This paper develops techniques to study the asymptotic distribution of number descents in random permutations. We relax an assumption Berry-Esseen theorem Bolthausen (1982) extend theorem's scope martingale differences time-dependent variances. present its applications other combinatorial statistics as they satisfy certain recurrence relation conditions. These include inversions, signed permuta...

We propose a class of very simple modifications gradient descent and stochastic leveraging Laplacian smoothing. show that when applied to large variety machine learning problems, ranging from logistic regression deep neural nets, the proposed surrogates can dramatically reduce variance, allow take larger step size, improve generalization accuracy. The methods only involve multiplying usual (sto...

the myth of the descent of adam, with all its complexities, has being preoccupied the mind of human kind from the very beginning stages of creation. the holy books of torah, bible and quran have each paid to different angles of this legend. studying the modern poetry, it can be found that the contemporary poets have been under the influence of quran and have used the teachings of old and new te...

The presence of speckle in ultrasound images makes it hard to segment them using active contours. Speckle causes the energy function of the active contours to have many local minima, and the gradient descent procedure used for evolving the contour gets trapped in these minima. A new algorithm, called tunnelling descent, is proposed in this paper for evolving active contours. Tunnelling descent ...