Graph Neural Networks model 3D granular flow simulations.
problem Accurate modeling of complex 3D granular flow processes.
method Graph Neural Networks approach to simulate 3D granular flow using LIGGGHTS.
result Machine learning trajectories match physical granular flow processes.
BGNNs model particle-boundary interactions efficiently.
problem Efficiently modeling geometric boundaries in 3D simulations.
method Introduce Boundary Graph Neural Networks (BGNNs) to dynamically modify graph structures.
result BGNNs accurately reproduce 3D granular flows without handcrafted conditions.
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
Neural HMM with AGA captures multi-scale dynamics in financial markets.
problem Capturing multi-scale temporal dynamics in financial markets.
method Parallel multi-resolution encoders, adaptive gating, and multi-head attention.
result Outperforms fixed-resolution baselines in predicting price movements and liquidity shocks.
Sharp 3D Alexandrov inequality applied to volume-preserving flows.
problem Volume-preserving geometric flows in 3D space.
method Sharp quantitative Alexandrov inequality for C2-regular sets. result Established a 3D sharp quantitative version of the Alexandrov inequality.
Ancient ovals are key blowup limits in 3D Ricci flow near singularities.
problem Understanding blowup limits in 3D Ricci flow near singularities.
method Proving ancient ovals are blowup limits if and only if spherical singularities accumulate.
result Ancient ovals are necessary and sufficient for blowup limits in 3D Ricci flow.
GAGA accelerates 3D molecular generation by replacing long trajectories with Gaussian approximations.
problem High computational cost of long generative trajectories in 3D molecular generation.
method GAGA identifies a characteristic step where molecular data becomes sufficiently Gaussian, replacing the trajectory with a Gaussian approximation.
result Significant improvement in both generation quality and computational efficiency.
We propose and document the evidence for an analogy between the dynamics of granular counter-flows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counter-flows of simulated pedestrians through a door display many stylized facts obser…
Complete Ricci flow from singular 3D manifold with pseudolocality.
problem Constructing complete Ricci flow from singular 3D manifold.
method Combining pseudolocality results for singular and nonsingular flows.
result Ricci flow is complete for positive times under certain conditions.
We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riema…
The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously relat…
Study how large-scale flows align small-scale vortices in 3D Euler equations.
problem Understanding how large-scale flows align small-scale vortices in 3D Euler equations.
method Constructing a Lagrangian coordinate to identify when the Lie bracket is zero and investigating the locality of the pressure term.
result Clarified conditions under which small-scale vortices are aligned by large-scale flows.
3D metrics get scalar curvature bounds via IMCF.
problem Bounding scalar curvature for C0 metrics. method Inverse Mean Curvature Flow (IMCF) and Hawking mass monotonicity.
result Stability theorem for nonnegative scalar curvature.
The study classifies flows of finite curvature in 3D space.
problem Classifying flows of finite curvature in 3D space.
method Partial classification of eternal mean convex flows.
result Topologically nonplanar flows must exit a catenoid.
Study sub-Riemannian geodesics on a Heisenberg 3D nil-manifold.
problem Characterize geodesics on a specific nil-manifold.
method Analyze the projection of sub-Riemannian structure, describe geodesic flow dynamics, and estimate sub-Riemannian geodesics.
result Sharp bounds and estimates for sub-Riemannian geodesics.
3D Ricci flows have bounded diameter before Type I singularities.
problem Bounding the diameter of 3D Ricci flows before Type I singularities.
method Introduced a neck-region concept and proved packing measure Ahlfors regularity.
result Uniformly bounded diameter up to Type I singular time.
Characterizes Anosov flows in 3D using symplectic and contact geometry.
problem Understanding Anosov flows in 3D.
method Purely contact and symplectic geometric methods.
result Characterization of Anosov flows based on Reeb flows and underlying (bi)-contact structures.
Establishes smooth Ricci flows from convex surfaces in 3D space.
problem Existence and uniqueness of Ricci flow starting from convex surfaces.
method Smooth Ricci flows starting from smooth convex surfaces.
result Uniform convergence of metrics to initial convex surface.
Paper classifies singularity models for 3D hypersurfaces in R^4.
problem Classifying singularity models for 3D hypersurfaces in R^4.
method Proving classification through mathematical proof.
result All noncollapsed translating hypersurfaces in R^4 are classified.
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
problem Constructing 3D dual field theories for Virasoro minimal models.
method 3D-3D correspondence and Seifert fiber spaces.
result 3D dual field theories constructed for Virasoro minimal models.
A machine learning method predicts rock permeability from 3D images.
problem Efficiently predict permeability of heterogeneous rocks for planetary and robotic applications.
method Machine learning guided 3D properties recognition of rock morphology from 3D micro CT and MRI images.
result The morphology decoder method accurately predicts permeability from 3D images.
DECAF optimizes molecular graphs for ensemble properties, improving drug design accuracy.
problem Designing molecules with ensemble properties rather than single conformations.
method DECAF uses Boltzmann-expected design with decoupled annealing flows to optimize molecular graphs.
result DECAF optimizes molecular graphs to shift ensemble properties towards targets, improving accuracy over single-conformer methods.
Hamilton's Ricci flow (RF) equations were recently expressed in terms of the edge lengths of a d-dimensional piecewise linear (PL) simplicial geometry, for d greater than or equal to 2. The structure of the simplicial Ricci flow (SRF) equations are dimensionally agnostic. These SRF equations were tested numerically and…
Paper proves minimizing movements match smooth droplet flow in 3D.
problem Consistency of minimizing movements with smooth mean curvature flow.
method Proved minimizing movements coincide with smooth droplet flow.
result Minimizing movements and smooth mean curvature flow are consistent in 3D.
