The study identifies all possible vector field structures on specific 2D shapes.
problem Optimal discrete gradient vector fields on surfaces with 1-2 critical cells.
method Analysis of discrete vector fields on 2D shapes with minimal critical cells.
result All possible structures of discrete Morse functions on specified shapes.
Generative model predicts cell and nuclear structure from images.
problem Predicting subcellular structures from microscopy images.
method Conditional generative model using autoencoders.
result Photo-realistic cell images generated with probabilistic interpretation.
We extend cell decomposition to moduli space of convex projective structures.
problem Cell decomposition of moduli space of convex projective structures.
method Use Fock and Goncharov's A-coordinates and edge-flipping algorithm. result Holonomy groups are semi-arithmetic in many cases.
Algorithm discovers dynamic cell structures for better neural network performance.
problem Finding optimal neural network architectures for diverse data samples and time steps.
method Combines recurrent and recursive neural networks to dynamically search for customized cell structures.
result Achieves better prediction accuracy compared to existing models.
Modeling curvature-sensitive cells in visual cortex with geometric structures.
problem Understanding the functional architecture of curvature-sensitive cells in the visual cortex.
method Geometric model based on Engel structure and SIM(2) symmetry.
result Identified SIM(2) as the natural symmetry group for curvature-sensitive cells.
The study describes a cell structure for multisets in a rectangle.
problem Understanding the space of multisets in a rectangle.
method Developed a piecewise Euclidean bi-simplicial cell structure.
result Connected to spaces of complex polynomials and permutahedra.
The moduli space of projective structures is tessellated using Euclidean cell decompositions.
problem Tessellating the moduli space of strictly convex projective structures.
method Using Euclidean cell decompositions, coordinates from Fock and Goncharov, and mapping class group actions.
result The moduli space has a natural cell decomposition.
HSSE framework embeds single-cell RNA-seq data at multiple scales.
problem Capturing heterogeneous local structure in single-cell RNA-seq data.
method Hierarchical sheaf spectral embedding (HSSE) framework.
result HSSE achieves competitive or improved performance in single-cell RNA-seq data representation learning.
Improved GPLVM model for single-cell RNA-seq data.
problem Lack of effective scalable models for clustering cell types in large-scale single-cell RNA-seq data.
method Introduces amortized stochastic variational Bayesian GPLVM (BGPLVM) tailored for single-cell RNA-seq.
result Matches the performance of scVI on synthetic and real-world datasets and reveals more interpretable latent structures.
We relate Kostant's theorem on the cohomology of a flag manifold G/B with the geometry of the Bruhat-Poisson structure. We express Kostant's harmonic forms in terms of the moment maps (for the torus action) and the Liouville volume forms for the symplectic structures on the Schubert cells induced by the Bruhat-Poisso…
NESS improves neighbor embedding for smooth cell-state transitions in single-cell data.
problem Challenges in extracting smooth, low-dimensional representations from noisy single-cell data.
method Builds on PCS framework to develop NESS, a stable machine learning approach.
result NESS consistently yields useful biological insights across diverse single-cell datasets.
IH-GAN models cellular structures accurately and improves structural performance.
problem Optimizing variable-density cellular structures with multiscale design challenges.
method Conditional deep generative model (IH-GAN) for property-to-geometry mapping using implicit function parameterization.
result Generates unit cells with high accuracy and improves structural performance.
A new method for state estimation on complex networks.
problem Reconstructing latent dynamics from multivariate time-series on topological cell complexes.
method Topology-aware state space framework derived from stochastic partial differential equations, with state evolution following heat-like topological diffusion.
result The proposed method successfully recovers latent states and topological structures in real-world networks.
For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form η is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells. Obtained manifold share many properties of cells. One of the more important are nullity c…
Proposes CXNs for neural network computations on cell complexes.
problem Performing neural network computations on complex topological spaces.
method Introduces a message passing scheme and a unified encoder-decoder framework for cell complexes.
result Generalizes message passing to cell complexes and provides a cell2vec representation.
