In this issue, we bring three articles, first one of which is of primary interest to a researcher in probability theory, second one of which is of primary interest to faculty involved in teaching Data Structures and Algorithms (DSA) course at the Under Graduate (UG) level, and third one of which is of interest to a technologist interested in usage of modern technology for ensuring compliance with COVID 19 Standard Operating Protocol (SOP) by the general public.
Sequences of integers that follow a specific pattern have always excited the researchers who are looking for special properties they exhibit. Each member of such a sequence (also called as ‘term’) is identified by its location in the sequence. The successive terms of the sequence are generated based on an algorithm.
One particular sequence of integers that has garnered a strong reputation in its utility and ubiquity is the Fibonacci sequence. In the Fibonacci sequence, successive terms are generated as the sum of the two preceding numbers. (i.e. 0, 1, 1, 2, 3, 5,…..). If we take any two successive numbers in the Fibonacci sequence, their ratio (Xn / Xn-1) gets closer to 1.618 which is what we call the ‘golden ratio’ usually denoted as φ.
Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the Universe. The latest or maybe one of the most recent discoveries that emanated from the understanding of this Fibonacci number sequence was the discovery which proved that stress will lead to a shorter life span as it reduces the length of the telomere of our DNA. Not surprisingly, this breakthrough discovery netted the Nobel Prize in medicine in 2009.
In their article titled ‘On the Probability Distributions Induced by Integer Sequences Generated by Re- currence Relations with Positive Integer Coefficients’, the authors have explored and proved certain optimal probabilistic limit properties of Fibonacci sequence. They claim to have proved that, among the distributions induced by k th order linear recurrence equations with positive integer coefficients, the limits of the mean and the variance are maximum for those generated by second order linear recurrence relation, corresponding to the Fibonacci sequence.
In the second article titled ‘GALA: A Gamified Approach to Learning Algorithms – Exploring Basics of Algorithmic Approach’ the authors introduce an interesting game to teach UG level algorithms to UG course, (a skill expected by potential employers). They introduce an interesting game to teach algorithms more effectively.
In the third article titled ‘Technology and Keeping Social Distancing’, the author explores possible technological solutions for ensuring social distancing. The author discusses issues such as office environment, benefits of work from home culture, mode of transmission of viruses, the need for keeping air safe in offices, etc. He opines that many of our problems in handling infectious diseases is due to the fact that public health services are still working in old fashioned ways. The author also brings to the attention of readers such issues as ‘invasion of privacy’ and ‘legal hurdles’ encountered while deploying technical solutions.
I am also happy to present you this Omnibus issue bringing you all the issues of Volume 4 (2020).
Finally, we wish all our readers a safe and healthy times all through the current pandemic.