Domain: toronto.edu
Stories and comments across the archive that link to toronto.edu.
Comments · 206
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Re:Why not use Rust?
Regardless of which language you use you'd end up with C or Assembly in the bottom.
I'm not sure if Rust is the way to go or if some different language is better. VMS/OpenVMS is using a large chunk of BLISS.
Another alternative I'd think of is Erlang. Or Prolog.
For the future - think outside the box. And that may not mean C, C++ or any of the traditional procedural languages.
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Re:deja vu
Yes, this is a dupe. Here is a brief synopsis of the previous discussion:
1. Many people do not think AI today is analogous to the "web" in 1993.
2. Machine learning is much harder than editing HTML. You aren't going to learn it in a 21 day "bootcamp".
3. If you are serious this is what you should do:
a. Learn plenty of linear algebra
b. Learn how to program GPUs using CUDA and OpenCL.
c. Learn basic theory, like backprop and autoencoders.
d. Write some code, read some books, write more code.Here are some good resources:
MIT Artificial Intelligence Course
Deep Learning by Ian Goodfellow and Yoshua Begino
Geoffrey Hinton's 2006 Science Paper that triggered the "deep learning" revolution.That will get you started.
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Re:Translation...
Fantastic summary!
The elephant in the room is that Silicon doesn't scale past 5 GHz. Everyone knows about it but no one in the commercial sector is interested in doing anything about it.
:-(Hell, even back in 2007 SiGe was proposed to get up past 50 GHz.
What's really freaky is that a close friend of mine was playing with 1+ GHz CPUs in the (late) 70's. I guess we'll never have those 100 GHz Gallium Arsenide CPU's anytime soon
... :-/ -
NP is the new P
Modern SAT solvers are able to solve SAT problems with millions of variables in seconds. Yes, there are hard problems with some hundred variables that are too hard to solve. But as it turned out, most useful problems are easy to solve. So if you have an NP-complete problem, you should just try to put it into minisat. If it can't be solved easily, there's still time left to despair.
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Re:Where is the bar?
Not exactly. The reward function was not learned (score function if you prefer), as far as I can understand from the paper here. This seems logical since otherwise there would be no way to tell the Deep-Learning CN whether a high score or low score was desirable.
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Re:absence of evidence
Occam's razor is not science.
No, Occam's razor is a theorem in Bayesian model fitting. Here's a pretty good introduction.
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The Cartoon Laws Of Physics
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Give it time
Give it some time.
As any AI researcher will tell you, we know how the brain works and Geoffrey Hinton's recent paper is nothing short of a breakthrough, and will lead to us having strong AI programs real soon.
We have IBM's Watson, a program that actually understands the information it's processing and will be used to augment medical diagnosis, SIRI, a personal assistant application that actually learns, and MAKO, a program who can do anything on a PC!
IBM is already making neural network chips that implement the way the brain really works, a program the learns the same way that a child learns, and many, many more!
We have courses that teach you AI, and
... it's easy!Give it some time! We need to let the AI mature like a fine wine, and filter down into consumer devices.
It's coming soon - it really is!
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Proof that 1=2 is based on simplifying x/x
I'm surprised no one has mentioned this yet, but allowing that x/x can be simplified when x=0 allows for strange equalities to emerge, basically that 0=1 or that 1=2. (This also serves as a proof by contradiction to the ability to simplify x/x for x=0) Consider the following reference: https://www.math.toronto.edu/m...
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Proof that 1=2
I'm surprised no one has mentioned this yet, but allowing that x/x can be simplified is dangerous ground because it allows us to prove equalities that are not true. (From another standpoint, then, we can prove by contradiction that x/x does not work for x=0.) For reference, consider the following site about the proof that 1=2. https://www.math.toronto.edu/m...
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Divide by zero != zero
Easiest way to see this is by graphing 1/x
https://en.m.wikipedia.org/wik...Notice from the negative side y is approaching - infinity as x nears 0, but from the positive side, when x approaches 0 y is becoming + infinity.
