Related papers: Persistent homology classifies parameter dependenc…

In a previous paper we generalized the parameterization method of Cabr\'{e}, Fontich and De la Llave to center manifolds of discrete dynamical systems. In this paper, we extend this result to several different settings. The natural setting…

The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…

Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…

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,…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic…

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…

In the study of ad hoc sensor networks, clustering plays an important role in energy conservation therefore analyzing the mechanics of such topology can be helpful to make logistic decisions .Using the theory of complex network the…

Finding clusters of well-connected nodes in a graph is an extensively studied problem in graph-based data analysis. Because of its many applications, a large number of distinct graph clustering objective functions and algorithms have…

In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…

Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We…

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…

This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…

Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and…

We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make it into an out-of-the-box clustering algorithm that…

An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…

Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…