Related papers: Signed Barcodes for Multi-Parameter Persistence vi…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition…
We study the combination of two recent coding approaches, in the context of DNA based data storage. Composite DNA alphabets leverage properties of the DNA synthesis and sequencing process. A composite symbol does not represent a single…
The matrix rank and its positive versions are robust for small approximations, i.e. they do not decrease under small perturbations. In contrast, the multipartite tensor rank can collapse for arbitrarily small errors, i.e. there may be a gap…
We present a framework to decompose real multivariate polynomials while preserving invariance and positivity. This framework has been recently introduced for tensor decompositions, in particular for quantum many-body systems. Here we…
Signed network embedding is an approach to learn low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining…
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the minimal size of a decomposition of a code into rank-one…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…
The traditional SegNet architecture commonly encounters significant information loss during the sampling process, which detrimentally affects its accuracy in image semantic segmentation tasks. To counter this challenge, we introduce an…
Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations…
In 2020, Cochoy and Oudot got the necessary and sufficient condition of the block-decomposition of 2-parameter persistence modules $\mathbb{R}^2 \to \textbf{Vec}_{\Bbbk}$. And in 2024, Lebovici, Lerch and Oudot resolve the problem of…
While accurate protein structure predictions are now available for nearly every observed protein sequence, predicted structures lack much of the functional context offered by experimental structure determination. We address this gap with…
As an increasing amount of image and video content will be analyzed by machines, there is demand for a new codec paradigm that is capable of compressing visual input primarily for the purpose of computer vision inference, while secondarily…
We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…
The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
Motivation: The scalable identification of bioactive compounds is essential for contemporary drug discovery. This process faces a key trade-off: structural screening offers scalability but lacks biological context, whereas high-content…
We present a signature scheme based on the Syndrome-Decoding problem in rank metric. It is a construction from multi-party computation (MPC), using a MPC protocol which is a slight improvement of the linearized-polynomial protocol used in…