So it's not the same as multiplying by 0 where everything results in 0. It's really and truly undefined. You can't average +/- infinity and get 0, it's the gap between them. It doesn't exist.
If you ignore a divide by zero, your results will be unpredictable and often nonsensical. For example:
The classic algebra trick to "prove" 1 = 2 -
Re:New law.
Also, you have failed to show that human brains are usefully non-deterministic (they may have non-deterministic random noise, but random noise is not useful).
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Re:The End-Users most of the time don't really car
From the End-User standpoint, really the only thing that they care about is that there is a "full featured" product that is free (as in beer) and they won't have to deal with marked-up license fees.
Which isn't necessarily a given. To give a concrete example, at the 24th International Conference on Field Programmable Logic and Applications, there was an award given to Jason Anderson for his 'contributions to open source high-level synthesis', in particular the LegUp project. Now, given this award and the fact that the front page of the web site starts with the phrase 'LegUp is an open source high-level synthesis tool', you might be forgiven for thinking that LegUp is open source. If you go and read their license, you will discover that it doesn't meet the open source definition. The license contains the phrase 'Only non-commercial, not-for-profit use of this software is permitted'. Given previous legal issues surrounding the definition of 'non-commercial', this license basically means 'don't use it if you care about legal liability at all' and is worse than no-warranty proprietary freeware from a legal perspective.
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Re:The End-Users most of the time don't really car
From the End-User standpoint, really the only thing that they care about is that there is a "full featured" product that is free (as in beer) and they won't have to deal with marked-up license fees.
Which isn't necessarily a given. To give a concrete example, at the 24th International Conference on Field Programmable Logic and Applications, there was an award given to Jason Anderson for his 'contributions to open source high-level synthesis', in particular the LegUp project. Now, given this award and the fact that the front page of the web site starts with the phrase 'LegUp is an open source high-level synthesis tool', you might be forgiven for thinking that LegUp is open source. If you go and read their license, you will discover that it doesn't meet the open source definition. The license contains the phrase 'Only non-commercial, not-for-profit use of this software is permitted'. Given previous legal issues surrounding the definition of 'non-commercial', this license basically means 'don't use it if you care about legal liability at all' and is worse than no-warranty proprietary freeware from a legal perspective.
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Re:hard-wired can be a computer
This satellite does not even have a computer; it is all 'hard-wired.'"
A lot of early computer systems were hard-wired in terms of instructions and logic paths. It didn't make them unusable, just arcane considering newer technologies like SoCs. We have come a long way.
Right. It has no integrated circuits. There's no way it doesn't have a computer. It couldn't receive signals and fire its thrusters otherwise. If there are no IC's out there that do what you need (which I assume is often the case with space craft) there's not much need for them. A lot of electronics I've built in the past has been simple enough that I did what we always called "Point to Point" meaning you have a board (like real wood!) with holes drilled into it, or metal posts... and you solder your components "point to point" with each other. There aren't even wires.
Here's a random image I found as an example: http://bgmb55.files.wordpress....
You use the physical shape of the component to design your board. There are often components on both sides of the board.
This doesn't lend itself well to very complicated circuits however. If you get too many components going, you can easy create a short hazard for yourself. But it makes simple circuits a lot easier to build and maintain. It also makes each components function a lot easier to understand at a glance. This picture is clearly a Tube Amplifer for example. You can see that just by glancing at it (and the tube sockets help to) -
hard-wired can be a computer
This satellite does not even have a computer; it is all 'hard-wired.'"
A lot of early computer systems were hard-wired in terms of instructions and logic paths. It didn't make them unusable, just arcane considering newer technologies like SoCs. We have come a long way.
