Related papers: Persistent Entropy as a Detector of Phase Transiti…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the…
Time lag between variables is a key characteristics of dynamical systems in different fields and identifying such time lag is an important problem in complex systems with many applications. Transfer Entropy (TE) was proposed as a tool for…
Permutation Entropy (PE) is a powerful tool for quantifying the complexity of a signal which includes measuring the regularity of a time series. Additionally, outside of entropy and information theory, permutations have recently been…
In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy.
Persistent homology is a popular technique in topological data analysis that tracks the lifespans of homological features in a nested sequence of spaces. This data is typically presented in a multi-set called a persistence diagram or a…
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…
Graph based entropy, an index of the diversity of events in their distribution to parts of a co-occurrence graph, is proposed for detecting signs of structural changes in the data that are informative in explaining latent dynamics of…
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…
Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…
Persistent excitation (PE) is a necessary and sufficient condition for uniform exponential parameter convergence in several adaptive, identification, and learning schemes. In this article, we consider, in the context of multi-input linear…
The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is…
Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} $H(P\|Q_1,\dots,Q_m)$, the minimum conditional entropy…
Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant.…
The entanglement entropy can be an effective diagnostic tool for probing topological phase transitions. In one-dimensional single particle systems, the periodic driving generates a variety of topological phases and edge modes. In this work,…