From the function-sheaf dictionary to quasicharacters of pp-adic tori

We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting. We find the group of isomorphism classes of character sheaves on $G$ and show that it is an extension of the group of characters of $G(k)$ by a cohomology group determined by the component group scheme of $G$. We also classify all morphisms in the category character sheaves on $G$. As an application, we study character sheaves on Greenberg transforms of locally finite type N\'eron models of algebraic tori over local fields. This provides a geometrization of quasicharacters of $p$-adic tori.Comment: Added examples and incorporated referee's suggestions. To be published in Journal of the Institute of Mathematics of Jussie

An investigation of the Speed and Power Limitations of a Copper-Doped Gallium Arsenide Photoconductive Switch

The processes of persistent photoconductivity followed by photo-quenching are demonstrated in copper-compensated, silicon-doped, semi-insulating gallium arsenide. These processes allow a switch to be developed that can be closed by the application of one laser pulse (λ = 1.06 μm) and opened by the application of a second laser pulse with a wavelength equal to twice that of the first laser (λ= 2.13 μm). Switch closure is primarily achieved by elevating electrons from a deep copper center which has been diffused into the material. The opening phase is a two-step process which relies initially on the absorption of the 2-μm laser causing electrons to be elevated from the valence band back into the copper center, and finally on the recombination of electrons in the conduction band with holes in the valence band. The second step requires a sufficient concentration of recombination centers in the material for opening to occur in the subnanosecond regime. Both an experimental and a theoretical investigation of the generation of recombination centers in copper-doped gallium arsenide material, for the purpose of enabling the switch to close as well as open in the subnanosecond regime, is presented. These recombination centers were generated in the bulk GaAs material by fast-neutron irradiation (-1-MeV). An enhanced recombination center density also allows the copper-compensated GaAs switches to open against average electric fields of up to 36 kV/cm corresponding to a switch voltage of 18 kV. Finally, a new high-power radio-frequency (RF) source topology is introduced which uses two copper-doped gallium arsenide switches to synthesize frequency-agile RF waveforms. These waveforms may have considerable advantages when used in high-power-microwave applications

President Gerald Ford\u27s impact on United States foreign policy from 1974 to 1991

To illustrate President Ford\u27s impact on United States\u27 foreign policy, this thesis looks at his early life, his Congressional career and his brief tenure as Vice President. From there, it focuses on the differences between Ford and President Nixon. The paper looks at their personalities, decision-making styles, and their styles of leadership. Next, it analyzes the major international events that took place during Ford\u27s years in the White House. These events include the fall of South Vietnam and Cambodia, communist intervention in Angola and Ford\u27s dealings with the Soviet Union and The Peoples\u27 Republic of China. Finally, the paper examines three post-Ford Administrations and the impact that Gerald Ford had on them. The evidence supports the author\u27s contention that Gerald Ford had a substantial impact on the foreign policy of the United States during and after his Presidency

IMAE for Noise-Robust Learning: Mean Absolute Error Does Not Treat Examples Equally and Gradient Magnitude's Variance Matters

In this work, we study robust deep learning against abnormal training data from the perspective of example weighting built in empirical loss functions, i.e., gradient magnitude with respect to logits, an angle that is not thoroughly studied so far. Consequently, we have two key findings: (1) Mean Absolute Error (MAE) Does Not Treat Examples Equally. We present new observations and insightful analysis about MAE, which is theoretically proved to be noise-robust. First, we reveal its underfitting problem in practice. Second, we analyse that MAE's noise-robustness is from emphasising on uncertain examples instead of treating training samples equally, as claimed in prior work. (2) The Variance of Gradient Magnitude Matters. We propose an effective and simple solution to enhance MAE's fitting ability while preserving its noise-robustness. Without changing MAE's overall weighting scheme, i.e., what examples get higher weights, we simply change its weighting variance non-linearly so that the impact ratio between two examples are adjusted. Our solution is termed Improved MAE (IMAE). We prove IMAE's effectiveness using extensive experiments: image classification under clean labels, synthetic label noise, and real-world unknown noise. We conclude IMAE is superior to CCE, the most popular loss for training DNNs.Comment: Updated Version. IMAE for Noise-Robust Learning: Mean Absolute Error Does Not Treat Examples Equally and Gradient Magnitude's Variance Matters Code: \url{https://github.com/XinshaoAmosWang/Improving-Mean-Absolute-Error-against-CCE}. Please feel free to contact for discussions or implementation problem

Fusing Continuous-valued Medical Labels using a Bayesian Model

With the rapid increase in volume of time series medical data available through wearable devices, there is a need to employ automated algorithms to label data. Examples of labels include interventions, changes in activity (e.g. sleep) and changes in physiology (e.g. arrhythmias). However, automated algorithms tend to be unreliable resulting in lower quality care. Expert annotations are scarce, expensive, and prone to significant inter- and intra-observer variance. To address these problems, a Bayesian Continuous-valued Label Aggregator(BCLA) is proposed to provide a reliable estimation of label aggregation while accurately infer the precision and bias of each algorithm. The BCLA was applied to QT interval (pro-arrhythmic indicator) estimation from the electrocardiogram using labels from the 2006 PhysioNet/Computing in Cardiology Challenge database. It was compared to the mean, median, and a previously proposed Expectation Maximization (EM) label aggregation approaches. While accurately predicting each labelling algorithm's bias and precision, the root-mean-square error of the BCLA was 11.78$\pm$0.63ms, significantly outperforming the best Challenge entry (15.37$\pm$2.13ms) as well as the EM, mean, and median voting strategies (14.76$\pm$0.52ms, 17.61$\pm$0.55ms, and 14.43$\pm$0.57ms respectively with $p<0.0001$)