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Academic literature on the topic 'Matroid Constraints'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Matroid Constraints"

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Dror, Amitay, Michal Feldman, and Erel Segal-Halevi. "On Fair Division under Heterogeneous Matroid Constraints." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (May 18, 2021): 5312–20. http://dx.doi.org/10.1609/aaai.v35i6.16670.

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We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors, and the allocation of conference papers to referees. We focus on the common fairness notion of envy-freeness up to one good (EF1). Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints, or allow free disposal of items. An open problem is the existence of EF1 complete allocations among heterogeneous agents, where the heterogeneity is both in the agents' feasibility constraints and in their valuations. In this work, we make progress on this problem by providing positive and negative results for different matroid and valuation types. Among other results, we devise poly-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous partition matroids and heterogeneous binary valuations, (ii) 2 agents with heterogeneous partition matroids and heterogeneous valuations, and (iii) at most 3 agents with heterogeneous binary valuations and identical base-orderable matroids.

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Kamiyama, Naoyuki. "MATROID INTERSECTION WITH PRIORITY CONSTRAINTS." Journal of the Operations Research Society of Japan 56, no. 1 (2013): 15–25. http://dx.doi.org/10.15807/jorsj.56.15.

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Friedrich, Tobias, and Frank Neumann. "Maximizing Submodular Functions under Matroid Constraints by Evolutionary Algorithms." Evolutionary Computation 23, no. 4 (December 2015): 543–58. http://dx.doi.org/10.1162/evco_a_00159.

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Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a simple single objective evolutionary algorithm called ([Formula: see text]) EA and a multiobjective evolutionary algorithm called GSEMO until they have obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints, we show that the GSEMO achieves a [Formula: see text]-approximation in expected polynomial time. For the case of monotone functions where the constraints are given by the intersection of [Formula: see text] matroids, we show that the ([Formula: see text]) EA achieves a ([Formula: see text])-approximation in expected polynomial time for any constant [Formula: see text]. Turning to nonmonotone symmetric submodular functions with [Formula: see text] matroid intersection constraints, we show that the GSEMO achieves a [Formula: see text]-approximation in expected time [Formula: see text].

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Do, Anh Viet, and Frank Neumann. "Pareto Optimization for Subset Selection with Dynamic Partition Matroid Constraints." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 14 (May 18, 2021): 12284–92. http://dx.doi.org/10.1609/aaai.v35i14.17458.

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In this study, we consider the subset selection problems with submodular or monotone discrete objective functions under partition matroid constraints where the thresholds are dynamic. We focus on POMC, a simple Pareto optimization approach that has been shown to be effective on such problems. Our analysis departs from singular constraint problems and extends to problems of multiple constraints. We show that previous results of POMC's performance also hold for multiple constraints. Our experimental investigations on random undirected maxcut problems demonstrate POMC's competitiveness against the classical GREEDY algorithm with restart strategy.

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Biswas, Arpita, and Siddharth Barman. "Matroid Constrained Fair Allocation Problem." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 9921–22. http://dx.doi.org/10.1609/aaai.v33i01.33019921.

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We consider the problem of allocating a set of indivisible goods among a group of homogeneous agents under matroid constraints and additive valuations, in a fair manner. We propose a novel algorithm that computes a fair allocation for instances with additive and identical valuations, even under matroid constraints. Our result provides a computational anchor to the existential result of the fairness notion, called EF1 (envy-free up to one good) by Biswas and Barman in this setting. We further provide examples to show that the fairness notions stronger than EF1 does not always exist in this setting.

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Gu, Yu-Ran, Chao Bian, and Chao Qian. "Submodular Maximization under the Intersection of Matroid and Knapsack Constraints." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 4 (June 26, 2023): 3959–67. http://dx.doi.org/10.1609/aaai.v37i4.25510.

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Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of constraint, while many real-world problems often involve several constraints. In this paper, we consider the problem of submodular maximization under the intersection of two commonly used constraints, i.e., k-matroid constraint and m-knapsack constraint, and propose a new algorithm SPROUT by incorporating partial enumeration into the simultaneous greedy framework. We prove that SPROUT can achieve a polynomial-time approximation guarantee better than the state-of-the-art algorithms. Then, we introduce the random enumeration and smooth techniques into SPROUT to improve its efficiency, resulting in the SPROUT++ algorithm, which can keep a similar approximation guarantee. Experiments on the applications of movie recommendation and weighted max-cut demonstrate the superiority of SPROUT++ in practice.

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Suksompong, Warut. "Constraints in fair division." ACM SIGecom Exchanges 19, no. 2 (November 2021): 46–61. http://dx.doi.org/10.1145/3505156.3505162.

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The fair allocation of resources to interested agents is a fundamental problem in society. While the majority of the fair division literature assumes that all allocations are feasible, in practice there are often constraints on the allocation that can be chosen. In this survey, we discuss fairness guarantees for both divisible (cake cutting) and indivisible resources under several common types of constraints, including connectivity, cardinality, matroid, geometric, separation, budget, and conflict constraints. We also outline a number of open questions and directions.