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Re: A looping simulation, apparently
There's lots of variations, but here's an easy one from https://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html
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Let a=b
Then a^2 = ab
a^2 + a^2 = a^2 + ab
2a^2 = a^2 + ab
2a^2 - 2ab = a^2 + ab - 2ab
and 2a^2 - 2ab = a^2 - ab
This can be written as 2(a^2 - ab) = 1(a^2 - ab)
and cancelling the (a^2 - ab) from both sides gives 1 = 2 .
(Couldn't figure out how to get the superscript working) -
Re:What's the point?
You're thinking of machine learning, which is a separate branch of AI that's more like an overfunded brand of applied statistics—their strategy is actually still to try and push the envelope (like Hinton, another U of T prof, did last year with dropout networks) but they do so in a more results-driven manner. The ML field as a whole is still sore from three or four decades of overpromising on the future, so they try to put their words where their mouths are, and focus on things that are attainable.
Levesque is in the knowledge representation group, which is more closely in step with cognitive science (the leading edge in modelling human thought) but still very philosophical in their approach. KR was the dominant AI field in the 80s (when Prolog and expert systems were all the rage) but it's matured a great deal since then. Here is his homepage, just to show you how different things are now.
Remember that neural networks aren't magic irreducible fairy dust: they're incredibly powerful, but at the end of the day there must be some program that is running within the network unless it's just a wildly complex ever-changing mapping function, which is unlikely given the illusion of consciousness. Given that quantum mechanics is believed to be Turing-complete, it's fairly likely we'll eventually discover some underlying model that lets us produce a human-like cognitive system without the same level of hardware parallelism that the brain has.
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Lie detectors don't work ..
"Federal agents have launched a criminal investigation of instructors who claim they can teach job applicants how to pass lie detector tests"
Lie detectors don't work, all it does is give a pretext for the testor to claim you lied. If you believe that the machine and tester can detect lies then you are more likly to tell the truth or cop to lying. Lie detector machines are pseudoscience at its worst.
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The Ontario Skeptic, Volume 16, Number 3 (Fall 2003) pp.1, 6.
'Prof. Furedy disputes the value of this procedure, known as the Control Question Test (CQT).
"It is not a test at all in the sense that, say, an IQ test is a test," he says.
The validity of IQ tests in determining intelligence may be controversial, but at least they are scientifically based and use standardized procedures, so the results found by one competent operator will be the same as those found by any other, says Furedy.
However, the so-called control questions of the CQT are designed by the individual examiner, based on discussions with the subject, and the entire examination can vary greatly in length and subject matter. Much of the procedure is often spent not trying to determine whether the subject is telling the truth but trying to elicit a confession of guilt. As a result it cannot be called a scientific or standardized test.
Even when administered by an "expert", the polygraph fails to distinguish between an anxious-but innocent person and an anxious-but guilty person, says Furedy'. -
Re:Obligatory
WTF 80 deg F (approx 27 deg C) is quite warm in a Data-centre especially in a "cold aisle" and 95% humidity is criminal.
You're used to classic datacentres, where the goal was "shove as much cold air into them as possible", i.e. "the lower the temperature the better". It all depends on how the datacentre was built, how its cooling system is/was engineered, and an almost indefinite number of variables. References for you to read (not skim) -- the study in the PDF will probably interest you the most:
http://www.datacenterknowledge.com/archives/2011/03/10/energy-efficiency-guide-data-center-temperature/
http://www.geek.com/chips/googles-most-efficient-data-center-runs-at-95-degrees-1478473/
http://blog.schneider-electric.com/datacenter/2013/05/06/getting-comfortable-with-elevated-data-center-temperatures/
http://www.cs.toronto.edu/~nosayba/temperature_cam.pdf (PDF)
http://www.dummies.com/how-to/content/data-center-temperature-and-humidity-range-recomme.htmlTL;DR -- 80F is not "quite warm" for a datacentre designed/built within the past 10-11 years.
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Re:Why would Intel want to kill the x86?
Uops on P6 were 118 bits: http://www.eecg.toronto.edu/~moshovos/ACA05/read/ppro1.pdf
That would have a slight impact on code density
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Re:Er, export restrictions?
