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We shall prove that the celebrated R\'enyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the $Z$-entropies. Each of them, under suitable hypotheses, generalizes the celebrated…
We present a very simple method for the calculation of Shannon, Fisher, Onicescu and Tsallis entropies in atoms, as well as SDL and LMC complexity measures, as functions of the atomic number Z. Fractional occupation probabilities of…
A well-known fact in the field of lossless text compression is that high-order entropy is a weak model when the input contains long repetitions. Motivated by this, decades of research have generated myriads of so-called dictionary…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
We share a small connection between information theory, algebra, and topology - namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
Domains like bioinformatics, version control systems, collaborative editing systems (wiki), and others, are producing huge data collections that are very repetitive. That is, there are few differences between the elements of the collection.…
Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
A combinatorial theory of associative $n$-categories has recently been proposed, with strictly associative and unital composition in all dimensions, and the weak structure arising as a combinatorial notion of homotopy with a natural…
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing…
In the algorithmic (Kolmogorov) view, agents are programs that track and compress sensory streams using generative programs. We propose a framework where the relevant structural prior is simplicity (Solomonoff) understood as…
Symbolic Extension Entropy Theorem (SEET) describes the possibility of a lossless digitalization of a dynamical system by extending it to a subshift. It gives an estimate on the entropy of symbolic extensions (and the necessary number of…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Document classification is the detection specific content of interest in text documents. In contrast to the data-driven machine learning classifiers, knowledge-based classifiers can be constructed based on domain specific knowledge, which…
Grammar compression is a general compression framework in which a string $T$ of length $N$ is represented as a context-free grammar of size $n$ whose language contains only $T$. In this paper, we focus on studying the limitations of…
Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML…