1,949 research outputs found
The quantum state vector in phase space and Gabor's windowed Fourier transform
Representations of quantum state vectors by complex phase space amplitudes,
complementing the description of the density operator by the Wigner function,
have been defined by applying the Weyl-Wigner transform to dyadic operators,
linear in the state vector and anti-linear in a fixed `window state vector'.
Here aspects of this construction are explored, with emphasis on the connection
with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple
quantum states from various choices of window are presented as illustrations.
Generalized Bargmann representations of the state vector appear as special
cases, associated with Gaussian windows. For every choice of window, amplitudes
lie in a corresponding linear subspace of square-integrable functions on phase
space. A generalized Born interpretation of amplitudes is described, with both
the Wigner function and a generalized Husimi function appearing as quantities
linear in an amplitude and anti-linear in its complex conjugate.
Schr\"odinger's time-dependent and time-independent equations are represented
on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and
further references adde
Atmospheric and Oceanographic Information Processing System (AOIPS) system description
The development of hardware and software for an interactive, minicomputer based processing and display system for atmospheric and oceanographic information extraction and image data analysis is described. The major applications of the system are discussed as well as enhancements planned for the future
Acute psychiatric in-patients tested for HIV status: a clinical profile
No Abstract.South African Psychiatry Review Vol. 10 (2) 2007: pp.83-8
Circular No. 59 - Control of Stinking Smut of Wheat with Copper Carbonate
Stinking smut or bunt of wheat is an ever-present and destructive disease in the wheat fields of Utah. During the past season (1925) this disease was especially prevalent, causing losses in certain fields of from 25 to 50 per cent, not counting the loss to the grower in reduced grade of grain. In the threshing of smutty wheat there is also the risk of loss from smut explosion. Almost every season cases of this sort are reported. In addition of all of the wheat tested by the U. S. Grain Inspector at Logan for Northern Utah and Southern Idaho 30 per cent showed smut infection in 1925. The average reduction for smut is near ten cents a bushel with a variation from five to twenty cents. The cost of producing a smutted crop may equal or even exceed the cost of producing a clean crop. Loss occurring from this disease, since it is preventable, can hardly be considered attached to the total gross returns; it is a subtraction from the net profit. Effective methods for the prevention of these losses by smut are now available to every grain grower
Deep Bilevel Learning
We present a novel regularization approach to train neural networks that
enjoys better generalization and test error than standard stochastic gradient
descent. Our approach is based on the principles of cross-validation, where a
validation set is used to limit the model overfitting. We formulate such
principles as a bilevel optimization problem. This formulation allows us to
define the optimization of a cost on the validation set subject to another
optimization on the training set. The overfitting is controlled by introducing
weights on each mini-batch in the training set and by choosing their values so
that they minimize the error on the validation set. In practice, these weights
define mini-batch learning rates in a gradient descent update equation that
favor gradients with better generalization capabilities. Because of its
simplicity, this approach can be integrated with other regularization methods
and training schemes. We evaluate extensively our proposed algorithm on several
neural network architectures and datasets, and find that it consistently
improves the generalization of the model, especially when labels are noisy.Comment: ECCV 201
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