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  • 1.
    Aboud, Mathilde
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Philosophy of mathematics in “La Science et l’Hypothèse”, from Henri Poincaré.2017Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
  • 2.
    Abouzaid, Mohammed
    et al.
    Columbia Univ, Dept Math, New York, NY 10027 USA.
    Kragh, Thomas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On the immersion classes of nearby Lagrangians2016Ingår i: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 9, nr 1, s. 232-244Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of Lagrangian immersions by Lagrangian embeddings, which, unlike previous obstructions, is sensitive to information that cannot be detected by Floer cochains. We show this by providing a concrete computation in the case of spheres.

  • 3.
    Abrahamsson, Linda
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Statistical models of breast cancer tumour growth for mammography screening data2012Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 4. Abramovic, A.
    et al.
    Pecaric, J.
    Persson, Lars-Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik.
    Varosanec, S.
    General inequalities via isotonic subadditive functionals2007Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, s. 15-28Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Hö̈lder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

  • 5.
    Aceto, Paolo
    et al.
    Alfred Renyi Inst Math, 13-15 Realtanoda U, H-1053 Budapest, Hungary..
    Golla, Marco
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Dehn surgeries and rational homology2017Ingår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 17, nr 1, s. 487-527Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsvath and Szabo's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on positive torus knots. Finally, combining these results with a lattice-theoretic obstruction based on Donaldson's theorem, we classify which integral surgeries along torus knots of the form Tkq 1; q bound rational homology balls.

  • 6.
    Aceto, Paolo
    et al.
    Alfred Renyi Inst Math, Realtanoda Ut 13-15, H-1053 Budapest, Hungary..
    Golla, Marco
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Larson, Kyle
    Michigan State Univ, Dept Math, 619 Red Cedar Rd, E Lansing, MI 48824 USA..
    Embedding 3-manifolds in spin 4-manifolds2017Ingår i: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 10, nr 2, s. 301-323Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An invariant of orientable 3-manifolds is defined by taking the minimum n such that a given 3-manifold embeds in the connected sum of n copies of S-2 x S-2, and we call this n the embedding number of the 3-manifold. We give some general properties of this invariant, and make calculations for families of lens spaces and Brieskorn spheres. We show how to construct rational and integral homology spheres whose embedding numbers grow arbitrarily large, and which can be calculated exactly if we assume the 11/8-Conjecture. In a different direction we show that any simply connected 4-manifold can be split along a rational homology sphere into a positive definite piece and a negative definite piece.

  • 7. Aczel, Peter
    et al.
    Crosilla, Laura
    Ishihara, Hajime
    Palmgren, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Schuster, Peter
    Binary refinement implies discrete exponentiation2006Ingår i: Studia Logica, Vol. 84, s. 361-368Artikel i tidskrift (Refereegranskat)
  • 8. Addario-Berry, Louigi
    et al.
    Devroye, Luc
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees2013Ingår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 41, nr 2, s. 1072-1087Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the height and width of a Galton-Watson tree with offspring distribution xi satisfying E xi = 1, 0 < Var xi < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of nodes at level k, for 1 <= k <= n.

  • 9. Addario-Berry, Louigi
    et al.
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    McDiarmid, Colin
    On the Spread of Random Graphs2014Ingår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 23, nr 4, s. 477-504Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The spread of a connected graph G was introduced by Alon, Boppana and Spencer [1], and measures how tightly connected the graph is. It is defined as the maximum over all Lipschitz functions f on V(G) of the variance of f(X) when X is uniformly distributed on V(G). We investigate the spread for certain models of sparse random graph, in particular for random regular graphs G(n,d), for Erdos-Renyi random graphs G(n,p) in the supercritical range p > 1/n, and for a `small world' model. For supercritical G(n,p), we show that if p = c/n with c > 1 fixed, then with high probability the spread of the giant component is bounded, and we prove corresponding statements for other models of random graphs, including a model with random edge lengths. We also give lower bounds on the spread for the barely supercritical case when p = (1 + o(1))/n. Further, we show that for d large, with high probability the spread of G(n, d) becomes arbitrarily close to that of the complete graph K-n.

