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Dynamic analyses are a standard approach to analyzing and testing concurrent programs. Such techniques observe program traces and analyze them to infer the presence or absence of bugs. At its core, each analysis maintains a partial order…
Much research has been devoted to optimizing algorithms of the Lempel-Ziv (LZ) 77 family, both in terms of speed and memory requirements. Binary search trees and suffix trees (ST) are data structures that have been often used for this…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
Transcript enumeration methods such as SAGE, MPSS, and sequencing-by-synthesis EST ``digital northern'', are important high-throughput techniques for digital gene expression measurement. As other counting or voting processes, these…
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an important pre-processing step consists of simplifying the input…
We introduce CASC: a new, modern, and header-only C++ library which provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension.…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
This paper addresses the search for a fast and meaningful image segmentation in the context of $k$-means clustering. The proposed method builds on a widely-used local version of Lloyd's algorithm, called Simple Linear Iterative Clustering…
Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix…
The \emph{strong collapse} of a simplicial complex, proposed by Barmak and Minian (\emph{Disc. Comp. Geom. 2012}), is a combinatorial collapse of a complex onto its sub-complex. Recently, it has received attention from computational…
The myriad complex systems with multiway interactions motivate the extension of graph-based pairwise connections to higher-order relations. In particular, the simplicial complex has inspired generalizations of graph neural networks (GNNs)…
We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of…
Nowadays, there is a rapid increase in the number of sensor data generated by a wide variety of sensors and devices. Data semantics facilitate information exchange, adaptability, and interoperability among several sensors and devices.…
\v{C}ech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becomes prohibitively expensive for large-sized data sets…
The simplicity Bias (SB) of neural networks, i.e.\ their tendency to represent simple functions, is a key factor in their generalization capabilities. Recent studies show that an excessive SB may harm performance on complex tasks, and the…
We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Document clustering is an unsupervised approach in which a large collection of documents (corpus) is subdivided into smaller, meaningful, identifiable, and verifiable sub-groups (clusters). Meaningful representation of documents and…
Temporal graphs represent binary relationships that change along time. They can model the dynamism of, for example, social and communication networks. Temporal graphs are defined as sets of contacts that are edges tagged with the temporal…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…