Related papers: Annotating Simplices with a Homology Basis and Its…
We are motivated by a tantalizing open question in exact algorithms: can we detect whether an $n$-vertex directed graph $G$ has a Hamiltonian cycle in time significantly less than $2^n$? We present new randomized algorithms that improve…
We present a statistical mechanical theory of the process of annotating an object with terms selected from an ontology. The term selection process is formulated as an ideal lattice gas model, but in a highly structured inhomogeneous field.…
Recently it was shown that, for every fixed k>1, given a finite simply connected simplicial complex X, the kth homotopy group \pi_k(X) can be computed in time polynomial in the number n of simplices of X. We prove that this problem is…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We develop a framework for computing the homology of weighted simplicial complexes with coefficients in a discrete valuation ring. A weighted simplicial complex, $(X,v)$, introduced by Dawson [Cah. Topol. G\'{e}om. Diff\'{e}r. Cat\'{e}g. 31…
Creating linguistic annotations requires more than just a reliable annotation scheme. Annotation can be a complex endeavour potentially involving many people, stages, and tools. This chapter outlines the process of creating end-to-end…
Pathological is crucial to cancer diagnosis. Usually, Pathologists draw their conclusion based on observed cell and tissue structure on histology slides. Rapid development in machine learning, especially deep learning have established…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…
Let $\mathcal{M}_{0,n+1}$ be the moduli space of genus zero Riemann surfaces with $n+1$ marked points. In this paper we compute $H_*^{\Sigma_n}(\mathcal{M}_{0,n+1};\mathbb{F}_p)$ and $H_*^{\Sigma_n}(\mathcal{M}_{0,n+1};\mathbb{F}_p(\pm 1))$…
Annotating datasets for question answering (QA) tasks is very costly, as it requires intensive manual labor and often domain-specific knowledge. Yet strategies for annotating QA datasets in a cost-effective manner are scarce. To provide a…
We study the complexity of a classic problem in computational topology, the homology problem: given a description of some space $X$ and an integer $k$, decide if $X$ contains a $k$-dimensional hole. The setting and statement of the homology…
A set $P = H \cup \{w\}$ of $n+1$ points in general position in the plane is called a wheel set if all points but $w$ are extreme. We show that for the purpose of counting crossing-free geometric graphs on such a set $P$, it suffices to…
As the NLP community increasingly addresses challenges associated with multilingualism, robust annotation tools are essential to handle multilingual datasets efficiently. In this paper, we introduce a code-mixed multilingual text annotation…
Two of the most common tasks in medical imaging are classification and segmentation. Either task requires labeled data annotated by experts, which is scarce and expensive to collect. Annotating data for segmentation is generally considered…
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be…
Given a finitely presented group $G$, Hopf's formula expresses the second integral homology of $G$ in terms of generators and relators. We give an algorithm that exploits Hopf's formula to estimate $H_2(G;k)$, with coefficients in a finite…
We revisit the method of small subgraph conditioning, used to establish that random regular graphs are Hamiltonian a.a.s. We refine this method using new technical machinery for random $d$-regular graphs on $n$ vertices that hold not just…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
The NLP community has long advocated for the construction of multi-annotator datasets to better capture the nuances of language interpretation, subjectivity, and ambiguity. This paper conducts a retrospective study to show how performance…
Annotation Query (AQ) is a program that provides the ability to query many different types of NLP annotations on a text, as well as the original content and structure of the text. The query results may provide new annotations, or they may…