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Király, Csaba, Zoltán Szigeti, and Shin-ichi Tanigawa. "Packing of arborescences with matroid constraints via matroid intersection." Mathematical Programming 181, no. 1 (April 2, 2019): 85–117. http://dx.doi.org/10.1007/s10107-019-01377-0.

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Srinivas, Mandayam A. "Matroid optimization with generalized constraints." Discrete Applied Mathematics 63, no. 2 (November 1995): 161–74. http://dx.doi.org/10.1016/0166-218x(94)00031-8.

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Ramalingam, Srikumar, Arvind Raghunathan, and Daniel Nikovski. "Submodular Function Maximization for Group Elevator Scheduling." Proceedings of the International Conference on Automated Planning and Scheduling 27 (June 5, 2017): 233–41. http://dx.doi.org/10.1609/icaps.v27i1.13799.

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We propose a novel approach for group elevator scheduling by formulating it as the maximization of submodular function under a matroid constraint. In particular, we propose to model the total waiting time of passengers using a quadratic Boolean function. The unary and pairwise terms in the function denote the waiting time for single and pairwise allocation of passengers to elevators, respectively. We show that this objective function is submodular. The matroid constraints ensure that every passenger is allocated to exactly one elevator. We use a greedy algorithm to maximize the submodular objective function, and derive provable guarantees on the optimality of the solution. We tested our algorithm using Elevate 8, a commercial-grade elevator simulator that allows simulation with a wide range of elevator settings. We achieve significant improvement over the existing algorithms.

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Dissertations / Theses on the topic "Matroid Constraints"

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Reimers, Arne Cornelis [Verfasser]. "Metabolic Networks, Thermodynamic Constraints, and Matroid Theory / Arne C. Reimers." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1058587331/34.

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Harini, Desiraju Harini. "Matrix models and Virasoro constraints." Thesis, Uppsala universitet, Teoretisk fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-276090.

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Flieger, Wojciech. "Constraints on neutrino mixing from matrix theory." Doctoral thesis, Katowice : Uniwersytet Śląski, 2021. http://hdl.handle.net/20.500.12128/21721.

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Jeden z kluczowych problemów współczesnej fizyki cząstek elementarnych dotyczy liczby zapachów neutrin występujących w naturze. Do tej pory udało się ustalić, ze istnieją trzy rodzaje neutrin aktywnych. Istotnym problemem jest ustalenie, czy istnieją inne dodatkowe stany neutrinowe. Neutrina takie nazywamy sterylnymi ze względu na fakt, ze ich oddziaływanie słabe ze znaną materią jest jak do tej pory poniżej eksperymentalnego progu detekcji. Niemniej jednak neutrina sterylne mogą się mieszać z neutrinami aktywnymi pozostawiając tym samym ślady swojego istnienia na poziomie Modelu Standardowego w postaci nieunitarności macierzy mieszania neutrin. Z tego powodu badanie nieunitarności macierzy mieszania jest tak istotne dla pełnego zrozumienia fizyki neutrin. W rozprawie przedstawiamy nową metodę analizy macierzy mieszania neutrin opartą na teorii macierzy. Fundament naszego podejścia do badania macierzy mieszania neutrin stanowią pojęcia wartości osobliwych oraz kontrakcji. Dzięki tym pojęciom zdefiniowaliśmy obszar fizycznie dopuszczalnych macierzy mieszania jako powłokę wypukłą rozpiętą na trójwymiarowych unitarnych macierzach mieszania wyznaczonych na podstawie danych eksperymentalnych. W rozprawie badamy geometryczne własności tego obszaru wyznaczając jego objętość wyrażoną poprzez miarę Haara rozkładu na wartości osobliwe oraz studiując jego strukturę wewnętrzną zależną od minimalnej liczby dodatkowych sterylnych neutrin. Stosując teorię unitarnej dylatacji pokazujemy jak wartości osobliwe pozwalają zidentyfikować nieunitarne macierze mieszania oraz jak tworzyć ich rozszerzenia do pełnej macierzy unitarnej wymiaru większego niż trzy, opisującej kompletną teorię zawierającą neutrina sterylne. Na tej podstawie wyznaczamy nowe ograniczenia w modelach gdzie aktywne neutrina mieszają się z jednym dodatkowym neutrinem sterylnym.

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Lecharlier, Loïc. "Blind inverse imaging with positivity constraints." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209240.

