This paper proposes a model predictive control method based on a dynamic event-triggered strategy for high-precision formation control of spacecraft formations using continuous low thrust. An optimal formation control problem is formulated based on the J2 linear time-varying relative dynamics using the Legendre pseudospectral method, and the model predictive controller is designed based on this optimization problem. Thereafter, a dynamic event-triggered strategy is introduced in the model predictive controller, in which the optimization problem is solved only when the event-triggered condition is violated. As a result, the computational pressure of the model predictive control algorithm is greatly reduced without increasing fuel consumption or degrading control accuracy. Meanwhile, the dynamic event-triggered condition allows for relatively even event-triggered intervals, which is more conducive to engineering applications. The feasibility and stability of this control strategy are demonstrated, and the simulation results under two different formation control scenarios show that the proposed controller achieves equivalent control performance to the conventional model predictive controller, and the computational pressure is greatly reduced by designing the dynamic event-triggered condition. Note to Practitioners—This paper presents a study on an event-triggered model predictive control (MPC) strategy for spacecraft formation control. The objective is to achieve high-precision control for spacecraft formations, including formation maintenance and reconfiguration, in the presence of bounded external disturbances. The proposed control strategy significantly reduces the computational burden of the model predictive control by introducing a dynamic event-triggered policy while preserving the control performance of the MPC. Moreover, the design of event-triggered conditions effectively prevents the occurrence of the Zeno phenomenon. The feasibility, system stability, and convergence of the control strategy are rigorously analyzed, and simulation-based verification is conducted in a binary-star formation control scenario. It is important to note that the event-triggered model predictive control strategy presented in this paper is applicable to various leader-follower type formation systems, extending beyond the scope of spacecraft formation control.

Polygenic risk score (PRS) has been recently developed for predicting complex traits and drug responses. It remains unknown whether multi-trait PRS (mtPRS) methods, by integrating information from multiple genetically correlated traits, can improve prediction accuracy and power for PRS analysis compared with single-trait PRS (stPRS) methods. In this paper, we first review commonly used mtPRS methods and find that they do not directly model the underlying genetic correlations among traits, which has been shown to be useful in guiding multi-trait association analysis in the literature. To overcome this limitation, we propose a mtPRS-PCA method to combine PRSs from multiple traits with weights obtained from performing principal component analysis (PCA) on the genetic correlation matrix. To accommodate various genetic architectures covering different effect directions, signal sparseness and across-trait correlation structures, we further propose an omnibus mtPRS method (mtPRS-O) by combining P values from mtPRS-PCA, mtPRS-ML (mtPRS based on machine learning) and stPRSs using Cauchy Combination Test. Our extensive simulation studies show that mtPRS-PCA outperforms other mtPRS methods in both disease and pharmacogenomics (PGx) genome-wide association studies (GWAS) contexts when traits are similarly correlated, with dense signal effects and in similar effect directions, and mtPRS-O is consistently superior to most other methods due to its robustness under various genetic architectures. We further apply mtPRS-PCA, mtPRS-O and other methods to PGx GWAS data from a randomized clinical trial in the cardiovascular domain and demonstrate performance improvement of mtPRS-PCA in both prediction accuracy and patient stratification as well as the robustness of mtPRS-O in PRS association test.

