18,482 research outputs found

    A New ±\pm Iwasawa Theory and Converse of Gross-Zagier and Kolyvagin Theorem (with an Appendix by Yangyu Fan)

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    Let p>3p>3 be a prime. In this paper we develop a new kind of anticyclotomic local ±\pm-Iwasawa theory at pp for Hecke characters of quadratic imaginary fields which is valid for all ramification types of pp (split, inert and ramified). As an application we deduce the converse of Gross-Zagier-Kolyvagin theorem for these CM forms, which states that Selmer rank one implies analytic rank one. To carry out the Iwasawa theory argument we employ a recent construction of a new type of pp-adic LL-function by Andreatta-Iovita, and generalized by Yangyu Fan to Shimura curves in the Appendix, and a ``virtual Heenger family'' made via a limiting procedure from a Heegner family along Coleman-Mazur eigencurve constructed by Jetchev-Loeffler-Zerbes.Comment: with an appendix by Yangyu Fa

    The Topology of Negatively Associated Distributions

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    We consider the sets of negatively associated (NA) and negatively correlated (NC) distributions as subsets of the space M\mathcal{M} of all probability distributions on Rn\mathbb{R}^n, in terms of their relative topological structures within the topological space of all measures on a given measurable space. We prove that the class of NA distributions has a non-empty interior with respect to the topology of the total variation metric on M\mathcal{M}. We show however that this is not the case in the weak topology (i.e. the topology of convergence in distribution), unless the underlying probability space is finite. We consider both the convexity and the connectedness of these classes of probability measures, and also consider the two classes on their (widely studied) restrictions to the Boolean cube in Rn\mathbb{R}^n

    Exploring Realist and Liberal Explanations of Armed Conflict Related to Economic Interdependence

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    "Over the course of the world's history war between states has existed as a constant possibility. War over land, over the acquisition of resources, over cultural norms and religion, misconceptions, quests for power, etc. There has never seemed to have been a shortage of reasons for war between states, there has however been a shortage of answers to truly explain the trend of why states take the risk of war knowing there is so much to be lost."(p.1) Since the mid-1880 economies have grown and developed to become more diverse and interconnected than ever before. While the economy has changed and interconnected states in new ways, the willingness of states to go into wars and risk economic instability comes into question. Realist theorists in this modern economy point to economic interdependence as a drain for a state and a potential detriment to success while liberal theorists see economic interdependence as a gateway to economic exchange and growth beyond the need for armed conflict. This research paper uses realist and liberal ideas present in the economic era created since the 1880s and analyzes the question of which theory does a better job of explaining the outcome of armed conflict between economically interdependent states. The findings of this paper indicate that both liberalism and realism offer explanations as to why the outcomes of economically interconnected conflicts end the way they do, pointing out the power that individual state policy choices in the direction of one theory over another have a large influence on the outcome of the entire event.No embargoAcademic Major: Philosophy, Politics and Economic

    On Curation: A Hermeneutical Approach

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    Starting point of this paper is the philosophical field of hermeneutics. Hermeneutics was established to account for different conditions of understanding and how they shape our interpretative processes. As different times constitute different conditions, the goal of the discipline essentially is to bridge the temporal gap between the creation of a work and its perception at a given point in time. Whereas traditionally, understanding was a matter of analyzing the historical tradition of author/artist and reader/viewer, nowadays, the perception and interpretation of art is shaped by another instance, the curator. Under the premise that selection and arrangement, i.e. curating, cannot be neutral, the author analyzes different contexts in which curating takes place and how different contexts account for different effects on our perception of art. After outlining the development of the curatorial practice—from institutional to independent curation—, a case study of Swiss curator Harald Szeemann serves as opportunity to examine specific phenomena and exhibitions in a detailed manner. A cultural and methodological cesura is proposed after which curators were able to execute the power and influence they have today: independent curation and the ahistorical exhibition. Ahistorical exhibitions disregard chronological display and enable curators to create individual narratives and themes by gathering artworks in a cross-temporal and geographical manner. Throughout the paper, it is assessed if and to what degree the application of hermeneutics onto the field of independent curation is fruitful. This theoretical analysis is followed by a market overview, in which various functions the curator fulfills in different institutions, e.g. museums, galleries, auction houses, are outlined and compared. Optimally, the consideration of cultural and commercial factors enables viewers to approach and see (curated) art in a differentiated way

    The embedding theorem in Hurwitz-Brill-Noether Theory

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    We generalize the Embedding Theorem of Eisenbud-Harris from classical Brill-Noether theory to the setting of Hurwitz-Brill-Noether theory. More precisely, in classical Brill-Noether theory, the embedding theorem states that a general linear series of degree d and rank r on a general curve of genus g is an embedding if r is at least 3. If f ⁣:CP1f \colon C \to \mathbb{P}^1 is a general cover of degree k, and L is a line bundle on C, recent work of the authors shows that the splitting type of fLf_* L provides the appropriate generalization of the pair (r, d) in classical Brill--Noether theory. In the context of Hurwitz-Brill-Noether theory, the condition that r is at least 3 is no longer sufficient to guarantee that a general such linear series is an embedding. We show that the additional condition needed to guarantee that a general linear series |L| is an embedding is that the splitting type of fLf_* L has at least three nonnegative parts. This new extra condition reflects the unique geometry of k-gonal curves, which lie on scrolls in Pr\mathbb{P}^r

    Image classification over unknown and anomalous domains

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    A longstanding goal in computer vision research is to develop methods that are simultaneously applicable to a broad range of prediction problems. In contrast to this, models often perform best when they are specialized to some task or data type. This thesis investigates the challenges of learning models that generalize well over multiple unknown or anomalous modes and domains in data, and presents new solutions for learning robustly in this setting. Initial investigations focus on normalization for distributions that contain multiple sources (e.g. images in different styles like cartoons or photos). Experiments demonstrate the extent to which existing modules, batch normalization in particular, struggle with such heterogeneous data, and a new solution is proposed that can better handle data from multiple visual modes, using differing sample statistics for each. While ideas to counter the overspecialization of models have been formulated in sub-disciplines of transfer learning, e.g. multi-domain and multi-task learning, these usually rely on the existence of meta information, such as task or domain labels. Relaxing this assumption gives rise to a new transfer learning setting, called latent domain learning in this thesis, in which training and inference are carried out over data from multiple visual domains, without domain-level annotations. Customized solutions are required for this, as the performance of standard models degrades: a new data augmentation technique that interpolates between latent domains in an unsupervised way is presented, alongside a dedicated module that sparsely accounts for hidden domains in data, without requiring domain labels to do so. In addition, the thesis studies the problem of classifying previously unseen or anomalous modes in data, a fundamental problem in one-class learning, and anomaly detection in particular. While recent ideas have been focused on developing self-supervised solutions for the one-class setting, in this thesis new methods based on transfer learning are formulated. Extensive experimental evidence demonstrates that a transfer-based perspective benefits new problems that have recently been proposed in anomaly detection literature, in particular challenging semantic detection tasks
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