  • 10. Adimurthi,
    et al.
    Marcos do O, Joao
    Tintarev, Kyril
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och tillämpad matematik.
    Cocompactness and minimizers for inequalities of Hardy-Sobolev type involving N-Laplacian2010Ingår i: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 17, nr 4, s. 467-477Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper studies quasilinear elliptic problems in the Sobolev spaces W-1,W-p(Omega), Omega subset of R-N, with p = N, that is, the case of Pohozhaev-Trudinger-Moser inequality. Similarly to the case p < N where the loss of compactness in W-1,W-p(R-N) occurs due to dilation operators u bar right arrow t((N-p)/p)u(tx), t > 0, and can be accounted for in decompositions of the type of Struwe's "global compactness" and its later refinements, this paper presents a previously unknown group of isometric operators that leads to loss of compactness in W-0(1,N) over a ball in R-N. We give a one-parameter scale of Hardy-Sobolev functionals, a "p = N"-counterpart of the Holder interpolation scale, for p > N, between the Hardy functional integral vertical bar u vertical bar(p)/vertical bar x vertical bar(p) dx and the Sobolev functional integral vertical bar u vertical bar(pN/(N-mp)) dx. Like in the case p < N, these functionals are invariant with respect to the dilation operators above, and the respective concentration-compactness argument yields existence of minimizers for W-1,W-N-norms under Hardy-Sobolev constraints.

  • 11.
    Adimurthi,
    et al.
    TIFR CAM, PB 6503, Bangalore 560065, Karnataka, India.
    Tintarev, Kyril
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Defect of compactness in spaces of bounded variation2016Ingår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 271, nr 1, s. 37-48Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. Let X be a Banach space continuously imbedded into a Banach space Y, and let D be a group of linear isometric operators on X. A profile decomposition in X, relative to D and Y, for a bounded sequence (x(k))(k is an element of N) subset of X is a sequence (S-k)(k is an element of N), such that (x(k) - S-k)(k is an element of N) is a convergent sequence in Y, and, furthermore, S-k has the particular form S-k = Sigma(n is an element of N)g(k)((n))W((n)) with g(k)((n)) is an element of D and w((n)) is an element of X. This paper extends the profile decomposition proved by Solimini [10] for Sobolev spaces (H) over dot(1,P)(R-N) with 1 < p < N to the non-reflexive case p = 1. Since existence of "concentration profiles" w((n)) relies on weak-star compactness, and the space (H) over dot(1,1) is not a conjugate of a Banach space, we prove a corresponding result for a larger space of functions of bounded variation. The result extends also to spaces of bounded variation on Lie groups.

  • 12. Adimurthi,
    et al.
    Tintarev, Kyril
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och tillämpad matematik.
    Hardy inequalities for weighted Dirac operator2010Ingår i: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 189, nr 2, s. 241-251Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r(-b) for functions in R-n. The exact Hardy constant c(b) = c(b) (n) is found and generalized minimizers are given. The constant cb vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in R-2. Analogous inequalities are proved in the case c(b) = 0 under constraints and, with error terms, for a bounded domain.

  • 13. Adimurthi,
    et al.
    Tintarev, Kyril
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och tillämpad matematik.
    On a version of Trudinger-Moser inequality with Möbius shift invariance2010Ingår i: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 39, nr 1-2, s. 203-212Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of the Trudinger-Moser inequality on the open unit disk B subset of R-2, recently proved by Mancini and Sandeep [g], (Arxiv 0910.0971). Unlike the original Trudinger-Moser inequality, this inequality is invariant with respect to the Mobius automorphisms of the unit disk, and as such is a closer analogy of the critical nonlinearity integral |u|(2)* in the higher dimension than the original Trudinger-Moser nonlinearity.