This paper investigates the attitude tracking problem for spacecraft with limited communication, network congestion, unknown model parameters, actuator saturation, and external disturbances. To alleviate communication load, a novel sigmoid event-triggered mechanism is proposed with the special ability to guarantee a high minimum inter-execution time to avoid network congestion like package loss or time delay effectively. A neural network-based adaptive control algorithm is designed to deal with unknown model parameters. Besides, the problem of actuator saturation is tackled by introducing a dynamic loop gain function-based approach. System stability is proved by Lyapunov stability analysis and the high minimum inter-event time is substantiated by Zeno Behavior analysis with explanatory remarks. Numerical simulation results also show that a high minimum inter-event time and a high average inter-event time can be realized on the premise of high attitude tracking accuracy. Compared with all the previous studies, the ratio of the minimum inter-execution time to the average minimum inter-execution time has been improved by nearly 10 times with the proposed approach. Note to Practitioners—This paper was motivated by the problem of spacecraft attitude takeover control, but it also applies to other aperiodic discrete-time control systems. Existing event-triggered control methods have solved the problem of limited communication for attitude takeover control of spacecraft by reducing the number of times wireless communication is required. This paper proposes a new method for realizing quasi-periodic control with a large time gap between any two consistent control impulses using a hyperbolic tangent function or another sigmoid function in an event-triggered mechanism. The proposed sigmoid event-triggered mechanism (ETM) can magnify the event-triggered threshold dozens of times in a short time to avoid unnecessary frequent triggering without decreasing the precision of control. It’s feasible to employ the proposed sigmoid ETM to deal with limited communication and network congestion in other network control systems that are constructed with similar dynamic structures. Furthermore, it would be marvelous if we could transform this sigmoid ETM into a high-efficiency decision-making mechanism in some control systems without using a wireless network. Now we are studying how to realize orbital-attitude (maneuver) control with a relatively average time interval and fewer times of orbit transfer by using the proposed sigmoid ETM. Besides, to further improve the system performance, we are also seeking to further increase the ratio of the minimum inter-execution time to the average inter-execution time. For the purpose of a more even distribution of the triggering events on the time axis, we may modify the proposed sigmoid event-triggered method or associate it with other methods.

The problem of attitude tracking control for spacecraft with limited communication rate is addressed in this article. To reduce the communication burden, an adaptive event-triggered control scheme is proposed. In the control scheme, only the sampling states at the event-triggering instants are sent to the control module, which can considerably decrease the data transmission rate. To address the inertia uncertainties and external disturbances, a radial basis function neural network (NN) is introduced. The bound of the uncertainties and disturbances is estimated for the proposed control scheme, which can simplify the NN and reduce the computation. Since the event-triggered error signal is discontinuous due to the event-triggered mechanism, the closed-loop system is formulated as an impulsive dynamical system to obtain the stability properties of the system. Finally, simulation results are given to demonstrate the effectiveness of the proposed control scheme.

