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  • 1.
    Abdallah, Nancy
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Hultman, Axel
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions2018In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 47, no 4, p. 543-560Article in journal (Refereed)
    Abstract [en]

    When acts on the flag variety of , the orbits are in bijection with fixed point free involutions in the symmetric group . In this case, the associated Kazhdan-Lusztig-Vogan polynomials can be indexed by pairs of fixed point free involutions , where denotes the Bruhat order on . We prove that these polynomials are combinatorial invariants in the sense that if is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then for all v amp;gt;= u.

  • 2.
    Abdulla, Ariyan
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Andersson, Erik
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Heuristiska algoritmer för schemaläggning i real-tidssystem med hänsyn till data beroenden2018Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    The schedule for the jobs in a real-time system can have a huge impact on how the system behave. Since real-time systems are common in safety applications it is important that the scheduling is done in a valid way. Furthermore, one can enhance the performance of the applications by minimizing data latency and jitter. A challenge is that jobs in real-time systems usually have complex constraints making it too time consuming to minimize data latency and jitter to optimality. The purpose of this report is to investigate the possibility of creating high quality schedules using heuristics, with the goal to keep the computational time under one minute. This will be done by comparing three different algorithms that will be used on real scheduling instances provided by the company Arcticus. The first algorithm is a greedy heuristic, the second one a local search and the third one is a metaheuristic, simulated annealing. The results indicate that the data latency can be reduced whilst keeping the computational time below one minute.

  • 3.
    Abidin, Aysajan
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Weaknesses of Authentication in Quantum Cryptography and Strongly Universal Hash Functions2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Authentication is an indispensable part of Quantum Cryptography, which is an unconditionally secure key distribution technique based on the laws of nature. Without proper authentication, Quantum Cryptography is vulnerable to “man-in-the-middle” attacks. Therefore, to guarantee unconditional security of any Quantum Cryptographic protocols, the authentication used must also be unconditionally secure. The standard in Quantum Cryptography is to use theWegman-Carter authentication, which is unconditionally secure and is based on the idea of universal hashing.

    In this thesis, we first investigate properties of a Strongly Universal hash function family to facilitate understanding the properties of (classical) authentication used in Quantum Cryptography. Then, we study vulnerabilities of a recently proposed authentication protocol intended to rule out a "man-in-the-middle" attack on Quantum Cryptography. Here, we point out that the proposed authentication primitive is not secure when used in a generic Quantum Cryptographic protocol. Lastly, we estimate the lifetime of authentication using encrypted tags when the encryption key is partially known. Under simplifying assumptions, we derive that the lifetime is linearly dependent on the length of the authentication key. Experimental results that support the theoretical results are also presented.

    List of papers
    1. Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography
    Open this publication in new window or tab >>Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography
    2009 (English)In: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, p. 289-293Conference paper, Published paper (Refereed)
    Abstract [en]

    Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

    Place, publisher, year, edition, pages
    New York: American Institute of Physics, 2009
    Keywords
    Quantum cryptography, Quantum theory, Probability
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-18738 (URN)10.1063/1.3109951 (DOI)
    Conference
    Foundations of Probability and Physics—5, Växjö, augusti 2008
    Projects
    ICG QC
    Available from: 2009-06-03 Created: 2009-06-03 Last updated: 2016-08-31
    2. Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"
    Open this publication in new window or tab >>Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"
    2009 (English)In: International Journal of Quantum Information, ISSN 0219-7499, Vol. 7, no 5, p. 1047-1052Article in journal (Refereed) Published
    Abstract [en]

    In this paper, we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography" [M. Peev et al., Int. J. Quant. Inf. 3 (2005) 225]. In particular, we point out that the proposed primitive is not secure when used in a generic protocol, and needs additional authenticating properties of the surrounding quantum-cryptographic protocol.

    Keywords
    Quantum cryptography, quantum key distribution, authentication
    National Category
    Natural Sciences
    Identifiers
    urn:nbn:se:liu:diva-20405 (URN)10.1142/S0219749909005754 (DOI)
    Projects
    ICG QC
    Available from: 2009-09-08 Created: 2009-09-07 Last updated: 2016-08-31Bibliographically approved
    3. Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially Known
    Open this publication in new window or tab >>Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially Known
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Quantum cryptography is an unconditionally secure key growing technique provided that an unconditionally secure authentication protocol is combined with it. This paper is about the study of the lifetime of a message authentication scheme, where a message to be authenticated is first hashed by a secret–but fixed–Strongly Universal hash function then the output is encrypted with a one-time-pad key to generate a tag for the message. If the onetime-pad is completely secret, then the lifetime is exponential in the tag length. If, however, the one-time-pad key is partially known in each authentication round, as is the case in practical quantum key distribution protocols, then the picture is different; because the adversary’s partial knowledge of the one-time-pad key in each authentication round contributes to his/her ability to identify the secret hash function. We estimate the lifetime of this type of authentication. Here the parameters are the length of the key identifying the secret hash function and the amount of knowledge that Eve has on the one-time-pad. A theoretical estimate is presented, along with experimental results that support it.