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Dans les problèmes inverses en imagerie, on suppose généralement connu l’opérateur ou matrice décrivant le système de formation de l’image. De façon équivalente pour un système linéaire, on suppose connue sa réponse impulsionnelle. Toutefois, ceci n’est pas une hypothèse réaliste pour de nombreuses applications pratiques pour lesquelles cet opérateur n’est en fait pas connu (ou n’est connu qu’approximativement). On a alors affaire à un problème d’inversion dite “aveugle”. Dans le cas de systèmes invariants par translation, on parle de “déconvolution aveugle” car à la fois l’image ou objet de départ et la réponse impulsionnelle doivent être estimées à partir de la seule image observée qui résulte d’une convolution et est affectée d’erreurs de mesure. Ce problème est notoirement difficile et pour pallier les ambiguïtés et les instabilités numériques inhérentes à ce type d’inversions, il faut recourir à des informations ou contraintes supplémentaires, telles que la positivité qui s’est avérée un levier de stabilisation puissant dans les problèmes d’imagerie non aveugle. La thèse propose de nouveaux algorithmes d’inversion aveugle dans un cadre discret ou discrétisé, en supposant que l’image inconnue, la matrice à inverser et les données sont positives. Le problème est formulé comme un problème d’optimisation (non convexe) où le terme d’attache aux données à minimiser, modélisant soit le cas de données de type Poisson (divergence de Kullback-Leibler) ou affectées de bruit gaussien (moindres carrés), est augmenté par des termes de pénalité sur les inconnues du problème. La stratégie d’optimisation consiste en des ajustements alternés de l’image à reconstruire et de la matrice à inverser qui sont de type multiplicatif et résultent de la minimisation de fonctions coût “surrogées” valables dans le cas positif. Le cadre assez général permet d’utiliser plusieurs types de pénalités, y compris sur la variation totale (lissée) de l’image. Une normalisation éventuelle de la réponse impulsionnelle ou de la matrice est également prévue à chaque itération. Des résultats de convergence pour ces algorithmes sont établis dans la thèse, tant en ce qui concerne la décroissance des fonctions coût que la convergence de la suite des itérés vers un point stationnaire. La méthodologie proposée est validée avec succès par des simulations numériques relatives à différentes applications telle que la déconvolution aveugle d'images en astronomie, la factorisation en matrices positives pour l’imagerie hyperspectrale et la déconvolution de densités en statistique.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Strabic, Natasa. "Theory and algorithms for matrix problems with positive semidefinite constraints." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/theory-and-algorithms-for-matrix-problems-with-positive-semidefinite-constraints(5c8ac15f-9666-4682-9297-73d976bed63e).html.

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This thesis presents new theoretical results and algorithms for two matrix problems with positive semidefinite constraints: it adds to the well-established nearest correlation matrix problem, and introduces a class of semidefinite Lagrangian subspaces. First, we propose shrinking, a method for restoring positive semidefiniteness of an indefinite matrix $M_0$ that computes the optimal parameter $\a_*$ in a convex combination of $M_0$ and a chosen positive semidefinite target matrix. We describe three algorithms for computing $\a_*$, and then focus on the case of keeping fixed a positive semidefinite leading principal submatrix of an indefinite approximation of a correlation matrix, showing how the structure can be exploited to reduce the cost of two algorithms. We describe how weights can be used to construct a natural choice of the target matrix and that they can be incorporated without any change to computational methods, which is in contrast to the nearest correlation matrix problem. Numerical experiments show that shrinking can be at least an order of magnitude faster than computing the \ncm\ and so is preferable in time-critical applications. Second, we focus on estimating the distance in the Frobenius norm of a symmetric matrix $A$ to its nearest correlation matrix $\Ncm(A)$ without first computing the latter. The goal is to enable a user to identify an invalid correlation matrix relatively cheaply and to decide whether to revisit its construction or to compute a replacement. We present a few currently available lower and upper bounds for $\dcorr(A) = \normF{A - \Ncm(A)}$ and derive several new upper bounds, discuss the computational cost of all the bounds, and test their accuracy on a collection of invalid correlation matrices. The experiments show that several of our bounds are well suited to gauging the correct order of magnitude of $\dcorr(A)$, which is perfectly satisfactory for practical applications. Third, we show how Anderson acceleration can be used to speed up the convergence of the \apm\ for computing the \ncm, and that the acceleration remains effective when it is applied to the variants of the nearest correlation matrix problem in which specified elements are fixed or a lower bound is imposed on the smallest eigenvalue. This is particularly significant for the nearest correlation matrix problem with fixed elements because no Newton method with guaranteed convergence is available for it. Moreover, alternating projections is a general method for finding a point in the intersection of several sets and this appears to be the first demonstration that these methods can benefit from Anderson acceleration. Finally, we introduce semidefinite Lagrangian subspaces, describe their connection to the unique positive semidefinite solution of an algebraic Riccati equation, and show that these subspaces can be represented by a subset $\mathcal{I} \subseteq \{1,2,\dots, n\}$ and a Hermitian matrix $X\in\mathbb{C}^{n\times n}$ that is a generalization of a quasidefinite matrix. We further obtain a semidefiniteness-preserving version of an optimization algorithm introduced by Mehrmann and Poloni [\textit{SIAM J.\ Matrix Anal.\ Appl.}, 33(2012), pp.\ 780--805] to compute a pair $(\mathcal{I}_{\opt},X_{\opt})$ with $M = \max_{i,j} \abs{(X_{\opt})_{ij}}$ as small as possible, which improves numerical stability in several contexts.

