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.
Under the Sebi Act, the regulator has the power to carry out search and seizure of books, registers, documents including electronics and digital devices from any person associated with the securities market. Elsewhere, version 8.6 of Telegram integrates the in-app camera option into the gallery, while a new navigation bar gives quick access to photos, files, location sharing, and more. The channel appears to be part of the broader information war that has developed following Russia's invasion of Ukraine. The Kremlin has paid Russian TikTok influencers to push propaganda, according to a Vice News investigation, while ProPublica found that fake Russian fact check videos had been viewed over a million times on Telegram. At its heart, Telegram is little more than a messaging app like WhatsApp or Signal. But it also offers open channels that enable a single user, or a group of users, to communicate with large numbers in a method similar to a Twitter account. This has proven to be both a blessing and a curse for Telegram and its users, since these channels can be used for both good and ill. Right now, as Wired reports, the app is a key way for Ukrainians to receive updates from the government during the invasion. To that end, when files are actively downloading, a new icon now appears in the Search bar that users can tap to view and manage downloads, pause and resume all downloads or just individual items, and select one to increase its priority or view it in a chat.
from vn
