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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 introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in…
We present a validation of the asdf method, an information-theoretic framework for computing thermodynamic entropy from molecular configurations. The method reformulates entropy estimation as the Shannon entropy of a residual mapping…
We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity…
Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy Description which we call the Fundamental Scale. This allowed us to create a novel space to represent music pieces by developing: a) a method to…
The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
Using the AdS/CFT correspondence, we examine entanglement entropy for a boundary theory deformed by a relevant operator and establish two results. The first is that if there is a contribution which is logarithmic in the UV cut-off, then the…
We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
Given an arbitrary measurement over a system of interest, the outcome of a posterior measurement can be used for improving the statistical estimation of the system state after the former measurement. Here, we realize an…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…
The aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: For a fixed probability measure $q^n$ on $\mathcal X^n$, ($\mathcal X$ is a finite set),…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
In the presence of symmetry, entanglement measures of quantum many-body states can be decomposed into contributions arising from distinct symmetry sectors. Here we investigate the decomposability of negativity, a measure of entanglement…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Information theory has provided foundations for the theories of several application areas critical for modern society, including communications, computer storage, and AI. A key aspect of Shannon's 1948 theory is a sharp lower bound on the…