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Chia, Liang. "Language shift in a Singaporean Chinese family and the matrix language frame model." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365765.

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Xu, Da. "Classical groups, integrals and Virasoro constraints." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/629.

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First, we consider the group integrals where integrands are the monomials of matrix elements of irreducible representations of classical groups. These group integrals are invariants under the group action. Based on analysis on Young tableaux, we investigate some related duality theorems and compute the asymptotics of the group integrals for fixed signatures, as the rank of the classical groups go to infinity. We also obtain the Viraosoro constraints for some partition functions, which are power series of the group integrals. Second, we show that the proof of Witten's conjecture can be simplified by using the fermion-boson correspondence, i.e., the KdV hierarchy and Virasoro constraints of the partition function in Witten's conjecture can be achieved naturally. Third, we consider the partition function involving the invariants that are intersection numbers of the moduli spaces of holomorphic maps in nonlinear sigma model. We compute the commutator of the representation of Virasoro algebra and give a fat graph(ribbon graph) interpretation for each term in the diferential operators.

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Bai, Shuanghua. "Numerical methods for constrained Euclidean distance matrix optimization." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/401542/.

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This thesis is an accumulation of work regarding a class of constrained Euclidean Distance Matrix (EDM) based optimization models and corresponding numerical approaches. EDM-based optimization is powerful for processing distance information which appears in diverse applications arising from a wide range of fields, from which the motivation for this work comes. Those problems usually involve minimizing the error of distance measurements as well as satisfying some Euclidean distance constraints, which may present enormous challenge to the existing algorithms. In this thesis, we focus on problems with two different types of constraints. The first one consists of spherical constraints which comes from spherical data representation and the other one has a large number of bound constraints which comes from wireless sensor network localization. For spherical data representation, we reformulate the problem as an Euclidean dis-tance matrix optimization problem with a low rank constraint. We then propose an iterative algorithm that uses a quadratically convergent Newton-CG method at its each step. We study fundamental issues including constraint nondegeneracy and the nonsingularity of generalized Jacobian that ensure the quadratic convergence of the Newton method. We use some classic examples from the spherical multidimensional scaling to demonstrate the exibility of the algorithm in incorporating various constraints. For wireless sensor network localization, we set up a convex optimization model using EDM which integrates connectivity information as lower and upper bounds on the elements of EDM, resulting in an EDM-based localization scheme that possesses both effciency and robustness in dealing with flip ambiguity under the presence of high level of noises in distance measurements and irregular topology of the concerning network of moderate size. To localize a large-scale network effciently, we propose a patching-stitching localization scheme which divides the network into several sub-networks, localizes each sub-network separately and stitching all the sub-networks together to get the recovered network. Mechanism for separating the network is discussed. EDM-based optimization model can be extended to add more constraints, resulting in a exible localization scheme for various kinds of applications. Numerical results show that the proposed algorithm is promising.

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Jin, Shengzhe. "Quality Assessment Planning Using Design Structure Matrix and Resource Constraint Analysis." University of Cincinnati / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1292518039.

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Menzel, Andreas. "Constraints on the Fourth-Generation Quark Mixing Matrix from Precision Flavour Observables." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2017. http://dx.doi.org/10.18452/17711.

