Practical Path Guiding for Efficient Light‐Transport Simulation

We present a robust, unbiased technique for intelligent light‐path construction in path‐tracing algorithms. Inspired by existing path‐guiding algorithms, our method learns an approximate representation of the scene's spatio‐directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio‐directional hybrid data structure, referred to as SD‐tree, for storing and sampling incident radiance. The SD‐tree consists of an upper part—a binary tree that partitions the 3D spatial domain of the light field—and a lower part—a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD‐tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular‐glossy light transport, achieving better performance than previous state‐of‐the‐art algorithms.     

Secret-Sharing Schemes for Very Dense Graphs

A secret-sharing scheme realizes a graph if every two vertices connected by an edge can reconstruct the secret while every independent set in the graph does not get any information on the secret. Similar to secret-sharing schemes for general access structures, there are gaps between the known lower bounds and upper bounds on the share size for graphs. Motivated by the question of what makes a graph “hard” for secret-sharing schemes (that is, they require large shares), we study very dense graphs, that is, graphs whose complement contains few edges. We show that if a graph with \(n\) vertices contains \(\left( {\begin{array}{c}n\\ 2\end{array}}\right) -n^{1+\beta }\) edges for some constant \(0 \le \beta <1\), then there is a scheme realizing the graph with total share size of \(\tilde{O}(n^{5/4+3\beta /4})\). This should be compared to \(O(n^2/\log (n))\), the best upper bound known for the total share size in general graphs. Thus, if a graph is “hard,” then the graph and its complement should have many edges. We generalize these results to nearly complete \(k\)-homogeneous access structures for a constant \(k\). To complement our results, we prove lower bounds on the total share size for secret-sharing schemes realizing very dense graphs, e.g., for linear secret-sharing schemes, we prove a lower bound of \(\Omega (n^{1+\beta /2})\) for a graph with \(\left( {\begin{array}{c}n\\ 2\end{array}}\right) -n^{1+\beta }\) edges.     

Interplay between size and crystal structure of molybdenum dioxide nanoparticles--synthesis, growth mechanism, and electrochemical performance

A detailed study is presented on the formation of MoO(2) nanoparticles from the dissolution of the precursor to the final rodlike product, with a focus on the exploration of the inorganic reaction occurring ahead of the nucleation step, and interplay between size and crystal structure of MoO(2). In situ X-ray absorption spectroscopy experiments show that the crystallization and the growth process of MoO(2) nanorods is initiated by rapid reduction of the MoO(2) Cl(2) precursor in benzyl alcohol and acetophenone. This reaction triggers the nucleation of 2 nm MoO(2) particles with spherical shape and hexagonal crystal structure. The transformation from spheres into rods emerges as a complex process driven by oriented attachment. High-resolution transmission electron microscopy and X-ray diffraction results provide evidence that the 2 nm particles first aggregate into 5-20 nm-large oriented assemblies. The increase in particle size induces the phase transition from hexagonal to the less symmetrical monoclinic crystal structure, and finally the transformation into rods. Is it shown that electrodes for lithium-ion batteries based on MoO(2) nanorods have a long-term cycling life. The specific discharge capacity even after 200 cycles at a discharge rate of 1 C is about 300 Ah kg(-1) .     

Housing Inequality in the United States: Explaining the White-Minority Disparities in Homeownership

As the homeownership rate in the United States reached its highest ever level in 2004, the distribution of homeownership remained uneven along racial and ethnic lines. Using data from the 2005–2007 3-Year Sample of the American Community Survey (ACS), this paper employs a multivariate regression model and a decomposition technique to delineate the socio-economic and demographic characteristics as well as the immigration and spatial patterns that shape racial and ethnic inequality in homeownership. The findings reveal three distinct patterns; the Asian-white homeownership gap is explained entirely by differences in immigration and spatial patterns of residence, whereas the disadvantage of blacks and Puerto Ricans is attributable to demographic, socio-economic and unobserved factors. For Mexicans and other Hispanics, all four sources influence homeownership patterns, with socio-economic factors relatively important for Mexicans and spatial variables relatively important for other Hispanics.     

Ribotyping and biotyping of Lactobacillus helveticus from the koumiss

The lactic acid bacteria are very important components involved in the milk products processing. Lactobacillus helveticus, a homofermentative thermophilic lactobacillus commonly occurring in cheeses, has been isolated as the prevailing species in natural koumiss in this work. The species identification of six studied L. helveticus strains was based on rep-PCR fingerprinting with (GTG)₅ primer. Biotyping (API 50CH kit, conventional tests) showed phenotypic heterogeneity among isolates and enabled the identification to the genus Lactobacillus only. Ribotyping with restriction enzyme EcoRI yielded a strain-specific restriction patterns and allowed good strain differentiation. Obtained ribotypes of the isolates originating from the koumiss gave unique band patterns with low similarity to the selected reference cultures of L. helveticus. Despite low number of strains analyzed, the ribotype data showed certain heterogeneity that seemed to be not only strain dependent, but also related to the source of isolates. We concluded that analyzed isolates from koumiss represent a new ecovar, L. helveticus ecovar Koumiss.