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  • 51. Ahlberg, Ragnar
    et al.
    Gustafsson, Bertil
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A note on parallel algorithms for partial differential equations1984Ingår i: Parallel Computing: 83, Amsterdam, The Netherlands: Elsevier Science , 1984, s. 93-98Konferensbidrag (Refereegranskat)
  • 52.
    Ahlkrona, Josefin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Computational Ice Sheet Dynamics: Error control and efficiency2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated.

    Delarbeten
    1. A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    Öppna denna publikation i ny flik eller fönster >>A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    2013 (Engelska)Ingår i: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, s. 417-435Artikel i tidskrift (Refereegranskat) Published
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:uu:diva-205727 (URN)10.1093/qjmam/hbt009 (DOI)000327457200001 ()
    Projekt
    eSSENCE
    Tillgänglig från: 2013-08-09 Skapad: 2013-08-22 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
    2. Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    Öppna denna publikation i ny flik eller fönster >>Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    2013 (Engelska)Ingår i: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, s. 2135-2152Artikel i tidskrift (Refereegranskat) Published
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:uu:diva-213571 (URN)10.5194/gmd-6-2135-2013 (DOI)000329050500017 ()
    Projekt
    eSSENCE
    Tillgänglig från: 2013-12-19 Skapad: 2013-12-28 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
    3. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    Öppna denna publikation i ny flik eller fönster >>Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    2016 (Engelska)Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, s. 1-19Artikel i tidskrift (Refereegranskat) Published
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:uu:diva-269822 (URN)10.1016/j.jcp.2015.12.025 (DOI)000369086700001 ()
    Projekt
    eSSENCE
    Tillgänglig från: 2015-12-17 Skapad: 2015-12-18 Senast uppdaterad: 2017-12-01Bibliografiskt granskad
    4. The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    Öppna denna publikation i ny flik eller fönster >>The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    2016 (Engelska)Rapport (Övrigt vetenskapligt)
    Serie
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-006
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:uu:diva-283438 (URN)
    Projekt
    eSSENCE
    Tillgänglig från: 2016-04-19 Skapad: 2016-04-13 Senast uppdaterad: 2016-05-16Bibliografiskt granskad
    5. A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    Öppna denna publikation i ny flik eller fönster >>A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    2016 (Engelska)Rapport (Övrigt vetenskapligt)
    Serie
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-005
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:uu:diva-283437 (URN)
    Projekt
    eSSENCE
    Tillgänglig från: 2016-04-19 Skapad: 2016-04-13 Senast uppdaterad: 2016-05-16Bibliografiskt granskad
  • 53.
    Ahlkrona, Josefin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation2016Rapport (Övrigt vetenskapligt)
  • 54.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling2013Ingår i: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, s. 417-435Artikel i tidskrift (Refereegranskat)
  • 55.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A numerical study of the validity of Shallow Ice Approximations2012Rapport (Övrigt vetenskapligt)
  • 56.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Accuracy of the zeroth and second order shallow ice approximation: numerical and theoretical results2013Ingår i: Geoscientific Model Development Discussions, ISSN 1991-9611, E-ISSN 1991-962X, Vol. 6, s. 4281-4325Artikel i tidskrift (Övrigt vetenskapligt)
  • 57.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results2013Ingår i: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, s. 2135-2152Artikel i tidskrift (Refereegranskat)
  • 58.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Lötstedt, Per
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Kirchner, Nina
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, s. 1-19Artikel i tidskrift (Refereegranskat)
  • 59.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Shcherbakov, Victor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2017Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, s. 633-649Artikel i tidskrift (Refereegranskat)
  • 60.
    Ahlkrona, Josefin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Shcherbakov, Victor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2016Rapport (Övrigt vetenskapligt)
  • 61.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    A zero-one law for l-colourable structures with a vectorspace pregeometry2012Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 62.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Combinatorial geometries in model theory2009Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Model theory and combinatorial pregeometries are closely related throughthe so called algebraic closure operator on strongly minimal sets. Thestudy of projective and ane pregeometries are especially interestingsince they have a close relation to vectorspaces. In this thesis we willsee how the relationship occur and how model theory can concludea very strong classi cation theorem which divides pregeometries withcertain properties into projective, ane and degenerate (trivial) cases.