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Das Standardmodell einer zusätzlichen sequentiellen Fermiongeneration (SM4) war 2012 auf Basis eines Fits an elektroschwache Präzisionsobservable und die Higgs-Signalstärken mit einer Signifikanz von 5.3 sigma ausgeschlossen worden. Komplementär dazu wurden in der vorliegenden Arbeit Fits des SM4 an eine Kombination eines typischen Satzes von Flavour-Observablen mit den Ergebnissen des zuvor durchgeführten Elektroschwachen Präzisionsfits durchgeführt. Im SM3-Kontext extrahierte Größen wurden gemäß ihrer Bedeutung im SM4 reinterpretiert und die angepassten theoretischen Ausdrücke angegeben. Die resultierenden Einschränkungen der CKM-Matrix des SM4, ihrer potentiell CP-verletzenden Phasen sowie der Masse des up-type-Quarks der 4. Generation t'' werden angegeben. Zum Vergleich des SM4 mit dem SM3 werden die erreichten chi^2-Werte genutzt. chi^2=15.53 im SM4 und 9.56 im SM3 passen fast vollkommen zu einer gleich guten Beschreibung der Experimente durch beide Modelle, wobei das SM3 aber sechs Freiheitsgrade mehr besitzt. Außerdem wurden die Vorhersagen des SM3 und des SM4 für die Dimyon-Ladungsasymmetrie ASL mit experimentellen Werten verglichen. Die Vorhersage des SM3 ist ca. 2 sigma vom experimentellen Wert entfernt, die des SM4 ca. 3 sigma.\par Die Ergebnisse deuten nicht darauf hin, dass die Signifikanz des 2012 erreichten Ausschlusses des SM4 durch die Hinzunahme von Flavour-Observablen zu den damals verwendeten elektroschwachen Präzisionsobservablen und Higgs-Querschnitten bedeutend verringert würde.\par Es konnte jedoch keine genaue quantitative Aussage über die Auswirkungen der Flavourobservablen auf diese Signifikanz getroffen werden, weil das Programm CKMfitter likelihood-ratio-Berechnung nur durchführen kann, wenn sich eines der untersuchten Modelle durch Fixierung von Parametern aus dem anderen ergibt (nested models), was hier nicht der Fall ist.
The Standard Model extended by an additional sequential generation of Dirac fermions (SM4) was excluded with a significance of 5.3 sigma in 2012. This was achieved in a combined fit of the SM4 to Electroweak Precision Observables and signal strengths of the Higgs boson. This thesis complements this excludion by a fit of the SM4 to a typical set of Flavour physics observables and the results of the previously performed Electroweak Precision fit. Quantities extracted in an SM3 framework are reinterpreted in SM4 terms and the adapted theoretical expressions are given. The resultant constraints on the SM4''s CKM matrix, its potentially CP-violating phases and the mass of the new up-type quark t'' are given. To compare the relative performance of the SM4 and the SM3, this work uses the chi^2 values achieved in the fit. The values of 15.53 for the SM4 and 9.56 for the SM4 are almost perfectly consistent with both models describing the experimental data equally well with the SM3 having six degrees of freedom more. The dimuon charge asymmetry ASL was not used as a fit input because the interpretation of its measurement was subject to debate at the time when the fits were produced, but its prediction in the fit was used as an additional test of the SM4. The SM3''s prediction differs from the experimental values by about 2 sigma, and the SM4''s prediction by about 3 sigma. \par In summary, these results do not suggest that any significant reduction of the 5.3 sigma exclusion could be achieved by combining the Electroweak Precision Observables and Higgs inputs with Flavour physics data. However, the exact effect of the Flavour physics input on the significance of the SM4''s exclusion cannot be given at this point because the CKMfitter software is currently not able to perform a statistically stringent likelihood comparison of non-nested models.

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Books on the topic "Matroid Constraints"

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C, Chamis C., and United States. National Aeronautics and Space Administration., eds. Composite laminate tailoring with probabilistic constraints and loads. [Washington, D.C.]: NASA, 1990.

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Li, Huacheng. Estimation of Q-matrix for DINA Model Using the Constrained Generalized DINA Framework. [New York, N.Y.?]: [publisher not identified], 2016.

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Soft constraints: exponential random graph models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0004.

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Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

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Its, Alexander R. Random matrix theory and integrable systems. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.10.

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This article discusses the interaction between random matrix theory (RMT) and integrable theory, leading to ordinary and partial differential equations (PDEs) for the eigenvalue distribution of random matrix models of size n and the transition probabilities of non-intersecting Brownian motion models, for finite n and for n → ∞. It first provides an overview of the connection between the theory of orthogonal polynomials and the KP-hierarchy in integrable systems before examining matrix models and the Virasoro constraints. It then considers multiple orthogonal polynomials, taking into account non-intersecting Brownian motions on ℝ (Dyson’s Brownian motions), a moment matrix for several weights, Virasoro constraints, and a PDE for non-intersecting Brownian motions. It also analyses critical diffusions, with particular emphasis on the Airy process, the Pearcey process, and Airy process with wanderers. Finally, it describes the Tacnode process, along with kernels and p-reduced KP-hierarchy.

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Beenakker, Carlo W. J. Extreme eigenvalues of Wishart matrices: application to entangled bipartite system. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.37.

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This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.

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Hu, Xuhui. The syntax and semantics of English resultatives. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198808466.003.0003.

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This chapter argues that the English resultative construction denotes a single event involving two predicates. Therefore, only a single EP is involved in the syntactic derivation. The special thematic relationship is due to constraints imposed by the Integration Conditions proposed in Chapter 2. Dispensing with the CAUSE head of the event decomposition approach, this chapter explains the possible lack of causative meaning in English resultatives. A secondary predicate in a resultative can get a dynamic BECOME meaning (such as flat in John hammered the metal flat) because the secondary predicate shares the dynamic [iDiv] feature provided by V. Since both the activity denoted by the matrix V and the dynamic change of state take place in the same temporal scope of EP, the interpretation of a potential (and cancellable) culmination point is derived.

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Hu, Xuhui. Encoding applied arguments. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198808466.003.0006.

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This chapter applies the theoretical framework of events to the study of non-core arguments. The applied argument in the symmetric applicative construction is introduced by a PP. This PP serves as the modifier of the event predicate, and its head, a null P, is incorporated into V. In an asymmetric applicative, including the ditransitive construction in English, two predicates are involved: in addition to the matrix verb, the other predicate is a PHAVEP. The derivation of this construction is therefore by nature identical to that of English resultatives. An implication of this chapter concerns the syntactic distinction between core arguments and non-core arguments. The core argument is merged in either [Spec EP] or [Spec FP], while the applied argument is introduced elsewhere providing its merge position is permitted by general syntactic constraints.

