## Common Mathmatical Libraries: Computation, History, and Trust

A common complaint among engineers is that modern computers obscure the details of the complicated math they produce. We cringe when children are exalted as “knowing computers” from a young age. Bill Gosper and Richard Greenblatt had perhaps the maximum benefit to “learn computers”. They didn’t have wolfram alpha or Continue Reading

## The Hierarchical Dirichlet Process Hidden Semi-Markov Model

In my work at DARPA, I’ve been exposed to hidden Markov models in applications as diverse as temporal pattern recognition such as speech, handwriting, gesture recognition, musical score following, and bioinformatics. My background is in stochastic modeling and optimization, and hidden Markov models are a fascinating intersection between my background Continue Reading

## One Time Pad Cryptography

This was much harder than it should have been. While this is the certainly the most trivial post on crypto-math on the webs, I wanted to share my MATLAB xor code in the hope that I save someone else’s time. It is a basic property of cryptography that a one Continue Reading

## Gradient Descent

It has been awhile since I’ve studied optimization, but gradient descent is always good to brush up on. Most optimization involves derivatives. Often known as the method of steepest descent, gradient descent works by taking steps proportional to the negative of the gradient of the function at the current point. Continue Reading

## FlexEvents: WOD 3 Simulation

During a recent CrossFit competition, flex on the mall, we had to accomplish a team chipper in which we were able to pick the order of team members in order to minimize our workout time. The workout was simple: 50 burpees, 40 over the box jumps, and 30 kettle-bell snatches. Continue Reading

## Fun with Bessel Functions

Well, I certainly forget things faster than I learn them. Today is a quick review of Bessel functions and their applications to signal processing. The Bessel functions appear in lots of situations (think wave propagation and static potentials), particularly those that involve cylindrical symmetry. While special types of what would Continue Reading

## Sampling Exploration

I needed to review the Nyquistâ€“Shannon sampling theorem. The coolest thing about Nyquist is that it expresses the sample-rate in terms of the function’s bandwidth and leads to a formula for the mathematically ideal interpolation algorithm. What is sampling? Sampling is nothing more than converting a signal into a numeric Continue Reading

## Wind speed calculation

I want to know the impact of wind on endurance. So we have something like this: This gives us 8 cases of wind direction: From this we can infer that going to the center from one of the 8 directions. So an overall flight path would look like this: If Continue Reading