Related papers: Iterated Function System Models in Data Analysis: …
We study locally constant skew-product maps over full shifts of finite symbols with arbitrary compact metric spaces as fiber spaces. We introduce a new criterion to determine the density of leaves of the strong unstable (and strong stable)…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…
A nonlinear-dynamical algorithm for city planning is proposed as an Impulse Pattern Formulation (IPF) for predicting relevant parameters like health, artistic freedom, or financial developments of different social or political stakeholders…
The purpose of the paper is a general analysis of path space measures. Our focus is a certain path space analysis on generalized Bratteli diagrams. We use this in a systematic study of systems of self-similar measures (the term ``IFS…
Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature…
Detecting multiple change points in functional data sequences has been increasingly popular and critical in various scientific fields. In this article, we propose a novel two-stage framework for detecting multiple change points in…
We study the problem of classifying interval-based temporal sequences (IBTSs). Since common classification algorithms cannot be directly applied to IBTSs, the main challenge is to define a set of features that effectively represents the…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
This paper proposes an interpretable non-model sharing collaborative data analysis method as one of the federated learning systems, which is an emerging technology to analyze distributed data. Analyzing distributed data is essential in many…
Traditional model-free feature selection methods treat each feature independently while disregarding the interrelationships among features, which leads to relatively poor performance compared with the model-aware methods. To address this…
We study the problem of learning a linear system model from the observations of $M$ clients. The catch: Each client is observing data from a different dynamical system. This work addresses the question of how multiple clients…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of so-called rare events that are characterized by transitions between metastable states separated by sizeable free energy barriers. Their…
We consider federated learning of linearly-parameterized nonlinear systems. We establish theoretical guarantees on the effectiveness of federated nonlinear system identification compared to centralized approaches, demonstrating that the…
In Industrial Control Systems (ICS/SCADA), machine to machine data traffic is highly periodic. Previous work showed that in many cases, it is possible to create an automata-based model of the traffic between each individual Programmable…
We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation…
We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex…
Iterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non-stationary and non-linear signals. Recently in [1] IF has been proved to be convergent for any $L^2$…