Rate of Mutual Information Between Coarse-Grained Non-Markovian Variables View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2013-11

AUTHORS

Andre C. Barato, David Hartich, Udo Seifert

ABSTRACT

The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general non-Markovian, therefore, an expression for their Shannon entropy rates in terms of the stationary probability distribution is not known. A numerical method to estimate the Shannon entropy rate of continuous time hidden-Markov processes from a single time series is developed. With this method the rate of mutual information can be determined numerically. Moreover, an analytical upper bound on the rate of mutual information is calculated for a class of Markov processes for which the transition rates have a bipartite character. Our general results are illustrated with explicit calculations for four-state networks. More... »

PAGES

460-478

Journal

TITLE

Journal of Statistical Physics

ISSUE

3

VOLUME

153

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-013-0834-5

DOI

http://dx.doi.org/10.1007/s10955-013-0834-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1003384936


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure 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": "University of Stuttgart", 
          "id": "https://www.grid.ac/institutes/grid.5719.a", 
          "name": [
            "II. Institut f\u00fcr Theoretische Physik, Universit\u00e4t Stuttgart, 70550, Stuttgart, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Barato", 
        "givenName": "Andre C.", 
        "id": "sg:person.01111727467.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01111727467.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Stuttgart", 
          "id": "https://www.grid.ac/institutes/grid.5719.a", 
          "name": [
            "II. Institut f\u00fcr Theoretische Physik, Universit\u00e4t Stuttgart, 70550, Stuttgart, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hartich", 
        "givenName": "David", 
        "id": "sg:person.01046427523.95", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01046427523.95"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Stuttgart", 
          "id": "https://www.grid.ac/institutes/grid.5719.a", 
          "name": [
            "II. Institut f\u00fcr Theoretische Physik, Universit\u00e4t Stuttgart, 70550, Stuttgart, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Seifert", 
        "givenName": "Udo", 
        "id": "sg:person.01351424514.94", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01351424514.94"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1103/physrevlett.98.080602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008080779"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.98.080602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008080779"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1209/0295-5075/101/60001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009629233"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.041125", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010621844"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.041125", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010621844"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1073/pnas.1207814109", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012596404"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0034-4885/75/12/126001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014658892"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1209/0295-5075/99/30003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018346170"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.84.1156", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022251300"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.84.1156", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022251300"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/1751-8113/45/16/162001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023038072"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.87.042104", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025930394"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.87.042104", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025930394"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.84.061110", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027050552"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.84.061110", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027050552"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01025996", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028806599", 
          "https://doi.org/10.1007/bf01025996"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.82.061120", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028958631"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.82.061120", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028958631"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.021104", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030116325"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.021104", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030116325"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1073/pnas.1204263109", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031848569"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.108.030601", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033291324"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.108.030601", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033291324"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.tcs.2008.01.012", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034069547"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.79.041118", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035351669"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.79.041118", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035351669"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10955-004-3455-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036762582", 
          "https://doi.org/10.1007/s10955-004-3455-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.109.180602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037523558"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.109.180602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037523558"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1209/0295-5075/94/10001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038500636"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.110.040601", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039681184"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.110.040601", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039681184"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.84.021123", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041723013"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.84.021123", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041723013"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.061127", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044091569"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.061127", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044091569"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10955-006-9254-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044664431", 
          "https://doi.org/10.1007/s10955-006-9254-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1209/0295-5075/95/10005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044878805"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/nphys2276", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047642092", 
          "https://doi.org/10.1038/nphys2276"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.031129", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048750215"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physreve.85.031129", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048750215"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1052295691", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-84942-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052295691", 
          "https://doi.org/10.1007/978-3-642-84942-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-84942-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052295691", 
          "https://doi.org/10.1007/978-3-642-84942-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/j.1538-7305.1948.tb01338.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052867467"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.104.090602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052926340"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.104.090602", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052926340"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.48.571", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060838840"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.48.571", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060838840"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tit.2002.1003838", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061649529"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tit.2006.878230", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061651046"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2013-11", 
    "datePublishedReg": "2013-11-01", 
    "description": "The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general non-Markovian, therefore, an expression for their Shannon entropy rates in terms of the stationary probability distribution is not known. A numerical method to estimate the Shannon entropy rate of continuous time hidden-Markov processes from a single time series is developed. With this method the rate of mutual information can be determined numerically. Moreover, an analytical upper bound on the rate of mutual information is calculated for a class of Markov processes for which the transition rates have a bipartite character. Our general results are illustrated with explicit calculations for four-state networks.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10955-013-0834-5", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1040979", 
        "issn": [
          "0022-4715", 
          "1572-9613"
        ], 
        "name": "Journal of Statistical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "153"
      }
    ], 
    "name": "Rate of Mutual Information Between Coarse-Grained Non-Markovian Variables", 
    "pagination": "460-478", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "101fa7355b147a9b78c1bb5a9f19bd77af452a031d743c8d0d4400a8194eb949"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10955-013-0834-5"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1003384936"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10955-013-0834-5", 
      "https://app.dimensions.ai/details/publication/pub.1003384936"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T22:31", 
    "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_8690_00000510.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs10955-013-0834-5"
  }
]
 