  • 63.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Homogenizable structures and model completeness2016Ingår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, nr 7-8, s. 977-995Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

  • 64.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    >k-homogeneous infinite graphs2018Ingår i: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, s. 160-174Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we give an explicit classification for the countably infinite graphs G which are, for some k, ≥k-homogeneous. It turns out that a ≥k  -homogeneous graph M is non-homogeneous if and only if it is either not 1-homogeneous or not 2-homogeneous, both cases which may be classified using ramsey theory.

  • 65.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Limit Laws, Homogenizable Structures and Their Connections2018Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis is in the field of mathematical logic and especially model theory. The thesis contain six papers where the common theme is the Rado graph R. Some of the interesting abstract properties of R are that it is simple, homogeneous (and thus countably categorical), has SU-rank 1 and trivial dependence. The Rado graph is possible to generate in a probabilistic way. If we let K be the set of all finite graphs then we obtain R as the structure which satisfy all properties which hold with assymptotic probability 1 in K. On the other hand, since the Rado graph is homogeneous, it is also possible to generate it as a Fraïssé-limit of its age.

    Paper I studies the binary structures which are simple, countably categorical, with SU-rank 1 and trivial algebraic closure. The main theorem shows that these structures are all possible to generate using a similar probabilistic method which is used to generate the Rado graph. Paper II looks at the simple homogeneous structures in general and give certain technical results on the subsets of SU-rank 1.

    Paper III considers the set K consisting of all colourable structures with a definable pregeometry and shows that there is a 0-1 law and almost surely a unique definable colouring. When generating the Rado graph we almost surely have only rigid structures in K. Paper IV studies what happens if the structures in K are only the non-rigid finite structures. We deduce that the limit structures essentially try to stay as rigid as possible, given the restriction, and that we in general get a limit law but not a 0-1 law.

    Paper V looks at the Rado graph's close cousin the random t-partite graph and notices that this structure is not homogeneous but almost homogeneous. Rather we may just add a definable binary predicate, which hold for any two elemenets which are in the same part, in order to make it homogeneous. This property is called being homogenizable and in Paper V we do a general study of homogenizable structures. Paper VI conducts a special case study of the homogenizable graphs which are the closest to being homogeneous, providing an explicit classification of these graphs.

    Delarbeten
    1. Simple structures axiomatized by almost sure theories
    Öppna denna publikation i ny flik eller fönster >>Simple structures axiomatized by almost sure theories
    2016 (Engelska)Ingår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, nr 5, s. 435-456Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    In this article we give a classification of the binary, simple, ω-categorical structures with SU-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as ω-stability or strong minimality.

    Nyckelord
    Random structure, Almost sure theory, Pregeometry, Supersimple, Countably categorical
    Nationell ämneskategori
    Algebra och logik
    Forskningsämne
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-276995 (URN)10.1016/j.apal.2016.02.001 (DOI)000372680500001 ()
    Tillgänglig från: 2016-03-01 Skapad: 2016-02-17 Senast uppdaterad: 2017-11-30Bibliografiskt granskad
    2. On sets with rank one in simple homogeneous structures
    Öppna denna publikation i ny flik eller fönster >>On sets with rank one in simple homogeneous structures
    2015 (Engelska)Ingår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, s. 223-250Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

    Nyckelord
    model theory, homogeneous structure, simple theory, pregeometry, rank, reduct, random structure
    Nationell ämneskategori
    Algebra och logik
    Forskningsämne
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-243006 (URN)10.4064/fm228-3-2 (DOI)000352858400002 ()
    Tillgänglig från: 2015-02-03 Skapad: 2015-02-03 Senast uppdaterad: 2017-12-05Bibliografiskt granskad
    3. Random l-colourable structures with a pregeometry
    Öppna denna publikation i ny flik eller fönster >>Random l-colourable structures with a pregeometry
    2017 (Engelska)Ingår i: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, nr 1-2, s. 32-58Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    We study finite -colourable structures with an underlying pregeometry. The probability measure that is usedcorresponds to a process of generating such structures by which colours are first randomly assigned to all1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions aresatisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure,where we now forget the specific colouring of the generating process, has a given property. With this measurewe get the following results: (1) A zero-one law. (2) The set of sentences with asymptotic probability 1 has anexplicit axiomatisation which is presented. (3) There is a formula ξ (x, y) (not directly speaking about colours)such that, with asymptotic probability 1, the relation “there is an -colouring which assigns the same colourto x and y” is defined by ξ (x, y). (4) With asymptotic probability 1, an -colourable structure has a unique-colouring (up to permutation of the colours).

