Amorphous Placement and Informed Diffusion for Timely Monitoring by Autonomous, Resource-Constrained, Mobile Sensors

Personal communication devices are increasingly equipped with sensors for passive monitoring of encounters and surroundings. We envision the emergence of services that enable a community of mobile users carrying such resource-limited devices to query such information at remote locations in the field in which they collectively roam. One approach to implement such a service is directed placement and retrieval (DPR), whereby readings/queries about a specific location are routed to a node responsible for that location. In a mobile, potentially sparse setting, where end-to-end paths are unavailable, DPR is not an attractive solution as it would require the use of delay-tolerant (flooding-based store-carry-forward) routing of both readings and queries, which is inappropriate for applications with data freshness constraints, and which is incompatible with stringent device power/memory constraints. Alternatively, we propose the use of amorphous placement and retrieval (APR), in which routing and field monitoring are integrated through the use of a cache management scheme coupled with an informed exchange of cached samples to diffuse sensory data throughout the network, in such a way that a query answer is likely to be found close to the query origin. We argue that knowledge of the distribution of query targets could be used effectively by an informed cache management policy to maximize the utility of collective storage of all devices. Using a simple analytical model, we show that the use of informed cache management is particularly important when the mobility model results in a non-uniform distribution of users over the field. We present results from extensive simulations which show that in sparsely-connected networks, APR is more cost-effective than DPR, that it provides extra resilience to node failure and packet losses, and that its use of informed cache management yields superior performance.

Estimating stochastic volatility diffusion using conditional moments of integrated volatility

We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps. © 2002 Elsevier Science B.V. All rights reserved.

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method.

While the Stokes-Einstein (SE) equation predicts that the diffusion coefficient of a solute will be inversely proportional to the viscosity of the solvent, this relation is commonly known to fail for solutes, which are the same size or smaller than the solvent. Multiple researchers have reported that for small solutes, the diffusion coefficient is inversely proportional to the viscosity to a fractional power, and that solutes actually diffuse faster than SE predicts. For other solvent systems, attractive solute-solvent interactions, such as hydrogen bonding, are known to retard the diffusion of a solute. Some researchers have interpreted the slower diffusion due to hydrogen bonding as resulting from the effective diffusion of a larger complex of a solute and solvent molecules. We have developed and used a novel micropipette technique, which can form and hold a single microdroplet of water while it dissolves in a diffusion controlled environment into the solvent. This method has been used to examine the diffusion of water in both n-alkanes and n-alcohols. It was found that the polar solute water, diffusing in a solvent with which it cannot hydrogen bond, closely resembles small nonpolar solutes such as xenon and krypton diffusing in n-alkanes, with diffusion coefficients ranging from 12.5x10(-5) cm(2)/s for water in n-pentane to 1.15x10(-5) cm(2)/s for water in hexadecane. Diffusion coefficients were found to be inversely proportional to viscosity to a fractional power, and diffusion coefficients were faster than SE predicts. For water diffusing in a solvent (n-alcohols) with which it can hydrogen bond, diffusion coefficient values ranged from 1.75x10(-5) cm(2)/s in n-methanol to 0.364x10(-5) cm(2)/s in n-octanol, and diffusion was slower than an alkane of corresponding viscosity. We find no evidence for solute-solvent complex diffusion. Rather, it is possible that the small solute water may be retarded by relatively longer residence times (compared to non-H-bonding solvents) as it moves through the liquid.

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

BOLD signal compartmentalization based on the apparent diffusion coefficient.

Functional MRI (fMRI) can detect blood oxygenation level dependent (BOLD) hemodynamic responses secondary to neuronal activity. The most commonly used method for detecting fMRI signals is the gradient-echo echo-planar imaging (EPI) technique because of its sensitivity and speed. However, it is generally believed that a significant portion of these signals arises from large veins, with additional contribution from the capillaries and parenchyma. Early experiments using diffusion-weighted gradient-echo EPI have suggested that intra-voxel incoherent motion (IVIM) weighting inherent in the sequence can selectively attenuate contributions from different vessels based on the differences in the mobility of the blood within them. In the present study, we used similar approach to characterize the apparent diffusion coefficient (ADC) distribution within the activated areas of BOLD contrast. It is shown that the voxel values of the ADCs obtained from this technique can infer various vascular contributions to the BOLD signal.

