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.
Minimal example found for two finite CW-complexes sharing a common covering.
problem Finding the minimum number of 2-cells in two finite CW-complexes that share a common covering.
method Constructing an almost minimal example with two 2-cells in each complex.
result Minimal example with two 2-cells in each complex.
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.
Proposes CCCVAE for better single-cell clustering with cell-cell communication.
problem Improving single-cell RNA sequencing clustering by incorporating cell-cell communication.
method Integrates cell-cell communication into a variational autoencoder framework.
result Empirical results show CCCVAE outperforms standard VAEs in clustering performance.
We prove that among four-dimensional ideal right-angled hyperbolic polytopes the 24-cell is of minimal volume and of minimal facet number. As a corollary, a dimension bound for ideal right-angled hyperbolic polytopes is obtained.
We construct a new class of maximal acyclic matchings on the Salvetti complex of a locally finite hyperplane arrangement. Using discrete Morse theory, we then obtain an explicit proof of the minimality of the complement. Our construction provides interesting insights also in the well-studied case of finite arrangements…
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.
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.
Hexagonal tilings minimize perimeter with unequal volumes.
problem Finding optimal tessellations with unequal cell volumes.
method Minimizing perimeter functionals for different classes of problems.
result Hexagonal tilings are optimal among partitions with almost equal areas.
Motivated by the work of Salvetti and Settepanella we introduce certain total orderings of the faces of any shellable regular CW-complex (called `shelling-type orderings') that can be used to explicitly construct maximum acyclic matchings of the poset of cells of the given complex. Building on an application of this me…
The paper studies geometric structures of polynomial spaces.
problem Understanding the geometric and combinatorial structures of polynomial spaces.
method Introducing and analyzing finite piecewise Euclidean cell complexes.
result The branched rectangle and annulus complexes are homeomorphic to specific polynomial spaces.
Improved LSTM cell for high-frequency trading forecasts.
problem Precise stock price forecasting with minimal lags.
method Revised long short-term memory (LSTM) cell with optimal gate/state selection.
result Lower forecasting error compared to other recurrent neural networks.
The paper provides convergence bounds for approximating a distribution using point clouds.
problem Approximating a distribution using discrete points with minimal Wasserstein distance.
method Lloyd's algorithm with Power cells, analyzed using gradient descent.
result Explicit upper bounds for the convergence speed of the Lloyd-type algorithm.
Study improves scalability of cell-free massive MIMO networks by optimizing UE-AP association.
problem Optimizing UE-AP association in cell-free massive MIMO networks.
method Deep learning algorithm using Bidirectional Long Short-Term Memory cells and hybrid probabilistic weight updating.
result Enhanced scalability without retraining, robust against pilot contamination.
Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.
problem Creating space-filling shapes without sharp corners.
method Edge bending algorithm to deform polyhedral tilings into soft tilings.
result Soft tilings derived from minimal surfaces can be continuously transformed into one another.
Study minimizes Willmore energy with constraints on surface properties.
problem Minimizing Willmore energy under specific surface properties.
method Adapting Keller-Mondino-Rivière, Bauer-Kuwert, and Ndiaye-Schätzle methods.
result Existence of smooth minimizers for a broad range of constraints.
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.
Cell-based NAS search spaces are redundant and lack novelty.
problem Redundancy and lack of novelty in cell-based neural architecture search.
method Empirical analysis of architectures from popular cell-based search spaces.
result Randomly sampled architectures can match or outperform state-of-the-art results.
Motivated by a simple model for elastic cell membranes, we minimize the Willmore functional among two-dimensional spheres embedded in R^3 with prescribed isoperimetric ratio.
sgdGMF efficiently estimates generalized matrix factorization models for single-cell RNA sequencing data.
problem Challenges in dimensionality reduction for large single-cell RNA sequencing datasets.
method Scalable adaptive stochastic gradient descent algorithm for generalized matrix factorization models.
result sgdGMF outperforms existing methods in scalability and accuracy for large datasets.
We prove that the complement of any affine 2-arrangement in R^d is minimal, that is, it is homotopy equivalent to a cell complex with as many i-cells as its i-th rational Betti number. For the proof, we provide a Lefschetz-type hyperplane theorem for complements of 2-arrangements, and introduce Alexander duality for co…
The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these cells for the complement of a complex hyperplane arrangement defined over real …
Let P be the right-angled dodecahedron or 120-cell in hyperbolic space, and let W be the group generated by reflections across codimension-one faces of P. We prove that if Gamma is a torsion-free subgroup of minimal index in W, then the corresponding hyperbolic manifold H^n/Gamma is determined up to homeomorphism by Ga…
New Morse theory for shapes at distances.
problem Understanding shapes at distances from a reference point.
method Defining Morse functions and using non-smooth analysis, geometric measure theory.
result Homotopy type changes at critical values, with one cell added per critical point.
Suppose that Sn is given a generic Riemannian metric with sectional curvatures which satisfy a suitable pinching condition formulated in terms of complex sectional curvatures. This pinching condition is satisfied by manifolds whose real sectional curvatures Kr(σ) satisfy 1/2<Kr(σ)≤1. Then the number o…
Study reduces complexity and uncertainty in human atrial cell models.
problem Uncertainty in parameter estimates from gating kinetics models.
method Approximate Bayesian computation to re-calibrate models, investigate two approaches: more complete datasets and less complex formulations.
result Less complex model with fewer parameters gives better fit and lower uncertainty.
