Critical behavior of cascading failures in overloaded networks.

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length ζ. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., ζ of the order of the system size L) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., ζ≪L) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks.

Discrete-Time Quantum Walk on Multilayer Networks.

A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.

Global coordination level in single-cell transcriptomic data.

Genes are linked by underlying regulatory mechanisms and by jointly implementing biological functions, working in coordination to apply different tasks in the cells. Assessing the coordination level between genes from single-cell transcriptomic data, without a priori knowledge of the map of gene regulatory interactions, is a challenge. A 'top-down' approach has recently been developed to analyze single-cell transcriptomic data by evaluating the global coordination level between genes (called GCL). Here, we systematically analyze the performance of the GCL in typical scenarios of single-cell RNA sequencing (scRNA-seq) data. We show that an individual anomalous cell can have a disproportionate effect on the GCL calculated over a cohort of cells. In addition, we demonstrate how the GCL is affected by the presence of clusters, which are very common in scRNA-seq data. Finally, we analyze the effect of the sampling size of the Jackknife procedure on the GCL statistics. The manuscript is accompanied by a description of a custom-built Python package for calculating the GCL. These results provide practical guidelines for properly pre-processing and applying the GCL measure in transcriptional data.