Spectral clustering for non-reversible Markov chains View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-11

AUTHORS

K. Fackeldey, A. Sikorski, M. Weber

ABSTRACT

Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We also extend this spectral clustering method to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension non-reversible Markov chains can be analyzed. Furthermore, the chains do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e., generalized PCCA), since it includes the case of non-reversible processes. We also apply the method to real-world eye-tracking data. More... »

PAGES

1-16

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40314-018-0697-0

DOI

http://dx.doi.org/10.1007/s40314-018-0697-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106387103


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/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Technical University of Berlin", 
          "id": "https://www.grid.ac/institutes/grid.6734.6", 
          "name": [
            "Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany", 
            "TU Berlin, Strasse des 17. Juni 135, 10623, Berlin, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Fackeldey", 
        "givenName": "K.", 
        "id": "sg:person.0653173503.70", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0653173503.70"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Zuse Institute Berlin", 
          "id": "https://www.grid.ac/institutes/grid.425649.8", 
          "name": [
            "Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sikorski", 
        "givenName": "A.", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Zuse Institute Berlin", 
          "id": "https://www.grid.ac/institutes/grid.425649.8", 
          "name": [
            "Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Weber", 
        "givenName": "M.", 
        "id": "sg:person.0746242713.74", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0746242713.74"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/s0167-7152(03)00095-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006562145"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0167-7152(03)00095-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006562145"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/nla.274", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006615527"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.laa.2004.10.026", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007598609"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.patcog.2007.01.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013782126"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-007-7606-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015331248", 
          "https://doi.org/10.1007/978-94-007-7606-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-007-7606-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015331248", 
          "https://doi.org/10.1007/978-94-007-7606-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.3502450", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021118815"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0024-3795(97)00333-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036359498"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-45231-7_31", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041037449", 
          "https://doi.org/10.1007/978-3-540-45231-7_31"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-45231-7_31", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041037449", 
          "https://doi.org/10.1007/978-3-540-45231-7_31"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4939-0419-8_9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042170615", 
          "https://doi.org/10.1007/978-1-4939-0419-8_9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0024-3795(00)00095-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042777955"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-44816-0_6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043851161", 
          "https://doi.org/10.1007/3-540-44816-0_6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11634-013-0134-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044425193", 
          "https://doi.org/10.1007/s11634-013-0134-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.powtec.2012.10.012", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044716076"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-31314-1_11", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046258996", 
          "https://doi.org/10.1007/3-540-31314-1_11"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.2404953", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057855110"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036144503424786", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062877809"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s089547989120267x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062881930"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aoap/1075828057", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064397865"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aoap/1177005981", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064398131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1909285", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069638447"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1913078", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069640500"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/cdc.2007.4434771", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1093985055"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1021/acs.jctc.8b00079", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1104261288"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-11", 
    "datePublishedReg": "2018-11-01", 
    "description": "Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We also extend this spectral clustering method to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension non-reversible Markov chains can be analyzed. Furthermore, the chains do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e., generalized PCCA), since it includes the case of non-reversible processes. We also apply the method to real-world eye-tracking data.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s40314-018-0697-0", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1284620", 
        "issn": [
          "2238-3603", 
          "0101-8205"
        ], 
        "name": "Computational and Applied Mathematics", 
        "type": "Periodical"
      }
    ], 
    "name": "Spectral clustering for non-reversible Markov chains", 
    "pagination": "1-16", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "43ad6a3583a16c8f5d695552db6603c2256a9014d4f16ad5270fef5756885970"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s40314-018-0697-0"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1106387103"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s40314-018-0697-0", 
      "https://app.dimensions.ai/details/publication/pub.1106387103"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T13:11", 
    "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_8659_00000494.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/s40314-018-0697-0"
  }
]
 

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/s40314-018-0697-0'

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/s40314-018-0697-0'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s40314-018-0697-0'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s40314-018-0697-0'


 

