| 1. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
-
Expedited analytical hierarchical process for multicriteria decision making
- 2022
-
Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151
-
Tidskriftsartikel (refereegranskat)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
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| 2. |
- Asratian, Armen, et al.
(författare)
-
Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
-
Ingår i: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
-
Tidskriftsartikel (refereegranskat)abstract
- An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.
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| 3. |
- Xia, Jiacheng, 1991
(författare)
-
Vector-valued Eisenstein series of congruence types and their products
- 2019
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
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| 4. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
-
Performance of the decision-making trial and evaluation laboratory
- 2023
-
Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
-
Tidskriftsartikel (refereegranskat)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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| 5. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
-
Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
-
Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 6. |
- Aas, Erik, et al.
(författare)
-
Limiting directions for random walks in classical affine Weyl groups
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
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| 7. |
- Brattström, Gudrun
(författare)
-
Leonardo da Pisa : Inger Christensen och Fibonacci
- 2008
-
Ingår i: Lyrikvännen. - 0460-0762. ; 55:6, s. 33-38
-
Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.
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| 8. |
- Andrén, Lina J., 1980-
(författare)
-
Avoidability by Latin squares of arrays of even order
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We prove that for any k and any 2k × 2k array A such that no cell in A contains more than k/2550 symbols, and no symbol occurs more than k/2550 times in any row or column, there is a Latin square such that no 2550cell in the Latin square contains a symbol that occurs in the corresponding cell in A. This proves a conjecture of Häggkvist [8] in the special case of arrays with even side.
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| 9. |
- Andrén, Lina J., 1980-
(författare)
-
Avoidability of random arrays
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- An n×n array that in each cell contains a subset of the symbols 1, . . . , n is avoidable if there exists a Latin square of order n such that no cell in the Latin square contains a symbol which belongs to the set of symbols in the corresponding cell of the array. Some results on deterministic conditions for avoidability of arrays have been found, but here we study the problem of having an array with randomly assigned subsets of C in its cells. This is equivalent to the problem of list-edge-coloring with randomly assigned lists from the set {1, . . . , n}. We show that an array where each symbol appears in each cell with probability p will be avoidable with very high probability even if p is such that the expected number of symbols forbidden in each cell is slightly higher than what deterministic theorems can prove is avoidable.
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| 10. |
- Andrén, Lina J., 1980-, et al.
(författare)
-
Avoiding arrays of odd order by Latin squares
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We prove that there exists a constant c such that for each pos- itive integer k every (2k+1)×(2k+1) array A on the symbols 1,...,2k+1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k+1) times in every row and column is avoidable; that is, there is a (2k+1)×(2k+1) Latin square S on the symbols 1,...,2k+1 such that for each cell (i, j) in S the symbol in (i, j) does not appear in the corresponding cell in A. This settles the last open case of a conjecture by Häggkvist.
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| 11. |
- Andrén, Lina J., 1980-
(författare)
-
Avoiding (m, m, m)-arrays of order n = 2k
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- An (m, m, m)-array of order n is an n × n array such that each cell is assigned a set of at most m symbols from {1,...,n} such that no symbol occurs more than m times in any row or column. An (m,m,m)- array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We show that there is a constant γ such that if m ≤ γ2k, then any (m,m,m)-array of order 2k is avoidable. Such a constant γ has been conjectured to exist for all n by Häggkvist.
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| 12. |
- Andrén, Lina J., 1980-
(författare)
-
On Latin squares and avoidable arrays
- 2010
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.
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| 13. |
|
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| 14. |
|
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| 15. |
-
Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings
- 2021
-
Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM.The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering.The book also contains 3 invited keynote papers.
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| 16. |
- Ekedahl, Torsten, 1955-
(författare)
-
Shellability of a Poset of Polygonal Subdivisions
- 2009
-
Ingår i: The Electronic Journal of Combinatorics. - : Annals of Mathematics. - 1097-1440 .- 1077-8926. ; 16:2, s. R23-
-
Tidskriftsartikel (refereegranskat)
|
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| 17. |
- Fleischner, Herbert, et al.
