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LLMs are emerging tools for simulating human behavior in business, economics, and social science, offering a lower-cost complement to laboratory experiments, field studies, and surveys. This paper evaluates how well LLMs replicate human…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
The emergence and continued reliance on the Internet and related technologies has resulted in the generation of large amounts of data that can be made available for analyses. However, humans do not possess the cognitive capabilities to…
In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
Nowadays both commercial and open-source academic LLM have become the mainstream models of NLP. However, there is still a lack of research on LLM consistency, meaning that throughout the various stages of LLM research and deployment, its…
Some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant (LTI) dynamics. The topology of this system is fixed but arbitrary, and every subsystem is…
Large Language Models (LLMs) have emerged as promising solutions for a variety of medical and clinical decision support applications. However, LLMs are often subject to different types of biases, which can lead to unfair treatment of…
Large language models (LLMs) are becoming useful in many domains due to their impressive abilities that arise from large training datasets and large model sizes. However, research on LLM-based approaches to document inconsistency detection…
Large language models (LLMs) have rapidly become familiar tools to researchers and practitioners. Concepts such as prompting, temperature, or few-shot examples are now widely recognized, and LLMs are increasingly used in Modeling &…
We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a…
We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
Large Language Models (LLMs) have emerged as powerful tools in various research domains. This article examines their potential through a literature review and firsthand experimentation. While LLMs offer benefits like cost-effectiveness and…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has…
Large Language Models (LLMs) have achieved remarkable success across a wide range of natural language tasks, and recent efforts have sought to extend their capabilities to multimodal domains and resource-constrained environments. However,…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
Tabular machine learning problems often require time-consuming and labor-intensive feature engineering. Recent efforts have focused on using large language models (LLMs) to capitalize on their potential domain knowledge. At the same time,…