Approximate parameter inference in systems biology using gradient matching: a comparative evaluation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-07-15

AUTHORS

Benn Macdonald, Mu Niu, Simon Rogers, Maurizio Filippone, Dirk Husmeier

ABSTRACT

BACKGROUND: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method. METHODS: Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here. RESULTS: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques. CONCLUSIONS: Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust. More... »

PAGES

80

References to SciGraph publications

  • 2015. FPGA Implementation for Cardiac Excitation-Conduction Simulation Based on FitzHugh-Nagumo Model in 5TH INTERNATIONAL CONFERENCE ON BIOMEDICAL ENGINEERING IN VIETNAM
  • 2011-03-30. Smooth functional tempering for nonlinear differential equation models in STATISTICS AND COMPUTING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1186/s12938-016-0186-x

    DOI

    http://dx.doi.org/10.1186/s12938-016-0186-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1013410920

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/27454253


    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/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0903", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Biomedical Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
            "name": "Humans", 
            "type": "DefinedTerm"
          }, 
          {
            "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
            "name": "Likelihood Functions", 
            "type": "DefinedTerm"
          }, 
          {
            "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
            "name": "Normal Distribution", 
            "type": "DefinedTerm"
          }, 
          {
            "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
            "name": "Systems Biology", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland", 
              "id": "http://www.grid.ac/institutes/grid.8756.c", 
              "name": [
                "School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Macdonald", 
            "givenName": "Benn", 
            "id": "sg:person.01203321237.78", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01203321237.78"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland", 
              "id": "http://www.grid.ac/institutes/grid.8756.c", 
              "name": [
                "School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Niu", 
            "givenName": "Mu", 
            "id": "sg:person.01366452107.31", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01366452107.31"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Computing Science, University of Glasgow, Glasgow, G12 8RZ Scotland", 
              "id": "http://www.grid.ac/institutes/grid.8756.c", 
              "name": [
                "School of Computing Science, University of Glasgow, Glasgow, G12 8RZ Scotland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rogers", 
            "givenName": "Simon", 
            "id": "sg:person.01240064014.24", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01240064014.24"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "EURECOM, Sophia Antipolis, France", 
              "id": "http://www.grid.ac/institutes/grid.28848.3e", 
              "name": [
                "EURECOM, Sophia Antipolis, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Filippone", 
            "givenName": "Maurizio", 
            "id": "sg:person.07706215665.03", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland", 
              "id": "http://www.grid.ac/institutes/grid.8756.c", 
              "name": [
                "School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Husmeier", 
            "givenName": "Dirk", 
            "id": "sg:person.0601451763.91", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0601451763.91"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s11222-011-9234-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025354923", 
              "https://doi.org/10.1007/s11222-011-9234-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-11776-8_29", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029034268", 
              "https://doi.org/10.1007/978-3-319-11776-8_29"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2016-07-15", 
        "datePublishedReg": "2016-07-15", 
        "description": "BACKGROUND: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method.\nMETHODS: Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here.\nRESULTS: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques.\nCONCLUSIONS: Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust.", 
        "genre": "article", 
        "id": "sg:pub.10.1186/s12938-016-0186-x", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.3863303", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1031014", 
            "issn": [
              "1475-925X"
            ], 
            "name": "BioMedical Engineering OnLine", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "Suppl 1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "15"
          }
        ], 
        "keywords": [
          "ordinary differential equations", 
          "parameter inference", 
          "Gaussian process", 
          "gradient matching", 
          "noise variance", 
          "kernel Hilbert space", 
          "parallel tempering scheme", 
          "current systems biology", 
          "differential equations", 
          "ODE system", 
          "Hilbert space", 
          "RKHS method", 
          "parameter estimation", 
          "penalty parameter", 
          "parallel tempering", 
          "numerical integration", 
          "systems biology", 
          "tempering scheme", 
          "computational cost", 
          "adaptive gradient", 
          "inference", 
          "range of scenarios", 
          "art methods", 
          "new method", 
          "RKHS", 
          "challenging problem", 
          "equations", 
          "conventional methods", 
          "matching method", 
          "better performance", 
          "AIC", 
          "estimation", 
          "scheme", 
          "contemporary methods", 
          "space", 
          "robustness", 
          "problem", 
          "approach", 
          "new concept", 
          "variance", 
          "matching", 
          "parameters", 
          "technique", 
          "different experimental settings", 
          "current state", 
          "experimental settings", 
          "methodology", 
          "stability", 
          "system", 
          "gradient", 
          "cost", 
          "detail", 
          "scenarios", 
          "state", 
          "analysis", 
          "promising results", 
          "performance", 
          "comparative analysis", 
          "concept", 
          "results", 
          "validation", 
          "integration", 
          "range", 
          "tempering", 
          "comparative evaluation", 
          "process", 
          "biology", 
          "setting", 
          "evaluation", 
          "sensitivity", 
          "study", 
          "need", 
          "biological pathways", 
          "method", 
          "pathway", 
          "paper", 
          "lax experimental settings", 
          "adaptive gradient matching method", 
          "gradient matching method", 
          "benchmark ODE systems", 
          "Approximate parameter inference"
        ], 
        "name": "Approximate parameter inference in systems biology using gradient matching: a comparative evaluation", 
        "pagination": "80", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1013410920"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1186/s12938-016-0186-x"
            ]
          }, 
          {
            "name": "pubmed_id", 
            "type": "PropertyValue", 
            "value": [
              "27454253"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1186/s12938-016-0186-x", 
          "https://app.dimensions.ai/details/publication/pub.1013410920"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:40", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_698.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1186/s12938-016-0186-x"
      }
    ]
     

