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  • Resultat 21-30 av 894
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21.
  • Björnberg, Jakob, 1983, et al. (författare)
  • STABLE SHREDDED SPHERES AND CAUSAL RANDOM MAPS WITH LARGE FACES
  • 2022
  • Ingår i: Annals of Probability. - 2168-894X .- 0091-1798. ; 50:5, s. 2056-2084
  • Tidskriftsartikel (refereegranskat)abstract
    • We introduce a new familiy of random compact metric spaces Sα for α ∈ (1, 2), which we call stable shredded spheres. They are constructed from excursions of α-stable Lévy processes on [0, 1] possessing no negative jumps. Informally, viewing the graph of the Lévy excursion in the plane, each jump of the process is “cut open” and replaced by a circle, and then all points on the graph at equal height, which are not separated by a jump, are identified. We show that the shredded spheres arise as scaling limits of models of causal random planar maps with large faces introduced by Di Francesco and Guitter. We also establish that their Hausdorff dimension is almost surely equal to α. Point identification in the shredded spheres is intimately connected to the presence of decrease points in stable spectrally positive Lévy processes, as studied by Bertoin in the 1990s.
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22.
  • Brubaker, B., et al. (författare)
  • Colored five-vertex models and Demazure atoms
  • 2021
  • Ingår i: Journal of Combinatorial Theory Series A. - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 178
  • Tidskriftsartikel (refereegranskat)abstract
    • Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a byproduct, we will construct Demazure atoms on Kashiwara's B-infinity crystal and give new algorithms for computing Lascoux-Schutzenberger keys. (C) 2020 Elsevier Inc. All rights reserved.
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23.
  • Mertens, M. H., et al. (författare)
  • Modular forms of virtually real-arithmetic type I: Mixed mock modular forms yield vector-valued modular forms
  • 2021
  • Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 28:2, s. 511-561
  • Tidskriftsartikel (refereegranskat)abstract
    • The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals. Applications beyond number theory range from combinatorics, geometry, and representation theory to string theory and conformal field theory. We unify these relaxed notions in the framework of vector-valued modular forms by introducing a new class of SL2(Z)-representations: virtually real-arithmetic types. The key point of the paper is that virtually real-arithmetic types are in general not completely reducible. We obtain a rationality result for Fourier and Taylor coefficients of associated modular forms.
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24.
  • Raum, Martin (författare)
  • Relations among Ramanujan-type congruences I
  • 2022
  • Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 409
  • Tidskriftsartikel (refereegranskat)abstract
    • We prove that Ramanujan-type congruences for integral weight modular forms away from the level and the congruence prime are equivalent to specific congruences for Hecke eigenvalues. In particular, we show that Ramanujan-type congruences are preserved by the action of the shallow Hecke algebra. More generally, we show for weakly holomorphic modular forms of integral weight, that Ramanujan-type congruences naturally occur for shifts in the union of two square-classes as opposed to single square-classes that appear in the literature on the partition function. We also rule out the possibility of square-free periods, whose scarcity in the case of the partition function was investigated recently. We complement our obstructions on maximal Ramanujan-type congruences with several existence statements. Our results are based on a framework that leverages classical results on integral models of modular curves via modular representation theory, and applies to congruences of all weakly holomorphic modular forms. Steinberg representations govern all maximal Ramanujan-type congruences for integral weights. We discern the scope of our framework in the case of half-integral weights through example calculations.(c) 2022 The Author(s). Published by Elsevier Inc. This is an (http://creativecommons.org/licenses/by/4.0/).
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25.
  • Westerholt-Raum, Martin, 1985, et al. (författare)
  • All modular forms of weight 2 can be expressed by Eisenstein series
  • 2020
  • Ingår i: Research in Number Theory. - : Springer Science and Business Media LLC. - 2522-0160 .- 2363-9555. ; 6:3
  • Tidskriftsartikel (refereegranskat)abstract
    • We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L-values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.
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26.
  • 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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27.
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28.
  • Dhamal, Swapnil Vilas, 1988, et al. (författare)
  • Resource Allocation Polytope Games: Uniqueness of Equilibrium, Price of Stability, and Price of Anarchy
  • 2018
  • Ingår i: AAAI 2018 - Proceedings of the 32nd AAAI Conference on Artificial Intelligence. ; , s. 997-1006
  • 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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29.
  • Fotedar, Sunney, 1989, et al. (författare)
  • Mathematical optimization of the tactical allocation of machining resources for an efficient capacity utilization in aerospace component manufacturing
  • 2019
  • Ingår i: Proceedings of the 10th Aerospace Technology Congress. - : Linköping University Electronic Press. - 1650-3686 .- 1650-3740. - 9789175190068 ; , s. 183-188
  • 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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30.
  • Obradovic, Gabrijela, 1994, et al. (författare)
  • Simultaneous scheduling of replacement and repair of common components in operating systems A multi-objective mathematical optimization model
  • 2022
  • Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 0254-5330 .- 1572-9338. ; 322, s. 147-65
  • Tidskriftsartikel (refereegranskat)abstract
    • In order for a system to stay operational, its components need maintenance. We consider two stakeholders-a system operator and a maintenance workshop-and a contract governing their joint activities. Components in the operating systems that are to be maintained are sent to the maintenance workshop, which should perform all maintenance activities on time in order to satisfy the contract. The maintained components are then sent back to be used in the operating systems. Our modeling of this system-of-systems includes stocks of damaged and repaired components, the workshop scheduling, and the planning of preventive maintenance for the operating systems. Our modeling is based on a mixed-binary linear optimization (MBLP) model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We generalize and extend this model with the flow of components through the workshop, including the stocks of spare components. The resulting scheduling model-a mixed-integer optimization (MILP) model-is then utilized to optimize the main contract in a bi-objective setting: maximizing the availability of repaired (or new) components and minimizing the costs of maintaining the operating systems over the time horizon. We analyze the main contract and briefly discuss a turn-around time contract. Our results concern the effect of our modeling on the levels of the stocks of components over time, in particular minimizing the risk for lack of spare components.
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