Related papers: Relaxation Oscillations in New IS-LM Model
Robustness of the solutions to the inflaton potential inverse problem based on the slow-roll approximation is addressed. With that aim it is introduced a measure of the difference of the outputs obtained using first and second order…
Following the success of Large Language Models (LLMs), Large Multimodal Models (LMMs), such as the Flamingo model and its subsequent competitors, have started to emerge as natural steps towards generalist agents. However, interacting with…
Power-law inflation has stood as a classical model in inflationary cosmology since the early 1980s, prized for its exact analytical solutions and ability to naturally resolve the Big Bang theory's horizon and flatness problems through…
In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The…
This paper studies the properties of debiased machine learning (DML) estimators under a novel asymptotic framework, offering insights for improving the performance of these estimators in applications. DML is an estimation method suited to…
The Ising model is well-known for illustrating the fundamental characteristics of phase transitions in closed systems. In this article, we propose a generalization of the two-dimensional Ising model to open systems, considering the…
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we…
We study the dynamics of the critical two-dimensional fully-frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value $z_c=2$. In a second…
The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple…
We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin configurations in corresponding Ising models, we…
In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard…
Delay differential equation model of a NOLM-NALM mode-locked laser is developed that takes into account finite relaxation rate of the gain medium and asymmetric beam splitting at the entrance of the nonlinear mirror loop. Asymptotic linear…
Relaxation processes of dislocation systems are studied by two-dimensional dynamical simulations. In order to capture generic features, three physically different scenarios were studied and power-law decays found for various physical…
This article presents a class of new relaxation modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). Using two positive diagonal matrices, we formulate a fixed-point equation and prove that…
The present work is dedicated to a better understanding of the stability properties of regularized lattice Boltzmann (LB) schemes. To this extent, linear stability analyses of two-dimensional models are proposed: the standard…
Large Language Models (LLMs) are powerful linguistic engines but remain susceptible to hallucinations: plausible-sounding outputs that are factually incorrect or unsupported. In this work, we present a mathematically grounded framework to…
The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…