Algorithm discovers dynamic cell structures for better neural network performance.
problem Finding optimal neural network architectures for diverse data samples and time steps.
method Combines recurrent and recursive neural networks to dynamically search for customized cell structures.
result Achieves better prediction accuracy compared to existing models.
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.
TNDE quantifies dynamic gene drivers from single-cell snapshots.
problem Reconstructing time-resolved regulatory effects in biological processes.
method Time-varying Network Driver Estimation (TNDE) using shared graph attention encoder and partial optimal transport.
result TNDE identifies stage-specific driver genes in mouse erythropoiesis.
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.
Until recently, transcriptomics was limited to bulk RNA sequencing, obscuring the underlying expression patterns of individual cells in favor of a global average. Thanks to technological advances, we can now profile gene expression across thousands or millions of individual cells in parallel. This new type of data has …
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.
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.
Dynamic cell-free networks reduce complexity in serving many devices with distributed APs and DRL.
problem Designing efficient cell-free networks with many devices and APs.
method Dynamic architecture, SIC, DAS, DRL for optimization.
result DRL significantly improves performance in dynamic cell-free networks.
New method learns cell trajectories and network interactions from single-cell data.
problem Network inference in systems biology from steady-state data.
method Min-entropy estimation for stochastic dynamics, leveraging both temporal and perturbational data.
result Jointly learns cellular trajectories and network interactions.
Latent variable models have been widely applied for the analysis of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present Variational Inference for Nonlinear Dynamics (VIND), a variational inference framework that is abl…
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.
Enhances forecasting of complex systems using FKMD.
problem Forecasting high-dimensional dynamical systems with unknown features.
method Featurized Koopman Mode Decomposition (FKMD) using delay embedding and learned Mahalanobis distance.
result Improves prediction accuracy for various complex systems.
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 extend cell decomposition to moduli space of convex projective structures.
problem Cell decomposition of moduli space of convex projective structures.
method Use Fock and Goncharov's A-coordinates and edge-flipping algorithm. result Holonomy groups are semi-arithmetic in many cases.
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
A novel circuit motif uses sister cells for inference with correlated priors.
problem Structured priors in neural systems pose architectural challenges.
method Proposes a novel circuit motif using sister cells to implement correlated priors without direct interactions.
result Demonstrates the efficacy of correlated priors for inference in noisy environments.
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.
problem Understanding the functional architecture of curvature-sensitive cells in the visual cortex.
method Geometric model based on Engel structure and SIM(2) symmetry.
result Identified SIM(2) as the natural symmetry group for curvature-sensitive cells.
Mathematical model describes how red blood cells return to equilibrium.
problem How red blood cells regain equilibrium after deformation.
method Gradient flow of the Canham-Helfrich functional, proving global existence and convergence for spheres and axisymmetric tori.
result Global existence and convergence of smooth solutions for spheres and axisymmetric tori under specific energy conditions.
The study describes a cell structure for multisets in a rectangle.
problem Understanding the space of multisets in a rectangle.
method Developed a piecewise Euclidean bi-simplicial cell structure.
result Connected to spaces of complex polynomials and permutahedra.
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 challenge in controlling stochastic systems in which low-probability events can set the system on catastrophic trajectories is to develop a robust ability to respond to such events without significantly compromising the optimality of the baseline control policy. This paper presents CelluDose, a stochastic simulatio…
RIMs improve generalization by specializing modular structures.
problem Improving generalization and robustness to changes in tasks.
method Recurrent Independent Mechanisms (RIMs) architecture with independent dynamics, sparing communication, and selective updates.
result RIMs lead to dramatic improvement in generalization on tasks with varying factors.
Method learns cell interaction rules from individual trajectories.
problem Inferring interaction rules from heterogeneous cellular data.
method WSINDy for second order IPSs, learning individual cell models.
result Efficiently identifies different species and best-fit models for each.
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.
In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked …
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…
Multi-StyleGAN simulates live cell microscopy imagery.
problem Costly and complex live cell experiments.
method Generative adversarial network (GAN) synthesizing multi-domain time-lapse images.
result Captures biophysical factors and time dependencies in cell imagery.
IH-GAN models cellular structures accurately and improves structural performance.
problem Optimizing variable-density cellular structures with multiscale design challenges.
method Conditional deep generative model (IH-GAN) for property-to-geometry mapping using implicit function parameterization.
result Generates unit cells with high accuracy and improves structural performance.
Introduces σ-Cell for improved financial volatility forecasting.
problem Improving volatility forecasting in financial markets.
method Combines GARCH and deep learning, incorporating stochastic layers and time-varying parameters.
result Demonstrates superior forecasting accuracy compared to traditional models.
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.
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.
CT improves neural network performance on cell complex data.
problem Improving predictive performance of neural networks on complex data.
method Introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes.
result CT achieves state-of-the-art performance on cell complex datasets without complex enhancements.
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, expon…
Tree complex linked to polyhedral shapes like associahedra and cyclohedra.
problem Understanding the structure of mapping class groups and complex dynamics.
method Characterizing associahedra and cyclohedra using planar tree embeddings and barycentric subdivision.
result Tree complex is a barycentric subdivision of a polyhedral cell complex made of associahedra and cyclohedra.
New cell structure on O(3)/O(1)3 derived from injectivity radius computation.
problem Constructing equivariant cell structures on flag manifolds.
method Injectivity radius computation and Dirichlet-Voronoi domains.
result New S3-equivariant cell structure on O(3)/O(1)3. The paper introduces optimal transport kernels for comparing cell complexes.
problem Lack of machine learning methods for CW complexes.
method Derives explicit expression for Wasserstein distance, extends Fused Gromov-Wasserstein, introduces novel kernels.
result Introduced novel kernels for comparing probability measures on CW complexes.
Local Poisson groupoids over mixed product Poisson structures defined and applied.
problem Defining and studying Poisson structures on groupoids.
method Using a local Lagrangian bisection in a double symplectic groupoid to twist a direct product of Poisson groupoids.
result Proving Gu,u is a Poisson groupoid over Ou. Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales, which do not comply with the nature of dynamical temporal patterns among sequences…
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…
Framework detects and classifies multi-label RBC images from microscopic images.
problem Challenges in separating touching or overlapping cells for classification.
method Region proposal model + CNN feature extraction + multi-label prediction networks.
result Framework achieves good performance in automatic cell detection and classification.
TrajectoryNet models dynamic cellular trajectories using optimal transport.
problem Modeling continuous and non-linear paths in dynamic processes.
method Continuous normalizing flows linked to dynamic optimal transport.
result TrajectoryNet improves interpolation of cellular distributions.
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…
Study of red blood cells using elastic surface theory.
problem Understanding the shape of red blood cells.
method Used Helfrich-Canham functional to model red blood cells as elastic surfaces.
result Cassinian ovals, except for the round sphere, do not solve the shape equation.
Bayesian model for cancer drug studies maps dose-response curves.
problem Mapping dose-response curves in cancer drug studies.
method Bayesian Tensor Filtering (BTF) with low-dimensional embeddings and structured shrinkage priors.
result BTF outperforms state-of-the-art methods in cancer drug studies.
Modeling curvature-sensitive cells in visual cortex using manifold geometry.
problem Understanding how curvature influences cell function in the visual cortex.
method Developed a 4D manifold with canonical Engel structure to represent orientation, position, curvature, and scale.
result Characterized curvature-sensitive receptive profiles using left-invariant generators of the Engel structure.
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…