    Ort, förlag, år, upplaga, sidor
    Wiley-VCH Verlagsgesellschaft, 2017
    Nationell ämneskategori
    Algebra och logik
    Forskningsämne
    Matematisk logik
    Identifikatorer
    urn:nbn:se:uu:diva-321515 (URN)10.1002/malq.201500006 (DOI)000400361900003 ()
    Tillgänglig från: 2017-05-06 Skapad: 2017-05-06 Senast uppdaterad: 2017-11-28Bibliografiskt granskad
    4. Limit laws and automorphism groups of random nonrigid structures
    Öppna denna publikation i ny flik eller fönster >>Limit laws and automorphism groups of random nonrigid structures
    2015 (Engelska)Ingår i: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, nr 2, s. 1-53, artikel-id 1Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

    Nyckelord
    finite model theory, limit law, zero-one law, random structure, automorphism group
    Nationell ämneskategori
    Algebra och logik
    Forskningsämne
    Matematisk logik
    Identifikatorer
    urn:nbn:se:uu:diva-248078 (URN)10.4115/jla.2015.7.2 (DOI)000359802400001 ()
    Tillgänglig från: 2015-03-26 Skapad: 2015-03-26 Senast uppdaterad: 2017-12-04Bibliografiskt granskad
    5. Homogenizable structures and model completeness
    Öppna denna publikation i ny flik eller fönster >>Homogenizable structures and model completeness
    2016 (Engelska)Ingår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, nr 7-8, s. 977-995Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

    Nyckelord
    Homogenizable, Model-complete, Amalgamation class, Quantifier-elimination
    Nationell ämneskategori
    Algebra och logik
    Forskningsämne
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-303714 (URN)10.1007/s00153-016-0507-6 (DOI)000385155700010 ()
    Tillgänglig från: 2016-09-22 Skapad: 2016-09-22 Senast uppdaterad: 2017-11-28Bibliografiskt granskad
    6. >k-homogeneous infinite graphs
    Öppna denna publikation i ny flik eller fönster >>>k-homogeneous infinite graphs
    2018 (Engelska)Ingår i: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, s. 160-174Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    In this article we give an explicit classification for the countably infinite graphs G which are, for some k, ≥k-homogeneous. It turns out that a ≥k  -homogeneous graph M is non-homogeneous if and only if it is either not 1-homogeneous or not 2-homogeneous, both cases which may be classified using ramsey theory.

    Nyckelord
    >k-homomogeneous, countably infinite graph
    Nationell ämneskategori
    Algebra och logik
    Forskningsämne
    Matematisk logik
    Identifikatorer
    urn:nbn:se:uu:diva-329362 (URN)10.1016/j.jctb.2017.08.007 (DOI)000417771100009 ()
    Tillgänglig från: 2017-09-26 Skapad: 2017-09-26 Senast uppdaterad: 2018-04-05Bibliografiskt granskad
  • 66.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Simple structures axiomatized by almost sure theories2016Ingår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, nr 5, s. 435-456Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we give a classification of the binary, simple, ω-categorical structures with SU-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as ω-stability or strong minimality.

  • 67.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    To infinity and back: Logical limit laws and almost sure theories2014Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
  • 68.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Limit laws and automorphism groups of random nonrigid structures2015Ingår i: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, nr 2, s. 1-53, artikel-id 1Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

  • 69.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On sets with rank one in simple homogeneous structures2015Ingår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, s. 223-250Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

  • 70.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Random l-colourable structures with a pregeometry2017Ingår i: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, nr 1-2, s. 32-58Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study finite -colourable structures with an underlying pregeometry. The probability measure that is usedcorresponds to a process of generating such structures by which colours are first randomly assigned to all1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions aresatisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure,where we now forget the specific colouring of the generating process, has a given property. With this measurewe get the following results: (1) A zero-one law. (2) The set of sentences with asymptotic probability 1 has anexplicit axiomatisation which is presented. (3) There is a formula ξ (x, y) (not directly speaking about colours)such that, with asymptotic probability 1, the relation “there is an -colouring which assigns the same colourto x and y” is defined by ξ (x, y). (4) With asymptotic probability 1, an -colourable structure has a unique-colouring (up to permutation of the colours).

