Related papers: Potential energy of complex networks: a novel pers…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
We reconstruct compactly supported potentials with only half a derivative in $L^2$ from the scattering amplitude at a fixed energy. For this we draw a connection between the recently introduced method of Bukhgeim, which uniquely determined…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schr\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we…
We relate structurally dynamic cellular networks, a class of models we developed in fundamental space-time physics, to SDCA, introduced some time ago by Ilachinski and Halpern. We emphasize the crucial property of a non-linear interaction…
In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
We prove spectral properties for random Landau Schr\"odinger operators on $L^2(\mathbb{R}^2)$ with bounded, random potentials supported in a square $\Lambda_L \subset \mathbb{R}^2$ of side length $L>0$, using semiclassical…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
The discrete Schr\"odinger equation with a quasiperiodic dichotomous potential specified by the Fibonacci sequence is known to have a singular continuous eigenvalue spectrum with all states being critically localized. This equation can be…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace…
Designing reliable networks consists in finding topological structures, which are able to successfully carry out desired processes and operations. When this set of activities performed within a network are unknown and the only available…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
We investigate recovery of the (Schr\"odinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a H\"older type stability which is a big improvement over a…
It is well-known that randomly initialized, push-forward, fully-connected neural networks weakly converge to isotropic Gaussian processes, in the limit where the width of all layers goes to infinity. In this paper, we propose to use the…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…