Model predicts ventricular tachyarrhythmias with high accuracy.
problem Predicting ventricular tachyarrhythmias for patient care.
method Multi-task neural network architecture with patient metadata.
result 74.02% prediction accuracy 60 seconds in advance.
MS-FCN improves cardiac left ventricle segmentation accuracy.
problem Accurate segmentation of left ventricle from MRI images.
method Multi-scale fully convolutional network with dense connectivity.
result MS-FCN achieves state-of-the-art Dice scores (0.93 on endocardium, 0.96 on epicardium).
In this paper, we propose a new deep feature selection method based on deep architecture. Our method uses stacked auto-encoders for feature representation in higher-level abstraction. We developed and applied a novel feature learning approach to a specific precision medicine problem, which focuses on assessing and prio…
Background: Cardiac MRI derived biventricular mass and function parameters, such as end-systolic volume (ESV), end-diastolic volume (EDV), ejection fraction (EF), stroke volume (SV), and ventricular mass (VM) are clinically well established. Image segmentation can be challenging and time-consuming, due to the complex a…
GANs improve echo frame generation with labeled patches.
problem Automated echocardiography with limited labels.
method Conditional GAN with patch-based discriminator.
result GAN-enhanced echo frames match given segmentation masks.
LU-Net improves cardiac segmentation accuracy and robustness.
problem Robustness and accuracy of deep learning cardiac segmentation.
method Multi-task end-to-end network designed to improve cardiac segmentation.
result Outperforms current best deep learning solution, reducing outliers and improving clinical indices.
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
Deep learning improves LV segmentation and volume estimation from cardiac MRI.
problem Accurate LV segmentation and volume estimation for cardiac MRI.
method Image preprocessing, U-Net architecture, postprocessing, end-to-end analytics pipeline.
result Improved accuracy in LV segmentation and volume estimation.
Study forecasts aortic pressure with deep learning models.
problem Forecasting noisy, non-stationary aortic pressure.
method Used deep learning models, specifically recurrent neural networks with Legendre Memory Unit, on 25 Hz time series data.
result Recurrent neural networks with Legendre Memory Unit achieved the best performance with an overall forecasting error of 1.8 mmHg.
Ventricular Fibrillation (VF), one of the most dangerous arrhythmias, is responsible for sudden cardiac arrests. Thus, various algorithms have been developed to predict VF from Electrocardiogram (ECG), which is a binary classification problem. In the literature, we find a number of algorithms based on signal processing…
Deep learning models trained on adult cardiac MRI data struggle to accurately segment rare congenital heart diseases.
problem Accuracy of U-Net-based segmentation models trained on adult cardiac MRI data when applied to rare congenital heart diseases like Tetralogy of Fallot.
method Cross-validation with four-fold, evaluation on unseen data from different pathologies.
result Deep learning models overfit to the training data, leading to significant accuracy drops when applied to other pathologies.
The increasing availability of electrocardiogram (ECG) data has motivated the use of data-driven models for automating various clinical tasks based on ECG data. The development of subject-specific models are limited by the cost and difficulty of obtaining sufficient training data for each individual. The alternative of…
Personalized deep learning reduces inappropriate shocks in VA detection.
problem High inappropriate shock rate in traditional VA detection methods.
method Personalized deep learning framework using CNN for real-time VA detection and collaborative inference.
result 6.6% reduction in inappropriate shock rate compared to traditional methods.
Generative adversarial network system improves ECG arrhythmia classification.
problem Improving automatic ECG arrhythmia classification accuracy.
method Generative adversarial network with patient-specific normal beats and generated abnormal beats.
result Superior overall classification performance for SVEB and VEB on MIT-BIH arrhythmia database.
Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.
problem Characterizing left-orderability in HNN extensions of groups.
method Analyzes HNN extensions of torsion-free nilpotent groups and left-orderable groups.
result Constructs examples of non-left-orderable HNN extensions of left-orderable groups.
Linear ODEs are solved by geodesics in hyperbolic geometry.
problem Solving real linear second order ODEs.
method Defined a Riemannian hyperbolic geometry and showed that solutions to ODEs correspond to geodesics in this geometry.
result Local solutions to ODEs correspond to geodesics in a specific hyperbolic geometry.
