GPRNs accurately model stellar activity affecting RV measurements of exoplanets.
problem Stellar activity limits detection and characterisation of exoplanets.
method Gaussian Process Regression Networks (GPRNs) for joint analysis of RV data and stellar activity indicators.
result GPRNs accurately describe solar RV data, correlating with activity at separations of a few days.
Generative models on spheres improve discrete sequence sampling.
problem Learning generative models for discrete sequences in continuous space.
method Work on sphere Sd−1, using von Mises-Fisher distribution and radial symmetry. result Improved results on Sudoku and language modeling with vMF path.
A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp uni…
This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It is assumed that attractive spots in the environment are responsible for modifyi…
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 ε-periodic in its position. First, by constructing a family of self-si…
Study spherical doubly warped spacetimes for stellar collapse and cosmology.
problem Analyzing spherically symmetric spacetimes for stellar collapse and cosmology.
method Obtained results for Weyl and Ricci tensors on general doubly warped spacetimes.
result Friedmann equations deviate from standard FRW cosmology due to electric tensor terms.
The paper generalizes radial curvature bounds on manifolds.
problem Bounding radial curvature on Riemannian manifolds.
method Introducing a new class of manifolds with radial curvature constraints.
result New insights into curvature properties of manifolds.
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.
problem Understanding movement patterns in high-dimensional data.
method DSNE is a variation of Stochastic Neighbor Embedding that learns velocity embeddings using Euclidean distances on a unit sphere.
result DSNE enables visualization of data movement in lower dimensions.
Study examines maximal domains of radial harmonic functions across different curvature types.
problem Understanding maximal domains of radial harmonic functions in various curvature settings.
method Analysis of harmonic spaces with positive, zero, and negative curvature.
result Characterization of maximal domains for radial harmonic functions in different curvature contexts.
Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.
problem Preserving convexity in hyperbolic and spherical geometries under radial transformations.
method Used Poincaré disk model for hyperbolic geometry and stereographic projection for spherical geometry to prove preservation of convexity under radial expansion and contraction.
result Radial expansion and contraction preserve hyperbolic and spherical convexity, respectively.
The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmit…
RFM improves CNFs by adding a boundary constraint term and matching velocity fields.
problem Flow matching on constrained domains leads to unnatural samples.
method RFM adds a boundary constraint term and matches velocity fields in a simulation-free manner.
result RFM achieves comparable or better results on standard image benchmarks and produces high-quality samples.
Log-ergodic model improves velocity of money prediction.
problem Improving velocity of money prediction for economic control.
method Log-ergodic processes to simulate monetary velocity.
result Log-ergodic model offers superior predictive power.
This study examines cores within superclusters, highlighting their transitional nature and dynamical state.
problem Understanding the morphology and dynamical properties of cores within superclusters.
method Projected and radial velocity distributions of galaxies, morphological analysis, entropy and mass estimates.
result Cores are transitional structures that evolve towards virialisation but remain gravitationally bound.
The study characterizes harmonic spaces and their radial eigen-functions and vector fields.
problem Characterizing harmonic spaces and their geometric properties.
method Examining radial eigen-spaces of Laplacians and using duality.
result Results extend to spaces harmonic with respect to a single point.
No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.
problem Finding radial balanced metrics on the unit ball of the Kepler manifold.
method Analyzing boundary behavior and weights of metrics.
result Explicit weights for radial metrics satisfying balanced condition identified.
Study complete gradient Ricci solitons with zero radial Weyl curvature.
problem Characterize complete gradient Ricci solitons with specific curvature properties.
method Classify complete gradient Ricci solitons with zero radial Weyl curvature for dimensions n≥4. result Completely classified complete gradient Ricci solitons with zero radial Weyl curvature.
Optimal self-distillation improves generative models' velocity risk and mode recovery.
problem Improving generative models' velocity risk and mode recovery.
method Proved optimal self-distillation for rectified flow via linear probing, derived mixing coefficient, and provided validation tuning.
result Optimal self-distillation improves velocity risk and mode recovery.
New method estimates velocity fields for minimizing f-divergences without overfitting.
problem Minimizing statistical discrepancies between target and particle distributions.
method Directly estimate velocity fields using interpolation techniques, proving consistency under mild conditions.
result Consistent estimators of velocity fields improve accuracy in applications like domain adaptation and missing data imputation.
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…
Proves strong solutions for graphical Brakke flows with L2 normal velocity.
problem Proving strong solutions for graphical Brakke flows with specific velocity conditions.
method Combining L2 normal velocity with parabolic regularity theory. result Graphical Brakke flows with forcing term in Lp,q and C0,α are strong and classical solutions. We consider smooth radial solutions to the Hamiltonian stationary equation which are defined away from the origin. We show that in dimension two all radial solutions on unbounded domains must be special Lagrangian. In contrast, for all higher dimensions there exist non-special Lagrangian radial solutions over unbounded…
New topologies for star-shaped sets without boundedness.
problem Defining convergence for unbounded star-shaped sets.
method Introducing radial distance functionals and new topologies.
result New topologies τWr and τAWr for star-shaped sets. New algorithm radVI improves variational inference by optimizing radial profiles.
problem Gaussian approximations often fail to capture the radial profile of complex distributions.
method Optimizes over radial profiles in variational inference, providing theoretical guarantees.
result Theoretical convergence guarantees for radVI, improving over existing VI methods.