  • 14. Adimurthi, no first name
    et al.
    Tintarev, Cyril
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    On compactness in the Trudinger-Moser inequality2014Ingår i: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 13, nr 2, s. 399-416Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that the Moser functional J(u) = integral Omega(e(4 pi u2) - 1) dx on the set B = {u is an element of H-0(1)(Omega) : parallel to del u parallel to(2) <= 1}, where Omega subset of R-2 is a bounded domain, fails to be weakly continuous only in the following exceptional case. Define g(s)w(r) = s(-1/2)w(r(s)) for s > 0. If u(k) -> u in B while lim inf J(u(k)) > J(u), then, with some s(k) -> 0, u(k) = g(sk) [(2 pi)(-1/2) min {1, log1/vertical bar x vertical bar}], up to translations and up to a remainder vanishing in the Sobolev norm. In other words, the weak continuity fails only on translations of concentrating Moser functions. The proof is based on a profile decomposition similar to that of Solimini [16], but with different concentration operators, pertinent to the two-dimensional case.

  • 15.
    Adle, Tobias
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Framtagning av metod för analys av livslängdsdata2017Självständigt arbete på grundnivå (yrkesexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Husqvarna AB has as of today an extensive research and development department.This department serves to control the active product as well as the upcoming ones.The way that is done is through two different sets of tests. The first one being a longterm endurance test with aimed to unveil the durability of a product. Second and finalsort of test is a more one dimensional one. The aim is to determine different specificunits of interest like for example Newton (N).

    Today the R&D department has a great knowledge within normal distributed data andsomewhat less when it comes to the opposite, so called none normal distributed data.When endurance is of interest the likelihood of that to be of the latter sort is morecommon than not. For now no complete method has been appointed to make iteasier to process a situation of this kind. Studying ever unique case individually, bylooking at the data, has been the way to go. This causes an inconsistency in theanalysis and makes it purely based on which individual that has done it. Lastly it mayalso, unintentionally, ignore the large picture of how a product has progressed.

    To solve these problems this thesis work was put together to propose and conduct amethod. To form this method was an ongoing process throughout the whole thesisperiod. Ideas and thoughts were put forward to be reviewed and discussed. After aseries of tweaks to steer it towards the overall goal the method was finalized. Themethod that was put forward was firmly tested. Also a wide laboration in what themethod actually meant was done.

    The result was a method to be applied on none normal distributed data. This methodhas three parts. The first being the report where everything is embraced. The secondpart is a short manual for an operator to use. Last part is an example where themethod is put to use.

  • 16. Agerholm, Troels
    et al.
    Mazorchuk, Volodymyr
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, geometri och logik.
    On selfadjoint functors satisfying polynomial relations2011Ingår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 330, nr 1, s. 448-467Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in particular, idempotents and square roots of a sum of identity functors. are classified. We also describe various natural constructions for new actions using external direct sums, external tensor products. Serre subcategories, quotients and centralizer subalgebras.

  • 17.
    Ahlberg, Daniel
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden..
    Griffiths, Simon
    Univ Oxford, Dept Stat, Oxford OX1 3TG, England..
    Morris, Robert
    IMPA, Rio De Janeiro, RJ, Brazil..
    Tassion, Vincent
    Univ Geneva, Dept Math, Geneva, Switzerland..
    Quenched Voronoi percolation2016Ingår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 286, s. 889-911Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that the probability of crossing a large square in quenched Voronoi percolation converges to 1/2 at criticality, confirming a conjecture of Benjamini, Kalai and Schramm from 1999. The main new tools are a quenched version of the box-crossing property for Voronoi percolation at criticality, and an Efron Stein type bound on the variance of the probability of the crossing event in terms of the sum of the squares of the influences. As a corollary of the proof, we moreover obtain that the quenched crossing event at criticality is almost surely noise sensitive.

