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Compositional data from a soil survey over North Canberra, Australian Capital Territory, are used to develop and test an empirical soil provenancing method. Mineralogical data from Fourier transform infrared spectroscopy (FTIR) and magnetic susceptibility (MS), and geochemical data from X‐ray fluorescence (XRF; for total major oxides) and inductively coupled plasma‐mass spectrometry (ICP‐MS; for both total and aqua regia‐soluble trace elements) are performed on the survey's 268 topsoil samples (0–5 cm depth; 1 sample per km2). Principal components (PCs) are calculated after imputation of censored data and centered log‐ratio transformation. The sequential provenancing approach is underpinned by (i) the preparation of interpolated raster grids of the soil properties (including PCs); (ii) the explicit quantification and propagation of uncertainty; (iii) the intersection of the soil property rasters with the values of the evidentiary sample (± uncertainty); and (iv) the computation of cumulative provenance rasters (“heat maps”) for the various analytical techniques. The sequential provenancing method is tested on the North Canberra soil survey with three “blind” samples representing simulated evidentiary samples. Performance metrics of precision and accuracy indicate that the FTIR and MS (mineralogy), as well as XRF and total ICP‐MS (geochemistry) analytical methods, offer the most precise and accurate provenance predictions. Inclusion of PCs in provenancing adds marginally to the performance. Maximizing the number of analytes/analytical techniques is advantageous in soil provenancing. Despite acknowledged limitations and gaps, it is concluded that the empirical soil provenancing approach can play an important role in forensic and intelligence applications.

Significance: Solutions for group-level analysis of connectivity from fNIRS observations exist, but groupwise explorative analysis with classical solutions is often cumbersome. Manifold-based solutions excel at data exploration, but there are infinite surfaces crossing the observations cloud of points. Aim: We aim to provide a systematic choice of surface for a manifold-based analysis of connectivity at group level with small surface interpolation error. Approach: This research introduces interpolated functional manifold (IFM). IFM builds a manifold from reconstructed changes in concentrations of oxygenated ΔcHbO2 and reduced ΔcHbR hemoglobin species by means of radial basis functions (RBF). We evaluate the root mean square error (RMSE) associated to four families of RBF. We validated our model against psychophysiological interactions (PPI) analysis using the Jaccard index (JI). We demonstrate the usability in an experimental dataset of surgical neuroergonomics. Results: Lowest interpolation RMSE was 1.26e − 4 ± 1.32e − 8 for ΔcHbO2 [A.U.] and 4.30e − 7 ± 2.50e − 13 [A.U.] for ΔcHbR. Agreement with classical group analysis was JI = 0.89 ± 0.01 for ΔcHbO2. Agreement with PPI analysis was JI = 0.83 ± 0.07 for ΔcHbO2 and JI = 0.77 ± 0.06 for ΔcHbR. IFM successfully decoded group differences [ANOVA: ΔcHbO2: F ( 2,117 ) = 3.07; p

Significance: Monte Carlo (MC) light transport simulations are most often performed in regularly spaced three-dimensional voxels, a type of data representation that naturally struggles to represent boundary surfaces with curvature and oblique angles. Not accounting properly for such boundaries with an index of refractivity, mismatches can lead to important inaccuracies, not only in the calculated angles of reflection and transmission but also in the amount of light that transmits through or reflects from these mismatched boundary surfaces. Aim: A new MC light transport algorithm is introduced to deal with curvature and oblique angles of incidence when simulated photons encounter mismatched boundary surfaces. Approach: The core of the proposed algorithm applies the efficient preprocessing step of calculating a gradient map of the mismatched boundaries, a smoothing step on this calculated 3D vector field to remove surface roughness due to discretization and an interpolation scheme to improve the handling of curvature. Results: Through simulations of light hitting the side of a sphere and going through a lens, the agreement of this approach with analytical solutions is shown to be strong. Conclusions: The MC method introduced here has the advantage of requiring only slight implementation changes from the current state-of-the-art to accurately simulate mismatched boundaries and readily exploit the acceleration of general-purpose graphics processing units. A code implementation, mcxyzn, is made available and maintained at https://omlc.org/software/mc/mcxyzn/.