Fast and adaptive fractal tree-based path planning for programmable bevel tip steerable needles

© 2016 IEEE. Steerable needles are a promising technology for minimally invasive surgery, as they can provide access to difficult to reach locations while avoiding delicate anatomical regions. However, due to the unpredictable tissue deformation associated with needle insertion and the complexity of many surgical scenarios, a real-time path planning algorithm with high update frequency would be advantageous. Real-time path planning for nonholonomic systems is commonly used in a broad variety of fields, ranging from aerospace to submarine navigation. In this letter, we propose to take advantage of the architecture of graphics processing units (GPUs) to apply fractal theory and thus parallelize real-time path planning computation. This novel approach, termed adaptive fractal trees (AFT), allows for the creation of a database of paths covering the entire domain, which are dense, invariant, procedurally produced, adaptable in size, and present a recursive structure. The generated cache of paths can in turn be analyzed in parallel to determine the most suitable path in a fraction of a second. The ability to cope with nonholonomic constraints, as well as constraints in the space of states of any complexity or number, is intrinsic to the AFT approach, rendering it highly versatile. Three-dimensional (3-D) simulations applied to needle steering in neurosurgery show that our approach can successfully compute paths in real-time, enabling complex brain navigation

Multiple zero modes of the Dirac operator in three dimensions

One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the construction of multiple zero modes has been sucessfully carried out only very recently. Here we generalise these results by discussing a much wider class of Dirac operators together with their zero modes. Further we show that those Dirac operators that do admit zero modes may be related to Hopf maps, where the Hopf index is related to the number of zero modes in a simple way.Comment: Latex file, 20 pages, no figure

An inquiry-based learning approach to teaching information retrieval

The study of information retrieval (IR) has increased in interest and importance with the explosive growth of online information in recent years. Learning about IR within formal courses of study enables users of search engines to use them more knowledgeably and effectively, while providing the starting point for the explorations of new researchers into novel search technologies. Although IR can be taught in a traditional manner of formal classroom instruction with students being led through the details of the subject and expected to reproduce this in assessment, the nature of IR as a topic makes it an ideal subject for inquiry-based learning approaches to teaching. In an inquiry-based learning approach students are introduced to the principles of a subject and then encouraged to develop their understanding by solving structured or open problems. Working through solutions in subsequent class discussions enables students to appreciate the availability of alternative solutions as proposed by their classmates. Following this approach students not only learn the details of IR techniques, but significantly, naturally learn to apply them in solution of problems. In doing this they not only gain an appreciation of alternative solutions to a problem, but also how to assess their relative strengths and weaknesses. Developing confidence and skills in problem solving enables student assessment to be structured around solution of problems. Thus students can be assessed on the basis of their understanding and ability to apply techniques, rather simply their skill at reciting facts. This has the additional benefit of encouraging general problem solving skills which can be of benefit in other subjects. This approach to teaching IR was successfully implemented in an undergraduate module where students were assessed in a written examination exploring their knowledge and understanding of the principles of IR and their ability to apply them to solving problems, and a written assignment based on developing an individual research proposal

Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes

We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, $S_3$, starting from leading-order perturbation theory. When generalized to higher-order ($p>3$) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the non-linear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum.Comment: 20 pages, 6 figures. Final version accepted by ApJ. Includes new paragraphs on factorizable hierarchical models and agreement of HEPT with the excursion set model for white-noise Gaussian fluctuation

Probing Primordial Non-Gaussianity with Large-Scale Structure

We consider primordial non-Gaussianity due to quadratic corrections in the gravitational potential parametrized by a non-linear coupling parameter fnl. We study constraints on fnl from measurements of the galaxy bispectrum in redshift surveys. Using estimates for idealized survey geometries of the 2dF and SDSS surveys and realistic ones from SDSS mock catalogs, we show that it is possible to probe |fnl|~100, after marginalization over bias parameters. We apply our methods to the galaxy bispectrum measured from the PSCz survey, and obtain a 2sigma-constraint |fnl|< 1800. We estimate that an all sky redshift survey up to z~1 can probe |fnl|~1. We also consider the use of cluster abundance to constrain fnl and find that in order to be sensitive to |fnl|~100, cluster masses need to be determined with an accuracy of a few percent, assuming perfect knowledge of the mass function and cosmological parameters.Comment: 15 pages, 7 figure

