Topic awaiting preservation: Obscure Technical Interests

I have been finding that as more time passes the things that I am doing and learning are becoming more and more obscure. I am looking for interests that are on the boarder or have just fallen off the edge of real relevance in respect to this board. Are you interested in things that just make other people look at you cross eyed? I know there are a number of people here that post things that just make me scratch my head. I can say cool, but really have no idea what is going on. Doesn't have to be super far outside the norm, doesn't really have to be ally that techy technical.

If you have one of these obscure interests please share what it is, and give a brief explanation. The hope here is that we can learn a bit more about each other, and about some of the cool fields people are doing things in that we might not know exist.

I will start it off.

Elliptic Curve Cryptography

This has been an interest of mine for the past couple of months. The idea is that by using the mathematics of an elliptic curve function, as opposed to standard math you can improve the security of particular cryptographic algorithms. I find the math here to be a whole lot of fun. I am not really building anything new with this, but there is a joy in just seeing what other people can come up with.

Getting a bit more technical. An elliptic curve is a function y^2 = x^3+ax+b. If you draw a line through the oval it will intersect the third line. The line through P-Q also intersects R. You can build a mathematical system based on saying that points P+Q = R. It is really nutty stuff, the scary thing is that it seems to work really well.



What are some of the cool obscure things you are interested in?

Dan @ Code Town

(Edited by WarMage on 05-19-2005 04:43)

Cool, but really I have no idea what is going on.

i'm interested in geometry myself lately. doing minizing calcualtions. for example you have N random points, whats the best plane or ellipse fitting them?

That's a good thread IMO. I like this kind of topics. But does it have to be technical? Because I'm off if so...

I can make a stick figure...

No, it doesn't have to be technical. What I am trying to get at, is more something you are currently enjoying doing, but really doesn't fit the mold of the everyday conversations that happen here.

Grumble, can you show an example, or what you would use it for?

Dan @ Code Town

Well... about 3/4ths of my life, I have no one to talk to about.

My current prime example is 'really really fast (o(1))' text searching. (that o(1) is for existence checks, not locating the actual place).
It is going to be quite usefull for my current semantic web & smart text retrieval research, but only about 3 people I personally know even understand what it's about...

I was working with prime numbers not too long ago. Not really heading in any specific direction, but hoping a lightbulb would come on if I stuck with it long enough and give me a little direction. I think I've kinda figured out what I want to do with it (start finding functions to describe parts of the list of primes or factors of non primes), but I've been too busy with real work to get any farther on it.

However, if anyone wants a txt file with all the primes below 25,000,000 I can send it to you (only 14.5 Mb)

Tyberius Prime: would you care to elaborate on the method you use ?

Well, the basic idea is to built a suffix array of the text(s) in question.
Then we convert that into a wavlet tree.
Then we convert that into a fancy binary structure I don't understand (called a FID), which a) provides H(0) compression b) allows checking for suffixes in o(1) (and returns a suffix range), and locating a text position for a given suffix in... about O(logn).

It's an extension of the FM Index (created by P. Ferragina and G. Manzini.) described by the same authors in a 2004 paper.
Somehow, I doubt that they actually implemented the version they described.

I'd be done for months now if I could just grasp that Raman, Raman, Rao paper about FIDs...

I have been tailoring custom-made Cost Manager workbooks in Excel to suit budgets for a Production Manager at a well-known British television production company. It isn't exactly technical, but it is certainly unusual for me - I'm an IT technician and gadget nut. I'd never be an accountant...

...but then, I charge a ludicrous amount for each cost manager - so it more than makes up for the effort.


Also, I carve Celtic designs in pillar candles as gifts and turn cigarette filters in freaky little bunches of flowers just for the hell of it.


Certainly not technical, but perhaps a little obscure...

my obscure technical interests are :

• preparing a demo in DHTML,
• working on Atari ST(e) i.e. doing a bootsector ( a little demo in 480 bytes ), some pictures, slowly preparing a demo on Atari STe, torturing my mind to find how to beat the 16x16x2bpl not masked record
• working on the sprites and design for a remake of R-Type on Pokemon Mini.

Tyberius Prime: Wavelets?! Doh! I wish I understand how to do wavelet transformations. The insight we had in Uni. seemed absolutely amazing. I'll check the paper you mentioned.



(Edited by poi on 05-19-2005 16:22)

I just finished an advanced CG class where we covered a wide range of topics, perhaps the most interesting were the alternatives to raytracing. The problem with raytracing being that it only computes light from the direct reflective and refractive directions, with a crude approximation of a specular component. Whereas in the real world, most objects bounce varying amounts of light in all directions. Of course the sum of all reflected light can be calculated as an integral, but one which can only be solved for the most trivial of scenes. Instead we resort to numeric techniques:

RADIOSITY

Radiosity is a technique developed by engineers to measure heat transfer between physical components. It is an energy conservative model that creates extremely realistic models of diffuse reflection, but unfortunately has no capacity for reflectivity or specularity.

The principle is that you divide the scene into small patches. Then you compute a form factor between every pair of patches in the scene. The form factor represents the percentage of total light reflecting from a given patch that reaches another patch. This is a purely geometric number, so it can be computed in advance for a static scene. The assumption here is that light striking all surfaces is reflected uniformly in all directions (ie. 100% diffuse reflection), which is what makes this a viable technique. Once you have all the form factors you create a huge matrix which which will solve for the brightness of each patch based on the 'lights' which are simply the patches that have some default energy in the matrix equation. The results are stunningly realistic images, but limited by the diffuse requirement.

