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  • 1.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

  • 2.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, 52-62 p.Conference paper (Other academic)
  • 3.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, 29-38 p.Article in journal (Refereed)
  • 4.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 5.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Faculty of Engineering Technology, University of Twente, AE Enschede, The Netherlands.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy Stability of the MUSCL Scheme2010In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, 65:1-8 p.Conference paper (Other academic)
  • 6.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, 61-68 p.Conference paper (Refereed)
  • 7.
    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, 289-293 p.Conference 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
    Keyword
    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, 1047-1052 p.Article 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.

    Keyword
    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.

    Keyword
    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
  • 8.
    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.

  • 9.
    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, 289-293 p.Conference 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?

  • 10.
    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.

  • 11.
    Abrahamsson, Olle
    Linköping University, Department of Electrical Engineering, Communication Systems.
    Hide and Seek in a Social Network2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis a known heuristic for decreasing a node's centrality scores while maintaining influence, called ROAM, is compared to a modified version specifically designed to decrease eigenvector centrality. The performances of these heuristics are also tested against the Shapley values of a cooperative game played over the considered network, where the game is such that influential nodes receive higher Shapley values. The modified heuristic performed at least as good as the original ROAM, and in some instances even better (especially when the terrorist network behind the World Trade Center attacks was considered). Both heuristics increased the influence score for a given targeted node when applied consecutively on the WTC network, and consequently the Shapley values increased as well. Therefore the Shapley value of the game considered in this thesis seems to be well suited for discovering individuals that are assumed to actively trying to evade social network analysis.

  • 12. Accardi, L
    et al.
    Brody, DC
    Belavkin, VP
    Kent, JT
    Bingham, NH
    Frey, JG
    Helland, IS
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Majumdar, NK
    Minozzo, M
    Thompson, JW
    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, 805-816 p.805-816 p.Article in journal (Refereed)
  • 13.
    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, 1131-1153 p.Article 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.

  • 14.
    Adolfsson, Anna
    et al.
    Linköping University, Department of Educational Science (IUV).
    Hesslid, Anna-Carin
    Linköping University, Department of Educational Science (IUV).
    Lärarens matematikundervisning: elevens matematikutveckling? En studie om matematiksvårigheter.2002Independent thesis Basic level (professional degree)Student thesis
    Abstract [sv]

    Examensarbetet ger en bild av både lärares och forskares syn på matematiksvårigheter samt deras uppfattning om orsakerna bakom problemen. Vi har undersökt vilka områden i matematiken som elever med matematiksvårigheter har mest problem med samt hur läraren förklarar och underlättar matematiken för dessa elever. Både forskningen och de lärare vi intervjuat är överens om att begreppet matematiksvårigheter är väldigt komplext. Orsakerna kan vara av medicinsk/neurologisk, psykologisk, sociologisk och didaktisk karaktär.

    I våra intervjuer framkommer att positionssystemet, bråk, procent, enheter, multiplikation och division är de områden som kan ställa till mest problem för elever med matematiksvårigheter. Dessa områden nämns även inom forskningen som möjliga problemområden. För att underlätta matematiken för elever med matematiksvårigheter anser forskarna att det är viktigt att undervisningen utgår från elevernas erfarenheter och förkunskaper. De påpekar också vikten av att undervisningen varieras och bör innefatta såväl laborativa som teoretiska arbetssätt där även diskussioner och gruppuppgifter ska förekomma. För att se på vilken nivå lärarna börjar förklara för elever med matematiksvårigheter gav vi dem tre uppgifter som de fick förklara. Svaren placerades in i fyra kategorier:

    1 Erfarenhet/vardag,

    2. Konkret material,

    3. Rita,

    4. Räkna.

    Resultatet visar att lärarna oftast börjar sin förklaring i kategori fyra. Många hamnar i kategori tre och väldigt få hamnar i kategori ett och två.

  • 15.
    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, 2872-2876 p.Article 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.

