Proposes a model for identifying 4G cells with network throughput problems.
problem Challenges in identifying 4G cells with network throughput issues due to network complexity and privacy concerns.
method Data-driven model using clustering and Deep Neural Networks (DNNs). Model parameters are learned from a small number of expert-labeled data. Multiple clustering models capture common features for problematic cells.
result The proposed model outperforms a simple classifier in identifying cells with network throughput problems.
We construct a relation among right-handed Dehn twists in the mapping class group of a compact oriented surface of genus g with 4g+4 boundary components. This relation gives an explicit topological description of 4g+4 disjoint (-1)-sections of a hyperelliptic Lefschetz fibration of genus g on the manifold {CP}^2#(4g+5)…
Let Σg(g>1) be a closed surface embedded in S3. If a group G can acts on the pair (S3,Σg), then we call such a group action on Σg extendable over S3. In this paper we show that the maximum order of extendable cyclic group actions is 4g+4 when g is even and 4g−4 when g is odd; the maximum ord…
Let Sg be a closed orientable surface of genus g≥2 and C a simple closed nonseparating curve in F. Let tC denote a left handed Dehn twist about C. A \textit{fractional power} of tC of \textit{exponent} $\fraction{\ell}{n}$ is an $h \in \Mod(S_g)$ such that hn=tCℓ. Unlike a root of a $t…
Let Mod_g be the mapping class group of a genus g >= 2 surface. The group Mod_g has virtual cohomological dimension 4g-5. In this note we use a theorem of Broaddus and the combinatorics of chord diagrams to prove that H^{4g-5}(Mod_g; Q) = 0.
We obtain the exact values of the systoles of these hyperbolic surfaces of genus g with cyclic symmetries of the maximum order and the next maximum order. Precisely: for genus g hyperbolic surface with order 4g+2 cyclic symmetry, the systole is 2arccosh(1+cos2g+1π+cos2g+12π) when $…
We study the twisted Alexander polynomial ΔK,ρ of a knot K associated to a non-abelian representation ρ of the knot group into $SL_2(\BC)$. It is known for every knot K that if K is fibered, then for every non-abelian representation, ΔK,ρ is monic and has degree 4g(K)−2 where g(K) is the genus of …
The paper explores methods to decompose periodic maps into Dehn twists.
problem Factoring periodic maps into Dehn twists.
method Various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy.
result Existence of conjugates of periodic maps whose product is pseudo-Anosov.
Kulkarni showed that, if g is greater than 3, a periodic map on an oriented surface S_g of genus g with order more than or equal to 4g is uniquely determined by its order, up to conjugation and power. In this paper, we show that, if g is greater than 30, the same phenomenon happens for periodic maps on the surfaces wit…
We show that, if g is more than or equal to 2, the virtual cohomological dimension of the mapping class group of a 3-dimensional handlebody of genus g is equal to 4g-5 and the Euler number of it is equal to 0.
We generalize the classical Szpiro inequality to the case of a semistable family of hyperelliptic curves. We show that for a semistable symplectic Lefschetz fibration of hyperelliptic curves of genus g, the number N of non-separating vanishing cycles and the number D of singular fibers satisfy the inequality $N \…
Using work of Ozsvath and Szabo, we show that if a nontrivial knot in S^3 admits a lens space surgery with slope p, then p <= 4g+3, where g is the genus of the knot. This is a close approximation to a bound conjectured by Goda and Teragaito.
A specific set of 4g+1 elements is shown to generate the Goeritz group of the genus g+1 Heegaard splitting of a genus g handlebody. These generators are consistent with Powell's proposed generating set for the Goeritz group of the genus g+1 splitting of S^3. There are two proofs: one using purely classical techniques a…
Let Sg be the closed oriented surface of genus g and let Mod±(Sg) be the extended mapping class group of Sg. When the genus is at least 5, we prove that Mod±(Sg) can be generated by two torsion elements. One of these generators is an order 2 element, and the other one is an order 4g+…
Improved lower bounds for faithful linear representations of mapping class groups.
problem Finding the minimum dimension of faithful linear representations of mapping class groups.
method Using finer study of commutation relations and specific pants decompositions to show representations must kill certain subgroups.
result Established lower bounds of 4g−3 for faithful representations of mapping class groups of genus g≥7. 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.
