It is shown that if { p j } is a discrete density function on the integers with support contained in {0 , 1 , ... , d }, and p 0 > 0, p 1 > 0, p d − 1 > 0, p d > 0, then there is an n 0 such that the n-fold convolution { p j } *n is unimodal for all n ≥ n 0 . Examples show that this result is nearly best possible, but weaker results are proved under less restrictive assumptions. On the Unimodal...

It is natural to ask, given a permutation with no three-term ascending subsequence, at what index the first ascent occurs. We shall show, using both a recursion and a bijection, that the number of 123-avoiding permutations at which the first ascent occurs at positions k, k + 1 is given by the k-fold Catalan convolution Cn,k. For 1  k  n, Cn,k is also seen to enumerate the number of 123-avoidi...

We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n + 1)-th order differential equation and give a simple method for obtaining the differential equation. Also we determine the exponents of the differential equation and derive a bound for the degree of the polynomials, whic...

Computer vision approaches, such as deep learning, potentially offer a range of benefits to entomology, particularly for the image-based identification taxa. An experiment was conducted gauge ability convolution neural network (CNN) identify genera Braconidae from images forewings. A learning CNN trained via transfer small set 488 57 genera. Three-fold cross-validation achieved an accuracy 96.7...

Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class Gp(N) of random graphs, the corresponding ßooding time is investigated. The ßooding time TN(p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the ßooding time TN(p) converges in distribution to the two-fold convolution Λ(2∗) of the Gumbel distribut...

This thesis studies theoretical and practical aspects of the computation of planar polygonal Minkowski sums via convolution methods. In particular we prove the “Convolution Theorem”, which is fundamental to convolution based methods, for the case of simple polygons. To the best of our knowledge this is the first complete proof for this case. Moreover, we describe a complete, exact and efficient...

In this paper, we present a simple and modularized neural network architecture, named primal-dual group convolutional neural networks (PDGCNets). The main point lies in a novel building block, a pair of two successive group convolutions: primal group convolution and dual group convolution. The two group convolutions are complementary: (i) the convolution on each primal partition in primal group...

In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving time dependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution variants of the conjugate gradient algorithm and two convolution variants of the GMRES algorithm and analyze...

Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending CNNs to the general spatial domain. Although various types of graph and geometric convolution methods have been proposed, their connections to traditional 2D-convolution are not wel...