Multi-level higher order QMC Galerkin discretization for affine parametric operator equations

We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-level first order analysis in [\emph{F.Y.~Kuo, Ch.~Schwab, and I.H.~Sloan, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficient} (in review)] and the single level higher order analysis in [\emph{J.~Dick, F.Y.~Kuo, Q.T.~Le~Gia, D.~Nuyens, and Ch.~Schwab, Higher order QMC Galerkin discretization for parametric operator equations} (in review)]. We cover, in particular, both definite as well as indefinite, strongly elliptic systems of partial differential equations (PDEs) in non-smooth domains, and discuss in detail the impact of higher order derivatives of {\KL} eigenfunctions in the parametrization of random PDE inputs on the convergence results. Based on our \emph{a-priori} error bounds, concrete choices of algorithm parameters are proposed in order to achieve a prescribed accuracy under minimal computational work. Problem classes and sufficient conditions on data are identified where multi-level higher order QMC Petrov-Galerkin algorithms outperform the corresponding single level versions of these algorithms. Numerical experiments confirm the theoretical results

Fast QMC matrix-vector multiplication

Quasi-Monte Carlo (QMC) rules $1/N \sum_{n=0}^{N-1} f(\boldsymbol{y}_n A)$ can be used to approximate integrals of the form $\int_{[0,1]^s} f(\boldsymbol{y} A) \,\mathrm{d} \boldsymbol{y}$, where $A$ is a matrix and $\boldsymbol{y}$ is row vector. This type of integral arises for example from the simulation of a normal distribution with a general covariance matrix, from the approximation of the expectation value of solutions of PDEs with random coefficients, or from applications from statistics. In this paper we design QMC quadrature points $\boldsymbol{y}_0, ..., \boldsymbol{y}_{N-1} \in [0,1]^s$ such that for the matrix $Y = (\boldsymbol{y}_{0}^\top, ..., \boldsymbol{y}_{N-1}^\top)^\top$ whose rows are the quadrature points, one can use the fast Fourier transform to compute the matrix-vector product $Y \boldsymbol{a}^\top$, $\boldsymbol{a} \in \mathbb{R}^s$, in $\mathcal{O}(N \log N)$ operations and at most $s-1$ extra additions. The proposed method can be applied to lattice rules, polynomial lattice rules and a certain type of Korobov $p$-set. The approach is illustrated computationally by three numerical experiments. The first test considers the generation of points with normal distribution and general covariance matrix, the second test applies QMC to high-dimensional, affine-parametric, elliptic partial differential equations with uniformly distributed random coefficients, and the third test addresses Finite-Element discretizations of elliptic partial differential equations with high-dimensional, log-normal random input data. All numerical tests show a significant speed-up of the computation times of the fast QMC matrix method compared to a conventional implementation as the dimension becomes large

Prediction of Body Fluids where Proteins are Secreted into Based on Protein Interaction Network

Determining the body fluids where secreted proteins can be secreted into is important for protein function annotation and disease biomarker discovery. In this study, we developed a network-based method to predict which kind of body fluids human proteins can be secreted into. For a newly constructed benchmark dataset that consists of 529 human-secreted proteins, the prediction accuracy for the most possible body fluid location predicted by our method via the jackknife test was 79.02%, significantly higher than the success rate by a random guess (29.36%). The likelihood that the predicted body fluids of the first four orders contain all the true body fluids where the proteins can be secreted into is 62.94%. Our method was further demonstrated with two independent datasets: one contains 57 proteins that can be secreted into blood; while the other contains 61 proteins that can be secreted into plasma/serum and were possible biomarkers associated with various cancers. For the 57 proteins in first dataset, 55 were correctly predicted as blood-secrete proteins. For the 61 proteins in the second dataset, 58 were predicted to be most possible in plasma/serum. These encouraging results indicate that the network-based prediction method is quite promising. It is anticipated that the method will benefit the relevant areas for both basic research and drug development

Predicting Biological Functions of Compounds Based on Chemical-Chemical Interactions

Given a compound, how can we effectively predict its biological function? It is a fundamentally important problem because the information thus obtained may benefit the understanding of many basic biological processes and provide useful clues for drug design. In this study, based on the information of chemical-chemical interactions, a novel method was developed that can be used to identify which of the following eleven metabolic pathway classes a query compound may be involved with: (1) Carbohydrate Metabolism, (2) Energy Metabolism, (3) Lipid Metabolism, (4) Nucleotide Metabolism, (5) Amino Acid Metabolism, (6) Metabolism of Other Amino Acids, (7) Glycan Biosynthesis and Metabolism, (8) Metabolism of Cofactors and Vitamins, (9) Metabolism of Terpenoids and Polyketides, (10) Biosynthesis of Other Secondary Metabolites, (11) Xenobiotics Biodegradation and Metabolism. It was observed that the overall success rate obtained by the method via the 5-fold cross-validation test on a benchmark dataset consisting of 3,137 compounds was 77.97%, which is much higher than 10.45%, the corresponding success rate obtained by the random guesses. Besides, to deal with the situation that some compounds may be involved with more than one metabolic pathway class, the method presented here is featured by the capacity able to provide a series of potential metabolic pathway classes ranked according to the descending order of their likelihood for each of the query compounds concerned. Furthermore, our method was also applied to predict 5,549 compounds whose metabolic pathway classes are unknown. Interestingly, the results thus obtained are quite consistent with the deductions from the reports by other investigators. It is anticipated that, with the continuous increase of the chemical-chemical interaction data, the current method will be further enhanced in its power and accuracy, so as to become a useful complementary vehicle in annotating uncharacterized compounds for their biological functions

Application of Non-dominated Sorting Genetic Algorithm in Calibration of HBV Rainfall-runoff Model: a Case Study of Tsengwen Reservoir Catchment in Southern Taiwan

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661

Predicting Drug-Target Interaction Networks Based on Functional Groups and Biological Features

Background: Study of drug-target interaction networks is an important topic for drug development. It is both timeconsuming and costly to determine compound-protein interactions or potential drug-target interactions by experiments alone. As a complement, the in silico prediction methods can provide us with very useful information in a timely manner. Methods/Principal Findings: To realize this, drug compounds are encoded with functional groups and proteins encoded by biological features including biochemical and physicochemical properties. The optimal feature selection procedures are adopted by means of the mRMR (Maximum Relevance Minimum Redundancy) method. Instead of classifying the proteins as a whole family, target proteins are divided into four groups: enzymes, ion channels, G-protein- coupled receptors and nuclear receptors. Thus, four independent predictors are established using the Nearest Neighbor algorithm as their operation engine, with each to predict the interactions between drugs and one of the four protein groups. As a result, the overall success rates by the jackknife cross-validation tests achieved with the four predictors are 85.48%, 80.78%, 78.49%, and 85.66%, respectively. Conclusion/Significance: Our results indicate that the network prediction system thus established is quite promising an

Neural Amortized Inference for Nested Multi-agent Reasoning

Multi-agent interactions, such as communication, teaching, and bluffing, often rely on higher-order social inference, i.e., understanding how others infer oneself. Such intricate reasoning can be effectively modeled through nested multi-agent reasoning. Nonetheless, the computational complexity escalates exponentially with each level of reasoning, posing a significant challenge. However, humans effortlessly perform complex social inferences as part of their daily lives. To bridge the gap between human-like inference capabilities and computational limitations, we propose a novel approach: leveraging neural networks to amortize high-order social inference, thereby expediting nested multi-agent reasoning. We evaluate our method in two challenging multi-agent interaction domains. The experimental results demonstrate that our method is computationally efficient while exhibiting minimal degradation in accuracy.Comment: 8 pages, 10 figure

A Comparison of Computational Methods for Identifying Virulence Factors

Bacterial pathogens continue to threaten public health worldwide today. Identification of bacterial virulence factors can help to find novel drug/vaccine targets against pathogenicity. It can also help to reveal the mechanisms of the related diseases at the molecular level. With the explosive growth in protein sequences generated in the postgenomic age, it is highly desired to develop computational methods for rapidly and effectively identifying virulence factors according to their sequence information alone. In this study, based on the protein-protein interaction networks from the STRING database, a novel network-based method was proposed for identifying the virulence factors in the proteomes of UPEC 536, UPEC CFT073, P. aeruginosa PAO1, L. pneumophila Philadelphia 1, C. jejuni NCTC 11168 and M. tuberculosis H37Rv. Evaluated on the same benchmark datasets derived from the aforementioned species, the identification accuracies achieved by the network-based method were around 0.9, significantly higher than those by the sequence-based methods such as BLAST, feature selection and VirulentPred. Further analysis showed that the functional associations such as the gene neighborhood and co-occurrence were the primary associations between these virulence factors in the STRING database. The high success rates indicate that the network-based method is quite promising. The novel approach holds high potential for identifying virulence factors in many other various organisms as well because it can be easily extended to identify the virulence factors in many other bacterial species, as long as the relevant significant statistical data are available for them