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.
Generalizes shape analysis to Lie groups and homogeneous spaces.
problem Shape analysis on non-Euclidean spaces.
method Square Root Velocity Transform (SRVT) generalization to Lie groups and homogeneous manifolds.
result Shape analysis on Lie groups and homogeneous spaces.
Extends square root velocity transform to handle curves in shape spaces of manifold-valued data.
problem Handling curves that leave the shape space in shape analysis.
method Generalizes absolutely continuous curves to strong Riemannian manifolds and extends SRVT to handle these curves.
result Computations in the SRVT framework can now be applied to curves in shape spaces of manifold-valued data.
Transforms curves and surfaces for efficient geometric analysis.
problem Efficiently analyzing and comparing curves and surfaces.
method Square root velocity transformation for curves and intrinsic comparison for surfaces.
result Fundamental geometric properties of curves under the transformation.
The paper extends square root velocity framework to curves in homogeneous spaces.
problem Computing metrics and analyzing curves in homogeneous spaces.
method Generalized square root velocity framework to homogeneous spaces, identifying curves with horizontal lifts in G G G , computing geodesics, and performing quotient operations. result Geodesics and Karcher means can be computed in quotient spaces of curves in homogeneous spaces.
Develops scalable model for learning velocity fields in complex traffic scenarios.
problem Learning heterogeneous and dynamic velocity fields in complex traffic scenarios.
method Nonparametric Bayesian modeling with hierarchical Dirichlet process and infinite hidden Markov model, Gaussian process prior, and scalable approximate inference.
result Demonstrates effective scalability and applicability to real-world traffic data.
DFM models are analyzed for generating distributions with provable convergence.
problem Training DFM models to generate distributions that match true data.
method Theoretical analysis decomposes error into approximation and estimation errors.
result DFM models converge to true data distribution as training set size increases.
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.
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …
Detects intraday market manipulation by analyzing velocity of market state, improving precision over recall.
problem Detecting brief, statistically similar intraday market manipulation in millions of quotes.
method Minute-level detection pipeline based on smoothed state velocity, SHAP attribution, and market regimes.
result Dynamic signature of pump-and-crash pattern in market velocity, improving precision over recall.
The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.
problem Comparing and analyzing shapes of curves.
method Construction and theoretical properties of quotient elastic metrics, special case of square root velocity metric, numerical approaches for estimation.
result Simplified expression for the square root velocity metric distance.
We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum i…
MeanFlow training is unstable due to misusing conditional velocity, leading to variance issues.
problem Unstable training of MeanFlow due to variance problems.
method Theoretical analysis and derivation of optimal coefficient in closed form.
result The optimal coefficient in MeanFlow training minimizes variance but not necessarily quality.
A neural network models pressure-Hessian from local velocity gradients in turbulent flows.
problem Modeling the pressure-Hessian from local velocity gradients in turbulent flows.
method Tensor basis neural network (TBNN) trained on DNS data.
result Neural network accurately captures key alignment statistics of the pressure-Hessian tensor.
Neural networks predict flow and elastic stresses in viscoelastic turbulence.
problem Predicting flow and elastic stresses in viscoelastic turbulent flows using limited experimental data.
method Convolutional neural networks trained on wall-normal velocity and pressure data.
result Neural networks accurately predict flow and elastic stresses, especially during low-drag events.
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.
The paper explores rectified flows and their relation to optimal transport.
problem Understanding the connection between rectified flows and optimal transport.
method Investigates invariance properties, explicit constructions, and analysis of rectified flows in various settings.
result Rectified flows, when gradient constrained, do not generally solve optimal transport problems.
A simple property of Weyl tensor in shear-free, vorticity-free, acceleration-free velocity fields.
problem Proving a property of the Weyl tensor in specific velocity fields.
method Analyzing the Weyl tensor's divergence and contraction properties in shear-free, vorticity-free, acceleration-free velocity fields.
result The covariant divergence of the Weyl tensor is zero if the contraction of the Weyl tensor with the velocity is zero, and vice versa.
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.
Flow Matching models help generative models stay within the subspace of real data.
problem How do generative models stay within the subspace of real data?
method Flow Matching models using a learned velocity field to transform a simple prior into a complex target distribution.
result Generated samples memorize real data points and represent the sample data subspace exactly.
Emulator speeds up landslide run-out modeling sensitivity analysis.
problem Computational challenges in assessing landslide run-out model sensitivity.
method Gaussian process emulation integrated into r.avaflow.
result Strong interactions detected between friction coefficients and release volume.
