Detecting sequence dependent transcriptional pauses from RNA and protein number time series

Background: Evidence suggests that in prokaryotes sequence-dependent transcriptional pauses a?ect the dynamics of transcription and translation, as well as of small genetic circuits. So far, a few pause-prone sequences have been identi?ed from in vitro measurements of transcription elongation kinetics.

Results: Using a stochastic model of gene expression at the nucleotide and codon levels with realistic parameter values, we investigate three di?erent but related questions and present statistical methods for their analysis. First, we show that information from in vivo RNA and protein temporal numbers is su?cient to discriminate between models with and without a pause site in their coding sequence. Second, we demonstrate that it is possible to separate a large variety of models from each other with pauses of various durations and locations in the template by means of a hierarchical clustering and a random forest classi?er. Third, we introduce an approximate likelihood function that allows to estimate the location of a pause site.

Conclusions: This method can aid in detecting unknown pause-prone sequences from temporal measurements of RNA and protein numbers at a genome-wide scale and thus elucidate possible roles that these sequences play in the dynamics of genetic networks and phenotype.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Facilitating needs based cancer care for people with a chronic disease : evaluation of an intervention using a multi-centre interrupted time series design

Background: Palliative care should be provided according to the individual needs of the patient, caregiver and family, so that the type and level of care provided, as well as the setting in which it is delivered, are dependent on the complexity and severity of individual needs, rather than prognosis or diagnosis. This paper presents a study designed to assess the feasibility and efficacy of an intervention to assist in the allocation of palliative care resources according to need, within the context of a population of people with advanced cancer. ---------- Methods/design: People with advanced cancer and their caregivers completed bi-monthly telephone interviews over a period of up to 18 months to assess unmet needs, anxiety and depression, quality of life, satisfaction with care and service utilisation. The intervention, introduced after at least two baseline phone interviews, involved a) training medical, nursing and allied health professionals at each recruitment site on the use of the Palliative Care Needs Assessment Guidelines and the Needs Assessment Tool: Progressive Disease - Cancer (NAT: PD-C); b) health professionals completing the NAT: PD-C with participating patients approximately monthly for the rest of the study period. Changes in outcomes will be compared pre-and post-intervention.---------- Discussion: The study will determine whether the routine, systematic and regular use of the Guidelines and NAT: PD-C in a range of clinical settings is a feasible and effective strategy for facilitating the timely provision of needs based care.

Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

A robust Bayesian two-sample test for detecting intervals of differential gene expression in microarray time series.

Understanding the regulatory mechanisms that are responsible for an organism's response to environmental change is an important issue in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question whether a gene is differentially expressed, they do not explicitly address the question when a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a two-sample test for identifying intervals of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates, and is robust with respect to outliers. We apply our algorithm to study the response of Arabidopsis thaliana genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 observed time points. In classification experiments, our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

An ontological characterization of time-series and state-sequences for data mining

Time-series and sequences are important patterns in data mining. Based on an ontology of time-elements, this paper presents a formal characterization of time-series and state-sequences, where a state denotes a collection of data whose validation is dependent on time. While a time-series is formalized as a vector of time-elements temporally ordered one after another, a state-sequence is denoted as a list of states correspondingly ordered by a time-series. In general, a time-series and a state-sequence can be incomplete in various ways. This leads to the distinction between complete and incomplete time-series, and between complete and incomplete state-sequences, which allows the expression of both absolute and relative temporal knowledge in data mining.

A framework for state-based time-series analysis and prediction

Time-series analysis and prediction play an important role in state-based systems that involve dealing with varying situations in terms of states of the world evolving with time. Generally speaking, the world in the discourse persists in a given state until something occurs to it into another state. This paper introduces a framework for prediction and analysis based on time-series of states. It takes a time theory that addresses both points and intervals as primitive time elements as the temporal basis. A state of the world under consideration is defined as a set of time-varying propositions with Boolean truth-values that are dependent on time, including properties, facts, actions, events and processes, etc. A time-series of states is then formalized as a list of states that are temporally ordered one after another. The framework supports explicit expression of both absolute and relative temporal knowledge. A formal schema for expressing general time-series of states to be incomplete in various ways, while the concept of complete time-series of states is also formally defined. As applications of the formalism in time-series analysis and prediction, we present two illustrating examples.

