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Ever since Claude Shannon used entropy for his "Mathematical Theory of Communication", entropy has become a buzzword in research circles with scientists applying entropy to describe any phenomena that are reminiscent of disorder. In this…
The fidelity-based smooth min-relative entropy is a distinguishability measure that has appeared in a variety of contexts in prior work on quantum information, including resource theories like thermodynamics and coherence. Here we provide a…
Machine learning applications, especially in the fields of me\-di\-cine and social sciences, are slowly being subjected to increasing scrutiny. Similarly to sample size planning performed in clinical and social studies, lawmakers and…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…
Decision tree ensembles are widely used in critical domains, making robustness and sensitivity analysis essential to their trustworthiness. We study the feature sensitivity problem, which asks whether an ensemble is sensitive to a specified…
Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing…
Surveys are an important research tool, providing unique measurements on subjective experiences such as sentiment and opinions that cannot be measured by other means. However, because survey data is collected from a self-selected group of…
Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…
The computer program "Histropy" is an interactive Python program for the quantification of selected features of two-dimensional (2D) images/patterns (in either JPG/JPEG, PNG, GIF, BMP, or baseline TIF/TIFF formats) using calculations based…
Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…
We present a comprehensive software framework for the finite-size security analysis of quantum random number generation (QRNG) and quantum key distribution (QKD) protocols, based on the Entropy Accumulation Theorem (EAT). Our framework…
In recent years, kernel methods are widespread in tasks of similarity measuring. Specifically, graph kernels are widely used in fields of bioinformatics, chemistry and financial data analysis. However, existing methods, especially entropy…
Systematic generalization remains challenging for current language models, which are known to be both sensitive to semantically similar permutations of the input and to struggle with known concepts presented in novel contexts. Although…
Phenotyping consists in applying algorithms to identify individuals associated with a specific, potentially complex, trait or condition, typically out of a collection of Electronic Health Records (EHRs). Because a lot of the clinical…
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,…
The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…
We introduce RVSNUpy, a new Python package designed to measure spectroscopic redshifts. Based on inverse-variance weighted cross-correlation, RVSNUpy determines the redshifts by comparing observed spectra with various rest-frame template…