Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.Comment: 18 pages, 6 figure

The qq-log-convexity of Domb's polynomials

In this paper, we prove the $q$-log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of $\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the $q$-log-convexity of Narayana polynomials of type $B$ and a criterion for determining $q$-log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273

On the qq-log-convexity conjecture of Sun

In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$ and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture

Geochemistry and petrogenesis of volcanic rocks from Daimao Seamount (South China Sea) and their tectonic implications

The South China Sea (SCS) experienced three episodes of seafloor spreading and left three fossil spreading centers presently located at 18°N, 17°N and 15.5°N. Spreading ceased at these three locations during magnetic anomaly 10, 8, and 5c, respectively. Daimao Seamount (16.6. Ma) was formed 10. my after the cessation of the 17°N spreading center. Volcaniclastic rocks and shallow-water carbonate facies near the summit of Daimao Seamount provide key information on the seamount's geologic history. New major and trace element and Sr-Nd-Pb isotopic compositions of basaltic breccia clasts in the volcaniclastics suggest that Daimao and other SCS seamounts have typical ocean island basalt-like composition and possess a 'Dupal' isotopic signature. Our new analyses, combined with available data, indicate that the basaltic foundation of Daimao Seamount was formed through subaqueous explosive volcanic eruptions at 16.6. Ma. The seamount subsided rapidly (>. 0.12. mm/y) at first, allowing the deposition of shallow-water, coral-bearing carbonates around its summit and, then, at a slower rate (<. 0.12. mm/y). We propose that the parental magmas of SCS seamount lavas originated from the Hainan mantle plume. In contrast, lavas from contemporaneous seamounts in other marginal basins in the western Pacific are subduction-related

Tertiary structure-based prediction of conformational B-cell epitopes through B factors

Motivation: B-cell epitope is a small area on the surface of an antigen that binds to an antibody. Accurately locating epitopes is of critical importance for vaccine development. Compared with wet-lab methods, computational methods have strong potential for efficient and large-scale epitope prediction for antigen candidates at much lower cost. However, it is still not clear which features are good determinants for accurate epitope prediction, leading to the unsatisfactory performance of existing prediction methods. Method and results: We propose a much more accurate B-cell epitope prediction method. Our method uses a new feature B factor (obtained from X-ray crystallography), combined with other basic physicochemical, statistical, evolutionary and structural features of each residue. These basic features are extended by a sequence window and a structure window. All these features are then learned by a two-stage random forest model to identify clusters of antigenic residues and to remove isolated outliers. Tested on a dataset of 55 epitopes from 45 tertiary structures, we prove that our method significantly outperforms all three existing structure-based epitope predictors. Following comprehensive analysis, it is found that features such as B factor, relative accessible surface area and protrusion index play an important role in characterizing B-cell epitopes. Our detailed case studies on an HIV antigen and an influenza antigen confirm that our second stage learning is effective for clustering true antigenic residues and for eliminating self-made prediction errors introduced by the first-stage learning. © 2014 The Author. Published by Oxford University Press. All rights reserved

Positive-unlabeled learning for the prediction of conformational B-cell epitopes

© 2015 Ren et al. Background: The incomplete ground truth of training data of B-cell epitopes is a demanding issue in computational epitope prediction. The challenge is that only a small fraction of the surface residues of an antigen are confirmed as antigenic residues (positive training data); the remaining residues are unlabeled. As some of these uncertain residues can possibly be grouped to form novel but currently unknown epitopes, it is misguided to unanimously classify all the unlabeled residues as negative training data following the traditional supervised learning scheme. Results: We propose a positive-unlabeled learning algorithm to address this problem. The key idea is to distinguish between epitope-likely residues and reliable negative residues in unlabeled data. The method has two steps: (1) identify reliable negative residues using a weighted SVM with a high recall; and (2) construct a classification model on the positive residues and the reliable negative residues. Complex-based 10-fold cross-validation was conducted to show that this method outperforms those commonly used predictors DiscoTope 2.0, ElliPro and SEPPA 2.0 in every aspect. We conducted four case studies, in which the approach was tested on antigens of West Nile virus, dihydrofolate reductase, beta-lactamase, and two Ebola antigens whose epitopes are currently unknown. All the results were assessed on a newly-established data set of antigen structures not bound by antibodies, instead of on antibody-bound antigen structures. These bound structures may contain unfair binding information such as bound-state B-factors and protrusion index which could exaggerate the epitope prediction performance. Source codes are available on request