Efficient articulated trajectory reconstruction using dynamic programming and filters

This paper considers the problem of reconstructing the motion of a 3D articulated tree from 2D point correspondences subject to some temporal prior. Hitherto, smooth motion has been encouraged using a trajectory basis, yielding a hard combinatorial problem with time complexity growing exponentially in the number of frames. Branch and bound strategies have previously attempted to curb this complexity whilst maintaining global optimality. However, they provide no guarantee of being more efficient than exhaustive search. Inspired by recent work which reconstructs general trajectories using compact high-pass filters, we develop a dynamic programming approach which scales linearly in the number of frames, leveraging the intrinsically local nature of filter interactions. Extension to affine projection enables reconstruction without estimating cameras.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Examining the influence of participant performance factors on contractor satisfaction : a structural equation model

Participant performance is critical to the success of projects. At the same time, enhancing the satisfaction of participants not only helps in problem solving but also improves their motivation and cooperation. However, previous research related to participant satisfaction is primarily concerned with clients and customers and relatively little attention has been paid to contractors. This paper investigates how the performance of project participants affects contractor project satisfaction in terms of the client's clarity of objectives (OC) and promptness of payments (PP), designer carefulness (DC), construction risk management (RM), the effectiveness their contribution (EW) and mutual respect and trust (RT). With 125 valid responses from contractors in Malaysia, a contractor satisfaction model is developed based on structural equation modelling. The results demonstrate the necessity for dividing abstract satisfaction into two dimensions, comprising economic-related satisfaction (ES) and production-related satisfaction (PS), with DC, OC, PP and RM having significant effects on ES, while DC, OC, EW and RM influence PS. In addition, the model tests the indirect effects of these performance variables on ES and PS. In particular, OC indirectly affects ES and PS through mediation of RM and DC respectively. The results also provide opportunities for improving contractor satisfaction and supplementing the contractor selection criteria for clients.

Reconstructing 3D x-ray CT images of polymer gel dosimeters using the zero-scan method

In this study x-ray CT has been used to produce a 3D image of an irradiated PAGAT gel sample, with noise-reduction achieved using the ‘zero-scan’ method. The gel was repeatedly CT scanned and a linear fit to the varying Hounsfield unit of each pixel in the 3D volume was evaluated across the repeated scans, allowing a zero-scan extrapolation of the image to be obtained. To minimise heating of the CT scanner’s x-ray tube, this study used a large slice thickness (1 cm), to provide image slices across the irradiated region of the gel, and a relatively small number of CT scans (63), to extrapolate the zero-scan image. The resulting set of transverse images shows reduced noise compared to images from the initial CT scan of the gel, without being degraded by the additional radiation dose delivered to the gel during the repeated scanning. The full, 3D image of the gel has a low spatial resolution in the longitudinal direction, due to the selected scan parameters. Nonetheless, important features of the dose distribution are apparent in the 3D x-ray CT scan of the gel. The results of this study demonstrate that the zero-scan extrapolation method can be applied to the reconstruction of multiple x-ray CT slices, to provide useful 2D and 3D images of irradiated dosimetry gels.

Infrared and Raman spectroscopic characterization of the phosphate mineral fairfieldite – Ca2(Mn2+,Fe2+)2(PO4)2·2(H2O)

Raman spectroscopy complimented with infrared spectroscopy has been used to determine the molecular structure of the phosphate mineral fairfieldite. The Raman phosphate (PO4)3- stretching region shows strong differences between the fairfieldite phosphate minerals which is attributed to the cation substitution for calcium in the structure. In the infrared spectra complexity exists with multiple (PO4)2- antisymmetric stretching vibrations observed, indicating a reduction of the tetrahedral symmetry. This loss of degeneracy is also reflected in the bending modes. Strong Raman bands around 600 cm-1 are assigned to v4 phosphate bending modes. Multiple bands in the 400–450 cm-1 region assigned to m2 phosphate bending modes provide further evidence of symmetry reduction of the phosphate anion. Three broadbands for fairfieldite are found at 3040, 3139 and 3271 cm-1 and are assigned to OH stretching bands. By using a Libowitzky empirical equation hydrogen bond distances of 2.658 and 2.730 A are estimated. Vibrational spectroscopy enables aspects of the molecular structure of the fairfieldite to be ascertained.

Design and interpretation of cell trajectory assays

Cell trajectory data is often reported in the experimental cell biology literature to distinguish between different types of cell migration. Unfortunately, there is no accepted protocol for designing or interpreting such experiments and this makes it difficult to quantitatively compare different published data sets and to understand how changes in experimental design influence our ability to interpret different experiments. Here, we use an individual based mathematical model to simulate the key features of a cell trajectory experiment. This shows that our ability to correctly interpret trajectory data is extremely sensitive to the geometry and timing of the experiment, the degree of motility bias and the number of experimental replicates. We show that cell trajectory experiments produce data that is most reliable when the experiment is performed in a quasi 1D geometry with a large number of identically{prepared experiments conducted over a relatively short time interval rather than few trajectories recorded over particularly long time intervals.