    Keywords
    Quantum cryptography, quantum key distribution, authentication, strongly universal hash functions, lifetime
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-57289 (URN)
    Projects
    ICG QC
    Available from: 2010-06-16 Created: 2010-06-16 Last updated: 2016-08-31
  • 4.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially KnownManuscript (preprint) (Other academic)
    Abstract [en]

    Quantum cryptography is an unconditionally secure key growing technique provided that an unconditionally secure authentication protocol is combined with it. This paper is about the study of the lifetime of a message authentication scheme, where a message to be authenticated is first hashed by a secret–but fixed–Strongly Universal hash function then the output is encrypted with a one-time-pad key to generate a tag for the message. If the onetime-pad is completely secret, then the lifetime is exponential in the tag length. If, however, the one-time-pad key is partially known in each authentication round, as is the case in practical quantum key distribution protocols, then the picture is different; because the adversary’s partial knowledge of the one-time-pad key in each authentication round contributes to his/her ability to identify the secret hash function. We estimate the lifetime of this type of authentication. Here the parameters are the length of the key identifying the secret hash function and the amount of knowledge that Eve has on the one-time-pad. A theoretical estimate is presented, along with experimental results that support it.

  • 5.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography2009In: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, p. 289-293Conference paper (Refereed)
    Abstract [en]

    Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

  • 6.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"2009In: International Journal of Quantum Information, ISSN 0219-7499, Vol. 7, no 5, p. 1047-1052Article in journal (Refereed)
    Abstract [en]

    In this paper, we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography" [M. Peev et al., Int. J. Quant. Inf. 3 (2005) 225]. In particular, we point out that the proposed primitive is not secure when used in a generic protocol, and needs additional authenticating properties of the surrounding quantum-cryptographic protocol.

  • 7.
    Abrahamsson, Olle
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    A Gröbner basis algorithm for fast encoding of Reed-Müller codes2016Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. Finally we show how to apply the representation of a code by its corresponding polynomial ring ideal to construct a class of codes containing the so called primitive Reed-Müller codes, with a few examples of this result.

  • 8.
    Accardi, Luigi
    et al.
    Università di Roma “Tor Vergata”, Italy.
    Brody, Dorje C.
    Imperial College, London, UK.
    Belavkin, V.P.
    University of Nottingham, UK.
    Kent, Johyn T.
    University of Leeds, UK.
    Bingham, N.H.
    Brunel University, Uxbridge, UK.
    Frey, Jeremy G.
    University of Southampton, UK.
    Helland, Inge S.
    University of Oslo, Norway.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Majumdar, NK
    London, UK.
    Minozzo, Marco
    University of Perugia, Italy.
    Thompson, J. W.
    University of Hull, UK.
    Discussion on "On quantum statistical inference" by Barndorff-Nielsen, Gill and Jupp2003In: Journal of The Royal Statistical Society Series B-statistical Methodology, ISSN 1369-7412, E-ISSN 1467-9868, Vol. 65, no 4, p. 805-816p. 805-816Article in journal (Refereed)
  • 9.
    Adamowicz, Tomasz
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points2014In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 31, no 6, p. 1131-1153Article in journal (Refereed)
    Abstract [en]

    We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

  • 10.
    Adamowicz, Tomasz
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Shanmugalingam, Nageswari
    University of Cincinnati, OH USA .
    Prime ends for domains in metric spaces2013In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 238, p. 459-505Article in journal (Refereed)
    Abstract [en]

    In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Caratheodory and Nakki. Modulus ends and prime ends, defined by means of the p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.

  • 11.
    Aerts, Sven
    et al.
    Fundamenten van de Exacte WetenschappenVrije Universiteit Brussel, Triomflaan 21050 Brussel, Belgium.
    Kwiat, Paul
    P-23, MS-H803, Los Alamos National Laboratory, Los Alamos, New Mexico, USA.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Zukowski, Marek
    Instytut Fizyki Teoretycznej i Astrofizyki, Uniwersytet Gdańsk, iPL-80-952 Gdańsk, Poland.
    Comment on Two-photon Franson-type experiment and local realism - Reply2001In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 86, no 9, p. 1909-1909Article in journal (Refereed)
    Abstract [en]

    A Reply to the Comment by Carlos Luiz Ryff.

  • 12.
    Aerts, Sven
    et al.
    Fundamenten van de Exacte Wetenschappen, Vrije Universiteit Brussel, Brussel, Belgium.
    Kwiat, Paul
    Los Alamos National Laboratory, Los Alamos, New Mexico.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Zukowski, Marek
    Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdański, Gdańsk, Poland .
    Two-photon Franson-type experiments and local realism1999In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 83, no 15, p. 2872-2876Article in journal (Refereed)
    Abstract [en]

    The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a “Bell test of local realism.” However, it has been suggested that this is incorrect due to the 50% postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rate determined by the internal geometry of the interferometers.