Improved delineation of short cortical association fibers and gray/white matter boundary using whole-brain three-dimensional diffusion tensor imaging at submillimeter spatial resolution.

Recent emergence of human connectome imaging has led to a high demand on angular and spatial resolutions for diffusion magnetic resonance imaging (MRI). While there have been significant growths in high angular resolution diffusion imaging, the improvement in spatial resolution is still limited due to a number of technical challenges, such as the low signal-to-noise ratio and high motion artifacts. As a result, the benefit of a high spatial resolution in the whole-brain connectome imaging has not been fully evaluated in vivo. In this brief report, the impact of spatial resolution was assessed in a newly acquired whole-brain three-dimensional diffusion tensor imaging data set with an isotropic spatial resolution of 0.85 mm. It was found that the delineation of short cortical association fibers is drastically improved as well as the definition of fiber pathway endings into the gray/white matter boundary-both of which will help construct a more accurate structural map of the human brain connectome.

Local kinetic interpretation of entropy production through reversed diffusion.

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.

A Diffusion MRI Tractography Connectome of the Mouse Brain and Comparison with Neuronal Tracer Data.

Interest in structural brain connectivity has grown with the understanding that abnormal neural connections may play a role in neurologic and psychiatric diseases. Small animal connectivity mapping techniques are particularly important for identifying aberrant connectivity in disease models. Diffusion magnetic resonance imaging tractography can provide nondestructive, 3D, brain-wide connectivity maps, but has historically been limited by low spatial resolution, low signal-to-noise ratio, and the difficulty in estimating multiple fiber orientations within a single image voxel. Small animal diffusion tractography can be substantially improved through the combination of ex vivo MRI with exogenous contrast agents, advanced diffusion acquisition and reconstruction techniques, and probabilistic fiber tracking. Here, we present a comprehensive, probabilistic tractography connectome of the mouse brain at microscopic resolution, and a comparison of these data with a neuronal tracer-based connectivity data from the Allen Brain Atlas. This work serves as a reference database for future tractography studies in the mouse brain, and demonstrates the fundamental differences between tractography and neuronal tracer data.

Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging.

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.

Modelling meso-scale diffusion processes in stochastic fluid bio-membranes

The space–time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded) inclusions and horizontally placed (surface) inclusions are considered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham–Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion parameter of this process acts as the link coupling the membrane shape fluctuations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces, the inclusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The model has potential use in such emerging fields as designing a targeted drug delivery system.

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution

Modeling the diffusion of solid copper into liquid solder alloys

During the soldering process, the copper atoms diffuse into liquid solders. The diffusion process determines integrity and the reworking possibility of a solder joint. In order to capture the diffusion scenarios of solid copper into liquid Sn–Pb and Sn–Cu solders, a computer modeling has been performed for 10 s. An analytical model has also been proposed for calculating the diffusion coefficient of copper into liquid solders. It is found that the diffusion coefficient for Sn–Pb solder is 2.74 × 10− 10 m2/s and for Sn–Cu solder is 6.44 × 10−9 m2/s. The modeling results reveal that the diffusion coefficient is one of the major factors that govern the rate at which solid Cu dissolve in the molten solder. The predicted dissolved amounts of copper into solders have been validated with the help of scanning electron microscopic analysis.

Local examination of skin diffusion using FTIR spectroscopic imaging and multivariate target factor analysis

In the context of trans-dermal drug delivery it is very important to have mechanistic insight into the barrier function of the skin's stratum corneum and the diffusion mechanisms of topically applied drugs. Currently spectroscopic imaging techniques are evolving which enable a spatial examination of various types of samples in a dynamic way. ATR-FTIR imaging opens up the possibility to monitor spatial diffusion profiles across the stratum corneum of a skin sample. Multivariate data analyses methods based on factor analysis are able to provide insight into the large amount of spectroscopically complex and highly overlapping signals generated. Multivariate target factor analysis was used for spectral resolution and local diffusion profiles with time through stratum corneum. A model drug, 4-cyanophenol in polyethylene glycol 600 and water was studied. Results indicate that the average diffusion profiles between spatially different locations show similar profiles despite the heterogeneous nature of the biological sample and the challenging experimental set-up.