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Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pipe dreams. Quantum double Schubert polynomials are polynomial representatives of Schubert classes in the torus-equivariant quantum cohomology of the complete flag variety, but no analogous combinatorial formulation had been discovered. We introduce a generalization of the bumpless pipe dreams called quantum bumpless pipe dreams, giving a novel combinatorial formula for quantum double Schubert polynomials as a sum of binomial weights of quantum bumpless pipe dreams. We give a bijective proof for this formula by showing that the sum of binomial weights satisfies a defining transition equation.
The concluding chapter discusses the implications of Hong Kong’s contentious politics within the global context of democratic backsliding and spontaneous mass mobilizations. We highlight the contributions of our theoretical framework and the implications of Hong Kong’s contentious pathways for hybrid regimes and beyond.
Autoimmune movement disorders, although relatively rare, are not to be missed because of the treatment implications. There is a broad clinical spectrum, but recognition of some characteristic forms, or associated red flags or other clues, can point to the diagnosis. This chapter covers the clinical spectrum of primary neurologic or systemic autoimmune disease presenting or mainly manifesting as a movement disorder, and addresses the underlying immune-pathophysiologic aspects.
Despite the promise of a well-ordered trading system and expansion of trade liberalization in the 1980s and 1990s, why is trade governance deadlocked? This puzzle is addressed by elaborating the meaning of “crisis of success” and what such a crisis looks like at the global trading order. I argue that the global trading system is revealing a “crisis of success” in that its current failure to ensure functional trade liberalization change is a result of the initial accomplishment in successfully undergoing a power shift in global trade governance especially at the WTO, marked by greater inclusion of new emerging powers. The success of the initial first phase of trade governance (1990s–2008/2012), especially in aiding an institutional power shift at the global level, created conditions for new problems, leading to a fragmented turn toward preferential trade agreements as well as trade-mediated conflictual strategies rather than sustainable peaceful change. The chapter’s dynamic historical argument delineates how early successes in global trade policies and governance led to maximalist peaceful change, followed by crisis leading to greater use of tariffs and ensuing US–China economic and trade competition. The mechanisms that underwrote the paradox of crisis despite institutional strength are elaborated.
Among all the narratives collected in the Bible, none tells a story quite like the Acts of the Apostles. Readers travel along with the action over very long distances and visit a range of cultural settings in this geographically expansive tale that brings a wide spectrum of people onto the narrative stage.
Jiří Adámek, Czech Technical University in Prague,Stefan Milius, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany,Lawrence S. Moss, Indiana University, Bloomington
This chapter provides a practitioner’s point of view on diplomatic images. The author is positioned to give a unique perspective as a freelance photographer who is currently based in Singapore, which has recently become a significant city-state for major global diplomatic events. Through his first-hand experiences of covering high-profile international diplomatic events, such as the 2018 Trump-Kim Summit held in Singapore, the author takes us backstage and demonstrates how famous diplomatic images are produced to represent the affective register of the moment. In so doing, the chapter illuminates the situational context of the photographer in taking diplomatic images, offering insight into the editorial process in which diplomatic images are produced by the media.
This chapter uses the lens of feminine rhetorical style to examine how gendered expectations affect first ladies’ public speeches and how their rhetorical styles evolved over time. Selected speeches of first ladies from Eleanor Roosevelt to Melania Trump are analyzed and five recurring themes are reviewed. These include the discussion of feminine topics such as family and childcare and envisioning women’s role in society, addressing masculine issues such as war and politics through feminine rhetoric, connecting with audiences as peers, use of personal narratives, and use of expert sources and statistics. The chapter concludes that first ladies’ addresses are usually delivered within the bounds of stereotypical gendered expectations, though subtle deviations can be found depending on the first lady’s public image, her professional experience, and the popular opinion of the times. The analysis of first ladies’ rhetorical styles helps us better understand their evolving role in US politics.
This chapter reviews equivalences of homotopy theories between Multicat, the category of small multicategories and multifunctors, PermCat^st, the category of small permutative categories and strict monoidal functors, and PermCat^su, the category of small permutative categories and strictly unital symmetric monoidal functors. These equivalences are given by a free left adjoint to the endomorphism functor. This material provides an important foundation for that of Part 2.
This chapter extends the material of Chapter 3 to a pointed free construction from pointed multicategories to permutative categories. This is not a restriction, along the inclusion of pointed multicategories among all multicategories, but an extension, along the functor that adjoins a disjoint basepoint. Essential results, such as the adjunction with the endomorphism construction and compatibility with stable equivalences, are likewise extended from Chapter 3.
This chapter gives an overview of data-driven methods applied to turbulence closure modeling for coarse graining. A non-exhaustive introduction of the various data-driven approaches that have been used in the context of closure modeling is provided which includes a discussion of model consistency, which is the ultimate indicator of a successful model, and other key concepts. More details are then presented for two specific methods, one a neural-network representative of nontransparent black-box approaches and one specific type of evolutionary algorithm representative of transparent approaches yielding explicit mathematical expressions. The importance of satisfying physical constraints is emphasized and methods to choose the most relevant input features are suggested. Several recent applications of data-driven methods to subgrid closure modeling are discussed, both for nonreactive and reactive flow configurations. The chapter is concluded with current trends and an assessment of what can be realistically expected of data-driven methods for coarse graining.