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 ...

In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a faster gradient descent method. For unconstrained convex quadratic optimization these methods can converge much faster than steepest descent. But the context of interest here ...

The purpose of this study is to analyze the performance of Back propagation algorithm with changing training patterns and the second momentum term in feed forward neural networks. This analysis is conducted on 250 different words of three small letters from the English alphabet. These words are presented to two vertical segmentation programs which are designed in MATLAB and based on portions (1...

BACKGROUND Studies have shown a clear relationship between depressive disorders and vitamin B12 deficiency. Gastroenteritis and Helicobacter pylori infections can cause vitamin B12 deficiency. Helicobacter pylori infections are not uncommon among people of Turkish descent in The Netherlands. AIM To examine the frequency of vitamin B12 deficiency in depressive patients of Turkish descent and c...

In this thesis I will describe an explicit method for performing an 8-descent on elliptic curves. First I will present some basics on descent, in particular I will give a generalization of the definition of n-coverings, which suits the needs of higher descent. Then I will sketch the classical method of 2-descent, and the two methods that are known for doing a second 2-descent, also called 4-des...

where B(v, w) = 12(Q(v + w) − Q(v) − Q(w)) is the bilinear form associated to Q. The transformation sw is linear, fixes the plane w⊥ = {v : v ⊥ w}, and acts by negation on the line through w. These properties characterize sw. We will use reflections associated to the four vectors e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1), and e1 + e2 + e3 = (1, 1, 1). The vectors e1, e2, and e3 form an ort...