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

147 TRIPLES      21 PREDICATES      48 URIs      17 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s40314-018-0697-0 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author N50fe2d6a3c8f4c6d826bd0aa1109162a
4 schema:citation sg:pub.10.1007/3-540-31314-1_11
5 sg:pub.10.1007/3-540-44816-0_6
6 sg:pub.10.1007/978-1-4939-0419-8_9
7 sg:pub.10.1007/978-3-540-45231-7_31
8 sg:pub.10.1007/978-94-007-7606-7
9 sg:pub.10.1007/s11634-013-0134-6
10 https://doi.org/10.1002/nla.274
11 https://doi.org/10.1016/j.laa.2004.10.026
12 https://doi.org/10.1016/j.patcog.2007.01.005
13 https://doi.org/10.1016/j.powtec.2012.10.012
14 https://doi.org/10.1016/s0024-3795(00)00095-1
15 https://doi.org/10.1016/s0024-3795(97)00333-9
16 https://doi.org/10.1016/s0167-7152(03)00095-6
17 https://doi.org/10.1021/acs.jctc.8b00079
18 https://doi.org/10.1063/1.2404953
19 https://doi.org/10.1063/1.3502450
20 https://doi.org/10.1109/cdc.2007.4434771
21 https://doi.org/10.1137/s0036144503424786
22 https://doi.org/10.1137/s089547989120267x
23 https://doi.org/10.1214/aoap/1075828057
24 https://doi.org/10.1214/aoap/1177005981
25 https://doi.org/10.2307/1909285
26 https://doi.org/10.2307/1913078
27 schema:datePublished 2018-11
28 schema:datePublishedReg 2018-11-01
29 schema:description Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We also extend this spectral clustering method to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension non-reversible Markov chains can be analyzed. Furthermore, the chains do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e., generalized PCCA), since it includes the case of non-reversible processes. We also apply the method to real-world eye-tracking data.
30 schema:genre research_article
31 schema:inLanguage en
32 schema:isAccessibleForFree false
33 schema:isPartOf sg:journal.1284620
34 schema:name Spectral clustering for non-reversible Markov chains
35 schema:pagination 1-16
36 schema:productId N33abd0bca19040db87bdd108c25895d2
37 Nd0fbc1c55de7483691a548eeb7e7c88b
38 Nfb685642cf0a4a9b9c6b86a3486f5090
39 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106387103
40 https://doi.org/10.1007/s40314-018-0697-0
41 schema:sdDatePublished 2019-04-10T13:11
42 schema:sdLicense https://scigraph.springernature.com/explorer/license/
43 schema:sdPublisher N715570dcffe14dfa855f517e31feb319
44 schema:url http://link.springer.com/10.1007/s40314-018-0697-0
45 sgo:license sg:explorer/license/
46 sgo:sdDataset articles
47 rdf:type schema:ScholarlyArticle
48 N039bacfc81794f14b1249b9949f049ef rdf:first N1c42c547f5484c01ac7025852beac48f
49 rdf:rest N9bec9432767242b7bd7f6f47d048d09a
50 N1c42c547f5484c01ac7025852beac48f schema:affiliation https://www.grid.ac/institutes/grid.425649.8
51 schema:familyName Sikorski
52 schema:givenName A.
53 rdf:type schema:Person
54 N33abd0bca19040db87bdd108c25895d2 schema:name dimensions_id
55 schema:value pub.1106387103
56 rdf:type schema:PropertyValue
57 N50fe2d6a3c8f4c6d826bd0aa1109162a rdf:first sg:person.0653173503.70
58 rdf:rest N039bacfc81794f14b1249b9949f049ef
59 N715570dcffe14dfa855f517e31feb319 schema:name Springer Nature - SN SciGraph project
60 rdf:type schema:Organization
61 N9bec9432767242b7bd7f6f47d048d09a rdf:first sg:person.0746242713.74
62 rdf:rest rdf:nil
63 Nd0fbc1c55de7483691a548eeb7e7c88b schema:name readcube_id
64 schema:value 43ad6a3583a16c8f5d695552db6603c2256a9014d4f16ad5270fef5756885970
65 rdf:type schema:PropertyValue
66 Nfb685642cf0a4a9b9c6b86a3486f5090 schema:name doi
67 schema:value 10.1007/s40314-018-0697-0
68 rdf:type schema:PropertyValue
69 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
70 schema:name Mathematical Sciences
71 rdf:type schema:DefinedTerm
72 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
73 schema:name Numerical and Computational Mathematics
74 rdf:type schema:DefinedTerm
75 sg:journal.1284620 schema:issn 0101-8205
76 2238-3603
77 schema:name Computational and Applied Mathematics
78 rdf:type schema:Periodical
79 sg:person.0653173503.70 schema:affiliation https://www.grid.ac/institutes/grid.6734.6
80 schema:familyName Fackeldey
81 schema:givenName K.
82 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0653173503.70
