Related papers: Using Dynamical Systems Theory to Quantify Complex…
Collaborative problem solving (CPS) enables student groups to complete learning tasks, construct knowledge, and solve problems. Previous research has argued the importance to examine the complexity of CPS, including its multimodality,…
Detectability of discrete event systems (DESs) is a question whether the current and subsequent states can be determined based on observations. Shu and Lin designed a polynomial-time algorithm to check strong (periodic) detectability and an…
Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…
The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard…
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…
We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
Explanations in Machine Learning come in many forms, but a consensus regarding their desired properties is yet to emerge. In this paper we introduce a taxonomy and a set of descriptors that can be used to characterise and systematically…
Observations are an essential component of the simulation based studies on artificial-evolutionary systems (AES) by which entities are identified and their behavior is observed to uncover higher-level "emergent" phenomena. Because of the…
One of the several obstacles in the widespread use of AI systems is the lack of requirements of interpretability that can enable a layperson to ensure the safe and reliable behavior of such systems. We extend the analysis of an agent…
The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis' conjecture: the long-term behavior is…
Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…
This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
In this report proofs are presented for a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing…
The BKL conjecture, stated in the 60s and early 70s by Belinski, Khalatnikov and Lifshitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated…
We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial…