arXiv research

The study identifies all possible vector field structures on specific 2D shapes.

We present a conditional generative model to learn variation in cell and nuclear morphology and the location of subcellular structures from microscopy images. Our model generalizes to a wide range of subcellular localization and allows for a probabilistic interpretation of cell and nuclear morphology and structure loca…

Modeling curvature-sensitive cells in visual cortex with geometric structures.

The study describes a cell structure for multisets in a rectangle.

Generalising a seminal result of Epstein and Penner for cusped hyperbolic manifolds, Cooper and Long showed that each decorated strictly convex projective cusped manifold has a canonical cell decomposition. Penner used the former result to describe a natural cell decomposition of decorated Teichmüller space of puncture…

HSSE framework embeds single-cell RNA-seq data at multiple scales.

In a recurrent setting, conventional approaches to neural architecture search find and fix a general model for all data samples and time steps. We propose a novel algorithm that can dynamically search for the structure of cells in a recurrent neural network model. Based on a combination of recurrent and recursive neura…

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

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.

IH-GAN models cellular structures accurately and improves structural performance.

A new method for state estimation on complex 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.

CT improves neural network performance on cell complex data.

New cell structure on $O(3)/O(1)^3$ derived from injectivity radius computation.

The paper introduces optimal transport kernels for comparing cell complexes.

Cell detection and cell type classification from biomedical images play an important role for high-throughput imaging and various clinical application. While classification of single cell sample can be performed with standard computer vision and machine learning methods, analysis of multi-label samples (region containi…

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…

Study of red blood cells using elastic surface theory.

Modeling curvature-sensitive cells in visual cortex using manifold geometry.

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. …

We show that associating the Euclidean cell decomposition due to Cooper and Long to each point of the moduli space of framed strictly convex real projective structures of finite volume on the once-punctured torus gives this moduli space a natural cell decomposition. The proof makes use of coordinates due to Fock and Go…

Paper introduces signal processing on cell complexes.

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.

Model detects patterns in noisy binary data, explaining neuron activity in terms of cell assemblies.

Understanding cell identity is an important task in many biomedical areas. Expression patterns of specific marker genes have been used to characterize some limited cell types, but exclusive markers are not available for many cell types. A second approach is to use machine learning to discriminate cell types based on th…

New method learns complex cell networks from millions of cells.

Given a standard complex semisimple Poisson Lie group $(G, π_{st})$, generalised double Bruhat cells $G^{u, v}$ and generalised Bruhat cells $O^u$ equipped with naturally defined holomorphic Poisson structures, where u, v are finite sequences of Weyl group elements, were defined and studied by Jiang Hua Lu and the auth…

Develops a new neural spike train decoding framework using topological data.

SMAI framework tests and integrates single-cell data alignability.

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.

New insights into data geometry reveal manifold structure in grid-cell activity.

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.

New method uses patchworking to represent oriented matroids.

We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detection of clusters of data in the presence of structural requirements which we encode as algebraic constraints in a linear program. Our cluste…

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.

Resource is an important constraint when deploying Deep Neural Networks (DNNs) on mobile and edge devices. Existing works commonly adopt the cell-based search approach, which limits the flexibility of network patterns in learned cell structures. Moreover, due to the topology-agnostic nature of existing works, including…

Organic Solar Cells are a promising technology for solving the clean energy crisis in the world. However, generating candidate chemical compounds for solar cells is a time-consuming process requiring thousands of hours of laboratory analysis. For a solar cell, the most important property is the power conversion efficie…

Euler's theorem extended to complex structures.

Selecting the right drugs for the right patients is a primary goal of precision medicine. In this manuscript, we consider the problem of cancer drug selection in a learning-to-rank framework. We have formulated the cancer drug selection problem as to accurately predicting 1). the ranking positions of sensitive drugs an…

ARMA cell simplifies neural autoregressive modeling for time series.

Quantization on even-dimensional compact manifolds using cell decomposition.

Model place cells as spatial embeddings for efficient path planning and cognitive map construction.

Machine learning predicts perovskite formability and classifies crystal structures.