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Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding algorithm as the input quantum register is increased through its critical size of $\mathfrak{m}_0=\lceil 2\log_2 r\rceil$ qubits (where $r$ is the period sought). Use of quadratic non-residues permits unequivocal predictions to be made about the outcome of the factoring algorithm., Comment: 10 pages, 3 figures

In the years 1917-1919 Tullio Levi-Civita published a number of papers presenting new solutions to Einstein's equations. This work, while partially translated, remains largely inaccessible to English speaking authors. In this paper we review these solutions, and present them in a modern, readable manner. We will also compute both Cartan-Karlhede and Carminati-Mclenaghan invariants such that these solutions are invariantly characterized by two distinct methods. These methods will allow for these solutions to be totally, and invariantly characterized. Because of the variety of solutions considered here, this paper will also be a useful reference for those seeking to learn to apply the Cartan-Karlhede algorithm in practice.

Proverbs are an essential component of language and culture, and though much attention has been paid to their history and currency, there has been comparatively little quantitative work on changes in the frequency with which they are used over time. With wider availability of large corpora reflecting many diverse genres of documents, it is now possible to take a broad and dynamic view of the importance of the proverb. Here, we measure temporal changes in the relevance of proverbs within three corpora, differing in kind, scale, and time frame: Millions of books over centuries; hundreds of millions of news articles over twenty years; and billions of tweets over a decade. We find that proverbs present heavy-tailed frequency-of-usage rank distributions in each venue; exhibit trends reflecting the cultural dynamics of the eras covered; and have evolved into contemporary forms on social media., Comment: Main paper: 16 pages, 9 figures, 1 table; Supplementary: 5 pages, 4 tables, 4 figures

A short review of scalar curvature invariants in gravity theories is presented. We introduce how these invariants are constructed and discuss the minimal number of invariants required for a given spacetime. We then discuss applications of these invariants and focus on three topics that are of particular interest in modern gravity theories., Comment: Essay written for the Gravity Research Foundation 2021 Awards for Essays on Gravitation

A process for using curvature invariants is applied to evaluate the accelerating Natario warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Nat\'ario spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants the Ricci scalar, r_1, r_2, and w_2. The invariant plots demonstrate how each curvature invariant evolves over the parameters of time, acceleration, skin depth and radius of the warp bubble. They show that the Ricci scalar has the greatest impact of the invariants on the surrounding spacetime. They also reveal key features of the Natario warp bubble such as a flat harbor in the center of it, a dynamic wake, and the internal structures of the warp bubble., Comment: 22 pages, 12 figures

The ability to produce nanowires through vapor- and solution-based processes has propelled nanowire material systems toward a wide range of technological applications. Conventional, vapor-based nanowire syntheses have enabled precise control over nanowire composition and phase. However, vapor-based nanowire growth employs batch processes with specialized pressure management systems designed to operate at high temperatures, limiting throughput. More recently developed solution-based nanowire growth processes have improved scalability but can require even more extensive pressure and temperature management systems. Here, we demonstrate a continuous-flow, solution-based nanowire growth process that utilizes the large Young-Laplace interfacial surface pressures and collective heating effects of colloidal metal nanocrystals under irradiation to drive semiconductor nanowire growth photothermally without the need for high-pressure or high-temperature equipment. In this process, a laser irradiates a solution containing metal nanocrystals and semiconductor precursors. Upon light absorption, the metal nanocrystals heat rapidly, inducing semiconductor precursor decomposition and nanowire growth. This process is performed on a benchtop in simple glassware under standard conditions. To demonstrate the generality of this technique, we synthesized three distinct semiconductor nanowire material systems: bismuth-seeded germanium nanowires, bismuth-seeded cadmium selenide nanowires, and indium-seeded germanium nanowires. The simplicity and versatility of this process opens the door to a range of experiments and technologies including in-line combinatorial identification of optimized reaction parameters, in situ spectroscopic measurements to study solution-based nanowire growth, and the potential production of nanowires with complex compositions or rationally incorporated dopants., Comment: 46 pages, 14 figures, submitted to Proceedings of the National Academy of Sciences of the United States of America

Photothermal heating represents a major constraint that limits the performance of many nanoscale optoelectronic and optomechanical devices including nanolasers, quantum optomechanical resonators, and integrated photonic circuits. Although radiation-pressure damping has been reported to cool an individual vibrational mode of an optomechanical resonator to its quantum ground state, to date the internal material temperature within an optomechanical resonator has not been reported to cool via laser excitation. Here we demonstrate the direct laser refrigeration of a semiconductor optomechanical resonator >20K below room temperature based on the emission of upconverted, anti-Stokes photoluminescence of trivalent ytterbium ions doped within a yttrium-lithium-fluoride (YLF) host crystal. Optically-refrigerating the lattice of a dielectric resonator has the potential to impact several fields including scanning probe microscopy, the sensing of weak forces, the measurement of atomic masses, and the development of radiation-balanced solid-state lasers. In addition, optically refrigerated resonators may be used in the future as a promising starting point to perform motional cooling for exploration of quantum effects at mesoscopic length scales,temperature control within integrated photonic devices, and solid-state laser refrigeration of quantum materials

On the basis of experiments conducted in the 1970s and earlier, it is believed that, in a compound nucleus (CN), fluctuations in transition strengths are drawn from a Porter-Thomas distribution (PTD), a $\chi^2$ distribution of one degree of freedom. However, work done post-1990 at the Los Alamos Neutron Science Center (LANSCE) and Oak Ridge Electron Linear Accelerator (ORELA) facilities has yielded instances of neutron resonance data sets of superior quality that are inconsistent with the PTD. In view of the importance of the status of the PTD to the foundations of statistical reaction theory, the question arises whether other data acquired at these facilities can be mined for evidence of deviations from the PTD? To date, the focus has been on data taken in the regime of isolated resonances. In this letter, arguments are put forward in support of the analysis of measurements of the total cross section in the regime where resonances are weakly overlapping., Comment: 4 pages, 1 figure