  • 71.
    Ahlsén, Daniel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Classifying Categories: The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 72.
    Ahlsén, Daniel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Limitless Analysis2014Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
  • 73. Ahmad, Fayyaz
    et al.
    Al-Aidarous, Eman S.
    Alrehaili, Dina A.
    Ekström, Sven-Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Furci, Isabella
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?2018Ingår i: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 78, s. 867-893Artikel i tidskrift (Refereegranskat)
  • 74. Ahmad, Fayyaz
    et al.
    Al-Aidarous, Eman S.
    Alrehaili, Dina A.
    Ekström, Sven-Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Furci, Isabella
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?2017Rapport (Övrigt vetenskapligt)
  • 75. Ahmad, Fayyaz
    et al.
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Zaka Ullah, Malik
    Al-Fhaid, A. Saleh
    A family of iterative methods for solving systems of nonlinear equations having unknown multiplicity2016Ingår i: Algorithms, ISSN 1999-4893, E-ISSN 1999-4893, Vol. 9, s. 5:1-10, artikel-id 5Artikel i tidskrift (Refereegranskat)
  • 76. Ahmad, Fayyaz
    et al.
    Soleymani, Fazlollah
    Khaksar Haghani, Farhad
    Serra-Capizzano, Stefano
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations2017Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 314, s. 199-211Artikel i tidskrift (Refereegranskat)
  • 77.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A homogeneity test of large dimensional covariance matrices under non-normality2018Ingår i: Kybernetika (Praha), ISSN 0023-5954, E-ISSN 1805-949X, Vol. 54, nr 5, s. 908-920Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as U-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.

  • 78.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A significance test of the RV coefficient in high dimensions2019Ingår i: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 131, s. 116-130Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The RV coefficient is an important measure of linear dependence between two multivariate data vectors. Using unbiased and computationally efficient estimators of its components, a modification to the RV coefficient is proposed, and used to construct a test of significance for the true coefficient. The modified estimator improves the accuracy of the original and, along with the test, can be applied to data with arbitrarily large dimensions, possibly exceeding the sample size, and the underlying distribution need only have finite fourth moment. Exact and asymptotic properties are studied under fairly general conditions. The accuracy of the modified estimator and the test is shown through simulations under a variety of parameter settings. In comparisons against several existing methods, both the proposed estimator and the test exhibit similar performance to the distance correlation. Several real data applications are also provided.

  • 79.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A unified approach to testing mean vectors with large dimensions2019Ingår i: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 103, nr 4, s. 593-618Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance matrices. Beginning with one-sample case, the construction of tests, underlying assumptions and asymptotic theory, is systematically extended to multi-sample case. Tests are defined in terms of U-statistics-based consistent estimators, and their limits are derived under a few mild assumptions. Accuracy of the tests is shown through simulations. Real data applications, including a five-sample unbalanced MANOVA analysis on count data, are also given.

  • 80.
    Ahmad, M Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Generalized tests of correlation for vectors with large dimensions using modified RV coefficient2019Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Tests of zero correlation between two or more vectors with large dimension, possibly largerthan the sample size, are considered when the data may not necessarily follow a normal distribution. A single sample case for several vectors is rst proposed, which is then extended tothe common covariance matrix under the assumption of homogeneity across several independentpopulations. The test statistics are constructed using a recently proposed modicationof the RV coecient for high-dimensional vectors. The accuracy of the tests is shown through simulations.

  • 81.
    Ahmad, M Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Location-invariant and non-invariant tests for large dimensional covariance matrices under normality and non-normality2014Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Test statistics for homogeneity, sphericity and identity of high-dimensional covariance matrices are presented under a wide variety of very general conditions when the dimension of the vector, $p$, may exceed the sample size, $n_i$, $i = 1, \ldots, g$. First, location-invariant tests are presented under normality assumption, followed by their robustness to normality by replacing the normality assumption with a mild alternative multivariate model. The two types of tests are then presented in non-invariant form, again under normality and non-normality. Tests of homogeneity of covariance matrices in all cases are immediately supplemented by the tests for sphericity and identity of the common covariance matrix under the null hypothesis. Both location-invariant and non-invariant tests are composed of estimators that are defined as $U$-statistics with kernels of different degrees. Hence, the asymptotic theory of $U$-statistics is employed to arrive at the limiting null and alternative distributions of tests for all cases. These limit distributions are derived using a very mild and practically viable set of assumptions mainly on the traces of the unknown covariance matrices. Finally, corrections and improvements of a few other tests are also presented.