  • 18.
    Ahlberg, Daniel
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.;Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden..
    Steif, Jeffrey E.
    Univ Gothenburg, Chalmers Univ Technol, Math Sci, SE-41296 Gothenburg, Sweden..
    Pete, Gabor
    Hungarian Acad Sci, Renyi Inst, 13-15 Realtanoda U, H-1053 Budapest, Hungary.;Budapest Univ Technol & Econ, Inst Math, 1 Egry Jozsef U, H-1111 Budapest, Hungary..
    Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome?2017Ingår i: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, E-ISSN 1778-7017, Vol. 53, nr 4, s. 2135-2161Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Consider a monotone Boolean function f : {0, 1}(n) -> {0, 1} and the canonical monotone coupling {eta(p) : p is an element of [0, 1]} of an element in {0, 1}(n) chosen according to product measure with intensity p is an element of [0, 1]. The random point p is an element of [0, 1] where f (eta(p)) flips from 0 to 1 is often concentrated near a particular point, thus exhibiting a threshold phenomenon. For a sequence of such Boolean functions, we peer closely into this threshold window and consider, for large n, the limiting distribution (properly normalized to be nondegenerate) of this random point where the Boolean function switches from being 0 to 1. We determine this distribution for a number of the Boolean functions which are typically studied and pay particular attention to the functions corresponding to iterated majority and percolation crossings. It turns out that these limiting distributions have quite varying behavior. In fact, we show that any nondegenerate probability measure on R arises in this way for some sequence of Boolean functions.

  • 19.
    Ahlberg, Peter
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Studier av mätdataregistrering för JAS 39 Gripen2002Självständigt arbete på avancerad nivå (magisterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
  • 20.
    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)
  • 21.
    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.

  • 22.
    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.

  • 23.
    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.

    Publikationen är tillgänglig i fulltext från 2019-09-05 16:29
  • 24.
    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
  • 25.
    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.

  • 26.
    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)
  • 27.
    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.

  • 28.
    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.

  • 29.
    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).

  • 30.
    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)
  • 31.
    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)
  • 32.
    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)
  • 33.
    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)
  • 34.
    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)
  • 35.
    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)
  • 36.
    Aleksandrov, Alexei B.
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Janson, Svante
    Peller, Vladimir V.
    Rochberg, Richard
    An interesting class of operators with unusual Schatten-von Neumann behavior2002Ingår i: Function Spaces, Interpolation Theory and Related Topics (Proceedings of the International Conference in honour of Jaak Peetre on his 65th birthday, Lund 2000), s. 61-150Artikel i tidskrift (Refereegranskat)
  • 37.
    Alexandrov A.B., Janson
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    S., Peller V.V.
    Rochberg R.,
    An interesting class of operators with unusual Schatten-von Neumann behavior2001Rapport (Övrigt vetenskapligt)
  • 38.
    Alghamdi, Azza
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Albaha University, Faculty of Science, Department of Mathematics.
    Klimek, Maciej
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Probabilistic approximation of partly filled-in composite Julia sets2017Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, nr 3, s. 203-220Artikel i tidskrift (Refereegranskat)
    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.

  • 39.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik. Matematisk statistik.
    Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions1998Ingår i: Extremes, Vol. 1, s. 111-126Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Given a Poisson process in two or three dimensions we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area.

    The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions.

    The accuracy of the approximation is checked through simulation.

  • 40.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Monotonicity of the difference between median and mean of Gamma distributions and of a related Ramanujan sequence2002Rapport (Övrigt vetenskapligt)
  • 41.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik. Matematisk statistik.
    Monotonicity of the difference between median and mean of gamma distributions and of a related Ramanujan sequence2003Ingår i: Bernoulli, ISSN 1350-7265, Vol. 9, nr 2, s. 351-371Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For $n\ge0$, let $\lambda_n$ be the median of the $\Gamma(n+1,1)$ distribution. We prove that the sequence $\{\alpha_n=\lambda_n-n\}$ decreases from $\log 2$ to $2/3$ as $n$ increases from 0 to $\infty$. The difference, $1-\alpha_n$, between the mean and the median thus increases from $1-\log 2$ to $1/3$.

    This result also proves the following conjecture by Chen \& Rubin about the Poisson distributions: Let $Y_{\mu}\sim\text{Poisson}(\mu)$, and \lambda_n$ be the largest $\mu$ such that $P(Y_{\mu}\le n)=1/2$, then $\lambda_n-n$ is decreasing in $n$.