A process for using curvature invariants is applied as a new means to evaluate the traversability of Lorentzian wormholes and to display the wormhole spacetime manifold. This approach was formulated by Henry, Overduin and Wilcomb for Black Holes in Reference [1]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates. The four independent Carminati and McLenaghan (CM) invariants are calculated and the non-zero curvature invariant functions are plotted. Three example traversable wormhole metrics (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric are investigated and are demonstrated to be traversable., Comment: 16 pages, 9 figures

We examine the autocorrelation function of the $^{235}$U(n,f) reaction with a view to quantify the presence of intermediate structure in the cross section. Fluctuations due to compound nucleus resonances on the eV energy scale are clearly visible up to $\sim100$ keV neutron energies. Structure on the one-keV energy scale is not present as a systematic feature of the correlation function, although it is present in the data covering the region around 20 keV., Comment: 25 pages and 12 figures. To be submitted to Physical Review C

Nanodiamonds have emerged as promising materials for quantum computing, biolabeling, and sensing due to their ability to host color centers with remarkable photostability and long spin-coherence times at room temperature. Recently, a bottom-up, high-pressure, high-temperature (HPHT) approach was demonstrated for growing nanodiamonds with color centers from amorphous carbon precursors in a laser-heated diamond anvil cell (LH-DAC) that was supported by a near-hydrostatic noble gas pressure medium. However, a detailed understanding of the photothermal heating and its effect on diamond growth, including the phase conversion conditions and the temperature-dependence of color center formation, has not been reported. In this work, we measure blackbody radiation during LH-DAC synthesis of nanodiamond from carbon aerogel to examine these temperature-dependent effects. Blackbody temperature measurements suggest that nanodiamond growth can occur at 16.3 GPa and 1800 K. We use Mie theory and analytical heat transport to develop a predictive photothermal heating model. This model demonstrates that melting the noble gas pressure medium during laser heating decreases the local thermal conductivity to drive a high spatial resolution of phase conversion to diamond. Finally, we observe a temperature-dependent formation of nitrogen vacancy centers and interpret this phenomenon in the context of HPHT carbon vacancy diffusion using CB{\Omega} theory., Comment: 5 Figures, 1 Table, Submitted

Prompted by plans to conduct a new neutron oscillation experiment at the European Spallation Source (ESS), we consider issues associated with the magnetic field that must be present, some of which are potentially exacerbated by the significantly larger length $l$ contemplated for the neutron propagation region. To this end, we introduce a stochastic model of the residual magnetic field within the propagation region which draws on features of magnetic profiles measured during the last free neutron oscillation experiment [conducted at the Institut Laue-Langevin (ILL) in the 1990's]. We average over both fluctuations in the magnetic field sampled by neutrons, and representative spectra of neutron speeds. We find that deviations from the quasi-free result for the antineutron probability do not depend quadratically on $l$ (as a naive perturbative estimate would suggest) but increase only linearly with $l$. As regards the large spikes in the magnetic field which can be expected at, for example, joints in the magnetic shielding of the propagation region (despite compensating currents and magnetic idealization of the shield), we demonstrate that their effect scales as $l/D^{3/2}$, where $D$ is the diameter of the cylindrical magnetic shielding. Our arguments suggest that, provided the dimensions of the propagation region are such that the ratio $l/D^{3/2}$ does not exceed the value pertinent to the ILL experiment, and these spikes occur close to either end of the propagation region, they can be neglected. We also establish that any large magnetic field encountered after the propagation region is exited will not diminish the probability for antineutron detection. For the range of values of $l$ of most interest to the ESS experiment, it should suffice to improve on the level of magnetic suppression achieved at the ILL by a factor of two., Comment: 18 pages, 1 figure

Most object detection methods operate by applying a binary classifier to sub-windows of an image, followed by a non-maximum suppression step where detections on overlapping sub-windows are removed. Since the number of possible sub-windows in even moderately sized image datasets is extremely large, the classifier is typically learned from only a subset of the windows. This avoids the computational difficulty of dealing with the entire set of sub-windows, however, as we will show in this paper, it leads to sub-optimal detector performance. In particular, the main contribution of this paper is the introduction of a new method, Max-Margin Object Detection (MMOD), for learning to detect objects in images. This method does not perform any sub-sampling, but instead optimizes over all sub-windows. MMOD can be used to improve any object detection method which is linear in the learned parameters, such as HOG or bag-of-visual-word models. Using this approach we show substantial performance gains on three publicly available datasets. Strikingly, we show that a single rigid HOG filter can outperform a state-of-the-art deformable part model on the Face Detection Data Set and Benchmark when the HOG filter is learned via MMOD.

This paper describes the system architecture of a newly constructed radio telescope - the Boolardy Engineering Test Array, which is a prototype of the Australian Square Kilometre Array Pathfinder telescope. Phased array feed technology is used to form multiple simultaneous beams per antenna, providing astronomers with unprecedented survey speed. The test array described here is a 6-antenna interferometer, fitted with prototype signal processing hardware capable of forming at least 9 dual-polarisation beams simultaneously, allowing several square degrees to be imaged in a single pointed observation. The main purpose of the test array is to develop beamforming and wide-field calibration methods for use with the full telescope, but it will also be capable of limited early science demonstrations., Comment: 17 pages, 12 figures, accepted for publication in PASA