Related papers: Recurrence Plots for the Analysis of Complex Syste…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
Recent experiments and simulations of amorphous solids plastically deformed by oscillatory drive have foundsurprising behavior - for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity…
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical…
Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
In this paper, we introduce the cyclic polygon plot, a representation based on a novel projection concept for multi-dimensional values. Cyclic polygon plots combine the typically competing requirements of quantitativeness, image-space…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
The describing function method is a useful tool for the qualitative analysis of limit cycles in the stability analysis of nonlinear systems. This method is inherently approximate; therefore, it should be used for a fast qualitative analysis…
Periodically occurring accumulations of events or measured values are present in many time-dependent datasets and can be of interest for analyses. The frequency of such periodic behavior is often not known in advance, making it difficult to…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…