Archive for the ‘Research’ category

Hough transform

16 January 2010

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

9 January 2010

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

5 January 2010

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 $10^{-13}$ sec of $10^{12}$ 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

3 January 2010

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

31 December 2009

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.

SAGE history and ODE solvers

12 December 2009

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.

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

10 December 2009

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