83 rdf:type schema:Person
84 sg:person.0746242713.74 schema:affiliation https://www.grid.ac/institutes/grid.425649.8
85 schema:familyName Weber
86 schema:givenName M.
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0746242713.74
88 rdf:type schema:Person
89 sg:pub.10.1007/3-540-31314-1_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046258996
90 https://doi.org/10.1007/3-540-31314-1_11
91 rdf:type schema:CreativeWork
92 sg:pub.10.1007/3-540-44816-0_6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043851161
93 https://doi.org/10.1007/3-540-44816-0_6
94 rdf:type schema:CreativeWork
95 sg:pub.10.1007/978-1-4939-0419-8_9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042170615
96 https://doi.org/10.1007/978-1-4939-0419-8_9
97 rdf:type schema:CreativeWork
98 sg:pub.10.1007/978-3-540-45231-7_31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041037449
99 https://doi.org/10.1007/978-3-540-45231-7_31
100 rdf:type schema:CreativeWork
101 sg:pub.10.1007/978-94-007-7606-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015331248
102 https://doi.org/10.1007/978-94-007-7606-7
103 rdf:type schema:CreativeWork
104 sg:pub.10.1007/s11634-013-0134-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044425193
105 https://doi.org/10.1007/s11634-013-0134-6
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1002/nla.274 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006615527
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1016/j.laa.2004.10.026 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007598609
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1016/j.patcog.2007.01.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013782126
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1016/j.powtec.2012.10.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044716076
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1016/s0024-3795(00)00095-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042777955
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1016/s0024-3795(97)00333-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036359498
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1016/s0167-7152(03)00095-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006562145
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1021/acs.jctc.8b00079 schema:sameAs https://app.dimensions.ai/details/publication/pub.1104261288
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1063/1.2404953 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057855110
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1063/1.3502450 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021118815
126 rdf:type schema:CreativeWork
127 https://doi.org/10.1109/cdc.2007.4434771 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093985055
128 rdf:type schema:CreativeWork
129 https://doi.org/10.1137/s0036144503424786 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062877809
130 rdf:type schema:CreativeWork
131 https://doi.org/10.1137/s089547989120267x schema:sameAs https://app.dimensions.ai/details/publication/pub.1062881930
132 rdf:type schema:CreativeWork
133 https://doi.org/10.1214/aoap/1075828057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064397865
134 rdf:type schema:CreativeWork
135 https://doi.org/10.1214/aoap/1177005981 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064398131
136 rdf:type schema:CreativeWork
137 https://doi.org/10.2307/1909285 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069638447
138 rdf:type schema:CreativeWork
139 https://doi.org/10.2307/1913078 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069640500
140 rdf:type schema:CreativeWork
141 https://www.grid.ac/institutes/grid.425649.8 schema:alternateName Zuse Institute Berlin
142 schema:name Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany
143 rdf:type schema:Organization
144 https://www.grid.ac/institutes/grid.6734.6 schema:alternateName Technical University of Berlin
145 schema:name TU Berlin, Strasse des 17. Juni 135, 10623, Berlin, Germany
146 Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany
147 rdf:type schema:Organization
 




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


...