Replica Exchange Light Transport

We solve the light transport problem by introducing a novel unbiased Monte Carlo algorithm called replica exchange light transport, inspired by the replica exchange Monte Carlo method in the fields of computational physics and statistical information processing. The replica exchange Monte Carlo method is a sampling technique whose operation resembles simulated annealing in optimization algorithms using a set of sampling distributions. We apply it to the solution of light transport integration by extending the probability density function of an integrand of the integration to a set of distributions. That set of distributions is composed of combinations of the path densities of different path generation types: uniform distributions in the integral domain, explicit and implicit paths in light (particle/photon) tracing, indirect paths in bidirectional path tracing, explicit and implicit paths in path tracing, and implicit caustics paths seen through specular surfaces including the delta function in path tracing. The replica‐exchange light transport algorithm generates a sequence of path samples from each distribution and samples the simultaneous distribution of those distributions as a stationary distribution by using the Markov chain Monte Carlo method. Then the algorithm combines the obtained path samples from each distribution using multiple importance sampling. We compare the images generated with our algorithm to those generated with bidirectional path tracing and Metropolis light transport based on the primary sample space. Our proposing algorithm has better convergence property than bidirectional path tracing and the Metropolis light transport, and it is easy to implement by extending the Metropolis light transport.     

An approximation algorithm dependent on edge-coloring number for minimum maximal matching problem

We consider the minimum maximal matching problem, which is NP-hard (Yannakakis and Gavril (1980) [18]). Given an unweighted simple graph G=(V,E), the problem seeks to find a maximal matching of minimum cardinality. It was unknown whether there exists a non-trivial approximation algorithm whose approximation ratio is less than 2 for any simple graph. Recently, Z. Gotthilf et al. (2008) [5] presented a -approximation algorithm, where c is an arbitrary constant.In this paper, we present a -approximation algorithm based on an LP relaxation, where χ^′(G) is the edge-coloring number of G. Our algorithm is the first non-trivial approximation algorithm whose approximation ratio is independent of |V|. Moreover, it is known that the minimum maximal matching problem is equivalent to the edge dominating set problem. Therefore, the edge dominating set problem is also -approximable. From edge-coloring theory, the approximation ratio of our algorithm is , where Δ(G) represents the maximum degree of G. In our algorithm, an LP formulation for the edge dominating set problem is used. Fujito and Nagamochi (2002) [4] showed the integrality gap of the LP formulation for bipartite graphs is at least . Moreover, χ^′(G) is Δ(G) for bipartite graphs. Thus, as far as an approximation algorithm for the minimum maximal matching problem uses the LP formulation, we believe our result is the best possible.     

A systolic algorithm for Euclidean distance transform

The Euclidean distance transform is one of the fundamental operations in image processing. It has been widely used in computer vision, pattern recognition, morphological filtering, and robotics. This paper proposes a systolic algorithm that computes the Euclidean distance map of an N /spl times/ N binary image in 3N clocks on 2N/sup 2/ processing cells. The algorithm is designed so that the hardware resources are reduced; especially no multipliers are used and, thus, it facilitates VLSI implementation.     

Magnification-type x-ray imaging system: optimum design and image restoration

A magnification-type x-ray imaging system, that is, an x-ray microscope, is evaluated by taking into account the partial coherency of the illumination of the objects. The transfer characteristic proposed in an earlier paper [J. Opt. Soc. Am. A 1, 11 (1984)] is used for the evaluation, and based on the results, an optimum design for a high-resolution x-ray imaging system is discussed. The image restoration method for this system is also shown.     

