Related papers: TopoLa: A Universal Framework to Enhance Cell Repr…
Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…
Transistor topology optimization is a critical step in standard cell design, directly dictating diffusion sharing efficiency and downstream routability. However, identifying optimal topologies remains a persistent bottleneck, as…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…
Understanding how cellular morphology, gene expression, and spatial context jointly shape tissue function is a central challenge in biology. Image-based spatial transcriptomics technologies now provide high-resolution measurements of cell…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
Accurately modeling multi-class cell topology is crucial in digital pathology, as it provides critical insights into tissue structure and pathology. The synthetic generation of cell topology enables realistic simulations of complex tissue…
Understanding how the brain represents and processes information is crucial for advancing neuroscience and artificial intelligence. Representational similarity analysis (RSA) has been instrumental in characterizing neural representations,…
We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how…
Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…
Mobile robots require comprehensive scene understanding to operate effectively in diverse environments, enriched with contextual information such as layouts, objects, and their relationships. Although advances like neural radiation fields…
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…
Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…
Surgical Scene Graphs abstract the complexity of surgical operating rooms (OR) into a structure of entities and their relations, but existing paradigms suffer from strictly dyadic structural limitations. Frameworks that predominantly rely…
Spatial transcriptomics clustering is pivotal for identifying cell subpopulations by leveraging spatial location information. While recent graph-based methods modeling cell-cell interactions have improved clustering accuracy, they remain…
Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…
Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered…