Algebraic Properties of Cores of Generalized Neurofunctions View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-11-22

AUTHORS

F. Geche, O. Mulesa

ABSTRACT

This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems. More... »

PAGES

1-9

References to SciGraph publications

  • 1980-03. Algebraic aspects of threshold logic in CYBERNETICS AND SYSTEMS ANALYSIS
  • 2010. Fast Training of Neural Networks for Image Compression in ADVANCES IN DATA MINING. APPLICATIONS AND THEORETICAL ASPECTS
  • 2017-12-07. Formalization and Classification of Combinatorial Optimization Problems in OPTIMIZATION METHODS AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10559-018-0090-4

    DOI

    http://dx.doi.org/10.1007/s10559-018-0090-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1110125762


    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": "Uzhhorod National University", 
              "id": "https://www.grid.ac/institutes/grid.77512.36", 
              "name": [
                "Uzhhorod National University, Uzhhorod, Ukraine"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Geche", 
            "givenName": "F.", 
            "id": "sg:person.015705062152.54", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015705062152.54"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Uzhhorod National University", 
              "id": "https://www.grid.ac/institutes/grid.77512.36", 
              "name": [
                "Uzhhorod National University, Uzhhorod, Ukraine"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Mulesa", 
            "givenName": "O.", 
            "id": "sg:person.015023120657.87", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015023120657.87"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.talanta.2012.01.044", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001829309"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01069103", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012229267", 
              "https://doi.org/10.1007/bf01069103"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01069103", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012229267", 
              "https://doi.org/10.1007/bf01069103"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-14400-4_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020203265", 
              "https://doi.org/10.1007/978-3-642-14400-4_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-14400-4_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020203265", 
              "https://doi.org/10.1007/978-3-642-14400-4_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s1005-8885(10)60077-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042712912"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.15587/1729-4061.2015.54812", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1067985883"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1078563044", 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.15587/1729-4061.2017.108404", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1092108395"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-68640-0_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099813841", 
              "https://doi.org/10.1007/978-3-319-68640-0_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-68640-0_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099813841", 
              "https://doi.org/10.1007/978-3-319-68640-0_11"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018-11-22", 
        "datePublishedReg": "2018-11-22", 
        "description": "This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10559-018-0090-4", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1130475", 
            "issn": [
              "1060-0396", 
              "1573-8337"
            ], 
            "name": "Cybernetics and Systems Analysis", 
            "type": "Periodical"
          }
        ], 
        "name": "Algebraic Properties of Cores of Generalized Neurofunctions", 
        "pagination": "1-9", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "3d797f0a23362c475fe58c583f075ac311a342d1cf05c64608cee28d6e6e90aa"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10559-018-0090-4"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1110125762"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10559-018-0090-4", 
          "https://app.dimensions.ai/details/publication/pub.1110125762"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T08:11", 
        "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/v90/0000000270_0000000270/records_9671_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs10559-018-0090-4"
      }
    ]
     

    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/s10559-018-0090-4'

    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/s10559-018-0090-4'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10559-018-0090-4'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10559-018-0090-4'


     

