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In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated…
Neurons in the brain behave as non-linear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge…
Decades of exponential scaling in high performance computing (HPC) efficiency is coming to an end. Transistor based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further…
We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality…
Coupled resonators form band-like optical states that support rich nonlinearities beyond what is possible in single resonators. In these systems, four-wave mixing mediates interband coupling, displaying multimode dynamics that span both…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We propose a neural network model, which, with appropriate assignment of the stability of its equilibrium points (EPs), achieves Hopfield-like associative memory. The oscillator Ising machine (OIM) is an ideal candidates for such a model,…
Neuronal ensemble activity, including coordinated and oscillatory patterns, exhibits hallmarks of nonequilibrium systems with time-asymmetric trajectories to maintain their organization. However, assessing time asymmetry from neuronal…
Numerical simulations are essential tools for exploring the dynamic scaling properties of the nonlinear Kadar-Parisi-Zhang (KPZ) equation. Yet the inherent nonlinearity frequently causes numerical divergence within the strong-coupling…
In this paper we report on the measurement and modelling of enhanced optical refractometric sensors based on whispering-gallery-modes. The devices under test are optical microresonators made of silicon nitride on silicon oxide. In our…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Many developments in science and engineering depend on tackling complex optimizations on large scales. The challenge motivates intense search for specific computing hardware that takes advantage from quantum features, nonlinear dynamics, or…
Real-world physical signals are continuous and high-dimensional, yet the statistical-mechanics machinery of associative memory operates on discrete Ising spins. We bridge this divide through a multilayer Ising framework that couples a…
Ising Machine is a promising computing approach for solving combinatorial optimization problems. It is naturally suited for energy-saving and compact in-memory computing implementations with emerging memories. A na\"ive in-memory computing…
We introduce a hybrid control system called a hybrid integrator-gain system (HIGS) based integral resonant controller (IRC) to stabilize negative imaginary (NI) systems. A HIGS-based IRC has a similar structure to an IRC, with the…
With the advent of advances in self-supervised learning, paired clean-noisy data are no longer required in deep learning-based image denoising. However, existing blind denoising methods still require the assumption with regard to noise…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…