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Highlight of 2012 (Pre-reqs: Classical Mechanics (Functional calculus based), some notion of Quantum Mechanics)

Abstract: We discuss a quantum counterpart, in the sense of the Berezin-Toeplitz quantization, of certain constraints on Poisson brackets coming from "hard" symplectic geometry. It turns out that they can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics. Our findings include various geometric mechanisms of quantum noise production and a noise-localization uncertainty relation. The methods involve Floer theory and Poisson bracket invariants originated in function theory on symplectic manifolds.

http://arxiv.org/abs/1206.3707

About the author: http://en.m.wikipedia.org/wiki/Leonid_Polterovich

Pretty interesting stuff about magnetics and plasma physics

NGC 6872 Declared The Largest-known Spiral Galaxy

http://www.science20.com/news_artic...l_galaxy-100742

A lot of big things are being found lately

http://www.huffingtonpost.com/2013/..._n_2455552.html

quote:

Originally posted by Terrence Parker A lot of big things are being found lately http://www.huffingtonpost.com/2013/..._n_2455552.html

Damn

http://www.telegraph.co.uk/science/...eakthrough.html

HUH.

quote:

Originally posted by Halcyon+On+On http://www.telegraph.co.uk/science/...eakthrough.html HUH.

Synthetic biology baby! It will revolutionize the 21 century as much as electromagnetism revolutionized the 20th century.

quote:

Originally posted by Halcyon+On+On http://www.telegraph.co.uk/science/...eakthrough.html HUH.

Neat

quote:

Originally posted by Halcyon+On+On http://www.telegraph.co.uk/science/...eakthrough.html HUH.

One step closer to quantum computers!

The algorithm they wrote for this is pretty clever actually, and the real genius of the work is how they got around the infidelity problem of dna replication.

quote:

Originally posted by Halcyon+On+On http://www.telegraph.co.uk/science/...eakthrough.html HUH.

That's actually a storyline in Call of Duty Black Ops 2.

nothing to do on a slow day at work? turn to science!

Never mind the noise: Quantum entanglement allows channel information rate to exceed Shannon zero-error capacity

Read more at: http://phys.org/news/2013-01-mind-n...hannel.html#jCp

(Phys.org)�As developed by Claude Shannon, information theory defines channel capacity as the maximum rate at which information can be sent through the channel. This capacity can be mathematically described using a graph associated with the channel. Specifically, a graph's Shannon zero-error capacity is the maximum rate at which messages can be sent through a noisy channel with zero probability of error. However, the Shannon capacity does not reflect the fact that on atomic scales, nature behaves according to quantum mechanics. Recently, scientists studying asymptotic behavior in entangled sender-receiver quantum systems at Centrum Wiskunde & Informatica, The Netherlands have identified families of graphs for which entanglement allows the Shannon capacity to be exceeded.

quote:

In entanglement-assisted communication, Bri�t explains, there are two parties (sender and receiver) and two resources (a noisy communication channel and a pair of entangled quantum systems). The sender has one of the systems and the receiver the other, and the two parties can perform measurements (that is, experiments) on their respective quantum systems. While the outcomes of such experiments can usually not be predicted in advance, making measurements on entangled systems can still lead to useful results because outcomes of an experiment done by the sender and an experiment done by the receiver, though random, can be strongly correlated. Read more at: http://phys.org/news/2013-01-mind-n...hannel.html#jCp

This is exciting to me because I have studied the crown poset independently, and I believe there are strong correlations between certain TQFTs and the Causal Interpretation (Causets) of Quantum Gravity from the view point of T0 spaces.

http://en.wikipedia.org/wiki/T0_space

Why the crown graph? Because it can also be interpreted as a prime knot. In essence, you can also mathematically describe these as fermat quintic threefolds (Calabi-Yau manifolds).

quote:

It took over two decades and a brilliant mathematician to compute the Shannon capacity of the pentagon, which is the graph associated with a particular channel that has only five inputs and outputs! Only for a very few special cases can we currently say something non-trivial about these parameters.

quote:

Originally posted by srussell0018 That's actually a storyline in Call of Duty Black Ops 2.

This almost makes me want to go back and play the campaign, instead of totally ignoring it and abusing multiplayer.

quote:

Originally posted by Lagrangian nothing to do on a slow day at work? turn to science! Never mind the noise: Quantum entanglement allows channel information rate to exceed Shannon zero-error capacity Read more at: http://phys.org/news/2013-01-mind-n...hannel.html#jCp (Phys.org)�As developed by Claude Shannon, information theory defines channel capacity as the maximum rate at which information can be sent through the channel. This capacity can be mathematically described using a graph associated with the channel. Specifically, a graph's Shannon zero-error capacity is the maximum rate at which messages can be sent through a noisy channel with zero probability of error. However, the Shannon capacity does not reflect the fact that on atomic scales, nature behaves according to quantum mechanics. Recently, scientists studying asymptotic behavior in entangled sender-receiver quantum systems at Centrum Wiskunde & Informatica, The Netherlands have identified families of graphs for which entanglement allows the Shannon capacity to be exceeded. This is exciting to me because I have studied the crown poset independently, and I believe there are strong correlations between certain TQFTs and the Causal Interpretation (Causets) of Quantum Gravity from the view point of T0 spaces. http://en.wikipedia.org/wiki/T0_space Why the crown graph? Because it can also be interpreted as a prime knot. In essence, you can also mathematically describe these as fermat quintic threefolds (Calabi-Yau manifolds).

