Related papers: Low Algorithmic Complexity Entropy-deceiving Graph…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
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…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…
The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…
Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Graphs can be used to describe complex systems. Recently, whole graph embedding (graph representation learning) can compress a graph into a compact lower-dimension vector while preserving intrinsic properties, earning much attention.…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct…
Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a…
Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for…
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to…