(författare)
-
Circuit double covers in special types of cubic graphs
- 2009
-
Ingår i: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 309:18, s. 5724-5728
-
Tidskriftsartikel (refereegranskat)abstract
- Suppose that a 2-connected cubic graph G of order n has a circuit C of length at least n−4 such that G−V(C) is connected. We show that G has a circuit double cover containing a prescribed set of circuits which satisfy certain conditions. It follows that hypohamiltonian cubic graphs (i.e., non-hamiltonian cubic graphs G such that G−v is hamiltonian for every v∈V(G)) have strong circuit double covers.
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| 18. |
|
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| 19. |
- Holmgren, Cecilia, 1984-, et al.
(författare)
-
Branching Markov chains: Stability and Applications
-
Annan publikation (populärvet., debatt m.m.)abstract
- We address the stability of certain tree algorithms used to solve the problem of communication between multiple users through a unique shared channel. We propose a general model based on branching Markov chains which allows us to write an intuitive stability condition. When the algorithm is stable, we show that there exist an asymptotic throughput, which is related to the asymptotic size of the underlying tree.
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| 20. |
- Holmgren, Cecilia, 1984-
(författare)
-
Novel Characteristics of Split Trees by use of Renewal Theory
- 2012
-
Ingår i: Electronic Journal of Probability. - 1083-6489 .- 1083-6489. ; 17, s. 5-
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate characteristics of random split trees introduced by Devroye [SIAM J Comput 28, 409-432, 1998]; split trees include e. g., binary search trees, m-ary search trees, quadtrees, median of (2k + 1)-trees, simplex trees, tries and digital search trees. More precisely: We use renewal theory in the studies of split trees, and use this theory to prove several results about split trees. A split tree of cardinality n is constructed by distributing n balls (which often represent data) to a subset of nodes of an infinite tree. One of our main results is a relation between the deterministic number of balls n and the random number of nodes N. In [5] there is a central limit law for the depth of the last inserted ball so that most nodes are close to depth lnn/mu + O(root lnn), where mu is some constant depending on the type of split tree; we sharpen this result by finding an upper bound for the expected number of nodes with depths >= lnn/mu - ln(1/2+epsilon) n or depths <= lnn/mu + ln(1/2+epsilon) n for any choice of epsilon > 0. We also find the first asymptotic of the variances of the depths of the balls in the tree.
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| 21. |
|
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| 22. |
- Holmgren, Cecilia, 1984-
(författare)
-
Random Records and Cuttings in Binary Search Trees
- 2010
-
Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 19:3, s. 391-424
-
Tidskriftsartikel (refereegranskat)abstract
- We study the number of random records in a binary search tree with n vertices (or equivalently, the number of cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. The asymptotic distribution of the (normalized) number of records or cuts is found to be weakly 1-stable.
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| 23. |
- Kiselman, Christer, 1939-
(författare)
-
Datorskärmens geometri
- 2008
-
Ingår i: Människor och matematik. - Göteborg : Göteborgs universitet, NCM. - 9789185143085 ; , s. 211-229
-
Bokkapitel (populärvet., debatt m.m.)
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| 24. |
- Kiselman, Christer, 1939-
(författare)
-
Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind
- 2008
-
Ingår i: Science in China Series A. - : Springer Science and Business Media LLC. - 1006-9283 .- 1862-2763. ; 51:4, s. 604-619
-
Tidskriftsartikel (refereegranskat)abstract
- We study the class of functions called monodiffric of the second kind by Isaacs. They are discrete analogues of holomorphic functions of one or two complex variables. Discrete analogues of the Cauchy-Riemann operator, of domains of holomorphy in one discrete variable, and of the Hartogs phenomenon in two discrete variables are investigated. Two fundamental solutions to the discrete Cauchy-Riemann equation are studied: one with support in a quadrant, the other with decay at infinity. The first is easy to construct by induction; the second is accessed via its Fourier transform.
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| 25. |
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| 26. |
- Leader, Imre, et al.
(författare)
-
Uncountable families of vertex-transitive graphs of finite degree
- 2006
-
Ingår i: Discrete Mathematics. ; 306:7, s. 678-679
-
Tidskriftsartikel (refereegranskat)abstract
- Recently the following question was relayed to the second author: What is the cardinality of the set of vertex transitive graphs of finite degree? Our aim in this short note is to show that there are $2^{\aleph_{0}}$ such graphs.