Actually, composing ciphers arbitrarily does not necessarily increase your security level:
http://secgroup.ext.dsi.unive.it/teaching/security-course/composition-of-ciphers/
Or if you prefer a more rigorous treatment of this topic,
http://www.cs.toronto.edu/~myers/BBCEuro.pdf
You should also be careful about composing a cipher with a compression function:
http://news.slashdot.org/story/11/05/26/1933219/Chapel-Hill-Computational-Linguists-Crack-Skype-Calls -
Re:Read the paper, not the graph
It's referring to a paper by Bianca Schroeder, presented at the FAST conference in 2007. In the paper, she takes data from several models of drives, the exact names of which are not revealed. So, this chart is referring to data from some of those drives.
Disclosure: I've worked with the other author of the paper, and provided the authors with some of the raw data they used. Therefore, posting anonymously.
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Re:Read the paper, not the graph
It's referring to a paper by Bianca Schroeder, presented at the FAST conference in 2007. In the paper, she takes data from several models of drives, the exact names of which are not revealed. So, this chart is referring to data from some of those drives.
Disclosure: I've worked with the other author of the paper, and provided the authors with some of the raw data they used. Therefore, posting anonymously.
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Python libraries
For those interested in Python libraries there is PyCuda and gnumpy I have not used either - I'm still learning how to use parallel python
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Re:Surprised Mann wasn't first
Better link http://www.eecg.toronto.edu/~mann/
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Re:innovative?
Front projection on lenticular screens is old hat.
Basically what Apple's patent adds to nearly 20 year old prior art is that instead of shifting the image mechanically they simply "waste" a lot of horizontal pixels (think of it like looking at a lenticular poster, you can only see a fraction of the poster at a time horizontally
... with Apple's scheme the empty space is filled by individual pixels they can not use, they limit the waste by using a very small viewing angle lenticular but that has other side effects). This isn't in prior art because they didn't have that amount of resolution to waste in those days.The device in Apple's patent is is not a true general multi-viewer system either. The viewing zones will repeat/alias, a problem it shares with normal lenticular displays unless they use a ridiculous amount of horizontal resolution to prevent it
... that option isn't open to Apple's method though, it's exit lens has to be at least as wide as the distance between views before they start repeating. So it's not all that useful.So, neither innovative nor useful.
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Apples are even older
Actually, it seems that apples are a bit older: "The genera of Maloid Rosaceae radiated an estimated 48-50 million years ago (Campbell et al. 2007)" (Source)
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Re:ECC Support
I second this. ECC Support is primary reason when I use AMD desktop processors. For something like an Asterisk server, ECC is great peace of mind. I don't need a fast processor, just something will be reliably run for great lengths of time. Remember this DRAM error report based on Google's servers? Makes sense to use AMD desktop processors when you don't need a real server.
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Re:Space Rays, My Ass
People have posted this in other stories about this topic. It is not as far fetched as you think. There's a statistical analysis of RAM errors in Google's server farm: DRAM Errors in the Wild: A Large-Scale Field Study. A large percentage of these errors are hard errros, i.e. defective electronics. The remaining random errors have other causes. The Google paper references other studies which examined the influence of cosmic radiation at ground level.
If you build safety critical systems, you have to build in redundancy, even if the software is provably correct. Hardware is never perfect.
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Re:Well, Yes
You just can't present more information to the audience than you started with.
Actually, even that isn't true anymore – or at least, soon won't be true anymore. It's true you can't create detail that never existed in the first (and probably wouldn't want to), but you can reconstruct detail from real life that isn't captured by the recording medium. Look at the kind of techniques here. This is not creating detail that didn't exist, but finding the detail that did exist from unexpected sources.
I would not be surprised if this demand for 3D would spark someone to discover a way to take the motion information from a movie and convert that into spatial information – assuming that hasn't already been done.
