Depth Sensitivity and Source-Detector Separations for Near Infrared Spectroscopy Based on the Colin27 Brain Template

Understanding the spatial and depth sensitivity of non-invasive near-infrared spectroscopy (NIRS) measurements to brain tissue–i.e., near-infrared neuromonitoring (NIN) – is essential for designing experiments as well as interpreting research findings. However, a thorough characterization of such sensitivity in realistic head models has remained unavailable. In this study, we conducted 3,555 Monte Carlo (MC) simulations to densely cover the scalp of a well-characterized, adult male template brain (Colin27). We sought to evaluate: (i) the spatial sensitivity profile of NIRS to brain tissue as a function of source-detector separation, (ii) the NIRS sensitivity to brain tissue as a function of depth in this realistic and complex head model, and (iii) the effect of NIRS instrument sensitivity on detecting brain activation. We found that increasing the source-detector (SD) separation from 20 to 65 mm provides monotonic increases in sensitivity to brain tissue. For every 10 mm increase in SD separation (up to ∼45 mm), sensitivity to gray matter increased an additional 4%. Our analyses also demonstrate that sensitivity in depth (S) decreases exponentially, with a “rule-of-thumb” formula S = 0.75*0.85depth. Thus, while the depth sensitivity of NIRS is not strictly limited, NIN signals in adult humans are strongly biased towards the outermost 10–15 mm of intracranial space. These general results, along with the detailed quantitation of sensitivity estimates around the head, can provide detailed guidance for interpreting the likely sources of NIRS signals, as well as help NIRS investigators design and plan better NIRS experiments, head probes and instruments

Spatial Locality of Galaxy Correlation Function in Phase Space: Samples from the 2MASS Extended Source Catalog

We analyze the statistical properties and dynamical implications of galaxy distributions in phase space for samples selected from the 2MASS Extended Source Catalog. The galaxy distribution is decomposed into modes $\delta({\bf k, x})$ which describe the number density perturbations of galaxies in phase space cell given by scale band $\bf k$ to ${\bf k}+\Delta {\bf k}$ and spatial range $\bf x$ to ${\bf x}+\Delta {\bf x}$. In the nonlinear regime, $\delta({\bf k, x})$ is highly non-Gaussian. We find, however, that the correlations between $\delta({\bf k, x})$ and $\delta({\bf k', x'})$ are always very weak if the spatial ranges (${\bf x}$, ${\bf x}+\Delta {\bf x}$) and (${\bf x'}$, ${\bf x'}+\Delta {\bf x'}$) don't overlap. This feature is due to the fact that the spatial locality of the initial perturbations is memorized during hierarchical clustering. The highly spatial locality of the 2MASS galaxy correlations is a strong evidence for the initial perturbations of the cosmic mass field being spatially localized, and therefore, consistent with a Gaussian initial perturbations on scales as small as about 0.1 h$^{-1}$ Mpc. Moreover, the 2MASS galaxy spatial locality indicates that the relationship between density perturbations of galaxies and the underlying dark matter should be localized in phase space. That is, for a structure consisting of perturbations on scales from $k$ to $k+\Delta {k}$, the nonlocal range in the relation between galaxies and dark matter should {\it not} be larger than $|{\Delta {\bf x}}|=2\pi/|\Delta {\bf k}|$. The stochasticity and nonlocality of the bias relation between galaxies and dark matter fields should be no more than the allowed range given by the uncertainty relation $|{\Delta {\bf x}|| \Delta{\bf k}}|=2\pi$.Comment: 27 pages, 9 figures, accepted by Ap

Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks

In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one internal measurement. The approach is based on a mixed reformulation of the governing equation and utilizes the standard least-squares objective to approximate the conductivity and flux simultaneously, with deep neural networks as ansatz functions. We provide a thorough analysis of the neural network approximations for both continuous and empirical losses, including rigorous error estimates that are explicit in terms of the noise level, various penalty parameters and neural network architectural parameters (depth, width and parameter bound). We also provide extensive numerical experiments in two- and multi-dimensions to illustrate distinct features of the approach, e.g., excellent stability with respect to data noise and capability of solving high-dimensional problems.Comment: 28 pages. 12 figure

Experimental Investigation of Longitudinal Space-Time Correlations of the Velocity Field in Turbulent Rayleigh-B\'{e}nard Convection

We report an experimental investigation of the longitudinal space-time cross-correlation function of the velocity field, $C(r,\tau)$, in a cylindrical turbulent Rayleigh-B\'{e}nard convection cell using the particle image velocimetry (PIV) technique. We show that while the Taylor's frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows [He & Zhang, \emph{Phys. Rev. E} \textbf{73}, 055303(R) (2006)] is valid for the present velocity field for all over the cell, i.e., the isocorrelation contours of the measured $C(r,\tau)$ have a shape of elliptical curves and hence $C(r,\tau)$ can be related to $C(r_E,0)$ via $r_E^2=(r-\beta\tau)^2+\gamma^2\tau^2$ with $\beta$ and $\gamma$ being two characteristic velocities. We further show that the fitted $\beta$ is proportional to the mean velocity of the flow, but the values of $\gamma$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell's central region. It is found that $\beta$ and $\gamma$ are approximately the same near the sidewall, while $\beta\simeq0$ at cell center.Comment: 16 pages, 15 figures, submitted to J. Fluid Mec

A simulated study on the performance of diesel engine with ethanol-diesel blend fuel

This paper describes the simulated study on atomization, wall-film formation, combustion and emission forming process of ethanol-diesel blend fuels in a high speed light duty diesel engine. The result shows that increased ethanol volume percentage of the blend fuels could improve atomization and reduce wall-film formation. However, in the meanwhile, with the increased ethanol volume percentage, low heat values of blend fuels decrease, while both total heat releases and cylinder pressures drop. By adding codes into the FIRE software, the NOx and soot formation region mass fractions are outputted. The simulated results display a good correlation with the NOx and soot formation. Besides, the NOx, soot and CO emissions decrease with the increased ethanol volume percentage. The power output of engine penalize, while energy utilization of blend fuels improve and combustion noise reduce, owing to the increased ethanol volume percentage

Downlink Channel Covariance Matrix Reconstruction for FDD Massive MIMO Systems with Limited Feedback

The downlink channel covariance matrix (CCM) acquisition is the key step for the practical performance of massive multiple-input and multiple-output (MIMO) systems, including beamforming, channel tracking, and user scheduling. However, this task is challenging in the popular frequency division duplex massive MIMO systems with Type I codebook due to the limited channel information feedback. In this paper, we propose a novel formulation that leverages the structure of the codebook and feedback values for an accurate estimation of the downlink CCM. Then, we design a cutting plane algorithm to consecutively shrink the feasible set containing the downlink CCM, enabled by the careful design of pilot weighting matrices. Theoretical analysis shows that as the number of communication rounds increases, the proposed cutting plane algorithm can recover the ground-truth CCM. Numerical results are presented to demonstrate the superior performance of the proposed algorithm over the existing benchmark in CCM reconstruction