a to z

Hough transform

alanzed — Sat, 16 Jan 2010 19:00:34 +0000

Hough transform of black image with broken lines

As part of an image recognition project I was working on today I was introduced to the Hough transform. This transform is useful for finding lines and other regular shapes (circles, ellipses) in an image. Every pixel on the image is sampled, and an accumulator array (whose dimension is equal to the number of parameters in the shape: line=2, circle=3, ellipse=5) is used to tabulate votes based on edges in that pixels neighborhood. This description shows several nice image pairs.

The similar Radon transform is in some sense a continuous version of the Hough transform, and used in tomography. The complex form of the Radon transform is the Penrose transform, which is somehow important in twistor theory.

Stochastic resonance

alanzed — Sun, 10 Jan 2010 05:00:51 +0000

The topic of stochastic resonance came up today and I was lent a copy of Noise by Kosko. SR occurs only with a non-linear system and a detector with a threshold (neurons are one example.) The psychophysics paper Visual perception of stochastic resonance has an image (right) that shows this property very nicely. The paper itself focuses on showing that the human brain’s visual system is nearly or as efficient at using SR as a computer to process information.

Linac Coherent Light Source

alanzed — Wed, 06 Jan 2010 05:12:32 +0000

The Linac Coherent Light Source (LCLS) came on line in September of 2009, capable of producing x-ray laser pulses of wavelengths from 1 to 0.15 nm. The source will be a laser pulsed photo-cathode in development (led by Howard Padmore) over the next 2 years. The x-ray free electron laser (XFEL) pulses are sec of photons. This photon pulse is so energetic it destroys the sample viewed, but not before a snapshot is collected. One technique for imaging proteins is to prepare an aerosol spray and inject a collimated stream into the electron beam. A large set of diffraction images (up to 10 million) of the molecule in random orientations are generated. The data is categorized, averaged, and fit together iteratively to form the best 3D diffraction representation. The 3D electron density map can then be generated from the assembled diffraction volume.

Criteria to observe mesoscopic emergence of protein biophysical properties

alanzed — Mon, 04 Jan 2010 03:59:27 +0000

Article summary of Criteria to observe mesoscopic emergence of protein biophysical properties

Proteins range in size from tens to tens of thousands of residues (TRP-Cage to Titin), with each individual atom known. When these proteins are folded, physical surface macro properties such as hydrophobicity and polarity emerge. This article abstractly attempts to set up a framework (a control theoretic construct) for stating how many atoms (or amino acids) are needed before an emergent property can be observed.

The article sites many references. New to me is that it is an interesting open issue that a bottom up approach to determining hydrphobicity and polarity has yet to be found. I did not yet find out what a control theoretic construct is.

Alpha helix to carbon nanotube

alanzed — Fri, 01 Jan 2010 04:00:28 +0000

Alpha helices in proteins and carbon nanotubes look alike. I wonder if it is possible to grow nanotubes from alpha-helices. I see there is one article out there – Carbon nanotubes self -assembled by amphiphilic alpha peptide helices – have to check it out. Generating graphene from a beta sheet seems less likely, because of the natural twist present in a beta sheet – I don’t find any articles at this time on that.

World of Warcraft

alanzed — Sat, 26 Dec 2009 04:00:24 +0000

Taking a short vacation, I gave the now mature online game of World of Warcraft a try. A fun, Blizzard did a good job creating a game with an immersive environment. I can see why it is so popular. Also found the add-ons and customizability using Lua very interesting, skimmed a couple books on writing add-ons, and wrote one for myself. The webisodes of the Guild, which play off of Wow, are entertaining.

Snowflake formation

alanzed — Sun, 13 Dec 2009 16:58:31 +0000

Stellar dendrite snow crystal

The forecasts predicting snow for this weekend were wrong, but it reminded me of a question I had – why would snowflakes form symmetrically? How does one individual branch “know” how the other 5 are growing? It turns out that the local conditions (temperature, altitude, etc) govern the crystal growth, and that snowflakes are different because of their trajectories through the atmosphere. Any one snowflake sees the same conditions and will grow in a symmetric fashion (though the majority of snowflakes are actually irregular)

Kenneth Libbrecht is a physicist studying snowflake formation, and has a great website discussing this, with great micrographs of snowflakes. He also has a paper The physics of snow crystals.

SAGE history and ODE solvers

alanzed — Sat, 12 Dec 2009 18:29:51 +0000

William Stein recently wrote up an interesting history of his trajectory in mathematics and creation of SAGE (which I’m a big fan of). This document lead me to discover (Pyrex and) Cython, which looks very useful for my work.

Fast numerical computations with cython – reviews the features and some parallel options

Also, after reviewing and debugging my RKF method, I’m ready to use the scipy solution, scipy.integrate.odeint, which provides and interface to LSODA in the ODEPACK. Getting to know ODEPACK intimately will be the key for implementing my ode.

Kinematic closure applied to protein folding

alanzed — Fri, 11 Dec 2009 05:00:48 +0000

Introduced to the work of Dr. Evangelos Coutsias at UNM, an read through a couple of his papers

Using quaternions to calculate RMSD – explaining the basics of using a result from kinematics, kinematic closure (KIC), and inverse kinematics, to analytically solve possible conformations for short peptide sequences.
Sub-angstrom accuracy in protein loop reconstruction by robotics-inspired conformational sampling – where the improvements from KIC on protein loops are exhibited, and the code has been added as an extension to the Rosetta program.

Reviewing ODE solvers

alanzed — Sun, 06 Dec 2009 05:00:30 +0000

Coded up primitive ODE solvers for Euler, RK2, RK4, RKF in Python on the plane and graphed comparative results. Here they are for

The green points are Euler, red are Runge-Kutta second order, light-blue RK4, and small purple are Runge-Kutta-Fehlberg (lying on the blue line for the mathematical solution