On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

Multi-parameter evaluation of fast sol–gel process by terahertz measurements

We present a feasibility study to apply terahertz (THz) spectroscopy and THz imaging as non-destructive diagnostic tools for sol–gel analysis, manufacturing and quality control. By performing THz spectroscopy on liquid and solid samples we were able to follow several key parameters during the sol–gel formation process and of the final product. Sol–gel transformations were monitored by THz absorption, whereas density changes have been observed through changes in refractive indices. Time domain spectroscopy (TDS), both in transmission and reflection geometries, was used to monitor the properties of fast sol–gel resins. THz imaging of gold coated, thin-film sol–gel enables us to determine inhomogeneities and defects in their internal structure. We demonstrated that THz spectroscopy can be implemented as an online analytical tool for multi-parameter evaluation of the sol–gel process during fabrication, and of the final product.     

On the number-average molecular weight of poly(1,4-trans isoprene) determined by conventional GPC

We became aware, in the course of our on-going research, that the number-average molecular weight of poly(1,4-trans isoprene) determined by conventional gel permeation chromatography (GPC) in tetrahydrofuran (THF) using polystyrene standards differs from its true value by a factor 2. As far as we know, the Mark-Houwink coefficients of this polymer in a widespread GPC eluent such as THF have never been determined. We provide in this contribution a simple relationship between the number-average molecular weight of poly(1,4-trans isoprene) determined by GPC in THF using polystyrene standards and its true value.     

Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams

AnO(n logn) algorithm for planning a purely translational motion for a simple convex object amidst polygonal barriers in two-dimensional space is given. The algorithm is based on a new generalization of Voronoi diagrams (similar to that proposed by Chew and Drysdale [1] and by Fortune [2]), and adapts and uses a recent technique of Yap for the efficient construction of these diagrams.Work on this paper by the second author has been supported in part by a grant from the U.S.-Israeli Binational Science Foundation.     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.     

Measurement of the conditioned turbulence and temperature field of a premixed Bunsen burner by planar laser Rayleigh scattering and stereo particle image velocimetry

The turbulence and temperature field of Bunsen-type turbulent lean methane/air flames has been investigated using planar laser Rayleigh scattering (PLRS) and stereo particle image velocimetry (stereo PIV). Temporally averaged reaction progress variable plots have been computed from PLRS measurements in order to provide a basis with regards to the verification of computational fluid dynamics (CFD) models. Turbulence was characterised by stereo PIV in one plane for all three velocity components. Averaged velocity fields have been calculated, as well as Reynolds-decomposed fluctuation vector fields. Conditioned root mean square (RMS) values of the turbulent fluctuations in terms of unburnt and burnt gas could be determined by making use of the information gained from a threshold setting procedure in the PIV raw images. Furthermore, several length scales were measured indirectly from PIV vector plots. In this context, all integral length scales being accessible with stereo PIV were computed separately for the burnt and unburnt regions and were compared to each other. It could be observed that all integral length scales increased in the burnt zone. Additionally, the conditioned Taylor and Kolmogorov lengths have been extracted from the PIV field data, derived either from the zero-radius curvature of the correlation function or from common turbulence theory relations.     

Lubricated squeezing flow of a Newtonian liquid between elastic and rigid plates

Theoretical force-time relationships were derived for squeezing flow of a Newtonian liquid between lubricated rigid and elastic plates. It is shown how the elastic number, representing the ratio between the elastic plate's rigidity and the specimen's viscosity, affects the force-time curve and under what circumstances the fluid specimen's thickness becomes a significant factor. Potential implications of the analysis in oral sensory evaluations of viscous foods are also considered.     

