New deep learning method improves 4D Flow MRI super-resolution under domain shift.
problem Domain shift in low-resolution 4D Flow MRI data.
method Distributional deep learning framework for domain generalization.
result Framework significantly outperforms traditional methods in real data applications.
Generative adversarial networks reconstruct MRI images without full data.
problem Lack of fully-sampled ground truth data for supervised MRI reconstruction.
method Generative adversarial networks for unsupervised MRI reconstruction.
result Reconstructed images show more anatomical structure than conventional methods.
Study characterizes bladder motion using dynamic MRI and statistical analysis.
problem Limited volume coverage in dynamic MRI sequences hinders 3D shape reconstruction.
method 3D dense velocity measurements, LDDMM framework, statistical characterization, mean curvature changes, surface deformation analysis.
result Stable shape descriptor for characterizing bladder surface dynamics.
New 1-parameter family of ovals identified in 4d Ricci flow classification.
problem Classifying κ-solutions in 4d Ricci flow. method Introducing conjectures and constructing new examples.
result Established canonical neighborhood theorem for 4d Ricci flow.
Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.
problem Classifying 4D gradient steady Ricci solitons and understanding their geometric properties.
method Analysis of 4D gradient steady Ricci solitons with O(3)-symmetry under a weak curvature decay condition.
result Find precise geometric asymptotics similar to 3D compact κ-solutions.
Global regularity proved for 4D Ricci flow with scalar curvature integral bound.
problem Global regularity of 4D Ricci flow with integral scalar curvature bound.
method Extended Ge-Jiang's result to include integral bound on scalar curvature.
result Global ε-regularity for 4D Ricci flow with integral scalar curvature bound. In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and ass…
The study finds static solutions in symplectic curvature flow in 4D.
problem Finding static solutions in symplectic curvature flow in 4D.
method Derived a local normal form for static solutions and used Cartan-Kahler theorem for solitons.
result Every complete static solution to symplectic curvature flow in 4D is Kahler-Einstein.
Advances in computational science offer a principled pipeline for predictive modeling of cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and surgical planning. Such models can be nowadays deployed on large patient-specific topologies of systemic arterial networks and return detail…
The study disproves rotating ancient flows in 4D space.
problem The existence of rotating ancient flows in R4. method Analysis of ancient noncollapsed flows in R4. result Nonexistence of rotating ancient flows among ancient noncollapsed flows in R4. The paper studies 4D Ricci flow manifolds with curvature constraints.
problem Investigating 4D Ricci flow manifolds with specific curvature conditions.
method Analyzing 4D manifolds with curvature constraints via Ricci flow.
result Proves topological and geometric gap theorems for maximal volume growth.
Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.
problem Investigating long-time dynamics of Yang-Mills heat flow with specific initial data.
method Analysis of SO(4)-equivariant Yang-Mills heat flow with SU(2) group in 4D space. result Global solutions can exhibit oscillatory behavior at time infinity.
Study on curvature flow in 4D ball, proving existence and convergence.
problem Existence of metrics with prescribed T-curvature on the 4D unit ball. method Using T-curvature flow and Morse-theoretic approach, combining Ache-Chang's inequality. result Existence results and exponential convergence to extremal metric.
The paper classifies ovals in 4D space for a specific flow.
problem Classifying ovals in 4D space for a specific flow.
method Proving classification through symmetry and flow properties.
result Classified ovals in 4D space, up to scaling and rigid motion.
In this work, a novel approach is proposed for joint analysis of high dimensional time-resolved cardiac motion features obtained from segmented cardiac MRI and low dimensional clinical risk factors to improve survival prediction in heart failure. Different methods are evaluated to find the optimal way to insert convent…
New algorithms improve vascular flow simulations in aortic aneurysms.
problem Limited accuracy of MRI in hemodynamics, patient-specific flow boundary conditions, and CFD's computational demands.
method Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) integrated with 3D Navier-Stokes equations.
result Improved computational efficiency and good agreement with CFD simulations.
In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as we…
The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.
problem Analyzing noncompact steady gradient Ricci solitons with nonnegative curvature operator.
method Examining the asymptotic behavior of noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative curvature operator away from a compact set.
result 4D noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling.
Generic low-entropy hypersurfaces in 4-6D flow with only generic singularities.
problem Analyzing mean curvature flow of low-entropy hypersurfaces.
method Proving flow encounters only generic singularities for specific entropy conditions.
result Proves flow encounters only generic singularities for low-entropy initial data.
New stable shrinking Ricci soliton found in 4D.
problem Stability of 4D Ricci shrinkers.
method Explicit metric description, tensor harmonic analysis, Kähler structure, selfduality insights.
result First non-cylindrical linearly stable shrinking Ricci soliton in 4D.
Improves MRI-based brain surface reconstruction with minimal deformation energy loss.
problem Ensuring optimal deformation energy and consistency in learning-based cortical surface reconstruction.
method Design and implementation of a Minimal Energy Deformation (MED) loss in the V2C-Flow model.
result Significant improvements in training consistency and reproducibility without sacrificing reconstruction accuracy and topological correctness.
Study of 4D flows with nilpotent symmetry, showing immortal solutions and blowdown limits.
problem Understanding 4D generalized Ricci flows with nilpotent symmetry.
method Immortal solutions, type III curvature and diameter estimates, new energy monotonicity.
result Blowdown limits lie in a finite-dimensional family of solutions.
Study on mean curvature flow through singularities in 3D and 4D.
problem Understanding mean curvature flow through singular points.
method General introduction and classification of singularities in R3 and R4. result Classification of all noncollapsed singularities in R4. Deep SCMs with deep learning infer counterfactuals from noisy data.
problem Inference of counterfactuals from noisy data in causal models.
method Normalizing flows and variational inference for deep SCMs.
result Tractable inference of exogenous noise variables for counterfactuals.
