Related papers: The information-theoretic complexity of differenti…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
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…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…
Information-based complexity (IBC) is a well-defined complexity measure of any object given a description in a language and a classifier that identifies those descriptions with the object. Of course, the exact numerical value will vary…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
We recall the definition of the $\epsilon$-distortion complexity of a set defined in \cite{bcc} and the results obtained in this paper for Cantor sets of the interval defined by iterated function systems. We state an analogous definition…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The complexity of round robin method of intraprocedural data flow analysis is measured in number of iterations over the control flow graph. Existing complexity bounds realistically explain the complexity of only Bit-vector frameworks which…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
We study the distributed message-passing model in which a communication network is represented by a graph G=(V,E). Usually, the measure of complexity that is considered in this model is the worst-case complexity, which is the largest number…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
In statistical setting of the pattern recognition problem the number of examples required to approximate an unknown labelling function is linear in the VC dimension of the target learning class. In this work we consider the question whether…