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Frascarelli, Mara. The interpretation of pro in consistent and partial null-subject languages. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198815853.003.0009.

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This chapter deals with the acceptability and interpretation of referential null subjects (NSs) and compares consistent pro-drop in Italian with equivalent sentences in Finnish (a partial NS language), in different syntactic constructions (matrix, completive, factive, and adverbial clauses). This leads to the formulation of an original proposal that opens new perspectives for future research. Specifically, based on the interpretive judgements of 273 native speakers of Finnish, it is shown that a Topic chain analysis (Frascarelli 2007) can (and should) be assumed in partial NS languages as well, and that ‘partiality’ cannot be explained through narrow syntactic constraints. The Locality requirement is thus re-proposed as an Interface Visibility Condition (IVC), according to which in partial NS languages a pro is preferably interpreted as referring to the closest overt link in a Topic chain. The Topic Criterion is thus proposed as a Macroparameter of NS languages and the necessity of a ‘graded analysis’ ascribed to the IVC (as a Mesoparameter).

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Ronen, Boaz, Joseph S. Pliskin, Shimeon Pass, and Donald M. Berwick. The Hospital and Clinic Improvement Handbook. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780190843458.001.0001.

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The Hospital and Clinic Improvement Handbook is about doing more using existing resources. For example, achieving more throughput in the operating rooms, reducing waiting times at the emergency department, and improving clinical quality. This is done using the well-established Lean techniques together with the breakthrough philosophies and techniques of the theory of constraints (TOC). These methods and their underlying tools are put together with techniques and methodologies implemented by the authors in dozens of healthcare organizations. The tools include the complete kit concept, the Pareto methodology, the focusing table, and the focusing matrix. The book introduces simple tools that can be implemented quite easily in any hospital or clinic. It also focuses on the implementation process using tools like the 3–1–1 model that directs managers where to focus their limited time resources to best improve the performance of their organizations. Finally, the book introduces effective yet simple performance measures and prescribes the process of ongoing improvement.

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Johnston, Ron. Geography and International Studies: The Foundations. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190846626.013.199.

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The discipline of geography is built around four key concepts—environment, place, space, and scale—that form a matrix for exploring and appreciating many aspects of contemporary society. The environment is the ultimate source of human sustenance; people have created places to realize that potential; and a spatial structure—nodes, routes, surfaces and bounded territories—has been erected within which human interactions are organised.The relationships between human societies and their environments—now very much changed from their pre-human “natural” state—involve competition for and conflicts over resources, of increasing intensity. Resolution of all but the smallest scale of those conflicts requires a body that is independent of the actors involved and can ensure that agreements are reached and then implemented. Such a body is the state, a territorially bounded apparatus that, through the operation of territoriality strategies, can ensure conflict resolution among its citizenry and thereby resolve environmental problems.Many of those problems—the most severe being global climate change resulting from anthropomorphically induced global warming—are not contained, and cannot be contained, within an individual state’s territory, however. Tackling them requires inter-state co-operation, at a global scale, but the absence of a super-national body with the power to require actions by individual states is a major constraint to problem resolution.

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Book chapters on the topic "Matroid Constraints"

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Benabbou, Nawal, Cassandre Leroy, Thibaut Lust, and Patrice Perny. "Interactive Optimization of Submodular Functions Under Matroid Constraints." In Algorithmic Decision Theory, 307–22. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87756-9_20.

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Henzinger, Monika, and Angelina Vidali. "Multi-parameter Mechanism Design under Budget and Matroid Constraints." In Algorithms – ESA 2011, 192–202. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23719-5_17.

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Kamiyama, Naoyuki. "The Popular Matching and Condensation Problems Under Matroid Constraints." In Combinatorial Optimization and Applications, 713–28. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12691-3_53.

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Liu, Zhicheng, Jing Jin, Donglei Du, and Xiaoyan Zhang. "Two-Stage Submodular Maximization Under Knapsack and Matroid Constraints." In Lecture Notes in Computer Science, 140–54. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-20350-3_13.

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Kamiyama, Naoyuki. "Stable Matchings with Ties, Master Preference Lists, and Matroid Constraints." In Algorithmic Game Theory, 3–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48433-3_1.

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Iwamasa, Yuni, and Kenjiro Takazawa. "Optimal Matroid Bases with Intersection Constraints: Valuated Matroids, M-convex Functions, and Their Applications." In Lecture Notes in Computer Science, 156–67. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59267-7_14.

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van Bevern, René, Oxana Yu Tsidulko, and Philipp Zschoche. "Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints." In Lecture Notes in Computer Science, 62–74. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17402-6_6.

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Friedrich, Tobias, and Frank Neumann. "Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms." In Parallel Problem Solving from Nature – PPSN XIII, 922–31. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10762-2_91.

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Buchbinder, Niv, Joseph Naor, R. Ravi, and Mohit Singh. "Approximation Algorithms for Online Weighted Rank Function Maximization under Matroid Constraints." In Automata, Languages, and Programming, 145–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31594-7_13.