The paper proves smoothness of mean curvature flow for generic initial data in 3D and 4D.
problem Smoothness of mean curvature flow for generic initial data.
method Long-time existence and uniqueness result for ancient mean curvature flows.
result Smooth mean curvature flow until disappearance in a round point for low-entropy hypersurfaces in 4D.
We propose a method to classify cardiac pathology based on a novel approach to extract image derived features to characterize the shape and motion of the heart. An original semi-supervised learning procedure, which makes efficient use of a large amount of non-segmented images and a small amount of images segmented manu…
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.
Survey on gradient Ricci solitons in 4D, focusing on geometry and classification.
problem Understanding gradient Ricci solitons in four dimensions.
method Geometric analysis and classification of solitons.
result Recent results on classification and rigidity of gradient Ricci solitons in 4D.
Study inextensible flows of curves in 4D pseudo-Galilean space and defines energy functions.
problem Analyzing inextensible flows and energy of curves in 4D pseudo-Galilean space.
method Expressed inextensible flows as partial differential equations, defined directional derivatives, and expressed bending elastic energy functions.
result Necessary and sufficient conditions for inextensible flows are given as partial differential equations.
XPDNet wins MRI reconstruction challenge with neural network.
problem MRI reconstruction from under-sampled data.
method Inspired by MRI and computer vision best practices, XPDNet uses a neural network.
result XPDNet achieved state-of-the-art results in the 2020 fastMRI challenge.
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
problem Voxel independence assumption limits model fitting reliability and repeatability.
method Self-supervised deep variational approach with Gaussian mixture prior.
result Our method outperforms current techniques in dMRI simulations and real data.
Stability of Morse index for Yang-Mills connections in 4D.
problem Stability of critical points in Yang-Mills energy relaxation.
method Establishing lower semi-continuity of Morse index and upper continuity of Morse index plus nullity.
result Yang-Mills fields are more stable than harmonic maps in 4D.
StaPLR improves Alzheimer's disease classification by identifying important MRI scan types and measures.
problem Classifying Alzheimer's disease using multi-source MRI data.
method Stacked penalized logistic regression (StaPLR) with hierarchical multi-view structure and new view importance measure.
result StaPLR identifies the most important MRI scan types and measures for Alzheimer's disease classification.
Human brain development is rapid during infancy and early childhood. Many disease processes impair this development. Therefore, brain developmental age estimation (BDAE) is essential for all diseases affecting cognitive development. Brain magnetic resonance imaging (MRI) of infants shows brain growth and morphologic pa…
In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d Kähler manifolds satisfying a Kähler-Ricci flow equation. We find that BP…
3D CNNs interpret brain MRI differences between men and women.
problem Interpreting 3D CNNs for voxel-wise brain MRI analysis.
method Three interpretation methods: Meaningful Perturbations, Grad CAM, and Guided Backpropagation.
result Voxel-wise 3D CNN interpretation of brain MRI data.
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space M=Rd⋊Sd−1 of positions and orientations as a Lie group…
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
Diffusion MRI is the modality of choice to study alterations of white matter. In past years, various works have used diffusion MRI for automatic classification of AD. However, classification performance obtained with different approaches is difficult to compare and these studies are also difficult to reproduce. In the …
CSGM framework applied to clinical MRI data for robust reconstructions.
problem Applying deep generative priors to clinical MRI data for high-quality reconstructions.
method Training a generative prior on brain scans from the fastMRI dataset and using Langevin dynamics for posterior sampling.
result Posterior sampling via Langevin dynamics achieves high quality reconstructions in clinical MRI data.
New neural network improves MRI reconstruction for non-Cartesian data.
problem Improving MRI reconstruction for non-Cartesian data acquisitions.
method Density-compensated unrolled neural networks.
result Density-compensated unrolled neural networks outperform baselines.
This study improves lung tumor segmentation in mice MRI scans with nnU-Net, reducing annotation needs.
problem Accurate lung tumor segmentation in mice MRI scans for drug discovery.
method Optimized nnU-Net 3D model for lung tumor segmentation with minimal annotations.
result nnU-Net 3D models outperform 2D models in MRI mice scans, requiring fewer annotations.
In compressed sensing MRI (CS-MRI), k-space measurements are under-sampled to achieve accelerated scan times. CS-MRI presents two fundamental problems: (1) where to sample and (2) how to reconstruct an under-sampled scan. In this paper, we tackle both problems simultaneously for the specific case of 2D Cartesian sampli…
Accelerating Magnetic Resonance Imaging (MRI) by taking fewer measurements has the potential to reduce medical costs, minimize stress to patients and make MRI possible in applications where it is currently prohibitively slow or expensive. We introduce the fastMRI dataset, a large-scale collection of both raw MR measure…
Study 4D solitons with specific curvature properties, proving curvature bounds and classifying solutions.
problem Investigate 4D gradient solitons with specific curvature properties.
method Analyze 4D gradient steady and shrinking solitons with nonnegative or half nonnegative isotropic curvature.
result Prove 2-nonnegativity of Ricci curvature and bound the curvature tensor for ancient solutions.
New method MRI improves machine learning models' ability to generalize to unseen data.
problem Machine learning models often fail to generalize well to out-of-distribution data.
method Introduces a new notion of invariance (MRI) and a practical version (MRI-v1) to improve model generalization.
result MRI-v1 guarantees invariant predictors and outperforms IRM-v1 in various settings.
New method optimizes MRI sampling patterns for faster scans.
problem Accelerate MRI scans without sacrificing image quality.
method Joint learning of adaptive sampling patterns and model-based recovery.
result Improved MR image quality compared to other methods.