How does Calanus helgolandicus maintain its population in a variable environment? Analysis of a 25-year time series from the English Channel

Calanus helgolandicus is a key copepod of the NE Atlantic and fringing shelves, with a distribution that is expanding northwards with oceanic warming. The Plymouth L4 site has warmed over the past 25-years, and experiences large variations in the timing and availability of food for C. helgolandicus. Here we examine the degree to which these changes translate into variation in reproductive output and subsequently C. helgolandicus population size. Egg production rates (eggs female−1 day−1) were maximal in the spring to early-summer period of diatom blooms and high ciliate abundance, rather than during the equally large autumn blooms of autotrophic dinoflagellates. Egg hatch success was lower in spring however, with a greater proportion of naupliar deformities then also. Both the timing and the mean summer abundance of C. helgolandicus (CI–CVI) reflected those of spring total reproductive output. However this relationship was driven by inter-annual variability in female abundance and not that of egg production per female, which ranged only two-fold. Winter abundance of C. helgolandicus at L4 was much more variable than abundance in other seasons, and reflected conditions from the previous growing season. However, these low winter abundances had no clear carry-over signal to the following season’s population size. Overall, the C. helgolandicus population appears to be surprisingly resilient at this dynamic, inshore site, showing no long-term phenology shift and only a four-fold variation in mean abundance between years. This dampening effect may reflect a series of mortality sources, associated with the timing of stratification in the early part of the season, likely affecting egg sinking and loss, plus intense, density-dependent mortality of early stages in mid-summer likely through predation.

Limitations of instantaneous water quality sampling in surface-water catchments: Comparison with near-continuous phosphorus time-series data.

The validity of load estimates from intermittent, instantaneous grab sampling is dependent on adequate spatial coverage by monitoring networks and a sampling frequency that re?ects the variability in the system under study. Catchments with a ?ashy hydrology due to surface runoff pose a particular challenge as intense short duration rainfall events may account for a signi?cant portion of the total diffuse transfer of pollution from soil to water in any hydrological year. This can also be exacerbated by the presence of strong background pollution signals from point sources during low flows. In this paper, a range of sampling methodologies and load estimation techniques are applied to phosphorus data from such a surface water dominated river system, instrumented at three sub-catchments (ranging from 3 to 5 km2 in area) with near-continuous monitoring stations. Systematic and Monte Carlo approaches were applied to simulate grab sampling using multiple strategies and to calculate an estimated load, Le based on established load estimation methods. Comparison with the actual load, Lt, revealed signi?cant average underestimation, of up to 60%, and high variability for all feasible sampling approaches. Further analysis of the time series provides an insight into these observations; revealing peak frequencies and power-law scaling in the distributions of P concentration, discharge and load associated with surface runoff and background transfers. Results indicate that only near-continuous monitoring that re?ects the rapid temporal changes in these river systems is adequate for comparative monitoring and evaluation purposes. While the implications of this analysis may be more tenable to small scale ?ashy systems, this represents an appropriate scale in terms of evaluating catchment mitigation strategies such as agri-environmental policies for managing diffuse P transfers in complex landscapes.

Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.

Tests of Joint Hypotheses for Time Series Regression with a Unit Root

This Paper Studies Tests of Joint Hypotheses in Time Series Regression with a Unit Root in Which Weakly Dependent and Heterogeneously Distributed Innovations Are Allowed. We Consider Two Types of Regression: One with a Constant and Lagged Dependent Variable, and the Other with a Trend Added. the Statistics Studied Are the Regression \"F-Test\" Originally Analysed by Dickey and Fuller (1981) in a Less General Framework. the Limiting Distributions Are Found Using Functinal Central Limit Theory. New Test Statistics Are Proposed Which Require Only Already Tabulated Critical Values But Which Are Valid in a Quite General Framework (Including Finite Order Arma Models Generated by Gaussian Errors). This Study Extends the Results on Single Coefficients Derived in Phillips (1986A) and Phillips and Perron (1986).

