Related papers: Generalized dimension reduction approach for heter…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…
It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned…
Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very…
While deep generative models (DGMs) have gained popularity, their susceptibility to biases and other inefficiencies that lead to undesirable outcomes remains an issue. With their growing complexity, there is a critical need for early…
Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple decomposition method is presented that decouples the…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements…
The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…
Networked dynamic systems are ubiquitous in various domains, such as industrial processes, social networks, and biological systems. These systems produce high-dimensional data that reflect the complex interactions among the network nodes…
Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…