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/s10955-013-0834-5'

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/s10955-013-0834-5'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10955-013-0834-5'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10955-013-0834-5'


 

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

181 TRIPLES      21 PREDICATES      61 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10955-013-0834-5 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Na448d1bf3bee45cb90b06401c1b5b773
4 schema:citation sg:pub.10.1007/978-3-642-84942-8
5 sg:pub.10.1007/bf01025996
6 sg:pub.10.1007/s10955-004-3455-1
7 sg:pub.10.1007/s10955-006-9254-0
8 sg:pub.10.1038/nphys2276
9 https://app.dimensions.ai/details/publication/pub.1052295691
10 https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
11 https://doi.org/10.1016/j.tcs.2008.01.012
12 https://doi.org/10.1073/pnas.1204263109
13 https://doi.org/10.1073/pnas.1207814109
14 https://doi.org/10.1088/0034-4885/75/12/126001
15 https://doi.org/10.1088/1751-8113/45/16/162001
16 https://doi.org/10.1103/physreve.79.041118
17 https://doi.org/10.1103/physreve.82.061120
18 https://doi.org/10.1103/physreve.84.021123
19 https://doi.org/10.1103/physreve.84.061110
20 https://doi.org/10.1103/physreve.85.021104
21 https://doi.org/10.1103/physreve.85.031129
22 https://doi.org/10.1103/physreve.85.041125
23 https://doi.org/10.1103/physreve.85.061127
24 https://doi.org/10.1103/physreve.87.042104
25 https://doi.org/10.1103/physrevlett.104.090602
26 https://doi.org/10.1103/physrevlett.108.030601
27 https://doi.org/10.1103/physrevlett.109.180602
28 https://doi.org/10.1103/physrevlett.110.040601
29 https://doi.org/10.1103/physrevlett.84.1156
30 https://doi.org/10.1103/physrevlett.98.080602
31 https://doi.org/10.1103/revmodphys.48.571
32 https://doi.org/10.1109/tit.2002.1003838
33 https://doi.org/10.1109/tit.2006.878230
34 https://doi.org/10.1209/0295-5075/101/60001
35 https://doi.org/10.1209/0295-5075/94/10001
36 https://doi.org/10.1209/0295-5075/95/10005
37 https://doi.org/10.1209/0295-5075/99/30003
38 schema:datePublished 2013-11
39 schema:datePublishedReg 2013-11-01
40 schema:description The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general non-Markovian, therefore, an expression for their Shannon entropy rates in terms of the stationary probability distribution is not known. A numerical method to estimate the Shannon entropy rate of continuous time hidden-Markov processes from a single time series is developed. With this method the rate of mutual information can be determined numerically. Moreover, an analytical upper bound on the rate of mutual information is calculated for a class of Markov processes for which the transition rates have a bipartite character. Our general results are illustrated with explicit calculations for four-state networks.
41 schema:genre research_article
42 schema:inLanguage en
43 schema:isAccessibleForFree true
44 schema:isPartOf N44a971439af5439cb1c67ca218c223c7
45 N4d9711c9ea5b429581e61b66ad91c052
46 sg:journal.1040979
47 schema:name Rate of Mutual Information Between Coarse-Grained Non-Markovian Variables
48 schema:pagination 460-478
49 schema:productId N66a087fc0c284a1b91a02ec51d83eee4
50 Na1828ca0587d414fa7900eeef0a5944b
51 Nc38c52847d1e4d87a4980b2da8451fb3
52 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003384936
53 https://doi.org/10.1007/s10955-013-0834-5
54 schema:sdDatePublished 2019-04-10T22:31
55 schema:sdLicense https://scigraph.springernature.com/explorer/license/
56 schema:sdPublisher N38b4a9b4c34b4a138b1a9711033454d8
57 schema:url http://link.springer.com/10.1007%2Fs10955-013-0834-5
58 sgo:license sg:explorer/license/
59 sgo:sdDataset articles
