Related papers: Tangle analysis of difference topology experiments…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…
Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…
Multispecific antibodies offer transformative therapeutic potential by engaging multiple epitopes simultaneously, yet their efficacy is an emergent property governed by complex molecular architectures. Rational design is often bottlenecked…
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…
Document structure analysis, such as zone segmentation and table recognition, is a complex problem in document processing and is an active area of research. The recent success of deep learning in solving various computer vision and machine…
Alternative splicing creates complex bubbles in splicing graphs where more than two transcript paths compete, challenging methods designed for simple binary events. We present a unified framework that compares paths using distinct exonic…
A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein…
Investigations of molecular bonds between single molecules and molecular complexes by the dynamic force spectroscopy are subject to large fluctuations at nanoscale and possible other aspecific binding, which mask the experimental output.…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in…
To understand the nature of a cell, one needs to understand the structure of its genome. For this purpose, experimental techniques such as Hi-C detecting chromosomal contacts are used to probe the three-dimensional genomic structure. These…
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
This project explores the mathematical study of knots and links in topology, focusing on differentiating between the two-component Unlink and the Hopf Link using a computational tool named LINKAGE. LINKAGE employs the linking number,…
The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here we showcase…
The three dimensional structure of DNA in the nucleus (chromatin) plays an important role in many cellular processes. Recent experimental advances have led to high-throughput methods of capturing information about chromatin conformation on…
Cellular nuclei recognition serves as a fundamental and essential step in the workflow of digital pathology. However, with disparate source organs and staining procedures among histology image clusters, the scanned tiles inherently conform…
Protein structure prediction remains a challenge in the field of computational biology. Traditional protein structure prediction approaches include template-based modelling (say, homology modelling, and threading), and ab initio. A…