  • 82.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension2017Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 44, nr 2, s. 500-523Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For two or more multivariate distributions with common covariance matrix, test statistics for certain special structures of the common covariance matrix are presented when the dimension of the multivariate vectors may exceed the number of such vectors. The test statistics are constructed as functions of location-invariant estimators defined as U-statistics, and the corresponding asymptotic theory is used to derive the limiting distributions of the proposed tests. The properties of the test statistics are established under mild and practical assumptions, and the same are numerically demonstrated using simulation results with small or moderate sample sizes and large dimensions.

  • 83.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Location-invariant tests of homogeneity of large-dimensional covariance matrices2017Ingår i: Journal of Statistical Theory and Practice, ISSN 1559-8608, E-ISSN 1559-8616, Vol. 11, nr 4, s. 731-745Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A test statistic for homogeneity of two or more covariance matrices of large dimensions is presented when the data are multivariate normal. The statistic is location-invariant and defined as a function of U-statistics of non-degenerate kernels so that the corresponding asymptotic theory is employed to derive the limiting normal distribution of the test under a few mild and practical assumptions. Accuracy of the test is shown through simulations with different parameter settings.

  • 84.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Multiple comparisons of mean vectors with large dimension under general conditions2019Ingår i: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, nr 6, s. 1044-1059Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Multiple comparisons for two or more mean vectors are considered when the dimension of the vectors may exceed the sample size, the design may be unbalanced, populations need not be normal, and the true covariance matrices may be unequal. Pairwise comparisons, including comparisons with a control, and their linear combinations are considered. Under fairly general conditions, the asymptotic multivariate distribution of the vector of test statistics is derived whose quantiles can be used in multiple testing. Simulations are used to show the accuracy of the tests. Real data applications are also demonstrated.

  • 85.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen. Uppsala Univ, Dept Stat, Uppsala, Sweden.
    On Testing Sphericity and Identity of a Covariance Matrix with Large Dimensions2016Ingår i: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 25, nr 2, s. 121-132Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Tests for certain covariance structures, including sphericity, are presented when the data may be high-dimensional but not necessarily normal. The tests are formulated as functions of location-invariant estimators defined as U-statistics of higher order kernels. Under a few mild assumptions, the limit distributions of the tests are shown to be normal. The accuracy of the tests is demonstrated by simulations.

  • 86.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality2017Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, nr 8, s. 3738-3753Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A test for homogeneity of g 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n(i), i = 1, ..., g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n(i), p . Under the null hypothesis, the test is extended for common covariance matrix to be of a specified structure, including sphericity. Theory of U-statistics is employed in constructing the tests and deriving their limits. Simulations are used to show the accuracy of tests.

  • 87.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Tests for independence of vectors with large dimension2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Given a random sample of n iid vectors, each of dimension p and partitioned into b sub- vectors of sizes pi, i = 1;:::;b. Location-invariant and non-invariant test statistics for independence of sub-vectors are presented when pi may exceed n and the distribution need not be normal. The tests are composed of U -statistics based estimators of the Frobenius norm of the di erence between the null and alternative hypotheses. Asymptotic distributions of the tests are provided for n;pi! 1, where their nite-sample performance is demonstrated through simulations. Some related and subsequent tests are brie y described. Relations of the proposed tests to certain multivariate measures are discussed, which are of interest on their own.

  • 88.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Tests of Zero Correlation Using Modified RV Coefficient for High-Dimensional Vectors2019Ingår i: Journal of Statistical Theory and Practice, ISSN 1559-8608, E-ISSN 1559-8616, Vol. 13, nr 3, artikel-id 43Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Tests of zero correlation between two or more vectors with large dimension, possibly larger than the sample size, are considered when the data may not necessarily follow a normal distribution. A single-sample case for several vectors is first proposed, which is then extended to the common covariance matrix under the assumption of homogeneity across several independent populations. The test statistics are constructed using a recently proposed modification of the RV coefficient (a correlation coefficient for vector-valued random variables) for high-dimensional vectors. The accuracy of the tests is shown through simulations.