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Re:Meh
Yeah, that's why it doesn't seem quite analogous to me. There's no real practical downside to a B&W->Color switch. There is some artistic interest in B&W over color, but it's fairly niche. But 3d TV requires glasses, which 2d TV doesn't, a big practical difference. And I think the number of people who find 3d annoying / motion-sickness-inducing / etc. to watch, and prefer 2d even just aesthetically, will be greater than the number who prefer b&w over color.
Here's what a 1997 review article (from Displays 17(2):100-110) concluded:
[A] broad range of fairly mature 3-D equipment is already on the market. The available systems, however, suffer from the drawback that users have to wear special devices to separate the left eye's and right eye's images. Such "aided viewing" systems have been firmly established in many professional applications. Yet further expansion to other fields will require "free viewing" systems with improved viewing comfort and closer adaptation to the mechanisms of binocular vision. The respective technologies are still under development.
...which is pretty much the state of technology in 2010 as well. -
Re:But how can you trust the results?
The Tesla c1060 processor boards sound like a very efficient way of packing in compute power, but unless they're neglecting to mention it, the 4GB of GDDR3 RAM each has on board has no error correction. Given the rates of correctable errors observed e.g. here, I could never recommend using it for computing simulations that matter. A flipped bit in a floating point number can have a disproportionate affect on the outcome of calculations that rely upon it, and short of running the whole simulation a second or third time, one couldn't be confident that such an error did not occur.
Large compute-intensive simulations can take weeks, and are used to justify engineering and business decisions that involve the disposition of large amounts of money and other resources — it is important that the computational part of the process can be relied upon.
Which is why the upcoming NVIDIA "Fermi" GPU based boards will support 4GB of ECC memory. Also, they'll have about 2 TFLOPS of single-precision power, and you can stack 4 of them in a box = 8 TFLOPS beside your desk.
I can't wait until the US government starts banning these things because they could be used by terrorists to design nuclear weapons or something. 8)
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But how can you trust the results?
The Tesla c1060 processor boards sound like a very efficient way of packing in compute power, but unless they're neglecting to mention it, the 4GB of GDDR3 RAM each has on board has no error correction. Given the rates of correctable errors observed e.g. here, I could never recommend using it for computing simulations that matter. A flipped bit in a floating point number can have a disproportionate affect on the outcome of calculations that rely upon it, and short of running the whole simulation a second or third time, one couldn't be confident that such an error did not occur.
Large compute-intensive simulations can take weeks, and are used to justify engineering and business decisions that involve the disposition of large amounts of money and other resources — it is important that the computational part of the process can be relied upon.
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Swine Flu perspective
Some quick "back of the envelope" swine flu risk calculations.
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Keep the camera opposite the screen
Back in the 90's, I did some work for the Ontario Telepresence Project. We did lots of studies on videoconferencing, shared mediaspaces...
What strikes me given the relative lack of outcome of the project, compared to the ubiquity of today's camera phones, is that the Telepresence project had it wrong when it wanted to have people *face* each other during conversations.
It turns out, this is not what we want. Staring at your interlocutor's face is not what you do in a usual conversation, it's even embarassing. You look at a shared point of interest. Turning the camera the opposite side of the screen was the way to go. First, you could use the cell phone as a camera, and second, in a phone conversation, it's much more useful to say "look at this", than to offer a nice view of you're hairy nose.
Or, to put it like St. Exupery:
Life has taught us that love does not consist in gazing at each other, but in looking outward together in the same direction... -
Re:What will be their next project?
It would be nice if there were distributed projects that were more closely linked to modern mathematics than the Golomb ruler computations. ABC@home is a start, but I'd be more interested in seeing something like a distributed expansion of tables like these fed into SAGE in an automated way. Other computations that might be useful include homotopy groups of spaces like spheres, Groebner basis calculations for various geometric objects, and knot invariant calculations, but I don't know how well these can be distributed. At any rate, I think building a freely accessible database of some sort is a more constructive use of computer time than brute-forcing single instances of ciphertext. Those sorts of challenges were a good cause in the 1990s, when people were fighting laws banning strong cryptosystems, but the good guys seem to have won that particular war.
