Construction of analytical many body wave functions for correlated bosons in a harmonic trap

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions, and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate, that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.Comment: 4 pages, 2 Figure

Explicitly correlated trial wave functions in Quantum Monte Carlo calculations of excited states of Be and Be-

We present a new form of explicitly correlated wave function whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of non-linear parameters usually encountered with basis sets of explicitly correlated wave functions. With this trial wave function we succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We applied this wave function to the calculation of the energies of Be 3P (1s22p2) and Be- 4So (1s22p3) by variational and diffusion Monte Carlo methods. The results compare favorably with those obtained by different types of explicitly correlated trial wave functions already described in the literature. The energies obtained are improved with respect to the best variational ones found in literature, and within one standard deviation from the estimated non-relativistic limitsComment: 19 pages, no figures, submitted to J. Phys.

webPRC: the Profile Comparer for alignment-based searching of public domain databases

Profile–profile methods are well suited to detect remote evolutionary relationships between protein families. Profile Comparer (PRC) is an existing stand-alone program for scoring and aligning hidden Markov models (HMMs), which are based on multiple sequence alignments. Since PRC compares profile HMMs instead of sequences, it can be used to find distant homologues. For this purpose, PRC is used by, for example, the CATH and Pfam-domain databases. As PRC is a profile comparer, it only reports profile HMM alignments and does not produce multiple sequence alignments. We have developed webPRC server, which makes it straightforward to search for distant homologues or similar alignments in a number of domain databases. In addition, it provides the results both as multiple sequence alignments and aligned HMMs. Furthermore, the user can view the domain annotation, evaluate the PRC hits with the Jalview multiple alignment editor and generate logos from the aligned HMMs or the aligned multiple alignments. Thus, this server assists in detecting distant homologues with PRC as well as in evaluating and using the results. The webPRC interface is available at http://www.ibi.vu.nl/programs/prcwww/

The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+21+\sqrt{2}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\in [-2,2]$ (the case $n=0$ corresponding to SAWs). We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be $y_{\rm c}=1+2/\sqrt{2-n}.$ This value plays a crucial role in our generalized identity, just as the value of growth constant did in Smirnov's identity. For the case $n=0$, corresponding to \saws\ interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height $T$, taken at its critical point $1/\mu$, tends to 0 as $T$ increases, as predicted from SLE theory.Comment: Major revision, references updated, 25 pages, 13 figure

The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

Evaluation of 3D-Jury on CASP7 models

<p>Abstract</p> <p>Background</p> <p>3D-Jury, the structure prediction consensus method publicly available in the Meta Server <url>http://meta.bioinfo.pl/</url>, was evaluated using models gathered in the 7^{<it>th </it>}round of the Critical Assessment of Techniques for Protein Structure Prediction (CASP7). 3D-Jury is an automated expert process that generates protein structure meta-predictions from sets of models obtained from partner servers.</p> <p>Results</p> <p>The performance of 3D-Jury was analysed for three aspects. First, we examined the correlation between the 3D-Jury score and a model quality measure: the number of correctly predicted residues. The 3D-Jury score was shown to correlate significantly with the number of correctly predicted residues, the correlation is good enough to be used for prediction. 3D-Jury was also found to improve upon the competing servers' choice of the best structure model in most cases. The value of the 3D-Jury score as a generic reliability measure was also examined. We found that the 3D-Jury score separates bad models from good models better than the reliability score of the original server in 27 cases and falls short of it in only 5 cases out of a total of 38. We report the release of a new Meta Server feature: instant 3D-Jury scoring of uploaded user models.</p> <p>Conclusion</p> <p>The 3D-Jury score continues to be a good indicator of structural model quality. It also provides a generic reliability score, especially important for models that were not assigned such by the original server. Individual structure modellers can also benefit from the 3D-Jury scoring system by testing their models in the new instant scoring feature <url>http://meta.bioinfo.pl/compare_your_model_example.pl</url> available in the Meta Server.</p

Island method for estimating the statistical significance of profile-profile alignment scores

<p>Abstract</p> <p>Background</p> <p>In the last decade, a significant improvement in detecting remote similarity between protein sequences has been made by utilizing alignment profiles in place of amino-acid strings. Unfortunately, no analytical theory is available for estimating the significance of a gapped alignment of two profiles. Many experiments suggest that the distribution of local profile-profile alignment scores is of the Gumbel form. However, estimating distribution parameters by random simulations turns out to be computationally very expensive.</p> <p>Results</p> <p>We demonstrate that the background distribution of profile-profile alignment scores heavily depends on profiles' composition and thus the distribution parameters must be estimated independently, for each pair of profiles of interest. We also show that accurate estimates of statistical parameters can be obtained using the "island statistics" for profile-profile alignments.</p> <p>Conclusion</p> <p>The island statistics can be generalized to profile-profile alignments to provide an efficient method for the alignment score normalization. Since multiple island scores can be extracted from a single comparison of two profiles, the island method has a clear speed advantage over the direct shuffling method for comparable accuracy in parameter estimates.</p

Considering scores between unrelated proteins in the search database improves profile comparison

<p>Abstract</p> <p>Background</p> <p>Profile-based comparison of multiple sequence alignments is a powerful methodology for the detection remote protein sequence similarity, which is essential for the inference and analysis of protein structure, function, and evolution. Accurate estimation of statistical significance of detected profile similarities is essential for further development of this methodology. Here we analyze a novel approach to estimate the statistical significance of profile similarity: the explicit consideration of background score distributions for each database template (subject).</p> <p>Results</p> <p>Using a simple scheme to combine and analytically approximate query- and subject-based distributions, we show that (i) inclusion of background distributions for the subjects increases the quality of homology detection; (ii) this increase is higher when the distributions are based on the scores to all known non-homologs of the subject rather than a small calibration subset of the database representatives; and (iii) these all known non-homolog distributions of scores for the subject make the dominant contribution to the improved performance: adding the calibration distribution of the query has a negligible additional effect.</p> <p>Conclusion</p> <p>The construction of distributions based on the complete sets of non-homologs for each subject is particularly relevant in the setting of structure prediction where the database consists of proteins with solved 3D structure (PDB, SCOP, CATH, etc.) and therefore structural relationships between proteins are known. These results point to a potential new direction in the development of more powerful methods for remote homology detection.</p

Detecting Remote Evolutionary Relationships among Proteins by Large-Scale Semantic Embedding

Virtually every molecular biologist has searched a protein or DNA sequence database to find sequences that are evolutionarily related to a given query. Pairwise sequence comparison methods—i.e., measures of similarity between query and target sequences—provide the engine for sequence database search and have been the subject of 30 years of computational research. For the difficult problem of detecting remote evolutionary relationships between protein sequences, the most successful pairwise comparison methods involve building local models (e.g., profile hidden Markov models) of protein sequences. However, recent work in massive data domains like web search and natural language processing demonstrate the advantage of exploiting the global structure of the data space. Motivated by this work, we present a large-scale algorithm called ProtEmbed, which learns an embedding of protein sequences into a low-dimensional “semantic space.” Evolutionarily related proteins are embedded in close proximity, and additional pieces of evidence, such as 3D structural similarity or class labels, can be incorporated into the learning process. We find that ProtEmbed achieves superior accuracy to widely used pairwise sequence methods like PSI-BLAST and HHSearch for remote homology detection; it also outperforms our previous RankProp algorithm, which incorporates global structure in the form of a protein similarity network. Finally, the ProtEmbed embedding space can be visualized, both at the global level and local to a given query, yielding intuition about the structure of protein sequence space