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Do, Anh Viet, and Frank Neumann. "Maximizing Submodular or Monotone Functions Under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms." In Parallel Problem Solving from Nature – PPSN XVI, 588–603. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58115-2_41.

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Conference papers on the topic "Matroid Constraints"

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Madan, Vivek, Aleksandar Nikolov, Mohit Singh, and Uthaipon Tantipongpipat. "Maximizing Determinants under Matroid Constraints." In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2020. http://dx.doi.org/10.1109/focs46700.2020.00059.

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Abbassi, Zeinab, Vahab S. Mirrokni, and Mayur Thakur. "Diversity maximization under matroid constraints." In KDD' 13: The 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2013. http://dx.doi.org/10.1145/2487575.2487636.

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Ceccarello, Matteo, Andrea Pietracaprina, and Geppino Pucci. "Fast Coreset-based Diversity Maximization under Matroid Constraints." In WSDM 2018: The Eleventh ACM International Conference on Web Search and Data Mining. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3159652.3159719.

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Clark, Andrew, Basel Alomair, Linda Bushnell, and Radha Poovendran. "Scalable and distributed submodular maximization with matroid constraints." In 2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt). IEEE, 2015. http://dx.doi.org/10.1109/wiopt.2015.7151103.

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Lee, Jon, Vahab S. Mirrokni, Viswanath Nagarajan, and Maxim Sviridenko. "Non-monotone submodular maximization under matroid and knapsack constraints." In the 41st annual ACM symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1536414.1536459.

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Ene, Alina, Huy L. Nguyễn, and Adrian Vladu. "Submodular maximization with matroid and packing constraints in parallel." In STOC '19: 51st Annual ACM SIGACT Symposium on the Theory of Computing. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3313276.3316389.

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Williams, Ryan K., Andrea Gasparri, and Giovanni Ulivi. "Decentralized matroid optimization for topology constraints in multi-robot allocation problems." In 2017 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2017. http://dx.doi.org/10.1109/icra.2017.7989038.

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Wu, Benwei, and Kai Han. "Fast Algorithm for Big Data Summarization with Knapsack and Partition Matroid Constraints." In 2022 International Conference on INnovations in Intelligent SysTems and Applications (INISTA). IEEE, 2022. http://dx.doi.org/10.1109/inista55318.2022.9894252.

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Kawase, Yasushi, Hanna Sumita, and Yu Yokoi. "Random Assignment of Indivisible Goods under Constraints." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/311.

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We investigate the problem of random assignment of indivisible goods, in which each agent has an ordinal preference and a constraint. Our goal is to characterize the conditions under which there always exists a random assignment that simultaneously satisfies efficiency and envy-freeness. The probabilistic serial mechanism ensures the existence of such an assignment for the unconstrained setting. In this paper, we consider a more general setting in which each agent can consume a set of items only if the set satisfies her feasibility constraint. Such constraints must be taken into account in student course placements, employee shift assignments, and so on. We demonstrate that an efficient and envy-free assignment may not exist even for the simple case of partition matroid constraints, where the items are categorized, and each agent demands one item from each category. We then identify special cases in which an efficient and envy-free assignment always exists. For these cases, the probabilistic serial cannot be naturally extended; therefore, we provide mechanisms to find the desired assignment using various approaches.

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Biswas, Arpita, and Siddharth Barman. "Fair Division Under Cardinality Constraints." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/13.

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We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-studied unconstrained fair division problem. The two central notions of fairness, in the context of fair division of indivisible goods, are envy freeness up to one good (EF1) and the (approximate) maximin share guarantee (MMS). We show that the existence and algorithmic guarantees established for these solution concepts in the unconstrained setting can essentially be achieved under cardinality constraints. Furthermore, focusing on the case wherein all the agents have the same additive valuation, we establish that EF1 allocations exist even under matroid constraints.

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Reports on the topic "Matroid Constraints"

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Heinstein, M. W. An algorithm for enforcement of contact constraints in quasistatic applications using matrix-free solution algorithms. Office of Scientific and Technical Information (OSTI), October 1997. http://dx.doi.org/10.2172/554827.

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Heinkenschloss, Matthias, Denis Ridzal, and Miguel Antonio Aguilo. Numerical study of a matrix-free trust-region SQP method for equality constrained optimization. Office of Scientific and Technical Information (OSTI), December 2011. http://dx.doi.org/10.2172/1038211.

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Carvalho, Joana, and Gerardo Reyes-Tagle. Risk Matrix and PPP Contract Standardization, Best Practice, and Gap Analysis in Brazil. Inter-American Development Bank, April 2022. http://dx.doi.org/10.18235/0004213.

