"Machine-Learning Mathematical Structures" (by Yang-Hui He): https://arxiv.org/abs/2101.06317

"We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years."

What is economic complexity? And how it is helping us understand the economy? More than a decade ago, two papers helped ignite the field.

The first comprehensive review of Economic Complexity in Nature Review Physics

https://t.co/hQTDpn9IMs

The Network Pages
The math and algorithms that keep us connected

https://www.networkpages.nl/

we will publish interactive demonstrations

🎞 The Structure of Complex Networks: Scale-Free and Small-World Random Graphs - Remco van der Hofstad

https://www.aparat.com/v/gryA3

Abstract:
Many phenomena in the real world can be phrased in terms of networks. Examples include the World-Wide Web, social interactions and Internet, but also the interaction patterns between proteins, food webs and citation networks.

Many large-scale networks have, despite their diversity in backgrounds, surprisingly much in common. Many of these networks are small worlds, in the sense that one requires few links to hop between pairs of vertices. Also the variability of the number of connections between elements tends to be enormous, which is related to the scale-free phenomenon.

In this lecture for a broad audience, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modeling in terms of graphs and how real-world networks can be modeled, as well as how these models help us to give sense to the empirical findings. We continue by discussing some random graph models for real-world networks and their properties, as well as their merits and flaws as network models. We conclude by discussing the implications of some of the empirical findings on information diffusion and competition on such networks.

We assume no prior knowledge in graph theory, probability or otherwise.

Scaling limits: from statistical mechanics to manifolds
September 1-3, 2021

http://www.statslab.cam.ac.uk/james60

This workshop will take James' work as a jumping-off point for an exploration of future research directions in probability. There will be 16 invited talks loosely covering the following themes:

Random growth processes and SPDEs
Yang-Mills measure
Limits of random graphs, random planar maps, and fragmentation processes
Markov chains, interacting particle systems and fluid limits
Diffusion processes and heat kernels.

Gady Kozma, Weizmann Institute

🎞 Critical and Near-Critical Percolation - 1

🎞 Critical and Near-Critical Percolation - 2

🎞 Critical and Near-Critical Percolation - 3

Video From 20ss230: Online Open Probability School

Souvik Dhara, Micrsoft Research and MIT

🎞 Critical percolation on random networks with given degrees

Files related to this video

Yuval Peres, Microsoft Research

🎞 Random walks on dynamical percolation

17w5119: Stochastic Analysis and its Applications

Remco Van der Hofstad, TU Eindhoven

🎞 Progress in high-dimensional percolation

16w5085: Random Structures in High Dimensions

Introduction to percolation theory.
Hugo Duminil-Copin
October 7, 2018

Abstract. These lecture notes present the content of a 10 hours class given for the Master 2 of Paris-Saclay.

🎞 Hugo Duminil-Copin - Sharp threshold phenomena in Statistical Physics

In this course, we will present different techniques developed over the past few years, enabling mathematicians to prove that phase transitions are sharp. We will focus on a few classical models of statistical physics, including Bernoulli percolation, the Ising model and the random-cluster model.

Organisé par Emmanuel Ullmo
Mars/avril 2017

Hugo DUMINIL COPIN Graphical representations of the Ising model

🎞 8 videos

Academics are one of the biggest groups using the #TwitterAPI to research what’s happening. Their work helps make the world (& Twitter) a better place, and now more than ever, we must enable more of it.
Introducing 🥁 the Academic Research product track!
https://t.co/nOFiGewAV2

3-year POSTDOC for an observer, computer scientist, or enthusiastic individual who just wants to play with state-of-the-art data from the latest space telescope @NASAWebb
Come join me at Bristol to work on guaranteed observations of #exoplanet atmospheres
https://t.co/ZubtGD2VoT

💰 Applications open for 33 #PhD studentships in applied maths, statistics & machine learning with exciting application areas in @ucddublin @MACSI @MU_Hamilton

