arXiv research

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

Estimates for $p$-capacities on symmetric manifolds.

In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, Pólya-Szegö and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is char…

The paper proves a new inequality linking mass and volume in 3D space.

Paper proves anisotropic Minkowski inequality and related inequalities.

The paper studies the consistency of mean curvature flow via volumetric varifolds.

DVAO predicts volumetric ambient occlusion for real-time volume rendering.

Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.

The paper proposes methods for volumetric parameterization of 3D solid manifolds.

In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its application to the problem of the existence in the space-time of compact and complete spacelike hypersurface.

Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere ($\mathbb{S}^2$) or a unit ball ($\mathbb{B}^3$)---…

Deep generative models are rapidly gaining traction in medical imaging. Nonetheless, most generative architectures struggle to capture the underlying probability distributions of volumetric data, exhibit convergence problems, and offer no robust indices of model uncertainty. By comparison, the autoregressive generative…

Paper extends 2D ZSAD to 3D MRI without training, achieving robust anomaly detection.

Deep learning improves 3D microscopy resolution without matched target images.

Resting-state functional MRI (rs-fMRI) scans hold the potential to serve as a diagnostic or prognostic tool for a wide variety of conditions, such as autism, Alzheimer's disease, and stroke. While a growing number of studies have demonstrated the promise of machine learning algorithms for rs-fMRI based clinical or beha…

Hyperbolic space outperforms Euclidean in learning hierarchical data.

Paper presents a consistent discretization for Hodge decomposition on volumetric meshes.

We explore a solution for learning disease signatures from weakly, yet easily obtainable, annotated volumetric medical imaging data by analyzing 3D volumes as a sequence of 2D images. We demonstrate the performance of our solution in the detection of emphysema in lung cancer screening low-dose CT images. Our approach u…

New method beats volumetric barrier for manifold recovery.

A new 2.5D U-net for 3D segmentation reduces memory constraints.

New dataset tests mental rotation from single images, improving model understanding of 3D scenes.

A neural atlas simplifies 3D geometry simulation by avoiding meshing.

Volumetric analysis of brain ventricle (BV) structure is a key tool in the study of central nervous system development in embryonic mice. High-frequency ultrasound (HFU) is the only non-invasive, real-time modality available for rapid volumetric imaging of embryos in utero. However, manual segmentation of the BV from H…

Radiological imaging of the prostate is becoming more popular among researchers and clinicians in searching for diseases, primarily cancer. Scans might be acquired with different equipment or at different times for prognosis monitoring, with patient movement between scans, resulting in multiple datasets that need to be…

Paper develops framework for valuing and assessing credit risk in renewable PPAs.

New framework reveals thermodynamic principles for LLM training.

Brain cancer can be very fatal, but chances of survival increase through early detection and treatment. Doctors use Magnetic Resonance Imaging (MRI) to detect and locate tumors in the brain, and very carefully analyze scans to segment brain tumors. Manual segmentation is time consuming and tiring for doctors, and it ca…

Method estimates section thickness and XY anisotropy in ssEM images.

We revisit the proof by Qin et al. (2014) of bounded regret of the C$^2$UCB contextual combinatorial bandit. We demonstrate an error in the proof of volumetric expansion of the moment matrix, used in upper bounding a function of context vector norms. We prove a relaxed inequality that yields the originally-stated regre…

A novel approach for 3D lung nodule segmentation using adaptive ROI and multi-view residual learning.

Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, furthermore, thus there is a need for its fully automatic segmentation from clinical images. In …

The paper compares heat kernels on manifolds with Robin boundary conditions.

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

Study on biharmonic map heat flow with monotonicity formula.

Generative models create synthetic MRI brain scans for research.

Understanding the heat usage of customers is crucial for effective district heating operations and management. Unfortunately, existing knowledge about customers and their heat load behaviors is quite scarce. Most previous studies are limited to small-scale analyses that are not representative enough to understand the b…

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…

The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…

The paper studies heat kernel asymptotics and proves Morse inequalities.

Derives gradient estimates for CR heat equation on pseudo-Hermitian manifolds.

New method predicts heat load in thermal grids using latent variables.

The Liouville theorem is proven for V T-harmonic map heat flow.

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…

New heat equation method solves intertwining problems in CR geometry.

Paper studies heat flow for maps on manifolds, avoiding singularities.

In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…

Proves upper bounds for heat kernels evolving on manifolds.

Formulae connect heat kernels on glued manifolds.