Related papers: TopoLa: A Universal Framework to Enhance Cell Repr…

The problem of embedding a set of objects into a low-dimensional Euclidean space based on a matrix of pairwise dissimilarities is fundamental in data analysis, machine learning, and statistics. However, the assumptions of many standard…

Unlike other tissue types, like epithelial tissue, which consist of cells with a much more homogeneous structure and function, the nervous tissue spans in a complex multilayer environment whose topographical features display a large…

In common real-world robotic operations, action and state spaces can be vast and sometimes unknown, and observations are often relatively sparse. How do we learn the full topology of action and state spaces when given only few and sparse…

This article revolves around shape and topology optimization, in the applicative context where the objective and constraint functionals depend on the solution to a physical boundary value problem posed on the optimized domain. We introduce…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

We study the topological components of the surface group representations into $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{PSL}(2,\mathbb{R})$. Utilizing the signature formula established in [14], we determine the number of connected components…

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…

Link prediction, as a frontier task in complex network topology analysis, aims to infer the existence of latent links between node pairs based on observed nodes and structural information. We propose an ensemble link prediction model that…

Large language models (LLMs) have demonstrated remarkable performance across various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for LLMs. In this study, we investigate the…

Cellular identity and function are linked to both their intrinsic genomic makeup and extrinsic spatial context within the tissue microenvironment. Spatial transcriptomics (ST) offers an unprecedented opportunity to study this, providing in…

Implicit spatial relations and deep semantic structures encoded in object attributes are crucial for procedural planning in embodied AI systems. However, existing approaches often over rely on the reasoning capabilities of vision language…

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…

The field of face recognition (FR) has undergone significant advancements with the rise of deep learning. Recently, the success of unsupervised learning and graph neural networks has demonstrated the effectiveness of data structure…

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a…

We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a…

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

Topological mapping offers a compact and robust representation for navigation, but progress in the field is hindered by the lack of standardized evaluation metrics, datasets, and protocols. Existing systems are assessed using different…

With the emergence of new photonic and plasmonic materials with optimized properties as well as advanced nanofabrication techniques, nanophotonic devices are now capable of providing solutions to global challenges in energy conversion,…