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

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

Pneumothorax complicating isolated clavicle fracture

Isolated clavicle fractures are among the commonest of traumatic fractures in the emergency department. Complications of isolated clavicle fractures are rare. Pneumothorax has been described as a complication of a fractured clavicle only rarely in English literature. In all the reported cases, the pneumothorax was treated by a thoracostomy and the clavicle fracture was treated conservatively. In our case, the pneumothorax required a chest drain insertion and the clavicle fracture was treated surgically with good result