  • 16.
    Aerts, Sven
    et al.
    Fundamenten van de Exacte Wetenschappen Vrije Universiteit Brussel.
    Larsson, Jan-Åke
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Kwiat, Paul
    Los Alamos National Laboratory.
    Zukowski, Marek
    Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdanski.
    Aerts et al. Reply2001In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 86, no 9, 1909-1909 p.Article in journal (Refereed)
  • 17.
    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, 519-528 p.Article 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.

  • 18.
    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, 243-251 p.Article 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.

  • 19.
    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, 161-170 p.Article 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.

  • 20.
    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.

  • 21.
    Ahlinder, Jon
    et al.
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Nordgaard, Anders
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Swedish National Forensic Centre (NFC), Linköping, Sweden.
    Wiklund Lindström, Susanne
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Chemometrics comes to court: evidence evaluation of chem–bio threat agent attacks2015In: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 29, no 5, 267-276 p.Article in journal (Refereed)
    Abstract [en]

    Forensic statistics is a well-established scientific field whose purpose is to statistically analyze evidence in order to support legal decisions. It traditionally relies on methods that assume small numbers of independent variables and multiple samples. Unfortunately, such methods are less applicable when dealing with highly correlated multivariate data sets such as those generated by emerging high throughput analytical technologies. Chemometrics is a field that has a wealth of methods for the analysis of such complex data sets, so it would be desirable to combine the two fields in order to identify best practices for forensic statistics in the future. This paper provides a brief introduction to forensic statistics and describes how chemometrics could be integrated with its established methods to improve the evaluation of evidence in court.

    The paper describes how statistics and chemometrics can be integrated, by analyzing a previous know forensic data set composed of bacterial communities from fingerprints. The presented strategy can be applied in cases where chemical and biological threat agents have been illegally disposed.

  • 22.
    Ahmad, M. Rauf
    Linköping University, Department of Mathematics.
    A note on the (n, p)-asymptotics of ATS for high dimensional multivariate data2010Report (Other academic)
  • 23.
    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).

  • 24.
    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)
  • 25.
    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.

  • 26.
    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.

  • 27.
    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, 2619-2631 p.Article 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.

  • 28.
    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, 1387-1398 p.Article 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.

  • 29.
    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, 81-99 p.Article 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.

  • 30.
    Ahnell, Torbjörn
    Linköping University, Department of Educational Science (IUV).
    Läromedelsanalys matematik A2006Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    Bakgrund: Rapporter från Skolverket, Nationellt Centrum för Matematikutbildning och Utbildnings-departementet visar att dagens matematikundervisning dominerande är traditionell, att eleverna har svårt för problemlösning och att eleverna i hög grad hänvisas till läromedlet. Studier visar också att inslag av undersökande pedagogik (problembaserat lärande, laborativ matematik) påverkar elevernas attityd och resultat positivt. Sedan lpf94 finns också krav i styrdokumenten som syftar till undersökande pedagogik. Mot bakgrund av detta formuleras den här studiens syfte så här:

    Syfte: Att se om inslagen av undersökande pedagogik i läromedlen för gymnasiets kurs Matematik A (eller motsvarande) har förändrat sig under perioden 1980-2006.

    Metod: ·Kvalitativ analys av stil och språkbruk.

    ·Andel uppgifter av undersökande karaktär

    ·Andel intresseväckande bilder som syftar till helhetssyn eller sammanhang.

    Resultat: Det syns tydligt ökade inslag av undersökande pedagogik sedan 80-talets läromedel Gamma Grön. Brytpunkten för denna utveckling var sannolikt början av 90-talet då gymnasiet reformerades. Sedan denna brytpunkt syns också en vidareutveckling, där nya läromedel som Den flygande matten väger in tungt.

  • 31.
    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, 161-170 p.Article 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.

  • 32.
    Aitken, Colin
    et al.
    University of Edinburgh - School of Mathematics.
    Nordgaard, Anders
    Linköping University, Faculty of Arts and Sciences. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Polismyndigheten - Nationellt Forensiskt Centrum.
    The Roles of Participants’ DifferingBackground Information in the Evaluation of Evidence2017In: Journal of Forensic Sciences, ISSN 0022-1198, E-ISSN 1556-4029Article in journal (Refereed)
  • 33.
    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, 4533-4606 p.Article 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.