  • 13.
    Aghapournahr, M
    et al.
    Arak University.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Finiteness properties of minimax and coatomic local cohomology modules2010In: ARCHIV DER MATHEMATIK, ISSN 0003-889X, Vol. 94, no 6, p. 519-528Article in journal (Refereed)
    Abstract [en]

    Let R be a noetherian ring, alpha an ideal of R, and M an R-module. We prove that for a finite module M, if H-alpha(i)(M) is minimax for all i andgt;= r andgt;= 1, then H-alpha(i)(M) is artinian for i andgt;= r. A local-global principle for minimax local cohomology modules is shown. If H-alpha(i)(M) is coatomic for i andlt;= r (M finite) then H-alpha(i)(M) is finite for i andlt;= r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing theorems are proved for local cohomology modules.

  • 14.
    Aghapournahr, Moharram
    et al.
    Arak University.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A natural map in local cohomology2010In: ARKIV FOR MATEMATIK, ISSN 0004-2080, Vol. 48, no 2, p. 243-251Article in journal (Refereed)
    Abstract [en]

    Let R be a Noetherian ring, a an ideal of R, M an R-module and n a non-negative integer. In this paper we first study the finiteness properties of the kernel and the cokernel of the natural map f: Ext(R)(n) (R/alpha, M) -andgt; Hom(R)(R/alpha, H-alpha(n) (M)), under some conditions on the previous local cohomology modules. Then we get some corollaries about the associated primes and Artinianness of local cohomology modules. Finally we will study the asymptotic behavior of the kernel and the cokernel of the natural map in the graded case.

  • 15.
    Aghapournahr, Moharram
    et al.
    Arak University, Iran .
    Melkersson, Leif
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Artinianness of local cohomology modules2014In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 1, p. 1-10Article in journal (Refereed)
    Abstract [en]

    Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about the artinianness of some special local cohomology modules in the graded case.

  • 16.
    Aghapournahr, Moharram
    et al.
    Arak Univ, Arak, Iran.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    COFINITENESS AND COASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES2009In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 105, no 2, p. 161-170Article in journal (Refereed)
    Abstract [en]

    Let R be a noetherian ring, alpha an ideal of R such that dim R/alpha = 1 and M a finite R-module. We will study cofiniteness and some other properties of the local cohomology modules H-alpha(i)(M). For an arbitrary ideal alpha and an R-module M (not necessarily finite), we will characterize alpha-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.

  • 17.
    Aghapournahr, Moharram
    et al.
    Teacher Training Univ, Fac Math Sci, Tehran 15614, Iran.
    Melkersson, Leif
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Local cohomology and Serre subcategories2008In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 320, no 3, p. 1275-1287Article in journal (Refereed)
    Abstract [en]

    The membership of the local cohomology modules H-a(n) (M) of a module M in certain Serre subcategories of the category of modules is studied from below (i < n) and from above (i > n). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory in the upper range just depends on the support of the module. (C) 2008 Elsevier Inc. All rights reserved.

  • 18.
    Agwa, Mohamed
    et al.
    Department of Mechanical Design and Production Engineering, Faculty of Engineering, Zagazig Egypt.
    Andersson, Lars-Erik
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Pinto da Costa, Ant´onio
    Departamento de Engenharia Civil, Instituto Superior T´ecnico and ICIST, Universidade T´ecnica de Lisboa, Avenida Rovisco Pais, 1049 􀀀 001 Lisboa, Portugal.
    Critical bounds for discrete frictional incremental problems, rateproblems and wedging problems2012Conference paper (Other academic)
    Abstract [en]

    Summary. Questions of existence and uniqueness for discrete frictional quasi-static incremental problems, rate problems and wedging problems are discussed. Various methods to compute critical bounds for the coefficient of friction which guarantee existence and uniqueness are described, as well as the sharpness of the bounds and their interdependence.

  • 19.
    Ahlquist, Mari
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    On Knots and DNA2017Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    Knot theory is the mathematical study of knots. In this thesis we study knots and one of its applications in DNA. Knot theory sits in the mathematical field of topology and naturally this is where the work begins. Topological concepts such as topological spaces, homeomorphisms, and homology are considered. Thereafter knot theory, and in particular, knot theoretical invariants are examined, aiming to provide insights into why it is difficult to answer the question "How can we tell knots appart?". In knot theory invariants such as the bracket polynomial, the Jones polynomial and tricolorability are considered as well as other helpful results like Seifert surfaces. Lastly knot theory is applied to DNA, where it will shed light on how certain enzymes interact with the genome.

  • 20.
    Ahmad, M. Rauf
    Linköping University, Department of Mathematics.
    A note on the (n, p)-asymptotics of ATS for high dimensional multivariate data2010Report (Other academic)
  • 21.
    Ahmad, M. Rauf
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A two-sample test statistic for high-dimensional multivariate data under non-normality2011Report (Other academic)
    Abstract [en]

    Ahmad, Ohlson, and von Rosen (2011a) present asymptotic distribution of a one-sample test statistic under non-normality, when the data are high dimensional, i.e., when the dimension of the vector, p, may exceed the sample size, n. This paper extends the case to a two-sample statistic to test the difference of mean vectors of two independent multivariate distributions, again under high-dimensional set up. Using the asymptotic theory of U-statistics, and under mild assumptions on the traces of the unknown covariance matrices, the statistic is shown to follow an approximate normal distribution when n and p are large. However, no relationship between n and p is assumed. An extension to the paired case is given, which, being essentially a one-sample statistic, supplements the asymptotic results obtained in Ahmad, Ohlson, and von Rosen (2011a).

