Related papers: Information topology identifies emergent model cla…

Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…

This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…

The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…

A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…

Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…

Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…

Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…

This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…

Humans communicate using systems of interconnected stimuli or concepts -- from language and music to literature and science -- yet it remains unclear how, if at all, the structure of these networks supports the communication of information.…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…