4 resultados para 340208 Macroeconomics (incl. Monetary and Fiscal Theory)
em Duke University
A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula
Resumo:
Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.
Resumo:
There are many sociopolitical theories to help explain why governments and actors do what they do. Securitization Theory is a process-oriented theory in international relations that focuses on how an actor defines another actor as an “existential threat,” and the resulting responses that can be taken in order to address that threat. While Securitization Theory is an acceptable method to analyze the relationships between actors in the international system, this thesis contends that the proper examination is multi-factorial, focusing on the addition of Role Theory to the analysis. Consideration of Role Theory, which is another international relations theory that explains how an actor’s strategies, relationships, and perceptions by others is based on pre-conceptualized definitions of that actor’s identity, is essential in order to fully explain why an actor might respond to another in a particular way. Certain roles an actor may enact produce a rival relationship with other actors in the system, and it is those rival roles that elicit securitized responses. The possibility of a securitized response lessens when a role or a relationship between roles becomes ambiguous. There are clear points of role rivalry and role ambiguity between Hizb’allah and Iran, which has directly impacted, and continues to impact, how the United States (US) responds to these actors. Because of role ambiguity, the US has still not conceptualized an effective way to deal with Hizb’allah and Iran holistically across all its various areas of operation and in its various enacted roles. It would be overly simplistic to see Hizb’allah and Iran solely through one lens depending on which hemisphere or continent one is observing. The reality is likely more nuanced. Both Role Theory and Securitization theory can help to understand and articulate those nuances. By examining two case studies of Hizb’allah and Iran’s enactment of various roles in both the Middle East and Latin America, the situations where roles cause a securitized response and where the response is less securitized due to role ambiguity will become clear. Using this augmented approach of combining both theories, along with supplementing the manner in which an actor, action, or role is analyzed, will produce better methods for policy-making that will be able to address the more ambiguous activities of Hizb’allah and Iran in these two regions.
Resumo:
From tendencies to reduce the Underground Railroad to the imperative "follow the north star" to the iconic images of Ruby Bridges' 1960 "step forward" on the stairs of William Frantz Elementary School, America prefers to picture freedom as an upwardly mobile development. This preoccupation with the subtractive and linear force of development makes it hard to hear the palpable steps of so many truant children marching in the Movement and renders illegible the nonlinear movements of minors in the Underground. Yet a black fugitive hugging a tree, a white boy walking alone in a field, or even pieces of a discarded raft floating downstream like remnants of child's play are constitutive gestures of the Underground's networks of care and escape. Responding to 19th-century Americanists and cultural studies scholars' important illumination of the child as central to national narratives of development and freedom, "Minor Moves" reads major literary narratives not for the child and development but for the fugitive trace of minor and growth.
In four chapters, I trace the physical gestures of Nathaniel Hawthorne's Pearl, Harriet Beecher Stowe's Topsy, Harriet Wilson's Frado, and Mark Twain's Huck against the historical backdrop of the Fugitive Slave Act and the passing of the first compulsory education bills that made truancy illegal. I ask how, within a discourse of independence that fails to imagine any serious movements in the minor, we might understand the depictions of moving children as interrupting a U.S. preoccupation with normative development and recognize in them the emergence of an alternative imaginary. To attend to the movement of the minor is to attend to what the discursive order of a development-centered imaginary deems inconsequential and what its grammar can render only as mistakes. Engaging the insights of performance studies, I regard what these narratives depict as childish missteps (Topsy's spins, Frado's climbing the roof) as dances that trouble the narrative's discursive order. At the same time, drawing upon the observations of black studies and literary theory, I take note of the pressure these "minor moves" put on the literal grammar of the text (Stowe's run-on sentences and Hawthorne's shaky subject-verb agreements). I regard these ungrammatical moves as poetic ruptures from which emerges an alternative and prior force of the imaginary at work in these narratives--a force I call "growth."
Reading these "minor moves" holds open the possibility of thinking about a generative association between blackness and childishness, one that neither supports racist ideas of biological inferiority nor mandates in the name of political uplift the subsequent repudiation of childishness. I argue that recognizing the fugitive force of growth indicated in the interplay between the conceptual and grammatical disjunctures of these minor moves opens a deeper understanding of agency and dependency that exceeds notions of arrested development and social death. For once we interrupt the desire to picture development (which is to say the desire to picture), dependency is no longer a state (of social death or arrested development) of what does not belong, but rather it is what Édouard Glissant might have called a "departure" (from "be[ing] a single being"). Topsy's hard-to-see pick-pocketing and Pearl's running amok with brown men in the market are not moves out of dependency but indeed social turns (a dance) by way of dependency. Dependent, moving and ungrammatical, the growth evidenced in these childish ruptures enables different stories about slavery, freedom, and childishness--ones that do not necessitate a repudiation of childishness in the name of freedom, but recognize in such minor moves a fugitive way out.
Resumo:
Confronting the rapidly increasing, worldwide reliance on biometric technologies to surveil, manage, and police human beings, my dissertation