Math

Software: LyX document processor that renders LatEx

lyx_logo_medium2[1]

Links

  • LyX – Main page 
  • LyX Instant Preview
  • Lyx Download – Choose the big bundle ~200Mb – perhaps you will not have to install Python & Elyxer on your own as I did.
  • Python  I had to add Python & Elyxer
  • Elyxer download
  • LyxBlogger – plugin to Lyx that is supposed to upload to your blog.  I tried it and it did not work. I am corresponding with the author hoping to push a solution whether it is me or the software.

R-J-Drofnats

Once upon a time in a galaxy called Ooc there lived a computer named R.J. Drofnats- or "R. J." as he preferred to be called-was happiest when hewas ate work typesetting beautiful documents. 

Drofnats is Stanford backwards.

By Fudgy McFarlen, ago

Sudoku Solver Paper

Links

Notes

  • Be flexible: There appears to be a tendency to focus on a subset of techniques using only rows.   Use the solver to work through some examples.  Observe casually the techniques used and note which ones you have been skipping or not using enough.  
  • Use your eyes to find probabilistic soft entry spots.  For example well populated row that passes through a well populated square.
  • Using the solver paper makes more work.  It is useful to observe patterns but gets in the way too.

Solve your sudoku using this paper.  Circle the given square number.  X out the eliminated values of the square.  The following jpg image is sized to print out on 8.5 x 11 paper

…..more

By Fudgy McFarlen, ago

What could be more boring than a traffic jam?

I always wondered why a freeway with no accidents or other driver diversions such as a policeman pulling over a speeder can come to an almost complete halt.  I think if have figured out this mystery.  The following graph is velocity versus distance on a freeway.  Here in Phoenix there is a location on the freeway where you can be driving at a normal highway rate and then encounter a traffic jam.  Once through the 4 miles of the traffic jam the freeway opens up again to acceptable conditions.

 

   

 

Note the oscillatory behavior in the jammed area where cars alternate between a maximum low speed and complete stop.

………more

By Fudgy McFarlen, ago

Video: Ultraconservation and living fossils Mysteries of the Human Genome

Genetic code is reused in exactly the same manner human programmers reuse code.  Thus once some random string of genetic coding is found useful there is a process that preserves it from change.  That change is called survival.  If it is a random string with no purpose then it is swept from the system by error.  Error is death.  Thus if you sequence the human genome you can compare useful portions with those of widely separated animals such as mice and find almost identical code.

Gill Bejerano holds a BSc, summa cum laude, in Mathematics, Physics, and Computer Science, and a PhD in Computer Science from the Hebrew University of Jerusalem, Israel. Twice recipient of the RECOMB best paper by a young scientist award, and a former Eshkol pre-doctoral Scholar and HHMI postdoc. As co-discoverer of ultraconserved elements, his research focuses on deciphering the function and evolution of the non-coding regions of the Human Genome. Gill is currently a postdoc with David Haussler at UC Santa Cruz, and in early 2007 he will join Stanford university as an Assistant Professor in the Department of Developmental Biology and the Department of Computer…

By Fudgy McFarlen, ago

Quantum Entanglement of Photons demonstrated in relatively low cost set up

  • Louis DeBroglie does not get the credit he deserves for original thinking in quantum machanics – DeBroglie thesis paper   – he won the Nobel Prize in 1929 for very good reasons which you will see if you read his thesis paper.
  • I am looking for the single photon counter used in this experimental setup

PowerPoint presentation of experiment Uses an SPCM-APD  ( Single Photon Counting Module – Avalanch Photo Detector )

One of the experimenters

Relatively simple setup uses spontaneous parametric downconversion of photon to create 2 photons that are entangled.  Then these are sent to 2 single photon detectors.   If you have any of the parts or pieces of this setup for sale I would be interested in buying.     

By Fudgy McFarlen, ago

Summary Outline of Richard Feynmans Thesis – Framework for learning QED and Quantum Mechanics in general

He was a fun guy.

 A reasonable strategy for learning QED would be to try to recreate Richard Feynman's path of discovery that lead him to his thesis paper.   If you are an electrical or computer engineer you should probably set about the task of learning the subject for sooner or later quantum computing and nanotechnology are going to go mainstream.  If I am successful in learning this subject it will mark the first time I have not been at least 10 years behind the technology curve when it finally hits.

Research Links

— The following summary is from his Nobel prize address in 1965 and yields some insight as to how he went about the problem of reformulating QED into a more usable form.   It includes some information about the wrong turns he took which of course is very instructive in and of itself. —

By Fudgy McFarlen, ago

Long hand division generation of polynomials

Do a long hand division of 1/{1-x}  

x greater than or equal to 1 does not result in convergence of this sum.  However this algorithm can still be used to do some interesting things.  Let us use a complex value of   x = .707+.707i  

Each power of x yields a result one step around this unit circle. Thus this series is the Z transform of the associated sequence.  [1,0] , [0.707,0.707] , [0,1] ……. This sequence is  Sin( (n-1)*pi/{4})  

Thus the z transform of this sequence is:   1/{1-(0.707+0.707i)*x}    

If you want to get express in terms of n instead of n-1 you can multiply by 1/x.  Since x is the place holder it is easy to see if you want to slide a series one unit to the left by dividing by x. 

 Sin( n*pi/{4})    : note this series starts at 45 degrees phase!

 

More information:

By Fudgy McFarlen, ago