It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorphic to the complement of the trefoil knot in S. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given by the Rademacher symbol, which is a homogenization of the classical Dedekind symbol. The Dedekind symbol arose historically in the transformation formula of the logarithm of Dedekind’s eta function...

The orthogonal functions, specially the Rademacher and Walsh functions are being increasingly used in Digital Signal Processing (DSP). Today’s DSP applications require fast processing time in order to meet the challenges of the real time systems. State-of-the-art implementation technologies are therefore being used. This study describes the design and implementation of Rademacher and Walsh func...

We describe how the Hardy–Ramanujan–Rademacher formula can be implemented to allow the partition function p(n) to be computed with softly optimal complexity O(n) and very little overhead. A new implementation based on these techniques achieves speedups in excess of a factor 500 over previously published software and has been used by the author to calculate p(10), an exponent twice as large as i...

This paper presents theoretical analysis on the generalization ability of listwise learning-to-rank algorithms using Rademacher Average. The paper first proposes a theoretical framework for ranking and then proves a theorem which gives a generalization bound to a listwise ranking algorithm based on Rademacher Average of the class of compound functions operating on the corresponding listwise los...

We propose a new approach, multi-view Laplacian support vector machines (SVMs), for semi-supervised learning under the multiview scenario. It integrates manifold regularization and multi-view regularization into the usual formulation of SVMs and is a natural extension of SVMs from supervised learning to multi-view semi-supervised learning. The function optimization problem in a reproducing kern...