Related papers: Quantifying topological features and irregularitie…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…
While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
In topological data analysis, a point cloud data P extracted from a metric space is often analyzed by computing the persistence diagram or barcodes of a sequence of Rips complexes built on $P$ indexed by a scale parameter. Unfortunately,…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they…
Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to…
In data clustering, it is often desirable to find not just a single partition into clusters but a sequence of partitions that describes the data at different scales (or levels of coarseness). A natural problem then is to analyse and compare…
Cell biologists study in parallel the morphology of cells with the regulation mechanisms that modify this morphology. Such studies are complicated by the inherent heterogeneity present in the cell population. It remains difficult to define…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
The area of topology optimization of continuum structures of which is allowed to change in order to improve the performance is now dominated by methods that employ the material distribution concept. The typical methods of the topology…
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…