The paper revisits the σk-Yamabe problem and proves the existence of a conformal metric with constant σ2-scalar curvature.
problem Finding a conformal metric with constant σk-scalar curvature on closed manifolds. method Analyzing the σ2-Yamabe constant and proving its achievability under certain conditions. result The σ2-Yamabe constant is achieved by a conformal metric, solving the σ2-Yamabe problem on manifolds with positive Yamabe constant. In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from $\mathcal …
In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. We also introduce the notion of a Manin triple for left-symmetric algebroids, which is equivalent to a left-symmet…
The paper proves foliations of solutions to the minimal surface equation in exterior domains.
problem Existence and properties of foliations by solutions to the exterior Dirichlet problem for minimal surfaces.
method Analyzes a 1-parameter family of solutions to the minimal surface equation in exterior domains with specific boundary conditions.
result Foliation of the open subset in R^(n+1) by graphs of solutions, with bounds and asymptotic behavior.
The paper examines differentiability of horizons along their generators in Lorentz manifolds.
problem Analyzing the differentiability of horizons along their generators in Lorentz manifolds.
method Using a result that every mathematical horizon locally coincides with a Cauchy horizon, the paper proves conditions for differentiability of horizons.
result Horizons are either continuously differentiable or have differentiability jumping points.
A new matrix concentration inequality for random products of matrices.
problem Understanding the behavior of random matrix products under bounded independent positive semidefinite matrices.
method Developed a non-asymptotic concentration inequality for the product of matrices.
result The inequality provides a bound on the deviation of the matrix product from its expected value.
The paper proves conditions under which solutions to certain PDEs in Lie groups are constant.
problem Conditions for constant solutions to geometric PDEs in Lie groups.
method Analyzes left-invariant PDEs in Lie groups with specific decay conditions on gradients.
result If a solution to a geometric PDE in a Lie group satisfies a gradient decay condition, the solution is constant.
The study shows involutory quandles of certain links are not left-orderable.
problem Determining left-orderability of involutory quandles of links.
method Using a non-left-orderability criterion for involutory quandles of non-split links, the study improved previous results and introduced new families of links.
result The involutory quandles of non-trivial alternating links and certain augmented alternating links are not left-orderable.
Study proves all left-invariant contact structures on 3D Lie groups are tight.
problem Characterizing tightness of left-invariant contact structures on 3D Lie groups.
method Riemannian methods and unique factorization property for Lie groups.
result All left-invariant contact structures on 3D Lie groups are tight.
Proposes a novel anomaly detection method for echocardiogram videos.
problem Anomaly detection in echocardiogram videos.
method Dynamic Variational Trajectory Models (TVAE-C, TVAE-R, TVAE-S) trained on healthy infant echocardiogram videos.
result Superior performance in detecting congenital heart defects and pulmonary hypertension.
This paper studies moduli spaces of statistical structures on Lie groups.
problem Understanding statistical structures on Lie groups.
method Introduced and studied moduli spaces for left-invariant statistical structures on Lie groups.
result Moduli spaces of left-invariant Riemannian metrics are singletons for certain Lie groups.
Study on harmonic spinors on specific Lie groups.
problem Existence of left-invariant harmonic spinors on 3D Lie groups.
method Revised spin Dirac operator formula for left-invariant spinors, identified constraints on Lie algebras, and classified metrics with harmonic spinors.
result Identified conditions and metrics for left-invariant harmonic spinors on 3D Lie groups.
Left orderability proven for certain 3-manifolds with specific foliations.
problem Proving left orderability for specific 3-manifolds with taut foliations.
method Analyzing the fundamental group of a 3-manifold with a co-orientable taut foliation.
result The fundamental group of the 3-manifold is left orderable.
A left order on a magma (e.g., semigroup) is a total order of its elements that is left invariant under the magma operation. A natural topology can be introduced on the set of all left orders of an arbitrary magma. We prove that this topological space is compact. Interesting examples of nonassociative magmas, whose spa…
Study on integrability of geodesic flows on Heisenberg group.
problem Integrability of geodesic flows on Heisenberg group.
method Investigation of two classes of normal geodesic flows associated with left-invariant sub-Riemannian metric.
result Left-left configuration is completely integrable in non-commutative sense, while left-right configuration exhibits non-commutative integrability in dimensions > 5.
