An overview of the applications of deep learning in ophthalmic diagnosis using retinal fundus images is presented. We also review various retinal image datasets that can be used for deep learning purposes. Applications of deep learning for segmentation of optic disk, blood vessels and retinal layer as well as detection…
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Deep learning has been successfully applied to a variety of image classification tasks. There has been keen interest to apply deep learning in the medical domain, particularly specialties that heavily utilize imaging, such as ophthalmology. One issue that may hinder application of deep learning to the medical domain is…
Objective: The advent of Electronic Medical Records (EMR) with large electronic imaging databases along with advances in deep neural networks with machine learning has provided a unique opportunity to achieve milestones in automated image analysis. Optical coherence tomography (OCT) is the most commonly obtained imagin…
In this paper, we seek a clinically-relevant latent code for representing the spectrum of macular disease. Towards this end, we construct retina-VAE, a variational autoencoder-based model that accepts a patient profile vector (pVec) as input. The pVec components include clinical exam findings and demographic informatio…
Diabetes is a globally prevalent disease that can cause visible microvascular complications such as diabetic retinopathy and macular edema in the human eye retina, the images of which are today used for manual disease screening. This labor-intensive task could greatly benefit from automatic detection using deep learnin…
Deep learning predicts AMD progression from longitudinal fundus images.
problem Predicting future stages of age-related macular degeneration (AMD).
method InceptionV3 feature vectors, interval scaling, Recurrent Neural Network.
result 0.878 sensitivity, 0.887 specificity, 0.950 AUC.
Exploiting Epistemic Uncertainty of Anatomy Segmentation for Anomaly Detection in Retinal OCTeess.IV
Diagnosis and treatment guidance are aided by detecting relevant biomarkers in medical images. Although supervised deep learning can perform accurate segmentation of pathological areas, it is limited by requiring a-priori definitions of these regions, large-scale annotations, and a representative patient cohort in the …
Diabetic eye disease is one of the fastest growing causes of preventable blindness. With the advent of anti-VEGF (vascular endothelial growth factor) therapies, it has become increasingly important to detect center-involved diabetic macular edema (ci-DME). However, center-involved diabetic macular edema is diagnosed us…
Proposes a neural network for dynamic risk prediction of AMD using longitudinal fundus images.
problem Dynamic risk prediction for progressive eye disorders like AMD.
method tdCoxSNN, a time-dependent Cox survival neural network integrating CNN.
result Demonstrates commendable predictive performance in AMD and PBC datasets.
ICODEN models survival data with interval-censored times using neural networks and ODEs.
problem Predicting time-to-event outcomes with interval-censored data, especially when models require strong assumptions or cannot handle high-dimensional predictors.
method ICODEN uses ordinary differential equations and deep neural networks to model the hazard function and cumulative hazard without proportional hazards assumption.
result ICODEN achieves satisfactory predictive accuracy across various simulation and real-world applications, handling high-dimensional predictors robustly.
Proves stable degeneration preserves symplectic forms and confirms Kaledin's conjecture.
problem Symplectic singularities and their degenerations.
method Combining volume minimization, deformation theory, and rigidity results.
result Kaledin's conjecture confirmed for symplectic singularities.
We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology. In particular, when the multispindle is a quandle , the degenerate homology of is completely determined by the quandle homology of . For this case (and generally for two term homology of …
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
An n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space . By means of the foca…
Study degenerate Bianchi transformations for pseudo-spherical submanifolds in 5D space.
problem Characterize three-dimensional pseudo-spherical submanifolds with degenerate Bianchi transformations.
method Complete description through holonomically degenerate Bianchi transformations.
result Obtained a complete description of degenerate pseudo-spherical submanifolds.
New stabilization found in planar elasticae with degenerate diffusion.
problem Existence of local minimizers in degenerate -elasticae.
method Analysis of pinned planar -elasticae with degenerate diffusion.
result Uncountably many local minimizers with diverging energy in degenerate regime.
Uniform estimates for Calabi-Yau degenerations proved.
problem Calabi-Yau degenerations of polarised algebraic manifolds.
method Uniform Skoda and -estimates for Kähler potentials.
result Uniform Skoda type estimate and -estimate for Calabi-Yau Kähler potentials proved.