  • 22.
    Ahmad, M. Rauf
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Robustness of a one-sample statistic for mean testing of high dimensional longitudinal data2010Report (Other academic)
  • 23.
    Ahmad, M. Rauf
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Ohlson, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality2011Report (Other academic)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of well-known Box's approximation, under high-dimensional set up.

  • 24.
    Ahmad, M. Rauf
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Ohlson, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    von Rosen, Dietrich
    Department of Energy and Technology, Swedish Univerity of Agricultural Sciences, SE-750 07 Uppsala, Sweden.
    Some Tests of Covariance Matrices for High Dimensional Multivariate Data2011Report (Other academic)
    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. 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 statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.

  • 25.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden; University of Munich, Germany.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Swedish University of Agriculture Science, Sweden.
    Tests for high-dimensional covariance matrices using the theory of U-statistics2015In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 85, no 13, p. 2619-2631Article in journal (Refereed)
    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 and#8811;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.

  • 26.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Sweden; Swedish University of Agriculture Science, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. Swedish University of Agriculture Science, Sweden.
    Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality2015In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 7, p. 1387-1398Article in journal (Refereed)
    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 greater thangreater than 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.

  • 27.
    Ahmad, M. Rauf
    et al.
    Swedish University of Agricultural Sciences, Uppsala, Sweden and Department of Statistics, Uppsala University, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    A note on mean testing for high dimensional multivariate data under non-normality2013In: Statistica neerlandica (Print), ISSN 0039-0402, E-ISSN 1467-9574, Vol. 67, no 1, p. 81-99Article in journal (Refereed)
    Abstract [en]

    A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p→∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.

  • 28.
    Aigner, Mats
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Existence of the Ginzburg-Landau vortex number2001In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 216, no 1, p. 17-22Article in journal (Refereed)
    Abstract [en]

    The existence of the Ginzburg-Landau vortex number is established for any configuration with finite action. As a consequence, Bogomol'nyi's formula for the critical action is valid for any finite action configuration.

  • 29.
    Aigner, Mats
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Tjatyrko, Vitalij A.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda .
    ON COUNTABLE FAMILIES OF SETS WITHOUT THE BAIRE PROPERTY2013In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 133, no 2, p. 179-187Article in journal (Refereed)
    Abstract [en]

    We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (R-n , tau), where n is an integer greater than= 1 and tau is any admissible extension of the Euclidean topology of R-n (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family F of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of F does not have the Baire property in X.

  • 30.
    Aigner, Mats
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tjatyrko, Vitalij
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda.
    THE ALGEBRA OF SEMIGROUPS OF SETS2015In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 116, no 2, p. 161-170Article in journal (Refereed)
    Abstract [en]

    We study the algebra of semigroups of sets (i.e. families of sets closed under finite unions) and its applications. For each n greater than 1 we produce two finite nested families of pairwise different semigroups of sets consisting of subsets of R" without the Baire property.

  • 31.
    Akram, Usman
    et al.
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Biology. Linköping University, Faculty of Science & Engineering.
    Metson, Genevieve
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Biology. Linköping University, Faculty of Science & Engineering. Linköping University, Centre for Climate Science and Policy Research, CSPR.
    Quttineh, Nils-Hassan
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Wennergren, Uno
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Biology. Linköping University, Faculty of Science & Engineering.
    Closing Pakistan’s yield gaps through nutrient recycling2018In: Frontiers in Sustainable Food Systems, E-ISSN 2571-581X, p. 1-14, article id 00024Article in journal (Refereed)
    Abstract [en]

    Achieving food security will require closing yield gaps in many regions, including Pakistan. Although fertilizer subsidies have facilitated increased nitrogen (N) application rates, many staple crop yields have yet to reach their maximum potential. Considering that current animal manure and human excreta (bio-supply) recycling rates are low, there is substantial potential to increase the reuse of nutrients in bio-supply. We quantified 2010 crop N, phosphorus (P), and potassium (K) needs along with bio-supply nutrient availability for Pakistani districts, and compared these values to synthetic fertilizer use and costs. We found that synthetic fertilizer use combined with low bio-supply recycling resulted in a substantial gap between nutrient supply and P and K crop needs, which would cost 3 billion USD to fill with synthetic fertilizers. If all bio-supply was recycled, it could eliminate K synthetic fertilizer needs and decrease N synthetic fertilizer needs to 43% of what was purchased in 2010. Under a full recycling scenario, farmers would still require an additional 0.28 million tons of synthetic P fertilizers, costing 2.77 billion USD. However, it may not be prohibitively expensive to correct P deficiencies. Pakistan already spends this amount of money on fertilizers. If funds used for synthetic N were reallocated to synthetic P purchases in a full bio-supply recycling scenario, crop needs could be met. Most recycling could happen within districts, with only 6% of bio-supply requiring between-district transport when optimized to meet national N crop needs. Increased recycling in Pakistan could be a viable way to decrease yield gaps.