60 rdf:type schema:ScholarlyArticle
61 N10e0a56896cd4257b990790ada799be2 rdf:first sg:person.01046427523.95
62 rdf:rest Nc5ae658533554304bb07412497120052
63 N38b4a9b4c34b4a138b1a9711033454d8 schema:name Springer Nature - SN SciGraph project
64 rdf:type schema:Organization
65 N44a971439af5439cb1c67ca218c223c7 schema:issueNumber 3
66 rdf:type schema:PublicationIssue
67 N4d9711c9ea5b429581e61b66ad91c052 schema:volumeNumber 153
68 rdf:type schema:PublicationVolume
69 N66a087fc0c284a1b91a02ec51d83eee4 schema:name dimensions_id
70 schema:value pub.1003384936
71 rdf:type schema:PropertyValue
72 Na1828ca0587d414fa7900eeef0a5944b schema:name doi
73 schema:value 10.1007/s10955-013-0834-5
74 rdf:type schema:PropertyValue
75 Na448d1bf3bee45cb90b06401c1b5b773 rdf:first sg:person.01111727467.48
76 rdf:rest N10e0a56896cd4257b990790ada799be2
77 Nc38c52847d1e4d87a4980b2da8451fb3 schema:name readcube_id
78 schema:value 101fa7355b147a9b78c1bb5a9f19bd77af452a031d743c8d0d4400a8194eb949
79 rdf:type schema:PropertyValue
80 Nc5ae658533554304bb07412497120052 rdf:first sg:person.01351424514.94
81 rdf:rest rdf:nil
82 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
83 schema:name Mathematical Sciences
84 rdf:type schema:DefinedTerm
85 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
86 schema:name Pure Mathematics
87 rdf:type schema:DefinedTerm
88 sg:journal.1040979 schema:issn 0022-4715
89 1572-9613
90 schema:name Journal of Statistical Physics
91 rdf:type schema:Periodical
92 sg:person.01046427523.95 schema:affiliation https://www.grid.ac/institutes/grid.5719.a
93 schema:familyName Hartich
94 schema:givenName David
95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01046427523.95
96 rdf:type schema:Person
97 sg:person.01111727467.48 schema:affiliation https://www.grid.ac/institutes/grid.5719.a
98 schema:familyName Barato
99 schema:givenName Andre C.
100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01111727467.48
101 rdf:type schema:Person
102 sg:person.01351424514.94 schema:affiliation https://www.grid.ac/institutes/grid.5719.a
103 schema:familyName Seifert
104 schema:givenName Udo
105 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01351424514.94
106 rdf:type schema:Person
107 sg:pub.10.1007/978-3-642-84942-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052295691
108 https://doi.org/10.1007/978-3-642-84942-8
109 rdf:type schema:CreativeWork
110 sg:pub.10.1007/bf01025996 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028806599
111 https://doi.org/10.1007/bf01025996
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/s10955-004-3455-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036762582
114 https://doi.org/10.1007/s10955-004-3455-1
115 rdf:type schema:CreativeWork
116 sg:pub.10.1007/s10955-006-9254-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044664431
117 https://doi.org/10.1007/s10955-006-9254-0
118 rdf:type schema:CreativeWork
119 sg:pub.10.1038/nphys2276 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047642092
120 https://doi.org/10.1038/nphys2276
121 rdf:type schema:CreativeWork
122 https://app.dimensions.ai/details/publication/pub.1052295691 schema:CreativeWork
123 https://doi.org/10.1002/j.1538-7305.1948.tb01338.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1052867467
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1016/j.tcs.2008.01.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034069547
126 rdf:type schema:CreativeWork
127 https://doi.org/10.1073/pnas.1204263109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031848569
128 rdf:type schema:CreativeWork
129 https://doi.org/10.1073/pnas.1207814109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012596404
130 rdf:type schema:CreativeWork
