Clueless Fundatma

I've been studying up Gaussian process modeling for machine learning. For someone seeing these concepts for the first time, I would r...

The mean-squared dislacement of a particle is defined simply as, \[\rho(t) = \langle r^2(t) \rangle = \int c(r) p(r,t) dr,\] where \(c(r) =...

In the previous posts ( 1 and 2 ), we wrote down the probability or concentration distribution of a bunch of Brownian diffusors initially ...

In the previous post , we saw how the probability distribution \(p(x,N)\) after \(N\) random steps on a unit lattice is given by, \[p(x, N)...

Consider a particle, initially at the origin, jumping around randomly on a 1D lattice. The particle tosses a fair coin, and decides to jump...

Suppose you have a large "sectioned" text file which looks like the following > cat bigfile.txt data1 1 2 3 data2 11 ...

Google Ngram Viewer allows us to visualize popularity of keywords as a function of time. It uses books archived on Google Books as its cor...

John D. Cook writes about a useful integration trick by rewriting trigonometric functions as complex variables. He recasts the integral \[\...

The total energy of a system can be decomposed into kinetic and potential parts: \[E = K + U.\] Using the thermodynamic relation, \[p = -...

Consider a pairwise potential, such as the Lennard Jones potential, \[U(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\...

Let \(\mathbf{A}\) be an \(n \times n\) matrix. Define the disks (i.e., circles) in the complex plane, for \(i = 1, 2,...,n\), by \[\mat...

I've been teaching myself some liquid state theory for a coarse-graining problem I am interested in. The classic "Theory of Simp...

In preparation for a language and platform agnostic course on Markov Chain Monte Carlo, I compiled links to random number generators (in ad...

Finally, I decided to compile a set of commonly used (by me) SymPy commands. Since Blogger's platform is somewhat unfriendly, I'm...

Continuing from the previous post , let us look at how to do subplots in Veusz. It's elementary, really! In this tutorial, I imported...

Over the past six months, I've pretty much completed the transition from Grace to Veusz , as my primary graphing software, for journal-...

Consider a set of n data-points \(\{ (w_1, R_1), (w_2, R_2), ..., (w_n, R_n) \}\), where w  is the weight, and R  is the observed data. We...

In a MCMC seminar that Peter and I run, we were recently discussing slice sampling . Here is an overview from Radford Neal himself (open ...

I wanted to put together four posts I did on molecular weight distributions (MWD) just for future reference: The relationship between siz...

Teacher : We now know how to rotate a vector \(u\) counter-clockwise by an angle \(\theta\) using a rotation matrix \(Q\). In this lesson,...