Related papers: Entropy and Long range correlations in literary En…
We discuss further our proposed modification of the Susskind-Horowitz-Polchinski scenario in which black hole entropy goes over to string entropy as one scales the string length scale up and the string coupling constant down, keeping…
Sentence is a basic linguistic unit, however, little is known about how information content is distributed across different positions of a sentence. Based on authentic language data of English, the present study calculated the entropy and…
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…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
Interest in the mathematical structure of poetry dates back to at least the 19th century: after retiring from his mathematics position, J. J. Sylvester wrote a book on prosody called $\textit{The Laws of Verse}$. Today there is interest in…
Understanding the complexity of human language requires an appropriate analysis of the statistical distribution of words in texts. We consider the information retrieval problem of detecting and ranking the relevant words of a text by means…
We analyze emotionally annotated massive data from IRC (Internet Relay Chat) and model the dialogues between its participants by assuming that the driving force for the discussion is the entropy growth of emotional probability distribution.…
This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
We describe general approach to classification of character sequences (texts, DNA) using relative entropy estimated by off-the-shelf compression and Markov Chains and find them precise enough. We also notice that the method for estimating…
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…
We study some properties of binary sequences generated by random substitutions of constant length. Specifically, assuming the alphabet $\{0,1\}$, we consider the following asymmetric substitution rule of length $k$: $0 \to \langle 0, 0,…
A language L over a finite alphabet is growth-sensitive (or entropy sensitive) if forbidding any set of subwords F yields a sub-language L^F whose exponential growth rate (entropy) is smaller than that of L. Let (X, E, l) be an infinite,…
The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is known as the residual entropy in studies of ice-type models on graphs. The spanning tree entropy depends similarly on the number of spanning…
This paper introduces new methods based on exponential families for modeling the correlations between words in text and speech. While previous work assumed the effects of word co-occurrence statistics to be constant over a window of several…
We show that the Zipf's law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipf's law for words in short English texts. For long…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator…
We investigate the consequences of two assumptions for String (or M) Theory, namely that: 1) all coordinates are compact and bound by the horizon of observation, 2) the ``dynamics'' of compactification is determined by the ``second law of…