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
SAGE generates subsurface velocity models from sparse well logs and seismic images.
problem Lack of high-quality subsurface velocity models due to limited data availability.
method Subsurface AI-driven geostatistical extraction using proxy posterior.
result SAGE produces geologically plausible and statistically accurate velocity realizations.
The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to …
Proves conditions for radial Kaehler metrics to be Kaehler-Einstein.
problem Characterizing radial Kaehler metrics as Kaehler-Einstein.
method Analyzes conditions for radial Kaehler metrics to be Kaehler-Einstein.
result Conditions for radial Kaehler metrics to be Kaehler-Einstein are provided.
Real projective structures on n-orbifolds are useful in understanding the space of representations of discrete groups into SL(n+1,R) or PGL(n+1,R). A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the o…
New method distinguishes cause from effect using causal velocity.
problem Inferring causal direction from bivariate data.
method Parametrization of bivariate SCMs in terms of causal velocity, using tools from measure transport.
result Method extends beyond known model classes and requires no assumptions on noise distributions.
Study radial processes in sub-Riemannian Brownian motions, proving stochastic completeness and eigenvalue estimates.
problem Analyzing sub-Riemannian Brownian motions and their radial processes.
method Application of Itô's formula and sub-Laplacian comparison theorems to prove stochastic completeness and eigenvalue estimates.
result Proved Cheng's type estimates for Dirichlet eigenvalues of sub-Riemannian metric balls.
We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support-they assign zero…
Study on gradient ρ-Einstein solitons with radially nonnegative Bach tensor.
problem Characterizing gradient ρ-Einstein solitons with specific tensor properties.
method Analyzing the properties of Bach tensor and using local warping to classify solitons.
result Gradient ρ-Einstein solitons with radially nonnegative Bach tensor are locally warped products of an interval and an Einstein manifold.
Radial graphs with constant mean curvature found in Euclidean space.
problem Existence of hypersurfaces with constant mean curvature.
method Radial graphs over domains of the unit sphere, Dirichlet problem.
result Existence of hypersurfaces with positive constant mean curvature.
LFIS uses a time-dependent velocity field to sample from complex distributions.
problem Sampling from unnormalized density functions.
method LFIS learns a time-dependent velocity field to transport samples from a simple initial distribution to a complex target distribution.
result LFIS achieves state-of-the-art performance on various benchmark problems.
NN-Turb generates turbulent velocity statistics using neural networks.
problem Creating a 1D field with turbulent velocity statistics.
method Fully-convolutional neural network (NN-Turb) to generate the field.
result NN-Turb generates a 1D field that satisfies Kolmogorov's 2/3 and 4/5 laws, exhibiting intermittency.
Bitcoin's monetary velocity is constrained by network friction, leading to significant utility contraction during shocks.
problem Bitcoin's monetary velocity is limited by network congestion, causing significant utility loss during economic shocks.
method Empirical analysis using Transaction Cost Index and threshold regression to identify structural breaks and velocity contraction.
result Network friction significantly reduces Bitcoin's monetary velocity, leading to a net utility contraction of -9.39% during shocks.
Let us fix two different radial eigenfunctions of a hyperbolic Laplacian and assume that both of them have the same value at the origin. Both eigenvalues can be complex numbers. The main goal of this paper is to estimate the lower bound for the interval (0,T], where these two eigenfunctions must assume different values…
Study proves radial symmetry in convex cones using subharmonic functions.
problem Proving radial symmetry in convex cones with boundary conditions.
method Using maximum principle and integral identities for subharmonic functions.
result Proves radial symmetry and Serrin-type results for partially overdetermined problems.
We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian n-manifold M having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of …
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…
We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.
A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.
problem Improving generative modeling by addressing non-conservatism issues.
method Proposes a conservative drifting method using kernel density estimator gradients to address non-conservatism.
result Proves finite-particle convergence rates for the conservative method, providing explicit quadrature constants.
We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.
Study on manifolds with density using modified Hessians for curvature comparison.
problem Developing comparison geometry on manifolds with density.
method Modified Hessian approach based on weighted sectional curvature framework.
result Derivation of Hessian comparison and shape operator comparison theorems.
Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.
problem Establishing inequalities for radial functions on hyperbolic spaces without zero boundary conditions.
method Novel approach considering both bounded and unbounded domains, focusing on weighted Sobolev and Adams-Trudinger-Moser embeddings.
result Theorems 1.2, 1.3, and 1.4 for weighted Sobolev embedding theorems, and Theorems 1.5 and 1.6 for Adams-Trudinger-Moser type embedding theorems.
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
problem Tackling the indistinguishability of spectral line profiles under scalar summaries.
method Introduces a geometric representation of line profiles using rough path theory, mapping profiles to a common velocity grid and defining descriptors from path properties.
result Compact descriptors separate morphologies with similar scalar summaries, revealing ordered line structures.