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work is in progress....
If a virtual machine would support something like DirectX or OpenGL so that I could have the kids running their games in a virtual machine (and being able to install them, etc.) I would have them set up with a locked down OS with a virtual system for their games. {...} But I'm sure the technology is getting closer.
Yup. Indeed.
/. mentioned recently "VMGL".
The extension is open source but currently only works for X11 OSes at both end.
But as you said, a working acceleration layer is bound to be developed in the near future for Windows too. -
Re:Possibly the stupidest idea ever
Not entirely true. Canadian universities can get
.edu domains, it's just the colleges that can't. For example, guess what's at www.toronto.edu? -
A few leading groups
This is an area with lots of crackpots, but also lots of really interesting stuff.
How do you tell the good stuff from the crackpot?
The good ones are published in top machine learning, computer vision, robotics, and AI conferences and journal. The crackpot stuff doesn't survive peer review.
Here are a few good examples:
- Geff Hinton (U. Toronto): http://www.cs.toronto.edu/~hinton/
- Yoshua Bengio (U. Montreal: http://www.iro.umontreal.ca/~bengioy/
- Yann LeCun (NYU): http://www.cs.nyu.edu/~yann/index.html
- Andrew Ng (Stanford): http://ai.stanford.edu/~ang/
- Sebastian Seung (MIT): http://hebb.mit.edu/people/seung/
- David Lowe (U British Columbia): http://www.cs.ubc.ca/~lowe/ -
Re:Literate programming...
Something like this might help: folding in vim. Emacs probably already has an 11-note chord that does this.
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Kids, parentheses and earlier work
Bah! Kids these days!
Although some of the concepts in TFA are interesting, it is certainly building on ideas that have passed before it.
Much work has been done on emergent behaviour in aggregates of simple organisms, for example the early work of Craig Reynolds is a pivotal paper in this area and widely regarded as a key work in this area. When you might ask? 1987 of course. Bonus points that it was done in LISP. (ObXkcd link). -
Re:How good are the programs
I hope they're using programs that've had a few computer scientists' eyes over them.
Seeing as how the lead researcher holds M.Sc. and Ph.D. degees in Computer Science, is cross-appointed to the Departments of Computer Science and Medical Biophysics at the University of Toronto, and is a Visiting Scientist with IBM's Center for Advanced Studies in Toronto...
...it seems likely that a computer scientist may have cast his eyes over the code once or twice.Where on Earth does this idea come from that multicenter, multimillion-dollar research projects are run by idiots? Neither funding nor talent are in particularly short supply in the field of cancer research, and squeezing extra speed and power out of massive bioinformatic analyses is a hot area.
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Re:To Elaborate on the Submission
I'm not sure how directly relevant it is, but you should definitely take a look at:
http://www.dgp.toronto.edu/people/stam/reality/Res earch/pdf/ns.pdf
(or better yet, find papers which cite this one)
As others have pointed out, multi-grid is a fine way to go, but there's some interesting work on using a combination of finite-element method with particles:
In a nut-shell, your finite-element grid holds the smoothly-varying components (those with c-less-than-1), while the particles hold the discontinuous aspects (those with c-much-greater-than-1). In the sonar case, the particles would correspond to the wavefront(s), while the grid would hold pressure and velocity.
(Stam describes how to re-inject the energy lost to damping in the (c-much-less-than-1) case, but this may or may-not be desirable depending on your problem domain)
One simple trick is to switch to a (symplectic) verlet leap-frog scheme to ensure energy is conserved: Update the grid at time={0, 2, 4, 6, ...) and update the particles at time {1, 3, 5, 7, ...}. ( http://artcompsci.org/kali/vol/two_body_problem_2/ ch01.html )
If your particle density is higher than the grid cells, you can get away with simple splatting (easy!). Otherwise, you need to use something more complicated, radial-basis-functions are great, but some kind of 8-way smearing operator might work too..