Sharp diameter bounds for Calabi-Yau degenerations proved.
problem Bounding the diameter of Calabi-Yau metrics during degeneration.
method Sharp upper and lower bounds derived for Ricci-flat Kahler metrics.
result Conjecture confirmed by obtaining precise diameter bounds.
Paper solves degenerated circle pattern metric problem in spherical geometry.
problem Existence and rigidity of (degenerated) circle pattern metrics with prescribed total geodesic curvatures.
method Defined prescribed combinatorial Ricci flows and studied their convergence.
result First degenerated result for total geodesic curvatures in spherical background geometry.
Paper studies degenerated circle packings in hyperbolic geometry and finds conditions for their existence.
problem Whether a prescribed total geodesic curvature can be realized by a degenerated circle packing.
method Introduced combinatorial Ricci flow to find the desired degenerated circle packed surface, analogous to Chow-Luo and Takatsu methods.
result Fully characterized sufficient and necessary conditions for the existence of degenerated circle packings and showed their uniqueness.
Proves unique degeneration of log Fano fibration germs.
problem Stable degeneration of log Fano fibration germs.
method Introduced the H-invariant for filtrations over log Fano fibration germs and used a unique quasi-monomial valuation to achieve the degeneration.
result Unique K-polystable special degeneration of log Fano fibration germs.
New insights on solutions to Allen-Cahn equation with degenerate minimal hypersurfaces.
problem Existence and rigidity of solutions to the Allen-Cahn equation.
method Analysis of degenerate minimal hypersurfaces as limit interfaces.
result New observations and examples of solutions to the Allen-Cahn equation.
Degenerate solutions found in 2D H-system bubbles with higher degrees.
problem Existence of degenerate solutions in H-system bubbles with degree ≥ 3.
method Algebraic characterization of degenerate bubbles.
result Degenerate solutions can exist for H-system bubbles with degree ≥ 3.
In this paper we study lightlike surfaces of Minkowski 3- space such that they have degenerate or non-degenerate planar normal sections. We first show that every lightlike surface of Minkowski space has degenerate planar normal sections. Then we study lightlike surfaces with non-degenerate planar normal sections a…
Study metric perturbations to make degenerate harmonic forms non-degenerate.
problem Dealing with degenerate harmonic 1-forms in Riemannian geometry.
method Combining analysis of local expansions with Nash-Moser implicit function theorem.
result Proves deformation to nearby non-degenerate Z/2-harmonic 1-forms.
Study higher rank inner products and their tilings to describe tori degenerations.
problem Understanding metric degenerations of tori.
method Introduce higher rank inner products and their tilings, use to describe degenerations.
result Describe metric degenerations of polarized tori and Hausdorff limits of tilings.
Study real semi-stable degenerations and describe real loci via blow-ups.
problem Describe the homeomorphism type of real loci in degenerations.
method Use real-oriented blow-ups to describe the homeomorphism type of real loci.
result Give more explicit descriptions of real loci as stratified spaces.
The paper studies degenerations of rational maps and their limits as geometrically finite rational maps.
problem Understanding the limits of quasi post-critically finite degenerations of rational maps.
method Constructing limits as geometrically finite rational maps on a tree of Riemann spheres, proving boundedness, and giving convergence criteria.
result Progress towards Thurston's compactness theorem and double limit theorem in complex dynamics.
Improved Morse Index Stability for Sequences of Harmonic Maps from Degenerating Riemann Surfacesmath.DG
Stability of Morse index for harmonic maps on degenerating surfaces analyzed.
problem Analyzing stability of Morse index for harmonic maps on degenerating Riemann surfaces.
method Analysis of second variation of energy, identification of conditions for upper semicontinuity, explicit contribution of geodesics.
result Sharper control of spectrum of Jacobi operator, explicit contribution of geodesic segments to Morse index.
The paper discovers new ways Riemann surfaces can degenerate.
problem Understanding degeneration of infinite-type Riemann surfaces.
method Constructing a concrete example to prove degeneration phenomena.
result Existence of degenerations in Bers boundary of infinite-type surfaces.