  • 32.
    Albarracín, Lluís
    et al.
    Universitat Autònoma de Barcelona.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Civil, Elisabeth
    Universitat Autònoma de Barcelona.
    Gorgorió, Núria
    Universitat Autònoma de Barcelona.
    Extending Modelling Activity Diagrams as a tool to characterise mathematical modelling processes2019In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 16, no 1-2, article id 10Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a qualitative study in which we analyse the video-recordings of four groups of students solving Fermi Problems. Previous studies show that Secondary School students solve this type of problems using complex problem solving processes and developing mathematical models. In order to analyse the students’ problem solving processes, so-called Modelling Activity Diagrams were used. The results of the present study demonstrate that solving Fermi problems is a complex matter, and that some of the theoretical tools used in the field of Mathematical Education fail to adequately reflect this level of complexity. In addition, Modelling Activity Diagrams are presented as a more detailed analysis tool to characterise student choices and actions, as well as to make the structure of the Fermi problem addressed more visible.

  • 33.
    Al-Chalabi, Mona
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Gymnasieelevers matematiska svårigheter att lösa linjära ekvationer och linjära ekvationssystem: En litteraturöversikt2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Many students of secondary school find it difficult to understand algebra, specifically linear equations and systems of linear equations, which prevents their further learning in both mathematics and other subjects. Teacher must therefore have a clear idea of what these difficulties are in order to assist their students in understanding and learning this area in algebra. The study examines the findings of the research literature as to what these difficulties are. Proven difficulties that have been illustrated with examples of students´ solutions are: deficiencies in their algebraic prerequisites, procedural knowledge and conceptual knowledge (especially about similarities, constants and variables), lack of knowledge of the algebraic syntax, and incorrect handling of the operations used to solve equations and systems of equations, for example how to handle negative coefficients and constants and use the substitution method.

  • 34.
    Alfonseca, M Angeles
    et al.
    N Dakota State University.
    Auscher, Pascal
    University Paris 11.
    Axelsson Rosén, Andreas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Hofmann, Steve
    University of Missouri.
    Kim, Seick
    Yonsei University.
    Analyticity of layer potentials and L-2 solvability of boundary value problems for divergence form elliptic equations with complex L-infinity coefficients2011In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 226, no 5, p. 4533-4606Article in journal (Refereed)
    Abstract [en]

    We consider divergence form elliptic operators of the form L = -div A (x)del, defined in Rn+1 = {(x, t) is an element of R-n x R}, n andgt;= 2, where the L-infinity coefficient matrix A is (n + 1) x (n + 1), uniformly elliptic, complex and t-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on L-2 (R-n) = L-2(partial derivative R-+(n+1)) is stable under complex, L-infinity perturbations of the coefficient matrix. Using a variant of the Tb Theorem, we also prove that the layer potentials are bounded and invertible on L-2(R-n) whenever A (x) is real and symmetric (and thus, by our stability result, also when A is complex, parallel to A - A(0)parallel to(infinity) is small enough and A(0) is real, symmetric, L-infinity and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with L-2 (resp. (L) over dot(1)(2)) data, for small complex perturbations of a real symmetric matrix. Previously, L-2 solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients A (j,n+1)= 0 = A(n+1,j), 1 andlt;= j andlt;= n, which corresponds to the Kato square root problem.

  • 35.
    Al-Shujary, Ahmed
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Kähler-Poisson Algebras2018Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The focus of this thesis is to introduce the concept of Kähler-Poisson algebras as analogues of algebras of smooth functions on Kähler manifolds. We first give here a review of the geometry of Kähler manifolds and Lie-Rinehart algebras. After that we give the definition and basic properties of Kähler-Poisson algebras. It is then shown that the Kähler type condition has consequences that allow for an identification of geometric objects in the algebra which share several properties with their classical counterparts. Furthermore, we introduce a concept of morphism between Kähler-Poisson algebras and show its consequences. Detailed examples are provided in order to illustrate the novel concepts.

  • 36.
    Alvarado, Ryan
    et al.
    University of Missouri.
    Brigham, Dan
    University of Missouri.
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mitrea, Marius
    University of Missouri.
    Ziade, Elia
    University of Missouri.
    Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 4, p. 613-620Article in journal (Refereed)
    Abstract [en]

    We discuss a sharp generalization of the Hopf-Oleinik boundary point principle (BPP) for domains satisfying an interior pseudo-ball condition, for non-divergence form, semi-elliptic operators with singular drift. In turn, this result is used to derive a version of the strong maximum principle under optimal pointwise blow-up conditions for the coefficients of the differential operator involved. We also explain how a uniform two-sided pseudo-ball condition may be used to provide a purely geometric characterization of Lyapunov domains, and clarify the role this class of domains plays vis-a-vis to the BPP.

