An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a new and efficient grid-free random walk method. Based on a modified `` Walk On Spheres" (WOS) algorithm \cite{Elepov-Mihailov1973} for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. The new simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.Comment: 12 pages, 5 figure

On the Rapid Estimation of Permeability for Porous Media Using Brownian Motion Paths

We describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample and terminate on contacting the porous sample. The first method associates the "penetration depth" with a specific property of the Brownian paths, then uses the standard relation between penetration depth and permeability to calculate the latter. The second method uses Brownian paths to calculate an effective capacitance for the sample, then relates the capacitance, via angle-averaging theorems to the translational hydrodynamic friction of the sample. Finally, a result of Felderhof is used to relate the latter quantity to the permeability of the sample. We find that the penetration depth method is highly accurate in predicting permeability of porous material

Algebraic Properties of Riemannian Manifolds

Algebraic properties are explored for the curvature tensors of Riemannian manifolds, using the irreducible decomposition of curvature tensors. Our method provides a powerful tool to analyze the irreducible basis as well as an algorithm to determine the linear dependence of arbitrary Riemann polynomials. We completely specify 13 independent basis elements for the quartic scalars and explicitly find 13 linear relations among 26 scalar invariants. Our method provides several completely new results, including some clues to identify 23 independent basis elements from 90 quintic scalars, that are difficult to find otherwise.Comment: A few typos corrected; 40 pages (4 appendices: 16 pages). To appear in General Relativity and Gravitatio

Shock Tube and Modeling Study of the H + O2 = OH + O Reaction over a Wide Range of Composition, Pressure, and Temperature

The rate coefficient of the reaction H + 02 = OH + 0 was determined using OH laser absorption spectroscopy behind reflected shock waves over the temperature range 1050-2500 K and the pressure range 0.7-4.0 atm. Eight mixtures and three stoichiometries were used. Two distinct and independent criteria were employed in the evaluation of k(sub 1). Our recommended expression for k(sub 1) is k(sub 1) = 7.13 x 10(exp 13)exp(-6957 K/T) cm(exp 3)mol(exp -1)s(exp -1) with a statistical uncertainty of 6%. A critical review of recent evaluations of k(sub 1) yields a consensus expression given by k(sub 1) = 7.82 x 10(exp 13)exp(-7105 K/7) cm(exp 3)mol(exp -1)s(exp -1) over the temperature range 960-5300 K. We do not support a non-Arrhenius rate coefficient expression, nor do we find evidence of composition dependence upon the determination of k(sub 1)

Adaptive Superpixel for Active Learning in Semantic Segmentation

Learning semantic segmentation requires pixel-wise annotations, which can be time-consuming and expensive. To reduce the annotation cost, we propose a superpixel-based active learning (AL) framework, which collects a dominant label per superpixel instead. To be specific, it consists of adaptive superpixel and sieving mechanisms, fully dedicated to AL. At each round of AL, we adaptively merge neighboring pixels of similar learned features into superpixels. We then query a selected subset of these superpixels using an acquisition function assuming no uniform superpixel size. This approach is more efficient than existing methods, which rely only on innate features such as RGB color and assume uniform superpixel sizes. Obtaining a dominant label per superpixel drastically reduces annotators' burden as it requires fewer clicks. However, it inevitably introduces noisy annotations due to mismatches between superpixel and ground truth segmentation. To address this issue, we further devise a sieving mechanism that identifies and excludes potentially noisy annotations from learning. Our experiments on both Cityscapes and PASCAL VOC datasets demonstrate the efficacy of adaptive superpixel and sieving mechanisms

Yang-Lee Zeros of the Triangular Ising Antiferromagnets

Using both the exact enumeration method (microcanonical transfer matrix) for a small system (L = 9) and the Wang-Landau Monte Carlo algorithm for large systems to L = 30, we obtain the exact and approximate densities of states g(M,E), as a function of magnetization M and exchange energy E, for the triangular-lattice Ising model. Based on the density of states g(M,E), we investigate the phase transition properties of Yang-Lee zeros for the triangular Ising antiferromagnets and obtain the magnetic exponents at various temperatures

