Statistical physics is the natural framework to model complex networks. In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organisation, scale invariance, mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents. At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models reproducing some features of empirical networks, but otherwise as random as possible. We review here the statistical physics approach for complex networks and the null models for the various physical problems, focusing in particular on the analytic frameworks reproducing the local features of the network. We show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks, as well as to reconstruct the network structure in case of incomplete information. We further survey the statistical physics frameworks that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, and the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.
Comments: To appear on Nature Reviews Physics. The revised accepted version will be posted 6 months after publication
Tag: physics
👓 Atiyah and the Fine-Structure Constant | Sean Carroll
Sir Michael Atiyah, one of the world’s greatest living mathematicians, has proposed a derivation of α, the fine-structure constant of quantum electrodynamics. A preprint is here. The math her…
👓 Jocelyn Bell Burnell Discovered Radio Pulsars in 1974, But the Credit Went to Her Advisor; In 2018, She Gets Her Due, Winning a $3 Million Physics Prize | Open Culture
Say you made a Nobel-worthy scientific discovery and the prize went to your thesis supervisor instead. How would you take it?
🔖 Statistical mechanics of complex networks | Rev. Mod. Phys. 74, 47 (2002)
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
h/t Disconnected, fragmented, or united? a trans-disciplinary review of network science by César A. Hidalgo (Applied Network Science | SpringerLink)
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👓 Andrew Jordan reviews Peter Woit’s Quantum Theory, Groups and Representations and finds much to admire. | Inference
Andrew Jordan reviews Peter Woit's Quantum Theory, Groups and Representations and finds much to admire.
For the tourists, I’ve noted before that Peter maintains a free copy of his new textbook on his website.
I also don’t think I’ve ever come across the journal Inference before, but it looks quite nice in terms of content and editorial.
Syndicated copies to:👓 Lost in Math | Peter Woit
Sabine Hossenfelder’s new book Lost in Math should be starting to appear in bookstores around now. It’s very good and you should get a copy. I hope that the book will receive a lot of attention, but suspect that much of this will focus on an oversimplified version of the book’s argument, ignoring some of the more interesting material that she has put together. Hossenfelder’s main concern is the difficult current state of theoretical fundamental physics, sometimes referred to as a “crisis” or “nightmare scenario”. She is writing at what is likely to be a decisive moment for the subject: the negative LHC results for popular speculative models are now in. What effect will these have on those who have devoted decades to studying such models?
I love that he calls out the review in Science.
Syndicated copies to:👓 Ultra-Accurate Clocks Lead Search for New Laws of Physics | Quanta Magazine
Atomic clocks are letting physicists tighten the lasso around elusive phenomena such as dark matter.
👓 Mathematicians Explore Mirror Link Between Two Geometric Worlds | Quanta Magazine
Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.
An interesting story in that physicists found the connection first and mathematicians are tying the two areas together after the fact. More often it’s the case that mathematicians come up with the theory and then physicists are applying it to something. I’m not sure I like some of the naming conventions laid out, but it’ll be another decade or two after it’s all settled before things have more logical sounding names. I’m a bit curious if any category theorists are playing around in either of these areas.
After having spent the last couple of months working through some of the “rigidity” (not the best descriptor in the article as it shows some inherent bias in my opinion) of algebraic geometry, now I’m feeling like symplectic geometry could be fun.
Syndicated copies to:🔖 [1803.08823] A high-bias, low-variance introduction to Machine Learning for physicists | arXiv
Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists maybe able to contribute. (Notebooks are available at this https URL )
👓 Caltech Mourns the Loss of Stephen Hawking | Caltech
👓 Stephen Hawking, Who Examined the Universe and Explained Black Holes, Dies at 76 | The New York Times
A physicist and best-selling author, Dr. Hawking did not allow his physical limitations to hinder his quest to answer “the big question: Where did the universe come from?”
Some sad news after getting back from Algebraic Geometry class tonight. RIP Stephen Hawking.
Syndicated copies to:The Physics of Life: Summer School | Center for the Physics of Biological Function
A summer school for advanced undergraduates June 11-22, 2018 @ Princeton University What would it mean to have a physicist’s understanding of life? How do DYNAMICS and the EMERGENCE of ORDER affect biological function? How do organisms process INFORMATION, LEARN, ADAPT, and EVOLVE? See how physics problems emerge from thinking about developing embryos, communicating bacteria, dynamic neural networks, animal behaviors, evolution, and more. Learn how ideas and methods from statistical physics, simulation and data analysis, optics and microscopy connect to diverse biological phenomena. Explore these questions, tools, and concepts in an intense two weeks of lectures, seminars, hands-on exercises, and projects.
👓 How 4,000 Physicists Gave a Vegas Casino its Worst Week Ever | Physics Buzz
What happens when several thousand distinguished physicists, researchers, and students descend on the nation’s gambling capital for a conference? The answer is "a bad week for the casino"—but you'd never guess why. The year was 1986, and the American Physical Society’s annual April meeting was slated to be held in San Diego. But when scheduling conflicts caused the hotel arrangements to fall through just a few months before, the conference's organizers were left scrambling to find an alternative destination that could accommodate the crowd—and ended up settling on Las Vegas's MGM grand.
Totally physics clickbait. The headline should have read: “Vegas won’t cater to physics conferences anymore because they’re too smart to gamble.”
Syndicated copies to:Physicists Aim to Classify All Possible Phases of Matter | Quanta Magazine
A complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.