    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.10.1186/s12938-016-0186-x'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s12938-016-0186-x'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s12938-016-0186-x'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s12938-016-0186-x'


     

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

    201 TRIPLES      22 PREDICATES      113 URIs      103 LITERALS      11 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1186/s12938-016-0186-x schema:about N5eb473d993a54ef0b4a19dc8501660c9
    2 N61f5a75126334fad937d7e541cf57dc1
    3 N630f016a13a8481e8b8d8029e55acdf0
    4 Na5c64a7b5b284d9d9254a3f356de9ab1
    5 anzsrc-for:09
    6 anzsrc-for:0903
    7 schema:author N40dee382fbcc494383bc5037a221188b
    8 schema:citation sg:pub.10.1007/978-3-319-11776-8_29
    9 sg:pub.10.1007/s11222-011-9234-3
    10 schema:datePublished 2016-07-15
    11 schema:datePublishedReg 2016-07-15
    12 schema:description BACKGROUND: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method. METHODS: Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here. RESULTS: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques. CONCLUSIONS: Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust.
    13 schema:genre article
    14 schema:inLanguage en
    15 schema:isAccessibleForFree true
    16 schema:isPartOf N24cffbe8b10042e984137be43b0bd496
    17 N4cbacafd0e7f4ff39cd6ad3995b79bbc
    18 sg:journal.1031014
    19 schema:keywords AIC
    20 Approximate parameter inference
    21 Gaussian process
    22 Hilbert space
    23 ODE system
    24 RKHS
    25 RKHS method
    26 adaptive gradient
    27 adaptive gradient matching method
    28 analysis
    29 approach
    30 art methods
    31 benchmark ODE systems
    32 better performance
    33 biological pathways
    34 biology
    35 challenging problem
    36 comparative analysis
    37 comparative evaluation
    38 computational cost
    39 concept
    40 contemporary methods
    41 conventional methods
    42 cost
    43 current state
    44 current systems biology
    45 detail
    46 different experimental settings
    47 differential equations
    48 equations
    49 estimation
    50 evaluation
    51 experimental settings
    52 gradient
    53 gradient matching
    54 gradient matching method
    55 inference
    56 integration
    57 kernel Hilbert space
    58 lax experimental settings
    59 matching
    60 matching method
    61 method
    62 methodology
    63 need
    64 new concept
    65 new method
    66 noise variance
    67 numerical integration
    68 ordinary differential equations
    69 paper
    70 parallel tempering
    71 parallel tempering scheme
    72 parameter estimation
    73 parameter inference
    74 parameters
    75 pathway
    76 penalty parameter
    77 performance
    78 problem
    79 process
    80 promising results
    81 range
    82 range of scenarios
    83 results
    84 robustness
    85 scenarios
    86 scheme
    87 sensitivity
    88 setting
    89 space
    90 stability
    91 state
    92 study
    93 system
    94 systems biology
    95 technique
    96 tempering
    97 tempering scheme
    98 validation
    99 variance
    100 schema:name Approximate parameter inference in systems biology using gradient matching: a comparative evaluation
    101 schema:pagination 80
    102 schema:productId N6c8f6ef0637c491b864173fd28da727b
    103 Nab0e7b6bf7424eddb90bc565d745b467
    104 Ne459241cbbb447b0bbc7c32d7b545671
    105 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013410920
    106 https://doi.org/10.1186/s12938-016-0186-x
    107 schema:sdDatePublished 2022-01-01T18:40
    108 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    109 schema:sdPublisher N2215c804257249a0b29f29ba9ea451aa
    110 schema:url https://doi.org/10.1186/s12938-016-0186-x
    111 sgo:license sg:explorer/license/
    112 sgo:sdDataset articles
    113 rdf:type schema:ScholarlyArticle
    114 N2215c804257249a0b29f29ba9ea451aa schema:name Springer Nature - SN SciGraph project
    115 rdf:type schema:Organization
    116 N24cffbe8b10042e984137be43b0bd496 schema:issueNumber Suppl 1
    117 rdf:type schema:PublicationIssue
    118 N40dee382fbcc494383bc5037a221188b rdf:first sg:person.01203321237.78
    119 rdf:rest Na2cec71762b04ee9894ab5389f0db91a
    120 N4cbacafd0e7f4ff39cd6ad3995b79bbc schema:volumeNumber 15
    121 rdf:type schema:PublicationVolume
