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Related papers: Relating Information and Proof

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The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…

Neurons and Cognition · Quantitative Biology 2019-06-10 Alberto Hernández-Espinosa , Héctor Zenil , Narsis A. Kiani , Jesper Tegnér

Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…

Machine Learning · Statistics 2024-10-30 Valero Laparra , J. Emmanuel Johnson , Gustau Camps-Valls , Raul Santos-Rodríguez , Jesus Malo

In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…

Numerical Analysis · Mathematics 2025-02-12 Wolfgang Bangerth , Chris R. Johnson , Dennis K. Njeru , Bart van Bloemen Waanders

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

Artificial Intelligence · Computer Science 2013-03-26 Arthur Ramer

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a…

Data Analysis, Statistics and Probability · Physics 2009-11-10 Kevin H. Knuth

The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…

Artificial Intelligence · Computer Science 2013-04-15 Norman C. Dalkey

Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…

Quantum Physics · Physics 2009-10-31 L. Henderson , V. Vedral

A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…

Data Analysis, Statistics and Probability · Physics 2013-01-18 Eugene Perevalov , David Grace

Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…

Artificial Intelligence · Computer Science 2011-02-02 Ping Zhu , Qiaoyan Wen

A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…

Data Analysis, Statistics and Probability · Physics 2009-11-10 Kevin H. Knuth

We investigate correlations in information carriers, e.g. texts and pieces of music, which are represented by strings of letters. For information carrying strings generated by one source (i.e. a novel or a piece of music) we find…

Statistical Mechanics · Physics 2007-05-23 Werner Ebeling , Thorsten Poeschel , Karl-Friedrich Albrecht

In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…

Information Theory · Computer Science 2025-01-20 Thomas F. Varley

Information value, a measure for decision sensitivity, can provide essential information in engineering and environmental assessments. It quantifies the potential for improved decision-making when reducing uncertainty in specific inputs. By…

The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…

Methodology · Statistics 2022-01-06 Stéphane Robin , Luca Scrucca

As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…

Computation and Language · Computer Science 2015-03-05 Marcelo A Montemurro , Damián H Zanette

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

Computational Complexity · Computer Science 2007-05-23 Paul Vitanyi

Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…

Neurons and Cognition · Quantitative Biology 2015-01-09 Robin A. A. Ince , Simon R. Schultz , Stefano Panzeri

We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…

Databases · Computer Science 2016-07-20 Fereidoon Sadri , Gayatri Tallur

In this article we provide a rebuttal against the possible perception that a single number, such as the Likelihood Ratio, can provide an objective, authoritative or definitive weight of evidence. We also illustrate the extent to which…

Applications · Statistics 2016-09-21 Steven P. Lund , Hari Iyer

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…

Biological Physics · Physics 2016-09-08 Elad Schneidman , Susanne Still , Michael J. Berry , William Bialek