Generalized Heisenberg algebra coherent states for Power-law potentials

Coherent states for power-law potentials are constructed using generalized Heisenberg algabras. Klauder's minimal set of conditions required to obtain coherent states are satisfied. The statistical properties of these states are investigated through the evaluation of the Mandel's parameter. It is shown that these coherent states are useful for describing the states of real and ideal lasers.Comment: 13 pages, 2 figure

Adjoint approach to the physical characterization of a shallow-water environment

In underwater acoustics a variety of different applications of adjoint models has been proposed in recent years. Adjoints have been derived for normal modes and for both the standard parabolic equation and Claerbout’s wide-angle approximation. This paper reviews the analytic nonlocal boundary control approach proposed in an earlier paper by the authors [Meyer & Hermand, ‘‘Optimal nonlocal boundary control of the wide-angle parabolic equation for inversion of a waveguide acoustic field,’’ J. Acoust. Soc. Am. 117, 2937–2948 (2005)] and presents a numerical extension that allows direct inversion of the geoacoustic parameters that are embedded in a discrete representation of the nonlocal boundary condition at the water-sediment interface. The effectiveness of this numerical adjoint approach for the physical characterization of a shallow-water environment is illustrated with applications for geoacoustic inversion and ocean acoustic tomography. In particular, it is shown how a joint inversion across multiple frequencies can enhance the performance of the optimization process, especially for the case of a sparse receiver array spanning part of the water column. In an additional example we combine the two applications and discuss the feasibility of geoacoustic inversion in the presence of an uncertain sound-speed profile

A numerical adjoint parabolic equation (PE) method for tomography and geoacoustic inversion in shallow water

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937–2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK ’94 experimental conditions

Validation of adjoint-generated environmental gradients for the acoustic monitoring of a shallow water area

In the framework of the recent Maritime Rapid Environmental Assessment sea trial MREA07/BP'07 [Le Gac&Hermand, 2007] that was conducted in the same area south of the island of Elba as the earlier Yellow Shark trial (YS94), this paper examines the original YS94 acoustic data and the recent MREA07 oceanographic data to demonstrate adjoint-based acoustic monitoring of environmental parameters in Mediterranean shallow waters. First, adjoint-generated environmental gradients are validated for the application in geoacoustic inversion where the bottom acoustic parameters of the YS94 layered seabed are determined from the long-range waterborne propagation of a multi-frequency signal. Then, for the application in ocean acoustic tomography, the temporal variability of the MREA07/BP'07 oceanographic data is analyzed in terms of empirical orthogonal functions and the adjoint-based inversion scheme is used to track the time-varying sound speed profile of the experimental transect

Smooth Loss Functions for Deep Top-k Classification

The top-k error is a common measure of performance in machine learning and computer vision. In practice, top-k classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed suggest that cross-entropy is an optimal learning objective for such a task in the limit of infinite data. In the context of limited and noisy data however, the use of a loss function that is specifically designed for top-k classification can bring significant improvements. Our empirical evidence suggests that the loss function must be smooth and have non-sparse gradients in order to work well with deep neural networks. Consequently, we introduce a family of smoothed loss functions that are suited to top-k optimization via deep learning. The widely used cross-entropy is a special case of our family. Evaluating our smooth loss functions is computationally challenging: a na\"ive algorithm would require $\mathcal{O}(\binom{n}{k})$ operations, where n is the number of classes. Thanks to a connection to polynomial algebra and a divide-and-conquer approach, we provide an algorithm with a time complexity of $\mathcal{O}(k n)$. Furthermore, we present a novel approximation to obtain fast and stable algorithms on GPUs with single floating point precision. We compare the performance of the cross-entropy loss and our margin-based losses in various regimes of noise and data size, for the predominant use case of k=5. Our investigation reveals that our loss is more robust to noise and overfitting than cross-entropy.Comment: ICLR 201

Training Neural Networks for and by Interpolation

In modern supervised learning, many deep neural networks are able to interpolate the data: the empirical loss can be driven to near zero on all samples simultaneously. In this work, we explicitly exploit this interpolation property for the design of a new optimization algorithm for deep learning, which we term Adaptive Learning-rates for Interpolation with Gradients (ALI-G). ALI-G retains the two main advantages of Stochastic Gradient Descent (SGD), which are (i) a low computational cost per iteration and (ii) good generalization performance in practice. At each iteration, ALI-G exploits the interpolation property to compute an adaptive learning-rate in closed form. In addition, ALI-G clips the learning-rate to a maximal value, which we prove to be helpful for non-convex problems. Crucially, in contrast to the learning-rate of SGD, the maximal learning-rate of ALI-G does not require a decay schedule, which makes it considerably easier to tune. We provide convergence guarantees of ALI-G in various stochastic settings. Notably, we tackle the realistic case where the interpolation property is satisfied up to some tolerance. We provide experiments on a variety of architectures and tasks: (i) learning a differentiable neural computer; (ii) training a wide residual network on the SVHN data set; (iii) training a Bi-LSTM on the SNLI data set; and (iv) training wide residual networks and densely connected networks on the CIFAR data sets. ALI-G produces state-of-the-art results among adaptive methods, and even yields comparable performance with SGD, which requires manually tuned learning-rate schedules. Furthermore, ALI-G is simple to implement in any standard deep learning framework and can be used as a drop-in replacement in existing code.Comment: Published at ICML 202

Variability Study of High Current Junctionless Silicon Nanowire Transistors

Silicon nanowires have numerous potential applications, including transistors, memories, photovoltaics, biosensors and qubits [1]. Fabricating a nanowire with characteristics required for a specific application, however, poses some challenges. For example, a major challenge is that as the transistors dimensions are reduced, it is difficult to maintain a low off-current (Ioff) whilst simultaneously maintaining a high on-current (Ion). This can be the result of quantum mechanical tunnelling, short channel effects or statistical variability [2]. A variety of new architectures, including ultra-thin silicon-on-insulator (SOI), double gate, FinFETs, tri-gate, junctionless and gate all-around (GAA) nanowire transistors, have therefore been developed to improve the electrostatic control of the conducting channel. This is essential since a low Ioff implies low static power dissipation and it will therefore improve power management in the multi-billion transistor circuits employed globally in microprocessors, sensors and memories

Effet de l’oxygène sur les radiations optiques émises lors de la pulvérisation de l’aluminium par un faisceau d’ions

La présence de l’oxygène au voisinage d’une surface métallique lors d’unbombardement ionique, provoque une décroissance du rendement totalde pulvérisation mais elle modifie considérablement les proportions desdiverses espèces éjectées de cette surface. Dans ce travail, nous noussommes intéressés à l’effet de l’oxygène sur la lumière émise lors de lapulvérisation d’une surface d’aluminium par des ions Kr+ d’énergiecinétique de 5 keV. Le spectre de luminescence relevé à une pression de10-7 Torr est comparé à celui mesuré lorsque la cible est soumise à uneatmosphère d’oxygène. L’examen des intensités des raies spectralesmontre que toutes les raies Al I manifestent une dépendance positiveavec la pression en oxygène alors que des raies Al II manifestent unedépendance négative. Nous avons aussi enregistré que des raies Al IIIrestent insensibles à la présence de ce gaz. Ces observations sontcomparées avec les spectres de luminescences de l’alumine bombardéedans les mêmes conditions expérimentales. Les résultats obtenus sontinterprétés dans le cadre du modèle de transfert d’électrons entre lasurface et la particule éjectée. La validité du modèle suggère qu'en présence de l'oxygène, une structure est formée et dont le schéma debandes d'énergie est intermédiaire entre celui de l'aluminium et celui del'alumine.Mots-clés : pulvérisation, émission optique, aluminium, alumine, modèlede transfert d’électrons; analyse de surface, spectroscopie optique