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Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote…
Recent studies have demonstrated advantages of information fusion based on sparsity models for multimodal classification. Among several sparsity models, tree-structured sparsity provides a flexible framework for extraction of…
Data comes in many forms. From a shallow perspective, they can be viewed as being either in structured (e.g., as a relation, as key-value pairs) or unstructured (e.g., text, image) formats. So far, machines have been fairly good at…
We use the "Millennium Simulation" to study the mass function of accreted sub-halos during merger events in the dark halo assembly history. Our study includes three kinds of sub-halo mergers: (1) mergers that happen to the main progenitor…
A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…
We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a…
This article proposes a generic framework to process jointly the spatial and spectral information of hyperspectral images. First, sub-images are extracted. Then each of these sub-images follows two parallel workflows, one dedicated to the…
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under…
In this paper we introduce the horizon visibility graph, a simple extension to the popular horizontal visibility graph representation of a time series, and show that it possesses a rigorous mathematical foundation in computational algebraic…
Cartesian tree matching is a form of generalized pattern matching where a substring of the text matches with the pattern if they share the same Cartesian tree. This form of matching finds application for time series of stock prices and can…
We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
Model merging combines the parameters of multiple neural networks into a single model without additional training. As fine-tuned large language models (LLMs) proliferate, merging offers a computationally efficient alternative to ensembles…
Binary neutron star mergers provide insight into strong-field gravity and the properties of ultra-dense nuclear matter. These events offer the potential to search for signatures of physics beyond the standard model, including dark matter.…
We present a method for hierarchical clustering of data called {\it mutual information clustering} (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects $X,…
The comparison of the CKM mixing angles with the leptonic mixings implied by the recent atmospheric and solar neutrino data exhibits an interesting complementarity. This pattern can be understood in the context of the SU(5) grand…
High-resolution N-body simulations of hierarchical clustering in a wide variety of cosmogonies show that the density profiles of dark matter halos are universal, with low mass halos being denser than their more massive counterparts. This…
In a data warehousing process, mastering the data preparation phase allows substantial gains in terms of time and performance when performing multidimensional analysis or using data mining algorithms. Furthermore, a data warehouse can…
Galaxies are thought to reside inside of large gravitationally bound structures of dark matter, so-called haloes. While the smallest of these haloes host no or only a few stars, the biggest host entire clusters of galaxies. Over cosmic…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…