相关论文: Convex Dynamics and Applications
Convolution, a cornerstone of signal processing and optical neural networks, has traditionally been implemented by mapping mathematical operations onto complex hardware. Here, we overcome this challenge by revealing that wave dynamics in…
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
State-of-the-art diffusion models can generate highly realistic images based on various conditioning like text, segmentation, and depth. However, an essential aspect often overlooked is the specific camera geometry used during image…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
An inherent fragility of quadrotor systems stems from model inaccuracies and external disturbances. These factors hinder performance and compromise the stability of the system, making precise control challenging. Existing model-based…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
Rotation Averaging is a non-convex optimization problem that determines orientations of a collection of cameras from their images of a 3D scene. The problem has been studied using a variety of distances and robustifiers. The intrinsic (or…
Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit.…
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associated averaged system, called slow system. Each resonance is…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to…
The prevalence and consequences of convection perpendicular to the plane of accretion discs have been discussed for several decades. Recent simulations combining convection and the magnetorotational instability have given fresh impetus to…