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| 27. |
- Schellwat, Holger
(författare)
-
Induced Cayley graphs and double covers
- 1995
-
Ingår i: Linear and multilinear algebra. - 0308-1087 .- 1563-5139. ; 39:1-2, s. 161-164
-
Tidskriftsartikel (refereegranskat)
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| 28. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
-
A Run-hierarchical Description of Upper Mechanical Words with Irrational Slopes Using Continued Fractions
- 2008
-
Ingår i: Proceedings of the 12th Mons Theoretical Science Days, Mons, Belgium 27-30 August 2008. - Mons, Belgium : Mons University.
-
Konferensbidrag (refereegranskat)abstract
- The main result is a run-hierarchical description (by continued fractions) of upper mechanical words with positive irrational slope less than 1 and intercept 0. We compare this description with two classical methods of forming of such words. In order to be able to perform the comparison, we present a quantitative analysis of our method. We use the denominator of the convergents of the continued fraction expansion of the slope to compute the length of the prefixes obtained by our method. Due to the special treatment which is given to the elements equal to 1, our method gives in some cases longer prefixes than the two other methods. Our method reflects the hierarchy of runs, by analogy to digital lines, which can give a new understanding of the construction of upper mechanical words.
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| 29. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
-
Continued fractions and digital lines with irrational slopes
- 2008
-
Ingår i: Proceedings of DGCI, the 14th International Conference on DISCRETE GEOMETRY for COMPUTER IMAGERY. DGCI 2008. - Berlin Heidelberg : Springer-Verlag. - 9783540791256 ; , s. 93-104
-
Konferensbidrag (refereegranskat)abstract
- This paper expands on previous work on relationships between digital linesand continued fractions (CF). The main result is a parsimonious description of the construction of the digital line based only on the elements of the CF representing its slope and containing only simple integer computations. The description reflects the hierarchy of digitization runs, which raises the possibility of dividing digital lines into equivalence classes depending on the CF expansions of their slopes. Our work is confined to irrational slopes since, to our knowledge, there exists no such description for these, in contrast to rational slopes which have been extensively examined. The description is exact and does not use approximations by rationals. Examples of lines withirrational slopes and with very simple digitization patterns are presented. These include both slopes with periodic and non-periodic CF expansions, i.e.\ both quadratic surds and other irrationals.
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| 30. |
- Uscka-Wehlou, Hania, 1973-
(författare)
-
Continued fractions, Fibonacci numbers, and some classes of irrational numbers
- 2010
-
Ingår i: Acta Mathematica Academiae Paedagogiace Nyíregyháziensis. - 1786-0091. ; 26:1, s. 17-30
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we define an equivalence relation on the set of positive irrational numbers less than 1. The relation is defined by means of continued fractions. Equivalence classes under this relation are determined by the places of some elements equal to 1 (called essential 1's) in the continued fraction expansion of numbers. Analysis of suprema of all equivalence classes leads to a solution which involves Fibonacci numbers and constitutes the main result of this paper. The problem has its origin in the author'sresearch on the construction of digital lines and upper and lower mechanical and characteristic words according to the hierarchy of runs.
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| 31. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
-
Digital lines, Sturmian words, and continued fractions
- 2009
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we present and solve selected problems arising from digital geometry and combinatorics on words. We consider digital straight lines and, equivalently, upper mechanical words with positive irrational slopes a<1 and intercept 0. We formulate a continued fraction (CF) based description of their run-hierarchical structure. Paper I gives a theoretical basis for the CF-description of digital lines. We define for each irrational positive slope less than 1 a sequence of digitization parameters which fully specifies the run-hierarchical construction. In Paper II we use the digitization parameters in order to get a description of runs using only integers. We show that the CF-elements of the slopes contain the complete information about the run-hierarchical structure of the line. The index jump function introduced by the author indicates for each positive integer k the index of the CF-element which determines the shape of the digitization runs on level k. In Paper III we present the results for upper mechanical words and compare our CF-based formula with two well-known methods, one of which was formulated by Johann III Bernoulli and proven by Markov, while the second one is known as the standard sequences method. Due to the special treatment of some CF-elements equal to 1 (essential 1's in Paper IV), our method is currently the only one which reflects the run-hierarchical structure of upper mechanical words by analogy to digital lines. In Paper IV we define two equivalence relations on the set of all digital lines with positive irrational slopes a<1. One of them groups into classes all the lines with the same run length on all digitization levels, the second one groups the lines according to the run construction in terms of long and short runs on all levels. We analyse the equivalence classes with respect to minimal and maximal elements. In Paper V we take another look at the equivalence relation defined by run construction, this time independently of the context, which makes the results more general. In Paper VI we define a run-construction encoding operator, by analogy with the well-known run-length encoding operator. We formulate and present a proof of a fixed-point theorem for Sturmian words. We show that in each equivalence class under the relation based on run length on all digitization levels (as defined in Paper IV), there exists exactly one fixed point of the run-construction encoding operator.
