interaction/particle groups in a math object context

27.x.XXX

This graph shows a few of the groups describing particle families based on fundamental interaction (force) fields in which they figure as gauge particle, or field generator / interactors (eg, the standard model aiming to include all particles, involves the cross product of three groups - for three fundamental interactions - note there is none for gravity, as no particle for it is yet known :)), in relation to other mathematical objects, including finite automata (computers).


It is reproduced from this earlier post. Made using Graphviz/2.22 :)

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graphing the tree of life

26.x.XXX

An XSLT script I wrote (latest version) that converts Tree of Life (TOL) XML data into graphs, has been useful for pruning and turning database XML dumps into graph scripts for graphviz.

The graph shown here is a rendering of the first few levels of TOL. it links to my original blog entry on the XLST script, where a full size version of the image is available as well as other relevant files.



The original XML data is provided to the public on TOL's website here: TOL XML tree

In its final version the XSLT script allows the user to start the graph from any given node in the tree , as well as control the coloring of the nodes (eg, alternating colors or a color gradient for the tree).

Original version of the XSLT script can be found here: xml2dot.xsl.

More importantly this script has also been useful in pruning and converting database dumps in XML - eg "mysqldump -X" output - into graphviz graphs. This is an example output, with the scripts i wrote provided below,

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Here are my script source codes for both directed and undirected graphs,


xml.mysql2dot.digraph.xsl

xml.mysql2dot.ugraph.xsl

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ideas dept: unshorten URLs

24.x.XXX

when we run into a shortened/shrunk URL that we dont want to visit but want to know where it points anyway, this application returns the original URL to the user, either by requesting the short URL to get the redir URL in the response or by querying the API of shortening services for the original URL. I doubt any of tiyURL bit.ly is.gd etc offer any such reverse lookups, but it wouldn't be needed anyway - but would save the service sending requests to many places instead of a closed list.
Naturally the best seat (deployment model) for this app is as a plugin for web mail im news and sms clients that shuttles url's with the app's server, and then switches URLs in the content or elsewhere.
input modalities should be preset and selectable, eg, URL substitution directly inside content or text input box for URls to unshorten (which is then replaced by a text/link label).

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how cometh dept: ortho fns that dont cancel out

13.x.1430

in [Waerden]** §3 :

*
Lin transformation product with scalar product of two orthogonal functions.
o
<φ_j,Aψ_k> = A<φ_j,ψ_k>
*
The scalar product should be zero b/c the two functions φ,ψ are orthogonal
*
And yet van der Waerden states this is what gives the coeffs of A:
o
<φ_j,Aψ_k> = A<φ_j,ψ_k> = a_jk
*
¡¡¡ How Cometh ?!!¿؟?



** [waerden] = van der Waerden, Group theory and quantum mechanics , Springer 1974.
English translation of Die gruppentheoretische methode in der quantenmechanik , Berlin: Springer Verlag, 1932.


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