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 f 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.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
problem Stochastic guidance of spin states of rigid bodies over a hard deadline.
method Structural analysis of Kantorovich optimal coupling formulation for nonlinear dynamics.
result Derives the ground cost for optimal transport of angular velocity.
Proves strong solutions for graphical Brakke flows with L 2 L^2 L 2 normal velocity.
problem Proving strong solutions for graphical Brakke flows with specific velocity conditions.
method Combining L 2 L^2 L 2 normal velocity with parabolic regularity theory. result Graphical Brakke flows with forcing term in L p , q L^{p,q} L p , q and C 0 , α C^{0,α} C 0 , α are strong and classical solutions. 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.
Method learns attractive areas from agent motions to represent environments.
problem Representing environments based on moving agents' nonlinear motions.
method Switching model of velocity fields, parametric representation of attractive spots.
result Dynamic map of attractive areas for online learning.
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.
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.
Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.
problem Characterizing rotationally symmetric solutions to a specific PDE on a ring-shaped domain.
method Introduced new arguments in the spirit of comparison geometry to overcome the lack of monotonicity.
result Simplest conditions are not sufficient; rotational symmetry requires finitely many maxima.
Paper develops a new model for forecasting ocean currents.
problem Forecasting the Loop Current and its eddies for the Gulf of Mexico.
method Physics-informed Tensor-train ConvLSTM, incorporating prior physical knowledge.
result PITT-ConvLSTM outperforms state-of-the-art methods in volumetric velocity forecasting.
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.
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.
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.
A novel method classifies shapes by their square-root velocity function.
problem Classifying shapes in infinite-dimensional, curved spaces.
method Square-root velocity function, tangent spaces, principal components, combining pairwise classifiers.
result Improves classification accuracy by separating shapes and reducing dimensionality.
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.
Neural solver computes Wasserstein geodesics and velocity fields efficiently.
problem Computing Wasserstein geodesics and velocity fields efficiently.
method Sample-based neural network approach to solve the minimax problem.
result Directly samples from target distribution and estimates velocity field.
Generative sampler learns velocity fields for efficient posterior inference.
problem Sampling from complex posterior distributions in high dimensions.
method Generative multivariate posterior sampler via flow matching, learning a velocity field for a deterministic transport map.
result Conditional Brenier map enables fast generation of credible sets with theoretical consistency guarantees.
This work analyzes the statistical properties of neural ODEs for distribution learning.
problem Statistical properties of neural ODEs for distribution learning.
method General nonparametric statistical convergence analysis for distribution learning via neural ODE models.
result Established nearly minimax-optimal convergence rates for neural ODEs.
A new framework for shape analysis on homogeneous spaces.
problem Efficiently comparing shapes on homogeneous manifolds.
method Generalized Square Root Velocity Transform framework for shapes on homogeneous manifolds.
result Variety of possibilities based on different Lie group actions and metrics.
Sharp stability threshold found for deep residual architectures.
problem Ensuring stable training and inference in deep residual networks.
method Sublinear-growth principle and optimal-control analysis.
result Stable training condition: input-magnitude exponent q ≤ 1.
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.
An ( r , n ) (r,n) ( r , n ) -velocity is an r r r -jet with source at 0 ∈ R n 0 \in \R^n 0 ∈ R n , and target in a manifold Y Y Y . An ( r , n ) (r,n) ( r , n ) -velocity is said to be regular, if it has a representative which is an immersion at 0 ∈ R n 0 \in \R^{n} 0 ∈ R n . The manifold T n r Y T^{r}_{n}Y T n r Y of ( r , n ) (r,n) ( r , n ) -velocities as well as its open, L n r L^{r}_{n} L n r -invariant, dense submanifold $\Imm …
Time dilation 1 1 − v 2 \frac{1}{\sqrt{1-v^2}} 1 − v 2 1 and relative velocity v v 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 …
CNFs learn distributions from samples with error bounds.
problem Learning probability distributions from finite samples.
method Continuous normalizing flows with linear interpolation and flow matching objective function.
result Non-asymptotic error bounds for distribution estimator in Wasserstein-2 distance.
New analysis shows FM learns underlying dynamical structure, not just trajectory replay.
problem Understanding whether flow matching models learn transferable dynamical structure or merely replay trajectories.
method Derived velocity field implied by FM objective, characterized as a continuous-time dynamical system.
result FM models can be seen as parametric surrogates of nonparametric solutions, providing strong probabilistic forecasts.