Data Structures and Algorithms

Image Deblurring: a Class of Matrices Approximating Toeplitz Matrices

Authors: Antonio Boccuto, Ivan Gerace, Valentina Giorgetti
Comments: 39 Pages.

We deal with the image deblurring problem. We assume that the blur mask has large dimensions. To restore the images, we propose a GNC-type technique, in which a convex approximation of the energy function is first minimized. The computational cost of the GNC algorithm depends strongly on the cost of such a first minimization. So, we propose of approximating the Toeplitz symmetric matrices in the blur operator by means of suitable matrices. Such matrices are chosen in a class of matrices which can be expressed as a direct sum between a circulant and a reverse circulant matrix.
Category: Data Structures and Algorithms

Recovery of 1990s Emails from Dr Michael Lennon

Authors: Sunny Daniels
Comments: 14 Pages. "Computers and Society" would appear to be the most appropriate arXiv category for this article, but there does not seem to be a corresponding category in viXra.

I have an old computer, probably manufactured in the 1990s, with e-mails from the late Dr Michael Lennon of Auckland University (passed away in 1999) on its hard drive. I think that these e-mails might be of significant historical interest to mathematicians (and probably others) because of the significant contribution that I believe Dr Michael Lennon made (in the 1970s I believe) to the knot theory breakthrough in the 1980s that resulted in the New Zealand mathematician Sir Vaughan Jones (who passed away in 2020 I believe) being awarded a Fields Medal in 1990. Because of the age of this computer and its hard drive, and the possible historical value of these old e-mails from Dr Michael Lennon, I wish to try to extract these e-mails from this old computer in such a way as to minimise the probability of triggering any hardware or software failure that could endanger this old data. I propose a method involving DTMF tones and also an alternative method involving a data logger attached to the serial port of this old computer. I would appreciate feedback on these proposed methods from people knowledable in this area (extraction of valuable data from possibly unreliable old computers) before attempting to go any further with the extraction process.
Category: Data Structures and Algorithms

The Need for Speed: Julia Vs. Python

Authors: Mason White
Comments: 6 Pages.

In a world that is dominated by speed and instant gratification, it comes as no surprise that the technologies that are necessary to power applications also have to be as fast as possible. Currently, the programming language Python is the ruler of the programming world. Python is being used to program everything from web applications to advanced AI systems. However, in recent years a challenger has emerged that is attempting to dethrone Python. Julia is a new programming language that is touted as a Python killer. Sporting an expressive syntax and a JIT compilation using LLVM it has the speed of C++ with the development feel of Python. Though it is often considered faster than Python there are several areas that most studies ignore such as code styling and general program architecture. As such, this study looks at the speeds of basic functionalities such as for loops, printing basic math equations to the console, and if statements of both Python and Julia to determine just how much faster Julia is. By only studying the listed commands all bias to architecture and coding style can be mitigated or eliminated and a true understanding of how much faster Julia is can be determined.
Category: Data Structures and Algorithms

Code Comments: How to Properly Comment Code

Authors: Mason White
Comments: 6 Pages.

A good codebase is a well-documented codebase. Many scientific programs are being developed by scientists as opposed to formally trained developers. As such, the need for scientists to know how to properly document code is growing. A well-documented codebase allows scientists to write better, easy to understand code that will ultimately free up resources that can be allocated for more productive tasks such as conducting their research as opposed to spending countless hours trying to modify a codebase that needs to meet new requirements. This document will give a brief tutorial on how to properly write code comments as well as API-level documentation that will make scientific software easier to understand and much more modifiable in the future.
Category: Data Structures and Algorithms

Вычисление спектров гармонических колебаний при помощи Метода Наименьших Квадратов
Calculation of Harmonic Oscillation Spectra Using the Least Squares Method. (Ru)

Authors: A. V. Antipin
Comments: 9 Pages. Это статья на РУССКОМ ЯЗЫКЕ.

Для определения периода и фазы колебаний, присутствующих в экспериментальных данных, разработан оригинальный компьютерный алгоритм, использующий метод полного перебора моделей, получаемых Методом Наименьших Квадратов (МНК). Отличительная черта алгоритма – возможность использовать исходные данные с пропусками, с произвольно расположенными по оси Х отсчётами, а также отсутствие необходимости предварительной подготовки данных в силу возможности задавать произвольные модели для МНК.

To determine the period and phase of the oscillations present in the experimental data, an original computer algorithm has been developed using the method of full iteration of models obtained by the Least Squares Method (LSM). A distinctive feature of the algorithm is the ability to use source data with omissions, with samples arbitrarily arranged along the X axis, as well as the absence of the need for preliminary data preparation due to the possibility of setting arbitrary models for LSM.
Category: Data Structures and Algorithms