Related papers: (Don't) Mind the Gap
The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been…
To render a sequence testable, namely capable of identifying and detecting errors, it is necessary to apply a transformation that increases its length by introducing statistical dependence among symbols, as commonly exemplified by the…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
Infinite sequences are considered in the framework of classical logic from a new point of view.
In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We…
The complexity of visual stimuli plays an important role in many cognitive phenomena, including attention, engagement, memorability, time perception and aesthetic evaluation. Despite its importance, complexity is poorly understood and…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…