Neural networks may seem mysterious to most people, and thus theirs capabilities are often overestimated. However, in truth, any neural network is just a combination of elementary mathematical operations and in turn, a computational graph. In this post, I am going to show you to how to build a simple neural network with two layers for a classification problem and the math behind it. Part I here is about forward-propagation and the computational graph.

Today we are going to look at Problem 40 from the book 50 Challenging Problems in Probability by Frederick Mosteller. However, instead of solving it analytically, we are going to use the Monte Carlo method (random sampling) to solve it.

The problem goes like this:

Shuffle an ordinary deck of 52 playing cards containing four aces. Then turn up cards from the top until the first ace appears. On the average, how many cards are required to produce the first ace?

I presented my work on sorbents of toxic compounds at AiChE 2019!

My work done at University of Florida on DNA electrophoresis was presented by my former advisor Dr. Kopelevich

A combination of a parallel electric field and pressure gradient can cause DNA molecules to migrate transverse to the field lines. We hypothesize that the phenomenon is due to an electrically induced velocity disturbance. A Brownian dynamics method for a bead-spring model of a polymer, that incorporates this electrically induced velocity disturbance, was constructed and used to predict the dynamics of DNA molecules transported through a microfluidic channel due to the pressure driven flow and electric field. Using simulation, we obtained the probability distribution of the centers-of-mass of the DNA molecules in multiple channels with different cross-sectional dimensions. Preliminary simulation results match, at least qualitatively, the extent of migration and the entry length measured in the experiments.

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