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Author: Rachel Traylor

Exploiting Chemistry for Better Packet Flow Management 2: Formal Model

Exploiting Chemistry for Better Packet Flow Management 2: Formal Model

This post is the second breaking down a report/review of a technical report by Meyer and Tschudin [11] that modifies the formal notion of an artificial chemistry and creates an artificial packets chemistry with the goal of designing better flow management by exploiting the natural behavior of chemical reactions.    Note: for those more interested…

Exploiting Chemistry for Better Packet Flow Management 1: Introduction

Exploiting Chemistry for Better Packet Flow Management 1: Introduction

Perhaps the phrase "don't reinvent the wheel" is overused. However, many newer disciplines, particularly in the technology sector, seem to insist on it. One thing physical engineers learned long ago was to study the world around them, work with it, and emulate it in their designs. Network engineering should be no different. In a technical…

Expecting the Unexpected: Borel’s Paradox

Expecting the Unexpected: Borel’s Paradox

One of the best ways to shorten a proof in statistics or probability is to use conditioning arguments. I myself have used the Law of Total Probability extensively in my work, as well as other conditioning arguments in my PhD dissertation. Like many things in mathematics, there are subtleties that, if ignored, can cause quite…

Using Boolean Algebra to Find all Maximal Independent Sets in a Graph

Using Boolean Algebra to Find all Maximal Independent Sets in a Graph

Graph theory may be one of the most widely applicable topics I've seen in mathematics. It's used in chemistry, coding theory, operations research, electrical and network engineering, and so many other places. The subject is mainly credited to have begun with the famous  Seven Bridges of Königsberg problem posed by Leonard Euler in 1736. Frank Harary…

Beyond Cookbook Mathematics, Part 2

Beyond Cookbook Mathematics, Part 2

The previous article discussed the importance of definitions to mathematical thought. We looked at a definition (of an end-vertex in a graph), and picked it apart by finding multiple ways to look at it. We also directly used the definition in a practical manner to find “weak links” in a network. This time, we’ll look…

Beyond Cookbook Mathematics, Part 1

Beyond Cookbook Mathematics, Part 1

This post is due to the requests of several independent engineers and programmers. They expressed disappointment at their mathematics education and its failure to impart a deeper understanding of the formulas and algorithms they were taught to use.  This also reflects my observations of teaching university mathematics over the years. I started as a TA…

The Hathlor Classification System

The Hathlor Classification System

Many researchers have their own libraries, and The Math Citadel is no different. Both Jason and I have spent many hours buried in the shelves of bookstores new and used, the stacks of university library shelves, and the rows of books in public libraries across four states now. During this time, we've amassed our own…

On the Essential Nature of Foundations

On the Essential Nature of Foundations

We get asked frequently a valid question: why fund our research? Why fund mathematics research, when I can't see what the finished product will be, and you can't give me a guaranteed code library next quarter? I'm going to use an analogy of building and stray from my usual temptation to use math analogies. Every…

Paper Review: Active Queue Management with Non-Linear Packet Dropping Function

Paper Review: Active Queue Management with Non-Linear Packet Dropping Function

As promised in the previous article, I plan to review Reference 2, Active Queue Management with Non-Linear Packet Dropping Function, by D. Augustyn, A. Domanski, and J. Domanska, published in HET-NETs 2010, which discusses a change in the structure of the packet drop probability function using the average queue length in a buffer. I mentioned previously that…

Networking Mathematics: Random Early Detection and TCP synchronization

Networking Mathematics: Random Early Detection and TCP synchronization

Computer networks are something most of us take for granted--speed, reliability, availability are expectations. In fact, network problems tend to make us very angry, whether it's dropped packets (yielding jittery Skype calls), congestion (that huge game download eating all the bandwidth), or simply a network outage. There's an awful lot going on underneath the hood…