Related papers: Spectral fluctuations and crossovers in multilayer…
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple…
The spectrum of the adjacency matrix plays several important roles in the mathematical theory of networks and in network data analysis, for example in percolation theory, community detection, centrality measures, and the theory of dynamical…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
A multiplex social network captures multiple types of social relations among the same set of people, with each layer representing a distinct type of relationship. Understanding the structure of such systems allows us to identify how social…
We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…
Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assumes infinitely wide networks. However, these assumptions…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
Given the overcrowding in the 300 MHz-3 GHz spectrum, millimeter wave (mmWave) spectrum is a promising candidate for the future generations of wireless networks. With the unique propagation characteristics at mmWave frequencies, one of the…
Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their…
The Global Magnetorotational Instability (MRI) is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
The effect of long wavelength fluctuations on the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $\beta$ regime is studied by means of the standard field-theoretical procedure for a genuine second-order phase transition.…
We study thermal fluctuations of a free-standing bilayer graphene subject to vanishing external tension. Within a phenomenological theory, the system is described as a stack of two continuum crystalline membranes, characterized by finite…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal)…