Related papers: Topological Data Analysis for Particulate Gels
Soft solids and their surface deformations control the response of many natural and artificial systems. Yet, their underlying properties are vigorously debated, particularly for polymer networks. While molecular-scale theories predict no…
Suspensions of attractive particles form space-spanning networks that endow the suspension with solid-like behavior at rest. The microstructure of these colloidal gels depends sensitively on the shear history and on the path followed across…
Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Unlike molecular crystals, soft self-assembled fibres, micelles, vesicles, etc., exhibit a certain order in the arrangement of their constitutive monomers, but also high structural dynamicity and variability. Defects and disordered local…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Mechanical metamaterials are structures designed to exhibit an exotic response, such as topological soft modes at a surface. Here we explore single-material 3D prints of these topological structures by translating a ball-and-spring model…
Based on the thermodynamic perturbation theory (TPT) and the Random phase approximation (RPA), we present a statistical theory of solutions of electrically neutral soft molecules, every of which is modelled as a set of sites that interact…
Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…
Protein-stabilised emulsion gels can be studied in the theoretical framework of colloidal gels, because both protein assemblies and droplets may be considered as soft colloids. These particles differ in their nature, size and softness, and…
We report surface shear rheological measurements on dense insoluble monolayers of micron sized colloidal spheres at the oil/water interface and of the protein $\beta$-lactoglobulin at the air/water surface. As expected, the elastic modulus…
Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image.…
We investigate the spatial correlations of microscopic stresses in soft particulate gels, using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations…
Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field,…
This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex…
Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…