Reply to Cherry, Barnes and Fullman

Asymptotics and Mellin-Barnes Integrals

A catalogue record for this book is available from the British Library.

Barnes-Hut-SNE

The paper presents an O(N logN)-implementation of t-SNE — an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots and that normally runs in O(N). The new implementation uses vantage-point trees to compute sparse pairwise similarities between the input data objects, and it uses a variant of the Barnes-Hut algorithm to approximate the forces be...

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Theory of Barnes Beta distributions

A new family of probability distributions βM,N , M = 0 · · ·N, N ∈ N on the unit interval (0, 1] is defined by the Mellin transform. The Mellin transform of βM,N is characterized in terms of products of ratios of Barnes multiple gamma functions, shown to satisfy a functional equation, and a Shintani-type infinite product factorization. The distribution log βM,N is infinitely divisible. If M < N...

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