Related papers: Multiscale Topological Inference for Marked Point …

For multivariate data, dependence beyond pair-wise can be important. This is true, for example, in using functional MRI (fMRI) data to investigate brain functional connectivity. When one has more than a few variables, however, the number of…

In a sequence of multivariate observations or non-Euclidean data objects, such as networks, local dependence is common and could lead to false change-point discoveries. We propose a new way of permutation -- circular block permutation with…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of…

Although topological materials have recently seen tremendous development, their applications have remained elusive. Simultaneously, there exists considerable interest in pushing the limits of topological materials, including the exploration…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…

The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…

The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…

In this paper, we introduce a novel unsupervised, graph-based filter feature selection technique which exploits the power of topologically constrained network representations. We model dependency structures among features using a family of…

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…

Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…

This paper is an introduction to work motivated by the question "can multipartite entanglement be detected by homological algebra?" We introduce cochain complexes associated to multipartite density states whose cohomology detects…

Marked Temporal Point Processes (MTPPs) provide a principled framework for modeling asynchronous event sequences by conditioning on the history of past events. However, most existing MTPP models rely on channel-mixing strategies that encode…

Cyberattacks on enterprise networks exploit complex dependencies among infrastructure, services, and applications, which challenge traditional analysis methods that focus on attack paths or network topology in isolation. In this study, we…

Images of scenes have various objects as well as abundant attributes, and diverse levels of visual categorization are possible. A natural image could be assigned with fine-grained labels that describe major components, coarse-grained labels…

In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…

In contemporary data analysis, it is increasingly common to work with non-stationary complex data sets. These data sets typically extend beyond the classical low-dimensional Euclidean space, making it challenging to detect shifts in their…