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

    88 TRIPLES      21 PREDICATES      32 URIs      16 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10559-018-0090-4 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N87ac304dcc0546b885ab7ddd80c3fd49
    4 schema:citation sg:pub.10.1007/978-3-319-68640-0_11
    5 sg:pub.10.1007/978-3-642-14400-4_13
    6 sg:pub.10.1007/bf01069103
    7 https://app.dimensions.ai/details/publication/pub.1078563044
    8 https://doi.org/10.1016/j.talanta.2012.01.044
    9 https://doi.org/10.1016/s1005-8885(10)60077-5
    10 https://doi.org/10.15587/1729-4061.2015.54812
    11 https://doi.org/10.15587/1729-4061.2017.108404
    12 schema:datePublished 2018-11-22
    13 schema:datePublishedReg 2018-11-22
    14 schema:description This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems.
    15 schema:genre research_article
    16 schema:inLanguage en
    17 schema:isAccessibleForFree false
    18 schema:isPartOf sg:journal.1130475
    19 schema:name Algebraic Properties of Cores of Generalized Neurofunctions
    20 schema:pagination 1-9
    21 schema:productId N2cc4170c4b854e318811460da8c10d77
    22 N6cbd99415e30456f80f873616380a246
    23 Na2cb7202ba904e279655d9061c29501d
    24 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110125762
    25 https://doi.org/10.1007/s10559-018-0090-4
    26 schema:sdDatePublished 2019-04-11T08:11
    27 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    28 schema:sdPublisher N6fb2c9595c9849209560069f8e0be2e4
    29 schema:url https://link.springer.com/10.1007%2Fs10559-018-0090-4
    30 sgo:license sg:explorer/license/
    31 sgo:sdDataset articles
    32 rdf:type schema:ScholarlyArticle
    33 N2cc4170c4b854e318811460da8c10d77 schema:name doi
    34 schema:value 10.1007/s10559-018-0090-4
    35 rdf:type schema:PropertyValue
    36 N6cbd99415e30456f80f873616380a246 schema:name readcube_id
    37 schema:value 3d797f0a23362c475fe58c583f075ac311a342d1cf05c64608cee28d6e6e90aa
    38 rdf:type schema:PropertyValue
    39 N6fb2c9595c9849209560069f8e0be2e4 schema:name Springer Nature - SN SciGraph project
    40 rdf:type schema:Organization
    41 N87ac304dcc0546b885ab7ddd80c3fd49 rdf:first sg:person.015705062152.54
    42 rdf:rest Nd34aa99f52264575b47e96f7f6434e4a
    43 Na2cb7202ba904e279655d9061c29501d schema:name dimensions_id
    44 schema:value pub.1110125762
    45 rdf:type schema:PropertyValue
    46 Nd34aa99f52264575b47e96f7f6434e4a rdf:first sg:person.015023120657.87
    47 rdf:rest rdf:nil
    48 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    49 schema:name Mathematical Sciences
    50 rdf:type schema:DefinedTerm
    51 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    52 schema:name Pure Mathematics
    53 rdf:type schema:DefinedTerm
    54 sg:journal.1130475 schema:issn 1060-0396
    55 1573-8337
    56 schema:name Cybernetics and Systems Analysis
    57 rdf:type schema:Periodical
    58 sg:person.015023120657.87 schema:affiliation https://www.grid.ac/institutes/grid.77512.36
    59 schema:familyName Mulesa
    60 schema:givenName O.
    61 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015023120657.87
    62 rdf:type schema:Person
    63 sg:person.015705062152.54 schema:affiliation https://www.grid.ac/institutes/grid.77512.36
    64 schema:familyName Geche
    65 schema:givenName F.
    66 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015705062152.54
    67 rdf:type schema:Person
    68 sg:pub.10.1007/978-3-319-68640-0_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099813841
    69 https://doi.org/10.1007/978-3-319-68640-0_11
    70 rdf:type schema:CreativeWork
    71 sg:pub.10.1007/978-3-642-14400-4_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020203265
    72 https://doi.org/10.1007/978-3-642-14400-4_13
    73 rdf:type schema:CreativeWork
    74 sg:pub.10.1007/bf01069103 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012229267
    75 https://doi.org/10.1007/bf01069103
    76 rdf:type schema:CreativeWork
    77 https://app.dimensions.ai/details/publication/pub.1078563044 schema:CreativeWork
    78 https://doi.org/10.1016/j.talanta.2012.01.044 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001829309
    79 rdf:type schema:CreativeWork
    80 https://doi.org/10.1016/s1005-8885(10)60077-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042712912
    81 rdf:type schema:CreativeWork
    82 https://doi.org/10.15587/1729-4061.2015.54812 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067985883
    83 rdf:type schema:CreativeWork
    84 https://doi.org/10.15587/1729-4061.2017.108404 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092108395
    85 rdf:type schema:CreativeWork
    86 https://www.grid.ac/institutes/grid.77512.36 schema:alternateName Uzhhorod National University
    87 schema:name Uzhhorod National University, Uzhhorod, Ukraine
    88 rdf:type schema:Organization
     




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


    ...