For visualization, see also: http://public.kitware.com/VTK
One last thing, if you're using a regular-grid for the finite-element, try and use an irregular representation for your terrain, or else you may find the directional components in the FEM influencing the outputs in the terrain..
Good luck! -
Re:GPU support questionSo do any of these solutions support 3D graphics (nvidia) hardware?
The only reason I currently have a windows partition at all is for gaming.
I recently read an article on the progress of just this. It sounds pretty cool and the initial results are impressive. This combined with the DX->OpenGL Wine code, that I'm sure will be open sourced from the makers of parallels (just had a slashdot story on this), makes for an exciting future for providing hardware acceleration to guest applications.
More information: http://www.cs.toronto.edu/~andreslc/vmgl/ -
Re:Agreed, but with reservations.
Mock footnotes? It's called IEEE Citation.
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Re:Question: Do cards have to support it?
And lo and behold, there is movement:
VMWare Fusion Beta 2 comes with "Experimental 3D Acceleration"
OK, so it's only for Macs so far. But that's a step in the right direction...
VMGL -- this one won't work for Windows guests, but can be used for Linux guests. A similar approach could definitely work for Windows guests, but you'd need to write a DirectX-compatible driver that translates the DX API calls into paravirtualized OpenGL API calls. Tricky, but I imagine possible. -
So 1 DOES equal 2!
Remember this classic phallacy:
1=2
It's all based on the inability to divide by zero. Now that we can, well.... -
0/0 can be many things...
As anyone who has done any calculus has learned, when dealing with operations over the real number field, 0 is a special number, in much the same vein as infinity.
In fact I remember having to solve this problem in my calculus lessons
What is sin(x)/x when x = 0? Now sin(0) = 0, so surely the answer to this should be Nullity?
If you try it on your calculator with x very small (but not quite zero) you'll see that the answer is 1.
Here is a proof
sin(x) = x - x**3/3! + x**5/5! - x**7/7! + ...
=> sin(x)/x = 1 - x**2/3! + x**4/5! - x**6/6! + ...
=> when x = 0, all terms except the first are 0, therefore
=> sin(x)/x = 0/0 = 1
I'm not sure it is really helpful having a symbol for 0/0. Might as well just call it x - the professors demonstration of what 0**0 would have worked just as well!
According to the professor
0**0 = 0**(1-1) = 0**1 * 0**-1 = (0/1)**1 * (0/1)**-1 = (0/1) * (1/0) = 0/0 = Nullity...
How about this version? Why did this get a different answer?
0**0 = 0**(1-1) = 0**1 * 0**-1 = (0/x)**1 * (0/x)**-1 = (0/x) * (x/0) = x/x = 1
If you start assuming that you can divide by 0 then you can prove anything (from http://www.math.toronto.edu/mathnet/plain/falsePro ofs/first1eq2.html )
a = b
=> a**2 = ab
=> a**2 + a**2 = a**2 + ab
=> 2*a**2 = a**2 + a*b
=> 2*a**2 - 2*a*b = a**2 + a*b - 2*a*b
=> 2*a**2 - 2*a*b = a**2 - a*b
=> 2*(a**2 - a*b) = 1*(a*2 - a*b)
=> 2 = 1
The last step is fallacious (a**2 - a*b) is 0 -
Re:This is just a proxy
Not quite just a Proxy.
Looking at the December 13th, 2004 Psiphon Final Report by Patrick Smith and Jeffrey Jia of Department
of Computer Science University Of Toronto (found it with Google, it's a PDF) reveals that Psiphon is
Python based and compiled into a stand alone cross platform GUI application that ANYONE can install and run.
IF they ever release it, Psiphon will amount to a personal https proxy, nothing new until we know the real details.