Ontology type: schema:ScholarlyArticle Open Access: True
2012-04
AUTHORSJameson Cahill, Peter G. Casazza, Shidong Li
ABSTRACTFusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator , which in turn is heavily dependent on the sparsity of . We will show that sparsity of the fusion frame operator naturally exists by introducing a notion of non-orthogonal fusion frames. We show that for a fusion frame {Wi,vi}i∈I, if dim(Wi)=ki, then the matrix of the non-orthogonal fusion frame operator has in its corresponding location at most a ki×ki block matrix. We provide necessary and sufficient conditions for which the new fusion frame operator is diagonal and/or a multiple of an identity. A set of other critical questions are also addressed. A scheme of multiple fusion frames whose corresponding fusion frame operator becomes an diagonal operator is also examined. More... »
PAGES287-308
http://scigraph.springernature.com/pub.10.1007/s00041-011-9200-7
DOIhttp://dx.doi.org/10.1007/s00041-011-9200-7
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1000454278
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/2008/0801",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Artificial Intelligence and Image Processing",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Information and Computing Sciences",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "University of Missouri",
"id": "https://www.grid.ac/institutes/grid.134936.a",
"name": [
"Department of Mathematics, University of Missouri, 65211-4100, Columbia, MO, USA"
],
"type": "Organization"
},
"familyName": "Cahill",
"givenName": "Jameson",
"id": "sg:person.015630506004.77",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015630506004.77"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Missouri",
"id": "https://www.grid.ac/institutes/grid.134936.a",
"name": [
"Department of Mathematics, University of Missouri, 65211-4100, Columbia, MO, USA"
],
"type": "Organization"
},
"familyName": "Casazza",
"givenName": "Peter G.",
"id": "sg:person.015252335555.42",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015252335555.42"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "San Francisco State University",
"id": "https://www.grid.ac/institutes/grid.263091.f",
"name": [
"Department of Mathematics, San Francisco State University, 94132, San Francisco, CA, USA"
],
"type": "Organization"
},
"familyName": "Li",
"givenName": "Shidong",
"id": "sg:person.015207652505.34",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015207652505.34"
],
"type": "Person"
}
],
"citation": [
{
"id": "https://doi.org/10.1117/12.826282",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1001573340"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jmaa.2005.09.039",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1002411476"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jmaa.2006.03.043",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1003159488"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.acha.2010.05.002",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1006228088"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1117/12.826327",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1010255446"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10444-006-9014-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1017783794",
"https://doi.org/10.1007/s10444-006-9014-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10444-006-9014-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1017783794",
"https://doi.org/10.1007/s10444-006-9014-3"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.acha.2007.10.001",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023655828"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00041-009-9098-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024419988",
"https://doi.org/10.1007/s00041-009-9098-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00041-009-9098-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024419988",
"https://doi.org/10.1007/s00041-009-9098-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00041-009-9098-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024419988",
"https://doi.org/10.1007/s00041-009-9098-5"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1117/12.825645",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1027681660"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1117/12.730719",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1027950455"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1117/12.825782",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030470996"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10444-010-9162-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1035172279",
"https://doi.org/10.1007/s10444-010-9162-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00041-004-3039-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1040595298",
"https://doi.org/10.1007/s00041-004-3039-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10440-008-9419-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1051423101",
"https://doi.org/10.1007/s10440-008-9419-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10440-008-9419-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1051423101",
"https://doi.org/10.1007/s10440-008-9419-8"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/78.330352",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061228871"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/tip.2012.2201489",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061643251"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/tsp.2010.2097255",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061802501"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/conm/345/06242",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1089200961"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/conm/464/09082",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1089202758"
],
"type": "CreativeWork"
}
],
"datePublished": "2012-04",
"datePublishedReg": "2012-04-01",
"description": "Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator , which in turn is heavily dependent on the sparsity of . We will show that sparsity of the fusion frame operator naturally exists by introducing a notion of non-orthogonal fusion frames. We show that for a fusion frame {Wi,vi}i\u2208I, if dim(Wi)=ki, then the matrix of the non-orthogonal fusion frame operator has in its corresponding location at most a ki\u00d7ki block matrix. We provide necessary and sufficient conditions for which the new fusion frame operator is diagonal and/or a multiple of an identity. A set of other critical questions are also addressed. A scheme of multiple fusion frames whose corresponding fusion frame operator becomes an diagonal operator is also examined.",
"genre": "research_article",
"id": "sg:pub.10.1007/s00041-011-9200-7",
"inLanguage": [
"en"
],
"isAccessibleForFree": true,
"isPartOf": [
{
"id": "sg:journal.1042645",
"issn": [
"1069-5869",
"1531-5851"
],
"name": "Journal of Fourier Analysis and Applications",
"type": "Periodical"
},
{
"issueNumber": "2",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "18"
}
],
"name": "Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators",
"pagination": "287-308",
"productId": [
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"02298cadaf05a22a533c8ee9f3ef0fbd821e14798ea8c11454a98a9ccb8c8140"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s00041-011-9200-7"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1000454278"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s00041-011-9200-7",
"https://app.dimensions.ai/details/publication/pub.1000454278"
],
"sdDataset": "articles",
"sdDatePublished": "2019-04-11T01:56",
"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_00000498.jsonl",
"type": "ScholarlyArticle",
"url": "http://link.springer.com/10.1007/s00041-011-9200-7"
}
]
Download the RDF metadata as: json-ld nt turtle xml License info
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/s00041-011-9200-7'
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/s00041-011-9200-7'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00041-011-9200-7'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00041-011-9200-7'
This table displays all metadata directly associated to this object as RDF triples.
140 TRIPLES
21 PREDICATES
46 URIs
19 LITERALS
7 BLANK NODES