    122 N5eb473d993a54ef0b4a19dc8501660c9 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
    123 schema:name Humans
    124 rdf:type schema:DefinedTerm
    125 N61f5a75126334fad937d7e541cf57dc1 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
    126 schema:name Systems Biology
    127 rdf:type schema:DefinedTerm
    128 N630f016a13a8481e8b8d8029e55acdf0 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
    129 schema:name Normal Distribution
    130 rdf:type schema:DefinedTerm
    131 N6c8f6ef0637c491b864173fd28da727b schema:name doi
    132 schema:value 10.1186/s12938-016-0186-x
    133 rdf:type schema:PropertyValue
    134 N6d5ae7e9eade4bfea17f0e65ba61d609 rdf:first sg:person.07706215665.03
    135 rdf:rest Nc26ab02e04704d6e9123b393aaa5ca7c
    136 N7a090e2db974482eb8cd3b3a2a285e89 rdf:first sg:person.01240064014.24
    137 rdf:rest N6d5ae7e9eade4bfea17f0e65ba61d609
    138 Na2cec71762b04ee9894ab5389f0db91a rdf:first sg:person.01366452107.31
    139 rdf:rest N7a090e2db974482eb8cd3b3a2a285e89
    140 Na5c64a7b5b284d9d9254a3f356de9ab1 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
    141 schema:name Likelihood Functions
    142 rdf:type schema:DefinedTerm
    143 Nab0e7b6bf7424eddb90bc565d745b467 schema:name pubmed_id
    144 schema:value 27454253
    145 rdf:type schema:PropertyValue
    146 Nc26ab02e04704d6e9123b393aaa5ca7c rdf:first sg:person.0601451763.91
    147 rdf:rest rdf:nil
    148 Ne459241cbbb447b0bbc7c32d7b545671 schema:name dimensions_id
    149 schema:value pub.1013410920
    150 rdf:type schema:PropertyValue
    151 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    152 schema:name Engineering
    153 rdf:type schema:DefinedTerm
    154 anzsrc-for:0903 schema:inDefinedTermSet anzsrc-for:
    155 schema:name Biomedical Engineering
    156 rdf:type schema:DefinedTerm
    157 sg:grant.3863303 http://pending.schema.org/fundedItem sg:pub.10.1186/s12938-016-0186-x
    158 rdf:type schema:MonetaryGrant
    159 sg:journal.1031014 schema:issn 1475-925X
    160 schema:name BioMedical Engineering OnLine
    161 schema:publisher Springer Nature
    162 rdf:type schema:Periodical
    163 sg:person.01203321237.78 schema:affiliation grid-institutes:grid.8756.c
    164 schema:familyName Macdonald
    165 schema:givenName Benn
    166 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01203321237.78
    167 rdf:type schema:Person
    168 sg:person.01240064014.24 schema:affiliation grid-institutes:grid.8756.c
    169 schema:familyName Rogers
    170 schema:givenName Simon
    171 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01240064014.24
    172 rdf:type schema:Person
    173 sg:person.01366452107.31 schema:affiliation grid-institutes:grid.8756.c
    174 schema:familyName Niu
    175 schema:givenName Mu
    176 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01366452107.31
    177 rdf:type schema:Person
    178 sg:person.0601451763.91 schema:affiliation grid-institutes:grid.8756.c
    179 schema:familyName Husmeier
    180 schema:givenName Dirk
    181 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0601451763.91
    182 rdf:type schema:Person
    183 sg:person.07706215665.03 schema:affiliation grid-institutes:grid.28848.3e
    184 schema:familyName Filippone
    185 schema:givenName Maurizio
    186 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03
    187 rdf:type schema:Person
    188 sg:pub.10.1007/978-3-319-11776-8_29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029034268
    189 https://doi.org/10.1007/978-3-319-11776-8_29
    190 rdf:type schema:CreativeWork
    191 sg:pub.10.1007/s11222-011-9234-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025354923
    192 https://doi.org/10.1007/s11222-011-9234-3
    193 rdf:type schema:CreativeWork
    194 grid-institutes:grid.28848.3e schema:alternateName EURECOM, Sophia Antipolis, France
    195 schema:name EURECOM, Sophia Antipolis, France
    196 rdf:type schema:Organization
    197 grid-institutes:grid.8756.c schema:alternateName School of Computing Science, University of Glasgow, Glasgow, G12 8RZ Scotland
    198 School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland
    199 schema:name School of Computing Science, University of Glasgow, Glasgow, G12 8RZ Scotland
    200 School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW Scotland
    201 rdf:type schema:Organization
     




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


    ...