Dominant stress region for crack initiation at interface edge of microdot on a substrate

In order to examine the mechanics of crack initiation at the free interface edge of a microcomponent on a substrate, delamination tests are carried out for two specimen shapes of Cr microdots on a SiO₂ substrate. The microdots of the first specimen are shaped like the frustum of a round cone. The Cr microdots are successfully delaminated from the SiO₂ substrate in a brittle manner and the critical load is measured by atomic force microscopy (AFM) with a lateral loading apparatus. Stress analysis reveals that a singular stress field exists near the interface edge and the strength for the crack initiation is governed by the intensified normal stress field. The critical stress intensity parameter is evaluated as K_σC ≈ 0.24 MPa m^0.39. Similar delamination tests are conducted for microdots shaped like the frustum of an oval cone. The stress distributions at the crack initiation of this specimen shape show a higher normal stress than the first specimen shape in the region near the interface edge of about x < 40 nm, while it is lower in the region of about x > 50 nm (x: distance from the edge). This suggests a limitation of conventional fracture mechanics: namely, the crack initiation in these specimens is not uniquely governed by the intensity of the singular field. It is found that the delamination crack is initiated when the averaged stress σ_ya in the region of 90-130 nm reaches 190-270 MPa, regardless of the specimen shape. This indicates that the dominant stress region of crack initiation is roughly estimated as 90-130 nm and the criterion is given in terms of the averaged stress in the region.     

Domain characteristics and chemical bonds of lithium niobate

Domain characteristics such as domain shape, domain switching, and etching rate at Z-surfaces of lithium niobate (LN) single crystals are comprehensively studied from the chemical bonding viewpoint. The present work shows that the domain characteristics are closely correlated to anisotropic bonding behaviors of constituent ions, which may be regarded as a microscopic reflection of detailed conditions of the chemical bonding geometry and strength of Li⁺ and Nb⁵⁺ cations in the LN crystallographic frame.     

LaBGeO5 single crystals in glass and second-harmonic generation

Flower-shaped crystals with diameters of 100–200 μm consisting of LaBGeO₅ (LBGO) single crystals similar to petals were observed in the interior of transparent LBGO surface-crystallized glasses. Each flower-shaped crystal was radially grown from the surface of the included bubbles. A more intense second-harmonic generation was observed from the LBGO crystallized glasses with the flower-shaped LBGO single crystals compared to the samples without such crystals based on the Maker fringe technique and second-harmonic (SH) generation microscopy. The SH intensity for the flower-shaped LBGO single crystals monotonically decreased with increasing temperature up to 350 °C, less than the Curie temperature reported so far (530 °C). It is considered that the internal compressive stress induced by the difference in the thermal expansion between the LBGO single crystal and the corresponding glass affect the ferroelectric property of the flower-shaped LBGO single crystals in glass.     

Calculations from texture of earing in deep drawing for FCC metal sheets

The present study aims to calculate the height at each peripheral position of a cup drawn from polycrystalline sheet using texture data. In the analytical treatment the polycrystalline sheet is simplified to an aggregation of many single crystals with various orientations, and the texture is represented by a three-dimensional crystallite orientation distribution function. The ear is calculated crystallographically using the orientation distribution function as a volume fraction of a certain oriented crystal. In the experiment aluminium, Al-Mg alloy and copper sheets which are treated under various conditions of cold rolling and heat treatment are used. The average textures over the thicknesses of the sheets are measured by the Schulz reflection method. The calculated ears based on the measured textures are compared with the experimental ears for each material. The results show that all the principal features of the ears of drawn cups are predicted satisfactorily by the calculation.     

Preparation and Intestinal Immunostimulating Activity of Low Molecular Weight Alginate from Saccharina (Laminaria) Species in Japan

We studied the structure of alginates extracted from five commercial Saccharina (Laminaria) species including three varieties (eight samples in all) harvested in Hokkaido, Japan. The algae used were Saccharina japonica, S. japonica var. diabolica, S. japonica var. ochotensis, S. japonica var. religiosa, S. longissima, S. coriacea, S. angustata, and S. sculpera (Kjellmaniella crassiforia). These alginates have molar fractions of mannuronic acid (F_M) ranging from 0.68 to 0.76 and weight average molecular weights (M_ws) ranging from 511,000 to 616,000. Alginate samples from both S. angustata (F_M = 0.76) and S. longissima (F_M = 0.68) showed intestinal immunological activity through Peyer’s patch cells of C3H/HeJ mice. Low molecular weight S. angustata alginate (F_M = 0.75, M_w = 70,000) degraded using a wet pulverizing system showed higher activity than the native one.