High temperature kinetic study of the reactions H + O2 = OH + O and O + H2 = OH + H in H2/O2 system by shock tube-laser absorption spectroscopy

The reactions: (1) H + O2 = OH + O; and (2) O + H2 = OH + H are the most important elementary reactions in gas phase combustion. They are the main chain-branching reaction in the oxidation of H2 and hydrocarbon fuels. In this study, rate coefficients of the reactions and have been measured over a wide range of composition, pressure, density and temperature behind the reflected shock waves. The experiments were performed using the shock tube - laser absorption spectroscopic technique to monitor OH radicals formed in the shock-heated H2/O2/Ar mixtures. The OH radicals were detected using the P(1)(5) line of (0,0) band of the A(exp 2) Sigma(+) from X(exp 2) Pi transition of OH at 310.023 nm (air). The data were analyzed with the aid of computer modeling. In the experiments great care was exercised to obtain high time resolution, linearity and signal-to-noise. The results are well represented by the Arrhenius expressions. The rate coefficient expression for reaction (1) obtained in this study is k(1) = (7.13 +/- 0.31) x 10(exp 13) exp(-6957+/- 30 K/T) cu cm/mol/s (1050 K less than or equal to T less than or equal to 2500 K) and a consensus expression for k(1) from a critical review of the most recent evaluations of k(1) (including our own) is k(1) = 7.82 x 10(exp 13) exp(-7105 K/T) cu cm/mol/s (960 K less than or equal to T less than or equal to 5300 K). The rate coefficient expression of k(2) is given by k(2) = (1.88 +/- 0.07) x 10(exp 14) exp(-6897 +/- 53 K/T) cu cm/mol/s (1424 K less than or equal to T less than or equal to 2427 K). For k(1), the temperature dependent A-factor and the correlation between the values of k(1) and the inverse reactant densities were not found. In the temperature range of this study, non-Arrhenius expression of k(2) which shows the upward curvature was not supported

An integrated database-pipeline system for studying single nucleotide polymorphisms and diseases

<p>Abstract</p> <p>Background</p> <p>Studies on the relationship between disease and genetic variations such as single nucleotide polymorphisms (SNPs) are important. Genetic variations can cause disease by influencing important biological regulation processes. Despite the needs for analyzing SNP and disease correlation, most existing databases provide information only on functional variants at specific locations on the genome, or deal with only a few genes associated with disease. There is no combined resource to widely support gene-, SNP-, and disease-related information, and to capture relationships among such data. Therefore, we developed an integrated database-pipeline system for studying SNPs and diseases.</p> <p>Results</p> <p>To implement the pipeline system for the integrated database, we first unified complicated and redundant disease terms and gene names using the Unified Medical Language System (UMLS) for classification and noun modification, and the HUGO Gene Nomenclature Committee (HGNC) and NCBI gene databases. Next, we collected and integrated representative databases for three categories of information. For genes and proteins, we examined the NCBI mRNA, UniProt, UCSC Table Track and MitoDat databases. For genetic variants we used the dbSNP, JSNP, ALFRED, and HGVbase databases. For disease, we employed OMIM, GAD, and HGMD databases. The database-pipeline system provides a disease thesaurus, including genes and SNPs associated with disease. The search results for these categories are available on the web page <url>http://diseasome.kobic.re.kr/</url>, and a genome browser is also available to highlight findings, as well as to permit the convenient review of potentially deleterious SNPs among genes strongly associated with specific diseases and clinical phenotypes.</p> <p>Conclusion</p> <p>Our system is designed to capture the relationships between SNPs associated with disease and disease-causing genes. The integrated database-pipeline provides a list of candidate genes and SNP markers for evaluation in both epidemiological and molecular biological approaches to diseases-gene association studies. Furthermore, researchers then can decide semi-automatically the data set for association studies while considering the relationships between genetic variation and diseases. The database can also be economical for disease-association studies, as well as to facilitate an understanding of the processes which cause disease. Currently, the database contains 14,674 SNP records and 109,715 gene records associated with human diseases and it is updated at regular intervals.</p