Related papers: Mind the Gap: A Study in Global Development throug…
We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological…
Growth rate of real GDP per capita is represented as a sum of two components -- a monotonically decreasing economic trend and fluctuations related to a specific age population change. The economic trend is modeled by an inverse function of…
Empirical growth analysis has three major problems --- variable selection, parameter heterogeneity and cross-sectional dependence --- which are addressed independently from each other in most studies. The purpose of this study is to propose…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
The brisk progression of the industrial digital innovation, leading to high degree of automation and big data transfer in manufacturing technologies, demands continuous development of appropriate off-line metrology methods to support…
Persistent homology is a method from computational algebraic topology that can be used to study the "shape" of data. We illustrate two filtrations --- the weight rank clique filtration and the Vietoris--Rips (VR) filtration --- that are…
With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
Urban development is shaped by historical, geographical, and economic factors, presenting challenges for planners in understanding urban form. This study models commute flows across multiple U.S. cities, uncovering consistent patterns in…
Demographic transition, characterized by declines in fertility and mortality, is a global phenomenon associated with modernization. While typical patterns of fertility decline are observed in Western countries, their applicability to other…
The Index of Dissimilarity (ID), widely utilized in economic literature as a measure of segregation, is inadequate for cross-country or time series studies due to its failure to account for structural variations across countries' labor…
We address the problem of estimating how different parts of the brain develop and change throughout the lifespan, and how these trajectories are affected by genetic and environmental factors. Estimation of these lifespan trajectories is…
The drastic changes in the global economy, geopolitical conditions, and disruptions such as the COVID-19 pandemic have impacted the cost of living and quality of life. It is important to understand the long-term nature of the cost of living…
We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms…