Related papers: Recurrence-based time series analysis by means of …

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a…

The evolutionary processes of complex systems contain critical information regarding their functional characteristics. The generation time of edges provides insights into the historical evolution of various networked complex systems, such…

Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…

Temporal networks are commonly used to model real-life phenomena. When these phenomena represent interactions and are captured at a fine-grained temporal resolution, they are modeled as link streams. Community detection is an essential…

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include…

Being able to capture the characteristics of a time series with a feature vector is a very important task with a multitude of applications, such as classification, clustering or forecasting. Usually, the features are obtained from linear…

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…

The study of complex systems in nature is essential to understand the interactions between different elements and how they influence one another. Complex network theory is a powerful tool that helps us to analyze these interactions and gain…

Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…

The inference of outcomes in dynamic processes from structural features of systems is a crucial endeavor in network science. Recent research has suggested a machine learning-based approach for the interpretation of dynamic patterns emerging…

In this paper, we systematically analyze the connecting architectures of recurrent neural networks (RNNs). Our main contribution is twofold: first, we present a rigorous graph-theoretic framework describing the connecting architectures of…

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…

Data is essential to performing time series analysis utilizing machine learning approaches, whether for classic models or today's large language models. A good time-series dataset is advantageous for the model's accuracy, robustness, and…

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…

Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…

A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of…

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…

The classification of time-series data is pivotal for streaming data and comes with many challenges. Although the amount of publicly available datasets increases rapidly, deep neural models are only exploited in a few areas. Traditional…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…