Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

One-dimensional improvement and two-dimensional and 3-dimensional treatments for stable oscillation condition, mode structure and power output in high-speed-flow lasers

For high-speed-flow lasers, the one-dimensional and first-order approximate treatment in[1] under approximation of geometrical optics is improved still within the scope of approx-imation of geometrical optics. The strict accurate results are obtained, and what is more,two- and three-dimensional treatments are done. Thus for two- and three-dimensional cases, thestable oscillation condition, the formulae of power output and analytical expression of modesunder approximation of geometrical optics (in terms of gain function) are derived. Accord-ing to the present theory, one-and two-dimensional calculations for the typical case of Gerry'sexperiment are presented. All the results coincide well with the experiment and are better thanthe results obtained in [1].In addition, the applicable scope of Lee's stable oscillation condition given by [1] is ex-panded; the condition for the approximation of gcometrical optics to be applied to mode con-structure in optical cavity is obtained for the first time and the difference between thiscondition and that for free space is also pointed out in the present work.

Information geometry theory of high-dimension space and application for speaker independent continuous digit speech recognition

In the light of descriptive geometry and notions in set theory, this paper re-defines the basic elements in space such as curve and surface and so on, presents some fundamental notions with respect to the point cover based on the High-dimension space (HDS) point covering theory, finally takes points from mapping part of speech signals to HDS, so as to analyze distribution information of these speech points in HDS, and various geometric covering objects for speech points and their relationship. Besides, this paper also proposes a new algorithm for speaker independent continuous digit speech recognition based on the HDS point dynamic searching theory without end-points detection and segmentation. First from the different digit syllables in real continuous digit speech, we establish the covering area in feature space for continuous speech. During recognition, we make use of the point covering dynamic searching theory in HDS to do recognition, and then get the satisfying recognized results. At last, compared to HMM (Hidden Markov models)-based method, from the development trend of the comparing results, as sample amount increasing, the difference of recognition rate between two methods will decrease slowly, while sample amount approaching to be very large, two recognition rates all close to 100% little by little. As seen from the results, the recognition rate of HDS point covering method is higher than that of in HMM (Hidden Markov models) based method, because, the point covering describes the morphological distribution for speech in HDS, whereas HMM-based method is only a probability distribution, whose accuracy is certainly inferior to point covering.

Theoretical analysis about the influence of channel layer thickness on the 2D electron gas and its distribution in InP-based high-electron-mobility transistors

The principle of high-electron-mobility transistor (HEMT) and the property of two-dimensional electron gas (2DEG) have been analyzed theoretically. The concentration and distribution of 2DEG in various channel layers are calculated by numerical method. Variation of 2DEG concentration in different subband of the quantum well is discussed in detail. Calculated results show that sheet electron concentration of 2DEG in the channel is affected slightly by the thickness of the channel. But the proportion of electrons inhabited in different subbands can be affected by the thickness of the channel. When the size of channel lies between 20-25 nm, the number of electrons occupying the second subband reaches the maximum. This result can be used in parameter design of materials and devices.

An Accelerated Chow and Liu Algorithm: Fitting Tree Distributions to High Dimensional Sparse Data

Chow and Liu introduced an algorithm for fitting a multivariate distribution with a tree (i.e. a density model that assumes that there are only pairwise dependencies between variables) and that the graph of these dependencies is a spanning tree. The original algorithm is quadratic in the dimesion of the domain, and linear in the number of data points that define the target distribution $P$. This paper shows that for sparse, discrete data, fitting a tree distribution can be done in time and memory that is jointly subquadratic in the number of variables and the size of the data set. The new algorithm, called the acCL algorithm, takes advantage of the sparsity of the data to accelerate the computation of pairwise marginals and the sorting of the resulting mutual informations, achieving speed ups of up to 2-3 orders of magnitude in the experiments.

Effect of Metal-Ceramic or All-Ceramic Superstructure Materials on Stress Distribution in a Single Implant-Supported Prosthesis: Three-Dimensional Finite Element Analysis

Purpose: This three-dimensional finite element analysis study evaluated the effect of different material combinations on stress distribution within metal-ceramic and all-ceramic single implant-supported prostheses. Materials and Methods: Three-dimensional finite element models reproducing a segment of the maxilla with a missing left first premolar were created. Five groups were established to represent different superstructure materials: GP, porcelain fused to gold alloy; GR, modified composite resin fused to gold alloy; TP, porcelain fused to titanium; TR, modified composite resin fused to titanium; and ZP, porcelain fused to zirconia. A 100-N vertical force was applied to the contact points of the crowns. All models were fixed in the superior region of bone tissue and in the mesial and distal faces of the maxilla section. Stress maps were generated by processing with finite element software. Results: Stress distribution and stress values of supporting bone were similar for the GP, GR, TP, and ZP models (1,574.3 MPa, 1,574.3 MPa, 1,574.3 MPa, and 1,574.2 MPa, respectively) and different for the TR model (1,838.3 MPa). The ZP model transferred less stress to the retention screw (785 MPa) than the other groups (939 MPa for GP, 961 MPa for GR, 1,010 MPa for TP, and 1,037 MPa for TR). Conclusion: The use of different materials to fabricate a superstructure for a single implant-supported prosthesis did not affect the stress distribution in the supporting bone. The retention screw received less stress when a combination of porcelain and zirconia was used. Int J Oral Maxillofac Implants 2011;26:1202-1209

