Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments

Neurobiological successor features for spatial navigation

The hippocampus has long been observed to encode a representation of an animal's position in space. Recent evidence suggests that the nature of this representation is somewhat predictive and can be modeled by learning a successor representation (SR) between distinct positions in an environment. However, this discretization of space is subjective making it difficult to formulate predictions about how some environmental manipulations should impact the hippocampal representation. Here, we present a model of place and grid cell firing as a consequence of learning a SR from a basis set of known neurobiological features—boundary vector cells (BVCs). The model describes place cell firing as the successor features of the SR, with grid cells forming a low‐dimensional representation of these successor features. We show that the place and grid cells generated using the BVC‐SR model provide a good account of biological data for a variety of environmental manipulations, including dimensional stretches, barrier insertions, and the influence of environmental geometry on the hippocampal representation of space

CoreTSAR: Task Scheduling for Accelerator-aware Runtimes

Heterogeneous supercomputers that incorporate computational accelerators such as GPUs are increasingly popular due to their high peak performance, energy efficiency and comparatively low cost. Unfortunately, the programming models and frameworks designed to extract performance from all computational units still lack the flexibility of their CPU-only counterparts. Accelerated OpenMP improves this situation by supporting natural migration of OpenMP code from CPUs to a GPU. However, these implementations currently lose one of OpenMP’s best features, its flexibility: typical OpenMP applications can run on any number of CPUs. GPU implementations do not transparently employ multiple GPUs on a node or a mix of GPUs and CPUs. To address these shortcomings, we present CoreTSAR, our runtime library for dynamically scheduling tasks across heterogeneous resources, and propose straightforward extensions that incorporate this functionality into Accelerated OpenMP. We show that our approach can provide nearly linear speedup to four GPUs over only using CPUs or one GPU while increasing the overall flexibility of Accelerated OpenMP

The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales

(Abridged) We present a comprehensive analysis of the relationship between star formation rate surface density (SFR SD) and gas surface density (gas SD) at sub-kpc resolution in a sample of 18 nearby galaxies. We use high resolution HI data from THINGS, CO data from HERACLES and BIMA SONG, 24 micron data from the Spitzer Space Telescope, and UV data from GALEX. We target 7 spiral galaxies and 11 late-type/dwarf galaxies and investigate how the star formation law differs between the H2-dominated centers of spiral galaxies, their HI-dominated outskirts and the HI-rich late-type/dwarf galaxies. We find that a Schmidt-type power law with index N=1.0+-0.2 relates the SFR SD and the H2 SD across our sample of spiral galaxies, i.e., that H2 forms stars at a constant efficiency in spirals. The average molecular gas depletion time is ~2*10^9 yrs. We interpret the linear relation and constant depletion time as evidence that stars are forming in GMCs with approximately uniform properties and that the H2 SD may be more a measure of the filling fraction of giant molecular clouds than changing conditions in the molecular gas. The relationship between total gas SD and SFR SD varies dramatically among and within spiral galaxies. Most galaxies show little or no correlation between the HI SD and the SFR SD. As a result, the star formation efficiency (SFE = SFR SD / gas SD) varies strongly across our sample and within individual galaxies. We show that in spirals the SFE is a clear function of radius, while the dwarf galaxies in our sample display SFEs similar to those found in the outer optical disks of the spirals. Another general feature of our sample is a sharp saturation of the HI SD at ~9 M_sol/pc^2 in both the spiral and dwarf galaxies.Comment: Accepted for publication in the AJ special THINGS issue. For a high-resolution version visit: http://www.mpia.de/THINGS/Publications.htm

Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

In this work, we study the Brinkman-Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next we discuss the continuity of the solution with respect to Brinkman's and Forchheimer's coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable

The unusual hydrocarbon emission from the early carbon star HD 100764: The connection between aromatics and aliphatics