Impact of projective curvature tensor in f(R,G), f(R,T) and f(R,Lm)-gravitygr-qc The study characterizes spacetime and modified gravity models using projective curvature tensor.
problem Characterizing spacetime and modified gravity models with projective curvature tensor.
method Analyzing $f\left(R,G
ight)$, $f\left(R,T
ight)$, and $f\left(R,L_{m}
ight)$-gravity models.
result Projectively flat perfect fluid spacetimes represent dark energy era and are locally isometric to Minkowski or de-Sitter spacetimes.
New criterion links circular-orderability to left-orderability.
problem Understanding when circularly-orderable groups are left-orderable.
method Introducing a criterion based on the product of a group with integers.
result Groups are left-orderable if their product with integers is circularly-orderable.
The Jones polynomial VL(t) for an oriented link L is a one-variable Laurent polynomial link invariant discovered by Jones. For any integer n≥3, we show that: (1) the difference of Jones polynomials for two oriented links which are Cn-equivalent is divisible by $\left(t-1\right)^{n}\left(t^{2}+t+1\right…
We call a connected Lie group endowed with a left-invariant Lorentzian flat metric Lorentzian flat Lie group. In this Note, we determine all Lorentzian flat Lie groups admitting a timelike left-invariant Killing vector field. We show that these Lie groups are 2-solvable and unimodular and hence geodesically complete. M…
In this paper, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics, and is based on the moduli space of left-invariant pseudo-Riemannian metrics. A…
For a Lie group G and a vector bundle E we study those actions of the Lie group TG on E for which the action map TG×E→E is a morphism of vector bundles, and call those \emph{affine actions}. We prove that the category VectTGaff(X) of such actions over a fixed G…
Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be cla…
Left-invariant metrics force 2-step nilpotent groups, preserving Kähler-like conditions.
problem Existence of left-invariant pluriclosed Hermitian metrics on Lie groups.
method Analyzing left-invariant metrics on unimodular Lie groups with abelian complex structures.
result Pluriclosed flow preserves Strominger Kähler-like conditions on 2-step nilpotent Lie groups.
The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method, we shall apply it to classify complete left-invariant affine structures on the os…
In this paper we determine the at least 4-dimensional affine reductive homogeneous manifolds for an at most 9-dimensional simple Lie group or an at most 6-dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable …
Compact neural network for ECG classification reduces resource needs.
problem Current reliance on deep learning for ECG analysis requires extensive resources and large datasets.
method Simple ANN architecture with advanced feature engineering.
result Achieved 97.36% accuracy in classifying 4 types of arrhythmias.
Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.
problem Determining the index of symmetry for solvable 3D Lie groups with left-invariant metrics.
method Examined all solvable three-dimensional Lie groups, combined with previous work on unimodular groups.
result Index of symmetry is positive for every solvable 3D Lie algebra with a left-invariant metric, and is never 2.
Study of Hamilton-Jacobi Theory with symmetries and integrability by quadratures.
problem Hamilton-Jacobi equation in systems with symmetries.
method Constructing complete solutions and solving reconstruction equations.
result Explicit expressions for exponential curves in Lie groups, valid for all elements in the Lie algebra.
The paper defines circular orderability for quandles and explores their properties.
problem Understanding the structure of quandles through circular orderings.
method Introduced circular orderability for quandles, showed embedding properties, and provided examples.
result Spaces of circular orderings embed in the space of all orderings, and examples of non-circularly orderable quandles are given.
Left invariant affine structures in a Lie group G are in one-to-one correspondence with left-symmetric algebras over its Lie algebra g=TeG (``over'' means that the commutator [x,y]=xy−yx coincides with the Lie bracket; left-symmetric algebras can be defined as Lie-admissible algebras such that the mult…
In this paper we consider simply connected Lie groups equipped with left invariant Randers metrics which arise from left invariant Riemannian metrics and left invariant vector fields. Then we study the intersection between automorphism and isometry groups of these spaces. Finally it has shown that for any left invarian…
Study shows surgeries on certain knots yield left-orderable 3-manifolds.
problem Integral Dehn surgeries on genus one fibered knots in lens spaces.
method Classification of genus one fibered knots by Baker and analysis of surgeries.
result All integral Dehn surgeries on these knots yield left-orderable 3-manifolds.