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Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
Moser & Tardos have developed a powerful algorithmic approach (henceforth "MT") to the Lovasz Local Lemma (LLL); the basic operation done in MT and its variants is a search for "bad" events in a current configuration. In the initial stage…
Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
Map generalization is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this paper, we explore how the map generalization process can be guided by the…
We address the problem of learning temporal properties from the branching-time behavior of systems. Existing research in this field has mostly focused on learning linear temporal properties specified using popular logics, such as Linear…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that…
Taylor's power law states that the variance function decays as a power law. It is observed for population densities of species in ecology. For random networks another power law, that is, the power law degree distribution is widely studied.…
The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian…
Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of…
We study the chaotic behavior of multidimensional Hamiltonian systems in the presence of nonlinearity and disorder. It is known that any localized initial excitation in a large enough linear disordered system spreads for a finite amount of…
We investigate spatial and temporal cross-correlations between streamwise and normal velocity components in three shear flows: a low-dimensional model for vortex-streak interactions, direct numerical simulations for a nearly homogeneous…
For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power law of the level-spacing distribution P(s) over a wide range of small spacings s. Going beyond Berry-Robnik statistics, we…
Signal Temporal Logic (STL) is a formal language for describing a broad range of real-valued, temporal properties in cyber-physical systems. While there has been extensive research on verification and control synthesis from STL…
The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from…
This paper proposes a spatial threshold GARCH-type model for dynamic spatio-temporal integer-valued data with network structure. The proposed model can simplify the parameterization by using network structure in data, and can capture the…