  • 34.
    Alnervik, Jonna
    et al.
    Linköping University, Department of Computer and Information Science, Statistics.
    Nord Andersson, Peter
    Linköping University, Department of Computer and Information Science, Statistics.
    En retrospektiv studie av vilka patientgrupper som erhåller insulinpump2010Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Målsättning

    Att utreda skillnader i tillgänglighet till insulinpump mellan olika patientgrupper samt vad som orsakar ett byte till insulinpump.

    Metod

    Data från 7224 individer med typ 1 diabetes vid tio olika vårdenheter analyserades för att utreda effekterna av njurfunktion, kön, långtidsblodsocker, insulindos, diabetesduration samt ålder. Jämförelsen mellan patientgrupper utfördes med logistisk regression som en tvärsnittsstudie och Cox-regression för att utreda vad som föregått ett byte till pump.

    Resultat

    Genom logistisk regression erhölls en bild av hur skillnader mellan patienter som använder insulinpump och patienter som inte gör det ser ut i dagsläget. Cox-regressionen tar med ett tidsperspektiv och ger på så sätt svar på vad som föregått ett byte till insulinpump. Dessa analyser gav liknande resultat gällande variabler konstanta över tiden. Kvinnor använder pump i större utsträckning än män och andelen pumpanvändare skiljer sig åt vid olika vårdenheter. I dagsläget visar sig hög ålder sänka sannolikheten att använda insulinpump, vilket bekräftas vid den tidsberoende studien som visade hur sannolikheten att byta till pump är avsevärt lägre vid hög ålder. Långtidsblodsockret har också tydlig effekt på sannolikheten att gå över till pump där ett högt långtidsblodsocker medför hög sannolikhet att byta till insulinpump.

    Slutsatser

    I dagsläget finns det skillnader i andelen insulinpumpanvändare mellan olika patientgrupper och skillnader finns även i de olika gruppernas benägenhet att byta från andra insulinbehandlingar till insulinpump. Beroende av patienters njurfunktion, kön, långtidsblodsocker, insulindos, diabetesduration och ålder har dessa olika sannolikheter att byta till insulinpump.

  • 35.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    The Geometric Phase of Stock Trading2016In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 11, no 8, e0161538- p.Article in journal (Refereed)
    Abstract [en]

    Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

  • 36.
    Alvbrant, Joakim
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Keshmiri, Vahid
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, Faculty of Science & Engineering.
    Wikner, Jacob
    Linköping University, Department of Electrical Engineering, Integrated Circuits and Systems. Linköping University, Faculty of Science & Engineering.
    Transfer Characteristics and Bandwidth Limitation in a Linear-Drift Memristor Model2015In: 2015 EUROPEAN CONFERENCE ON CIRCUIT THEORY AND DESIGN (ECCTD), IEEE , 2015, 332-335 p.Conference paper (Refereed)
    Abstract [en]

    The linear-drift memristor model, suggested by HP Labs a few years ago, is used in this work together with two window functions. From the equations describing the memristor model, the transfer characteristics of a memristor is formulated and analyzed. A first-order estimation of the cut-off frequency is shown, that illustrates the bandwidth limitation of the memristor and how it varies with some of its physical parameters. The design space is elaborated upon and it is shown that the state speed, the variation of the doped and undoped regions of the memristor, is inversely proportional to the physical length, and depth of the device. The transfer characteristics is simulated for Joglekar-Wolf, and Biolek window functions and the results are analyzed. The Joglekar-Wolf window function causes a distinct behavior in the tranfer characteristics at cut-off frequency. The Biolek window function on the other hand gives a smooth state transfer function, at the cost of loosing the one-to-one mapping between charge and state. We also elaborate on the design constraints derived from the transfer characteristics.

  • 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, 1017-1054 p.Article 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.

    Keyword
    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.

    Keyword
    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.

    Keyword
    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.

    Keyword
    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: 2013-08-30Bibliographically 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.

    Keyword
    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.
    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.