MOTIVATION: Many GWAS conducted in the past decade have identified tens of thousands of disease related variants, which in total explained only part of the heritability for most traits. There remain many more genetics variants with small effect sizes to be discovered. This has motivated the development of sequencing studies with larger sample sizes and increased resolution of genotyped variants, e.g., the ongoing NHLBI Trans-Omics for Precision Medicine (TOPMed) whole genome sequencing project. An alternative approach is the development of novel and more powerful statistical methods. The current dominating approach in the field of GWAS analysis is the "single trait single variant" association test, despite the fact that most GWAS are conducted in deeply-phenotyped cohorts with many correlated traits measured. In this paper, we aim to develop rigorous methods that integrate multiple correlated traits and multiple variants to improve the power to detect novel variants. In recognition of the difficulty of accessing raw genotype and phenotype data due to privacy and logistic concerns, we develop methods that are applicable to publicly available GWAS summary data. RESULTS: We build rigorous statistical models for GWAS summary statistics to motivate novel multi-trait SNP-set association tests, including variance component test, burden test and their adaptive test, and develop efficient numerical algorithms to quickly compute their analytical P-values. We implement the proposed methods in an open source R package. We conduct thorough simulation studies to verify the proposed methods rigorously control type I errors at the genome-wide significance level, and further demonstrate their utility via comprehensive analysis of GWAS summary data for multiple lipids traits and glycemic traits. We identified many novel loci that were not detected by the individual trait based GWAS analysis. AVAILABILITY AND IMPLEMENTATION: We have implemented the proposed methods in an R package freely available at http://www.github.com/baolinwu/MSKAT. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Genetics hold great promise to precision medicine by tailoring treatment to the individual patient based on their genetic profiles. Toward this goal, many large-scale genome-wide association studies (GWAS) have been performed in the last decade to identify genetic variants associated with various traits and diseases. They have successfully identified tens of thousands of disease-related variants. However they have explained only a small proportion of the overall trait heritability for most traits and are of very limited clinical use. This is partly owing to the small effect sizes of most genetic variants, and the common practice of testing association between one trait and one genetic variant at a time in most GWAS, even when multiple related traits are often measured for each individual. Increasing evidence suggests that many genetic variants can influence multiple traits simultaneously, and we can gain more power by testing association of multiple traits simultaneously. It is appealing to develop novel multi-trait association test methods that need only GWAS summary data, since it is generally very hard to access the individual-level GWAS phenotype and genotype data. RESULTS: Many existing GWAS summary data-based association test methods have relied on ad hoc approach or crude Monte Carlo approximation. In this article, we develop rigorous statistical methods for efficient and powerful multi-trait association test. We develop robust and efficient methods to accurately estimate the marginal trait correlation matrix using only GWAS summary data. We construct the principal component (PC)-based association test from the summary statistics. PC-based test has optimal power when the underlying multi-trait signal can be captured by the first PC, and otherwise it will have suboptimal performance. We develop an adaptive test by optimally weighting the PC-based test and the omnibus chi-square test to achieve robust performance under various scenarios. We develop efficient numerical algorithms to compute the analytical P-values for all the proposed tests without the need of Monte Carlo sampling. We illustrate the utility of proposed methods through application to the GWAS meta-analysis summary data for multiple lipids and glycemic traits. We identify multiple novel loci that were missed by individual trait-based association test. AVAILABILITY AND IMPLEMENTATION: All the proposed methods are implemented in an R package available at http://www.github.com/baolinwu/MTAR. The developed R programs are extremely efficient: it takes less than 2 min to compute the list of genome-wide significant single nucleotide polymorphisms (SNPs) for all proposed multi-trait tests for the lipids GWAS summary data with 2.5 million SNPs on a single Linux desktop. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

High-throughput mRNA sequencing (RNA-Seq) is widely used for transcript quantification of gene isoforms. Since RNA-Seq data alone is often not sufficient to accurately identify the read origins from the isoforms for quantification, we propose to explore protein domain-domain interactions as prior knowledge for integrative analysis with RNA-Seq data. We introduce a Network-based method for RNA-Seq-based Transcript Quantification (Net-RSTQ) to integrate protein domain-domain interaction network with short read alignments for transcript abundance estimation. Based on our observation that the abundances of the neighboring isoforms by domain-domain interactions in the network are positively correlated, Net-RSTQ models the expression of the neighboring transcripts as Dirichlet priors on the likelihood of the observed read alignments against the transcripts in one gene. The transcript abundances of all the genes are then jointly estimated with alternating optimization of multiple EM problems. In simulation Net-RSTQ effectively improved isoform transcript quantifications when isoform co-expressions correlate with their interactions. qRT-PCR results on 25 multi-isoform genes in a stem cell line, an ovarian cancer cell line, and a breast cancer cell line also showed that Net-RSTQ estimated more consistent isoform proportions with RNA-Seq data. In the experiments on the RNA-Seq data in The Cancer Genome Atlas (TCGA), the transcript abundances estimated by Net-RSTQ are more informative for patient sample classification of ovarian cancer, breast cancer and lung cancer. All experimental results collectively support that Net-RSTQ is a promising approach for isoform quantification. Net-RSTQ toolbox is available at http://compbio.cs.umn.edu/Net-RSTQ/.

