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

Sterile Neutrino Hot, Warm, and Cold Dark Matter

We calculate the incoherent resonant and non-resonant scattering production of sterile neutrinos in the early universe. We find ranges of sterile neutrino masses, vacuum mixing angles, and initial lepton numbers which allow these species to constitute viable hot, warm, and cold dark matter (HDM, WDM, CDM) candidates which meet observational constraints. The constraints considered here include energy loss in core collapse supernovae, energy density limits at big bang nucleosynthesis, and those stemming from sterile neutrino decay: limits from observed cosmic microwave background anisotropies, diffuse extragalactic background radiation, and Li-6/D overproduction. Our calculations explicitly include matter effects, both effective mixing angle suppression and enhancement (MSW resonance), as well as quantum damping. We for the first time properly include all finite temperature effects, dilution resulting from the annihilation or disappearance of relativistic degrees of freedom, and the scattering-rate-enhancing effects of particle-antiparticle pairs (muons, tauons, quarks) at high temperature in the early universe.Comment: 24 pages, including 8 figures. v3: to match version in PRD, added references and numerous minor changes. High resolution color figures available at http://superbeast.ucsd.edu/~kev/nucd

Rheo-processing of an alloy specifically designed for semi-solid metal processing on the Al-Mg-Si system

Semi-solid metal (SSM) processing is a promising technology for forming alloys and composites to near-net shaped products. Alloys currently used for SSM processing are mainly conventional aluminium cast alloys. This is an obstacle to the realisation of full potential of SSM processing, since these alloys were originally designed for liquid state processing and not for semi-solid state processing. Therefore, there is a significant need for designing new alloys specifically for semi-solid state processing to fulfil its potential. In this study, thermodynamic calculations have been carried out to design alloys based on the Al-Mg-Si system for SSM processing via the ‘Rheo-route’. The suitability of a selected alloy composition has been assessed in terms of the criteria considered by the thermodynamic design process, mechanical properties and heat treatability. The newly designed alloy showed good processability with rheo-processing in terms of good control of solid fraction during processing and a reasonably large processing window. The mechanical property variation was very small and the alloy showed good potential for age hardening by T5 temper heat treatment after rheo-processing

An experimental and theoretical study of the flow phenomena within a vortex sink rate sensor

Tests were conducted to obtain a description of the flow field within a vortex sink rate sensor and to observe the influence of viscous effects on its performance. The characteristics of the sensor are described. The method for conducting the test is reported. It was determined that for a specific mass flow rate and the geometry of the vortex chamber, the flow in the vortex chamber was only affected, locally, by the size of the sink tube diameter. Within the sink tube, all three velocity components were found to be higher for the small sink tube diameters. As the speed of rotation of the sensor was increased, the tangential velocities within the vortex chamber, as well as in the sink tube, increased in proportion to the speed of rotation

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

A Deep Learning Approach to Structured Signal Recovery

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach

Atmospheric modelling for NOMAD-UVIS on board the ExoMars Trace Gas Orbiter mission

The Ultraviolet and Visible Spectrometer (UVIS) instrument development process requires the construction of an atmospheric model to provide synthetic UV transmission spectra. We discuss the requirements of the model to enable observational limits to be found, and the potential for certain atmospheric parameters to be further constrained

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