Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets

Computer-controlled apparatus for automated development of continuous flow methods

An automated apparatus to assist in the development of analytical continuous flow methods is described. The system is capable of controlling and monitoring a variety of pumps, valves, and detectors through an IBM PC-AT compatible computer. System components consist of two types of peristaltic pumps (including a multiple pump unit), syringe pumps, electrically and pneumatically actuated valves, and an assortment of spectrophotometric and electrochemical detectors. Details of the interface circuitry are given where appropriate. To demonstrate the utility of the system, an automatically generated response surface is presented for the flow injection determination of iron(II) by its reaction with 1,10-phenanthroline

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe

Cavitation induced by explosion in a model of ideal fluid

We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent view for rebound bubbles in superfluid and we indentify the loss of energy between the successive rebounds as radiated waves. We compute self-similar solution of the explosion for the early stage, when no bubbles have been nucleated. The solution also gives the wave number of the excitations emitted through the shock wave.Comment: 21 pages,13 figures, other comment

Multivariate curve resolution of time course microarray data

BACKGROUND: Modeling of gene expression data from time course experiments often involves the use of linear models such as those obtained from principal component analysis (PCA), independent component analysis (ICA), or other methods. Such methods do not generally yield factors with a clear biological interpretation. Moreover, implicit assumptions about the measurement errors often limit the application of these methods to log-transformed data, destroying linear structure in the untransformed expression data. RESULTS: In this work, a method for the linear decomposition of gene expression data by multivariate curve resolution (MCR) is introduced. The MCR method is based on an alternating least-squares (ALS) algorithm implemented with a weighted least squares approach. The new method, MCR-WALS, extracts a small number of basis functions from untransformed microarray data using only non-negativity constraints. Measurement error information can be incorporated into the modeling process and missing data can be imputed. The utility of the method is demonstrated through its application to yeast cell cycle data. CONCLUSION: Profiles extracted by MCR-WALS exhibit a strong correlation with cell cycle-associated genes, but also suggest new insights into the regulation of those genes. The unique features of the MCR-WALS algorithm are its freedom from assumptions about the underlying linear model other than the non-negativity of gene expression, its ability to analyze non-log-transformed data, and its use of measurement error information to obtain a weighted model and accommodate missing measurements

Nucleation and condensational growth to CCN sizes during a sustained pristine biogenic SOA event in a forested mountain valley

The Whistler Aerosol and Cloud Study (WACS 2010), included intensive measurements of trace gases and particles at two sites on Whistler Mountain. Between 6–11 July 2010 there was a sustained high-pressure system over the region with cloud-free conditions and the highest temperatures of the study. During this period, the organic aerosol concentrations rose from <1 μg m<sup>−3</sup> to ∼6 μg m<sup>−3</sup>. Precursor gas and aerosol composition measurements show that these organics were almost entirely of secondary biogenic nature. Throughout 6–11 July, the anthropogenic influence was minimal with sulfate concentrations <0.2 μg m<sup>−3</sup> and SO<sub>2</sub> mixing ratios ≈ 0.05–0.1 ppbv. Thus, this case provides excellent conditions to probe the role of biogenic secondary organic aerosol in aerosol microphysics. Although SO<sub>2</sub> mixing ratios were relatively low, box-model simulations show that nucleation and growth may be modeled accurately if <i>J</i><sub>nuc</sub> = 3 × 10<sup>−7</sup>[H<sub>2</sub>SO<sub>4</sub>] and the organics are treated as effectively non-volatile. Due to the low condensation sink and the fast condensation rate of organics, the nucleated particles grew rapidly (2–5 nm h<sup>−1</sup>) with a 10–25% probability of growing to CCN sizes (100 nm) in the first two days as opposed to being scavenged by coagulation with larger particles. The nucleated particles were observed to grow to ∼200 nm after three days. Comparisons of size-distribution with CCN data show that particle hygroscopicity (κ) was ∼0.1 for particles larger 150 nm, but for smaller particles near 100 nm the κ value decreased near midway through the period from 0.17 to less than 0.06. In this environment of little anthropogenic influence and low SO<sub>2</sub>, the rapid growth rates of the regionally nucleated particles – due to condensation of biogenic SOA – results in an unusually high efficiency of conversion of the nucleated particles to CCN. Consequently, despite the low SO<sub>2</sub>, nucleation/growth appear to be the dominant source of particle number

Genetic Networks Controlling Structural Outcome of Glucosinolate Activation across Development

Most phenotypic variation present in natural populations is under polygenic control, largely determined by genetic variation at quantitative trait loci (QTLs). These genetic loci frequently interact with the environment, development, and each other, yet the importance of these interactions on the underlying genetic architecture of quantitative traits is not well characterized. To better study how epistasis and development may influence quantitative traits, we studied genetic variation in Arabidopsis glucosinolate activation using the moderately sized Bayreuth×Shahdara recombinant inbred population, in terms of number of lines. We identified QTLs for glucosinolate activation at three different developmental stages. Numerous QTLs showed developmental dependency, as well as a large epistatic network, centered on the previously cloned large-effect glucosinolate activation QTL, ESP. Analysis of Heterogeneous Inbred Families validated seven loci and all of the QTL×DPG (days post-germination) interactions tested, but was complicated by the extensive epistasis. A comparison of transcript accumulation data within 211 of these RILs showed an extensive overlap of gene expression QTLs for structural specifiers and their homologs with the identified glucosinolate activation loci. Finally, we were able to show that two of the QTLs are the result of whole-genome duplications of a glucosinolate activation gene cluster. These data reveal complex age-dependent regulation of structural outcomes and suggest that transcriptional regulation is associated with a significant portion of the underlying ontogenic variation and epistatic interactions in glucosinolate activation

The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix

In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace $T_P$ of initial opinions (where $P$ is the influence matrix) that \emph{ensure} consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to $T_P$ by orthogonal projection and (2) subsequent iterations of the transformation $P.$ The properties of this method are studied. It is shown that for any non-periodic stochastic matrix $P,$ the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of $P.$Comment: 19 pages, 2 figure

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results to decentralized control and touch upon some problems of spectral graph theory.Comment: 15 pages, 2 figures, 40 references. To appear in Automation and Remote Control, Vol.70, No.3, 200

The Complex Genetic Architecture of the Metabolome

Discovering links between the genotype of an organism and its metabolite levels can increase our understanding of metabolism, its controls, and the indirect effects of metabolism on other quantitative traits. Recent technological advances in both DNA sequencing and metabolite profiling allow the use of broad-spectrum, untargeted metabolite profiling to generate phenotypic data for genome-wide association studies that investigate quantitative genetic control of metabolism within species. We conducted a genome-wide association study of natural variation in plant metabolism using the results of untargeted metabolite analyses performed on a collection of wild Arabidopsis thaliana accessions. Testing 327 metabolites against >200,000 single nucleotide polymorphisms identified numerous genotype–metabolite associations distributed non-randomly within the genome. These clusters of genotype–metabolite associations (hotspots) included regions of the A. thaliana genome previously identified as subject to recent strong positive selection (selective sweeps) and regions showing trans-linkage to these putative sweeps, suggesting that these selective forces have impacted genome-wide control of A. thaliana metabolism. Comparing the metabolic variation detected within this collection of wild accessions to a laboratory-derived population of recombinant inbred lines (derived from two of the accessions used in this study) showed that the higher level of genetic variation present within the wild accessions did not correspond to higher variance in metabolic phenotypes, suggesting that evolutionary constraints limit metabolic variation. While a major goal of genome-wide association studies is to develop catalogues of intraspecific variation, the results of multiple independent experiments performed for this study showed that the genotype–metabolite associations identified are sensitive to environmental fluctuations. Thus, studies of intraspecific variation conducted via genome-wide association will require analyses of genotype by environment interaction. Interestingly, the network structure of metabolite linkages was also sensitive to environmental differences, suggesting that key aspects of network architecture are malleable