Related papers: Persistent Entropy as a Detector of Phase Transiti…
A key challenge in systems biology is the elucidation of the underlying principles, or fundamental laws, which determine the cellular phenotype. Understanding how these fundamental principles are altered in diseases like cancer is important…
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned…
Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…
Run-and-tumble particles (RTPs) have emerged as a paradigmatic example for studying nonequilibrium phenomena in statistical mechanics. The invariant measure of a wide class of RTPs subjected to a potential possesses a density that is…
This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a…
In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by…
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series or point clouds sampled close to a manifold. Given random…
We introduce the eigen microstate entropy ($S_{\text{EM}}$), a novel metric of complexity derived from the probabilities of statistically independent eigen microstates. After establishing its scaling behavior in equilibrium systems and…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
Observer-based methods are widely used to estimate the disturbances of different dynamic systems. However, a drawback of the conventional disturbance observers is that they all assume persistent excitation (PE) of the systems. As a result,…
There is no doubt that the information hidden in entanglement entropy (EE), for example, the $n$-th order R\'enyi EE, i.e., $S^{A}_n=\frac{1}{1-n}\ln \Tr (\rho_A^n)$ where $\rho_A=\mathrm{Tr}_{\overline{A}}\rho$ is the reduced density…
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
Quantum informatic quantities such as entanglement entropy are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known…
High-order finite volume and discontinuous Galerkin methods are often stabilized by separate nonlinear devices for admissibility, entropy control, and oscillation suppression. This separation hides a simple geometric fact: all three act on…
We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded…