122,050 research outputs found
Local models of Shimura varieties and a conjecture of Kottwitz
We give a group theoretic definition of "local models" as sought after in the
theory of Shimura varieties. These are projective schemes over the integers of
a -adic local field that are expected to model the singularities of integral
models of Shimura varieties with parahoric level structure. Our local models
are certain mixed characteristic degenerations of Grassmannian varieties; they
are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and
the second-named author to mixed characteristics and to the case of general
(tamely ramified) reductive groups. We study the singularities of local models
and hence also of the corresponding integral models of Shimura varieties. In
particular, we study the monodromy (inertia) action and show a commutativity
property for the sheaves of nearby cycles. As a result, we prove a conjecture
of Kottwitz which asserts that the semi-simple trace of Frobenius on the nearby
cycles gives a function which is central in the parahoric Hecke algebra.Comment: 88 pages, several corrections and change
3-D Microwave Imaging for Breast Cancer
We introduce a novel microwave imaging technique for breast cancer detection. Our approach provides a one-pass inverse image solution, which is completely new and unprecedented, unrelated to tomography or radar-based algorithms, and unburdened by the optimization toil which lies at the heart of numerical schemes. It operates effectively at a single frequency, without requiring the bandwidth of radar techniques. Underlying this new method is our unique Field Mapping Algorithm (FMA), which transforms electromagnetic fields acquired upon one surface, be it through outright measurement or some auxiliary computation, into those upon another in an exact sense
A Computational Study Of The Role Of Spatial Receptive Field Structure In Processing Natural And Non-Natural Scenes
The center-surround receptive field structure, ubiquitous in the visual system, is hypothesized to be evolutionarily advantageous in image processing tasks. We address the potential functional benefits and shortcomings of spatial localization and center-surround antagonism in the context of an integrate-and-fire neuronal network model with image-based forcing. Utilizing the sparsity of natural scenes, we derive a compressive-sensing framework for input image reconstruction utilizing evoked neuronal firing rates. We investigate how the accuracy of input encoding depends on the receptive field architecture, and demonstrate that spatial localization in visual stimulus sampling facilitates marked improvements in natural scene processing beyond uniformly-random excitatory connectivity. However, for specific classes of images, we show that spatial localization inherent in physiological receptive fields combined with information loss through nonlinear neuronal network dynamics may underlie common optical illusions, giving a novel explanation for their manifestation. In the context of signal processing, we expect this work may suggest new sampling protocols useful for extending conventional compressive sensing theory
Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results
Various astronomical observations have been consistently making a strong case
for the existence of a component of dark energy with negative pressure in the
universe. It is now necessary to take the dark energy component(s) into account
in gravitational lensing statistics and other cosmological tests. By using the
comoving distance we derive analytic but simple expressions for the optical
depth of multiple image, the expected value of image separation and the
probability distribution of image separation caused by an assemble of singular
isothermal spheres in general FRW cosmological models with dark energy
component(s). We also present the kinematical and dynamical properties of these
kinds of cosmological models and calculate the age of the universe and the
distance measures, which are often used in classical cosmological tests. In
some cases we are able to give formulae that are simpler than those found
elsewhere in the literature, which could make the cosmological tests for dark
energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil
Gravitational Lensing Statistics as a Probe of Dark Energy
By using the comoving distance, we derive an analytic expression for the
optical depth of gravitational lensing, which depends on the redshift to the
source and the cosmological model characterized by the cosmic mass density
parameter , the dark energy density parameter and its
equation of state . It is shown that, the larger the
dark energy density is and the more negative its pressure is, the higher the
gravitational lensing probability is. This fact can provide an independent
constraint for dark energy.Comment: 9 pages, 2 figure
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