A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study evaluates MRIQC pipeline's generalization on large multi-center datasets.
Conformal qc geometry of spherical qc manifolds are investigated. We construct the qc Yamabe operators on qc manifolds, which are covariant under the conformal qc transformations. A qc manifold is scalar positive, negative or vanishing if and only if its qc Yamabe invariant is positive, negative or zero, respectively. …
It is shown that the qc Yamabe problem has a solution on any compact qc manifold which is non-locally qc equivalent to the standard 3-Sasakian sphere. Namely, it is proved that on a compact non-locally spherical qc manifold there exists a qc conformal qc structure with constant qc scalar curvature
A quaternionic contact (qc) heat equation and the corresponding qc energy functional are introduced. It is shown that the qc energy functional is monotone non-increasing along the qc heat equation on a compact qc manifold provided certain positivity conditions are satisfied.
We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space $\Hnn$ and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in $\Hnn$ is contained in one of the three qc-hyperquadrics in $\Hnn$. Moreover, we show tha…
We show that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. We also show that any nowhere umbilical qc hypersurface in a hyper-Kähler manifold is endowed with an involutiv…
We study positive definite quaternionic contact -manifolds (-manifold for short). Just like the -structure contains the class of Sasaki manifolds, the -structure admits a class of -Sasaki manifolds with integrable distribution isomorphic to . A big difference concerning the inte…
The paper establishes sub-gradient estimates and entropy formulas for quaternionic contact geometry heat equations.
We prove a quaternionic contact versions of the Obata's sphere theorems. We show that if the first positive eigenvalue of the sub-Laplacian on a compact qc manifold of dimension bigger than seven takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard…
QC-ST and CoCo methods correct batch effects in metabolomics data.
The paper proves new curvature estimates in quaternionic contact geometry.
The main result is that the qc-scalar curvature of a seven dimensional quaternionic contact Einstein manifold is a constant. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local structure equations. Finally, regular qc-Ricci flat structures are shown to fibre…
A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension as well as on the quaternionic Heisenberg group is given. A uniqueness theorem for the qc Yamabe problem in a compact locally 3-Sasakian manifold is shown.
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical imaging, computer graphics and computer vision. Existing computational QC theor…
Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…
The 'anholonomic frame' method (see gr-qc/0005025, gr-qc/0001060 and hep-th/0110250) is applied for constructing new classes of exact solutions of vacuum Einstein equations with off-diagonal metrics in 4D and 5D gravity. We examine several black tori solutions generated by anholonomic transforms with non-trivial topolo…
In this note, we prove that the CR manifold which is induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard.
We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of Carnot-Carathéodory metric in the conformal class. The result of this computation has appli…
We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)H^*, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in se…
New knots not rationally concordant to their reverses found.
Quaternion Conformer GAN (QC-GAN) is a parameter-efficient speech enhancement framework that combines a Quaternion Conformer generator with MetricGAN-based training.
Quantum computing improves fault diagnosis in industrial processes.
Unified AI system for data quality control and governance in regulated environments.
On 7D quaternionic contact manifolds, eigenvalue bounds imply special structure.
A novel density-based approach QC detects outliers in data with high precision.
We investigate the Fefferman spaces of conformal type which are induced, via parabolic geometry, by the quaternionic contact (qc) manifolds introduced by O.Biquard. Equivalent characterizations of these spaces are proved: as conformal manifolds with symplectic conformal holonomy of the appropriate signature; as pseudo-…
We prove that the groups of orientation preserving quasiconformal or bilipschitz homeomorphisms of S^n are simple in dimensions 2 and higher.
This paper analyzes convergence of DP-SGD with adaptive quantile clipping.
Question classification (QC) is the primary step of the Question Answering (QA) system. Question Classification (QC) system classifies the questions in particular classes so that Question Answering (QA) System can provide correct answers for the questions. Our system categorizes the factoid type questions asked in natu…
Let be an infinite hyperbolic surface endowed with an upper bounded geodesic pants decomposition. Alessandrini, Liu, Papadopoulos, Su and Sun \cite{ALPSS}, \cite{ALPS} parametrized the quasiconformal Teichmüller space and the length spectrum Teichmüller space using the Fenchel-Nielsen coordi…
Study heat kernel on quaternionic contact manifolds, finding linear dependence of coefficients on curvature.
XPDNet wins MRI reconstruction challenge with neural network.
Generative adversarial networks reconstruct MRI images without full data.
QC methods improve reliability of machine learning-based image segmentation.
A novel method automates quality control of fMRI scans, improving accuracy and generalizability.
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional…
We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution. We prove a general Myers theorem and establish a Cartan-Hadamard result for almost qc-Einstein manifolds.
StaPLR improves Alzheimer's disease classification by identifying important MRI scan types and measures.
QC-SPHARM detects Alzheimer's Disease early using hippocampal surface geometry.
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…
Deep learning improves MRI image quality from down-sampled data.
3D CNNs interpret brain MRI differences between men and women.
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.
New neural network improves MRI reconstruction for non-Cartesian data.
This study improves lung tumor segmentation in mice MRI scans with nnU-Net, reducing annotation needs.
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…