings within Hamming...

We propose a new method for computing the tree edit distance between two unordered trees by problem encoding. Our method transforms an instance of the computation into an instance of some IP problems and solves it by an efficient IP solver. The tree edit distance is defined as the minimum cost of a sequence of edit operations (either substitution, deletion, or insertion) to transform a tree int...

This paper describes an application of agent-based modeling to investigate the effect of a distance-based transaction cost on trade. Long-distance trade is rapidly increasing, but may ultimately be constrained by our ability to move material goods between sellers and buyers. Unlike information exchange, trade in material goods is dependent on the price of oil and vulnerable to future scarcities...

We consider indexing and range searching in metric spaces. The best method known is AESA, in practice requiring the fewest number of distance evaluations to answer range queries. The problem with AESA is its space complexity, requiring storage for Θ(n) distance values to index n objects. We give several methods to reduce this cost. The main observation is that exact distance values are not need...

Gliding is thought to be an economical form of locomotion. However, few data on the climbing and gliding of free-ranging gliding mammals are available. This study employed an animal-borne three-dimensional acceleration data-logging system to collect continuous data on the climbing and gliding of free-ranging Malayan colugos, Galeopterus variegatus. We combined these movement data with empirical...

We investigate a new research area: we are interested in the ultimate ther-modynamic cost of computing from x to y. Other than its fundamental importance , such research has potential implications in miniaturization of VLSI chips and applications in pattern recognition. It turns out that the theory of thermodynamic cost of computation can be axiomatically developed. Our fundamental theorem conn...