CT improves neural network performance on cell complex data.
problem Improving predictive performance of neural networks on complex data.
method Introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes.
result CT achieves state-of-the-art performance on cell complex datasets without complex enhancements.
New cell structure on O(3)/O(1)3 derived from injectivity radius computation.
problem Constructing equivariant cell structures on flag manifolds.
method Injectivity radius computation and Dirichlet-Voronoi domains.
result New S3-equivariant cell structure on O(3)/O(1)3. The paper introduces optimal transport kernels for comparing cell complexes.
problem Lack of machine learning methods for CW complexes.
method Derives explicit expression for Wasserstein distance, extends Fused Gromov-Wasserstein, introduces novel kernels.
result Introduced novel kernels for comparing probability measures on CW complexes.
Local Poisson groupoids over mixed product Poisson structures defined and applied.
problem Defining and studying Poisson structures on groupoids.
method Using a local Lagrangian bisection in a double symplectic groupoid to twist a direct product of Poisson groupoids.
result Proving Gu,u is a Poisson groupoid over Ou. We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by…
Framework detects and classifies multi-label RBC images from microscopic images.
problem Challenges in separating touching or overlapping cells for classification.
method Region proposal model + CNN feature extraction + multi-label prediction networks.
result Framework achieves good performance in automatic cell detection and classification.
Study of red blood cells using elastic surface theory.
problem Understanding the shape of red blood cells.
method Used Helfrich-Canham functional to model red blood cells as elastic surfaces.
result Cassinian ovals, except for the round sphere, do not solve the shape equation.
Modeling curvature-sensitive cells in visual cortex using manifold geometry.
problem Understanding how curvature influences cell function in the visual cortex.
method Developed a 4D manifold with canonical Engel structure to represent orientation, position, curvature, and scale.
result Characterized curvature-sensitive receptive profiles using left-invariant generators of the Engel structure.
In this article we describe cell decompositions of the moduli space of Riemann surfaces and their relationship to a Hurwitz problem. The cells possess natural linear structures and with respect to this they can be described as rational convex polytopes which come equipped with natural integer points and a volume form. …
Double Bruhat cells are shown to be Poisson groupoids over flag varieties.
problem Understanding the structure of double Bruhat cells in Lie groups.
method Analyzing the Poisson structure on double Bruhat cells and their relationship to flag varieties.
result Double Bruhat cells are naturally Poisson groupoids over Bruhat cells in flag varieties.
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.
Enhances solar cell efficiency prediction using deep neural networks.
problem Predicting HOMO values for organic solar cells from limited experimental data.
method Ensemble deep neural network (SINet) using SMILES and InChI molecular representations.
result Significant performance improvement from transfer learning and dual molecular representations.
Paper introduces signal processing on cell complexes.
problem Processing signals on non-Euclidean domains.
method Signal processing on abstract regular cell complexes.
result Hodge Laplacians for cell complexes enable convolutional filters.
AutoShrink optimizes neural architectures by shrinking cell structures.
problem Resource constraints in deploying DNNs on mobile devices.
method Topology-aware node-based Neural Architecture Search (NAS).
result AutoShrink achieves up to 48% parameter reduction and 34% MACs savings.
Deep neural networks encode gene expression profiles into cell identity codes.
problem Limited exclusive markers for many cell types.
method Used deep autoencoders to encode GEPs into a 30-value code.
result Deep autoencoders can accurately reproduce GEPs from CICs.
The paper computes the cellular homology of real flag manifolds.
problem Computing the cellular homology of real flag manifolds.
method Explicit parametrizations of Schubert cells by closed balls (cubes) in R^n, using them to compute the boundary operator.
result Explicit formula for the boundary operator with refined coefficients.
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.
Deep learning model classifies drug effects based on structure and cell responses.
problem Limited ability to classify chemicals based on their modes of action.
method Integrative deep learning architecture combining molecular structures and cell responses.
result Improved classification performance, reducing error by 4.6%.
