Related papers: Analytic continuation over complex landscapes
The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two…
This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…
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…
We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains $N$ Boolean elements each with $K$ inputs. A directed state space network (SSN) is constructed by linking each dynamical state,…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
A complete understanding of the precipitous onset of slow dynamics in systems such as supercooled liquids requires making direct connections between dynamics and the underlying potential energy landscape. With the aid of a switch in…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation,…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
The relationship between the macroscopic response of the slope and the macrostructure of the force chain network under the action of the metal plate was studied by the particle discrete element method and the persistent homology. The…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
Regular patterns of vegetation are considered widespread landscapes, although their global extent has never been estimated. Among them, spotted landscapes are of particular interest in the context of climate change. Indeed, regularly spaced…