Related papers: Simplicial complexes and complex systems
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
This paper lays the foundations of an approach to applying Gromov's ideas on quantitative topology to topological data analysis. We introduce the "contiguity complex", a simplicial complex of maps between simplicial complexes defined in…
What is a complex network? How do we characterize complex networks? Which systems can be studied from a network approach? In this text, we motivate the use of complex networks to study and understand a broad panoply of systems, ranging from…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
We analyze the time series obtained from different dynamical regimes of the logistic map by constructing their equivalent time series (TS) networks, using the visibility algorithm. The regimes analyzed include both periodic and chaotic…
The statistical tools of Complex Network Analysis are of great use to understand salient properties of complex systems, may these be natural or pertaining human engineered infrastructures. One of these that is receiving growing attention…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
Over the past decade network theory has turned out to be a powerful methodology to investigate complex systems of various sorts. Through data analysis, modeling, and simulation quite an unparalleled insight into their structure, function,…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
The study of complex systems has captured widespread attention in recent years, emphasizing the exploration of interactions and emergent properties among system units. Network analysis based on graph theory has emerged as a powerful…
Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different…
Concepts such as energy dependence, random deployment, dynamic topological update, self-organization, varying large number of nodes are among many factors that make WSNs a type of complex system. However, when analyzing WSNs properties…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…
Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…
Topological representations are rapidly becoming a popular way to capture and encode higher-order interactions in complex systems. They have found applications in disciplines as different as cancer genomics, brain function, and…