Order and information in the patterns of spinning magnetic micro-disks at the air-water interface

A local measure based on the Shannon entropy establishes connections among information, structures, and interactions.

Global and local community memberships for estimating spreading capability of nodes in social networks

The analysis of spreading processes within complex networks can offer many important insights for the application in contexts such as epidemics, information dissemination or rumours. Particularly, structural factors of the network which either contribute or hinder the spreading are of interest, as they can be used to control or predict such processes. In social networks, the community structure is especially relevant, as actors usually participate in different densely connected social groups which emerge from various contexts, potentially allowing them to inject the spreading process into many different communities quickly. This paper extends our recent findings on the community membership of nodes and how it can be used to predict their individual spreading capability (Krukowski and Hecking, in: Benito, Cherifi, Cherifi, Moro, Rocha, Sales-Pardo (eds) Complex networks & their applications IX. Springer, Cham, pp 408–419, 2021) by further evaluating it on additional networks (both real-world networks and artificially generated networks), while additionally introducing a new local measure to identify influential spreaders that—in contrast to most other measures, does not rely on knowledge of the global network structure. The results confirm our recent findings, showing that the community membership of nodes can be used as a predictor for their spreading capability, while also showing that especially the local measure proves to be a good predictor, effectively outperforming the global measure in many cases. The results are discussed with regard to real-world use cases, where knowledge of the global structure is often not given, yet a prediction regarding the spreading capability highly desired (e.g., contact-tracing apps).

The Dominant Nodes Index in Shortest Paths (DNISP) as A Local Measure of Source Looking for the Target in Complex Networks

<p>When there are multiple alternate shortest paths between any two nodes in a complex network, there is a need to know details about the content of the paths and the dominance of the nodes within it, this need comes to maximize, control and speed of the information diffusion. This paper discusses the creation of a new special measure as a local scale for any X node in the network. This measure will give each neighbour of the node X a domination value to access the rest of the network, in other words any nodes included in the shortest path (X,Y) will be given a control value, taking into account the existence of more than one shortest path between (X,Y). Such a measure is called a DNISP, which stands for Dominant Nodes Index in Shortest Paths. The X-node needs to examine all shortest paths that connect it with any other nodes across the ones that are directly associated with it. This measure provides an insight into how information flows between nodes according to dominant values with each node.</p>

The negativity contour: a quasi-local measure of entanglement for mixed states

In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the negativity contour, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude. We construct an explicit contour function for Gaussian states using the fermionic partial-transpose. We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity. Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results. In particular, it rigorously satisfies the positivity condition for all holographic states and those obeying the quasi-particle picture. We apply this formalism to quantum field theories with a Fermi surface, contrasting the entanglement structure of Fermi liquids and holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi liquids show anomalous temperature dependence of the negativity depending on the dynamical critical exponent. We further compute the negativity contour following a quantum quench and discuss how this may clarify certain aspects of thermalization.