Related papers: Iteration entropy
Normal approximations for descents and inversions of permutations of the set $\{1,2,...,n\}$ are well known. A number of sequences that occur in practice, such as the human genome and other genomes, contain many repeated elements. Motivated…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the…
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…
Although algorithmic randomness with respect to various non-uniform computable measures is well-studied, little attention has been paid to algorithmic randomness with respect to computable \emph{trivial} measures, where a measure $\mu$ on…
A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…
We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical…
The use of rapidity gaps is proposed as a measure of the spatial pattern of an event. When the event multiplicity is low, the gaps between neighboring particles carry far more information about an event than multiplicity spikes, which may…
For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…
Shannon entropy is widely used to quantify the uncertainty of discrete random variables. But when normalized to the unit interval, as is often done in practice, it no longer conveys the alphabet sizes of the random variables being studied.…
We consider the one-parameter family of interval maps arising from generalized continued fraction expansions known as alpha-continued fractions. For such maps, we perform a numerical study of the behaviour of metric entropy as a function of…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…
A convergent iterative procedure is proposed for the calculation of the relative entropy of entanglement of a given bipartite quantum state. When this state turns out to be non-separable the algorithm provides the corresponding optimal…