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A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
Locomotion in the real world involves unexpected perturbations, and therefore requires strategies to maintain stability to successfully execute desired behaviours. Ensuring the safety of locomoting systems therefore necessitates a…
Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
A minimalist approach to the linear stability problem in fluid dynamics is developed that ensures efficiency by utilizing only the essential elements required to find the eigenvalues for given boundary conditions. It is shown that the…
When representing convective instability mechanisms with the streamwise BiGlobal stability approach, results suffer from a sensitivity to the streamwise domain truncation length and boundary conditions. The methodology proposed in this…
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Static analysis techniques enhance the security, performance, and reliability of programs by analyzing and portraiting program behaviors without the need for actual execution. In essence, static analysis takes the Intermediate…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Self-supervised methods have emerged as a promising avenue for representation learning in the recent years since they alleviate the need for labeled datasets, which are scarce and expensive to acquire. Contrastive methods are a popular…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…