  • 37.
    Alvino, Angelo
    et al.
    University Napoli Federico II.
    Cianchi, Andrea
    University Florence.
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mercaldo, Anna
    University Napoli Federico II.
    Well-posed elliptic Neumann problems involving irregular data and domains2010In: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, ISSN 0294-1449, Vol. 27, no 4, p. 1017-1054Article in journal (Refereed)
    Abstract [en]

    Non-linear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are established under a suitable balance between the integrability of the datum and the (ir)regularity of the domain. The latter is described in terms of isocapacitary inequalities. Applications to various classes of domains are also presented. (C) 2010 Elsevier Masson SAS. All rights reserved.

  • 38.
    Amankwah, Henry
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Mathematical Optimization Models and Methods for Open-Pit Mining2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Open-pit mining is an operation in which blocks from the ground are dug to extract the ore contained in them, and in this process a deeper and deeper pit is formed until the mining operation ends. Mining is often a highly complex industrial operation, with respect to both technological and planning aspects. The latter may involve decisions about which ore to mine and in which order. Furthermore, mining operations are typically capital intensive and long-term, and subject to uncertainties regarding ore grades, future mining costs, and the market prices of the precious metals contained in the ore. Today, most of the high-grade or low-cost ore deposits have already been depleted, and to obtain sufficient profitability in mining operations it is therefore today often a necessity to achieve operational efficiency with respect to both technological and planning issues.

    In this thesis, we study the open-pit design problem, the open-pit mining scheduling problem, and the open-pit design problem with geological and price uncertainty. These problems give rise to (mixed) discrete optimization models that in real-life settings are large scale and computationally challenging.

    The open-pit design problem is to find an optimal ultimate contour of the pit, given estimates of ore grades, that are typically obtained from samples in drill holes, estimates of costs for mining and processing ore, and physical constraints on mining precedence and maximal pit slope. As is well known, this problem can be solved as a maximum flow problem in a special network. In a first paper, we show that two well known parametric procedures for finding a sequence of intermediate contours leading to an ultimate one, can be interpreted as Lagrangian dual approaches to certain side-constrained design models. In a second paper, we give an alternative derivation of the maximum flow problem of the design problem.

    We also study the combined open-pit design and mining scheduling problem, which is the problem of simultaneously finding an ultimate pit contour and the sequence in which the parts of the orebody shall be removed, subject to mining capacity restrictions. The goal is to maximize the discounted net profit during the life-time of the mine. We show in a third paper that the combined problem can also be formulated as a maximum flow problem, if the mining capacity restrictions are relaxed; in this case the network however needs to be time-expanded.

    In a fourth paper, we provide some suggestions for Lagrangian dual heuristic and time aggregation approaches for the open-pit scheduling problem. Finally, we study the open-pit design problem under uncertainty, which is taken into account by using the concept of conditional value-atrisk. This concept enables us to incorporate a variety of possible uncertainties, especially regarding grades, costs and prices, in the planning process. In real-life situations, the resulting models would however become very computationally challenging.

    List of papers
    1. On the use of Parametric Open-Pit Design Models for Mine Scheduling - Pitfalls and Counterexamples
    Open this publication in new window or tab >>On the use of Parametric Open-Pit Design Models for Mine Scheduling - Pitfalls and Counterexamples
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    This paper discusses a Lagrangian relaxation interpretation of the Picard and Smith (2004) parametric approach to open-pit mining, which finds a sequence of intermediate contours leading to an ultimate one. This method is similar to the well known parametric approach of Lerchs and Grossmann (1965). We give examples of worst case performance, as well as best case performance of the Picard-Smith approach. The worst case behaviour can be very poor in that we might not obtain any intermediate contours at all. We also discuss alternative parametric methods for finding intermediate contours, but conclude that such methods seem to have inherent weaknesses.

    Keywords
    Open-pit mining, Picard-Smith model, Lagrangian relaxation, pit design, block value, scheduling
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-70838 (URN)
    Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2013-08-30Bibliographically approved
    2. A Duality-Based Derivation of the Maximum Flow Formulation of the Open-Pit Design Problem
    Open this publication in new window or tab >>A Duality-Based Derivation of the Maximum Flow Formulation of the Open-Pit Design Problem
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Open-pit mining is a surface mining operation whereby ore, or waste, is excavated from the surface of the land. The open-pit design problem is deciding on which blocks of an ore deposit to mine in order to maximize the total profit, while obeying digging constraints concerning pit slope and block precedence. The open-pit design problem can be formulated as a maximum flow problem in a certain capacitated network, as first shown by Picard in 1976. His derivation is based on a restatement of the problem as a quadratic binary program. We give an alternative derivation of the maximum flow formulation, which uses only linear programming duality.

    Keywords
    Open-pit mining, pit design, maximum flow, maximum profit, block model
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-70840 (URN)
    Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2013-08-30Bibliographically approved
    3. A Multi-Parametric Maximum Flow Characterization of the Open-Pit Scheduling Problem
    Open this publication in new window or tab >>A Multi-Parametric Maximum Flow Characterization of the Open-Pit Scheduling Problem
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    We consider the problem of finding an optimal mining schedule for an openpit during a number of time periods, subject to a mining capacity restriction for each time period. By applying Lagrangian relaxation to the capacities, a multi-parametric formulation is obtained. We show that this formulation can be restated as a maximum flow problem in a time-expanded network. This result extends a well-known result of Picard from 1976 for the open-pit design problem, that is, the single-period case, to the case of multiple time periods.

