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