The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling constants, across different levels of resolution. It also provides a way to identify critical points of phase transitions and study the system's behaviour around them by distinguishing between relevant and irrelevant details, the latter being unnecessary to describe the emergent macroscopic properties. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, various approaches have tried to extend RG concepts to the ubiquitous realm of complex networks where explicit geometric coordinates do not necessarily exist, nodes and subgraphs can have very different properties, and homogeneous lattice-like symmetries are absent. The strong heterogeneity of real-world networks significantly complicates the definition of consistent renormalization procedures. In this review, we discuss the main attempts, the most important advances, and the remaining open challenges on the road to network renormalization.
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling constants, across different levels of resolution. It also provides a way to identify critical points of phase transitions and study the system's behaviour around them by distinguishing between relevant and irrelevant details, the latter being unnecessary to describe the emergent macroscopic properties. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, various approaches have tried to extend RG concepts to the ubiquitous realm of complex networks where explicit geometric coordinates do not necessarily exist, nodes and subgraphs can have very different properties, and homogeneous lattice-like symmetries are absent. The strong heterogeneity of real-world networks significantly complicates the definition of consistent renormalization procedures. In this review, we discuss the main attempts, the most important advances, and the remaining open challenges on the road to network renormalization.
In 2018, Russia banned Telegram although it reversed the prohibition two years later. You may recall that, back when Facebook started changing WhatsApp’s terms of service, a number of news outlets reported on, and even recommended, switching to Telegram. Pavel Durov even said that users should delete WhatsApp “unless you are cool with all of your photos and messages becoming public one day.” But Telegram can’t be described as a more-secure version of WhatsApp. Telegram was co-founded by Pavel and Nikolai Durov, the brothers who had previously created VKontakte. VK is Russia’s equivalent of Facebook, a social network used for public and private messaging, audio and video sharing as well as online gaming. In January, SimpleWeb reported that VK was Russia’s fourth most-visited website, after Yandex, YouTube and Google’s Russian-language homepage. In 2016, Forbes’ Michael Solomon described Pavel Durov (pictured, below) as the “Mark Zuckerberg of Russia.” In December 2021, Sebi officials had conducted a search and seizure operation at the premises of certain persons carrying out similar manipulative activities through Telegram channels. On February 27th, Durov posted that Channels were becoming a source of unverified information and that the company lacks the ability to check on their veracity. He urged users to be mistrustful of the things shared on Channels, and initially threatened to block the feature in the countries involved for the length of the war, saying that he didn’t want Telegram to be used to aggravate conflict or incite ethnic hatred. He did, however, walk back this plan when it became clear that they had also become a vital communications tool for Ukrainian officials and citizens to help coordinate their resistance and evacuations.
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