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.
New features from early battery cycles predict lifetime with high accuracy.
problem Accurately predicting battery lifetime under varying conditions is challenging due to manufacturing variability and usage-dependent degradation.
method Extracted features from regularly scheduled reference performance tests and used them to predict battery lifetime using a hierarchical Bayesian regression model.
result Demonstrated a lifetime prediction of in-distribution cells with 15.1% mean absolute percentage error using only the first 15% of data.
We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.
Euler's theorem extended to complex structures.
problem Generalizing Euler's theorem to complex structures.
method Analyzing strongly connected, pure n-dimensional regular CW-complexes. result Evenness of cells is equivalent to generalized cycle decomposition and traversability.
SRCA reduces high-dimensional data to lower dimensions while preserving geometric structures.
problem High-dimensional datasets with underlying geometric structures.
method Spherical Rotation Component Analysis (SRCA) incorporating geometric loss functions.
result SRCA provides a low-rank spherical representation of data with general theoretic guarantees.
CTEF fits ellipsoids to noisy data in any dimension.
problem Fitting ellipsoids to noisy data in arbitrary dimensions.
method Uses the Cayley transform to fit ellipsoids.
result CTEF outperforms other methods, especially when data are not uniformly distributed.
New method learns cell trajectories from multiple snapshots.
problem Inferring cell trajectories from limited, single-time-point data.
method Multi-marginal Schrödinger Bridges with iterative reference refinement.
result Effective in capturing long-term dependencies and learning from multiple time points.
Study homology of periodic cell complexes using quotient spaces and spectral sequences.
problem Quantifying homology in periodic cell complexes.
method Finite representation of periodic cell complexes, Mayer-Vietoris spectral sequence.
result Full recovery of homology generators for d-periodic graphs. 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 …
A closed formula is obtained for the integral ∫Hˉg1κ1ψ2g−2 of tautological classes over the locus of hyperelliptic Weierstraß points in the moduli space of curves. As a corollary, a relation between Hodge integrals is obtained. The calculation utilizes the homeomorphism between the moduli…
Study of Betti numbers in prodsimplicial complexes for directed graphs, focusing on DNA recombination.
problem Analyzing Betti numbers in directed graphs for DNA recombination.
method Custom prodsimplicial complexes for acyclic directed graphs, investigating Betti numbers.
result Investigated Betti numbers and cycles in prodsimplicial complexes for DNA recombination.
A new method learns manifold-valued latents without an encoder.
problem Distorting data with intrinsic non-Euclidean structure.
method Riemannian generative decoder that learns latents directly.
result Learned representations respect the prescribed geometry and capture intrinsic non-Euclidean structure.
Accurately predicting the future capacity and remaining useful life of batteries is necessary to ensure reliable system operation and to minimise maintenance costs. The complex nature of battery degradation has meant that mechanistic modelling of capacity fade has thus far remained intractable; however, with the advent…
DPA preserves data distribution in reduced dimensions.
problem Loss of data distribution in dimension reduction.
method DPA combines encoder and decoder to match data distribution.
result DPA successfully reconstructs data distribution.
The paper introduces a new metric to quantify uncertainty's impact on multiple objectives.
problem Quantifying the impact of uncertainty on multiple objectives in complex systems.
method Proposes the mean multi-objective cost of uncertainty (multi-objective MOCU) to quantify uncertainty.
result Demonstrates the effectiveness of the multi-objective MOCU in real-world applications.
We study Lagrangian embeddings of a class of two-dimensional cell complexes Lp,q into the complex projective plane. These cell complexes, which we call pinwheels, arise naturally in algebraic geometry as vanishing cycles for quotient singularities of type p21(pq−1,1) (Wahl singularities). We show that …
In this paper, we propose a novel application of Generative Adversarial Networks (GAN) to the synthesis of cells imaged by fluorescence microscopy. Compared to natural images, cells tend to have a simpler and more geometric global structure that facilitates image generation. However, the correlation between the spatial…
This article introduces vortex nerve complexes in CW (Closure finite Weak) topological spaces, which first appeared in works by P. Alexandroff, H. Hopf and J.H.C. Whitehead during the 1930s. A vortex nerve is a CW complex containing one or more intersecting path-connected cycles. Each vortex nerve has its own distincti…
This is the first of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a there is dg--PROP action of a version of Sullivan Chord diagrams which acts on the …
Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic l1-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexe…
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.
Deep learning model explains breast cancer subtypes using logistic regression.
problem Clarifying the mechanisms of breast cancer subtypes for better treatment.
method Developed a PWL model that generates custom-made logistic regression for each patient.
result The PWL model reveals genes relevant to cell cycle-related pathways.
