Thinking ultrametrically, thinking p-adically

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We describe the use of ultrametric topology and closely associated p-adic number theory in a wide range of fields that all share strong elements of common mathematical and computational underpinnings. These include data analysis, including in the “big data” world of massive and high dimensional data sets; physics at very small scales; search and discovery in general information spaces; and in logic and reasoning.

Original languageEnglish
Title of host publicationClusters, Orders, and Trees
Subtitle of host publicationMethods and Applications: In Honor of Boris Mirkin's 70th Birthday
EditorsFuad Aleskerov, Boris Goldengorin, Panos M. Pardalos
PublisherSpringer New York
Pages249-272
Number of pages24
ISBN (Electronic)9781493907427
ISBN (Print)9781493907410
DOIs
Publication statusPublished - 3 May 2014
Externally publishedYes

Publication series

NameSpringer Optimization and Its Applications
Volume92
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

Fingerprint

P-adic numbers
Number theory
High-dimensional Data
Data analysis
Reasoning
Physics
Logic
Topology
Range of data

Cite this

Murtagh, F. (2014). Thinking ultrametrically, thinking p-adically. In F. Aleskerov, B. Goldengorin, & P. M. Pardalos (Eds.), Clusters, Orders, and Trees: Methods and Applications: In Honor of Boris Mirkin's 70th Birthday (pp. 249-272). (Springer Optimization and Its Applications; Vol. 92). Springer New York. https://doi.org/10.1007/978-1-4939-0742-7_16
Murtagh, Fionn. / Thinking ultrametrically, thinking p-adically. Clusters, Orders, and Trees: Methods and Applications: In Honor of Boris Mirkin's 70th Birthday. editor / Fuad Aleskerov ; Boris Goldengorin ; Panos M. Pardalos. Springer New York, 2014. pp. 249-272 (Springer Optimization and Its Applications).
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Murtagh, F 2014, Thinking ultrametrically, thinking p-adically. in F Aleskerov, B Goldengorin & PM Pardalos (eds), Clusters, Orders, and Trees: Methods and Applications: In Honor of Boris Mirkin's 70th Birthday. Springer Optimization and Its Applications, vol. 92, Springer New York, pp. 249-272. https://doi.org/10.1007/978-1-4939-0742-7_16

Thinking ultrametrically, thinking p-adically. / Murtagh, Fionn.

Clusters, Orders, and Trees: Methods and Applications: In Honor of Boris Mirkin's 70th Birthday. ed. / Fuad Aleskerov; Boris Goldengorin; Panos M. Pardalos. Springer New York, 2014. p. 249-272 (Springer Optimization and Its Applications; Vol. 92).

Research output: Chapter in Book/Report/Conference proceedingChapter

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AU - Murtagh, Fionn

PY - 2014/5/3

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AB - We describe the use of ultrametric topology and closely associated p-adic number theory in a wide range of fields that all share strong elements of common mathematical and computational underpinnings. These include data analysis, including in the “big data” world of massive and high dimensional data sets; physics at very small scales; search and discovery in general information spaces; and in logic and reasoning.

KW - Clustering

KW - Complexity

KW - Data analytics

KW - Hierarchy

KW - Information storage and retrieval

KW - Multivariate data analysis

KW - p-Adic

KW - Pattern recognition

KW - Ultrametric topology

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SN - 9781493907410

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SP - 249

EP - 272

BT - Clusters, Orders, and Trees

A2 - Aleskerov, Fuad

A2 - Goldengorin, Boris

A2 - Pardalos, Panos M.

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Murtagh F. Thinking ultrametrically, thinking p-adically. In Aleskerov F, Goldengorin B, Pardalos PM, editors, Clusters, Orders, and Trees: Methods and Applications: In Honor of Boris Mirkin's 70th Birthday. Springer New York. 2014. p. 249-272. (Springer Optimization and Its Applications). https://doi.org/10.1007/978-1-4939-0742-7_16