Performance bounds for Reduced Order Models with Application to Parametric Transport

The Kolmogorov $n$-width is an established benchmark to judge the performance of reduced basis and similar methods that produce linear reduced spaces. Although immensely successful in the elliptic regime, this width, shows unsatisfactory slow convergence rates for transport dominated problems. While this has triggered a large amount of work on nonlinear model reduction techniques, we are lacking a benchmark to evaluate their optimal performance. Nonlinear benchmarks like manifold/stable/Lipschitz width applied to the solution manifold are often trivial if the degrees of freedom exceed the parameter dimension and ignore desirable structure as offline/online decompositions. In this paper, we show that the same benchmarks applied to the full reduced order model pipeline from PDE to parametric quantity of interest provide non-trivial benchmarks and we prove lower bounds for transport equations

Density fluctuations in κ\kappa-deformed inflationary universe

We study the spectrum of metric fluctuation in $\kappa$-deformed inflationary universe. We write the theory of scalar metric fluctuations in the $\kappa-$deformed Robertson-Walker space, which is represented as a non-local theory in the conventional Robertson-Walker space. One important consequence of the deformation is that the mode generation time is naturally determined by the structure of the $\kappa-$deformation. We expand the non-local action in $H^2/\kappa^2$, with $H$ being the Hubble parameter and $\kappa$ the deformation parameter, and then compute the power spectra of scalar metric fluctuations both for the cases of exponential and power law inflations up to the first order in $H^2/\kappa^2$. We show that the power spectra of the metric fluctuation have non-trivial corrections on the time dependence and on the momentum dependence compared to the commutative space results. Especially for the power law inflation case, the power spectrum for UV modes is weakly blue shifted early in the inflation and its strength decreases in time. The power spectrum of far-IR modes has cutoff proportional to $k^3$ which may explain the low CMB quadrupole moment.Comment: final revision; 19 pages, 3 figures; to appear in Phys. Rev.

Volumetric three-dimensional intravascular ultrasound visualization using shape-based nonlinear interpolation

BACKGROUND: Intravascular ultrasound (IVUS) is a standard imaging modality for identification of plaque formation in the coronary and peripheral arteries. Volumetric three-dimensional (3D) IVUS visualization provides a powerful tool to overcome the limited comprehensive information of 2D IVUS in terms of complex spatial distribution of arterial morphology and acoustic backscatter information. Conventional 3D IVUS techniques provide sub-optimal visualization of arterial morphology or lack acoustic information concerning arterial structure due in part to low quality of image data and the use of pixel-based IVUS image reconstruction algorithms. In the present study, we describe a novel volumetric 3D IVUS reconstruction algorithm to utilize IVUS signal data and a shape-based nonlinear interpolation. METHODS: We developed an algorithm to convert a series of IVUS signal data into a fully volumetric 3D visualization. Intermediary slices between original 2D IVUS slices were generated utilizing the natural cubic spline interpolation to consider the nonlinearity of both vascular structure geometry and acoustic backscatter in the arterial wall. We evaluated differences in image quality between the conventional pixel-based interpolation and the shape-based nonlinear interpolation methods using both virtual vascular phantom data and in vivo IVUS data of a porcine femoral artery. Volumetric 3D IVUS images of the arterial segment reconstructed using the two interpolation methods were compared. RESULTS: In vitro validation and in vivo comparative studies with the conventional pixel-based interpolation method demonstrated more robustness of the shape-based nonlinear interpolation algorithm in determining intermediary 2D IVUS slices. Our shape-based nonlinear interpolation demonstrated improved volumetric 3D visualization of the in vivo arterial structure and more realistic acoustic backscatter distribution compared to the conventional pixel-based interpolation method. CONCLUSIONS: This novel 3D IVUS visualization strategy has the potential to improve ultrasound imaging of vascular structure information, particularly atheroma determination. Improved volumetric 3D visualization with accurate acoustic backscatter information can help with ultrasound molecular imaging of atheroma component distribution

Validation of Dunbar's number in Twitter conversations

Modern society's increasing dependency on online tools for both work and recreation opens up unique opportunities for the study of social interactions. A large survey of online exchanges or conversations on Twitter, collected across six months involving 1.7 million individuals is presented here. We test the theoretical cognitive limit on the number of stable social relationships known as Dunbar's number. We find that users can entertain a maximum of 100-200 stable relationships in support for Dunbar's prediction. The "economy of attention" is limited in the online world by cognitive and biological constraints as predicted by Dunbar's theory. Inspired by this empirical evidence we propose a simple dynamical mechanism, based on finite priority queuing and time resources, that reproduces the observed social behavior.Comment: 8 pages, 6 figure

The Sun as a planet-host star : proxies from SDO images for HARPS radial-velocity variations

RDH gratefully acknowledges STFC studentship grant number ST/J500744/1, and a grant from the John Templeton Foundation. ACC and RF acknowledge support from STFC consolidated grants numbers ST/J001651/1 and ST/M001296/1. JL acknowledges support from NASA Origins of the Solar System grant No. NNX13AH79G and from STFC grant ST/M001296/1.The Sun is the only star whose surface can be directly resolved at high resolution, and therefore constitutes an excellent test case to explore the physical origin of stellar radial-velocity (RV) variability. We present HARPS observations of sunlight scattered off the bright asteroid 4/Vesta, from which we deduced the Sun's activity-driven RV variations. In parallel, the Helioseismic and Magnetic Imager instrument on board the Solar Dynamics Observatory provided us with simultaneous high spatial resolution magnetograms, Dopplergrams and continuum images of the Sun in the Fe i 6173 Å line. We determine the RV modulation arising from the suppression of granular blueshift in magnetized regions and the flux imbalance induced by dark spots and bright faculae. The rms velocity amplitudes of these contributions are 2.40 and 0.41 m s−1, respectively, which confirms that the inhibition of convection is the dominant source of activity-induced RV variations at play, in accordance with previous studies. We find the Doppler imbalances of spot and plage regions to be only weakly anticorrelated. Light curves can thus only give incomplete predictions of convective blueshift suppression. We must instead seek proxies that track the plage coverage on the visible stellar hemisphere directly. The chromospheric flux index R′HK derived from the HARPS spectra performs poorly in this respect, possibly because of the differences in limb brightening/darkening in the chromosphere and photosphere. We also find that the activity-driven RV variations of the Sun are strongly correlated with its full-disc magnetic flux density, which may become a useful proxy for activity-related RV noise.PostprintPeer reviewe

Trying to understand confinement in the Schroedinger picture

We study the gauge-invariant gaussian ansatz for the vacuum wave functional and show that it potentially possesses many desirable features of the Yang--Mills theory, like asymptotic freedom, mass generation through the transmutation of dimensions and a linear potential between static quarks. We point out that these (and other) features can be studied in a systematic way by combining perturbative and 1/n expansions. Contrary to the euclidean approach, confinement can be easily formulated and easily built in, if not derived, in the variational Schroedinger approach.Comment: 21 pages, 1 figure. Lecture given at the 4th St.Petersburg Winter School in Theoretical Physics, Feb. 22-28, 199