Lipid necks, large curvature bridges, are shown to be metastable.
problem Understanding the energetically prohibitive yet ubiquitous lipid necks in cell membranes.
method Geometric triality approach to demonstrate metastability.
result Lipid necks can exist for finite but potentially long times without stabilizing mechanisms.
This study reviews and evaluates clustering methods for single-cell RNA-seq data.
problem Identifying and characterizing novel cell types from single-cell RNA-seq data.
method Review and performance comparison of clustering methods.
result Performance comparison experiments on two datasets.
Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one…
This is the second of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a there is dg--PROP action of a version of Sullivan Chord diagrams which acts on the…
Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.
problem Whether a 2-dimensional CW complex embeds in R4. method Operations preserving embeddability, constructions of non-preserving transformations, study of 4-flat graphs.
result Prove 78 graphs of Heawood family are excluded minors for 4-flat graphs.
New model identifies cell-specific genes for cancer prognosis.
problem No statistical model to integrate multiscale cancer data.
method Bayesian generalized promotion time cure models (GPTCMs).
result Improves cancer prognosis by identifying cell-specific genes.
Forest Fire Clustering discovers cell types from single-cell data.
problem Discovering cell types from large-scale single-cell sequencing data.
method Iterative label propagation and parallelized Monte Carlo simulation.
result Forest Fire Clustering outperforms state-of-the-art methods on diverse benchmarks.
Kernel testing compares cell states in single-cell data.
problem Comparing non-linear cell states in single-cell data.
method Kernel-based testing framework for non-linear distribution comparison.
result Identifies subtle population variations in cell states.
Topology-enhanced loss improves 3D object reconstruction from 2D images.
problem Challenges in reconstructing 3D objects from 2D images, especially capturing shape information.
method Integrates multi-scale topological features into the reconstruction loss using cubical complexes and optimal transport distance.
result Topology-aware loss substantially improves 3D reconstruction quality.
This article introduces proximal cell complexes in a hyperconnected space. Hyperconnectedness encodes how collections of path-connected sub-complexes in a Alexandroff-Hopf-Whitehead CW space are near to or far from each other. Several main results are given, namely, a hyper-connectedness form of CW (Closure Finite Weak…
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.
New model clusters cells and individuals, revealing genetic influences on cell types.
problem Clustering nested data with group-level and observation-level variables.
method Nested Atoms Model (NAM), Bayesian nonparametric approach.
result Identifies clusters of genetically similar individuals with homogeneous cell-type profiles.
Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done toward estimating time-varyin…
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.
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical …
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.
MarkerMap selects key genes for cell type analysis in single-cell RNA-seq.
problem Selecting informative genes from large single-cell RNA-seq datasets is challenging and computationally intensive.
method MarkerMap is a generative model that identifies minimal gene sets explaining cell type variability.
result MarkerMap outperforms existing methods in both supervised and unsupervised marker selection.
SimCD simultaneously clusters cells and identifies differential gene expression in scRNA-seq data.
problem Separate clustering and differential expression analysis for scRNA-seq data leads to suboptimal results.
method Develops SimCD, a unified hierarchical gamma-negative binomial model for simultaneous cell clustering and differential expression analysis.
result SimCD outperforms existing methods in discovering cell clusters and capturing dynamic expression changes.
We present a Bayesian hierarchical multi-view mixture model termed Symphony that simultaneously learns clusters of cells representing cell types and their underlying gene regulatory networks by integrating data from two views: single-cell gene expression data and paired epigenetic data, which is informative of gene-gen…
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.
We give an algorithm to compute the integer cohomology groups of any real partial flag manifold, by computing the incidence coefficients of the Schubert cells. For even flag manifolds we determine the integer cohomology groups, by proving that any torsion class has order 2 (generalizing a result of Ehresmann). We conje…
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.
Single-cell gene expression data provide invaluable resources for systematic characterization of cellular hierarchy in multi-cellular organisms. However, cell lineage reconstruction is still often associated with significant uncertainty due to technological constraints. Such uncertainties have not been taken into accou…
New model generates realistic single-cell gene expression data.
problem Generating realistic single-cell gene expression profiles is challenging.
method scLDM, a latent diffusion model using Diffusion Transformers and linear interpolants.
result Superior performance in generating realistic single-cell gene expression data.
This work introduces novel methods to identify and compare cycles across topological objects.
problem Identifying and comparing topological features, particularly cycles, across different topological objects.
method Two complementary approaches: dendrogram-based merge-tree algorithms and Stratified Gradient Sampling.
result Transformed cycle matching into hierarchical clustering and topological optimization framework.
Graph Attention Networks predict disease state from single-cell data.
problem Predicting disease state from single-cell data.
method Graph Attention Networks (GAT) for learning from both features and graph structures.
result Achieved 92% accuracy in predicting MS from single-cell data.