Archive for the ‘Mathematics’ Category

Attended the presentation: “An excursion through flatland: Braiding interactions of anyons” by Gavin K. Brennen, Dept. of Physics, Macquarie University, Sydney.

Friday, April 12th, 2013

Attended the presentation “An excursion through flatland: Braiding interactions of anyons,” by Gavin K. Brennen, Dept. of Physics, Macquarie University, Sydney.  Anyons are hypothetical particles.  They interact as a function of braiding, knotting or topological relationship with other particles rather than with distance (as with other matter).  Majorana fermions are an example of fermionic anyons.

Just finished reading “Transportability across studies: A formal Approach” by Judea Pearl and Elias Bareinboim, March 2012, UCLA, Technical Report R-372.

Tuesday, April 9th, 2013

Another gem by Professor Pearl and Elias Bareinboim.  It identifies the external validity practice of making threats versus license.  The causal mechanisms in an experimental group and the observational group influence license for external validity.   There is even help  for moving from an observational situation to another observational population.   This is a must reading for any serious statistician or practitioner that creates statistical models and then applies them.

Just finished reading “Commentator: A Front-End User-Interface Module for Graphical and Structural Equation Modeling” by Trent Mamoru Kyono, May 2010, UCLA, Technical Report R-364.

Monday, April 8th, 2013

Requires the compilation of the included C code for the module using Microsoft Visual Studio 2008.  Uses the Structural Equation Modeling software EQS software version 6.1 2006.  A first step in implementing Pearl’s causality interpretation of SEM (Structural Equation Models) using graphical diagrams to encode the causality and provides a means to determine structural causality zeros and constraints.  I have the trial version of the EQS software and plan on compiling the code to replicate some of the examples int he paper.

Wrote an excel script to compute a probability for one binomial variable exceeding another.

Monday, April 8th, 2013

Check out the problem and solution at:
It is number 22013 on the webpage.
An excel file is included to dynamically change model parameters and recompute the solution.

Just finished reading “The Causal Foundations of Structural Equation Modeling” by Judea Pearl, February 2012, UCLA, Technical Report R-370.

Saturday, April 6th, 2013

This paper has many very useful ideas.
One it highlights and resolves is the symmetry/asymmetry problem or paradox that exists in the fact that the linear model
in statistics has a symmetry between the independent and dependent variables which are then consequently labeled and treated differently.
Dr. Pearl traces the cause back to the equality sign in the linear model.
In one sense it is treated as an assignment equality sign as in computer science and in another sense it is treated as the equality sign in mathematics.
The solution to the paradox is found in the use of structural equation modeling and the treatment of causality.
The methodology requires the specification of causal assumptions, quries of interest and data.
The structural equation methodology results in: logical implications of the assumptions, causal inference, testable implications, statistical inference, model testing (goodness of fit) and conditional claims.
If you ever noticed and were concerned about the symmetry in the linear model and its apparent assymetry in modeling then this is a great paper to read!

I enjoyed Dr. Pearl’s talk at the Joint Statistical meetings and this paper is a great followup to that presentation. for data analyis

Saturday, April 6th, 2013

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Decomposed a 10,000 by 10,000 matrix on Gibbs today.

Tuesday, April 2nd, 2013

I was able to create a random dimension 10,000 Hermitian matrix and determine its eigenvalues and eigenvectors on the supercomputer Gibbs today.

Super Computer Timing of Creation of a General Hermitian Marix and Its Eigendecomposition in Matlab

Monday, April 1st, 2013

Using the supercomputer Gibbs at the University of New Mexico I get the following timings for various number of nodes for the creation of a random Hermitian matrix and its Eigen decomposition.  Each node used 16 processors.   JGW_Graphic