Real Necessity: A Reply to Barnes

A Problem in Avicennas View on the Origination of the Soul and a Reply to It

A symbolic approach to some identities for Bernoulli – Barnes

The Bernoulli–Barnes polynomials are defined as a natural multidimensional extension of 21 the classical Bernoulli polynomials. Many of the properties of the Bernoulli polynomials 22 admit extensions to this new family. A specific expression involving the Bernoulli–Barnes 23 polynomials has recently appeared in the context of self-dual sequences. The work pre24 sented here provides a proof of t...

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...

A Reply to Pickering

I felt I should reply to Andy Pickering’s short Response to my long Review of his book; I did not want to leave it uncontested in the literature.1 I will pick up a couple of points from his comments to indicate just what it is that he has failed to grasp about my Review. If these points are understood, then all else falls into place. Though Pickering writes that my critical remarks ‘form a disc...

A Reply to