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A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
We report the observation of a quasi-coherent density fluctuation (QCF) by the Doppler backscattering system in the scrape-off layer (SOL) region of the DIII-D tokamak. This QCF is observed in high-power, high-performance hybrid plasmas…
Discrete-variable (DV) quantum key distribution (QKD) based on single-photon detectors and sources have been successfully deployed for long-range secure key distribution. On the other hand, continuous-variable (CV) quantum key distribution…
We propose a frequency-division multiplexed (FDM) continuous-variable quantum key distribution (CV-QKD) system with enhanced spectral efficiency through dense multiplexing of low-symbol-rate signals. A four-channel 10-Mbaud FDM-CV-QKD…
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…
Computational fluid dynamics (CFD) is a specialised branch of fluid mechanics that utilises numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing,…
Quantum state diffusion (QSD) as a tool to solve quantum-optical master equations by stochastic simulation can be made several orders of magnitude more efficient if states in Hilbert space are represented in a moving basis of excited…
Diffusion models excel in image generation but are computational and resource-intensive due to their reliance on iterative Markov chain processes, leading to error accumulation and limiting the effectiveness of naive compression techniques.…
Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute…
The timestep of the Finite-Difference Time-Domain method (FDTD) is constrained by the stability limit known as the Courant-Friedrichs-Lewy (CFL) condition. This limit can make FDTD simulations quite time consuming for structures containing…
Diffusion models have achieved remarkable success in generative tasks but suffer from high computational costs due to their iterative sampling process and quadratic attention costs. Existing training-free acceleration strategies that reduce…
This paper develops a quantized Q-learning algorithm for the optimal control of controlled diffusion processes on $\mathbb{R}^d$ under both discounted and ergodic (average) cost criteria. We first establish near-optimality of finite-state…
A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
Text-to-image diffusion models are computationally intensive, often requiring dozens of forward passes through large transformer backbones. For instance, Stable Diffusion XL generates high-quality images with 50 evaluations of a…
In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear…
Twin-field (TF) quantum key distribution (QKD) fundamentally alters the rate-distance relationship of QKD, offering the scaling of a single-node quantum repeater. Although recent experiments have demonstrated the new opportunities for…
Dropout is a technique that silences the activity of units stochastically while training deep networks to reduce overfitting. Here we introduce Quantal Synaptic Dilution (QSD), a biologically plausible model of dropout regularisation based…
Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods…
In practical implementation of quantum key distributions (QKD), it requires efficient, real-time feedback control to maintain system stability when facing disturbance from either external environment or imperfect internal components.…