  • 89.
    Ahmad, M. Rauf
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Pavlenko, Tatjana
    KTH, Stockholm, Sweden.
    A U-classifier for high-dimensional data under non-normality2018Ingår i: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 167, s. 269-283Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A classifier for two or more samples is proposed when the data are high-dimensional and the distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable components, the U-component and the P-component. The U-component is a linear combination of U-statistics of bilinear forms of pairwise distinct vectors from independent samples. The P-component, the discriminant score, is a function of the projection of the U-component on the observation to be classified. Together, the two components constitute an inherently bias-adjusted classifier valid for high-dimensional data. The classifier is linear but its linearity does not rest on the assumption of homoscedasticity. Properties of the classifier and its normal limit are given under mild conditions. Misclassification errors and asymptotic properties of their empirical counterparts are discussed. Simulation results are used to show the accuracy of the proposed classifier for small or moderate sample sizes and large dimensions. Applications involving real data sets are also included.

  • 90.
    Ahmad, M. Rauf
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    von Rosen, D.
    Tests for high-dimensional covariance matrices using the theory of U-statistics2015Ingår i: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 85, nr 13, s. 2619-2631Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

  • 91.
    Ahmad, M. Rauf
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Von Rosen, Dietrich
    Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality2015Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, nr 7, s. 1387-1398Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp >> n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.

  • 92.
    Ahmady Phoulady, Hady
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Brownian Motions and Scaling Limits of Random Trees2011Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 93.
    Ahmady Phoulady, Hady
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och tillämpad matematik.
    Monte Carlo Methods in American Put Option Pricing2011Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 94.
    Al Homsi, Rania
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Equation Solving in Indian Mathematics2018Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
  • 95.
    Albahaca, Juan Carlos
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Analytical and Numerical Study of the Poincaré Map with Applications on the Computation of Periodic Orbits2015Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
  • 96.
    Aldberg, Henrik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Bond Pricing in Stochastic Volatility Models2008Självständigt arbete på avancerad nivå (magisterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 97. Alfredsson, Lena
    et al.
    Bråting, Kajsa
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Fakulteten för utbildningsvetenskaper, Institutionen för pedagogik, didaktik och utbildningsstudier.
    Erixon, Patrik
    Heikne, Hans
    Matematik 5000, kurs 1b2011Bok (Övrig (populärvetenskap, debatt, mm))
  • 98. Alfredsson, Lena
    et al.
    Bråting, Kajsa
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Fakulteten för utbildningsvetenskaper, Institutionen för pedagogik, didaktik och utbildningsstudier.
    Erixon, Patrik
    Heikne, Hans
    Matematik 5000, kurs 2c2012Bok (Övrig (populärvetenskap, debatt, mm))
  • 99. Alfredsson, Lena
    et al.
    Bråting, Kajsa
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Fakulteten för utbildningsvetenskaper, Institutionen för pedagogik, didaktik och utbildningsstudier.
    Erixon, Patrik
    Heikne, Hans
    Matematik 5000, kurs 42013Bok (Övrig (populärvetenskap, debatt, mm))
  • 100.
    Alghamdi, Azza
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Approximation of pluricomplex Green functions: A probabilistic approach2018Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This PhD thesis focuses on probabilistic methods of approximation of pluricomplex Green functions and is based on four papers.

    The thesis begins with a general introduction to the use of pluricomplex Green functions in multidimensional complex analysis and a review of their main properties. This is followed by short description of the main results obtained in the enclosed papers.

    In Paper I, we study properties of the metric space of pluriregular sets, that is zero sets of continuous pluricomplex Green functions. The best understood non-trivial examples of such sets are composite Julia sets, obtained by iteration of finite families of polynomial mappings in several complex variables. We prove that the so-called chaos game is applicable in the case of such sets. We also visualize some composite Julia sets using escape time functions and Monte Carlo simulation.