    Keywords
    Open-pit mining, scheduling, maximum flow, minimum cut, Lagrangian relaxation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-70841 (URN)
    Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2013-08-30Bibliographically approved
    4. Open-Pit Production Scheduling - Suggestions for Lagrangian Dual Heuristic and Time Aggregation Approaches
    Open this publication in new window or tab >>Open-Pit Production Scheduling - Suggestions for Lagrangian Dual Heuristic and Time Aggregation Approaches
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Open-pit production scheduling deals with the problem of deciding what and when to mine from an open-pit, given potential profits of the different fractions of the mining volume, pit-slope restrictions, and mining capacity restrictions for successive time periods. We give suggestions for Lagrangian dual heuristic approaches for the open-pit production scheduling problem. First, the case with a single mining capacity restriction per time period is considered. For this case, linear programming relaxations are solved to find values of the multipliers for the capacity restrictions, to be used in a Lagrangian relaxation of the constraints. The solution to the relaxed problem will not in general satisfy the capacity restrictions, but can be made feasible by adjusting the multiplier values for one time period at a time. Further, a time aggregation approach is suggested as a way of reducing the computational burden of solving linear programming relaxations, especially for largescale real-life mine problems. For the case with multiple capacity restrictions per time period we apply newly developed conditions for optimality and nearoptimality in general discrete optimization problems to construct a procedure for heuristically constructing near-optimal intermediate pits.

    Keywords
    Open-pit mining, mine scheduling, Lagrangian relaxation, maximum flow, time aggregation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-70842 (URN)
    Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2018-06-25Bibliographically approved
    5. Open-Pit Mining with Uncertainty - A Conditional Value-at-Risk Approach
    Open this publication in new window or tab >>Open-Pit Mining with Uncertainty - A Conditional Value-at-Risk Approach
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty, and also the future market behaviour of metal prices and foreign exchange rates, which are impossible to be known with certainty, make mining a high risk business.

    Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does however have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev (2000) introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex problem.

    An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and price uncertainties.

    Keywords
    Conditional value-at-risk (CVaR), open-pit mining, geological uncertainty, price uncertainty
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-70843 (URN)
    Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2013-08-30Bibliographically approved
  • 39.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A Duality-Based Derivation of the Maximum Flow Formulation of the Open-Pit Design ProblemManuscript (preprint) (Other academic)
    Abstract [en]

    Open-pit mining is a surface mining operation whereby ore, or waste, is excavated from the surface of the land. The open-pit design problem is deciding on which blocks of an ore deposit to mine in order to maximize the total profit, while obeying digging constraints concerning pit slope and block precedence. The open-pit design problem can be formulated as a maximum flow problem in a certain capacitated network, as first shown by Picard in 1976. His derivation is based on a restatement of the problem as a quadratic binary program. We give an alternative derivation of the maximum flow formulation, which uses only linear programming duality.

  • 40.
    Amankwah, Henry
    et al.
    University of Cape Coast, Ghana .
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A maximum flow formulation of a multi-period open-pit mining problem2014In: Operational Research, ISSN 1109-2858, E-ISSN 1866-1505, Vol. 14, no 1, p. 1-10Article in journal (Refereed)
    Abstract [en]

    We consider the problem of finding an optimal mining sequence for an open pit during a number of time periods subject to only spatial and temporal precedence constraints. This problem is of interest because such constraints are generic to any open-pit scheduling problem and, in particular, because it arises as a Lagrangean relaxation of an open-pit scheduling problem. We show that this multi-period open-pit mining problem can be solved as a maximum flow problem in a time-expanded mine graph. Further, the minimum cut in this graph will define an optimal sequence of pits. This result extends a well-known result of J.-C. Picard from 1976 for the open-pit mine design problem, that is, the single-period case, to the case of multiple time periods.

  • 41.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A Multi-Parametric Maximum Flow Characterization of the Open-Pit Scheduling ProblemManuscript (preprint) (Other academic)
    Abstract [en]

    We consider the problem of finding an optimal mining schedule for an openpit during a number of time periods, subject to a mining capacity restriction for each time period. By applying Lagrangian relaxation to the capacities, a multi-parametric formulation is obtained. We show that this formulation can be restated as a maximum flow problem in a time-expanded network. This result extends a well-known result of Picard from 1976 for the open-pit design problem, that is, the single-period case, to the case of multiple time periods.

  • 42.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the use of Parametric Open-Pit Design Models for Mine Scheduling - Pitfalls and CounterexamplesManuscript (preprint) (Other academic)
    Abstract [en]

    This paper discusses a Lagrangian relaxation interpretation of the Picard and Smith (2004) parametric approach to open-pit mining, which finds a sequence of intermediate contours leading to an ultimate one. This method is similar to the well known parametric approach of Lerchs and Grossmann (1965). We give examples of worst case performance, as well as best case performance of the Picard-Smith approach. The worst case behaviour can be very poor in that we might not obtain any intermediate contours at all. We also discuss alternative parametric methods for finding intermediate contours, but conclude that such methods seem to have inherent weaknesses.

