Mathematical Challenges
darpa.mil
darpa.mil
Huh? As far as I'm concerned that's the wrong way to think about neuroscience. Although perhaps the goal here is to replicate parts of the brain's function without regard to the underlying structure, in which case I suppose this is a fair way to go about it.
And "The Geometry of Genome Space: What notion of distance is needed to incorporate biological utility?" is a question I work on every day!
I find many of the rest to be quite vague though. "What are the Fundamental Laws of Biology?" huh? The same fundamental laws as the rest of the universe . . .
Mathematical Challenge 15: The Geometry of Genome Space
What notion of distance is needed to incorporate biological utility?
That was the point where I decided that I want to crawl into a hole and die [1]. The biology related "challenges" on this list drive me particularly crazy, though most of the others are pretty bad, too, since they're not well defined enough to even have much to say about.
[1] It's not that I don't think "notions of distance" are an important thing to understand, or anything like that, they certainly are, and biologists do worry about that type of stuff - I'd guess that the computational bio folks out there understand that stuff a lot better than a lot of mathematicians. But this question...it's the type of thing a philosophy major would ask after hearing about the concept of a metric space, getting stoned, and seeing a Darwin poster, not something anyone that actually knows both math and biology would (should?) ever ask.
Although I suppose the probability that DARPA was thinking about gene regulation when they wrote this is slim to none :/
The challenge means that current computational neuroscience models by and large are mainly descriptions of the data we've gathered and seldom are able to extrapolate beyond that. Somewhat embarrassingly, perhaps the field's biggest success in achieving a deeper understanding is what bootstrapped it 60 years ago -- the Hodgkin-Huxley model. Admittedly, neuroscience is extremely challenging and our experimental techniques are still relatively primitive. However, having testable, predictive models is essential to moving the field forward.
Indeed. I'm not sure what they mean by that. In my view, the best way to understand biology is to develop a greater understanding of QM and then model macroscopic structures through simulation. Biology is really just an emergent phenomenon after all.
Absolutely, and it enrages me that there are many in the field who don't think like this.
I would point out, however, that the physics/chem we have is likely good enough for the representation biological systems. A more nuanced understanding of QM or fundamental physics in general, while obviously necessary in the end, is not going to do a whole lot to further the biological sciences at this moment. Unless of course, there's some sort of fundamental physics we're missing that is somehow intrinsic to protein/RNA folding, but that's a vanishingly unlikely prospect.
EDIT: oh I see, you do MD stuff, which helps explain your mindset :P I work in developmental genetics and the mindset/goals are very different.
The computational power needed for the treatment of a very large system (e.g. whole-organism, or even whole-cell) using fundamental physical laws (like QM, and probably even a classical approximation) will be out of reach for at least the next few decades (probably :)). So I would argue that while it's technically true that biology is a phenomenon which emerges from fundamental physical laws, it's sufficient for the time being to treat biology as a field distinct from, but ultimately dependent on, physics.
Is that a settled question? I can see that the laws may be well defined, but what about the initial conditions? Can we determine the initial conditions precisely enough, assuming there are fundamental limits on what we can measure?
I guess that is equivalent to the question of whether if the initial conditions are approximately right, is there an in-built stability in the system, which makes a biological simulation converge to a to a meaningful result. Do errors get magnified or eliminated? (Presumably the latter, otherwise thermal noise would make us fall apart, but is this confirmed?)
As an aside, since you are in the molecular dynamics field, can you recommend a starting point for a novice that is interested in getting involved? Books? Open source software? I've always thought it would be fun to program an FPGA with the relevant equations, let it run, and see what happens.
Also, check out Molecular Dynamics Simulation (http://www.amazon.com/Molecular-Dynamics-Simulation-Elementa...)
and Computer Simulation of Liquids (http://www.amazon.com/Computer-Simulation-Liquids-M-Allen/dp...)
Which kind of ties into the parent's musings into the mathematical model of thought. The point is to create models that avoid invoking as much of the underlying low-level processes as possible. It would be -amazing- if we could create a mass of DEs that would -think-, especially if those DEs weren't just a straight representation of a massive neural network that happened to be copied right out of our brains.
You'll get a much better response to this idea if you remove the word 'just'. Much better.
But it's such a useful mental model. It allows you to gloss over irrelevant low-level details while focusing on the aspects of the complex emergent system that are actually relevant.
> I'm not implying in any way that biology is easy
This is what saying it's 'just' emergent behavior comes off as, though. I understand (and agree with) your perspective, but being a little more tactical with your word use can head off pointless (as opposed to interesting) arguments.
I'd love to hear anyone's thoughts on...
Mathematical Challenge 6: Computational Duality Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
Mathematical Challenge 7: Occam’s Razor in Many Dimensions As data collection increases can we “do more with less” by finding lower bounds for sensing complexity in systems? This is related to questions about entropy maximization algorithms.
I am neither clear on 7. I wish I knew what he meant about MaxEnt in particular, there's a lot of neat explorations from the connections between entropy and learning.
But specific to what I interpret as a better Occam's Razor, my vote will have to go to Marcus Hutter as the person who is currently doing the most interesting work in that area. Specifically his work on approximating universal priors. Schmidhuber also has interesting stuff on complexity, search for his talks - they're great.
Described to me by a number theorist as: "That's where number theorists go to die".