The study optimizes cell membranes' shapes based on curvature and proves existence of minimizers.
problem Optimizing cell membranes' shapes with respect to curvature.
method Modeling cell membranes as optimal shapes with L2-deficit of mean curvature to spontaneous curvature, and proving lower semi-continuity and existence of minimizers. result Smoothly embedded minimizers and diameter bounds are obtained.
Bayesian modeling predicts hydroxide ion conductivity in polymer membranes.
problem Quantitative relationship between hydrophilic domain size and hydroxide ion conductivity in polymer membranes is unknown.
method Bayesian sparse modeling applied to copolymer composition data.
result Composition-derived features are identified as critical for predicting hydroxide ion conductivity.
Multi-cell cooperative processing with limited backhaul traffic is studied for cellular uplinks. Aiming at reduced backhaul overhead, a sparsity-regularized multi-cell receive-filter design problem is formulated. Both unstructured distributed cooperation as well as clustered cooperation, in which base station groups ar…
The paper proposes a method to infer differentiation trees from RNA velocity data.
problem Reconstructing dynamic cellular processes from sequencing data.
method Defining varifold distances between RNA velocity curves to approximate shortest-path distances in a tree.
result The varifold distance method approximates the shortest-path distance in a tree isomorphic to the target differentiation tree.
Deep neural networks predict B-cell epitopes for SARS-CoV and SARS-CoV-2.
problem Accurate prediction of B-cell epitopes for vaccine design.
method Deep neural network model with regularization techniques and key features analysis.
result Overall accuracy of 82% in predicting COVID-19 cases.
There are various algorithms and methodologies used for automated screening of cervical cancer by segmenting and classifying cervical cancer cells into different categories. This study presents a critical review of different research papers published that integrated AI methods in screening cervical cancer via different…
This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.
problem Hexagonal grid firing patterns in grid cells.
method Learning a distance-preserving position embedding in neural space using a recurrent neural network.
result The conformal isometric embedding of 2D physical space into neural space explains hexagonal grid firing patterns.
Confirms isoperimetric conjectures on R^n and S^n for q ≤ min(5, n+1).
problem Minimizing total perimeter among bubbles enclosing prescribed volume.
method Tandem consideration of R^n and S^n, Möbius geometry, conformal Killing fields.
result Spherical interfaces and connected cells in minimizers, resolving Heppes conjecture.
Bound critical points for minimal Radó functions.
problem Counting interior critical points for minimal Radó functions.
method Bounding critical points in terms of boundary data and domain Euler characteristic.
result Bound the number of interior critical points.
Donor-aware scRNA-seq benchmarks improve classification accuracy in inflammatory bowel disease.
problem Influenza disease classification from scRNA-seq data is prone to donor-level confounding.
method Developed and evaluated three feature representations across two IBD cohorts.
result Compartment-stratified CLR composition and GatedStructuralCFN embeddings outperform linear models in classification accuracy.
Built the smallest non-commensurable hyperbolic 4-manifold.
problem Finding the smallest non-commensurable hyperbolic 4-manifold.
method Gluing copies of a polytope to build the manifold.
result The constructed manifold has twice the minimal volume.
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical properties, e.g. the principal curvature directions dynamics on surfaces or the stress…
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Fr…
A Morse function f on a manifold with corners M allows the characterization of the Morse data for a critical point by the Morse index. In fact, a modified gradient flow allows a proof of the Morse theorems in a manner similar to that of classical Morse theory. It follows that M is homotopy equivalent to a CW-complex wi…
SnapMMD forecasts cell differentiation outcomes from snapshot data.
problem Forecasting cell differentiation outcomes from limited snapshot data.
method SnapMMD learns dynamics by directly fitting the joint distribution of state measurements and observation time with MMD loss, allowing for unknown and state-dependent volatilities.
result SnapMMD delivers accurate forecasts and an R2-style statistic for diagnosing fit.
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behaviour of the surfaces at the big cell boundary,…
The minimal number of critical points is studied for smooth functions on closed manifolds.
problem Determining the minimal number of critical points for smooth functions on closed manifolds.
method Investigates cylindrical ball neighborhoods and exotic critical points, proving the conjecture for certain types of critical points.
result The minimal number of critical points is the same for smooth functions without exotic critical points on closed manifolds of dimension at least 6.
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.
SOCP uses SOM to find groups and local calibration buffers for better regional coverage.
problem Heterogeneous regional coverage gaps in conformal prediction.
method Self-Organizing Map (SOM) for group discovery; local calibration buffers at BMU or fixed grid.
result Reduces regional coverage gaps on 7/8 benchmarks by 7.1%.
The critical catenoid is uniquely determined by certain symmetries of its boundary.
problem Uniqueness of free boundary minimal annuli in a half-ball.
method Symmetry analysis and boundary conditions.
result An embedded free boundary minimal annulus with specific symmetries is congruent to the critical catenoid.
The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching μ on a finite regular CW complex X, Forman introduced a discrete analogue of gradient flows. Although Forman's gradient flow has been proved to be useful in practical computations of homology groups, i…
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.