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Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
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…
Topological data analysis (TDA) is an expanding field that leverages principles and tools from algebraic topology to quantify structural features of data sets or transform them into more manageable forms. As its theoretical foundations have…
This paper investigates how Transformer language models (LMs) fine-tuned for acceptability classification capture linguistic features. Our approach uses the best practices of topological data analysis (TDA) in NLP: we construct directed…
We present an investigation of the applicability of topological data analysis (TDA) to the study of high-resolution confocal microscopy images of fibrin network structures from patients with oesophageal cancer undergoing intended curative…
Microscopic examination of slides prepared from tissue samples is the primary tool for detecting and classifying cancerous lesions, a process that is time-consuming and requires the expertise of experienced pathologists. Recent advances in…
Many models have been proposed for vision and language tasks, especially the image-text retrieval task. All state-of-the-art (SOTA) models in this challenge contained hundreds of millions of parameters. They also were pretrained on a large…
Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and…
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…
Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…
This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been…
Retrieval-Augmented Generation (RAG) enhances the reasoning ability of Large Language Models (LLMs) by dynamically integrating external knowledge, thereby mitigating hallucinations and strengthening contextual grounding for structured data…
We develop novel hierarchical reciprocal graphical models to infer gene networks from heterogeneous data. In the case of data that can be naturally divided into known groups, we propose to connect graphs by introducing a hierarchical prior…
Accurate bone strength prediction is essential for assessing fracture risk, particularly in aging populations and individuals with osteoporosis. Bone imaging has evolved from X-rays and DXA to clinical computed tomography (CT), and now to…
Modern phylogenetics research is often performed within a Bayesian framework, using sampling algorithms such as Markov chain Monte Carlo (MCMC) to approximate the posterior distribution. These algorithms require careful evaluation of the…
Detecting structural instability and anomalies in high-dimensional financial time series is challenging due to complex temporal dependence and evolving cross-sectional structure. We propose ReGEN-TAD, an interpretable generative framework…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed…
Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of…