| 1. |
- Dhamal, Swapnil Vilas, 1988, et al.
(författare)
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Resource Allocation Polytope Games: Uniqueness of Equilibrium, Price of Stability, and Price of Anarchy
- 2018
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Ingår i: AAAI 2018 - Proceedings of the 32nd AAAI Conference on Artificial Intelligence. ; , s. 997-1006
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Konferensbidrag (refereegranskat)abstract
- We consider a two-player resource allocation polytope game, in which the strategy of a player is restricted by the strategy of the other player, with common coupled constraints. With respect to such a game, we formally introduce the notions of independent optimal strategy profile, which is the profile when players play optimally in the absence of the other player; and common contiguous set, which is the set of top nodes in the preference orderings of both the players that are exhaustively invested on in the independent optimal strategy profile. We show that for the game to have a unique PSNE, it is a necessary and sufficient condition that the independent optimal strategies of the players do not conflict, and either the common contiguous set consists of at most one node or all the nodes in the common contiguous set are invested on by only one player in the independent optimal strategy profile. We further derive a socially optimal strategy profile, and show that the price of anarchy cannot be bound by a common universal constant. We hence present an efficient algorithm to compute the price of anarchy and the price of stability, given an instance of the game. Under reasonable conditions, we show that the price of stability is 1. We encounter a paradox in this game that higher budgets may lead to worse outcomes.
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| 2. |
- Fotedar, Sunney, 1989, et al.
(författare)
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Mathematical optimization of the tactical allocation of machining resources for an efficient capacity utilization in aerospace component manufacturing
- 2019
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Ingår i: Proceedings of the 10th Aerospace Technology Congress. - : Linköping University Electronic Press. - 1650-3686 .- 1650-3740. - 9789175190068 ; , s. 183-188
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Konferensbidrag (refereegranskat)abstract
- In the aerospace industry, with low volumes and many products, there is a critical need to efficiently use available manufacturing resources. Currently, at GKN Aerospace, resource allocation decisions that in many cases will last for several years are to some extent made with a short-term focus so as to minimize machining time, which results in a too high load on the most capable machines, and too low load on the less capable ones. This creates an imbalance in capacity utilization that leads to unnecessary queuing at some machines, resulting in long lead times and in an increase in tied-up capital. Tactical resource allocation on the medium to long-range planning horizon (six months to several years) aims to address this issue by allocating resources to meet the predicted future demand as effectively as possible, in order to ensure long range profitability. Our intent is to use mathematical optimization to find the best possible allocations.
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| 3. |
- Johansson, Moa, 1981, et al.
(författare)
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Conjectures, tests and proofs: An overview of theory exploration
- 2021
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Ingår i: Electronic Proceedings in Theoretical Computer Science, EPTCS. - 2075-2180. ; 341, s. 1-16
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Konferensbidrag (refereegranskat)abstract
- A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to automatically discover interesting conjectures about a given set of functions. QuickSpec works by interleaving term generation with random testing to form candidate conjectures. This is made tractable by starting from small sizes and ensuring that only terms that are irreducible with respect to already discovered conjectures are considered. QuickSpec has been successfully applied to generate lemmas for automated inductive theorem proving as well as to generate specifications of functional programs. We give an overview of typical use-cases of QuickSpec, as well as demonstrating how to easily connect it to a theorem prover of the user’s choice.
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| 4. |
- Alexandersson, Per, et al.
(författare)
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P-partitions and p-positivity
- 2019
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Ingår i: FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics. - : Formal Power Series and Algebraic Combinatorics. ; :82B
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Konferensbidrag (refereegranskat)abstract
- Using the combinatorics of a-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that generating functions of reverse P-partitions expand positively into quasisymmetric power sums. Consequently any nonnegative linear combination of such functions is p-positive whenever it is symmetric. We apply this method to derive positivity results for chromatic quasisymmetric functions and unicellular LLT polynomials.
