Related papers: General Oscillator-Based Ising Machine Models with…
Many combinatorial optimization problems fall into the non-polynomial time NP-hard complexity class, characterized by computational demands that increase exponentially with the size of the problem in the worst case. Solving large-scale…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
Using numerical simulations we investigate the properties of the dynamic phase transition that is encountered in the three-dimensional Ising model subjected to a periodically oscillating magnetic field. The values of the critical exponents…
Airfoil shape optimization presents a challenge where classical solvers frequently struggle with computational efficiency and local minima. In the promising paradigm of quantum computing, the coherent Ising machine (CIM), a specialized…
Physically accurate and mathematically tractable models are presented to characterize scattering and reflection properties of reconfigurable intelligent surfaces (RISs). We take continuous and discrete strategies to model a single patch and…
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…
The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…
In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
A high temperature expansion is employed to map some complex anisotropic nonhermitian three and four dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. We also address the dimensional…
A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems owing to optical processing with spatial parallelism. However, iterative feedback in the search for optimal solutions limits processing speed…
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic…
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal.…
We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants,…