Related papers: NoLiTiA: An Open-Source Toolbox for Nonlinear Time…

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…

The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…

This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…

Time series analysis is crucial in fields like finance, transportation, and industry. However, traditional models often focus solely on temporal features, limiting their ability to capture underlying information. This paper proposes a novel…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…

While mechanistic interpretability has developed powerful tools to analyze the internal workings of Large Language Models (LLMs), their complexity has created an accessibility gap, limiting their use to specialists. We address this…

In many real-world application, e.g., speech recognition or sleep stage classification, data are captured over the course of time, constituting a Time-Series. Time-Series often contain temporal dependencies that cause two otherwise…

Time series analysis is a field of data science which is interested in analyzing sequences of numerical values ordered in time. Time series are particularly interesting because they allow us to visualize and understand the evolution of a…

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the…

The evaluation of explanation methods is a research topic that has not yet been explored deeply, however, since explainability is supposed to strengthen trust in artificial intelligence, it is necessary to systematically review and compare…

Nowadays Artificial Intelligence (AI) has become a fundamental component of healthcare applications, both clinical and remote, but the best performing AI systems are often too complex to be self-explaining. Explainable AI (XAI) techniques…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in condensed phase. To facilitate effective development,…