Related papers: Relaxation Oscillations in New IS-LM Model

We propose a new class of inflationary solutions to the standard cosmological problems (horizon, flatness, monopole,...), based on a modification of old inflation. These models do not require a potential which satisfies the normal…

The inflationary paradigm is the most successful model that explains the observed spectrum of primordial perturbations. However, the precise emergence of such inhomogeneities and the quantum-to-classical transition of the perturbations has…

Large language models (LLMs) enable researchers to analyze text at unprecedented scale and minimal cost. Researchers can now revisit old questions and tackle novel ones with rich data. We provide an econometric framework for realizing this…

We review recent results concerning finite size corrections to the Ising model free energy on lattices with non-trivial topology and curvature. From conformal field theory considerations two distinct universal terms are expected, a…

Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds…

Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep…

Ising machines exploit the natural dynamics of physical systems to minimize the Ising Hamiltonian and thereby address computationally hard combinatorial optimization problems. This paradigm has motivated a range of physical implementations.…

We consider a class of inflationary models with small oscillations imprinted on an otherwise smooth inflaton potential. These oscillations are manifest as oscillations in the power spectrum of primordial perturbations, which then give rise…

This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…

Large language models (LLMs) often generate inaccurate yet credible-sounding content, known as hallucinations. This inherent feature of LLMs poses significant risks, especially in critical domains. I analyze LLMs as a new class of…

Dynamical Ising machines are based on continuous dynamical systems evolving from a generic initial state to a state strongly related to the ground state of the classical Ising model on a graph. Reaching the ground state is equivalent to…

Many combinatorial optimization problems can be reformulated as finding the ground state of the Ising model. Existing Ising solvers are mostly inspired by simulated annealing. Although annealing techniques offer scalability, they lack…

In this work, we consider homogeneous oscillations of the inflaton field after inflation. In particular, we obtain an analytical result for the (average) equation of state for the oscillating inflaton field for the simplest…

This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…

Using the Metropolis algorithm, we simulate the relaxation process of the three-dimensional kinetic Ising model. Starting from a random initial configuration, we first present the average equilibration time across the entire phase boundary.…

We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…

A special class of conformal gravity theories is proposed to solve the long standing problem of the fine-tuned cosmological constant. In the proposed model time evolution of the inflaton field leaves behind a nearly vanishing, but finite…

We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…

Despite the many advances of Large Language Models (LLMs) and their unprecedented rapid evolution, their impact and integration into every facet of our daily lives is limited due to various reasons. One critical factor hindering their…

In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…