David M. Bradley

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Historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations Much the same can be said for Euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics More recently we have been forced to consider multidimensional extensions encompassing(More)
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional(More)
Prior work has shown that features which appear to be biologically plausible as well as empirically useful can be found by sparse coding with a prior such as a laplacian (L1) that promotes sparsity. We show how smoother priors can preserve the benefits of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it(More)
The DARPA PerceptOR program implements a rigorous evaluative test program which fosters the development of field relevant outdoor mobile robots. Autonomous ground vehicles are deployed on diverse test courses throughout the USA and quantitatively evaluated on such factors as autonomy level, waypoint acquisition, failure rate, speed, and communications(More)
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the(More)
The Maximum Margin Planning (MMP) (Ratliff et al., 2006) algorithm solves imitation learning problems by learning linear mappings from features to cost functions in a planning domain. The learned policy is the result of minimum-cost planning using these cost functions. These mappings are chosen so that example policies (or trajectories) given by a teacher(More)
This paper presents a real-time implementation of a topological localization method based on matching image features. This work is supported by a unique sensor pod design that provides stand-alone sensing and computing for localizing a vehicle on a previously traveled road. We report extensive field test results from outdoor environments, with the sensor(More)
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulæ for the distribution of the sum of n non-identically distributed uniform(More)
A key challenge for autonomous navigation in cluttered outdoor environments is the reliable discrimination between obstacles that must be avoided at all costs, and lesser obstacles which the robot can drive over if necessary. Chlorophyll-rich vegetation in particular is often not an obstacle to a capable off-road vehicle, and it has long been recognized in(More)
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation (Tropp et al., 2006)) in terms of a(More)