Termination of rewriting strategies: a generic approach

We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying narrowing and abstracting steps. The induction principle is applied through the abstraction mechanism, where terms are replaced by variables representing any of their normal forms. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. Abstraction constraints can be used to control the narrowing mechanism, well known to easily diverge. The generic method is then instantiated for the innermost, outermost and local strategies.Comment: 49 page

When can we kick (some) humans “out of the loop”? An examination of the use of ai in medical imaging for lumbar spinal stenosis

Artificial intelligence (AI) has attracted an increasing amount of attention, both positive and negative. Its potential applications in healthcare are indeed manifold and revolutionary, and within the realm of medical imaging and radiology (which will be the focus of this paper), significant increases in accuracy and speed, as well as significant savings in cost, stand to be gained through the adoption of this technology. Because of its novelty, a norm of keeping humans “in the loop” wherever AI mechanisms are deployed has become synonymous with good ethical practice in some circles. It has been argued that keeping humans “in the loop” is important for reasons of safety, accountability, and the maintenance of institutional trust. However, as the application of machine learning for the detection of lumbar spinal stenosis (LSS) in this paper’s case study reveals, there are some scenarios where an insistence on keeping humans in the loop (or in other words, the resistance to automation) seems unwarranted and could possibly lead us to miss out on very real and important opportunities in healthcare—particularly in low-resource settings. It is important to acknowledge these opportunity costs of resisting automation in such contexts, where better options may be unavailable. Using an AI model based on convolutional neural networks developed by a team of researchers at NUH/NUS medical school in Singapore for automated detection and classification of the lumbar spinal canal, lateral recess, and neural foraminal narrowing in an MRI scan of the spine to diagnose LSS, we will aim to demonstrate that where certain criteria hold (e.g., the AI is as accurate or better than human experts, risks are low in the event of an error, the gain in wellbeing is significant, and the task being automated is not essentially or importantly human), it is both morally permissible and even desirable to kick the humans out of the loop

Self-quenching of fundamental phase and amplitude noise in semiconductor lasers with dispersive loss

We show theoretically that the incorporation of a frequency-dependent loss mechanism in a semiconductor laser can lead, in concert with the amplitude-to-phase coupling, to major reductions of the fundamental intensity and phase noise. A loss dispersion of the wrong sign, on the other hand, leads to an increase of the noise and, at a certain strength, to instability

The steady state quantum statistics of a non-Markovian atom laser

We present a fully quantum mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit where atom-atom interactions are negligible, we have been able to solve this model without making the Born and Markov approximations. When coupling into free space, it is shown that for reasonable parameters there is a bound state which does not disperse, which means that there is no steady state. This bound state does not exist when gravity is included, and in that case the system reaches a steady state. We develop equations of motion for the two-time correlation in the presence of pumping and gravity in the output modes. We then calculate the steady-state output energy flux from the laser.Comment: 14 pages (twocloumn), 6 figure

Beyond Strong Coupling in a Massively Multimode Cavity

The study of light-matter interaction has seen a resurgence in recent years, stimulated by highly controllable, precise, and modular experiments in cavity quantum electrodynamics (QED). The achievement of strong coupling, where the coupling between a single atom and fundamental cavity mode exceeds the decay rates, was a major milestone that opened the doors to a multitude of new investigations. Here we introduce multimode strong coupling (MMSC), where the coupling is comparable to the free spectral range (FSR) of the cavity, i.e. the rate at which a qubit can absorb a photon from the cavity is comparable to the round trip transit rate of a photon in the cavity. We realize, via the circuit QED architecture, the first experiment accessing the MMSC regime, and report remarkably widespread and structured resonance fluorescence, whose origin extends beyond cavity enhancement of sidebands. Our results capture complex multimode, multiphoton processes, and the emergence of ultranarrow linewidths. Beyond the novel phenomena presented here, MMSC opens a major new direction in the exploration of light-matter interactions.Comment: 14 pages, 11 figures. References added, typos correcte

Model of the optical emission of a driven semiconductor quantum dot: phonon-enhanced coherent scattering and off-resonant sideband narrowing

We study the crucial role played by the solid-state environment in determining the photon emission characteristics of a driven quantum dot. For resonant driving, we predict a phonon-enhancement of the coherently emitted radiation field with increasing driving strength, in stark contrast to the conventional expectation of a rapidly decreasing fraction of coherent emission with stronger driving. This surprising behaviour results from thermalisation of the dot with respect to the phonon bath, and leads to a nonstandard regime of resonance fluorescence in which significant coherent scattering and the Mollow triplet coexist. Off-resonance, we show that despite the phonon influence, narrowing of dot spectral sideband widths can occur in certain regimes, consistent with an experimental trend.Comment: Published version. 5 pages, 2 figures, plus 4 page supplement. Title changed, figure 1 revised, various edits and additions to the tex

Suppression of Zeeman gradients by nuclear polarization in double quantum dots

We use electric dipole spin resonance to measure dynamic nuclear polarization in InAs nanowire quantum dots. The resonance shifts in frequency when the system transitions between metastable high and low current states, indicating the presence of nuclear polarization. We propose that the low and the high current states correspond to different total Zeeman energy gradients between the two quantum dots. In the low current state, dynamic nuclear polarization efficiently compensates the Zeeman gradient due to the $g$-factor mismatch, resulting in a suppressed total Zeeman gradient. We present a theoretical model of electron-nuclear feedback that demonstrates a fixed point in nuclear polarization for nearly equal Zeeman splittings in the two dots and predicts a narrowed hyperfine gradient distribution

Superconductivity-Induced Transfer of In-Plane Spectral Weight in Bi2Sr2CaCu2O8: Resolving a Controversy

We present a detailed analysis of the superconductivity-induced redistribution of optical spectral weight in Bi2Sr2CaCu2O8 near optimal doping. It confirms the previous conclusion by Molegraaf et al. (Science 66, 2239 (2002)), that the integrated low-frequency spectral weight shows an extra increase below Tc. Since the region, where the change of the integrated spectral weight is not compensated, extends well above 2.5 eV, this transfer is caused by the transfer of spectral weight from interband to intraband region and only partially by the narrowing of the intraband peak. We show that the opposite assertion by Boris et al. (Science 304, 708 (2004)) regarding this compound, is unlikely the consequence of any obvious discrepancies between the actual experimental data.Comment: ReVTeX, 9 pages, 8 encapsulated postscript figures, several typo's correcte