Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by $n^{-1/2}$ in the limit $n\to\infty$ satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for $\hbox{Tr}G(z)$ and then extend the result on the linear eigenvalue statistics $\hbox{Tr}\phi(A)$ of any function $\phi:\mathbb{R}\to\mathbb{R}$ which increases, together with its first two derivatives, at infinity not faster than an exponential.Comment: 22 page

The psychophysics of bouncing: Perceptual constraints, physical constraints, animacy, and phenomenal causality

In the present study we broadly explored the perception of physical and animated motion in bouncing-like scenarios through four experiments. In the first experiment, participants were asked to categorize bouncing-like displays as physical bounce, animated motion, or other. Several parameters of the animations were manipulated, that is, the simulated coefficient of restitution, the value of simulated gravitational acceleration, the motion pattern (uniform acceleration/deceleration or constant speed) and the number of bouncing cycles. In the second experiment, a variable delay at the moment of the collision between the bouncing object and the bouncing surface was introduced. Main results show that, although observers appear to have realistic representations of physical constraints like energy conservation and gravitational acceleration/deceleration, the amount of visual information available in the scene has a strong modulation effect on the extent to which they rely on these representations. A coefficient of restitution >1 was a crucial cue to animacy in displays showing three bouncing cycles, but not in displays showing one bouncing cycle. Additionally, bouncing impressions appear to be driven by perceptual constraints that are unrelated to the physical realism of the scene, like preference for simulated gravitational attraction smaller than g and perceived temporal contiguity between the different phases of bouncing. In the third experiment, the visible opaque bouncing surface was removed from the scene, and the results showed that this did not have any substantial effect on the resulting impressions of physical bounce or animated motion, suggesting that the visual system can fill-in the scene with the missing element. The fourth experiment explored visual impressions of causality in bouncing scenarios. At odds with claims of current causal perception theories, results indicate that a passive object can be perceived as the direct cause of the motion behavior of an active object

Momentum transferred to a trapped Bose-Einstein condensate by stimulated light scattering

The response of a trapped Bose-Einstein condensed gas to a density perturbation generated by a two-photon Bragg pulse is investigated by solving the time-dependent Gross-Pitaevskii equation. We calculate the total momentum imparted to the condensate as a function of both the time duration of the pulse and the frequency difference of the two laser beams. The role of the dynamic response function in characterizing the time evolution of the system is pointed out, with special emphasis to the phonon regime. Numerical simulations are compared with the predictions of local density approximation. The relevance of our results for the interpretation of current experiments is also discussed.Comment: 7 pages, 3 postscript figure

The impact of bioceramic scaffolds on bone regeneration in preclinical in vivo studies: A systematic review

Bioceramic scaffolds are appealing for alveolar bone regeneration, because they are emerging as promising alternatives to autogenous and heterogenous bone grafts. The aim of this systematic review is to answer to the focal question: in critical-sized bone defects in experimental animal models, does the use of a bioceramic scaffolds improve new bone formation, compared with leaving the empty defect without grafting materials or using autogenous bone or deproteinized bovine-derived bone substitutes? Electronic databases were searched using specific search terms. A hand search was also undertaken. Only randomized and controlled studies in the English language, published in peer-reviewed journals between 2013 and 2018, using critical-sized bone defect models in non-medically compromised animals, were considered. Risk of bias assessment was performed using the SYRCLE tool. A meta-analysis was planned to synthesize the evidence, if possible. Thirteen studies reporting on small animal models (six studies on rats and seven on rabbits) were included. The calvarial bone defect was the most common experimental site. The empty defect was used as the only control in all studies except one. In all studies the bioceramic materials demonstrated a trend for better outcomes compared to an empty control. Due to heterogeneity in protocols and outcomes among the included studies, no meta-analysis could be performed. Bioceramics can be considered promising grafting materials, though further evidence is needed

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Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at T=0K. We demonstrate that within the linear response regime, both a quantum field theory treatment and a meanfield Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a meanfield formalism. We analyse the behaviour of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (meanfield, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the meanfield treatment, and can be interpreted in terms of the interference of the u and v quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.Comment: RevTeX4 format, 16 pages plus 7 eps figures; Update to published version: minors changes and an additional figure. (To appear in Phys. Rev. A

Understanding the microstructure of mortars for cultural heritage using X-ray CT and MIP

In this study, the microstructure of mock-up mortar specimens for a historic environment, composed of different mixtures, was studied using mercury intrusion porosity (MIP) and micro-computed tomography (\ub5CT), highlighting the advantages and drawbacks of both techniques. Po-rosity, sphericity, and pores size distribution were studied, evaluating changes according to mortar composition (aerial and hydraulic binders, quartz sand, and crushed limestone aggregate). The \ub5CT results were rendered using 3D visualization software, which provides complementary information for the interpretation of the data obtained using 3D data-analysis software. Moreover, \ub5CT contrib-utes to the interpretation of MIP results of mortars. On the other hand, MIP showed significant ink-bottle effects in lime and cement mortars samples that should be taken into account when interpret-ing the results. Moreover, the MIP results highlighted how gypsum mortar samples display a porosity distribution that is best studied using this technique. This multi-analytical approach provides important insights into the interpretation of the porosimetric data obtained. This is crucial in the characterization of mortars and provides key information for the study of building materials and cultural heritage conservation

How to measure the Bogoliubov quasiparticle amplitudes in a trapped condensate

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum $q$, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes $u_{q}$ and $v_{q}$ characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation.Comment: 12 pages, 4 figures include