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

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

Investigating microstructural variation in the human hippocampus using non-negative matrix factorization

In this work we use non-negative matrix factorization to identify patterns of microstructural variance in the human hippocampus. We utilize high-resolution structural and diffusion magnetic resonance imaging data from the Human Connectome Project to query hippocampus microstructure on a multivariate, voxelwise basis. Application of non-negative matrix factorization identifies spatial components (clusters of voxels sharing similar covariance patterns), as well as subject weightings (individual variance across hippocampus microstructure). By assessing the stability of spatial components as well as the accuracy of factorization, we identified 4 distinct microstructural components. Furthermore, we quantified the benefit of using multiple microstructural metrics by demonstrating that using three microstructural metrics (T1-weighted/T2-weighted signal, mean diffusivity and fractional anisotropy) produced more stable spatial components than when assessing metrics individually. Finally, we related individual subject weightings to demographic and behavioural measures using a partial least squares analysis. Through this approach we identified interpretable relationships between hippocampus microstructure and demographic and behavioural measures. Taken together, our work suggests non-negative matrix factorization as a spatially specific analytical approach for neuroimaging studies and advocates for the use of multiple metrics for data-driven component analyses

Editorial: Why Free Speech?

Many of us struggle to make sense of what is without doubt a deepening global socio-economic and political crisis, and at the heart of this crisis lies an unprecedented and multi-directional assault on freedom of speech. But what is free speech? How should it be exercised and to what ends? These are more difficult questions to navigate in contexts of growing divisions in society, the crises of state governabilities, people’s governmentalities and disparities in power and wealth. Debates about freedom of speech are not new; however, the form they take now seems particularly vindictive and violent. Across the world, we are witness to disturbing moves to curtail free speech in liberal democracies and totalitarian states alike and among left wing as well as right wing movements. As recent events show, free speech is the first casualty of all forms of authoritarianism including religious fundamentalism. And from this flow a range of other crackdowns on civil society and serious human rights violations that cannot be challenged. This is why the debate on freedom of speech has become increasingly urgent

Flux Tube Model Signals for Baryon Correlations in Heavy Ion Collisions

The flux tube model offers a pictorial description of what happens during the deconfinement phase transition in QCD. The 3-point vertices of a flux tube network lead to formation of baryons upon hadronisation. Therefore, correlations in the baryon number distribution at the last scattering surface are related to the preceding pattern of the flux tube vertices, and provide a signature of the nearby deconfinement phase transition. I discuss the nature of the expected signal, which should be observable in heavy ion collisions at RHIC and LHC.Comment: LaTeX, 9 pages, 5 figures, (v2) Several arguments expanded for clarity, (v3) Minor typesetting changes, published versio

Techniques for the Synthesis of Reversible Toffoli Networks

This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and technology oriented cost metrics are used. Our synthesis techniques are independent of the cost metrics. Two new iterative synthesis procedure employing Reed-Muller spectra are introduced and shown to complement earlier synthesis approaches. The template simplification suggested in earlier work is enhanced through introduction of a faster and more efficient template application algorithm, updated (shorter) classification of the templates, and presentation of the new templates of sizes 7 and 9. A novel ``resynthesis'' approach is introduced wherein a sequence of gates is chosen from a network, and the reversible specification it realizes is resynthesized as an independent problem in hopes of reducing the network cost. Empirical results are presented to show that the methods are effective both in terms of the realization of all 3x3 reversible functions and larger reversible benchmark specifications.Comment: 20 pages, 5 figure

Orientation in upper gastrointestinal endoscopy—the only way is up

BACKGROUND Oesophagogastroduodenoscopy is the gold standard investigation for the upper gastrointestinal (UGI) tract. Orientation during endoscopy is challenging and United Kingdom training focusses on technical competence and procedural safety. The reported location of UGI pathologies is crucial to post-endoscopic planning. AIM To evaluate endoscopists’ ability to spatially orientate themselves within the UGI tract. METHODS A cross sectional descriptive study elicited, using an anonymised survey, the ability of endoscopists to orientate themselves within the UGI tract. The primary outcome was percentage of correct answers from all surveyed; secondary outcomes were percentage of correct answers from experienced vs novice endoscopists. Pearson’s χ2 test was applied to compare groups. RESULTS Of 188 respondents, 86 were experienced endoscopists having completed over 1000 endoscopies. 44.4% of respondents correctly identified the anterior stomach and 47.3% correctly identified the posterior of the second part of the duodenum (D2). Experienced endoscopists were significantly more likely than novice to identify the anterior stomach correctly [61.6% vs 31.3%, X2 (1, n = 188) = 11.10, P = 0.001]. There was no significant difference between the two groups in identifying the posterior of D2. CONCLUSION The majority of endoscopists surveyed were unable to identify key landmarks within the UGI tract. Endoscopic orientation appears to improve with experience yet there are some areas still not well recognised. This has potential considerable impact on post-endoscopic management of patients with posterior duodenal ulcers being more likely to perforate and associated with a higher rebleeding risk. We suggest the development of a consensus statement on endoscopic description

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