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In the first chapter of Shannon's "A Mathematical Theory of Communication," it is shown that the maximum entropy rate of an input process of a constrained system is limited by the combinatorial capacity of the system. Shannon considers…

Information Theory · Computer Science 2009-11-20 Georg Böcherer , Valdemar Cardoso da Rocha Junior , Cecilio Pimentel

Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…

Computation · Statistics 2025-12-25 Brani Vidakovic

Deep learning (DL) algorithms are the state of the art in automated classification of wildlife camera trap images. The challenge is that the ecologist cannot know in advance how many images per species they need to collect for model…

Computer Vision and Pattern Recognition · Computer Science 2020-10-19 Saleh Shahinfar , Paul Meek , Greg Falzon

Grammar compression represents a string as a context free grammar. Achieving compression requires encoding such grammar as a binary string; there are a few commonly used encodings. We bound the size of practically used encodings for several…

Data Structures and Algorithms · Computer Science 2020-05-21 Michał Gańczorz

Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…

Computation and Language · Computer Science 2025-11-14 Benjamin L. Badger , Matthew Neligeorge

Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism…

Populations and Evolution · Quantitative Biology 2026-05-29 Adrita Samanta , Hananel Hazan , Michael Levin

We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…

Information Theory · Computer Science 2021-01-07 Kang Gao , Bertrand Hochwald

The goal of animal movement analysis is to understand how organisms explore and exploit the complex and varying environment. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviors to highly random…

Quantitative Methods · Quantitative Biology 2014-01-17 Xiaofeng Liu , Ning Xu , Aimin Jiang

In a genetic algorithm, fluctuations of the entropy of a genome over time are interpreted as fluctuations of the information that the genome's organism is storing about its environment, being this reflected in more complex organisms. The…

Computational Engineering, Finance, and Science · Computer Science 2010-11-04 Manuel Cebrian , Manuel Alfonseca , Alfonso Ortega

Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…

Computation and Language · Computer Science 2019-05-20 E. Estevez-Rams , A. Mesa Rodriguez , D. Estevez-Moya

Calculating the Shannon entropy for symbolic sequences has been widely considered in many fields. For descriptive statistical problems such as estimating the N-gram entropy of English language text, a common approach is to use as much data…

Information Theory · Computer Science 2018-05-24 Andrew D. Back , Daniel Angus , Janet Wiles

To quantify how well natural language understanding models can capture consistency in a general conversation, we introduce the DialoguE COntradiction DEtection task (DECODE) and a new conversational dataset containing both human-human and…

Computation and Language · Computer Science 2020-12-29 Yixin Nie , Mary Williamson , Mohit Bansal , Douwe Kiela , Jason Weston

A major obstacle in analyzing the evolution of information exchange and processing is our insufficient understanding of the underlying signaling and decision-making biological mechanisms. For instance, it is unclear why are humans unique in…

Populations and Evolution · Quantitative Biology 2008-09-06 A. Feigel

Besides humans, several marine mammal species exhibit prerequisites to evolve language: high cognitive abilities, flexibility in vocal production and advanced social interactions. Here, we describe and analyse the vocal repertoire of…

Quantitative Methods · Quantitative Biology 2015-06-15 Heike Vester , Kurt Hammerschmidt , Marc Timme , Sarah Hallerberg

Birdsong often contains large amounts of rapid frequency modulation (FM). It is believed that the use or otherwise of FM is adaptive to the acoustic environment, and also that there are specific social uses of FM such as trills in…

Sound · Computer Science 2015-09-22 Dan Stowell , Mark D. Plumbley

The entropy rate of printed English is famously estimated to be about one bit per character, a benchmark that modern large language models (LLMs) have only recently approached. This entropy rate implies that English contains nearly 80…

Computation and Language · Computer Science 2026-02-19 Weishun Zhong , Doron Sivan , Tankut Can , Mikhail Katkov , Misha Tsodyks

In many fields, such as language acquisition, neuropsychology of language, the study of aging, and historical linguistics, corpora are used for estimating the diversity of grammatical structures that are produced during a period by an…

Computation and Language · Computer Science 2024-12-10 Fermin Moscoso del Prado Martin

The past decade has witnessed a groundbreaking rise of machine learning for human language analysis, with current methods capable of automatically accurately recovering various aspects of syntax and semantics - including sentence structure…

Animal sounds can be recognised automatically by machine learning, and this has an important role to play in biodiversity monitoring. Yet despite increasingly impressive capabilities, bioacoustic species classifiers still exhibit imbalanced…

Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…

Information Retrieval · Computer Science 2012-07-19 Lawrence Zitnick , Takeo Kanade