131 https://doi.org/10.1088/0034-4885/75/12/126001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014658892
132 rdf:type schema:CreativeWork
133 https://doi.org/10.1088/1751-8113/45/16/162001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023038072
134 rdf:type schema:CreativeWork
135 https://doi.org/10.1103/physreve.79.041118 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035351669
136 rdf:type schema:CreativeWork
137 https://doi.org/10.1103/physreve.82.061120 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028958631
138 rdf:type schema:CreativeWork
139 https://doi.org/10.1103/physreve.84.021123 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041723013
140 rdf:type schema:CreativeWork
141 https://doi.org/10.1103/physreve.84.061110 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027050552
142 rdf:type schema:CreativeWork
143 https://doi.org/10.1103/physreve.85.021104 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030116325
144 rdf:type schema:CreativeWork
145 https://doi.org/10.1103/physreve.85.031129 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048750215
146 rdf:type schema:CreativeWork
147 https://doi.org/10.1103/physreve.85.041125 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010621844
148 rdf:type schema:CreativeWork
149 https://doi.org/10.1103/physreve.85.061127 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044091569
150 rdf:type schema:CreativeWork
151 https://doi.org/10.1103/physreve.87.042104 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025930394
152 rdf:type schema:CreativeWork
153 https://doi.org/10.1103/physrevlett.104.090602 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052926340
154 rdf:type schema:CreativeWork
155 https://doi.org/10.1103/physrevlett.108.030601 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033291324
156 rdf:type schema:CreativeWork
157 https://doi.org/10.1103/physrevlett.109.180602 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037523558
158 rdf:type schema:CreativeWork
159 https://doi.org/10.1103/physrevlett.110.040601 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039681184
160 rdf:type schema:CreativeWork
161 https://doi.org/10.1103/physrevlett.84.1156 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022251300
162 rdf:type schema:CreativeWork
163 https://doi.org/10.1103/physrevlett.98.080602 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008080779
164 rdf:type schema:CreativeWork
165 https://doi.org/10.1103/revmodphys.48.571 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060838840
166 rdf:type schema:CreativeWork
167 https://doi.org/10.1109/tit.2002.1003838 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061649529
168 rdf:type schema:CreativeWork
169 https://doi.org/10.1109/tit.2006.878230 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061651046
170 rdf:type schema:CreativeWork
171 https://doi.org/10.1209/0295-5075/101/60001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009629233
172 rdf:type schema:CreativeWork
173 https://doi.org/10.1209/0295-5075/94/10001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038500636
174 rdf:type schema:CreativeWork
175 https://doi.org/10.1209/0295-5075/95/10005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044878805
176 rdf:type schema:CreativeWork
177 https://doi.org/10.1209/0295-5075/99/30003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018346170
178 rdf:type schema:CreativeWork
179 https://www.grid.ac/institutes/grid.5719.a schema:alternateName University of Stuttgart
180 schema:name II. Institut für Theoretische Physik, Universität Stuttgart, 70550, Stuttgart, Germany
181 rdf:type schema:Organization
 




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


...