Related papers: Some Proofs on Statistical Magnitudes for Continuo…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains.…
We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a…
Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the…
We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of…
In this paper, we present a new multi-scale information content calculation method based on Shannon information (and Shannon entropy). The original method described by Claude E. Shannon and based on the logarithm of the probability of…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…
These notes are a self-contained short proof of the stability of persistence diagrams.
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
The Shannon information-entropy uncertainty (in brief as "information uncertainty") is used to analyze the fragments in the measured 140$A$ MeV $^{40, 48}$Ca + $^{9}$Be and $^{58, 64}$Ni + $^{9}$Be reactions. A scaling phenomenon is found…
We formulate an analytic method to study the discontinuities in superconducting cosmic strings. Equations of discontinuities and conditions of their existence are derived from the intrinsic and extrinsic equations of motion. It is the…
The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be…
Shannon information has, in the past, been applied to quantify the genetic diversity of many natural populations. Here, we apply the Shannon concept to consecutive generations of alleles as they evolve over time. We suppose a genetic system…