Daily Papers

We consider the incompressible Euler and Navier-Stokes equations on the three dimensional torus, in velocity form, perturbed by a transport or transport-stretching Stratonovich noise. Closed control of the noise contributions in energy estimates are demonstrated, for any positive integer ordered Sobolev Space and the equivalent Stokes Space; difficulty arises due to the presence of the Leray Projector disrupting cancellation of the top order derivative. This is particularly pertinent in the case of a transport noise without stretching, where the vorticity form cannot be used. As a consequence we obtain, for the first time, the existence of a local strong solution to the corresponding stochastic Euler equation. Furthermore, smooth solutions are shown to exist until blow-up in L^1left([0,T];W^{1,infty}right).

The nature of the spiral structure of the Milky Way has long been debated. Only in the last decade have astronomers been able to accurately measure distances to a substantial number of high-mass star-forming regions, the classic tracers of spiral structure in galaxies. We report distance measurements at radio wavelengths using the Very Long Baseline Array for eight regions of massive star formation near the Local spiral arm of the Milky Way. Combined with previous measurements, these observations reveal that the Local Arm is larger than previously thought, and both its pitch angle and star formation rate are comparable to those of the Galaxy's major spiral arms, such as Sagittarius and Perseus. Toward the constellation Cygnus, sources in the Local Arm extend for a great distance along our line of sight and roughly along the solar orbit. Because of this orientation, these sources cluster both on the sky and in velocity to form the complex and long enigmatic Cygnus X region. We also identify a spur that branches between the Local and Sagittarius spiral arms.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

Existing video frame interpolation (VFI) methods blindly predict where each object is at a specific timestep t ("time indexing"), which struggles to predict precise object movements. Given two images of a baseball, there are infinitely many possible trajectories: accelerating or decelerating, straight or curved. This often results in blurry frames as the method averages out these possibilities. Instead of forcing the network to learn this complicated time-to-location mapping implicitly together with predicting the frames, we provide the network with an explicit hint on how far the object has traveled between start and end frames, a novel approach termed "distance indexing". This method offers a clearer learning goal for models, reducing the uncertainty tied to object speeds. We further observed that, even with this extra guidance, objects can still be blurry especially when they are equally far from both input frames (i.e., halfway in-between), due to the directional ambiguity in long-range motion. To solve this, we propose an iterative reference-based estimation strategy that breaks down a long-range prediction into several short-range steps. When integrating our plug-and-play strategies into state-of-the-art learning-based models, they exhibit markedly sharper outputs and superior perceptual quality in arbitrary time interpolations, using a uniform distance indexing map in the same format as time indexing. Additionally, distance indexing can be specified pixel-wise, which enables temporal manipulation of each object independently, offering a novel tool for video editing tasks like re-timing.

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead velocity, streamlines, which are also pathlines in this frame, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connecting the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, a novel formulation of the viscoelastic stress term in the momentum transport equation proposes a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

In this third paper of a series, we study the kinematics of the ionised gas and stars, calculating the dynamical masses of the circumnuclear star-forming regions in the ring of of the face-on spiral NGC 7742. We have used high spectral resolution data from the MEGARA instrument attached to the Gran Telescopio Canarias (GTC) to measure the kinematical components of the nebular emission lines of selected HII regions and the stellar velocity dispersions from the CaT absorption lines that allow the derivation of the associated cluster virialized masses. The emission line profiles show two different kinematical components: a narrow one with velocity dispersion sim 10 km/s and a broad one with velocity dispersion similar to those found for the stellar absorption lines. The derived star cluster dynamical masses range from 2.5 times 10^6 to 10.0 times 10^7 M_odot. The comparison of gas and stellar velocity dispersions suggests a scenario where the clusters have formed simultaneously in a first star formation episode with a fraction of the stellar evolution feedback remaining trapped in the cluster, subject to the same gravitational potential as the cluster stars. Between 0.15 and 7.07 % of the total dynamical mass of the cluster would have cooled down and formed a new, younger, population of stars, responsible for the ionisation of the gas currently observed.

We construct a time-dependent, incompressible, and uniformly-in-time Lipschitz continuous velocity field on T^3 that produces exponential growth of the magnetic energy along a subsequence of times, for every positive value of the magnetic diffusivity. Because this growth is not uniform in time but occurs only along a diverging sequence of times, we refer to the resulting mechanism as a limsup fast dynamo. Our construction is based on suitably rescaled Arnold-Beltrami-Childress (ABC) flows, each supported on long time intervals. The analysis employs perturbation theory to establish continuity of the exponential growth rate with respect to both the initial data and the diffusivity parameter. This proves the weak form of the fast dynamo conjecture formulated by Childress and Gilbert on T^3, but the considerably more challenging version proposed by Arnold on T^3 remains an open problem.

