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  • 1.
    Conder, Marston
    et al.
    University of Auckland, New Zealand.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system. National University of Ireland Maynooth, Co. Kildare, Ireland.
    New methods for finding minimum genus embeddings of graphs on orientable and non-orientable surfaces2019Inngår i: Ars Mathematica Contemporanea, ISSN 1855-3966, Vol. 17, nr 1, s. 1-35Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The question of how to find the smallest genus of all embeddings of a given finite connected graph on an orientable (or non-orientable) surface has a long and interesting history. In this paper we introduce four new approaches to help answer this question, in both the orientable and non-orientable cases. One approach involves taking orbits of subgroups of the automorphism group on cycles of particular lengths in the graph as candidates for subsets of the faces of an embedding. Another uses properties of an auxiliary graph defined in terms of compatibility of these cycles. We also present two methods that make use of integer linear programming, to help determine bounds for the minimum genus, and to find minimum genus embeddings. This work was motivated by the problem of finding the minimum genus of the Hoffman-Singleton graph, and succeeded not only in solving that problem but also in answering several other open questions.

  • 2.
    Griggs, Terry
    et al.
    The Open University, UK.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    On Pentagonal Geometries with Block Size 3, 4 or 52016Inngår i: Symmetries in Graphs, Maps, and Polytopes: 5th SIGMAP Workshop, West Malvern, UK, July 2014 / [ed] Jozef Širáň, Robert Jajcay, Springer, 2016, s. 147-157Kapittel i bok, del av antologi (Fagfellevurdert)
  • 3.
    Izquierdo, Milagros
    et al.
    Department of Mathematics, Linköping University, Linköping, Sweden.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Isometric point-circle configurations on surfaces from uniform maps2016Inngår i: Symmetries in Graphs, Maps, and Polytopes: 5th SIGMAP Workshop, West Malvern, UK, July 2014 / [ed] Jozef Širáň, Robert Jajcay, Springer, 2016, s. 201-212Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle v4 configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.

  • 4.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Irreducibility of configurations2016Inngår i: Ars Mathematica Contemporanea, ISSN 1855-3966, Vol. 10, nr 1, s. 169-181Artikkel i tidsskrift (Fagfellevurdert)
  • 5.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Patterns of ideals of numerical semigroups2016Inngår i: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 93, nr 1, s. 180-200Artikkel i tidsskrift (Fagfellevurdert)
  • 6.
    Stokes, Klara
    et al.
    Universitat Oberta de Catalunya, Barcelona, Spain .
    Bras-Amorós, Maria
    Universitat Rovira i Virgili, Tarragona, Spain .
    A Survey on the Use of Combinatorial Configurations for Anonymous Database Search2015Inngår i: Advanced Research in Data Privacy / [ed] Guillermo Navarro-Arribas, Vicenç Torra, Springer, 2015, s. 407-419Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    The peer-to-peer user-private information retrieval (P2P UPIR) protocol is an anonymous database search protocol in which the users collaborate in order to protect their privacy. This collaboration can be modelled by a combinatorial configuration. This chapter surveys currently available results on how to choose combinatorial configurations for P2P UPIR.

  • 7.
    Stokes, Klara
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Izquierdo, Milagros
    Department of Mathematics, Linköping University, Linköping Sweden.
    Geometric point-circle pentagonal geometries from Moore graphs2016Inngår i: Ars Mathematica Contemporanea, ISSN 1855-3966, Vol. 11, nr 1, s. 215-229Artikkel i tidsskrift (Fagfellevurdert)
  • 8.
    Stokes, Klara
    et al.
    Universitat Oberta de Catalunya, Barcelona, Spain.
    Torra, Vicenç
    Consejo Superior de Investigaciones Científicas (CSIC), Spain.
    Multiple releases of k-anonymous data sets and k-anonymous relational databases2012Inngår i: International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, ISSN 0218-4885, Vol. 20, nr 6, s. 839-853Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In data privacy, the evaluation of the disclosure risk has to take into account the fact that several releases of the same or similar information about a population are common. In this paper we discuss this issue within the scope of k-anonymity. We also show how this issue is related to the publication of privacy protected databases that consist of linked tables. We present algorithms for the implementation of k-anonymity for this type of data.

  • 9.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Tarragona, Spain.
    Torra, Vicenç
    Universitat Autònoma de Barcelona (UAB), Spain.
    On some clustering approaches for graphs2011Inngår i: Fuzzy Systems (FUZZ), 2011, IEEE conference proceedings, 2011, s. 409-415Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we discuss some tools for graph perturbation with applications to data privacy. We present and analyse two different approaches. One is based on matrix decomposition and the other on graph partitioning. We discuss these methods and show that they belong to two traditions in data protection: noise addition/microaggregation and k-anonymity.

