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It's fairly intuitive that a model should accurately represent the data. But what exactly does that mean? Fitting the data In order for a model to be useful at all, it should reasonably fit the data. What constitutes 'reasonable' depends on the fitting method as well as the purpose of the model. Prediction If the… Continue reading Prediction and Inference in Mathematical Modeling

Big data can be intimidating, but sorting and extracting information becomes easy when a sort of mental 'algorithm' is applied. The pseudocode is in ~Matlab notation, but the basic concepts apply to any programming language. Step 1: Observe layout of raw data Raw data will have some kind of format connecting 'inputs' and 'outputs'. For… Continue reading Data sorting for noobs

The simplest way to curve fit multiple equations while conserving some parameter values is by converting the problem into matrix form. For example, for a set of two equations such as: $latex \frac{ d X(t)}{ d t}= - \alpha X(t) -\gamma Z(t)\\ \frac{ d Y(t)}{d t}=\alpha W(t)-\epsilon Y(t) $ we may write the solution matrix as: $latex… Continue reading Curve fitting to multiple equations simultaneously

Motor control with the raspberry pi is pretty simple. In addition to the pi, you may use a board such as DC+Stepper Motor HAT board from Adafruit and some stepper motors. (Here's how stepper motors work.) I have some makeshift adapters to attach the motor tubing to check valves. The motor wiring is attached to the board… Continue reading Motor Control with the Raspberry Pi