  • 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.
    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.

  • 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.
    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.

  • 43.
    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, 117-139 p.Conference 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.

  • 44.
    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.

  • 45.
    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, B297-B326 p.Article 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.

  • 46.
    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.

  • 47.
    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, 573-590 p.Article 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.

  • 48.
    Anderskär, Erika
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Thomasson, Frida
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Inkrementell responsanalys av Scandnavian Airlines medlemmar: Vilka kunder ska väljas vid riktad marknadsföring?2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Scandinavian Airlines has a large database containing their Eurobonus members. In order to analyze which customers they should target with direct marketing, such as emails, uplift models have been used. With a binary response variable that indicates whether the customer has bought or not, and a binary dummy variable that indicates if the customer has received the campaign or not conclusions can be drawn about which customers are persuadable. That means that the customers that buy when they receive a campaign and not if they don't are spotted. Analysis have been done with one campaign for Sweden and Scandinavia. The methods that have been used are logistic regression with Lasso and logistic regression with Penalized Net Information Value. The best method for predicting purchases is Lasso regression when comparing with a confusion matrix. The variable that best describes persuadable customers in logistic regression with PNIV is Flown (customers that have own with SAS within the last six months). In Lassoregression the variable that describes a persuadable customer in Sweden is membership level1 (the rst level of membership) and in Scandinavia customers that receive campaigns with delivery code 13 are persuadable, which is a form of dispatch.

  • 49.
    Andersson, Aina
    et al.
    Linköping University, Department of Behavioural Sciences and Learning. Linköping University, Faculty of Educational Sciences.
    Persson, Ing-Marie
    Linköping University, Department of Behavioural Sciences and Learning. Linköping University, Faculty of Educational Sciences.
    Svagt arbetsminne - orsaken till matematiksvårigheter?2013Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien var att se om det finns ett samband mellan matematiksvårigheter och elevens arbetsminne. Utifrån ett befintligt resultat från screeningtest valdes 19 elever ut med matematiksvårigheter, och ytterligare 20 som kontrollgrupp. Därefter genomfördes arbetsminnestester samt test av antalsuppfattning. Undersökningarna utfördes i år 3 och 4 på två olika skolor. Arbetsminnestesterna testade den centrala exekutiven, fonologiska loopen, visuella skissblocket, process-hastighet. Resultaten som analyserades med variansanalys visade att det finns samband mellan arbetsminne och matematiksvårigheter. Studien visar på specifika störningar i centrala exekutiven, men också störningar i den medfödda antalsuppfattningen.

     

  • 50.
    Andersson, Anna
    Linköping University, Department of Behavioural Sciences and Learning.
    Ett laborativt arbetssätt i matematik: I skolår 1 och 22007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    Ett intresse för matematik och nyfikenhet över hur jag i framtiden ska kunna göra matematiklektionerna meningsfulla och vardagsnära för mina elever bidrog till att jag, när jag fick den, tog chansen att genomföra ett temaarbete med ett laborativt arbetssätt och göra en fallstudie över detta.

    Tidigare forskning visar att det är viktigt att utgå från elevers olika individuella förutsättningar, göra lektionerna vardagsnära, meningsfulla, varierande och även gärna lustfyllda. Forskningen visar även på kommunikationens betydelse, särskilt vikten av att kommunicera så att eleverna förstår både vad de förväntas lära och vad de kan utveckla.

    Detta examensarbete är skrivet utifrån ett sociokulturellt perspektiv efter att en fallstudie, inspirerad av aktionsforskning, bestående av såväl observationer, intervjuer, samtal och enkäter genomförts.

    Resultatet visar att ett laborativt arbetssätt gynnar alla elever, inte minst de svaga då det ger många möjligheter till att låta eleverna uppleva och upptäcka. Lärarna betonar vikten av att noggrant planera lektionerna samt att vara medveten om hur man kommunicerar undervisningsinnehållet. De menar också att ett laborativt arbetssätt ger goda möjligheter till individanpassning eftersom arbetet kan utgå från de enskilda elevernas individuella behov.

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