Related papers: Nonlinear Diffusion Through Large Complex Networks…
Heat-transport mechanism mediated by near-field interactions in plasmonic nanostructures networks is shown to be analogous to a generalized random-walk process. Existence of superdiffusive regimes is demonstrated both in linear ordered…
Heat transport in nanoscale systems is both hard to measure microscopically, and hard to interpret. Ballistic and diffusive heat flow coexist, adding confusion. This paper looks at a very simple case: a nanoscale crystal repeated…
Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…
The existence of Steiner triple systems STS(n) of order n containing no nontrivial subsystem is well known for every admissible n. We generalize this result in two ways. First we define the expander property of 3-uniform hypergraphs and…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…
We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indexes. Focusing on the example of thermal transport in class D (`Majorana') quantum wires, we…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to…
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,…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
The galaxies of nonstandard enlargements of conventionally infinite as well as of transfinite graphs are defined, analyzed, and illustrated by some examples. It is then shown that any such enlargement either has exactly one galaxy, its…
We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas…
Transductive tasks on graphs differ fundamentally from typical supervised machine learning tasks, as the independent and identically distributed (i.i.d.) assumption does not hold among samples. Instead, all train/test/validation samples are…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…