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We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To…
Efficient skill acquisition, representation, and on-line adaptation to different scenarios has become of fundamental importance for assistive robotic applications. In the past decade, dynamical systems (DS) have arisen as a flexible and…
This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. The method is a novel application of a technique used for…
When modeling complex robot systems such as branched robots, whose kinematic structures are a tree, current techniques often require modeling the whole structure from scratch, even when partial models for the branches are available. This…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated…
Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…
The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…
Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
Numerous industrial processes can be defined using distributed parameter systems (DPSs). This study introduces a two-stage spatial construction approach for real-time modeling of DPSs in cases of limited sensors. Initially, a discrete…
Model compression is essential in the deployment of large Computer Vision models on embedded devices. However, static optimization techniques (e.g. pruning, quantization, etc.) neglect the fact that different inputs have different…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…
We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
This paper gives convex conditions for synthesis of a distributed control system for large-scale networked nonlinear dynamic systems. It is shown that the technique of control contraction metrics (CCMs) can be extended to this problem by…