    In Paper II, we extend results in Paper I to the case of infinite compact families of proper polynomials mappings. With composition as the semigroup operation, we generate families of infinite iterated function systems with compact attractors. We show that such attractors can be approximated probabilistically in a manner of the classic chaos game.

    In Paper III, we study numerical approximation and visualisation of pluricomplex Green functions based on the Monte-Carlo integration. Unlike alternative methods that rely on locating a sequence of carefully chosen finite sets of points satisfying some optimal conditions for approximation purposes, our approach is simpler and more direct by relying on generation of pseudorandom points. We examine numerically the errors of approximation for some simple geometric shapes for which the pluricomplex Green functions are known. If the pluricomplex Green functions are not known, the errors in Monte Carlo integration can be expressed with the aid of statistics in terms of confidence intervals.

    Finally, in Paper IV, we study how perturbations of an orthonomalization procedure influence the resulting approximate Bergman functions. To this end we consider the concept of near orthonormality of a finite set of vectors in an inner product space, understood as closeness of the Gram matrix of those vectors to the identity matrix. We provide estimates for the errors resulting from using nearly orthogonal bases instead of orthogonal ones. The motivation for this work comes from Paper III: when Gram matrices are calculated via Monte Carlo integration, the outcomes of standard orthogonalisation algorithms are nearly orthonormal bases.

    Delarbeten
    1. Probabilistic approximation of partly filled-in composite Julia sets
    Öppna denna publikation i ny flik eller fönster >>Probabilistic approximation of partly filled-in composite Julia sets
    2017 (Engelska)Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, nr 3, s. 203-220Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.

    Nyckelord
    composite Julia sets, pluricomplex Green functions, iterated function system, the chaos game, complex dynamics, Monte-Carlo simulation
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-339527 (URN)10.4064/ap4100-8-2017 (DOI)000417986400002 ()
    Tillgänglig från: 2018-01-22 Skapad: 2018-01-22 Senast uppdaterad: 2018-07-06Bibliografiskt granskad
    2. Attractors of compactly generated semigroups of regular polynomial mappings.
    Öppna denna publikation i ny flik eller fönster >>Attractors of compactly generated semigroups of regular polynomial mappings.
    2018 (Engelska)Ingår i: Complexity, ISSN 1076-2787, E-ISSN 1099-0526, artikel-id 5698021Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    We investigate the metric space of pluriregular sets as well as the contractions on that space induced by infinite compact families of proper polynomial mappings of several complex variables. The topological semigroups generated by such families, with composition as the semigroup operation, lead to the constructions of a variety of Julia-type pluriregular sets. The generating families can also be viewed as infinite iterated function systems with compact attractors. We show that such attractors can be approximated both deterministically and probabilistically in a manner of the classic chaos game.

    Nyckelord
    Julia sets, pluricomplex Green function, iterated function systems
    Nationell ämneskategori
    Matematisk analys
    Identifikatorer
    urn:nbn:se:uu:diva-355806 (URN)10.1155/2018/5698021 (DOI)000450216100001 ()
    Tillgänglig från: 2018-07-05 Skapad: 2018-07-05 Senast uppdaterad: 2018-12-19Bibliografiskt granskad
    3. Approximation of pluricomplex Green functions based on Monte Carlo integration
    Öppna denna publikation i ny flik eller fönster >>Approximation of pluricomplex Green functions based on Monte Carlo integration
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Nyckelord
    Pluricomplex Green functions, pluriregular sets, Bernstein-Markov property, orthogonal polynomials, Monte Carlo simulation
    Nationell ämneskategori
    Beräkningsmatematik
    Forskningsämne
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-355808 (URN)
    Tillgänglig från: 2018-07-05 Skapad: 2018-07-05 Senast uppdaterad: 2018-07-06
    4. Bergman Functions and Nearly Orthonormal Polynomials
    Öppna denna publikation i ny flik eller fönster >>Bergman Functions and Nearly Orthonormal Polynomials
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Nyckelord
    Bergman function, nearly orthonormal polynomials, orthogonal polynomials, Monte Carlo simulation.
    Nationell ämneskategori
    Matematisk analys
    Identifikatorer
    urn:nbn:se:uu:diva-355809 (URN)
    Tillgänglig från: 2018-07-05 Skapad: 2018-07-05 Senast uppdaterad: 2018-07-06
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