Deep learning detects glaucoma from raw OCT volumes, outperforming classical methods.
problem Glaucoma diagnosis from OCT measurements using traditional features.
method 3D Convolutional Neural Network (CNN) for unsegmented OCT volumes.
result Deep learning achieved higher accuracy (AUC 0.94) compared to logistic regression (AUC 0.89).
Paper tackles depth estimation and optic disc-cup segmentation from color fundus images.
problem Depth estimation and optic disc-cup segmentation from color fundus images.
method Uses fully convolutional networks for monocular retinal depth estimation and optic disc-cup segmentation.
result Demonstrates improved accuracy in depth estimation and optic disc-cup segmentation.
The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.
problem Generalizing bundle gerbes over groupoids and their properties.
method Developed a functorial correspondence between PB groupoids and bundle gerbes over groupoids.
result Built a correspondence between PB groupoids and bundle gerbes over groupoids, including partial quotients.
Deep learning improves retinal fundus image analysis for eye diseases.
problem Improving accuracy in diagnosing eye diseases using retinal images.
method Review of deep learning models and datasets for retinal image analysis.
result Deep learning enhances detection and classification of eye diseases.
Bayesian U-Net exploits epistemic uncertainty for anomaly detection in retinal OCT images.
problem Anomaly detection in retinal OCT images using weak labels of healthy anatomy.
method Bayesian U-Net trained on weak labels of healthy anatomy, using Monte Carlo dropout for uncertainty estimation, and post-processing to transfer uncertainty to anomaly segmentations.
result Achieved a Dice index of 0.789 in an independent test set of AMD cases.
Researchers shrink U-Net to find limits of retinal vessel segmentation.
problem Improving retinal vessel segmentation with deep learning.
method Modified U-Net with functional blocks, then simplified to extreme conditions.
result U-Net does not degrade until very minimal configurations.
Deep networks reveal colour opponent cells under retinal constraints.
problem Understanding colour vision in deep neural networks.
method Classifying cells in early layers of anatomically constrained convolutional neural networks.
result Emergence of single and double opponent cells in deep networks.
STNMF method uncovers neural circuit components in retinal ganglion cells.
problem Deciphering complex neuronal circuit components in the brain.
method Spike-triggered non-negative matrix factorization (STNMF) method.
result STNMF can detect various properties of upstream bipolar cells and recover synaptic connection strengths.
A central challenge in neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of…
The paper introduces vortex nerve complexes and new Betti numbers in CW spaces.
problem Understanding the structure and properties of CW complexes and their nerves.
method Introducing vortex nerve complexes and defining new Betti numbers for CW complexes.
result New Betti numbers (vortex Bvtex, vortex nerve BvNrv, shape Bsh) are introduced and studied. Automated process links oral health to systemic conditions using machine learning.
problem Correlating oral health with systemic health conditions.
method Intraoral fluorescent biomarker imaging, machine learning segmentation, and clinical examination.
result Machine learning classifier achieved AUC of 0.677, indicating a learned association between disease signatures in images and periodontal disease.
It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely from feedforward processing. We set out to find such codes in the context of one…
Deep neural networks classify T2D from retinal images with high accuracy.
problem Detecting early-stage Type 2 Diabetes from retinal images.
method Employed deep neural networks and multi-target learning to differentiate T2D from healthy individuals.
result Classification performance improved to AUC = 0.758 [±0.003] using images from both eyes. This paper uses Ghrist barcodes to track persistent shapes in video frames.
problem Detecting and tracking persistent shapes in video frames.
method Introduces Ghrist barcodes for persistent Betti numbers derived from vortex nerve complexes in triangulated video frames.
result Persistent Betti numbers of vortex nerves are k+2 for k edges. OTRE uses OT to improve retinal images, outperforming existing methods.
problem Improving quality of non-mydriatic retinal images for accurate diagnoses.
method OT theory for image-to-image translation, regularization by enhancing.
result OTRE outperforms state-of-the-art methods on various retinal image tasks.