Local strain distribution in real three-dimensional alveolar geometries

Mechanical ventilation is not only a life saving treatment but can also cause negative side effects. One of the main complications is inflammation caused by overstretching of the alveolar tissue. Previously, studies investigated either global strains or looked into which states lead to inflammatory reactions in cell cultures. However, the connection between the global deformation, of a tissue strip or the whole organ, and the strains reaching the single cells lining the alveolar walls is unknown and respective studies are still missing. The main reason for this is most likely the complex, sponge-like alveolar geometry, whose three-dimensional details have been unknown until recently. Utilizing synchrotron-based X-ray tomographic microscopy, we were able to generate real and detailed three-dimensional alveolar geometries on which we have performed finite-element simulations. This allowed us to determine, for the first time, a three-dimensional strain state within the alveolar wall. Briefly, precision-cut lung slices, prepared from isolated rat lungs, were scanned and segmented to provide a three-dimensional geometry. This was then discretized using newly developed tetrahedral elements. The main conclusions of this study are that the local strain in the alveolar wall can reach a multiple of the value of the global strain, for our simulations up to four times as high and that thin structures obviously cause hotspots that are especially at risk of overstretching.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Supramolecular control of the magnetic anisotropy in two-dimensional high-spin Fe arrays at a metal interface

Magnetic atoms at surfaces are a rich model system for solid-state magnetic bits exhibiting either classical(1,2) or quantum(3,4) behaviour. Individual atoms, however, are difficult to arrange in regular patterns(1-5). Moreover, their magnetic properties are dominated by interaction with the substrate, which, as in the case of Kondo systems, often leads to a decrease or quench of their local magnetic moment(6,7). Here, we show that the supramolecular assembly of Fe and 1,4-benzenedicarboxylic acid molecules on a Cu surface results in ordered arrays of high-spin mononuclear Fe centres on a 1.5nm square grid. Lateral coordination with the molecular ligands yields unsaturated yet stable coordination bonds, which enable chemical modification of the electronic and magnetic properties of the Fe atoms independently from the substrate. The easy magnetization direction of the Fe centres can be switched by oxygen adsorption, thus opening a way to control the magnetic anisotropy in supramolecular layers akin to that used in metallic thin films.

Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs

Let n points be placed independently in d-dimensional space according to the density f(x) = A(d)e(-lambda parallel to x parallel to alpha), lambda, alpha > 0, x is an element of R-d, d >= 2. Let d(n) be the longest edge length of the nearest-neighbor graph on these points. We show that (lambda(-1) log n)(1-1/alpha) d(n) - b(n) converges weakly to the Gumbel distribution, where b(n) similar to ((d - 1)/lambda alpha) log log n. We also prove the following strong law for the normalized nearest-neighbor distance (d) over tilde (n) = (lambda(-1) log n)(1-1/alpha) d(n)/log log n: (d - 1)/alpha lambda <= lim inf(n ->infinity) (d) over tilde (n) <= lim sup(n ->infinity) (d) over tilde (n) <= d/alpha lambda almost surely. Thus, the exponential rate of decay alpha = 1 is critical, in the sense that, for alpha > 1, d(n) -> 0, whereas, for alpha <= 1, d(n) -> infinity almost surely as n -> infinity.

Rectilinear Path Following in 3D Space

This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

Plume structure in high-Rayleigh-number convection

Near-wall structures in turbulent natural convection at Rayleigh numbers of $10^{10}$ to $10^{11}$ at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log–normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

Ferroelectric origin in one-dimensional undoped ZnO towards high electromechanical response

Ferroelectricity in ZnO is an unlikely physical phenomenon. Here, we show ferroelectricity in undoped 001] ZnO nanorods due to zinc vacancies. Generation of ferroelectricity in a ZnO nanorod effectively increases its piezoelectricity and turns the ZnO nanorod into an ultrahigh-piezoelectric material. Here using piezoelectric force microscopy (PFM), it is observed that increasing the frequency of the AC excitation electric field decreases the effective d(33). Subsequently, the existence of a reversible permanent electric dipole is also found from the P-E hysteresis loop of the ZnO nanorods. Under a high resolution transmission electron microscope (HRTEM), we observe a zinc blende stacking in the wurtzite stacking of a single nanorod along the growth axis. The zinc blende nature of this defect is also supported by the X-ray diffraction (XRD) and Raman spectra. The presence of zinc vacancies in this basal stacking fault modulates p-d hybridization of the ZnO nanorod and produces a magnetic moment through the adjacent oxygen ions. This in turn induces a reversible electric dipole in the non-centrosymmetric nanostructure and is responsible for the ultrahigh-piezoelectric response in these undoped ZnO nanorods. We reveal that this defect engineered ZnO can be considered to be in the competitive class of ultrahigh-piezoelectric nanomaterials for energy harvesting and electromechanical device fabrication.