A rumble in the dark: signatures of self-interacting dark matter in supermassive black hole dynamics and galaxy density profiles

We explore for the first time the effect of self-interacting dark matter (SIDM) on the dark matter (DM) and baryonic distribution in massive galaxies formed in hydrodynamical cosmological simulations, including explicit baryonic physics treatment. A novel implementation of supermassive black hole (SMBH) formation and evolution is used, as in Tremmel et al., allowing us to explicitly follow the SMBH dynamics at the centre of galaxies. A high SIDM constant cross-section is chosen, σ = 10 cm2gr−1, to amplify differences from CDM models. Milky Way-like galaxies form a shallower DM density profile in SIDM than they do in cold dark matter (CDM), with differences already at 20 kpc scales. This demonstrates that even for the most massive spirals, the effect of SIDM dominates over the adiabatic contraction due to baryons. Strikingly, the dynamics of SMBHs differs in the SIDM and reference CDM case. SMBHs in massive spirals have sunk to the centre of their host galaxy in both the SIDM and CDM run, while in less massive galaxies about 80 per cent of the SMBH population is off-centred in the SIDM case, as opposed to the CDM case in which ∼ 90 per cent of SMBHs have reached their host’s centre. SMBHs are found as far as ∼9 kpc away from the centre of their host SIDM galaxy. This difference is due to the increased dynamical friction time-scale caused by the lower DM density in SIDM galaxies compared to CDM, resulting in core stalling. This pilot work highlights the importance of simulating in a full hydrodynamical context different DM models combined to the SMBH physics to study their influence on galaxy formation

Skewness as a probe of non-Gaussian initial conditions

We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate analytically the ratio between the skewness due to non-linear clustering and the part due to the intrinsic non-Gaussianity of the models. We finally extend our estimates to higher moments.Comment: 5 pages, 2 ps-figs., accepted for publication in PRD, rapid com

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays

We demonstrate quantum walks of correlated photons in a 2D network of directly laser written waveguides coupled in a 'swiss cross' arrangement. The correlated detection events show high-visibility quantum interference and unique composite behaviour: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal non-classical behaviour in a non-planar structure.Comment: 5 pages, 5 figure

The Power Spectrum, Bias Evolution, and the Spatial Three-Point Correlation Function

We calculate perturbatively the normalized spatial skewness, $S_3$, and full three-point correlation function (3PCF), $\zeta$, induced by gravitational instability of Gaussian primordial fluctuations for a biased tracer-mass distribution in flat and open cold-dark-matter (CDM) models. We take into account the dependence on the shape and evolution of the CDM power spectrum, and allow the bias to be nonlinear and/or evolving in time, using an extension of Fry's (1996) bias-evolution model. We derive a scale-dependent, leading-order correction to the standard perturbative expression for $S_3$ in the case of nonlinear biasing, as defined for the unsmoothed galaxy and dark-matter fields, and find that this correction becomes large when probing positive effective power-spectrum indices. This term implies that the inferred nonlinear-bias parameter, as usually defined in terms of the smoothed density fields, might depend on the chosen smoothing scale. In general, we find that the dependence of $S_3$ on the biasing scheme can substantially outweigh that on the adopted cosmology. We demonstrate that the normalized 3PCF, $Q$, is an ill-behaved quantity, and instead investigate $Q_V$, the variance-normalized 3PCF. The configuration dependence of $Q_V$ shows similarly strong sensitivities to the bias scheme as $S_3$, but also exhibits significant dependence on the form of the CDM power spectrum. Though the degeneracy of $S_3$ with respect to the cosmological parameters and constant linear- and nonlinear-bias parameters can be broken by the full configuration dependence of $Q_V$, neither statistic can distinguish well between evolving and non-evolving bias scenarios. We show that this can be resolved, in principle, by considering the redshift dependence of $\zeta$.Comment: 41 pages, including 12 Figures. To appear in The Astrophysical Journal, Vol. 521, #