Related papers: Convective regularization for optical flow
We combine resolvent-mode decomposition with techniques from convex optimization to optimally approximate velocity spectra in a turbulent channel. The velocity is expressed as a weighted sum of resolvent modes that are dynamically…
We derive an RG flow equation that is satisfied by the regularized partition function for noncritical strings in background fields. The flow refers to change in the position of a ``boundary'' in the liouville direction. The boundary is…
This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity…
This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and…
We present an approximate analytic model that has been developed for examining hydrodynamic flow near the surface of a fiber optic sensor. An analysis of the conservation of momentum, the continuity equation and the Navier-Stokes equation…
For an arbitrary velocity field $\mathbf{v}$ defined on a finite, fixed spatial domain, we find the closest rigid-body velocity field $\mathbf{v}_{RB}$ to $\mathbf{v}$ in the $L^2$ norm. The resulting deformation velocity component,…
Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…
A novel method to improve the accuracy of pressure field estimation from time-resolved Particle Image Velocimetry data is proposed. This method generates several new time-series of velocity field by propagating in time the original one…
Recovering the camera motion and scene geometry from visual data is a fundamental problem in the field of computer vision. Its success in standard vision is attributed to the maturity of feature extraction, data association and multi-view…
Consider the time-periodic flow of an incompressible viscous fluid past a body performing a rigid motion with non-zero translational and rotational velocity. We introduce a framework of homogeneous Sobolev spaces that renders the resolvent…
We consider the $3$D problem of shape optimization of blood flows in moving domains. Such a geometry is adopted to take into account the modeling of rotating systems and blood pumps for instance. The blood flow is described by generalized…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
We investigate the renormalization group flow of projectable Horava gravity in $(3+1)$ dimensions generated by marginal operators with respect to the Lifshitz scaling. The flow possesses a number of asymptotically free fixed points. We find…
In a Hilbertian framework, for the minimization of a general convex differentiable function $f$, we introduce new inertial dynamics and algorithms that generate trajectories and iterates that converge fastly towards the minimizer of $f$…
A review is made of recent efforts to define linear connections and their corresponding curvature within the context of noncommutative geometry. As an application it is suggested that it is possible to identify the gravitational field as a…
In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
It is hard to densely track a nonrigid object in long term, which is a fundamental research issue in the computer vision community. This task often relies on estimating pairwise correspondences between images over time where the error is…
We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a $C^2$ boundary. We use a stream-function formulation after…