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Physical interpretation of the Manifold Hypothesishttps://mathoverflow.net/q/351368/56328?stw=2 …
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'Fractional Calculus and Variational Mechanics' //http://large.stanford.edu/courses/2007/ph210/noriega2/ … An explanation of how the fractional calculus allows an extension of the Lagrangian to non-conservative systems.
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Aidan Rocke Retweeted
Bridging Motor and Cognitive Control: It’s About Time!
@harrison_ritz,@amitaishenhav, & Romy Frömer highlight recent@NatureNeuro work revealing similarities in the algorithms that control our thoughts and movements@mjaztwit,@EggerSethhttps://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(19)30277-3#back-bib3 …Thanks. Twitter will use this to make your timeline better. UndoUndo -
@ampanmdagaba,@NoahGuzman14 do you guys think this can work for problems in theoretical neuroscience? I mean interesting problems which won't be worked out in the next 10 years otherwise as they simultaneously require a combination of skills and solving a coordination problem.Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo -
'The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution.' link:https://polymathprojects.org/
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Note: I think this might be one of the most interesting open problems in machine learning and neural information processing, unless a theoretical neuroscientist has already adequately addressed this question in a slightly different setting.
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Finally, we are all on Twitter to exchange ideas and not one-up each other so I hope everyone feels free to share their perspective. :)
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I haven't seen this question properly formulated anywhere so this represents my attempt. From my discussions with an applied topologist it has yet to be properly addressed. I also highly doubt that this is one of those problems where there will be a single ‘eureka’ moment. ;)
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@NatashaMhatre I think this is also related to our previous discussion on the controllability and stability of complex dynamical systems. Instead of framing the question in the abstract I think we can connect it to an existing hypothesis in machine learning. :)Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo -
This might also interest
@KaiUeltzhoeffer,@DaltonSakthi,@marceljuenglingShow this threadThanks. Twitter will use this to make your timeline better. UndoUndo -
I think this question might interest
@KordingLab,@xaqlab,@benlansdell,@antoniocbscosta,@rbhar90,@Aras121,@a_tschantz,@NoahGuzman14Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo -
In recognition that many scientists I admire are regularly harassed on Twitter, I wrote a few rules for scientific discourse: http://bit.ly/2S4ezni (also in my Twitter bio) (1) Feel free to use/share this list. (2) It is essential to define boundaries without being vindictive.
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If you want to have civil discussions on Twitter, it is important to treat other scientists like human beings. Otherwise you are normalising this kind of behaviour. Those who sit back and say nothing are legitimising the status quo.
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This is also not the first time I have observed this, which is why I am reluctant to name particular people. Check the 'Gradients in the Brain' debate as well: https://twitter.com/KordingLab/status/1201876087002869763 … A lot of the comments are unnecessarily adversarial.
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I won't name names but I find that
@KordingLab is always remarkably tolerant and tactful. Go through this thread and you'll understand what I mean. I really think a little bit more empathy can go a long way.https://twitter.com/KordingLab/status/1222985352211648513 …Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo -
Aidan Rocke Retweeted
Using simple linear models as building blocks, we are able to segment complex dynamics into interpretable segments. From brain to behavior, we find near-critical dynamics and show evidence of its modulation.
@PNASNews#biophysics#behavior#neuroscience https://tinyurl.com/yaaw6dsu https://twitter.com/greg_stephens/status/1086318208490061824 …Thanks. Twitter will use this to make your timeline better. UndoUndo -
I like the way
@KordingLab calls this an 'intuition' question. :) For problems in high-dimension I think the best approach is to use inequalities and analyse them mathematically. Every time I use my intuition I get the answer completely wrong.https://twitter.com/KordingLab/status/1222985352211648513 …Thanks. Twitter will use this to make your timeline better. UndoUndo -
Concerning the almost-all property the way this helps is that if we have a deterministic controller F that is piece-wise linear and each Jacobian is square, we only have to add gaussian noise ~N(0,epsilon) to this Jacobian so that F is locally invertible with probability one.
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I am pretty confident this idea has been explored so I am curious about references. I think such a theory should work for pretty complex inverse dynamics since the composition of a sequence of invertible functions is also invertible.
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Might there be a theory as to how organisms are dynamically stable? If mammals model dynamics using piece-wise linear functions, then we know that almost all square matrices are invertible so an inverse exists locally. cc:
@GunnarBlohm,@JCashaback,@KordingLab,@JonAMichaelsShow this threadThanks. Twitter will use this to make your timeline better. UndoUndo
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