The Sample Complexity of Dictionary Learning

A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications, including classification, denoising and signal separation, learn a dictionary from a set of signals to be represented. Can we expect that the representation found by such a dictionary for a previously unseen example from the same source will have L_2 error of the same magnitude as those for the given examples? We assume signals are generated from a fixed distribution, and study this questions from a statistical learning theory perspective. We develop generalization bounds on the quality of the learned dictionary for two types of constraints on the coefficient selection, as measured by the expected L_2 error in representation when the dictionary is used. For the case of l_1 regularized coefficient selection we provide a generalization bound of the order of O(sqrt(np log(m lambda)/m)), where n is the dimension, p is the number of elements in the dictionary, lambda is a bound on the l_1 norm of the coefficient vector and m is the number of samples, which complements existing results. For the case of representing a new signal as a combination of at most k dictionary elements, we provide a bound of the order O(sqrt(np log(m k)/m)) under an assumption on the level of orthogonality of the dictionary (low Babel function). We further show that this assumption holds for most dictionaries in high dimensions in a strong probabilistic sense. Our results further yield fast rates of order 1/m as opposed to 1/sqrt(m) using localized Rademacher complexity. We provide similar results in a general setting using kernels with weak smoothness requirements

Performance evaluation of on-chip wavelength conversion based on InP/In1−x_{1-x}Gax_xAsy_yP1−y_{1-y} semiconductor waveguide platforms

We propose and design the high confinement InP/In1-xGaxAsyP1-y semiconductor waveguides and report the results of effective wavelength conversion based on this platform. Efficient confinement and mode field area fluctuation at different wavelength is analyzed to achieve the high nonlinear coefficient. The numerical results show that nearly zero phase-mismatch condition can be satisfied through dispersion tailoring of InP/In1-xGaxAsyP1-y waveguides, and the wavelength conversion ranging over 40 nm with the maximum conversion efficiency -26.3 dB is achieved for fixing pump power 100 mW. Meanwhile, the influences of the doping parameter y and pumping wavelength on the bandwidth and conversion efficiency are also discussed and optimized. It is indicated the excellent optical properties of the InP/In1-xGaxAsyP1-y waveguides and pave the way towards direct integration telecom band devices on stand semiconductor platforms.Comment: 21 page

The Data Acquisition System for the KOTO Experiment

We developed and built a new system of readout and trigger electronics, based on the waveform digitization and pipeline readout, for the KOTO experiment at J-PARC, Japan. KOTO aims at observing the rare kaon decay $K_{L}\rightarrow\pi^{0}\nu\bar{\nu}$. A total of 4000 readout channels from various detector subsystems are digitized by 14-bit 125-MHz ADC modules equipped with a 10-pole Bessel filter in order to reduce the pile-up effects. The trigger decision is made every 8-ns using the digitized waveform information. To avoid dead time, the ADC and trigger modules have pipelines in their FPGA chips to store data while waiting for the trigger decision. The KOTO experiment performed the first physics run in May 2013. The data acquisition system worked stably during the run.Comment: 5 pages,12 figures, Transactions on Nuclear Science, Proceedings of the 19th Real Time Conference, Preprin

A vibration powered wireless mote on the Forth Road Bridge

The conventional resonant-approaches to scavenge kinetic energy are typically confined to narrow and single-band frequencies. The vibration energy harvester device reported here combines both direct resonance and parametric resonance in order to enhance the power responsiveness towards more efficient harnessing of real-world ambient vibration. A packaged electromagnetic harvester designed to operate in both of these resonant regimes was tested in situ on the Forth Road Bridge. In the field-site, the harvester, with an operational volume of ~126 cm3, was capable of recovering in excess of 1 mW average raw AC power from the traffic-induced vibrations in the lateral bracing structures underneath the bridge deck. The harvester was integrated off-board with a power conditioning circuit and a wireless mote. Duty- cycled wireless transmissions from the vibration-powered mote was successfully sustained by the recovered ambient energy. This limited duration field test provides the initial validation for realising vibration-powered wireless structural health monitoring systems in real world infrastructure, where the vibration profile is both broadband and intermittent

Real World Assessment of an Auto-parametric Electromagnetic Vibration Energy Harvester

The convention within the eld of vibration energy harvesting (VEH) has revolved around designing resonators with natural frequencies that match single fixed frequency sinusoidal input. However, real world vibrations can be random, multi-frequency, broadband and time-varying in nature. Building upon previous work on auto-parametric resonance, the fundamentally different approach allows multiple axes vibration and has the potential to achieve higher power density as well as wider operational frequency bandwidth. This paper presents the power response of a packaged auto-parametric VEH prototype (practical operational volume 126 cm^3) towards various real world vibration sources including vibration of a bridge, a compressor motor as well as an automobile. At auto-parametric resonance (driven at 23.5 Hz and 1 grms), the prototype can output a peak of 78.9 mW and 4.5 Hz of -3dB bandwidth. Furthermore, up to ~1 mW of average power output was observed from the harvester on the Forth Road Bridge. The harvested electrical energy from various real world sources were used to power up a power conditioning circuit, a wireless sensor mote, a MEMS (micro-electromechanical system) accelerometer and other low power sensors. This demonstrates the concept of self-sustaining vibration-powered wireless sensor systems in real world scenarios, to potentially realise maintenance-free autonomous structural health and condition monitoring.This work was supported by EPSRC (grant EP/L010917/1) and the Cambridge Centre for Smart Infrastructure and Construction

Preface: The Second Generation of Second Amendment Law & Policy

Over 70% of China’s domestic oil production is obtained from nine giant oilfields. Understanding the behaviour of these fields is essential to both domestic oil production and future Chinese oil imports. This study utilizes decline curves and depletion rate analysis to create some future production outlooks for the Chinese giants. Based on our study, we can only conclude that China’s future domestic oil production faces a significant challenge caused by maturing and declining giant fields. Evidence also indicates that the extensive use of water flooding and enhanced oil recovery methods may be masking increasing scarcity and may result in even steeper future decline rates than the ones currently being seen. Our results suggest that a considerable drop in oil production from the Chinese giants can be expected over the next decades

Structure–function relations in diF-TES-ADT blend organic field effect transistors studied by scanning probe microscopy

We develop structure–property relations for organic field effect transistors using a polymer/small-molecule blend active layer. An array of bottom gate, bottom contact devices using a polymeric dielectric and a semiconductor layer of 2,8-difluoro-5,11-bis(triethylsilylethynyl)anthradithiophene (diF-TES-ADT) is described and shown to have good device-to-device uniformity. We describe the nucleation and growth processes that lead to the formation of four structurally distinct regimes of the diF-TES-ADT semiconductor film, including evidence of layer-by-layer growth when spin-coated onto silver electrodes and an organic dielectric as part of a polymer blend. Devices exhibiting a maximum saturation mobility of 1.5 cm2 V−1 s−1 and maximum current modulation ratio (Ion/Ioff) of 1.20 × 105 are visualised by atomic force microscopy and appear to have excellent domain connectivity and aligned crystallography across the channel. In contrast, poorly performing devices tend to show a phase change in semiconductor crystallinity in the channel centre. These observations are enhanced by direct visualisation of the potential drop across the channel using Kelvin probe microscopy, which confirms the importance of large, well-aligned and well-connected semiconductor domains across the transistor channel

Split-domain calibration of an ecosystem model using satellite ocean colour data

The application of satellite ocean colour data to the calibration of plankton ecosystem models for large geographic domains, over which their ideal parameters cannot be assumed to be invariant, is investigated. A method is presented for seeking the number and geographic scope of parameter sets which allows the best fit to validation data to be achieved. These are independent data not used in the parameter estimation process. The goodness-of-fit of the optimally calibrated model to the validation data is an objective measure of merit for the model, together with its external forcing data. Importantly, this is a statistic which can be used for comparative evaluation of different models. The method makes use of observations from multiple locations, referred to as stations, distributed across the geographic domain. It relies on a technique for finding groups of stations which can be aggregated for parameter estimation purposes with minimal increase in the resulting misfit between model and observations.The results of testing this split-domain calibration method for a simple zero dimensional model, using observations from 30 stations in the North Atlantic, are presented. The stations are divided into separate calibration and validation sets. One year of ocean colour data from each station were used in conjunction with a climatological estimate of the station’s annual nitrate maximum. The results demonstrate the practical utility of the method and imply that an optimal fit of the model to the validation data would be given by two parameter sets. The corresponding division of the North Atlantic domain into two provinces allows a misfit-based cost to be achieved which is 25% lower than that for the single parameter set obtained using all of the calibration stations. In general, parameters are poorly constrained, contributing to a high degree of uncertainty in model output for unobserved variables. This suggests that limited progress towards a definitive model calibration can be made without including other types of observations