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Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings
- 2021
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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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| 3. |
- Holmgren, Cecilia, 1984-, et al.
(författare)
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Branching Markov chains: Stability and Applications
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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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| 4. |
- Holmgren, Cecilia, 1984-
(författare)
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Novel Characteristics of Split Trees by use of Renewal Theory
- 2012
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Ingår i: Electronic Journal of Probability. - 1083-6489. ; 17, s. 5-
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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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| 5. |
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| 6. |
- Holmgren, Cecilia, 1984-
(författare)
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Random Records and Cuttings in Binary Search Trees
- 2010
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Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 19:3, s. 391-424
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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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| 7. |
- Kiselman, Christer, 1939-
(författare)
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Datorskärmens geometri
- 2008
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Ingår i: Människor och matematik. - Göteborg : Göteborgs universitet, NCM. - 9789185143085 ; , s. 211-229
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Bokkapitel (populärvet., debatt m.m.)
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| 8. |
- Kiselman, Christer, 1939-
(författare)
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Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind
- 2008
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Ingår i: Science in China Series A. - : Springer Science and Business Media LLC. - 1006-9283 .- 1862-2763. ; 51:4, s. 604-619
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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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| 10. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
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A Run-hierarchical Description of Upper Mechanical Words with Irrational Slopes Using Continued Fractions
- 2008
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Ingår i: Proceedings of the 12th Mons Theoretical Science Days, Mons, Belgium 27-30 August 2008. - Mons, Belgium : Mons University.
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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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