It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such…
3D contact manifolds have optimal higher systolic ratios.
problem Optimizing higher systolic ratios in 3D contact manifolds.
method Proving Besse contact forms maximize certain ratios.
result Besse contact forms are local maximizers of higher systolic ratios.
New modularity function improves clustering of spatially embedded networks.
problem Improving clustering in spatially embedded networks for unsupervised learning.
method Developed a new modularity function and compared its performance with existing methods.
result Our modularity function outperforms existing methods in partitioning 2D and 3D granular assemblies.
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-N…
A neural flow method minimizes Willmore energy for 2-surfaces in 3D space.
problem Minimizing Willmore energy for closed oriented 2-surfaces in 3D space.
method Introducing neural Willmore flow to model and minimize the Willmore energy using neural architectures.
result The neural flow reproduces expected round sphere and Clifford torus for genus 0 and 1 surfaces, respectively, and finds minimal Willmore surfaces for genus 2.
Study magnetic flows on 3D contact sub-Riemannian manifolds using Rumin complex.
problem Understanding magnetic flows on 3D contact sub-Riemannian manifolds.
method Introducing horizontal magnetic flows via closed Rumin differential two-forms and analyzing the lifted sub-Riemannian structure.
result Horizontal magnetic flows can be interpreted as geodesic flows on a suitably lifted structure, which is of Engel type when the magnetic field is non-vanishing.
Study on minimal foliations in 3D manifolds with specific conditions.
problem Characterizing minimal foliations in 3D manifolds.
method Analyzing Anosov foliations and their intersections.
result Necessary and sufficient conditions for orbit foliation of Anosov flows.
HLTF generates chemically valid 3D molecules with improved topology control.
problem Generating chemically valid 3D molecules is challenging due to bond topology errors.
method HLTF uses a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures.
result HLTF achieves high validity and uniqueness on QM9 and GEOM-DRUGS datasets.
An approach to utilize recent advances in deep generative models for anomaly detection in a granular (continuous) sense on a real-world image dataset with quality issues is detailed using recent normalizing flow models, with implications in many other applications/domains/data types. The approach is completely unsuperv…
Smoothly conjugate Anosov flows on 3D manifolds are actually smoothly conjugate.
problem Smoothly conjugate 3D Anosov flows are not always smoothly conjugate.
method Proved smooth rigidity for volume preserving Anosov flows on 3-manifolds.
result Smooth conjugacy implies smooth conjugacy for volume preserving Anosov flows.
Proves unknottedness of certain 3D shapes with multiple ends.
problem Determining the structure of complex 3D shapes.
method Used mean curvature flow to analyze shapes with multiple ends.
result Proves unknottedness of shapes with multiple asymptotically conical ends.
Study proves curvature flow existence on CR manifolds.
problem Existence of curvature flow solutions on CR manifolds.
method Prescribed Webster scalar curvature flow approach.
result Proves existence of curvature flow solutions on 3D CR manifolds.
We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…
Brain tumor segmentation from Magnetic Resonance Images (MRIs) is an important task to measure tumor responses to treatments. However, automatic segmentation is very challenging. This paper presents an automatic brain tumor segmentation method based on a Normalized Gaussian Bayesian classification and a new 3D Fluid Ve…
Slender marine structures such as deep-water marine risers are subjected to currents and will normally experience Vortex Induced Vibrations (VIV), which can cause fast accumulation of fatigue damage. The ocean current is often three-dimensional (3D), i.e., the direction and magnitude of the current vary throughout the …
This paper focuses on a novel generative approach for 3D point clouds that makes use of invertible flow-based models. The main idea of the method is to treat a point cloud as a probability density in 3D space that is modeled using a cloud-specific neural network. To capture the similarity between point clouds we rely o…
Survey classifies singularity models in 3D Ricci flow.
problem Understanding singularity formation in 3D Ricci flow.
method Analysis of ancient κ-solutions and steady gradient Ricci solitons.
result Complete classification of singularity models in 3D.
New ancient curve shortening flows created from grim reapers.
problem Ancient curve shortening flows in 3D space.
method Built from translating grim reapers in perpendicular planes.
result Constructed new nonplanar ancient solutions.
Model nonstationary spatial processes using normalizing flows.
problem Difficult selection of spatial warping functions.
method Neural autoregressive flows (NAFs) for complex, high-dimensional warpings.
result NAFs model has greater representational capacity than other spatial process models.
Proves uniqueness of translators in 3D space.
problem Uniqueness of pitchfork and helicoid translators in mean curvature flow.
method Arc-counting argument and rotational maximum principle.
result Proves conjecture on uniqueness of translators.
Study shows generic surfaces avoid complex flow patterns.
problem Understanding flow patterns of surfaces in 3D space.
method Analyzes mean curvature flow of closed surfaces in R3. result Non-cylindrical self-shrinkers cannot arise generically.
The paper studies rigid sphere packings on 3D manifolds with boundary.
problem Investigating rigid sphere packings on 3D manifolds with boundary.
method Introducing generalized sphere packings, proving rigidity, introducing combinatorial curvature flows.
result Generalized sphere packing metrics are determined by combinatorial scalar curvature.
GBOC detects anomalies in time series data using granular-ball vectors.
problem Challenges in modeling normal behavior in dynamic, nonlinear time series data.
method Granular-ball Vector Data Description (GVDD) and Granular-ball One-Class Network (GBOC).
result GBOC improves anomaly detection in time series data.
An outsider's overview of Anosov flows in 3D.
problem Understanding Anosov flows in 3D and their interactions.
method Overview and discussion of main results and questions.
result Highlighting the interaction with topology and symplectic geometry.