Logarithmic Sobolev inequalities for mollified compactly supported measures

We show that the convolution of a compactly supported measure on $\mathbb{R}$ with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). We use this result to give a new proof of a classical result in random matrix theory that states that, under certain hypotheses, the empirical law of eigenvalues of a sequence of random real symmetric matrices converges weakly in probability to its mean. We then examine the optimal constants in the LSIs for the convolved measures in terms of the variance of the convolving Gaussian. We conclude with partial results on the extension of our main theorem to higher dimensions.Comment: arXiv admin note: text overlap with arXiv:1405.258

Foreign Operations of Swedish Manufacturing Firms - Evidence from the IUI Survey on Multinationals 2003

The paper serves as a documentation of the survey IUI has conducted on Swedish multinational firms (MNEs) in 2004. It describes recent trends in the operations of Swedish multinational firms participating in the survey and foreign direct investment (FDI) of Swedish firms in general. The survey is a follow-up of the surveys made by IUI since 1970s. The database covers information about the Swedish part of manufacturing multinational firms and the foreign affiliates of the firms. The following years are covered: 1965, 1970, 1974, 1978, 1986, 1990, 1994, 1998 and 2003. Multinational Enterprises; Foreign Direct Investment; Spillovers; Research and Development

STED imaging performance estimation by means of Fourier transform analysis

Due to relatively high powers used in STED, biological samples may be affected by the illumination in the process of image acquisition. Similarly, the performance of the system may be limited by the sample itself. Optimization of the STED parameters taking into account the sample itself is therefore a complex task as there is no clear methodology that can determine the image improvement in an objective and quantitative manner. In this work, a method based on Fourier transform formalism is presented to analyze the performance of a STED system. The spatial frequency distribution of pairs of confocal and STED images are compared to obtain an objective parameter, the Azimuth Averaged Spectral Content Spread (AASCS), that is related to the performance of the system in which the sample is also considered. The method has been first tested on samples of beads, and then applied to cell samples labeled with multiple fluorescent dyes. The results show that a single parameter, the AASCS, can be used to determine the optimal settings for STED image acquisition in an objective way, only by using the information provided by the images from the sample themselves. The AASCS also helps minimize the depletion power, for better preservation of the samples.Peer ReviewedPostprint (published version

Spin relaxation and spin Hall transport in 5d transition-metal ultrathin films

The spin relaxation induced by the Elliott-Yafet mechanism and the extrinsic spin Hall conductivity due to the skew-scattering are investigated in 5d transition-metal ultrathin films with self-adatom impurities as scatterers. The values of the Elliott-Yafet parameter and of the spin-flip relaxation rate reveal a correlation with each other that is in agreement with the Elliott approximation. At 10-layer thickness, the spin-flip relaxation time in 5d transition-metal films is quantitatively reported about few hundred nanoseconds at atomic percent which is one and two orders of magnitude shorter than that in Au and Cu thin films, respectively. The anisotropy effect of the Elliott-Yafet parameter and of the spin-flip relaxation rate with respect to the direction of the spin-quantization axis in relation to the crystallographic axes is also analyzed. We find that the anisotropy of the spin-flip relaxation rate is enhanced due to the Rashba surface states on the Fermi surface, reaching values as high as 97% in 10-layer Hf(0001) film or 71% in 10-layer W(110) film. Finally, the spin Hall conductivity as well as the spin Hall angle due to the skew-scattering off self-adatom impurities are calculated using the Boltzmann approach. Our calculations employ a relativistic version of the first-principles full-potential Korringa-Kohn-Rostoker Green function method

Contribution of speckle noise in near-infrared spectroscopy measurements

Near-infrared spectroscopy (NIRS) is widely used in biomedical optics with applications ranging from basic science, such as in functional neuroimaging, to clinical, as in pulse oximetry. Despite the relatively low absorption of tissue in the near-infrared, there is still a significant amount of optical attenuation produced by the highly scattering nature of tissue. Because of this, designers of NIRS systems have to balance source optical power and source–detector separation to maximize the signal-to-noise ratio (SNR). However, theoretical estimations of SNR neglect the effects of speckle. Speckle manifests as fluctuations of the optical power received at the detector. These fluctuations are caused by interference of the multiple random paths taken by photons in tissue. We present a model for the NIRS SNR that includes the effects of speckle. We performed experimental validations with a NIRS system to show that it agrees with our model. Additionally, we performed computer simulations based on the model to estimate the contribution of speckle noise for different collection areas and source–detector separations. We show that at short source–detector separation, speckle contributes most of the noise when using long coherence length sources. Considering this additional noise is especially important for hybrid applications that use NIRS and speckle contrast simultaneously, such as in diffuse correlation spectroscopy.R01 EB025145 - NIBIB NIH HHS; R24 NS104096 - NINDS NIH HHSPublished versio

Strong spin-orbit fields and Dyakonov-Perel spin dephasing in supported metallic films

Spin dephasing by the Dyakonov-Perel mechanism in metallic films deposited on insulating substrates is revealed, and quantitatively examined by means of density functional calculations combined with a kinetic equation. The surface-to-substrate asymmetry, probed by the metal wave functions in thin films, is found to produce strong spin-orbit fields and a fast Larmor precession, giving a dominant contribution to spin decay over the Elliott-Yafet spin relaxation up to a thickness of 70 nm. The spin dephasing is oscillatory in time with a rapid (sub-picosecond) initial decay. However, parts of the Fermi surface act as spin traps, causing a persistent tail signal lasting 1000 times longer than the initial decay time. It is also found that the decay depends on the direction of the initial spin polarization, resulting in a spin-dephasing anisotropy of 200% in the examined cases