| 11. |
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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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| 12. |
- Gäfvert, Oliver, 1991-
(författare)
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Topological and geometrical methods in data analysis
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. The shape is described using a persistence module, which characterizes the topological features of the filtration, and the final step of the pipeline extracts algebraic invariants from this object. The second pipeline, referred to as the geometric data analysis (GDA) pipeline, associates an algebraic variety to a given data set and aims to describe the structure of this variety. Its structure is described using homology, an invariant which for most algebraic varieties can only be computed numerically using sampling methods.In Paper A we consider invariants on multi-parameter persistence modules. We explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard.In Paper B we introduce an efficient algorithm to compute a minimal presentation of a multi-parameter persistent homology module, given a chain complex of free modules as input. Our approach extends previous work on this problem in the 2-parameter case, and draws on ideas underlying the F4 and F5 algorithms for Gröbner basis computation. In the r-parameter case, our algorithm computes a presentation for the homology of C ->F A ->G B, with modules of rank l,n,m respectively, in O(r2nr+1 + nrm + nr-1m2 + rn2 l) arithmetic operations. We implement this approach in our new software Muphasa, written in C++. In preliminary computational experiments on synthetic TDA examples, we compare our approach to a version of a classical approach based on Schreyer's algorithm, and find that ours is substantially faster and more memory efficient. In the course of developing our algorithm for computing presentations, we also introduce algorithms for the closely related problems of computing Gröbner bases for the image and kernel of the morphism G. This algorithm runs in time O(nrm + nr-1m2) and memory O(n2 + mn + nr + K), where K is the size of the output.Paper C analyzes the complexity of fitting a variety, coming from a class of varieties, to a configuration of points in RN. The complexity measure, called the algebraic complexity, computes the Euclidean Distance Degree (EDD) of a certain variety called the hypothesis variety as the number of points in the configuration increases. Finally, we establish a connection to complexity of architectures of polynomial neural networks. For the problem of fitting an (N-1)-sphere to a configuration of m points in RN, we give a closed formula for the algebraic complexity of the hypothesis variety as m grows for the case of N=1. For the case N>1 we conjecture a generalization of this formula supported by numerical experiments.In Paper D we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing bottlenecks of the variety. Using geometric information such as the bottlenecks and the local reach we also provide bounds on the density of the sample needed in order to guarantee that the homology of the variety can be recovered from the sample. An implementation of the algorithm is provided together with numerical experiments and a computational comparison to the algorithm by Dufresne et. al. (2019).
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| 13. |
- Fotedar, Sunney, 1989, et al.
(författare)
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A criterion space decomposition approach to generalized tri-objective tactical resource allocation
- 2023
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Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 20:1
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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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| 14. |
- 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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| 15. |
- 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
-
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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| 16. |
- Asekritova, Irina, et al.
(författare)
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Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
- 2009
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Ingår i: Mathematical modelling of wave phenomena. - Melville, New York : American Institute of Physics. ; , s. 224-232, s. 224-232
-
Konferensbidrag (refereegranskat)abstract
- Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.
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| 17. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.
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| 18. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
-
Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
- 2009
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.
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| 19. |
- Enstedt, Mattias
(författare)
-
Selected Topics in Partial Differential Equations
- 2011
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This Ph.D. thesis consists of five papers and an introduction to the main topics of the thesis. In Paper I we give an abstract criteria for existence of multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators. In paper II we establish existence of infinitely many solutions to the quasirelativistic Hartree-Fock equations for Coulomb systems along with properties of the solutions. In Paper III we establish existence of a ground state to the magnetic Hartree-Fock equations. In Paper IV we study the Choquard equation with general potentials (including quasirelativistic and magnetic versions of the equation) and establish existence of multiple solutions. In Paper V we prove that, under some assumptions on its nonmagnetic counterpart, a magnetic Schrödinger operator admits a representation with a positive Lagrange density and we derive consequences of this property.
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| 20. |
- Hamon, Thierry, et al.
(författare)
-
Combining Compositionality and Pagerank for the Identification of Semantic Relations between Biomedical Words
- 2012
-
Ingår i: BioNLP. - 9781937284206 - 1937284204 ; , s. 109-117
-
Konferensbidrag (refereegranskat)abstract
- The acquisition of semantic resources and relations is an important task for several applications, such as query expansion, information retrieval and extraction, machine translation. However, their validity should also be computed and indicated, especially for automatic systems and applications. We exploit the compositionality based methods for the acquisition of synonymy relations and of indicators of these synonyms. We then apply pagerank-derived algorithm to the obtained semantic graph in order to filter out the acquired synonyms. Evaluation performed with two independent experts indicates that the quality of synonyms is systematically improved by 10 to 15% after their filtering.
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