13 citations · 24 across the 13 of their papers we have counts for
14 papers
A Persistent Homology Signature of Knotting
Aurelie Jodelle Kemme, Collins A. Agyingi, Colleen Farrelly +1
We ask whether knotting can be recognised using persistent homology. Starting from a point-cloud representation of a curve, we compute one-dimensional persistent homology, extract…
Topologically Directed Simulations Reveal the Impact of Geometric Constraints on Knotted Proteins
Agnese Barbensi, Alexander R. Klotz, Dimos Gkountaroulis
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological…
An exploration of low crossing and chiral cosmetic bands with grid diagrams
Agnese Barbensi, Daniele Celoria, Christopher Ktenidis +3
We computationally explore non-coherent band attachments between low crossing number knots, using grid diagrams. We significantly improve the current H(2)-distance table. In partic…
Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework
Stephen Y Zhang, Fangfei Lan, Youjia Zhou +4
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however,…
Topological Optimal Transport for Geometric Cycle Matching
Stephen Y Zhang, Michael P H Stumpf, Tom Needham +1
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant t…
Knot intensity distribution: a local measure of entanglement
Agnese Barbensi, Daniele Celoria
The problem of finding robust and effective methods for locating entanglement in embedded curves is relevant to both applications and theoretical investigations. Rather than focusi…
Hypergraphs for multiscale cycles in structured data
Agnese Barbensi, Iris H. R. Yoon, Christian Degnbol Madsen +3
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of man…
GridPyM: a Python module to handle grid diagrams
Agnese Barbensi, Daniele Celoria
Grid diagrams are a combinatorial version of classical link diagrams, widely used in theoretical, computational and applied knot theory. Motivated by questions from (bio)-physical…
Homology of homologous knotted proteins
Katherine Benjamin, Lamisah Mukta, Gabriel Moryoussef +4
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systema…
A topological selection of folding pathways from native states of knotted proteins
Agnese Barbensi, Naya Yerolemou, Oliver Vipond +3
Understanding the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geomet…
Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology
Agnese Barbensi, Daniele Celoria, Heather A. Harrington +2
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether…
-distance of knotoids and protein structure
Agnese Barbensi, Dimos Goundaroulis
Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of…
Double branched covers of knotoids
Agnese Barbensi, Dorothy Buck, Heather A. Harrington +1
By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in the 2-sphere, up to orientation reversion and rotation, and knots with a…
The Reidemeister graph is a complete knot invariant
Agnese Barbensi, Daniele Celoria
We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and pro…