Apply directly on our application portal
https://t.co/b5xe239wwr

Closing date Feb 5th 2021
Start date Sept 1st 2021!📈

2020 is almost over, we can get ready for 2021! Apply now for the Spring College on the Physics of Complex Systems: https://t.co/eoXGuCUTdT

#ComplexSystems

Unlocking US vaccine distribution

COVID vaccine distribution in the United States has been hobbled by a web of mismatched technology systems, inconsistent vaccine supplies, under-resourced states and a lack of coordination about getting shots to people once they arrive at local clinics. US President Joe Biden's administration has a goal of delivering 100 million doses in 100 days. To keep that promise, experts say the federal government will need to supply states with better resources and technology. “National coordination will be a game-changer,” says Hana Schank, from the think-tank New America

https://www.technologyreview.com/2021/01/27/1016790/covid-vaccine-distribution-us

Giraffes have a very familiar skin/fur pattern, but you probably never knew that there's more than one and that they are different on a regional and genetic basis [source, read more: https://buff.ly/2TLKoSr]

💉 Let’s talk about where variants ARE coming from and under what circumstances?
Ashish K. Jha, MD, MPH

Variants arise when infections run wild and selection pressures lead to dangerous mutations that can then thrive. Remember, every infection creates opportunities for “errors” – or mutations.

Most mutations are meaningless. They will have no real clinical implications. But every once in a while, a set of mutations will lead the virus to become more contagious, more lethal, or improve its ability to escape our vaccines

🦠 So where are the variants coming from?

UK , South Africa, Brazil –and possibly US (LA variant still being sorted out). Each of these countries had large outbreaks even before their variants took off. So what are implications if we ever want to end this pandemic? We have to bring pandemic under control everywhere.

Letting virus run wild, like US, Brazil did, endangers everyone. Imagine this; Some nations are largely vaccinated but outbreaks are surging elsewhere. What might happen? We might see rise of variants that eventually escape the vaccines. And make everyone vulnerable again.

In a future where US is vaccinated but others are not, we could see rise of variants that can infect, cause outbreaks here and other vaccinated places requiring us to update our vaccines and vaccinate everyone again! It’s the nightmare scenario of a never-ending pandemic.

🦠 There is only one solution to put this nightmare pandemic behind us; Get outbreaks under control everywhere. How?
Put in place virus control policies, get people to wear high quality masks, have more testing AND Vaccinate the world NOW As quickly as possible.

This is what makes herd immunity advocates (remember Great Barrington Declaration?) so naive; They literally advocated for virus to have more chances to mutate and what makes U.S. isolationist policies so naive because we live on one planet and variants travel!

🦠 Want to end the pandemic?

Lets marshal global manufacturing effort to make lots of vaccine quickly and vaccinate everyone! Because large outbreaks anywhere can give rise to variants that can escape vaccines everywhere. At the end of the day, we really are in this together.

https://twitter.com/ashishkjha/status/1354995270619181056

Percolation on complex networks: Theory and application

🔗 arxiv.org/abs/2101.11761

In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components composing the complex systems. As a paradigm for random and semi-random connectivity, percolation model plays a key role in the development of network science and its applications. On the one hand, the concepts and analytical methods, such as the emergence of the giant cluster, the finite-size scaling, and the mean-field method, which are intimately related to the percolation theory, are employed to quantify and solve some core problems of networks. On the other hand, the insights into the percolation theory also facilitate the understanding of networked systems, such as robustness, epidemic spreading, vital node identification, and community detection. Meanwhile, network science also brings some new issues to the percolation theory itself, such as percolation of strong heterogeneous systems, topological transition of networks beyond pairwise interactions, and emergence of a giant cluster with mutual connections. So far, the percolation theory has already percolated into the researches of structure analysis and dynamic modeling in network science. Understanding the percolation theory should help the study of many fields in network science, including the still opening questions in the frontiers of networks, such as networks beyond pairwise interactions, temporal networks, and network of networks. The intention of this paper is to offer an overview of these applications, as well as the basic theory of percolation transition on network systems.