相关论文: Convex Dynamics and Applications

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…

Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional…

This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…

Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…

Accurate color reproduction is important in many applications of 3D printing, from design prototypes to 3D color copies or portraits. Although full color is available via other technologies, multi-jet printers have greater potential for…

It is known that each symmetric stable distribution in $R^d$ is related to a norm on $R^d$ that makes $R^d$ embeddable in $L_p([0,1])$. In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to…

Diffusion models have successfully been applied to generative tasks in various continuous domains. However, applying diffusion to discrete categorical data remains a non-trivial task. Moreover, generation in continuous domains often…

The problem of inpainting involves reconstructing the missing areas of an image. Inpainting has many applications, such as reconstructing old damaged photographs or removing obfuscations from images. In this paper we present the directional…

Image stitching from different captures often results in non-rectangular boundaries, which is often considered unappealing. To solve non-rectangular boundaries, current solutions involve cropping, which discards image content, inpainting,…

We study the problem of Arnold's diffusion in an example of isochronous system by using a geometrical method known as Windows Method. Despite the simple features of this example, we show that the absence of an anisochrony term leads to…

Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…

The bulk circulation associated with convective clouds includes not only a region of updraft and cloudy air but also a region of compensating descent and cloud-free air and horizontal motions coupling these regions. The Kinematic…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…

Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. In natural doubly diffusive convection, the gradients of…

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…

Most motion deblurring algorithms rely on spatial-domain convolution models, which struggle with the complex, non-linear blur arising from camera shake and object motion. In contrast, we propose a novel single-image deblurring approach that…

Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly-averaged equations of motion. The coupled perturbations affect the…