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…
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.
Classifies lattices from knot surgeries, defining a concordance invariant.
problem Classifying lattices from knot surgeries.
method Classifies lattices as the intersection form of a four manifold with boundary.
result Defines a concordance invariant and generalizes a theorem on lens space surgeries.
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.
Matching cells over time has long been the most difficult step in cell tracking. In this paper, we approach this problem by recasting it as a classification problem. We construct a feature set for each cell, and compute a feature difference vector between a cell in the current frame and a cell in a previous frame. Then…
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.
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.
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.
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.
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.
In recent years, the advances in single-cell RNA-seq techniques have enabled us to perform large-scale transcriptomic profiling at single-cell resolution in a high-throughput manner. Unsupervised learning such as data clustering has become the central component to identify and characterize novel cell types and gene exp…
New metric scores perturbations across populations, not cells, improving model comparison.
problem Single-cell perturbation data overlaps, making per-cell accuracy unreliable.
method Average per-cell probability vectors over all cells of a perturbation to form a population profile and rank candidate perturbations.
result Classifier Discrimination Score (CDS) identifies true perturbation more reliably than pseudobulk-based scores.
Cataloging the neuronal cell types that comprise circuitry of individual brain regions is a major goal of modern neuroscience and the BRAIN initiative. Single-cell RNA sequencing can now be used to measure the gene expression profiles of individual neurons and to categorize neurons based on their gene expression profil…
The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene expression patterns cannot explain the development of the precise geometry of an organism and its parts in space. Here, we suggest a set of …
Hippocampal dentate granule cells are among the few neuronal cell types generated throughout adult life in mammals. In the normal brain, new granule cells are generated from progenitors in the subgranular zone and integrate in a typical fashion. During the development of epilepsy, granule cell integration is profoundly…
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.
We establish that, for every hyperbolic orbifold of type (2, q, ∞) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a …
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.
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.
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…
Teichmüller space and hyperelliptic surfaces parametrized by angles.
problem Parametrizing Teichmüller space and hyperelliptic surfaces using angles.
method Proved parametrization using 6g-5 and 4g-2 angle parameters for Teichmüller space and hyperelliptic surfaces respectively.
result Proved parametrization of Teichmüller space and hyperelliptic surfaces by angle parameters.
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.
The study examines exceptional surgeries on hyperbolic fibered knots and their properties.
problem Understanding the bounds and characterizing slopes of surgeries on hyperbolic fibered knots.
method Analyzes the monodromy of knots and their surgeries, using properties of fibered knots and Seifert fibered spaces.
result Proves bounds on slopes of surgeries and characterizes certain knots.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
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.
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…
In a lens space X of order r a knot K representing an element of the fundamental group pi_1 X = Z/rZ of order s <= r contains a connected orientable surface S properly embedded in its exterior X-N(K) such that the boundary of S intersects the meridian of K minimally s times. Assume S has just one boundary component. Le…
Two simple homotopy equivalent 2-complexes K2 and L2 are related by an algebraic criterion of their corresponding presentations as stated in [HoMeSier]. Frank Quinn set it into a topological context (see [Qu1]) and call these 2-complexes related by an s-move. Using elementary 3-expansions, K2 extends to 3-cells in K3 r…
We construct a small regular cellular decomposition of the Fulton MacPherson operad FM2 that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti operad. We compute the generating functions counting the cells, that are algebrai…
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. Despite fluorescent cell-labelling being widely employed in biomedical studies, some of its drawbacks are inevitable, with unsuitable fluorescent probes or probes inducing a functional change being the main limitations. Consequently, the demand for and development of label-free methodologies to classify cells is strong…
The moduli space of Riemann surfaces with at least two punctures can be decomposed into a cell complex by using a particular family of ribbon graphs called Nakamura graphs. We distinguish the moduli space with all punctures labelled from that with a single labelled puncture. In both cases, we describe a cell decomposit…