Cox regression is commonly used to predict the outcome by the time to an event of interest and in addition, identify relevant features for survival analysis in cancer genomics. Due to the high-dimensionality of high-throughput genomic data, existing Cox models trained on any particular dataset usually generalize poorly to other independent datasets. In this paper, we propose a network-based Cox regression model called Net-Cox and applied Net-Cox for a large-scale survival analysis across multiple ovarian cancer datasets. Net-Cox integrates gene network information into the Cox's proportional hazard model to explore the co-expression or functional relation among high-dimensional gene expression features in the gene network. Net-Cox was applied to analyze three independent gene expression datasets including the TCGA ovarian cancer dataset and two other public ovarian cancer datasets. Net-Cox with the network information from gene co-expression or functional relations identified highly consistent signature genes across the three datasets, and because of the better generalization across the datasets, Net-Cox also consistently improved the accuracy of survival prediction over the Cox models regularized by L(2) or L(1). This study focused on analyzing the death and recurrence outcomes in the treatment of ovarian carcinoma to identify signature genes that can more reliably predict the events. The signature genes comprise dense protein-protein interaction subnetworks, enriched by extracellular matrix receptors and modulators or by nuclear signaling components downstream of extracellular signal-regulated kinases. In the laboratory validation of the signature genes, a tumor array experiment by protein staining on an independent patient cohort from Mayo Clinic showed that the protein expression of the signature gene FBN1 is a biomarker significantly associated with the early recurrence after 12 months of the treatment in the ovarian cancer patients who are initially sensitive to chemotherapy. Net-Cox toolbox is available at http://compbio.cs.umn.edu/Net-Cox/.

MOTIVATION: A central problem in biomarker discovery from large-scale gene expression or single nucleotide polymorphism (SNP) data is the computational challenge of taking into account the dependence among all the features. Methods that ignore the dependence usually identify non-reproducible biomarkers across independent datasets. We introduce a new graph-based semi-supervised feature classification algorithm to identify discriminative disease markers by learning on bipartite graphs. Our algorithm directly classifies the feature nodes in a bipartite graph as positive, negative or neutral with network propagation to capture the dependence among both samples and features (clinical and genetic variables) by exploring bi-cluster structures in a graph. Two features of our algorithm are: (1) our algorithm can find a global optimal labeling to capture the dependence among all the features and thus, generates highly reproducible results across independent microarray or other high-thoughput datasets, (2) our algorithm is capable of handling hundreds of thousands of features and thus, is particularly useful for biomarker identification from high-throughput gene expression and SNP data. In addition, although designed for classifying features, our algorithm can also simultaneously classify test samples for disease prognosis/diagnosis. RESULTS: We applied the network propagation algorithm to study three large-scale breast cancer datasets. Our algorithm achieved competitive classification performance compared with SVMs and other baseline methods, and identified several markers with clinical or biological relevance with the disease. More importantly, our algorithm also identified highly reproducible marker genes and enriched functions from the independent datasets. AVAILABILITY: Supplementary results and source code are available at http://compbio.cs.umn.edu/Feature_Class. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p >> n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.

The author would like to apologize for the omission on the Appendix from this article. The Appendix can be found with the article online as Supplementary Material. Supplementary data are available at Bioinformatics online.

BACKGROUND: Inference of population stratification and individual admixture from genetic markers is an integrative part of a study in diverse situations, such as association mapping and evolutionary studies. Bayesian methods have been proposed for population stratification and admixture inference using multilocus genotypes and widely used in practice. However, these Bayesian methods demand intensive computation resources and may run into convergence problem in Markov Chain Monte Carlo based posterior samplings. RESULTS: We have developed PSMIX, an R package based on maximum likelihood method using expectation-maximization algorithm, for inference of population stratification and individual admixture. CONCLUSION: Compared with software based on Bayesian methods (e.g., STRUCTURE), PSMIX has similar accuracy, but more efficient computations.PSMIX and its supplemental documents are freely available at http://bioinformatics.med.yale.edu/PSMIX.

In this paper, we address the multiple peak alignment problem in sequential data analysis with an approach based on the Gaussian scale-space theory. We assume that multiple sets of detected peaks are the observed samples of a set of common peaks. We also assume that the locations of the observed peaks follow unimodal distributions (e.g., normal distribution) with their means equal to the corresponding locations of the common peaks and variances reflecting the extension of their variations. Under these assumptions, we convert the problem of estimating locations of the unknown number of common peaks from multiple sets of detected peaks into a much simpler problem of searching for local maxima in the scale-space representation. The optimization of the scale parameter is achieved using an energy minimization approach. We compare our approach with a hierarchical clustering method using both simulated data and real mass spectrometry data. We also demonstrate the merit of extending the binary peak detection method (i.e., a candidate is considered either as a peak or as a nonpeak) with a quantitative scoring measure-based approach (i.e., we assign to each candidate a possibility of being a peak).

