Related papers: Free-space Optical Diffraction and the Fisher Info…
We consider non-linear regression models corrupted by generic noise when the regression functions form a non-linear subspace of L^2, relevant in non-linear PDE inverse problems and data assimilation. We show that when the score of the model…
We propose a model for demixing of two species by assuming a density-dependent effective diffusion coefficient of the particles. Both sorts of microswimmers diffuse as active overdamped Brownian particles with a noise intensity that is…
Polarization optical fiber sensors are based on modifications of fiber birefringence by an external measurand (e.g. strain, pressure, acoustic waves). Yet, this means that different input states of polarization will result in very distinct…
Strong intensity attenuation limits the use of conventional diffraction-free optical elements. We show a possible solution to the exponential intensity attenuation limiting the use of Fresnel-type diffraction-free nanometer-scale optics by…
We predict that the speed of a diffusion front is modified by tidal forces. This effect is small in astrophysical situations, but could be significant - indeed tunably so - in "gravitational analogues" such as gradient-index lenses.…
We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
The growing adoption of batteries in the electric vehicle industry and various consumer products has created an urgent need for effective recycling solutions. These products often contain a mix of compliant and rigid components, making…
Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an…
We present an extensive Monte Carlo study on light transport in optically thin slabs, addressing both axial and transverse propagation. We completely characterize the so-called ballistic-to-diffusive transition, notably in terms of the…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
We derive upper bounds on the quantum Fisher information in interferometry with $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence of arbitrarily correlated Gaussian dephasing including independent and collective…
We provide a Lyapunov convergence analysis for time-inhomogeneous variable coefficient stochastic differential equations (SDEs). Three typical examples include overdamped, irreversible drift, and underdamped Langevin dynamics. We first…