PHOTON MAPPING

In order to capture all light interaction, the only computationally viable techniques are what are known as Monte Carlo methods, because they are based on random sampling. In raytracing we send one ray for each pixel, and calculate all its reflections and refractions down to some predetermined depth. A better technique is to send out multiple rays for each pixel, and give them some randomness in how they bounce, so you can capture diffuse as well as specular reflection. Of course, you have to send out a considerable number of rays to capture everything, and if you don't send enough, the result will be noise in the image. But probability pretty much guarantees that your image will converge to photorealism.

There is one notable effect that doesn't converge, however. That is the effect of focused light through a lens. Such as the bright spot underneath a wine glass. The reason this is not captured is because when we send rays from the viewer, they bounce off the table in random directions, not enough of which will go through the lens to be refracted into the light. The solution is to compute a 'photon map' first. In other words, we start from each light source and send out a number of 'photons' in all directions and record where the hit. Then when the rays hit the table, we already know how much light is there based on the photon map.

See http://www.pbrt.org/ for some mindblowing renderings using this technique.

My favorite is this dragon: http://www.pbrt.org/gallery/01F12.jpg

-jiblet

This is all really interesting stuff. Keep it up. Like keeps being said, we have some really talented people here who do some pretty amazing things. It is great to keep having this re-affirmed.

WhiteHawk, can you share some photos of your work, the carvings, and the filter flowers?

TP, what is the runtime of the pre-compile step? Would I be on the correct trail if I look at this as a sort of super-increasing knapsack type data structure?

Jiblet, what projects have you done with this? Do you have any personal examples? Monte Carlo and Las Vegas probability based algorithms are great. They did a lot of work in the field of primality testing when there was no polynomial time algorithm for it. I think that those algorithms will eventually lead to one that can be done in polynomial time. However, if they will be able to implement it, that is another story.

Fukutoku, are you trying to describe ranges, say 10^3 through 10^20? or are you trying to describe parts of prime numbers like their first/last bunch of digits?

Dan @ Code Town

Well, this is slightly technical then... But I have to say I was completely obsessed with that a few years ago, and I still love talking about this, even if the conversation normally ends up very shortly with most of the people I talk about this. There don't know their classics, I'm telling you...

So I used to unscrew the deleting thingy (head?) of a tape recorder and record many things on top of each other. I know I haven't actually made anything out, but I was enjoying it so much I used to spend afternoons doing that! I also sometimes recorded weird noises like nuclear alarms (they test them every year) and tried to include them in other funny songs, like (not a hazard of course) the Beatles' Revolution no 9 or the Stranglers' Bats' Waltz (or something like that). So this is it... my only technical ambitions...

/*plus*/

Oh and I also loved listening to songs backwards... I've written a few of my own songs like that, it's great inspiration!

(Edited by kimson on 05-19-2005 17:26)

I'm into building radio-controlled scale model airplanes, unfortunately between work and family I don't get much time for it.

I'll see if I can dig up some pics.

TP, that sounded familiar, I know we talked about it a while back but I sumbled over an old bookmark: http://www.mfn.unipmn.it/~manzini/fmindex/ that seems to be roughly on a similar track (at least from what a total non-math dude can understand)

/Dan

{cell 260} {Blog}
-{ ?There are two major products that come out of Berkeley: LSD and UNIX. We don't believe this to be a coincidence. - Jeremy S. Anderson" }-

Warmage: Actually, if you're willing to use some scary math, you can built this thingy in O(n) time and o(n) space - though the best algorithm is is o(5.03n) in space, and I believe o(n * log(n)).

Dms: You're on the right track - but that's the 'simple' fm-index which compresses less well, and is a tad bit slower.
The new wavlet based index can compress up to the H(k) entropy of the input (meaning it's dependant on any number of earlier characters), provided you use another algorithm I don't quite yet understand to split the string (Mazini and Ferragini proved that their splitting algorithm can turn any H(0) compression algorithm into a H(k) algorithm).


I can provide you with all the papers necessary, but you'll need to spent your own months comprehending ;-)

Thank you TP, but I'm still trying to figure out what language the last one you pointed me to was written in...

I'm really impressed with you math-heads out there, I've never got my head around high school math
/Dan

{cell 260} {Blog}
-{ ?There are two major products that come out of Berkeley: LSD and UNIX. We don't believe this to be a coincidence. - Jeremy S. Anderson" }-

^right there with you, DmS.

Actually, Warmage, I'd be happier sharing a poem, but it doesn't really seem appropriate. Maybe Ozone Asylum needs a writer's corner...

There could be a writer's version of PS Pong..! *excited hopping*

...

*shrug*

Warmage-

I implemented a radiosity renderer on top of a pretty crappy raytracer, but my results had a few errors which led to suboptimal renderings. I have those around somewhere, but they're in exr format and not very impressive.

For the photon mapping, we simply used pbrt to model and render the Cornell radiosity box... My results are at http://www.websaviour.com/diffuse2.html I only included the link to the official website because their images are so much cooler

-jiblet

WarMage - Yep
Actually, I'd been tossing the ranges of primes around in my head more than pieces of primes. But a lot of the reading I've found on primes is pretty interesting, especially when they get to the algorithm to figure out if a particular number is actually prime... At least I find it interesting.

Stuff like Mersenne Primes. There's a page there explaining just how they factor a number with several million digits. (The largest known prime so far, which is a Mersenne Prime, is 7,816,230 digits long)

However, lately, I'm just trying not to go insane at work.

My (slightly obscure?) interests have lain in hacking of one sort or another recently. I've been doing some development for my Nintendo DS of all things (gave me a good reason to finally learn C++ ;p)

But elliptic curve cryptography? I might have to look into that. No doubt I'll have difficulty understanding even the basics, but perhaps it could be useful if I manage to get an interview at Cambridge for maths

Wrayal