Modeling Principles Almost all, if not all, applied science is based on the idea of a model. There are problems in the real world, and we would like to create a theory to solve such problems. One of the pillars or the main foundation of quantitative modeling is its effectiveness. But how can a model be effective? By demonstrating that it is simple, reproducible, and applicable in other areas of knowledge.

Previously I wrote about latin squares and set a puzzle. We can demonstrate this for an n x n latin square where n = 12 In the above images, the normalised latin square only has 12 different pairs out of a possible 66. The density plot shows the pairings in the lower triangle, grey represents 0. A randomly generated latin square (where all rows and all columns feature 1 to 12 exactly once) is shown where all possible pairs are captured.

This post has been in my drafts folder for a while. With the World Cup here, it’s time to post it! It’s a rule that a 3D assembly of hexagons must have at least twelve pentagons in order to be a closed polyhedral shape. This post takes a look at why this is true. First, some examples from nature. The stinkhorn fungus Clathrus ruber , has a largely hexagonal layout, with pentagons inserted.

Many projects in the lab involve quantifying circular objects. Microtubules, vesicles and so on are approximately circular in cross section. This quick post is about how to find the diameter of these objects using a computer. So how do you measure the diameter of an object that is approximately circular? Well, if it was circular you would measure the distance from one edge to the other, crossing the centre of the object.

To validate our analyses, I’ve been using randomisation to show that the results we see would not arise due to chance. For example, the location of pixels in an image can be randomised and the analysis rerun to see if – for example – there is still colocalisation. A recent task meant randomising live cell movies in the time dimension , where two channels were being correlated with one another.