Search on a Hypercubic Lattice using a Quantum Random Walk: I. d>2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, i.e. finding a marked vertex on a $d$-dimensional hypercubic lattice. The restriction on movement hardly matters for $d>2$, and scaling behaviour close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimise the proportionality constants of the scaling behaviour, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean field theory or the $d\to\infty$ limit). In particular, the scaling behaviour for $d=3$ is only about 25% higher than the optimal $d\to\infty$ value.Comment: 11 pages, Revtex (v2) Introduction and references expanded. Published versio

String-Dust Distributions with the Kerr-NUT symmetry

We attempt to solve the Einstein equations for string dust and null flowing radiation for the general axially symmetric metric, which we believe is being done for the first time. We obtain the string-dust and radiating generalizations of the Kerr and the NUT solutions. There also occurs an interesting case of radiating string-dust which arises from string-dust generalization of Vaidya's solution of a radiating star.Comment: 15 pages, TeX version. tex error correcte

Search on a Hypercubic Lattice through a Quantum Random Walk: II. d=2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretised according to the staggered lattice fermion formalism. $d=2$ is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behaviour. As a result, the construction used in our accompanying article \cite{dgt2search} provides an $O(\sqrt{N}\log N)$ algorithm, which is not optimal. The scaling behaviour can be improved to $O(\sqrt{N\log N})$ by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi \cite{tulsi}. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimise the proportionality constants of the scaling behaviour of the algorithm by numerically tuning the parameters.Comment: Revtex4, 5 pages (v2) Introduction and references expanded. Published versio

Synthesis and Characterization of N-Substituted Tetrahydroiso-quinoline Derivatives via a Pictet-Spengler Condensation

Synthesis of N-substituted 1,2,3,4 –tetrahydroisoquinoline derivatives and bis-isoquinoline has been carried out via a Pictet-Spengler condensation. Tetrahydroisoquinolines were obtained from 2-(3',4'-dimethoxyphenyl) ethylamine in four steps. The entire synthesized compounds were characterized by IR, 1H NMR and mass spectral data

The prevalence of occult hepatitis B virus (hbv) infection in a large multi-ethnic haemodialysis cohort.

Haemodialysis patients are at increased risk of exposure to blood borne viruses. To reduce transmission in the UK, all haemodialysis patients are regularly screened, and if susceptible to Hepatitis B virus (HBV) infection, vaccinated

Symptomatic adrenal insufficiency during inhaled corticosteroid treatment

Symptomatic adrenal insufficiency, presenting as hypoglycaemia or poor weight gain, may occur on withdrawal of corticosteroid treatment but has not previously been reported during inhaled corticosteroid treatment. This case series illustrates the occurence of clinically significant adrenal insufficiency in asthmatic children while patients were on inhaled corticosteroid treatment and the unexpected modes of presentation. General practitioners and paediatricians need to be aware that this unusual but acute serious complication may occur in patients treated

Numerical Investigation of Second Mode Attenuation over Carbon/Carbon Surfaces on a Sharp Slender Cone

We have carried out axisymmetric numerical simulations of a spatially developing hypersonic boundary layer over a sharp 7$^{\circ{}}$-half-angle cone at $M_\infty=7.5$ inspired by the experimental investigations by Wagner (2015). Simulations are first performed with impermeable (or solid) walls with a one-time broadband pulse excitation applied upstream to determine the most convectively-amplified frequencies resulting in the range 260kHz -- 400kHz, consistent with experimental observations of second-mode instability waves. Subsequently, we introduce harmonic disturbances via continuous periodic suction and blowing at 270kHz and 350kHz. For each of these forcing frequencies complex impedance boundary conditions (IBC), modeling the acoustic response of two different carbon/carbon (C/C) ultrasonically absorptive porous surfaces, are applied at the wall. The IBCs are derived as an output of a pore-scale aeroacoustic analysis -- the inverse Helmholtz Solver (iHS) -- which is able to return the broadband real and imaginary components of the surface-averaged impedance. The introduction of the IBCs in all cases leads to a significant attenuation of the harmonically-forced second-mode wave. In particular, we observe a higher attenuation rate of the introduced waves with frequency of 350kHz in comparison with 270kHz, and, along with the iHS impedance results, we establish that the C/C surfaces absorb acoustic energy more effectively at higher frequencies.Comment: AIAA-SciTech 201

Equivalent Mid-Term Results of Open vs Endoscopic Gluteal Tendon Tear Repair Using Suture Anchors in Forty-Five Patients.

BackgroundLittle is known about the relative efficacy of open (OGR) vs endoscopic (EGR) gluteal tendon repair of gluteal tendon tears in minimizing pain and restoring function. Our aim is to compare these 2 surgical techniques and quantify their impact on clinical outcomes.MethodsAll patients undergoing gluteal tendon tear repair at our institution between 2015 and 2018 were retrospectively reviewed. Pain scores, limp, hip abduction strength, and the use of analgesics were recorded preoperatively and at last follow-up. The Hip disability and Osteoarthritis Outcome Score Junior and Harris Hip Score Section1 were obtained at last follow-up. Fatty degeneration was quantified using the Goutallier-Fuchs Classification (GFC). Statistical analysis was conducted using one-way analysis of variance and t-tests.ResultsForty-five patients (mean age 66, 87% females) met inclusion criteria. Average follow-up was 20.3 months. None of the 10 patients (22%) undergoing EGR had prior surgery. Of 35 patients (78%) undergoing OGR, 12 (27%) had prior hip replacement (75% via lateral approach). The OGRs had more patients with GFC ≥2 (50% vs 11%, P = .02) and used more anchors (P = .03). Both groups showed statistical improvement (P ≤ .01) for all outcomes measured. GFC >2 was independently associated with a worst limp and Harris Hip Score Section 1 score (P = .05). EGR had a statistically higher opioid use reduction (P < .05) than OGR. Other comparisons between EGR and OGR did not reach statistical significance.ConclusionIn this series, open vs endoscopic operative approach did not impact clinical outcomes. More complex tears were treated open and with more anchors. Fatty degeneration adversely impacted outcomes. Although further evaluation of the efficacy of EGR in complex tears is indicated, both approaches can be used successfully