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| 32. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
-
Run-hierarchical structure of digital lines with irrational slopes in terms of continued fractions and the Gauss map
- 2009
-
Ingår i: Pattern Recognition. - : Elsevier. - 0031-3203 .- 1873-5142. ; 42:10, s. 2247-2254
-
Tidskriftsartikel (refereegranskat)abstract
- We study relations between digital lines and continued fractions. The main result is a parsimonious description of the construction of the digital line based only on the elements of the continued fraction representing its slope and containing only simple integer computations. The description reflects the hierarchy of digitization runs, which raises the possibility of dividing digital lines into equivalence classes depending on the continued fraction expansions of their slopes. Our work is confined to irrational slopes since, to our knowledge,there exists no such description for these, in contrast to rational slopes which have been extensively examined. The description is exact (it does not use approximations by rationals). Examples of lines with irrational slopes and with very simple digitization patterns are presented. These include both slopes with periodic and non-periodic continued fraction expansions, i.e.\ both quadratic surds and other irrationals. We also derive the connection between the Gauss map and the digitization parameters introduced by the author in 2007.
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| 33. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
-
Sturmian words with balanced construction
- 2009
-
Ingår i: Proceedings of Words 2009, the 7th International Conference on Words (Salerno, Italy), 14--18 September 2009. - Italy : Salerno University.
-
Konferensbidrag (refereegranskat)abstract
- In this paper we define Sturmian words with balanced construction. We formulate a fixed-point theorem for Sturmian words and analyze the set of all fixed points. The inspiration for this work came from the Kolakoski word and the general idea of self-reading sequences by P\u{a}un and Salomaa. The basis for this article is the author's earlier research on the influence of the continued fraction elements in the expansion of a positive irrational slope $a<1$ on the construction of runs for the upper mechanical word with slope $a$and intercept $0$.
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| 34. |
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| 35. |
- Öhman, Lars-Daniel
(författare)
-
Partial latin squares are avoidable
- 2011
-
Ingår i: Annals of Combinatorics. - : Springer Science and Business Media LLC. - 0218-0006 .- 0219-3094. ; 15:3, s. 485-497
-
Tidskriftsartikel (refereegranskat)abstract
- A square array is avoidable if for each set of n symbols there is an n x n Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for m >= 2 any partial Latin square of order 4m - 1 is avoidable, thus concluding the proof that any partial Latin square of order at least 4 is avoidable.
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| 36. |
- Fotedar, Sunney, 1989, et al.
(författare)
-
A criterion space decomposition approach to generalized tri-objective tactical resource allocation
- 2023
-
Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 20:1
-
Tidskriftsartikel (refereegranskat)abstract
- We present a tri-objective mixed-integer linear programming model of the tactical resource allocation problem with inventories, called the generalized tactical resource allocation problem (GTRAP). We propose a specialized criterion space decomposition strategy, in which the projected two-dimensional criterion space is partitioned and the corresponding sub-problems are solved in parallel by application of the quadrant shrinking method (QSM) (Boland in Eur J Oper Res 260(3):873–885, 2017) for identifying non-dominated points. To obtain an efficient implementation of the parallel variant of the QSM we suggest some modifications to reduce redundancies. Our approach is tailored for the GTRAP and is shown to have superior computational performance as compared to using the QSM without parallelization when applied to industrial instances.
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| 37. |
- Fotedar, Sunney, 1989
(författare)
-
Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item , multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to functional workshops where costly and/or time- and resource-demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory. In Paper I , we propose a new bi-objective mixed-integer (linear) optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. In Paper II , we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. In Paper III , we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV , using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap .
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| 38. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
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Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model
- 2024
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Ingår i: Journal of Scheduling. - 1099-1425 .- 1094-6136. ; 27:1, s. 87-101
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Tidskriftsartikel (refereegranskat)abstract
- Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and themaintenanceworkshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon.We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.
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| 39. |
- Ardila, Federico, et al.
(författare)
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The equivariant Ehrhart theory of the permutahedron
- 2020
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 148:12, s. 5091-5107
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Tidskriftsartikel (refereegranskat)abstract
- Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.
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| 40. |
- Eur, Christopher, et al.
(författare)
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The universal valuation of Coxeter matroids
- 2021
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Ingår i: Bulletin of the London Mathematical Society. - : Wiley. - 0024-6093 .- 1469-2120. ; 53:3, s. 798-819
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Tidskriftsartikel (refereegranskat)abstract
- Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We compute the universal valuative invariant of Coxeter matroids. A key ingredient is the family of Coxeter Schubert matroids, which correspond to the Bruhat cells of flag varieties. In the process, we compute the universal valuation of generalized Coxeter permutohedra, a larger family of polyhedra that model Coxeter analogues of combinatorial objects such as matroids, clusters, and posets.
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| 41. |
- Lundman, Anders, 1985-, et al.
(författare)
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A note on higher order Gauss Maps
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X, with k > 1, then the Gauss map of order k has finite fibers, unless X = P^n is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a combinatorial description of the Gauss maps of order k, its image and the general fibers.
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| 42. |
- Lundman, Anders, 1985-
(författare)
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Computing Seshardi constants on smooth toric surfaces
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we compute the Seshadri constants at the general point on many smooth polarized toric surfaces. We consider the case when the degree of jet separation is small or the core of the associated polygon is a line segment. Our main result is that in this case the Seshadri constant at the general point can often be determined in terms of easily computable invariants of the surfaces at hand. Lastly we consider the case that the core of the associated polygon is a point for a smooth polarized toric surface (X, L ). We show that in this case X can be constructed via consecutive equivariant blow-ups of either P^2 or P^1 x P^1.
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| 43. |
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| 44. |
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| 45. |
- Thunberg, Hans, 1956-
(författare)
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Tonsättaren Per Nörgårds ''oändlighetsserie"
- 2013
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Ingår i: Normat. - : Scandinavian University Press. - 0801-3500. ; 61:1, s. 33-47
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Tidskriftsartikel (refereegranskat)abstract
- This article presents a mathematical description, in terms of recursively defined number sequences, of the algorithms devised by the Danish composer Nørgård. The ambition of the latter was to generate from a very short sequence of tones melodies rich in symmetries and selfsimilarities, melodies which could be aperiodic and hence infinite in length. Given the mathematical presentation a variety of results can be formulated and proved. Note that the well-known Thue-Morse sequence is essentially a special case.
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| 46. |
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| 47. |
- Kurujyibwami, Celestin
(författare)
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Admissible transformations and the group classification of Schrödinger equations
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
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| 48. |
- Alexandersson, Per, et al.
(författare)
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Refined Catalan and Narayana cyclic sieving
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of “ears”, non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.
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| 49. |
- Casselgren, Carl Johan, et al.
(författare)
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Edge precoloring extension of hypercubes
- 2020
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Ingår i: Journal of Graph Theory. - : John Wiley & Sons. - 0364-9024 .- 1097-0118. ; 95:3, s. 410-444
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most d − 1 edges of the d‐dimensional hypercube Qd can be extended to a proper d‐edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d‐edge colorings of Qd.
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| 50. |
- Eriksen, Niklas, 1974-
(författare)
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Expected number of breakpoints after t random reversals in genomes with duplicate genes
- 2008
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Ingår i: Discrete Applied Mathematics. - Amsterdam, Netherlands : Elsevier. - 0166-218X .- 1872-6771. ; 156:12, s. 2320-2335
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Tidskriftsartikel (refereegranskat)abstract
- In comparative genomics, one wishes to deduce the evolutionary distance between different species by studying their genomes. Using gene order information, we seek the number of times the gene order has changed between two species. One approach is to compute the method of moments estimate of this edit distance from a measure of dissimilarity called the breakpoint measure. In this paper, we extend formulae and bounds of this estimate on gene permutations to genomes with duplicate genes.
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