How on Earth did Shannon develop a topic of information theory without considering quantum mechanical effects?

Information Theory boils down to Quantum Mechanics

Also, Information Theory is the future

http://www.math.princeton.edu/event...inerva-lectures

Very forward thinking here, I was reading a while back about the Motzkin number and how no one had thought about the topological/geometrical implications of it until now...

Oddly enough, I thought about these while thinking about 'traffic lights' and 'highways', I would ponder if we were mathematically able to deduce 'how traffic lights' mimicked the behavior of Cellular Automata. From first principles, I understood we would be forced to think in terms of Category Theory: Traffic lights as classifiers!

Well, Princeton's Fine Hall lectures are always insightful, and once again they seem to be peeking inside my brain lol just kidding. Anyways, they seem to take Motzkin's theorems to a higher level of abstraction and in the right direction: using the language of Cobordism and Spectral sequences they are able to tie conceptual knots that might be crucial in proving Hodge's theorem and Higher homotopy/Holonomy.

Awesome toy
also technical wise


http://madlabindustries.com/hackers...pod-quadcopter/

http://gizmodo.com/5981800/scientis...s?post=57032026

quote:

Originally posted by Halcyon+On+On http://gizmodo.com/5981800/scientis...s?post=57032026

I'm reasonably sure I'm not getting the full picture here.... put stem cells in, get stem cells out... huh?

Just a step closer to organs and limbs on demand. Obviously they can't synthesize stem cells (that would be something), but they have a 3D Printer that you can load designs and cellular mapping into, and with the right material, can do wondrous things. I was just going to use scissors and a workbench myself, but I guess this way is faster.

I'm sure new hearts will be the 2nd most popular organ in the future; when we all need new ones to accommodate the blood demand by our brand-new enormous cocks.

World�s largest prime number discovered -- all 17 million digits

http://www.foxnews.com/science/2013.../#ixzz2KFNq7XAC

quote:

Originally posted by Trance-MB World�s largest prime number discovered -- all 17 million digits http://www.foxnews.com/science/2013.../#ixzz2KFNq7XAC

That is fn awesome. Sounds like the greatest super nerd hobby of all time.

"so what do you like to do for fun"

"discover new prime numbers"

quote:

Originally posted by paulversuspaul That is fn awesome. Sounds like the greatest super nerd hobby of all time. "so what do you like to do for fun" "discover new prime numbers"

I'm more interested in Group Theory.

Here's GAP:
http://www.gap-system.org/

Some Open Problems:


(H1) (a) Are hyperbolic groups residually finite?


(FP6) Is every knot group virtually free-by-cyclic?

(O1) The Andrews-Curtis conjecture. Let F = F_n be the free group of a finite rank n with a fixed set X = {x_1,...,x_n} of free generators.

(a) A set Y = {y_1,...,y_n} of elements of F generates the group F as a normal subgroup if and only if Y is Andrews-Curtis equivalent to X, which means one can get from X to Y by a sequence of Nielsen transformations together with conjugations by elements of F.


http://www.sci.ccny.cuny.edu/~shpil.../oproblems.html

quote:

Originally posted by Trance-MB World�s largest prime number discovered -- all 17 million digits http://www.foxnews.com/science/2013.../#ixzz2KFNq7XAC

Prime Numbers are incredibly useful in the field of Cryptography and Computational Group Theory:

http://en.m.wikipedia.org/wiki/RSA_numbers

http://www.telegraph.co.uk/health/h...e-his-life.html

quote:

Originally posted by Lagrangian I'm more interested in Group Theory. Here's GAP: http://www.gap-system.org/ Some Open Problems: (H1) (a) Are hyperbolic groups residually finite? (FP6) Is every knot group virtually free-by-cyclic? (O1) The Andrews-Curtis conjecture. Let F = F_n be the free group of a finite rank n with a fixed set X = {x_1,...,x_n} of free generators. (a) A set Y = {y_1,...,y_n} of elements of F generates the group F as a normal subgroup if and only if Y is Andrews-Curtis equivalent to X, which means one can get from X to Y by a sequence of Nielsen transformations together with conjugations by elements of F. http://www.sci.ccny.cuny.edu/~shpil.../oproblems.html

Math is a great hobby to have as unlike some other scientific disciplines, you dont need expensive equipment or resources outside of brain power to partake in it.

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