Related papers: Topologically Mapping the Macroeconomy

Topological mapping offers a compact and robust representation for navigation, but progress in the field is hindered by the lack of standardized evaluation metrics, datasets, and protocols. Existing systems are assessed using different…

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Corporate failure resonates widely leaving practitioners searching for understanding of default risk. Managers seek to steer away from trouble, credit providers to avoid risky loans and investors to mitigate losses. Applying Topological…

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…

One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…

In the aftermath of the financial crisis, the growing literature on financial networks has widely documented the predictive power of topological characteristics (e.g. degree centrality measures) to explain the systemic impact or systemic…

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…

Software ecosystems have had a tremendous impact on computing and society, capturing the attention of businesses, researchers, and policy makers alike. Massive ecosystems like the JavaScript node package manager (npm) is evidence of how…

Language models are often evaluated with scalar metrics like accuracy, but such measures fail to capture how models internally represent ambiguity, especially when human annotators disagree. We propose a topological perspective to analyze…

Inspired by Christopher Alexanders conception of the world - space is not lifeless or neutral but a living structure involving far more small things than large ones a topological representation has been previously developed to characterize…

Economic issues, such as inflation, energy costs, taxes, and interest rates, are a constant presence in our daily lives and have been exacerbated by global events such as pandemics, environmental disasters, and wars. A sustained history of…

Entity alignment has always had significant uses within a multitude of diverse scientific fields. In particular, the concept of matching entities across networks has grown in significance in the world of social science as communicative…

The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…

Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage…

In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large…