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Time delay has been incorporated in models to reflect certain physical or biological meaning. The theory of delay differential equations (DDEs), which has seen extensive growth in the last seventy years or so, can be used to examine the…
In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…
This paper introduces the design and implementation of PyOptInterface, a modeling language for mathematical optimization embedded in Python programming language. PyOptInterface uses lightweight and compact data structure to bridge…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
Mixture-of-Experts (MoE) models enable scalable computation and performance in large-scale deep learning but face quantization challenges due to sparse expert activation and dynamic routing. Existing post-training quantization (PTQ) methods…
We apply a recently proposed method for the acceleration of model predictive control (MPC) to 36 MPC implementations, which result from combining six sample receding horizon control problems with six quadratic programming solvers. We…
In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial dimension coupled with a set of Ordinary Differential…
The general theory of Lyapunov's stability of first-order differential inclusions in Hilbert spaces has been studied by the authors in a previous work. This new contribution focuses on the natural case when the maximally monotone operator…
We introduce MixFunn, a novel neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability. The architecture comprises two key components: the mixed-function…
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from…
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of…
What limits how fast a Lyapunov function can decay under input bounds? We address this question by showing how the shape of Lyapunov comparison functions governs guaranteed decay for control affine systems. Using a windowed nominal…
Often in the study the periodic orbits in dynamical systems, the computation of the Lyapunov Coeficients is needed. In this paper, the calculations of this coeficients were done via complex variable transformation in order to obtain the…
Learning under non-smooth objectives remains a fundamental challenge in machine learning, as abrupt changes in conditioning variables can induce highly non-smooth loss landscapes and destabilize optimization. This difficulty is particularly…
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…
This paper deals with evaluating constant terms of a special class of rational functions, the Elliott-rational functions. The constant term of such a function can be read off immediately from its partial fraction decomposition. We combine…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and…