Related papers: Measures of $\e$-complexity
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
We propose a generic numerical measure of inconsistency of a database with respect to a set of integrity constraints. It is based on an abstract repair semantics. A particular inconsistency measure associated to cardinality-repairs is…
The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
We show that the 2-abelian complexity of the infinite Thue-Morse word is 2-regular, and other properties of the 2-abelian complexity, most notably that it is a concatenation of palindromes of increasing length. We also show sharp bounds for…
We define and study a metric independence notion in a homogeneous metric abstract elementary class with perturbations that is $d^p$-superstable (superstable wrt. the perturbation topology), weakly simple and has complete type spaces and we…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The…
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…
We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…
In this study, we investigate quantum nonseparability between an observed system and a measuring apparatus, or multiple measuring apparatuses. We show that the physical meaning of the outcome of the measuring apparatus obtained by weak…
Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter…
In this work, we investigate the H\"older spectrum of typical measures (in the Baire category sense) in a general compact set and we compute the multifractal spectrum of a typical measures supported by a self-similar set. Such mesures…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…
Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity…
We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we…
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…