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Public-private partnerships (PPPs) have been used to address the need for the implementation of huge investment programs and to bridge the infrastructure gap that exists in Latin American and Caribbean (LAC) countries. As is explained throughout this paper, under certain circumstances, PPPs represent an important tool to help governments implement their investment programs, thereby benefiting not only from private investment (which often includes foreign investment) but also from the various advantages that are typically associated with the PPP model. However, the need to secure financing for investment needs, especially in a situation of scarce public resources and fiscal constraints, should not be the only reason for choosing the PPP model. The objective of this paper is to highlight that the PPP model can be a valuable tool for undertaking public projects in an efficient and innovative manner and that it can provide more efficient and innovative public services in certain circumstances as well. In addition, when correctly used, it can generate public savings and create the fiscal space that LAC countries need to carry out their investments.

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Brenan, J. M., K. Woods, J. E. Mungall, and R. Weston. Origin of chromitites in the Esker Intrusive Complex, Ring of Fire Intrusive Suite, as revealed by chromite trace element chemistry and simple crystallization models. Natural Resources Canada/CMSS/Information Management, 2021. http://dx.doi.org/10.4095/328981.

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To better constrain the origin of the chromitites associated with the Esker Intrusive Complex (EIC) of the Ring of Fire Intrusive Suite (RoFIS), a total of 50 chromite-bearing samples from the Black Thor, Big Daddy, Blackbird, and Black Label chromite deposits have been analysed for major and trace elements. The samples represent three textural groups, as defined by the relative abundance of cumulate silicate phases and chromite. To provide deposit-specific partition coefficients for modeling, we also report on the results of laboratory experiments to measure olivine- and chromite-melt partitioning of V and Ga, which are two elements readily detectable in the chromites analysed. Comparison of the Cr/Cr+Al and Fe/Fe+Mg of the EIC chromites and compositions from previous experimental studies indicates overlap in Cr/Cr+Al between the natural samples and experiments done at &gt;1400oC, but significant offset of the natural samples to higher Fe/Fe+Mg. This is interpreted to be the result of subsolidus Fe-Mg exchange between chromite and the silicate matrix. However, little change in Cr/Cr+Al from magmatic values, owing to the lack of an exchangeable reservoir for these elements. A comparison of the composition of the EIC chromites and a subset of samples from other tectonic settings reveals a strong similarity to chromites from the similarly-aged Munro Township komatiites. Partition coefficients for V and Ga are consistent with past results in that both elements are compatible in chromite (DV = 2-4; DGa ~ 3), and incompatible in olivine (DV = 0.01-0.14; DGa ~ 0.02), with values for V increasing with decreasing fO2. Simple fractional crystallization models that use these partition coefficients are developed that monitor the change in element behaviour based on the relative proportions of olivine to chromite in the crystallizing assemblage; from 'normal' cotectic proportions involving predominantly olivine, to chromite-only crystallization. Comparison of models to the natural chromite V-Ga array suggests that the overall positive correlation between these two elements is consistent with chromite formed from a Munro Township-like komatiitic magma crystallizing olivine and chromite in 'normal' cotectic proportions, with no evidence of the strong depletion in these elements expected for chromite-only crystallization. The V-Ga array can be explained if the initial magma responsible for chromite formation is slightly reduced with respect to the FMQ oxygen buffer (~FMQ- 0.5), and has assimilated up to ~20% of wall-rock banded iron formation or granodiorite. Despite the evidence for contamination, results indicate that the EIC chromitites crystallized from 'normal' cotectic proportions of olivine to chromite, and therefore no specific causative link is made between contamination and chromitite formation. Instead, the development of near- monomineralic chromite layers likely involves the preferential removal of olivine relative to chromite by physical segregation during magma flow. As suggested for some other chromitite-forming systems, the specific fluid dynamic regime during magma emplacement may therefore be responsible for crystal sorting and chromite accumulation.

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HIGH PRECISION IDENTIFICATION METHOD OF MASS AND STIFFNESS MATRIX FOR SHEAR-TYPE FRAME TEST MODEL. The Hong Kong Institute of Steel Construction, June 2023. http://dx.doi.org/10.18057/ijasc.2023.19.2.6.

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In the direct method of identifying the physical parameters of the shear-type frame structures through the frequencies and modes from the experimental modal analysis (EMA), the accuracy of the lumped mass depends on the initial mass, while the identified mass matrix and stiffness matrix are prone to generate some matrix elements without any physical meaning. In this paper, based on the natural frequencies and modes obtained from the EMA, an iterative constrained optimization solution for correcting mass matrix and a least squares solution for the lateral stiffness are proposed. The method takes the total mass of the test model as the constraint condition and develops an iterative correction method for the lumped mass, which is independent of the initial lumped mass. When the measured modes are exact, the iterative solution converges to the exact solution. On this basis, the least squares calculation equation of the lateral stiffness is established according to the natural frequencies and modes. Taking the numerical model of a 3-story steel frame structure as an example, the influence of errors of measured modes on the identification accuracy is investigated. Then, a 2-story steel frame test model is used to identify the mass matrix and stiffness matrix under three different counterweights. Numerical and experimental results show that the proposed method has good accuracy and stability, and the identified mass matrix and stiffness matrix have clear physical significance.

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