  • 10.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Tarragona, Spain.
    Torra, Vicenç
    Universitat Autònoma de Barcelona (UAB), Spain.
    On the Relationship Between Clustering and Coding Theory2012Inngår i: 2012 IEEE International Conference on Fuzzy Systems: Brisbane, Australia (June 10-15, 2012) / [ed] Hussein Abbass, Daryl Essam & Ruhul Sarker, IEEE conference proceedings, 2012, s. Article number 6250783-Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we discuss the relations between clustering and error correcting codes. We show that clustering can be used for constructing error correcting codes. We review the previous works found in the literature about this issue, and propose a modification of a previous work that can be used for code construction from a set of proposed codewords.

  • 11.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
    Torra, Vicenç
    IIIA, Institut d’Investigació en Intel ligència Artificial CSIC, Consejo Superior de Investigaciones Científicas, Bellaterra, Catalonia, Spain.
    Reidentification and k-anonymity: a model for disclosure risk in graphs2012Inngår i: Soft Computing - A Fusion of Foundations, Methodologies and Applications, ISSN 1432-7643, E-ISSN 1433-7479, Vol. 16, nr 10, s. 1657-1670Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modeling the anonymity of a database table and we prove that n-confusion is a generalization of k-anonymity. After a short survey on the different available definitions of k-anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k, l)-anonymous graph. Our definition of (k, l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally, we provide a set of algorithms for k-anonymization of graphs.

  • 12.
    Torra, Vicenç
    et al.
    Högskolan i Skövde, Institutionen för informationsteknologi. Högskolan i Skövde, Forskningscentrum för Informationsteknologi.
    Navarro-Arribas, Guillermo
    Universitat Autònoma de Barcelona, Barcelona, Spain.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    An Overview of the Use of Clustering for Data Privacy2016Inngår i: Unsupervised Learning Algorithms / [ed] M. Emre Celebi, Kemal Aydin, Springer, 2016, s. 237-251Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this chapter we review some of our results related to the use of clustering in the area of data privacy. The paper gives a brief overview of data privacy and, more specifically, on data driven methods for data privacy and discusses where clustering can be applied in this setting. We discuss the role of clustering in the definition of masking methods, and on the calculation of information loss and data utility.

  • 13.
    Torra, Vicenç
    et al.
    Högskolan i Skövde, Institutionen för informationsteknologi. Högskolan i Skövde, Forskningscentrum för Informationsteknologi.
    Navarro-Arribas, Guillermo
    Universitat Autònoma de Barcelona, Campus UAB, Bellaterra, Spain.
    Stokes, Klara
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Data privacy2019Inngår i: Data science in Practice / [ed] Alan Said, Vicenç Torra, Springer, 2019, s. 121-132Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this chapter we present an overview of the topic data privacy. We review privacy models and measures of disclosure risk. These models and measures provide computational definitions of what privacy means, and of how to evaluate the privacy level of a data set. Then, we give a summary of data protection mechanisms. We provide a classification of these methods according to three dimensions: whose privacy is being sought, the computations to be done, and the number of data sources. Finally, we describe masking methods. Such methods are the data protection mechanisms used for databases when the data use is undefined and the protected database is required to be useful for several data uses. We also provide a definition of information loss (or data utility) for this type of data protection mechanism. The chapter finishes with a summary.

  • 14.
    Torra, Vicenç
    et al.
    Institut d'Investigacío en Intellig̀encia Artificial, Consejo Superior de Investigaciones Cient́ficas, Universitat Aut̀onoma de Barcelona, Bellaterra, Catalonia, Spain.
    Stokes, Klara
    Departments of Computer Science and Mathematics, Universitat Rovira i Virgili, Tarragona, Spain / UNESCO Chair in Data Privacy, Tarragona, Catalonia, Spain.
    Narukawa, Yasuo
    Toho Gakuen, Tokyo, Japan / Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan.
    An extension of fuzzy measures to multisets and its relation to distorted probabilities2012Inngår i: IEEE transactions on fuzzy systems, ISSN 1063-6706, E-ISSN 1941-0034, Vol. 20, nr 6, s. 1032-1045Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Fuzzy measures are monotonic set functions on a reference set; they generalize probabilities replacing the additivity condition by monotonicity. The typical application of these measures is with fuzzy integrals. Fuzzy integrals integrate a function with respect to a fuzzy measure, and they can be used to aggregate information from a set of sources (opinions from experts or criteria in a multicriteria decision-making problem). In this context, background knowledge on the sources is represented by means of the fuzzy measures. For example, interactions between criteria are represented by means of nonadditive measures. In this paper, we introduce fuzzy measures on multisets. We propose a general definition, and we then introduce a family of fuzzy measures for multisets which we show to be equivalent to distorted probabilities when the multisets are restricted to proper sets

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