    The sequence $\{\alpha_n\}$ is related to a sequence $\{\theta_n\}$, introduced by Ramanujan, which is known to be decreasing and of the form

    $\theta_n=\frac13+\frac4{135(n+k_n)}$, where $\frac2{21}<k_n\le\frac8{45}$. We also show that the sequence $\{k_n\}$ is decreasing.

  • 42.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    On measures of average degree for lattices2003Rapport (Övrigt vetenskapligt)
  • 43.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    On Measures of Average Degree for Lattices2006Ingår i: Combinatorics, Probability and Computing, Vol. 15, nr 4, s. 477-488Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices.

    These measures are compared on a class of lattices and are analyzed using a Markov chain describing a random walk on the lattice. Using the new measure, we conjecture the order of both the critical probabilities for bond percolation and the connective constants for self-avoiding walks on these lattices.

  • 44.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    On monoticity of some binomial probabilities2010Rapport (Övrigt vetenskapligt)
  • 45.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Upper and Lower Bounds for the Connective Constants of Self-avoiding Walks on the Archimedean and Laves Lattices2005Ingår i: J. Phys. A: Math. Gen., nr 38, s. 2055-2080Artikel i tidskrift (Refereegranskat)
  • 46.
    Alm, Sven Erick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Upper and Lower Bounds for the Connective Constants of Self-avoiding Walks on the Archimedean and Laves Lattices2004Rapport (Övrigt vetenskapligt)
  • 47.
    Alm, Sven Erick
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Deijfen, Maria
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden..
    First Passage Percolation on \(\mathbb {Z}^2\): A Simulation Study2015Ingår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, nr 3, s. 657-678Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.

  • 48.
    Alm, Sven Erick
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och tillämpad matematik.
    Linusson, Svante
    Correlations for Paths in Random Orientations of G(n, p) and G(n, m)2011Ingår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 39, nr 4, s. 486-506Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study random graphs, both G(n, p) and G(n, m), with random orientations on the edges. For three fixed distinct vertices s, a, b we study the correlation, in the combined probability space, of the events {a -> s} and {s -> b}. For G(n, p), we prove that there is a p(c) = 1/2 such that for a fixed p < p(c) the correlation is negative for large enough n and for p > p(c) the correlation is positive for large enough n. We conjecture that for a fixed n >= 27 the correlation changes sign three times for three critical values of p. For G(n, m) it is similarly proved that, with p = m/((n)(2)), there is a critical p(c) that is the solution to a certain equation and approximately equal to 0.7993. A lemma, which computes the probability of non existence of any l directed edges in G(n, m), is thought to be of independent interest. We present exact recursions to compute P(a -> s) and P(a -> s, s -> b). We also briefly discuss the corresponding question in the quenched version of the problem.

  • 49.
    Alm, Sven Erick
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Linusson, Svante
    First critical probability for a problem on random orientations in G(n,p)2014Ingår i: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 19, s. 69-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the random graph G (n,p) with a random orientation. For three fixed vertices s, a, b in G(n,p) we study the correlation of the events {a -> s} (there exists a directed path from a to s) and {s -> b}. We prove that asymptotically the correlation is negative for small p, p < C-1/n, where C-1 approximate to 0.3617, positive for C-1/n < p < 2/n and up to p = p(2)(n). Computer aided computations suggest that p(2)(n) = C-2/n, with C-2 approximate to 7.5. We conjecture that the correlation then stays negative for p up to the previously known zero at 1/2; for larger p it is positive.

  • 50.
    Alm, Sven Erick
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Linusson, Svante
    A Counter-Intuitive Correlation in a Random Tournament2011Ingår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 20, nr 1, s. 1-9Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertices in V. We study the correlation between the events {a -> s} and {s -> b}. We show that, counter-intuitively, when G is the complete graph K-n, n >= 5, then the correlation is positive. (It is negative for n = 3 and zero for n = 4.) We briefly discuss and pose problems for the same question on other graphs.

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