Paper proposes a method to enhance low-quality retinal images using optimal transport.
problem Artifacts and imperfections in retinal images lead to diagnostic inaccuracies.
method Leveraging optimal transport theory, an unpaired image-to-image translation scheme is proposed.
result The method improves perceptually and quantitatively the quality of low-quality retinal images.
A new method tracks retinal vessels more accurately than existing methods.
problem Tracking retinal vessels accurately in spherical images.
method Computing cusp-free, crossing-preserving geodesics on spherical positions and orientations.
result Crossing-preserving tracking shows clear advantages over non-crossing-preserving tracking.
Graev's nerve implies invariant Einstein metrics on homogeneous spaces.
problem Existence of invariant Einstein metrics on homogeneous spaces.
method Lie-theoretic definition of Graev's nerve and curvature estimates.
result Detailed description of Graev's work and curvature estimates.
We show that a regular cover of a general topological space provides structure similar to a triangulation. In this general setting we define analogues of simplicial maps and prove their existence and uniqueness up to homotopy. As an application we give simple proofs of sharpened versions of nerve theorems of K. Borsuk …
The Rips complex at scale r is homotopy equivalent to the nerve of a cover of diameter r.
problem Reconstructing spaces using Rips complexes and covers.
method Functorial Dowker-Nerve Diagram, homotopy equivalence, cover of diameter r.
result General framework for reconstructing spaces by Rips complexes.
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
problem Characterize polyhedrally-complete intermediate logics.
method Developed Nerve Criterion to characterize polyhedrally-complete logics combinatorially.
result Nerve Criterion provides a necessary and sufficient condition for polyhedrally-completeness.
Novel approach localizes optic disc and fovea centers efficiently.
problem Localizing optic disc and fovea centers in retinal images.
method Simultaneously process optic disc and fovea, modeling their relative geometry and appearance.
result Improves localization and recognition by incorporating object-object relations.
This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive proximity. A 1-cycle is a closed, connected path with a zero boundary in a simplicial c…
Novel method combines wavelet transform and FCNN for retinal vessel segmentation.
problem Automatic vessel segmentation for retinal vascular diseases.
method Combines multiscale Stationary Wavelet Transform with multiscale FCNN, using rotation operations for data augmentation and prediction.
result Achieved high accuracy and robustness on multiple databases.
Improved retinal vessel segmentation with topology preservation trade-off.
problem Retinal vessel segmentation accuracy and topology preservation trade-off.
method Topology preserving term in the loss function and orientation score guided convolutional module.
result Model achieves higher topological accuracy at the expense of lower overlap metrics.
Deep convolutional neural networks (CNNs) have demonstrated impressive performance on visual object classification tasks. In addition, it is a useful model for predication of neuronal responses recorded in visual system. However, there is still no clear understanding of what CNNs learn in terms of visual neuronal circu…
Synthesizing images of the eye fundus is a challenging task that has been previously approached by formulating complex models of the anatomy of the eye. New images can then be generated by sampling a suitable parameter space. In this work, we propose a method that learns to synthesize eye fundus images directly from da…
This paper defines ribbons and ribbon complexes in CW spaces and analyzes their topological properties.
problem Characterizing and analyzing topological structures in CW spaces.
method Introducing planar ribbons, ribbon complexes, and ribbon nerves in Alexandroff-Hopf-Whitehead CW spaces, and studying their topological properties.
result Characterization of ribbons and ribbon nerves by Betti numbers and homotopy types.
The paper presents algorithms for diagnosing Pathological Myopia and detecting retinal structures.
problem Diagnosing Pathological Myopia and detecting retinal structures in fundus images.
method The approach uses Deep Learning techniques, including transfer learning with Xception and YOLO architecture.
result The method has shown satisfactory results in the Pathologic Myopia Challenge.
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
Unified framework for Morita invariant cohomology of Lie groupoids.
problem Proving Morita invariance of cohomology theories for Lie groupoids.
method Viewing cohomology as sheaves of modules on the nerve of the groupoid and establishing criteria for Morita invariance.
result Established criteria for Morita invariant cohomology theories.
