arXiv research

Improved GPLVM model for single-cell RNA-seq data.

New features from early battery cycles predict lifetime with high accuracy.

We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.

Euler's theorem extended to complex structures.

SRCA reduces high-dimensional data to lower dimensions while preserving geometric structures.

CTEF fits ellipsoids to noisy data in any dimension.

New method learns cell trajectories from multiple snapshots.

Study homology of periodic cell complexes using quotient spaces and spectral sequences.

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 $\int_{\mathcal{\bar{H}}_g^1}κ_{1}ψ^{2g-2}$ 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.

A new method learns manifold-valued latents without an encoder.

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.

The paper introduces a new metric to quantify uncertainty's impact on multiple objectives.

We study Lagrangian embeddings of a class of two-dimensional cell complexes $L_{p,q}$ 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 $\frac{1}{p^2}(pq-1,1)$ (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 article introduces planar ribbons, Vergili ribbon complexes and ribbon nerves in Alexandroff-Hopf-Whitehead CW (Closure finite Weak) topological spaces. A {\em planar ribbon} (briefly, {ribbon}) in a CW space is the closure of a pair of nesting, non-concentric filled cycles that includes the boundary but does not …

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 $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexe…

Deep learning model explains breast cancer subtypes using logistic regression.

Lipid necks, large curvature bridges, are shown to be metastable.

This study reviews and evaluates clustering methods for single-cell RNA-seq data.

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.

New model identifies cell-specific genes for cancer prognosis.

Forest Fire Clustering discovers cell types from single-cell data.

Kernel testing compares cell states in single-cell data.

Topology-enhanced loss improves 3D object reconstruction from 2D images.

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.

New model clusters cells and individuals, revealing genetic influences on cell types.

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.

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.

MarkerMap selects key genes for cell type analysis in single-cell RNA-seq.

SimCD simultaneously clusters cells and identifies differential gene expression in scRNA-seq data.

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.

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.

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.

This work introduces novel methods to identify and compare cycles across topological objects.

Graph Attention Networks predict disease state from single-cell data.