Let be a hyperkaehler manifold, and a closed, positive (1,1)-form which is degenerate everywhere on . We associate to a family of complex structures on , called a degenerate twistor family, and parametrized by a complex line. When is a pullback of a Kaehler form under a Lagrangian fibration , a…
A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that the diffeomorphism is conformal (when the condition is fulfilled for weakly degene…
Study small eigenvalues on Kähler manifolds degenerating with induced metrics.
problem Analyzing the asymptotic rates of small eigenvalues on degenerate Kähler manifolds.
method Combining Li's uniform Skoda inequality with Monge-Ampère equations.
result Established exact asymptotic rates for small eigenvalues.
Non-Archimedean balanced metrics and their application to totally degenerate abelian varietiesmath.AG
Non-Archimedean balanced metrics approximate cscK metrics for totally degenerate abelian varieties
problem Non-Archimedean balanced metrics for polarized abelian varieties
method Non-Archimedean analogue of the cscK metric
result Uniform estimate for Calabi-Yau metrics on fibers
New class of singular complex manifolds studied with degenerate theory.
problem Understanding singular complex manifolds.
method Developed degenerate Kodaira-Hodge theory for new class.
result New degenerate theory for singular complex manifolds.
Unique K-polystable degenerations for Fano varieties confirmed.
problem Algebraic uniqueness of Kähler-Ricci flow limits on Fano manifolds.
method Study of optimal degeneration problems via new functionals of real valuations.
result Confirm algebraic uniqueness of Kähler-Ricci flow limits on Fano manifolds.
Study oscillatory integrals with degenerate singular points in multivariable phase functions.
problem Analyzing oscillatory integrals with degenerate singular points in phase functions.
method Using asymptotic expansions and results from one variable, the study examines multivariable phase functions.
result Asymptotic expansions of oscillatory integrals for multivariable phase functions with degenerate singular points.
Study existence of harmonic and Dirac-harmonic maps from degenerating surfaces.
problem Existence of harmonic and Dirac-harmonic maps from degenerating surfaces.
method Using the Sacks and Uhlenbeck scheme, analyze a sequence of maps from degenerating surfaces to non-positive curved manifolds.
result Existence of limiting harmonic and Dirac-harmonic maps under certain conditions.
The paper proves rigidity for warped product spaces with degenerate ends.
problem Proving rigidity for warped product spaces with degenerate ends.
method Analyzing scalar curvature for specific classes of warped product spaces.
result Proves scalar curvature extremality and rigidity for certain degenerate spaces.
We establish Liouville type theorems for degenerate conformally invariant equations.
Proves generic surjectivity of vector bundles via degeneration.
problem Understanding generic surjectivity of vector bundles.
method Uses degeneration argument, Berndtsson's theorem, and Lempert's proof.
result Generalizes previous work on division theorem.
Smooth solutions up to evolving free boundaries for degenerate equations.
problem Degenerate parabolic equations with evolving free boundaries.
method Smooth short-time existence using linear degenerate equations on a fixed domain.
result Smoothness up to the free boundary for the -Laplacian evolution equation and -Gauss curvature flow.
Study on hypersurfaces with minimized distance between rulings.
problem Characterizing singularities and properties of two-ruled hypersurfaces.
method Characterization through striction curves and examination of pseudo-non-degenerate properties.
result Two-ruled hypersurfaces constructed from specific curves are pseudo-non-degenerate.
On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metricmath-ph
We provide a complete list of two- and three-component Poisson structures of hydrodynamic type with degenerate metric, and study their homogeneous deformations. In the non-degenerate case any such deformation is trivial, that is, can be obtained via Miura transformation. We demonstrate that in the degenerate case this …
On the variety of Lie algebras endowed with complex structures: degenerations and deformationsmath.RT
Study Lie algebras with complex structures, focusing on degenerations and deformations.
problem Understanding the space of Lie algebras with complex structures and their transformations.
method Identifying invariants that remain consistent under degenerations and applying to four-dimensional case.
result Found invariants that help in understanding the behavior of Lie algebras under complex structures.
New examples of degenerating metrics on R^4 found.
problem Degenerating Poincaré-Einstein metrics on R^4.
method Riemannian ansatz of Debever and Deimaniański, constructing families.
result Continuous families of metrics with cusps and unexpected degenerations.
The Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifoldsmath.AP
Solves a specific Dirichlet problem on Riemannian manifolds.
problem Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds.
method Derives existence of -solutions under appropriate assumptions.
result Existence of -solutions.
Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and mathematical finance, concerning degenerate diffusion processes. We show that th…