Aggregate and fractal tessellations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2001-10

AUTHORS

Konstantin Tchoumatchenko, Sergei Zuyev

ABSTRACT

Consider a sequence of stationary tessellations {Θn}, n=0,1,…, of ℝd consisting of cells {Cn(xin)}with the nuclei {xin}. An aggregate cell of level one, C01(xi0), is the result of merging the cells of Θ1 whose nuclei lie in C0(xi0). An aggregate tessellation Θ0n consists of the aggregate cells of level n, C0n(xi0), defined recursively by merging those cells of Θn whose nuclei lie in Cn−1(xi0). We find an expression for the probability for a point to belong to atypical aggregate cell, and obtain bounds for the rate of itsexpansion. We give necessary conditions for the limittessellation to exist as n→∞ and provide upperbounds for the Hausdorff dimension of its fractal boundary and forthe spherical contact distribution function in the case ofPoisson-Voronoi tessellations {Θn}. More... »

PAGES

198-218

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00008802

DOI

http://dx.doi.org/10.1007/pl00008802

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1053393745


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0601", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biochemistry and Cell Biology", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/06", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biological Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Orange (France)", 
          "id": "https://www.grid.ac/institutes/grid.89485.38", 
          "name": [
            "France Telecom R&D, 38-40 rue du G\u00e9n\u00e9ral Leclerc, 92794 Issy-Moulineaux, France. e-mail: Konstantin.Tchoumatchenko@rd.francetelecom.com, FR"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Tchoumatchenko", 
        "givenName": "Konstantin", 
        "id": "sg:person.012543676275.16", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012543676275.16"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Strathclyde", 
          "id": "https://www.grid.ac/institutes/grid.11984.35", 
          "name": [
            "Statistics and Modelling Science Department, University of Strathclyde, 26 Richmond str., Glasgow, G1 1XH, UK. e-mail: sergei@stams.strath.ac.uk, GB"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zuyev", 
        "givenName": "Sergei", 
        "id": "sg:person.014553476476.08", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014553476476.08"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1287/opre.47.4.619", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064731167"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2001-10", 
    "datePublishedReg": "2001-10-01", 
    "description": "Consider a sequence of stationary tessellations {\u0398n}, n=0,1,\u2026, of \u211dd consisting of cells {Cn(xin)}with the nuclei {xin}. An aggregate cell of level one, C01(xi0), is the result of merging the cells of \u03981 whose nuclei lie in C0(xi0). An aggregate tessellation \u03980n consists of the aggregate cells of level n, C0n(xi0), defined recursively by merging those cells of \u0398n whose nuclei lie in Cn\u22121(xi0). We find an expression for the probability for a point to belong to atypical aggregate cell, and obtain bounds for the rate of itsexpansion. We give necessary conditions for the limittessellation to exist as n\u2192\u221e and provide upperbounds for the Hausdorff dimension of its fractal boundary and forthe spherical contact distribution function in the case ofPoisson-Voronoi tessellations {\u0398n}.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/pl00008802", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1053886", 
        "issn": [
          "0178-8051", 
          "1432-2064"
        ], 
        "name": "Probability Theory and Related Fields", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "121"
      }
    ], 
    "name": "Aggregate and fractal tessellations", 
    "pagination": "198-218", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "fe522d4dabe507b5414607eac115d638c205ca28744b3f9b512011719cf7b53f"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/pl00008802"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1053393745"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/pl00008802", 
      "https://app.dimensions.ai/details/publication/pub.1053393745"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T01:55", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8700_00000492.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/PL00008802"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/pl00008802'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/pl00008802'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/pl00008802'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/pl00008802'


 

This table displays all metadata directly associated to this object as RDF triples.