We have used the Infrared Spectrograph (IRS) on the Spitzer Space Telescope to obtain spectra of HD 100764, an apparently single carbon star with a circumstellar disk. The spectrum shows emission features from polycyclic aromatic hydrocarbons (PAHs) that are shifted to longer wavelengths than normally seen, as characteristic of ``class C'' systems in the classification scheme of Peeters et al. All seven of the known class C PAH sources are illuminated by radiation fields that are cooler than those which typically excite PAH emission features. The observed wavelength shifts are consistent with hydrocarbon mixtures containing both aromatic and aliphatic bonds. We propose that the class C PAH spectra are distinctive because the carbonaceous material has not been subjected to a strong ultraviolet radiation field, allowing relatively fragile aliphatic materials to survive.Comment: 11 pages (in emulateapj), 5 tables, 7 figures. Accepted for publication in Ap

Money, Finance and Demography: The Consequences of Ageing

A significant ageing trend can be observed in Europe and in other parts of the world. Fertility is decreasing and life expectancy increasing. The impact of migration is growing. The book deals with the implications for financial markets of these demographic trends. Leading economists and financial experts from Europe and the United States evaluate the challenges to public pension systems and the private pension industry. Based on long-term projections of productivity and employment they look at potential growth in GDP per capita and implications for savings and wealth. Pension fund portfolio management is discussed together with the ability of capital markets to serve retirement-financing purposes. Fiscal as well as financial sustainability are analysed in depth. The roles of global imbalances and international capital movements are included. Most chapters also discuss policy implications - in particular with regard to how pension saving incentives and rules and incentives for retirement should be in order to ensure fiscal and financial sustainability. All contributions in the book are based on presentations at the 26th SUERF Colloquium on "Money, Finance and Demography - the Consequences of Ageing" held on 12-14 October, 2006 in Lisbon sponsored by Banco de Portugal and Millennium bcp and in cooperation with the Universidade Nova de Lisboa.

GALEX UV Color Relations for Nearby Early-Type Galaxies

We use GALEX/optical photometry to construct color-color relationships for early-type galaxies sorted by morphological type. We have matched objects in the GALEX GR1 public release and the first IR1.1 internal release, with the RC3 early-type galaxies having a morphological type -5.5<T<-1.5 with mean error in T<1.5, and mean error on (B-V)T<0.05. After visual inspection of each match, we are left with 130 galaxies with a reliable GALEX pipeline photometry in the far-UV and near-UV bands. This sample is divided into Ellipticals (-5.5<T<-3.5) and Lenticulars (-3.5<T<-1.5). After correction for the Galactic extinction, the color-color diagrams FUV-NUV vs. (B-V)_{Tc} are plotted for the two subsamples. We find a tight anti-correlation between the FUV-NUV and (B-V)_{Tc} colors for Ellipticals, the UV color getting bluer when the (B-V)_{Tc} get redder. This relationship very likely is an extension of the color-metallicity relationship into the GALEX NUV band. We suspect that the main source of the correlation is metal line blanketing in the NUV band. The FUV-NUV vs B-V correlation has larger scatter for lenticular galaxies; we speculate this reflects the presence of low level star formation. If the latter objects (i.e. those that are blue both in FUV-NUV and B-V) are interpreted as harboring recent star formation activity, this would be the case for a few percent (~4%) of Ellipticals and ~15% of Lenticulars; this would make about 10% of early-type galaxies with residual star formation in our full sample of 130 early-type galaxies. We also plot FUV-NUV vs. the Mg_2 index and central velocity dispersion. We find a tight anti-correlation between FUV-NUV and the Mg_2 index(...).Comment: 25 pages, 5 figures, accepted for publication in ApJS (abstract abridged), typos corrected in section 2.

Mutual Influence Between Macrospin Reversal Order and Spin-Wave Dynamics in Isolated Artificial Spin-Ice Vertices

We theoretically and experimentally investigate magnetization reversal and associated spin-wave dynamics of isolated threefold vertices that constitute a Kagome lattice. The three permalloy macrospins making up the vertex have an elliptical cross section and a uniform thickness. We study the dc magnetization curve and the frequency versus field curves (dispersions) of those spin-wave modes that produce the largest response. We also investigate each macrospin reversal from a dynamic perspective, by performing micromagnetic simulations of the reversal processes, and revealing their relationships to the soft-mode profile calculated at the equilibrium state immediately before reversal. The theoretical results are compared with the measured magnetization curves and ferromagnetic resonance spectra. The agreement achieved suggests that a much deeper understanding of magnetization reversal and accompanying hysteresis can be achieved by combining theoretical calculations with static and dynamic magnetization experiments