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In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems…
Despite linear regression being the most popular statistical modelling technique, in real-life we often need to deal with situations where the true relationship between the response and the covariates is nonlinear in parameters. In such…
Nonlinear relations, such as the curvilinear relationship between childhood trauma and resilience in patients with schizophrenia and the moderation relationship between mentalizing, and internalizing and externalizing symptoms and quality…
Natural language understanding often requires deep semantic knowledge. Expanding on previous proposals, we suggest that some important aspects of semantic knowledge can be modeled as a language model if done at an appropriate level of…
The Mamba layer offers an efficient selective state space model (SSM) that is highly effective in modeling multiple domains, including NLP, long-range sequence processing, and computer vision. Selective SSMs are viewed as dual models, in…
Unsupervised mixture learning (UML) aims at identifying linearly or nonlinearly mixed latent components in a blind manner. UML is known to be challenging: Even learning linear mixtures requires highly nontrivial analytical tools, e.g.,…
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface.…
We design specific neural networks (NNs) for the identification of switching nonlinear systems in the state-space form, which explicitly model the switching behavior and address the inherent coupling between system parameters and switching…
Despite their linguistic competence, Large Language Models (LLMs) often struggle to reason reliably and flexibly. To identify these shortcomings, we introduce the Non-Linear Reasoning (NLR) dataset, a collection of 55 unique, hand-designed…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…
Nonlinear charge transport in strongly coupled semiconductor superlattices is described by Wigner-Poisson kinetic equations involving one or two minibands. Electron-electron collisions are treated within the Hartree approximation whereas…
This paper presents an LLM-driven, end-to-end workflow that addresses the lack of automation and intelligence in power system transient stability assessment (TSA). The proposed agentic framework integrates large language models (LLMs) with…
We construct a two dimensional nonlinear $\sigma$-model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear…
How can we extend a pre-trained model to many language understanding tasks, without labeled or additional unlabeled data? Pre-trained language models (PLMs) have been effective for a wide range of NLP tasks. However, existing approaches…
We describe how to use quantum linear algebra to simulate a physically realistic model of disordered non-interacting electrons. The physics of disordered electrons outside of one dimension challenges classical computation due to the…
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling…
Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems…
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
Extensions of the Standard Model of elementary particle physics to noncommutative geometries have been proposed as a low energy limit of string models. Independent of this motivation, one may consider such a model as an effective field…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…