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## The areas of expertise I didn’t know I was an expert on.

I guess I’m easing my way back to writing blog posts. Of course, I could bore you to death with the list of things I was actually doing instead of writing here, but that will really have to wait for another day.

Today, I will just give you some information on some of the recent spam in my e-mail folder that comes from Open Journals (which I have discussed about in the past) and random conferences around the world. I just have the impression that my e-mail is in a “general list of scientists”, or “general list of scholars”, or “general list of people who have written something” that the companies buy and then bombard with queries asking me to select them for publishing in. The rest is a (sufficiently edited) list of such that I have gotten invited to contribute recently in:

1. Journals of Statistics.
2. Journals of Geometry.
3. Journals of quantum information.
4. Journals of applied mathematics.
5. Journals of law. (US law in particular).

I’m not really an expert on any one of these, although I could probably  do something with my research that might be considered for journals 1, 2, 3, 4 with a long stretch. But in item 5 I declare myself a complete amateur even though I do follow some court rulings and such because I find them interesting.

My inbox would also suggest that I am expert on informatics, engineering, cybernetics, communications, computing, molecular and cell biology, as I seem to keep getting invited to attend conferences on these subjects and maybe even chair one session or two on them. It makes me wonder how the hell I got into their e-mail databases.

In the meantime, I’ll go back to my cave where I will be back doing the things that I usually do that force me away from writing posts like this one on a regular basis.

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## Novel Numerical Methods for Strongly Coupled Quantum Field Theory and Quantum Gravity

Here is an announcement of a program I will be organizing at the KITP from Jan 17 thru March 9 2012. It is a program on numerical methods for gravity and QFT. The web page of the program is located here.

Here is the image I made to illustrate the program: it is generated by taking a set of modes in a box with a UV cutoff. Then amplitudes are seeded for these modes with random numbers and phases multiplied by the typical quantum uncertainty on each mode. The result is a picture like the one below.

It is also fun to animate it.

Right now I have to start chasing people and reminding them that the (first) deadline for applications is coming soon (April 30th).

In the meantime stay tuned.

Image of Fluctuations of quantum fields

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## Making mistakes

Here is an example of what happens when one makes a mistake.

There is a good implementation of a function, and there is one where a sign went wrong. This is a rather common occurrence.

Check carefully if you can spot the difference. You can hardly tell the two plots apart 😉 You can only tell which one is right if you have some expectations of what the end product is supposed to look like.

Good coding

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## Leapfrog

Many times in physics one wants to solve systems of ordinary second order differential equations (equations of motion for example). If the dynamics comes from a Lagrangian,  it is standard to try to put them into first order formalism by going to the Hamiltonian formalism and working in “phase space”. Once you get to this stage, hyou can try putting the system on a computer by evolving the equations of motion discretely. Many times this destroys certain aspects of the dynamics. However, if you do things right, you can get some things to work better then expected.

For example, in the Hamiltonian formalism of the Kepler problem, one would have a Hamiltonian of the form

$H= \frac {p_1^2 + p_2^2}{2m} - \frac{K}{r}$

where

$r= \sqrt{x_1^2+x_2^2}$

The sign indicates that one has smaller energy where $r$ gets smaller (the potential energy is attractive).

A naive implementation of the evolution of the system is given by evolving

$p_i [t+\delta t ] = p_i[t] - \partial_{x_i} V[r[t]] \delta t$

and

$r_i[t+\delta t]= r_i[t]+ \frac{p_i}{m} \delta t$

However, after staring at this for a while, one notices that the dynamics is not reversible: both x,p have changed, so going back by changing $\delta t\to -\delta t$ does not get you exactly back to where you started.

There is a very nice fix to this problem: you think of momenta as being evaluated at half times, and positions at full times. This is, we get

$p_i[t+\delta t/2] = p_i[t-\delta t/2]+ \partial_{x_i} V(r[t]) \delta t$

and

$x_i[t+\delta t]= x_i[t]+ p_i[t+\delta t/2] \delta t$

and even though this looks almost identical to what we had before, it is now time reversible (just send $\delta t\to -\delta t$ and do appropriate shifts to check that you really get back to where you started).

This is called the leap-frog algorithm. For problems like the one above, it has rather nice properties. The most important one is that it preserves Liouville’s theorem (it keeps the volume element of phase space constant).

In examples like the one above, it does something else that is quite amazing. If you remember Kepler’s second law (sweeping equal areas in equal time intervals), it is the law of angular momentum conservation. I’ll leave it to you to find a proof that the above system sweeps equal areas in equal times around the origin $x_{1,2}= 0$. I learned this fact recently in a conversation in my office and I was quite pleased with it, so I thought it would be nice to share it.

This algorithm does quite well on a lot of other systems (like the one I’m studying now for my research). If you have a system with a lot of symmetries, sometimes the leapfrog algorithm will preserve a lot of these symmetries and also the conserved quantities, so that you can evolve the system for much larger values of $\delta t$ without loss of information.

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## Move to INSPIRE

As many of you probably know, the place to look for references in High Energy Physics for as long as I can remember has been hosted by the SPIRES website, hosted at SLAC.  In the last few year the system has become slow and clunky and I have heard various complaints about it. There is a mirror at Fermilab that works better, but it sometimes still freezes. The next generation of the search engine is called INSPIRE, and it is far superior to the SPIRES engine. This has ben jointly developed with CERN, I’m not sure who else is involved.

This week the SPIRES website is urging the visitors to move on and try INSPIRE. It is in beta testing (has  been for a while and I have used it before), but now it seems to be working much faster.

One of the things that SPIRES had troubles with was citation counts. There are some double counts that appear in some places and not in some others and the results had an inherent noise in them.

INSPIRE seems to have corrected those issues and now the counts seem to match everywhere. I have not found anything broken with the new system yet, but I have not been pushing it either.

In any case, SPIRES is  obsolete (has been for a while) and the transition is now. I think so far they have done a good job with the new software and the move to the new system is worthwhile.

I think the funniest catch phrase one can write about it is the title of this post:

Move to inspire.

It sounds like a slogan for a charity. Oh well.

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## More blobs of goop

I thought I would share another view of the data I’m analyzing

3D visualization

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## Coloring graphs.

Coloring scheme I.

Coloring scheme II.

At the top you can see two different frames for visualizations of information during different times of a particular simulation. I’m not going to tell you the details of the simulation, nor what the graphs are going to represent (this is still in the ‘top secret’ category: it is work in progress and a lot of stuff can change before we decide to go public with this). In the meantime enjoy the pretty pictures. What I’m trying to figure out is which color scheme looks better. Warning: don’t expect to see graphs like this in any of my papers in the near future.

Here is the deal: coloring schemes produce emotions in the recipient. Different coloring schemes give people different feelings about information. For example, red is usually associated to hot, while blue is associated to cool. However, a blue star is hotter than a red star. The red/blue association is probably due to fire/ice. Fire tends to be reddish, and ice is kind of bluish, but when we see things according to the radiated energy at different frequencies we get a completely different picture.

When presenting scientific information, choices like this one often present themselves. And it makes a difference on how the recipient audiences perceive the quality of the work… or even better: the coolness factor of the work.

The big questions are: what emotions do the above graphs give you? Which one do you like best? Why?

In the end they are conveying sufficiently similar raw information, but though I know this is true, I feel different about it. They have a different artistic feel to them. I just thought I’d share some of these issues and maybe even get some feedback.

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