Complex Systems Studies
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What's up in Complexity Science?!
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@ComplexSys

#complexity #complex_systems #networks #network_science

📨 Contact us: @carimi
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Four #postdoc/research fellow positions in complex networks at the Czech Academy of Sciences in Prague
cobra.cs.cas.cz
I am currently looking for a #phd student to investigate the impact of network structures, interventions, and ranking algorithms on collective social behavior.

https://www.socialnetworks.uzh.ch/en/no-open-positions.html
Three open positions in data science & AI/ML methods and applications at Dpt of Computing, Turku, Finland for #PhD / project researcher / assistant.

1) Scientific data analysis; DL Sep 30.
2) Microbiome & metagenome research; DL Sep 19
3) Computational humanities; DL Sep 30
I am happy to announce that I made a group for all Persian Kagglists around the globe. I made this group wishing to gather all Persian Kagglist and interested people under the same roof. Communication is the key! This group would help people to find and know each other. This will also help to increase the chance of being seen for finding a desired data science job. Please spread the word. Thanks!
#kaggle #datascience
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AI4Science #Call for fellows!
Deadline: Oct. 31, 2022

The #Fellowship gives researchers the chance to collaborate EPFL faculties on accelerating the use and furthering the understanding of #MachineLearning methods in the scientific discovery process. You hold a PhD, in any field relevant to this endeavour, are fluent in English and have a collaborative spirit.

https://www.epfl.ch/research/domains/cis/call-for-fellows/
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Spontaneous Symmetry Breaking
A little thread by Michael Sentef

Did you know that there was a connection to nonequilibrium physics?
Take a collection of bar magnets (it's all classical physics), with a force between neighboring ones that wants to align them with one another. We call this "ferromagnetic exchange". Now, each little magnet is free to rotate in space. So is the collective magnetization.

This is the energy of the system. x is the spatial location of the "spin", and delta is a vector connecting nearest neighbors. J is the ferromagnetic exchange interaction. The collective magnetization M is the sum of all spin vectors. As written above, the energy is minimal when all spins are aligned, and the modulus |M| is maximal then. But where will the M-vector point in space? This is *impossible* to predict from our theory. Why?

The energy functional written above does not tell us! This is precisely what we call spontaneous symmetry breaking. And this is what we all learn in our textbooks.

Now, here is a plot twist. We also learn in statistical mechanics how to compute thermal expectation values of stuff. Take all states (all possible spin configurations). Take their magnetization (=sum of little spins). Attach a "Boltzmann weight". Sum over all states. This statistical <M> value will always be zero! Why? Because the E-functional does not tell us which direction M should point into. There is no preferred direction.

In other words, stat-mech tells us that spontaneous symmetry breaking does not exist. Ummm... but you told us that it did, right? Also, how does my fridge magnet work if stat-mech forbids it to exist?

Here is an answer: We should consider the "thermodynamic limit". Which is "singular". How so? The prescription that we still all learn is the following: Pretend that there is a preferred direction, given by this little h-field (an "external magnetic field" -- where it comes from doesn't matter here).

Now all spins align with this h-field, and with one another. All problems solved? Not quite. We have to consider two limits. We can first let h->0 and then the number of little magnets N->infinity, or vice versa. The order of limits matters! (They do not "commute"). When we let h->0 for any finite system, <M> will be zero. When we first let N->infinity (the thermodynamic limit) and then h->0, <M> will remain finite and maximal, and will remember the direction in which h pointed originally. This is still all well known.

But here is a conundrum. We think of spontaneous symmetry breaking only in the thermodynamic limit. It is being taught like this everywhere. But ... nothing is infinite in nature! Yet we have fridge magnets, and they work! Why? Nonequilibrium comes to the rescue! How quickly does a fridge magnet de-magnetize after it has been magnetized? I.e., how does the limiting process in which we apply the h-field for a finite (but large) collection of spins, then turn the h-field off, work in real time? When the number of spins is large, they need to "fluctuate" away from the perfectly aligned configuration spontaneously in order to de-magnetize. This is increasingly unlikely when (a) the temperature is low and (b) N is large.

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The system does not explore its state space. More precisely, the state space is not explored according to the "Boltzmann weights" mentioned above. We call this behavior "non-ergodic". Relaxation to a non-magnetic configuration is super slow for your fridge magnet. Wait long enough, and it will fall off the fridge. But "long" means "almost till eternity", provided that the magnet is sufficiently strong and sufficiently large. This is what we mean by "thermodynamic limit" for all practical purposes. The time scale on which we see "thermalization" is really really large. Now, this was all somewhere in the back of my mind, but I never thought about it so clearly. Who did? These guys: Aron J. Beekman, Louk Rademaker, Jasper van Wezel. Props to Aron, Louk and Jasper for spelling out what one rarely finds spelled out in textbooks.
I highly recommend reading their lecture notes. I should do it as well.

https://twitter.com/sentefmi/status/1572463208262434817

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Watch two full days' worth of talks from our 2022 #ScienceOfScience workshop

https://youtube.com/playlist?list=PLZlVBTf7N6GqpWzuv0IjFtgwXhBsF4XI6
Applications for our 2023 #PhD programme in Theoretical Neuroscience and Machine Learning are now open! Fully funded regardless of nationality.

ℹ️ Info and how to apply: http://ucl.ac.uk/gatsby/study-and-work/phd-programme

Deadline: 13 November 2022
A series of 14 seminars on the most influential papers of Parisi will give the opportunity to dive into the history of disordered systems (and beyond),

https://sites.google.com/gssi.it/giorgioparisiseminars
A series of 14 seminars on the most influential papers of Parisi will give the opportunity to dive into the history of disordered systems (and beyond),

https://sites.google.com/gssi.it/giorgioparisiseminars
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The data science and AI division at CSE is recruiting a #PhD student in machine learning for a project on the efficient generalization using causality and auxiliary information.

https://www.chalmers.se/en/about-chalmers/Working-at-Chalmers/Vacancies/Pages/default.aspx?rmpage=job&rmjob=10849&rmlang=UK
PostDoc-ERCSocsemics2022-CSS.pdf
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Postdoctoral fellowship (18 months, possibly extendable) in computational social science in Berlin.
Hello Quantum World! A rigorous but accessible first-year university course in quantum information science
https://arxiv.org/abs/2210.02868
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