Interferences in the analysis of nanomolar concentrations of nitrate and phosphate in oceanic waters

This paper reports on investigations into interferences with the measurements of nanomolar nitrate + nitrite and soluble reactive phosphate (SRP) in oceanic surface seawater using a segmented continuous flow autoanalyser (SCFA) interfaced with a liquid-waveguide capillary flow-cell (LWCC). The interferences of silicate and arsenate with the analysis of SRP, the effect of sample filtration on the measurement of nanomolar nitrate + nitrite and SRP concentrations, and the stability of samples during storage are described.The investigation into the effect of arsenate (concentrations up to 100 nM) on phosphate analysis (concentrations up to 50 nM) indicated that the arsenate interference scaled linearly with phosphate concentrations, resulting in an overestimation of SRP concentrations of 4.6 ± 1.4% for an assumed arsenate concentration of 20 nM. The effect of added Si(OH)₄ was to increase SRP signals by up to 36 ± 19 nM (at 100 μM Si(OH)₄). However, at silicate concentrations below 1.5 μM, which are typically observed in oligotrophic surface ocean waters, the effect of silicate on the phosphate analysis was much smaller (≤0.78 ± 0.15 nM change in SRP). Since arsenate and silicate interferences vary between analytical approaches used for nanomolar SRP analysis, it is important that the interferences are systematically assessed in any newly developed analytical system.Filtration of surface seawater samples resulted in a decrease in concentration of 1.7-2.7 nM (±0.5 nM) SRP, and a small decrease in nitrate concentrations which was within the precision of the method (±0.6 nM). A stability study indicated that storage of very low concentration nutrient samples in the dark at 4 °C for less than 24 h resulted in no statistically significant changes in nutrient concentrations. Freezing unfiltered surface seawater samples from an oligotrophic ocean region resulted in a small but significant increase in the SRP concentration from 12.0 ± 1.3 nM (n = 3) to 14.7 ± 0.6 nM (n = 3) (Student's t-test; p = 0.021). The corresponding change in nitrate concentration was not significant (Student's t-test; p > 0.05).     

Mononuclear and dinuclear chiral vanadium(V) complexes with tridentate Schiff bases derived from R(−)-1,2-diaminopropane: Synthesis,structure, characterization and catalytic properties

A series of vanadium(V) complexes with unsymmetrical tridentate Schiff base ligands, obtained by the single condensation of R(−)-1,2-diaminopropane with salicylaldehyde and its derivatives, 2-hydroxy-1-naphthaldehyde, 2-hydroxyacetophenone, 1-hydroxy-2-acetonaphthone and 2-hydroxybenzophenone, were prepared. The complexes were characterized by elemental analysis and by their IR, CD, UV–Vis, 1D (¹H, ⁵¹V) and 2D (COSY, NOESY, gHSQC) NMR spectra. Crystal structures of the mononuclear complex {R(−)-2-amino-1-N-[(2′-oxido-κO-4′,6′-dimethoxyphenyl)methylene]aminopropane-κ²N}dioxidovanadium(V), VO₂(C₁₂H₁₇N₂O₃), 4, and of the dinuclear complex, di-μ-oxido-bis({R(−)-2-[1-(2-aminopropylimino)ethyl]-4-methylphenolato-κ³N,N′,O}oxidovanadium(V)), V₂O₄(C₁₁H₁₅N₂O)₂, 5, have been obtained by X-ray diffraction studies. The structure of 4 was revealed to be a distorted trigonal–bipyramidal coordination geometry, rarely encountered in VO₂(tridentate Schiff base) complexes. Complexes 2 and 3 have the ability to catalyze the oxidation of prochiral sulfide substrates PhSR (R = Me, Bz) utilizing hydrogen peroxide or cumene hydroperoxide (CHPO) as the oxidant.     

Construction of the tricyclic 5-7-6 scaffold of fungi-derived diterpenoids. Total synthesis of (±)-heptemerone G and an approach to Danishefsky's intermediate for guanacastepene A synthesis

An efficient and operationally simple synthesis of the neodolestane diterpenoids (±)-heptemerone G and (±)-guanacastepene A is reported. The common tricyclic scaffold (±)-4 was prepared from 2-methylcyclopent-2-en-1-one via 23 isolated intermediates in 5.1% yield. The key features include a novel annulation sequence combining tandem conjugate addition, methylenation, and metathesis reaction and completely diastereoselective transformation of the azulene derivative 23 into rings AB building block 32. Stereochemistry of alkylation of both saturated trans-azulene enolate 38 and its α,β-unsaturated counterpart 48 was examined. Rather surprisingly, a different facial selectivity was recorded. Several synthetic methods were modified or developed, including an alternative methodology for the Wharton-type rearrangement, ketalization of epimerizable ketone under mild conditions, and efficient alkylation of a ketone via its kinetic enolate.