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Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for…
Researchers in the field of connectomics are working to reconstruct a map of neural connections in the brain in order to understand at a fundamental level how the brain processes information. Constructing this wiring diagram is done by…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
Many works in the recent literature introduce semantic mapping methods that use CNNs (Convolutional Neural Networks) to recognize semantic properties in images. The types of properties (eg.: room size, place category, and objects) and their…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…
We consider the problem of recovering the topology and the edge conductance value, as well as characterizing a set of electrical networks that satisfy the limitedly available Thevenin impedance measurements. The measurements are obtained…
We showcase a topological mapping framework for a challenging indoor warehouse setting. At the most abstract level, the warehouse is represented as a Topological Graph where the nodes of the graph represent a particular warehouse…
Geometric data augmentation is widely used in segmentation workflows, but polygon annotations are often assumed to remain valid after transformation. This assumption can fail in structured domains such as architectural floorplan analysis,…
Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
In dynamical systems reconstruction (DSR) we seek to infer from time series measurements a generative model of the underlying dynamical process. This is a prime objective in any scientific discipline, where we are particularly interested in…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…
In this paper, we present a novel workflow consisting of algebraic algorithms and data structures for fast and topologically accurate conversion of vector data models such as Boundary Representations into voxels (topological voxelization);…
The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…
We develop methods to efficiently reconstruct the topology and line parameters of a power grid from the measurement of nodal variables. We propose two compressed sensing algorithms that minimize the amount of necessary measurement resources…