Infrared and Raman spectroscopic characterization of the arsenate mineral ceruleite Cu2Al7(AsO4)4(OH)13⋅11.5(H2O)

The molecular structure of the arsenate mineral ceruleite has been assessed using a combination of Raman and infrared spectroscopy. The most intense band observed at 903 cm-1 is assigned to the (AsO4)3- symmetric stretching vibrational mode. The infrared spectrum shows intense bands at 787, 827 and 886 cm-1, ascribed to the triply degenerate m3 antisymmetric stretching vibration. Raman bands observed at 373, 400, 417 and 430 cm-1 are attributed to the m2 vibrational mode. Three broad bands for ceruleite found at 3056, 3198 and 3384 cm-1 are assigned to water OH stretching bands. By using a Libowitzky empirical equation, hydrogen bond distances of 2.65 and 2.75 Å are calculated. Vibrational spectra enable the molecular structure of the ceruleite mineral to be determined and whilst similarities exist in the spectral patterns with the roselite mineral group, sufficient differences exist to be able to determine the identification of the minerals.

Structural characterization and vibrational spectroscopy of the arsenate mineral wendwilsonite

In this paper, we have investigated on the natural wendwilsonite mineral with the formulae Ca2(Mg,Co)(AsO4)2⋅2(H2O). Raman spectroscopy complimented with infrared spectroscopy has been used to determine the molecular structure of the wendwilsonite arsenate mineral. A comparison is made with the roselite mineral group with formula Ca2B(AsO4)2⋅2H2O (where B may be Co, Fe2+, Mg, Mn, Ni, Zn). The Raman spectra of the arsenate related to tetrahedral arsenate clusters with stretching region shows strong differences between that of wendwilsonite and the roselite arsenate minerals which is attributed to the cation substitution for calcium in the structure. The Raman arsenate (AsO4)3− stretching region shows strong differences between that of wendwilsonite and the roselite arsenate minerals which is attributed to the cation substitution for calcium in the structure. In the infrared spectra complexity exists of multiple to tetrahedral (AsO4)3− clusters with antisymmetric stretching vibrations observed indicating a reduction of the tetrahedral symmetry. This loss of degeneracy is also reflected in the bending modes. Strong Raman bands around 450 cm−1 are assigned to ν4 bending modes. Multiple bands in the 350–300 cm−1 region assigned to ν2 bending modes provide evidence of symmetry reduction of the arsenate anion. Three broad bands for wendwilsonite found at 3332, 3119 and 3001 cm−1 are assigned to OH stretching bands. By using a Libowitzky empirical equation, hydrogen bond distances of 2.65 and 2.75 Å are estimated. Vibrational spectra enable the molecular structure of the wendwilsonite mineral to be determined and whilst similarities exist in the spectral patterns with the roselite mineral group, sufficient differences exist to be able to determine the identification of the minerals.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women

Lean body mass (LBM) and muscle mass remains difficult to quantify in large epidemiological studies due to non-availability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n= 2220; 36% females; age 18-79 y) representing a wide range of body mass index (14-44 kg/m2) participated in this study. Their LBM including ALST was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height and weight explained > 90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of SFTs) increased the explained variation by 5-8% in the fully adjusted models predicting LBM and ALST. More complex equations using all the above anthropometric variables could predict the DXA measured LBM and ALST accurately as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively) as well as good agreement by Bland Altman analyses. These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition.

Development of empirical equations for irradiance profile of a standard parabolic trough collector using Monte Carlo ray tracing technique

Irradiance profile around the receiver tube (RT) of a parabolic trough collector (PTC) is a key effect of optical performance that affects the overall energy performance of the collector. Thermal performance evaluation of the RT relies on the appropriate determination of the irradiance profile. This article explains a technique in which empirical equations were developed to calculate the local irradiance as a function of angular location of the RT of a standard PTC using a vigorously verified Monte Carlo ray tracing model. A large range of test conditions including daily normal insolation, spectral selective coatings and glass envelop conditions were selected from the published data by Dudley et al. [1] for the job. The R2 values of the equations are excellent that vary in between 0.9857 and 0.9999. Therefore, these equations can be used confidently to produce realistic non-uniform boundary heat flux profile around the RT at normal incidence for conjugate heat transfer analyses of the collector. Required values in the equations are daily normal insolation, and the spectral selective properties of the collector components. Since the equations are polynomial functions, data processing software can be employed to calculate the flux profile very easily and quickly. The ultimate goal of this research is to make the concentrating solar power technology cost competitive with conventional energy technology facilitating its ongoing research.