MOTIVATION: Genomic DNA copy number alterations are characteristic of many human diseases including cancer. Various techniques and platforms have been proposed to allow researchers to partition the whole genome into segments where copy numbers change between contiguous segments, and subsequently to quantify DNA copy number alterations. In this paper, we incorporate the spatial dependence of DNA copy number data into a regression model and formalize the detection of DNA copy number alterations as a penalized least squares regression problem. In addition, we use a stationary bootstrap approach to estimate the statistical significance and false discovery rate. RESULTS: The proposed method is studied by simulations and illustrated by an application to an extensively analyzed dataset in the literature. The results show that the proposed method can correctly detect the numbers and locations of the true breakpoints while appropriately controlling the false positives. AVAILABILITY: http://bioinformatics.med.yale.edu/DNACopyNumber CONTACT: [email protected] SUPPLEMENTARY INFORMATION: http://bioinformatics.med.yale.edu/DNACopyNumber.

UNLABELLED: Differential gene expression detection using microarrays has received lots of research interests recently. Many methods have been proposed, including variants of F-statistics, non-parametric approaches and empirical Bayesian methods etc. The SAM statistics has been shown to have good performance in empirical studies. SAM is more like an ad hoc shrinkage method. The idea is that for small sample microarray data, it is often useful to pool information across genes to improve efficiency. Under Bayesian framework Smyth formally derived the test statistics with shrinkage using the hierarchical models. In this paper we cast differential gene expression detection in the familiar framework of linear regression model. Commonly used test statistics correspond to using least squares to estimate the regression parameters. Based on the vast literature of research on linear models, we can naturally consider other alternatives. Here we explore the penalized linear regression. We propose the penalized t-/F-statistics for two-class microarray data based on [Formula: see text] penalty. We will show that the penalized test statistics intuitively makes sense and through applications we illustrate its good performance. AVAILABILITY: Supplementary information including program codes, more detailed analysis results and R functions for the proposed methods can be found at http://www.biostat.umn.edu/~baolin/research CONTACT: [email protected] SUPPLEMENTARY INFORMATION: http://www.biostat.umn.edu/~baolin/research.

The rapid advances in high-throughput biotechnologies such as DNA microarrays and mass spectrometry have generated vast amounts of data ranging from gene expression to proteomics data. The large size and complexity involved in analyzing such data demand a significant amount of computing power. High-performance computation (HPC) is an attractive and increasingly affordable approach to help meet this challenge. There is a spectrum of techniques that can be used to achieve computational speedup with varying degrees of impact in terms of how drastic a change is required to allow the software to run on an HPC platform. This paper describes a high- productivity/low-maintenance (HP/LM) approach to HPC that is based on establishing a collaborative relationship between the bioinformaticist and HPC expert that respects the former's codes and minimizes the latter's efforts. The goal of this approach is to make it easy for bioinformatics researchers to continue to make iterative refinements to their programs, while still being able to take advantage of HPC. The paper describes our experience applying these HP/LM techniques in four bioinformatics case studies: (1) genome-wide sequence comparison using Blast, (2) identification of biomarkers based on statistical analysis of large mass spectrometry data sets, (3) complex genetic analysis involving ordinal phenotypes, (4) large-scale assessment of the effect of possible errors in analyzing microarray data. The case studies illustrate how the HP/LM approach can be applied to a range of representative bioinformatics applications and how the approach can lead to significant speedup of computationally intensive bioinformatics applications, while making only modest modifications to the programs themselves.

