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Month: April 2018

Simulating Soundscapes Using Convolutions

Simulating Soundscapes Using Convolutions

One of the most powerful areas of electrical engineering that flourished in the 20th century is the field of signal processing. The field is broad and rich in some beautiful mathematics, but by way of introduction, here we'll take a look at some basic properties of signals and how we can use these properties to…

Sequences & Tendency: Topology Basics Pt. 2

Sequences & Tendency: Topology Basics Pt. 2

Introduction In my previous post I presented abstract topological spaces by way of two special characteristics. These properties are enough to endow a given set with vast possibilities for analysis. Fundamental to mathematical analysis of all kinds (real, complex, functional, etc.) is the sequence. We have covered the concept of sequences in some of our…

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…

Little’s Law: For Estimation Only

Little’s Law: For Estimation Only

I had been intending on writing some posts on queuing theory for a while now, as this branch is the closest to my research interests and was the spark that sent me down the road that eventually led to my PhD dissertation. Most are quite familiar with the concepts of queuing theory, at least intuitively,…

Building a Ground Floor: Topology Basics Pt. 1

Building a Ground Floor: Topology Basics Pt. 1

Like some other terms in mathematics ("algebra" comes to mind), topology is both a discipline and a mathematical object. Moreover like algebra, topology as a subject of study is at heart an artful mathematical branch devoted to generalizing existing structures like the field of real numbers for their most convenient properties. It is also a…