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| 5. |
- Hellström, Lars, 1974-
(författare)
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Critical Pairs in Network Rewriting
- 2014
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Ingår i: IWC 2014. ; , s. 9-13
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Konferensbidrag (refereegranskat)abstract
- This extended abstract breifly introduces rewriting of networks (directed acyclic graphs with the extra structure needed to serve as expressions for PROducts and Permutations categories) and describes the critical pairs aspects of this theory. The author's interest in these comes from wanting to do equational reasoning in algebraic theories (such as Hopf algebras) that mix ordinary operations with co-operations; networks then serve as a formalism for expressions.The main message is to point out two phenomena that arise in network rewriting. The first is that of non-convexity of rules, wherein the left hand side of a rule need not be syntactically similar to a symbol in any extension of the underlying signature. The second is one of critical pairs potentially arising where two redexes wrap around each other even when they do not intersect.
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| 6. |
- Diaz Andino, Fidel Ernesto, et al.
(författare)
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Unitary Branching Programs: Learnability and Lower Bounds
- 2021
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Ingår i: Proceedings of Machine Learning Research. - 2640-3498. ; 139, s. 297 -306
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Konferensbidrag (refereegranskat)abstract
- Bounded width branching programs are a formalism that can be used to capture the notion of non-uniform constant-space computation. In this work, we study a generalized version of bounded width branching programs where instructions are defined by unitary matrices of bounded dimension. We introduce a new learning framework for these branching programs that leverages on a combination of local search techniques with gradient descent over Riemannian manifolds. We also show that gapped, read-once branching programs of bounded dimension can be learned with a polynomial number of queries in the presence of a teacher. Finally, we provide explicit near-quadratic size lower-bounds for bounded-dimension unitary branching programs, and exponential size lower-bounds for bounded-dimension read-once gapped unitary branching programs. The first lower bound is proven using a combination Neeiporuk's lower bound technique with classic results from algebraic geometry. The second lower bound is proven within the framework of communication complexity theory.
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| 7. |
- Curic, Vladimir, et al.
(författare)
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Salience-Based Parabolic Structuring Functions
- 2013
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Ingår i: Mathematical Morphology and Its Applications to Signal and Image Processing. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642382932 ; 7883, s. 183-194
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Konferensbidrag (refereegranskat)abstract
- It has been shown that the use of the salience map based on the salience distance transform can be useful for the construction of spatially adaptive structuring elements. In this paper, we propose salience-based parabolic structuring functions that are defined for a fixed, predefined spatial support, and have low computational complexity. In addition, we discuss how to properly define adjunct morphological operators using the new spatially adaptive structuring functions. It is also possible to obtain flat adaptive structuring elements by thresholding the salience-based parabolic structuring functions.
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| 8. |
- Fotedar, Sunney, 1989, et al.
(författare)
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A decision-making tool to identify routings for an efficient utilization of machining resources: the decision makers’ perspective
- 2020
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Ingår i: PLANs forsknings-och tillämpningskonferens.
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Konferensbidrag (refereegranskat)abstract
- In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers (which includes, measures of quality and lead-times ) and keeps the tied-up working capital in check. The proposed decision-making tool, described in this paper, aims to combine information and knowledge of manufacturing and logistics experts in a company to improve flow of materials through the factory. The material flow situation is different for a large aerospace tier-1 supplier as opposed to flow-based manufacturing company; when there is no pandemic or natural calamity, having relatively stable demand due to long-term contract is common, but there exists short-term demand variability. There is a complex flow of products at GKN Aerospace, as the products share machining resources, thus, resulting in uneven loads at machines and sometimes excess loading at certain machines. This along with short-term demand variability results in long queues in-front of machines which contributes with the biggest share of the total lead-time. Thus, long waiting times at one/many machine/s is common and may lead to bottlenecks in many places in the production pipeline. So, there is potential benefit in having rerouting-flexibility for products which can help in reducing queuing. However, qualifying a product for a new machine is time-consuming activity, and thus, should be done few years in advance. We propose a mathematical model aimed at improving some of these deficiencies of commonly used methods by facilitating balanced resource loading levels, i.e. to provide more degrees of freedom to the planner to absorb demand variations. The output provided by the model includes production routings in each time period (quarter) for the next 4–5 years; new qualifications to be done by technical staff for allocation of part types/products to machines which are not yet qualified/used for a given product. We keep the resource loading levels that are above a given threshold as low as possible and reduce the time/money spent for qualifying new allocations.
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| 9. |
- Freij-Hollanti, Ragnar, et al.
(författare)
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Matroid Theory via Examples
- 2016
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Ingår i: International Zurich Seminar on Communications - Proceedings. ; , s. 45-49
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Konferensbidrag (refereegranskat)
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| 10. |
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