We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a conjecture of Kojima, Mizushima and Tan, we prove that the forgetful map sending …
The boundary of certain hyperbolic groups is like a Menger curve.
problem Characterizing boundaries of hyperbolic Coxeter groups.
method Analyzing the nerve of hyperbolic right-angled Coxeter groups.
result Many triangulations and disks have boundaries homeomorphic to the Menger curve.
Developed algorithms to compute three polynomial invariants of veering triangulations.
problem Computing polynomial invariants of veering triangulations.
method Introduced and used algorithms for taut, veering, and Teichmüller polynomials based on upper and lower tracks of veering triangulations.
result Proved that the lower and upper taut polynomials are equal but the veering polynomials can differ.
The main results of this paper are: (1) If a space X can be embedded as a cellular subspace of Rn then X admits arbitrary fine open coverings whose nerves are homeomorphic to the n-dimensional cube Dn; (2) Every n-dimensional cell-like compactum can be embedded into (2n+1)-dimensional …
In this paper, an ensemble-based method for the screening of diabetic retinopathy (DR) is proposed. This approach is based on features extracted from the output of several retinal image processing algorithms, such as image-level (quality assessment, pre-screening, AM/FM), lesion-specific (microaneurysms, exudates) and …
We give a necessary and sufficient condition for a hyperbolic Coxeter group with planar nerve to have Sierpiński curve as its Gromov boundary.
Existing supervised approaches didn't make use of the low-level features which are actually effective to this task. And another deficiency is that they didn't consider the relation between pixels, which means effective features are not extracted. In this paper, we proposed a novel convolutional neural network which mak…
Model detects patterns in noisy binary data, explaining neuron activity in terms of cell assemblies.
problem Detecting structure in noisy or approximate repeats of patterns in sparse binary data.
method Probabilistic binary latent variable model based on Noisy-OR model, inferring sparse activity in latent variables.
result Model successfully extracts and explains latent structure in spiking neural data.
UOLO detects and segments objects in medical images, achieving state-of-the-art performance.
problem Automatic detection and segmentation of objects in medical images.
method UOLO combines object segmentation and detection using a novel loss function.
result UOLO achieves state-of-the-art performance on optic disc and fovea detection and segmentation from retinal images.
Deep learning predicts diabetic macular edema from fundus photos.
problem Diabetic macular edema diagnosis from fundus photos is inaccurate.
method Trained deep learning model on color fundus photographs.
result Deep learning model has higher sensitivity and PPV than human specialists.
We show that for a differential graded Lie algebra g whose components vanish in degrees below -1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V.Hinich.
Computed BNSR-invariants of Houghton groups, confirming a conjecture.
problem Computing BNSR-invariants of Houghton groups.
method Covering subcomplexes of a CAT(0) cube complex and applying the Nerve Lemma. result Confirmed conjecture about BNSR-invariants of Houghton groups.
The paper bridges diffeological bundle theory with higher topos theory.
problem Comparing Čech cohomology of diffeological spaces with existing notions.
method Using Čech model structure on simplicial presheaves and diffeological spaces as discrete simplicial presheaves.
result Nerve of diffeological principal G-bundles is weak homotopy equivalent to G-principal ∞-bundles. Unified Lie structures in homotopy and isotopy calculus.
problem Compatibility of Lie structures in homotopy and isotopy calculus.
method New technical tool: bracket on total homotopy fibres of collapsing cubes of wedge sums.
result Unified understanding of Lie structures in homotopy and isotopy calculus.
Describes spectral data for singular fibres of a specific Hitchin system.
problem Characterizing singular fibres of the SL(2,C)-Hitchin system. method Using Hecke transformations and analysis of parameter spaces, the paper stratifies and compactifies the singular spaces.
result Large classes of singular fibres are shown to be fibre bundles over Prym varieties.
We classify semi-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to three and the metrics induced on fibres are negative definite. Also, we obtain the classificat…
Ozsváth and Szabó conjectured that knot Floer homology detects fibred links. We will verify this conjecture for closed 3-braids, by classifying fibred closed 3-braids. In particular, given a nontrivial closed 3-braid, either it is fibred, or it differs from a fibred link by a half twist. The proof uses Gabai's method o…