Related papers: The Topological Stability Index: A Variance-Based …
In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation $-$or shock. A complementary notion of growing popularity is…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…
Prediction-market price moves are widely treated as informationally equivalent: a price jump is read the same way regardless of whether it reflects durable Bayesian updating, transient liquidity pressure, strategic position adjustment, or…
In this paper we consider estimating the system parameters and designing stable observer for unknown noisy linear time-invariant (LTI) systems. We propose a Support Vector Regression (SVR) based estimator to provide adjustable asymmetric…
In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Monitoring the long term voltage stability of the power grid is necessary to ensure its secure operation. This paper presents a new phasor based methodology that distinguishes between long term voltage stability caused by distribution…
We have characterized a transition of turbulence intensity (TI) scaling for friction Reynolds numbers $Re_{\tau} \sim 10^4$ in the companion papers [Basse, N.T. Scaling of global properties of fluctuating and mean streamwise velocities in…
We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During…
In this paper, we introduce the persistence transformation, a novel methodology in Topological Data Analysis (TDA) for applications in time series data which can be obtained in various areas such as science, politics, economy, healthcare,…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative…
This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…
The Rayleigh-Taylor Instability (RTI) under multi-mode perturbation in compressible flow is probed via the Discrete Boltzmann Modeling (DBM) with tracers. The distribution of tracers provides clear boundaries between light and heavy fluids…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
Let $f_{i},i=1,2$ be continuous bundle random dynamical systems over an ergodic compact metric system $(\Omega,\mathcal{F},\mathbb{P},\vartheta)$. Assume that ${\bf a}=(a_{1},a_{2})\in\mathbb{R}^{2}$ with $a_{1}>0$ and $a_{2}\geq0$, $f_{2}$…
The abundance of modern health data provides many opportunities for the use of machine learning techniques to build better statistical models to improve clinical decision making. Predicting time-to-event distributions, also known as…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and propose topological markers directly measurable from ground state correlation functions. These quantities remain powerful tools in the…