This survey covers earlier work of the author as well as recent work on Riemann's moduli space, its canonical cell decomposition and compactification, and the related operadic structure of arc complexes.
New method learns complex cell networks from millions of cells.
problem Existing methods fail to scale to large datasets.
method Multi-axis Gaussian graphical models.
result Method scales to millions of cells in minutes.
NAS favors wide and shallow cell structures, leading to fast convergence but not necessarily better generalization.
problem Understanding and improving the architectures generated by NAS algorithms.
method Empirical and theoretical study of existing NAS algorithms (DARTS, ENAS) and their architectures.
result Existing NAS algorithms favor wide and shallow cell structures, leading to fast convergence but not necessarily better generalization.
Develops a new neural spike train decoding framework using topological data.
problem Decoding neural spike trains from head direction and grid cells.
method Combines simplicial complex discovery with deep learning to capture higher-order connectivity.
result Demonstrates effectiveness on head direction and trajectory prediction datasets.
SMAI framework tests and integrates single-cell data alignability.
problem Lack of a rigorous statistical test for alignability and distortion during alignment.
method Spectral manifold alignment and inference (SMAI) framework.
result SMAI outperforms existing methods in alignability testing and integration.
A finite subset S of a closed hyperbolic surface F canonically determines a "centered dual decomposition" of F: a cell structure with vertex set S, geodesic edges, and 2-cells that are unions of the corresponding Delaunay polygons. Unlike a Delaunay polygon, a centered dual 2-cell Q is not determined by its collection …
A new model for complex cells accounts for insensitivity to image shifts.
problem Complex cells' response to image shifts.
method Linear combination of Gaussian derivatives at a single position.
result Maximum response insensitive to small shifts of the image.
New insights into data geometry reveal manifold structure in grid-cell activity.
problem Understanding the roles of different dimensions in data geometry.
method Generalised Hanson-Wright inequality and random function model analysis.
result Persistence diagrams reveal latent homology and manifold structure.
Counting and classifying blood cells is an important diagnostic tool in medicine. Support Vector Machines are increasingly popular and efficient and could replace artificial neural network systems. Here a method to classify blood cells is proposed using SVM. A set of statistics on images are implemented in C++. The MPE…
scICML integrates multi-omics data from single cells using co-clustering.
problem High noise and sparsity in multi-omics data from single cells.
method Information-theoretic co-clustering-based multi-view learning.
result Improves clustering performance and provides biological insights.
New model reconstructs cell differentiation paths from single-cell RNA data.
problem Reconstructing dynamic biological phenomena from noisy, heterogeneous, and sparse single-cell RNA-seq data.
method Developed a generative model using Dirichlet diffusion tree and Markov chain Monte Carlo sampler.
result Recovered latent trajectories from simulated single-cell transcriptomes.
New method uses patchworking to represent oriented matroids.
problem Representing oriented matroids from polyhedral structures.
method Variant of Viro's patchworking, controlled cell merging process.
result Achieved a combinatorial manifestation of patchworking.
The history and proofs of Topological Tverberg Theorem are discussed.
problem Understanding the proofs and properties of Topological Tverberg Theorem.
method Historical overview and detailed cell structure analysis of classifying space.
result Clarification of the cell structure of the classifying space K(Sr,1). The notion of a Bing cell is introduced, and it is used to define invariants, link groups, of 4-manifolds. Bing cells combine some features of both surfaces and 4-dimensional handlebodies, and the link group λ(M) measures certain aspects of the handle structure of a 4-manifold M. This group is a quotient of the fundame…
New method improves clustering accuracy in noisy single-cell data.
problem Challenges in clustering single-cell RNA sequencing data due to noise and variability.
method Latent plug-and-play diffusion framework with input-space steering.
result Improved clustering accuracy on synthetic and real-world single-cell data.