74 TRIPLES      21 PREDICATES      28 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/pl00008802 schema:about anzsrc-for:06
2 anzsrc-for:0601
3 schema:author Ncc4617bbe9b043eda3b51592462576cd
4 schema:citation https://doi.org/10.1287/opre.47.4.619
5 schema:datePublished 2001-10
6 schema:datePublishedReg 2001-10-01
7 schema:description Consider a sequence of stationary tessellations {Θn}, n=0,1,…, of ℝd consisting of cells {Cn(xin)}with the nuclei {xin}. An aggregate cell of level one, C01(xi0), is the result of merging the cells of Θ1 whose nuclei lie in C0(xi0). An aggregate tessellation Θ0n consists of the aggregate cells of level n, C0n(xi0), defined recursively by merging those cells of Θn whose nuclei lie in Cn−1(xi0). We find an expression for the probability for a point to belong to atypical aggregate cell, and obtain bounds for the rate of itsexpansion. We give necessary conditions for the limittessellation to exist as n→∞ and provide upperbounds for the Hausdorff dimension of its fractal boundary and forthe spherical contact distribution function in the case ofPoisson-Voronoi tessellations {Θn}.
8 schema:genre research_article
9 schema:inLanguage en
10 schema:isAccessibleForFree true
11 schema:isPartOf N8e73e0c035054d67a9f501bc69f93651
12 Na3eb5dc6f2e345938874456e2b372ce8
13 sg:journal.1053886
14 schema:name Aggregate and fractal tessellations
15 schema:pagination 198-218
16 schema:productId N9d1bfe4e68ba4796a5d1ebd60404d606
17 Nc6d7d29e188c4f4ab2d9df8de0f39b26
18 Nda30cb17fc714757b7beea21c4352a4c
19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053393745
20 https://doi.org/10.1007/pl00008802
21 schema:sdDatePublished 2019-04-11T01:55
22 schema:sdLicense https://scigraph.springernature.com/explorer/license/
23 schema:sdPublisher Na2f3df70a9e043299fade51f125e85d1
24 schema:url http://link.springer.com/10.1007/PL00008802
25 sgo:license sg:explorer/license/
26 sgo:sdDataset articles
27 rdf:type schema:ScholarlyArticle
28 N50febee0aaca4bf59cbccc8e3ab687e0 rdf:first sg:person.014553476476.08
29 rdf:rest rdf:nil
30 N8e73e0c035054d67a9f501bc69f93651 schema:volumeNumber 121
31 rdf:type schema:PublicationVolume
32 N9d1bfe4e68ba4796a5d1ebd60404d606 schema:name readcube_id
33 schema:value fe522d4dabe507b5414607eac115d638c205ca28744b3f9b512011719cf7b53f
34 rdf:type schema:PropertyValue
35 Na2f3df70a9e043299fade51f125e85d1 schema:name Springer Nature - SN SciGraph project
36 rdf:type schema:Organization
37 Na3eb5dc6f2e345938874456e2b372ce8 schema:issueNumber 2
38 rdf:type schema:PublicationIssue
39 Nc6d7d29e188c4f4ab2d9df8de0f39b26 schema:name dimensions_id
40 schema:value pub.1053393745
41 rdf:type schema:PropertyValue
42 Ncc4617bbe9b043eda3b51592462576cd rdf:first sg:person.012543676275.16
43 rdf:rest N50febee0aaca4bf59cbccc8e3ab687e0
44 Nda30cb17fc714757b7beea21c4352a4c schema:name doi
45 schema:value 10.1007/pl00008802
46 rdf:type schema:PropertyValue
47 anzsrc-for:06 schema:inDefinedTermSet anzsrc-for:
48 schema:name Biological Sciences
49 rdf:type schema:DefinedTerm
50 anzsrc-for:0601 schema:inDefinedTermSet anzsrc-for:
51 schema:name Biochemistry and Cell Biology
52 rdf:type schema:DefinedTerm
53 sg:journal.1053886 schema:issn 0178-8051
54 1432-2064
55 schema:name Probability Theory and Related Fields
56 rdf:type schema:Periodical
57 sg:person.012543676275.16 schema:affiliation https://www.grid.ac/institutes/grid.89485.38
58 schema:familyName Tchoumatchenko
59 schema:givenName Konstantin
60 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012543676275.16
61 rdf:type schema:Person
62 sg:person.014553476476.08 schema:affiliation https://www.grid.ac/institutes/grid.11984.35
63 schema:familyName Zuyev
64 schema:givenName Sergei
65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014553476476.08
66 rdf:type schema:Person
67 https://doi.org/10.1287/opre.47.4.619 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064731167
68 rdf:type schema:CreativeWork
69 https://www.grid.ac/institutes/grid.11984.35 schema:alternateName University of Strathclyde
70 schema:name Statistics and Modelling Science Department, University of Strathclyde, 26 Richmond str., Glasgow, G1 1XH, UK. e-mail: sergei@stams.strath.ac.uk, GB
71 rdf:type schema:Organization
72 https://www.grid.ac/institutes/grid.89485.38 schema:alternateName Orange (France)
73 schema:name France Telecom R&D, 38-40 rue du Général Leclerc, 92794 Issy-Moulineaux, France. e-mail: Konstantin.Tchoumatchenko@rd.francetelecom.com, FR
74 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...