Related papers: Pattern recognition in complex systems via vector-…
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…
Modeling biological rhythms helps understand the complex principles behind the physical and psychological abnormalities of human bodies, to plan life schedules, and avoid persisting fatigue and mood and sleep alterations due to the…
Learning in the space-time domain remains a very challenging problem in machine learning and computer vision. Current computational models for understanding spatio-temporal visual data are heavily rooted in the classical single-image based…
Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…
Temporal sequences of satellite images constitute a highly valuable and abundant resource for analyzing regions of interest. However, the automatic acquisition of knowledge on a large scale is a challenging task due to different factors…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…
Large volumes of spatio-temporal data are increasingly collected and studied in diverse domains including, climate science, social sciences, neuroscience, epidemiology, transportation, mobile health, and Earth sciences. Spatio-temporal data…
The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal…
Understanding the dynamics of spatially extended systems represents a challenge in diverse scientific disciplines, ranging from physics and mathematics to the earth and climate sciences or the neurosciences. This challenge has stimulated…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and…
The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector…
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range of tools and techniques for time series analysis already exist, the increasing…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture…
We associate learning and adaptation in living systems with the shaping of the velocity vector field in the respective dynamical systems in response to external, generally random, stimuli. With this, a mathematical concept of self-shaping…
Based on multiple simulation trajectories, which started from dispersively selected initial conformations, the weighted ensemble dynamics method is designed to robustly and systematically explore the hierarchical structure of complex…