Comparing meta-analysis and ecological-longitudinal analysis in time-series studies: a case study of the effects of air pollution on mortality in three Spanish cities

The objective of this paper is to introduce a diVerent approach, called the ecological-longitudinal, to carrying out pooled analysis in time series ecological studies. Because it gives a larger number of data points and, hence, increases the statistical power of the analysis, this approach, unlike conventional ones, allows the complementation of aspects such as accommodation of random effect models, of lags, of interaction between pollutants and between pollutants and meteorological variables, that are hardly implemented in conventional approaches. Design—The approach is illustrated by providing quantitative estimates of the short-termeVects of air pollution on mortality in three Spanish cities, Barcelona,Valencia and Vigo, for the period 1992–1994. Because the dependent variable was a count, a Poisson generalised linear model was first specified. Several modelling issues are worth mentioning. Firstly, because the relations between mortality and explanatory variables were nonlinear, cubic splines were used for covariate control, leading to a generalised additive model, GAM. Secondly, the effects of the predictors on the response were allowed to occur with some lag. Thirdly, the residual autocorrelation, because of imperfect control, was controlled for by means of an autoregressive Poisson GAM. Finally, the longitudinal design demanded the consideration of the existence of individual heterogeneity, requiring the consideration of mixed models. Main results—The estimates of the relative risks obtained from the individual analyses varied across cities, particularly those associated with sulphur dioxide. The highest relative risks corresponded to black smoke in Valencia. These estimates were higher than those obtained from the ecological-longitudinal analysis. Relative risks estimated from this latter analysis were practically identical across cities, 1.00638 (95% confidence intervals 1.0002, 1.0011) for a black smoke increase of 10 μg/m3 and 1.00415 (95% CI 1.0001, 1.0007) for a increase of 10 μg/m3 of sulphur dioxide. Because the statistical power is higher than in the individual analysis more interactions were statistically significant,especially those among air pollutants and meteorological variables. Conclusions—Air pollutant levels were related to mortality in the three cities of the study, Barcelona, Valencia and Vigo. These results were consistent with similar studies in other cities, with other multicentric studies and coherent with both, previous individual, for each city, and multicentric studies for all three cities

The 30-year TAMSAT African rainfall climatology and time-series (TARCAT) dataset

African societies are dependent on rainfall for agricultural and other water-dependent activities, yet rainfall is extremely variable in both space and time and reoccurring water shocks, such as drought, can have considerable social and economic impacts. To help improve our knowledge of the rainfall climate, we have constructed a 30-year (1983–2012), temporally consistent rainfall dataset for Africa known as TARCAT (TAMSAT African Rainfall Climatology And Time-series) using archived Meteosat thermal infra-red (TIR) imagery, calibrated against rain gauge records collated from numerous African agencies. TARCAT has been produced at 10-day (dekad) scale at a spatial resolution of 0.0375°. An intercomparison of TARCAT from 1983 to 2010 with six long-term precipitation datasets indicates that TARCAT replicates the spatial and seasonal rainfall patterns and interannual variability well, with correlation coefficients of 0.85 and 0.70 with the Climate Research Unit (CRU) and Global Precipitation Climatology Centre (GPCC) gridded-gauge analyses respectively in the interannual variability of the Africa-wide mean monthly rainfall. The design of the algorithm for drought monitoring leads to TARCAT underestimating the Africa-wide mean annual rainfall on average by −0.37 mm day−1 (21%) compared to other datasets. As the TARCAT rainfall estimates are historically calibrated across large climatically homogeneous regions, the data can provide users with robust estimates of climate related risk, even in regions where gauge records are inconsistent in time.