Affine-invariant geodesic geometry of deformable 3D shapes

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R³ in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.     

Implicit representation in genetic algorithms using redundancy

A new representation combining redundancy and implicit fitness constraints is introduced that performs better than a simple genetic algorithm (GA) and a structured GA in experiments. The implicit redundant representation (IRR) consists of a string that is over-specified, allowing for sections of the string to remain inactive during function evaluation. The representation does not require the user to prespecify the number of parameters to evaluate or the location of these parameters within the string. This information is obtained implicitly by the fitness function during the GA operations. The good performance of the IRR can be attributed to several factors: less disruption of existing fit members due to the increased probability of crossovers and mutation affecting only redundant material; discovery of fit members through the conversion of redundant material into essential information; and the ability to enlarge or reduce the search space dynamically by varying the number of variables evaluated by the fitness function. The IRR GA provides a more biologically parallel representation that maintains a diverse population throughout the evolution process. In addition, the IRR provides the necessary flexibility to represent unstructured problem domains that do not have the explicit constraints required by fixed representations.     

Rotational motion under pressure in the solid molecular hydrogen isotopes

Rotational states as functions of pressure for H₂, D₂, T₂ HD, and HT molecules are calculated in the corresponding molecular solids. Sudden transitions from spherically symmetric rotational states occur in para-H₂, para-T₂, ortho-D₂, and in HD and HT as the pressure increases. Only the predicted T₂ transition pressure of about 24 kbar lies within current experimentally accessible ranges. All other transitions occur in the region 150–300 kbar.Supported in part by NSF Grant No. GH-35581, National Aeronautics and Space Administration Grant No. NGR 06-002-159, and United States Energy Research and Development Administration.     

Interactive direct rendering of trivariate B-spline scalarfunctions

This paper presents a direct rendering paradigm of trivariate B-spline functions that is able to incrementally update complex volumetric data sets in the order of millions of coefficients at interactive rates of several frames per second on modern workstations. This incremental rendering scheme can hence be employed in modeling sessions of volumetric trivariate functions, offering interactive volumetric sculpting capabilities. The rendering is conducted from a fixed viewpoint and in two phases. The first, preprocessing stage accumulates the effect that the coefficients of the trivariate function have on the pixels in the image. This preprocessing stage is conducted offline and only once per trivariate and viewing direction. The second stage conducts the actual rendering of the trivariate functions. As an example, during a volumetric sculpting operation, the artist can sculpt the volume and get a displayed feedback, in interactive rates     

Electrochemical reduction of dilute nitric acid

The conditions for electrolytic reduction of dilute nitric acid without the formation of ammonia, and without the addition of foreign substances, have been investigated. Dilute nitric acid is reduced at a graphite electrode at controlled potentials, nitrogen dioxide and carbon dioxide being the main products. A mechanism for this reduction is suggested.     

Fourth molars: a clinical study

Supernumerary teeth may be found in both the primary and permanent dentition, although they are more common in the permanent dentition. Presence of a fourth molar is rare, and such a tooth is almost invariably impacted. Dental practitioners should be aware of the possibility of encountering this rare supernumerary, its diagnosis and treatment. The authors of this article conducted a survey of patients in Montreal, looking specifically at the prevalence, aetiology, diagnosis, pathology and treatment of fourth molars. Their findings are reported here, and compared with data from the literature over the past 15 years.     

The energy spectrum of isolated ortho-hydrogen molecular pairs

The orientational energy eigenvalues and eigenvectors of an isolated pair of ortho-hydrogen molecules are calculated over a range of molar volumes 7.8 cm³/moleV22.65 cm³/mole. Admixtures of free-rotator basis vectors withJ>1, used in describing the system eigenstates, are shown to provide important contributions to the qualitative structure of the eigenvalue spectrum. On this basis,J=1 is not necessarily a good quantum number. TheJ=3 band is explicitly given, and the effect of high pressures on the system is described.     

A high-pressure calculation used to determine the helium pair interaction

The pressures and compressibilities of solid³He and⁴He are calculated over the volume range 3 cm³/mole V 13 cm³/mole, using a simple Heitler-London variational approach. For volumesV 8 cm³/mole, the calculation is sufficiently exact to make possible a meaningful comparison of the results, obtained using four different semiphenomenological forms for the potential, with experimental data. The results indicate that the Beck potential is the best existing representation of the helium pair potential.     

Ground-state properties of solid H2 at high pressures

A simple variational calculation, based on a Heitler-London wave function, is used to describe the high-pressure properties of solid hydrogen at O K. The system properties are expressed as a power series in , which is utilized to investigate the onset of classical behavior. The high-pressure results for the energy and the pressure-volume relation are in close agreement with a recent calculation which used the Domb-Salter approximation. Information is given on the pressure dependence of the two-body correlations in the solid.