MOTIVATION: To understand cancer etiology, it is important to explore molecular changes in cellular processes from normal state to cancerous state. Because genes interact with each other during cellular processes, carcinogenesis related genes may form differential co-expression patterns with other genes in different cell states. In this study, we develop a statistical method for identifying differential gene-gene co-expression patterns in different cell states. RESULTS: For efficient pattern recognition, we extend the traditional F-statistic and obtain an Expected Conditional F-statistic (ECF-statistic), which incorporates statistical information of location and correlation. We also propose a statistical method for data transformation. Our approach is applied to a microarray gene expression dataset for prostate cancer study. For a gene of interest, our method can select other genes that have differential gene-gene co-expression patterns with this gene in different cell states. The 10 most frequently selected genes, include hepsin, GSTP1 and AMACR, which have recently been proposed to be associated with prostate carcinogenesis. However, genes GSTP1 and AMACR cannot be identified by studying differential gene expression alone. By using tumor suppressor genes TP53, PTEN and RB1, we identify seven genes that also include hepsin, GSTP1 and AMACR. We show that genes associated with cancer may have differential gene-gene expression patterns with many other genes in different cell states. By discovering such patterns, we may be able to identify carcinogenesis related genes.

BACKGROUND: Identifying protein-protein interactions is fundamental for understanding the molecular machinery of the cell. Proteome-wide studies of protein-protein interactions are of significant value, but the high-throughput experimental technologies suffer from high rates of both false positive and false negative predictions. In addition to high-throughput experimental data, many diverse types of genomic data can help predict protein-protein interactions, such as mRNA expression, localization, essentiality, and functional annotation. Evaluations of the information contributions from different evidences help to establish more parsimonious models with comparable or better prediction accuracy, and to obtain biological insights of the relationships between protein-protein interactions and other genomic information. RESULTS: Our assessment is based on the genomic features used in a Bayesian network approach to predict protein-protein interactions genome-wide in yeast. In the special case, when one does not have any missing information about any of the features, our analysis shows that there is a larger information contribution from the functional-classification than from expression correlations or essentiality. We also show that in this case alternative models, such as logistic regression and random forest, may be more effective than Bayesian networks for predicting interactions. CONCLUSIONS: In the restricted problem posed by the complete-information subset, we identified that the MIPS and Gene Ontology (GO) functional similarity datasets as the dominating information contributors for predicting the protein-protein interactions under the framework proposed by Jansen et al. Random forests based on the MIPS and GO information alone can give highly accurate classifications. In this particular subset of complete information, adding other genomic data does little for improving predictions. We also found that the data discretizations used in the Bayesian methods decreased classification performance.

MOTIVATION: Novel methods, both molecular and statistical, are urgently needed to take advantage of recent advances in biotechnology and the human genome project for disease diagnosis and prognosis. Mass spectrometry (MS) holds great promise for biomarker identification and genome-wide protein profiling. It has been demonstrated in the literature that biomarkers can be identified to distinguish normal individuals from cancer patients using MS data. Such progress is especially exciting for the detection of early-stage ovarian cancer patients. Although various statistical methods have been utilized to identify biomarkers from MS data, there has been no systematic comparison among these approaches in their relative ability to analyze MS data. RESULTS: We compare the performance of several classes of statistical methods for the classification of cancer based on MS spectra. These methods include: linear discriminant analysis, quadratic discriminant analysis, k-nearest neighbor classifier, bagging and boosting classification trees, support vector machine, and random forest (RF). The methods are applied to ovarian cancer and control serum samples from the National Ovarian Cancer Early Detection Program clinic at Northwestern University Hospital. We found that RF outperforms other methods in the analysis of MS data.

An evolutionary procedure is proposed for the design of the fuzzy gain scheduling controller (FGSC) for nonlinear control systems. The FGSC makes use of the structure of conventional gain scheduling controllers and incorporates the Tanaka-Sugeno (TS) fuzzy system structure. A learning algorithm based on evolutionary programming is used for learning the structure and optimising the parameters of the FGSC. Simulation results are shown to demonstrate the effectiveness of the scheme.