Research Papers/Topics in Applied Mathematics

FOUR AND FIVE FIGURES OF LEKAN (POWER OF BASE 5) AND ANTILEKAN (ANTIPOWER OF BASE 5) TABLES AS A TOOL FOR MATHEMATICAL COMPUTATION

This paper presents the four and five figures of Lekan (Power of base 5) and AntiLekan (Antipower of base 5) tables as a tool for mathematical computation.

Proofs for the Four Fundamental Equations of the Backpropagation and Algorithms in Feedforward Neural Networks

This paper will focus on proving the four fundamental equations of the backpropagation. Then I will show how to use this algorithm combined with the stochastic gradient descent technique to implement the network for recognizing the handwritten digits. Parts of the proof are provided by the author Michael Nielsen in his online book Neural Networks and Deep Learning. Meanwhile, this paper will provide more details of his proofs and some basic definitions of gradient.

About Crawling Scheduling Problems

Abstract This paper investigates the task of scheduling jobs across several servers in a software system similar to the Enterprise Desktop Grid. One of the features of this system is that it has a specific area of action – collects outbound hyperlinks for a given set of websites. The target set is scanned continuously (and regularly) at certain time intervals. Data obtained from previous scans are used to construct the next scanning task for the purpose of enhancing efficiency (shorte...