Related papers: Estimation of Persistence Diagrams via the Three G…
Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…
This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies…
Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
Abrupt transitions ("tipping") in nonlinear dynamical systems are often accompanied by changes in the geometry of the attracting set, but quantifying such changes from partial and noisy observations in high-dimensional systems remains…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
We provide a polynomial time 4/3 approximation algorithm for TSP on metrics arising from the metric completion of cubic 3-edge connected graphs.
Real-world graphs often manifest as a massive temporal stream of edges. The need for real-time analysis of such large graph streams has led to progress on low memory, one-pass streaming graph algorithms. These algorithms were designed for…
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
Discrete-time switched linear systems where switchings are governed by a digraph are considered. The minimum (or average) dwell time that guarantees the asymptotic stability can be computed by calculating the maximum cycle ratio (or maximum…
Symmetry is an implicit objective in structural form-finding that often reconciles efficiency and aesthetics. This paper identifies the symmetry of polyhedral diagrams in three-dimensional graphic statics (3DGS) as point groups and…
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…
Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a…
We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix…