相关论文: Correlation lengths in the language of computable …
Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data…
Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no…
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…
Normalized information distance (NID) uses the theoretical notion of Kolmogorov complexity, which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program.…
While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse…
Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of "phase" based on the standard concept of order…
Normalized information distance (NID) uses the theoretical notion of Kolmogorov complexity, which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program.…
For finite random systems, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
Distance correlation coefficient (DCC) can be used to identify new associations and correlations between multiple variables. The distance correlation coefficient applies to variables of any dimension, can be used to determine smaller sets…
In Science, Reshef et al. (2011) proposed the concept of equitability for measures of dependence between two random variables. To this end, they proposed a novel measure, the maximal information coefficient (MIC). Recently a PNAS paper…
The article investigates the possibility of measuring the strength of a linear correlation relationship between nominal data and numerical data. Correlation coefficients for variables coded with real numbers as well as for variables coded…
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of…
Conceptually, partial information decomposition (PID) is concerned with separating the information contributions several sources hold about a certain target by decomposing the corresponding joint mutual information into contributions such…
We measure and compare three correlation lengths proposed to describe the extent of structural order in amorphous systems. In particular, the recently proposed "patch correlation length" is measured as a function of temperature and…
The estimation of the correlation between time series is often hampered by the asynchronicity of the signals. Cumulating data within a time window suppresses this source of noise but weakens the statistics. We present a method to estimate…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
Recently, it has been claimed that a linear relationship between a measure of information content and word length is expected from word length optimization and it has been shown that this linearity is supported by a strong correlation…
Motivated by a $2$-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are…
Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…