Related papers: Annotating Simplices with a Homology Basis and Its…
We compute the cohomology ring $H^*(U,\mathbb{Z}/n\mathbb{Z})$ for $U=X\setminus S$ where $X$ is the spectrum of the ring of integers of a number field $K$ and $S$ is a finite set of finite primes. As a consequence, we obtain an efficient…
In this expository paper we present some ideas of algebraic topology (more precisely, of homology theory) in a language accessible to non-specialists in the area. A $1$-cycle in a graph is a set $C$ of edges such that every vertex is…
Described the algebraic structure on the space of homotopy classes of cycles with marked topological flags of disks. This space is a non-commutative monoid, with an Abelian quotient corresponding to the group of singular homologies…
In the recent years, DNA has emerged as a potentially viable storage technology. DNA synthesis, which refers to the task of writing the data into DNA, is perhaps the most costly part of existing storage systems. Accordingly, this high cost…
Annotating images with tags is useful for indexing and retrieving images. However, many available annotation data include missing or inaccurate annotations. In this paper, we propose an image annotation framework which sequentially performs…
We study two optimization problems on simplicial complexes with homology over $\mathbb{Z}_2$, the minimum bounded chain problem: given a $d$-dimensional complex $\mathcal{K}$ embedded in $\mathbb{R}^{d+1}$ and a null-homologous…
We consider Hamilton-Jacobi equations in one space dimension with Hamiltonians of the form $H(p,x,\omega) = G(p) + \beta V(x,\omega)$, where $V(\cdot,\omega)$ is a stationary and ergodic potential of unit amplitude. The homogenization of…
Single individual haplotyping is an NP-hard problem that emerges when attempting to reconstruct an organism's inherited genetic variations using data typically generated by high-throughput DNA sequencing platforms. Genomes of diploid…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
High-quality human annotations are necessary to create effective machine learning systems for social media. Low-quality human annotations indirectly contribute to the creation of inaccurate or biased learning systems. We show that human…
For all integers $k$ with $k\geq 2$, if $G$ is a balanced $k$-partite graph on $n\geq 3$ vertices with minimum degree at least \[…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…
Manually annotating object segmentation masks is very time-consuming. While interactive segmentation methods offer a more efficient alternative, they become unaffordable at a large scale because the cost grows linearly with the number of…
Human-annotated labels and explanations are critical for training explainable NLP models. However, unlike human-annotated labels whose quality is easier to calibrate (e.g., with a majority vote), human-crafted free-form explanations can be…
The HuggingFace Datasets Hub hosts thousands of datasets, offering exciting opportunities for language model training and evaluation. However, datasets for a specific task type often have different schemas, making harmonization challenging.…
State-of-the-art question answering (QA) relies upon large amounts of training data for which labeling is time consuming and thus expensive. For this reason, customizing QA systems is challenging. As a remedy, we propose a novel framework…
An algorithm, based on the OPP reduction method, to automatically compute any one-loop amplitude, for all momentum, color and helicity configurations of the external particles, is presented. It has been implemented using the tree-order…
We derive improved upper bounds on the number of crossing-free straight-edge spanning cycles (also known as Hamiltonian tours and simple polygonizations) that can be embedded over any specific set of $N$ points in the plane. More…
Let $s$ denote a distinguished source vertex of a non-negatively real weighted and undirected graph $G$ with $n$ vertices and $m$ edges. In this paper we present two efficient \emph{single-source approximate-distance sensitivity oracles},…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…