Related papers: Pattern recognition in complex systems via vector-…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Although deep learning-based methods have shown great success in spatiotemporal predictive learning, the framework of those models is designed mainly by intuition. How to make spatiotemporal forecasting with theoretical guarantees is still…
Spatiotemporal graph represents a crucial data structure where the nodes and edges are embedded in a geometric space and can evolve dynamically over time. Nowadays, spatiotemporal graph data is becoming increasingly popular and important,…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…
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…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…
Graph learning aims to infer a network structure directly from observed data, enabling the analysis of complex dependencies in irregular domains. Traditional methods focus on scalar signals at each node, ignoring dependencies along…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
High resolution satellite image sequences are multidimensional signals composed of spatio-temporal patterns associated to numerous and various phenomena. Bayesian methods have been previously proposed in (Heas and Datcu, 2005) to code the…
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with…
The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie…
In general, comprehension of any type of complex system depends on the resolution used to examine the phenomena occurring within it. However, identifying a priori, for example, the best time frequencies/scales to study a certain system…
Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and…
Recent advances in sensing technologies require the design and development of pattern recognition models capable of processing spatiotemporal data efficiently. In this study, we propose a spatially and temporally aware tensor-based neural…