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

We present N-body simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 M_{odot}. The models are evolved with the N-body code bifrost to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star-BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About sim 20-30 per cent of the stars within the spheres of influence of the black holes form Bahcall-Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500 up to 1300 TDEs, depending on the initial cluster structure. Most (> 95 per cent) of the TDEs originate from stars in the Bahcall-Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density and velocity dispersion of the clusters (N_{TDE} propto M_{BH} rho sigma^{-3}). We find that TDEs can lead a 300 M_{odot} BH to reach sim 7000 M_{odot} within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters.

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number n of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the mean of the generated mixture and the mean of the target mixture, which we show decays as Theta_n(1{n}). Finally, this rate is shown to be in fact Bayes-optimal.

We study stellar core growth in simulations of merging massive (M_star>10^{11},M_odot) elliptical galaxies by a supermassive black hole (SMBH) displaced by gravitational wave induced recoil velocity. With controlled, dense sampling of the SMBH recoil velocity, we find the core radius originally formed by SMBH binary scouring can grow by a factor of 2-3 when the recoil velocity exceeds sim50 per cent of the central escape velocity, and the mass deficit grows by up to a factor of sim4. Using Bayesian inference we predict the distribution of stellar core sizes formed through this process to peak at sim1,kpc. An orbital decomposition of stellar particles within the core reveals that radial orbits dominate over tube orbits when the recoil velocity exceeds the velocity dispersion of the core, whereas tube orbits dominate for the lowest recoil kicks. A change in orbital structure is reflected in the anisotropy parameter, with a central tangential bias present only for recoil velocities less than the local stellar velocity dispersion. Emulating current integral field unit observations of the stellar line-of-sight velocity distribution, we uncover a distinct signature in the Gauss-Hermite symmetric deviation coefficient h_4 that uniquely constrains the core size due to binary scouring. This signature is insensitive to the later evolution of the stellar mass distribution due to SMBH recoil. Our results provide a novel method to estimate the SMBH recoil magnitude from observations of local elliptical galaxies, and implies these galaxies primarily experienced recoil velocities less than the stellar velocity dispersion of the core.

Event-based cameras are ideal for line-based motion estimation, since they predominantly respond to edges in the scene. However, accurately determining the camera displacement based on events continues to be an open problem. This is because line feature extraction and dynamics estimation are tightly coupled when using event cameras, and no precise model is currently available for describing the complex structures generated by lines in the space-time volume of events. We solve this problem by deriving the correct non-linear parametrization of such manifolds, which we term eventails, and demonstrate its application to event-based linear motion estimation, with known rotation from an Inertial Measurement Unit. Using this parametrization, we introduce a novel minimal 5-point solver that jointly estimates line parameters and linear camera velocity projections, which can be fused into a single, averaged linear velocity when considering multiple lines. We demonstrate on both synthetic and real data that our solver generates more stable relative motion estimates than other methods while capturing more inliers than clustering based on spatio-temporal planes. In particular, our method consistently achieves a 100% success rate in estimating linear velocity where existing closed-form solvers only achieve between 23% and 70%. The proposed eventails contribute to a better understanding of spatio-temporal event-generated geometries and we thus believe it will become a core building block of future event-based motion estimation algorithms.

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Astrophysical uncertainties in dark matter direct detection experiments are typically addressed by parametrizing the velocity distribution in terms of a few uncertain parameters that vary around some central values. Here we propose a method to optimize over all velocity distributions lying within a given distance measure from a central distribution. We discretize the dark matter velocity distribution as a superposition of streams, and use a variety of information divergences to parametrize its uncertainties. With this, we bracket the limits on the dark matter-nucleon and dark matter-electron scattering cross sections, when the true dark matter velocity distribution deviates from the commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and could be applied to other physics scenarios where a given physical observable depends on a function that is uncertain.

A research division plays an important role of driving innovation in an organization. Drawing insights, following trends, keeping abreast of new research, and formulating strategies are increasingly becoming more challenging for both researchers and executives as the amount of information grows in both velocity and volume. In this paper we present a use case of how a corporate research community, IBM Research, utilizes Semantic Web technologies to induce a unified Knowledge Graph from both structured and textual data obtained by integrating various applications used by the community related to research projects, academic papers, datasets, achievements and recognition. In order to make the Knowledge Graph more accessible to application developers, we identified a set of common patterns for exploiting the induced knowledge and exposed them as APIs. Those patterns were born out of user research which identified the most valuable use cases or user pain points to be alleviated. We outline two distinct scenarios: recommendation and analytics for business use. We will discuss these scenarios in detail and provide an empirical evaluation on entity recommendation specifically. The methodology used and the lessons learned from this work can be applied to other organizations facing similar challenges.