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The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
Jointly identifying a mixture of discrete and continuous factors of variability without supervision is a key problem in unraveling complex phenomena. Variational inference has emerged as a promising method to learn interpretable mixture…
Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…
Enhanced sampling methods typically require predefined collective variables (CVs) that presuppose knowledge of reaction coordinates, restricting the discovery of unanticipated transition mechanisms or intermediates. Here, we show that a…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…
Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's…
In this paper, we consider the {\it tensor absolute value equations} (TAVEs), which is a newly introduced problem in the context of multilinear systems. Although the system of TAVEs is an interesting generalization of matrix {\it absolute…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
In this paper, we consider an exponential scalar auxiliary variable (E-SAV) approach to obtain energy stable schemes for a class of phase field models. This novel auxiliary variable method based on exponential form of nonlinear free energy…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Variational Bayes (VB) has shown itself to be a powerful approximation method in many application areas. This paper describes some diagnostics methods which can assess how well the VB approximates the true posterior, particularly with…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…
Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under…
We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and…
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…
This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…
Control-based continuation (CBC) is a general and systematic method to explore the dynamic response of a physical system and perform bifurcation analysis directly during experimental tests. Although CBC has been successfully demonstrated on…