
Mathematical Challenges - kevinalexbrown
http://www.darpa.mil/Our_Work/DSO/Programs/23_Mathematical_Challenges.aspx
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thronemonkey
"Develop a mathematical theory to build a functional model of the brain that
is mathematically consistent and predictive rather than merely biologically
inspired."

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 .
. .

~~~
Xcelerate
>> 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 .
. .

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.

~~~
thronemonkey
>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.

~~~
tomjakubowski
As a (hopefully interesting!) aside, on the scale of most biological molecular
dynamics simulations, quantum mechanical contributions can largely be ignored,
because the mechanics of the large, heavy nuclei dominate the system. There
are a few instances where a hybrid classical/quantum force field is necessary
though, like any simulation involving breaking/formation of chemical bonds
(where electrons must be treated explicitly).

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.

~~~
thronemonkey
Yeah, I largely agree. My comment was more to indicate that when Xcelerate
thinks about simulating a biological process, he thinks on the level of
simulating individual atoms, which is much more likely to make someone think
about the fundamental physics of the problem. When I simulate biological
processes, I think in terms of chemistry or stat mech. Rather than one
molecule I'm dealing with collections of many types of molecules whose
interactions are often ill defined anyway, so I'm much more likely to think
"eh, the chemistry we have is good enough, let's just get on with it"

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bo1024
A lot of these are really cool/thought-provoking.

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.

~~~
Dn_Ab
There are many definitions of duality in mathematics so I am not entirely
clear on 6. For example the notion of duals from category theory has already
been very helpful in understanding or developing many algorithms. In fact a
generous viewing will allow for even enterprise software in the form of LINQ
and Observables to have made use of duals in their development.

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.

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Volpe
> Mathematical Challenge 19: Settle the Riemann Hypothesis The Holy Grail of
> number theory.

Described to me by a number theorist as: "That's where number theorists go to
die".

~~~
masterzora
To be fair that was pretty much the same thing said about Fermat's Last
Hypothesis until Wiles got cheeky in 1994 and made a hundred-page margin.

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Jach
I knew that "23 being the number" was familiar. All throughout I was thinking
"This is just a poor rip off trying to imitate Hilbert's problems", and sure
enough there are 23 of them.
<http://en.wikipedia.org/wiki/Hilbert%27s_problems> I think I'd rather people
pursue the (in my view) more clearly worded list of friendly AI problems:
[http://friendlyai.tumblr.com/post/11957913150/yudkowskys-
sin...](http://friendlyai.tumblr.com/post/11957913150/yudkowskys-singularity-
summit-2011-talk)

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toomuchcoffee
"Develop a mathematical theory to end, once and for all, humanity's fatal
attraction to War; to the glorification of State power, and to the ideology
that ends always justifies the means; and in particular, to the perceived need
to dominate and control other human beings at scale and through nearly
limitless violence and coercion, generally."

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pav3l
So, is P vs NP not useful enough for DARPA? Or is it just not a sexy problem
anymore?

