arXiv research

Proves strong solutions for graphical Brakke flows with $L^2$ normal velocity.

RFM improves CNFs by adding a boundary constraint term and matching velocity fields.

We investigate the evolution of closed strictly convex hypersurfaces in $\mathbb{R}^{n+1}$, n=3, for contracting normal velocities, including powers of the mean curvature, of the norm of the second fundamental form, and of the Gauss curvature. We prove convergence to a round point for 2-pinched initial hypersurfaces. I…

A theorem proves a surface evolution graph satisfies a PDE under specific conditions.

We study convex entire graphs evolving with normal velocity equal to a positive power of the mean curvature. Under mild assumptions we prove longtime existence.

We consider flows with normal velocities equal to powers strictly larger than one of the Gauss curvature. Under such flows closed strictly convex surfaces converge to points. In his work on the square of the norm of the second fundamental form, Schnürer proposes criteria for selecting quantities that are suitable for p…

Study uses neural networks to predict wall quantities in turbulent flows.

The paper studies how grid cell patterns emerge in neural networks.

Neural networks predict flow and elastic stresses in viscoelastic turbulence.

New optimality conditions for sub-Riemannian geodesics derived.

Bitcoin's monetary velocity is constrained by network friction, leading to significant utility contraction during shocks.

A new method for normalizing flows using stochastic interpolants simplifies likelihood estimation and improves efficiency.

Sharp stability threshold found for deep residual architectures.

We show that strictly convex surfaces contracting with normal velocity equal to |A|^2 shrink to a point in finite time. After appropriate rescaling, they converge to spheres. We indicate how we used a computer to find the main test function.

Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general lineal group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are established, and regularity properties of these extremal paths are obtained. Minimi…

We propose a predictive neural network architecture that can be utilized to update reference velocity models as inputs to the full waveform inversion. Deep learning models are explored to augment velocity model building workflows during processing the 3D seismic volume in salt-prone environments. Specifically, a neural…

Study on Gaussian interpolation flows for generative modeling.

Proposes a method combining CNFs and rejection-resampling for sampling from unnormalized densities.

Neural network predicts turbulence near-wall regions efficiently.

Develops a method for non-equilibrium importance sampling to estimate expectations and constants.

CNFs learn distributions from samples with error bounds.

We consider geometric flow equations for contracting and expanding normal velocities, including powers of the Gauss curvature, of the mean curvature, and of the norm of the second fundamental form, and ask whether - after appropriate rescaling - closed strictly convex surfaces converge to spheres. To prove this, many a…

A translating soliton is a hypersurface $M$ in $\mathbb{R}^{n+1}$ such that the family $M_t= M- t \,\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at that point $\mathbf{H}=\mathbf{e}_{n+1}^{\perp}.$ In this paper we obtain a cha…

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike F…

DSNE visualizes data velocity in lower dimensions.

The paper studies how certain surfaces evolve over time.

Log-ergodic model improves velocity of money prediction.

Flow matching adapts to manifold structures without diffusion.

Optimal self-distillation improves generative models' velocity risk and mode recovery.

New method estimates velocity fields for minimizing $f$-divergences without overfitting.

We prove that, in a space-time of dimension n>3 with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant divergence of the Weyl tensor is zero if the contraction of the Weyl tensor with the velocity is zero. The other way, if the covariant divergence of the Weyl tensor is zero, then…

Curve shortening problem solved via Schwarz function.

In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$ ($n\geqslant2$) is mean convex and star-shaped. Several interesting examples and some hyperbol…

CCVFM uses coreset to improve generative models by refining residual flows.

SAGE generates subsurface velocity models from sparse well logs and seismic images.

New method distinguishes cause from effect using causal velocity.

LFIS uses a time-dependent velocity field to sample from complex distributions.

NN-Turb generates turbulent velocity statistics using neural networks.

We analyze a gradient flow of closed planar curves minimizing the anisoperimetric ratio. For such a flow the normal velocity is a function of the anisotropic curvature and it also depends on the total interfacial energy and enclosed area of the curve. In contrast to the gradient flow for the isoperimetric ratio, we sho…

The determinants of the velocity of money have been examined based on life-cycle hypothesis. The velocity of money can be expressed by reciprocal of the average value of holding time which is defined as interval between participating exchanges for one unit of money. This expression indicates that the velocity is govern…

A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.

A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.

We consider a mean curvature flow in a cone, that is, a hypersurface in a cone which moves toward the opening with normal velocity equaling to the mean curvature, and the contact angle between the hypersurface and the cone boundary being $\varepsilon$-periodic in its position. First, by constructing a family of self-si…

Neural solver computes Wasserstein geodesics and velocity fields efficiently.

Develops scalable model for learning velocity fields in complex traffic scenarios.

Generative sampler learns velocity fields for efficient posterior inference.

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

An $(r,n)$-velocity is an $r$-jet with source at $0 \in \R^n$, and target in a manifold $Y$. An $(r,n)$-velocity is said to be regular, if it has a representative which is an immersion at $0 \in \R^{n}$. The manifold $T^{r}_{n}Y$ of $(r,n)$-velocities as well as its open, $L^{r}_{n}$-invariant, dense submanifold $\Imm …