  • 43.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Open-Pit Mining with Uncertainty - A Conditional Value-at-Risk ApproachManuscript (preprint) (Other academic)
    Abstract [en]

    The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty, and also the future market behaviour of metal prices and foreign exchange rates, which are impossible to be known with certainty, make mining a high risk business.

    Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does however have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev (2000) introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex problem.

    An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and price uncertainties.

  • 44.
    Amankwah, Henry
    et al.
    University of Cape Coast, Ghana .
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Open-pit mining with uncertainty: A conditional value-at-risk approach2013In: Optimization Theory, Decision Making, and Operations Research Applications: Proceedings of the 1st International Symposium and 10th Balkan Conference on Operational Research / [ed] Athanasios Migdalas, Angelo Sifaleras, Christos K. Georgiadis, Jason Papathanasiou, Emmanuil Stiakakis, New York: Springer, 2013, p. 117-139Conference paper (Refereed)
    Abstract [en]

    The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty and also the future market behavior of metal prices and foreign exchange rates, which are always uncertain, make mining a high risk business. Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does, however, have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev [J. Risk 2, 21-41 (2000)] introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex optimization problem. An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and market uncertainties.

  • 45.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Open-Pit Production Scheduling - Suggestions for Lagrangian Dual Heuristic and Time Aggregation ApproachesManuscript (preprint) (Other academic)
    Abstract [en]

    Open-pit production scheduling deals with the problem of deciding what and when to mine from an open-pit, given potential profits of the different fractions of the mining volume, pit-slope restrictions, and mining capacity restrictions for successive time periods. We give suggestions for Lagrangian dual heuristic approaches for the open-pit production scheduling problem. First, the case with a single mining capacity restriction per time period is considered. For this case, linear programming relaxations are solved to find values of the multipliers for the capacity restrictions, to be used in a Lagrangian relaxation of the constraints. The solution to the relaxed problem will not in general satisfy the capacity restrictions, but can be made feasible by adjusting the multiplier values for one time period at a time. Further, a time aggregation approach is suggested as a way of reducing the computational burden of solving linear programming relaxations, especially for largescale real-life mine problems. For the case with multiple capacity restrictions per time period we apply newly developed conditions for optimality and nearoptimality in general discrete optimization problems to construct a procedure for heuristically constructing near-optimal intermediate pits.

  • 46.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation2016In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 2, p. B297-B326Article in journal (Refereed)
    Abstract [en]

    The accurate and fast prediction of potential propagation in neuronal networks is of prime importance in neurosciences. This work develops a novel structure-preserving model reduction technique to address this problem based on Galerkin projection and nonnegative operator approximation. It is first shown that the corresponding reduced-order model is guaranteed to be energy stable, thanks to both the structure-preserving approach that constructs a distinct reduced-order basis for each cable in the network and the preservation of nonnegativity. Furthermore, a posteriori error estimates are provided, showing that the model reduction error can be bounded and controlled. Finally, the application to the model reduction of a large-scale neuronal network underlines the capability of the proposed approach to accurately predict the potential propagation in such networks while leading to important speedups.

  • 47.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2012Report (Other academic)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate dierence schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the rst demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial dierential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

  • 48.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, p. 573-590Article in journal (Refereed)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin–Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

  • 49.
    Andersen, Lisa
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tebring, Sandra
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Metakognitiva förmågors påverkan på elevers prestationer i matematisk problemlösning2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Problemlösning är en central matematisk förmåga och anses av många vara matematikens kärna. I ett försök att finna svar på hur den optimala undervisningen i problemlösning borde bedrivas, uppkom idén att studera elevers prestationer inom problemlösning kopplat till metakognition. Metakognition kan beskrivas som tänkande över det egna tänkandet och är en nödvändig förmåga i flera olika sammanhang. Denna litteraturstudie har till syfte att undersöka om metakognitiv förmåga påverkar elevers prestationer i matematisk problemlösning.Studien utgår från åtta artiklar som hittades via databasen UniSearch och det är dessa åtta artiklar som utgör resultatet. Artiklarnas metoder skiljer sig från varandra då vissa jämför elevers metakognitiva förmåga med deras prestationer inom problemlösning, medan andra testar effekten av olika undervisningsmetoder baserade på metakognition. Trots detta visar studiens resultat på att det finns ett samband mellan god metakognitiv förmåga och att prestera väl inom matematisk problemlösning. Utifrån detta dras slutsatsen att det är av stor vikt att elever får undervisning i metakognition, speciellt de svaga eleverna.

  • 50.
    Andersson, Carina
    Linköping University, Department of Mathematics.
    Taluppfattning: En undersökning av elevers förståelse av decimaltal2006Independent thesis Basic level (professional degree), 10 points / 15 hpStudent thesis
    Abstract [sv]

    I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.

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