Category: Operations Research
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Autoscoring with Matlab
While I qualified a long time ago on the M9, I never really learned to be a good shot. Now, I’m trying to learn to shoot well and wanted to automatically score my targets, keep the data, and get better. There are apps to do this, but none of them did what I wanted. One…
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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 even spreadsheets, they had to…
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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 and my more recent work…
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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 time pad must be used…
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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. Mathematically, gradient descent is defined…
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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. Each exercise had to be…
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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 later be known as Bessel…
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Sampling Exploration
I needed to review the Nyquist–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 sequence. Shannon states: If a…
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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 each grid cell is a…