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(Hughes et al., 2010) JTK_CYCLE: an efficient nonparametric algorithm for detecting rhythmic components in genome-scale data sets. J Biol Rhythms.

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Generates high-resolution maps. CircadiOmics (i) provides a common repository for circadian cycle-related metabolic data; (ii) mines and integrates these data with other omic data across multiple biological web services and databases; and (iii) produces high-resolution biological networks displaying, for instance, metabolites, enzymes, transcription factors and their interactions, and concentration changes over time throughout the circadian cycle.

Reconstructs sample order in the absence of time-of-day information. CYCLOPS can determine rhythms in expression across the body that persist at the population-level. It can serve to discover genetic associations by studying how the human cyclers influence drug action. This tool can be used to demonstrate that the circadian clock may contribute to ‘the missing heritability’ problem.

Detects periodically expressed genes from gene expression time series data. The proposed method is based on a robust spectral estimator which is incorporated into the hypothesis testing framework using a so-called g-statistic together with correction for multiple testing.

Detects rhythmic signals. Instead of using mathematical functions (e.g. sinusoidal) to describe shape of rhythmic signals, ORIOS uses mathematical inequalities. Consequently, it is robust and not limited by the biologist’s choice of the mathematical model. The ORIOS methodology can also be extended to handle heteroscedasticity, non-normality and dependent time course experiments using resampling procedures such as the bootstrap.

Provides a direct method to treat missing values and unevenly spaced time points. Lomb-Scargle is a tool for finding periodic gene expression profiles in microarray data, especially when data may be collected at arbitrary time points or when a significant proportion of data is missing. This algorithm proposes the combination of a Lomb–Scargle test statistic for periodicity and a multiple hypothesis testing procedure with controlled false discovery rate to detect significant periodic gene expression patterns.

Combines time domain and frequency domain analysis for extracting and characterizing rhythmic expression profiles from temporal microarray data. ARSER employs autoregressive spectral estimation to predict an expression profile’s periodicity from the frequency spectrum and then models the rhythmic patterns by using a harmonic regression model to fit the time-series. ARSER describes the rhythmic patterns by four parameters: period, phase, amplitude and mean level, and measures the multiple testing significance by false discovery rate q-value.

Provides two functions-meta2d and meta3d for detecting rhythmic signals from time-series datasets. MetaCycle is an R package for evaluating periodicity in large scale time-series datasets. MetaCycle has two functions, meta2d and meta3d, designed to analyze two-dimensional and three-dimensional time-series datasets, respectively. Meta2d implements N-version programming concepts using a suite of algorithms and integrating their results.

A three-step periodicity detection algorithm. LSPR first preprocesses the raw time-series by removing the linear trend and filtering noise. In the second step, the method employs a Lomb–Scargle periodogram to estimate the periodicity in the time-series. Finally, harmonic regression is applied to model the cyclic components. LSPR was applied to analyze two independent datasets from the studies of the diurnal gene expression of a model plant, Arabidopsis. The method is capable of identifying periodic transcripts more accurately than existing algorithms.

An analysis of variance (ANOVA) periodicity detector and its Bayesian extension that can be used to discover periodic transcripts of arbitrary shapes from replicated gene expression profiles. The models are applicable when the profiles are collected at comparable time points for at least two cycles.

A machine learning method to detect molecular species that oscillate in high-throughput circadian experiments. This method is based on BIO_CYCLE, a dataset including both synthetic and real-world biological time series, and both periodic and aperiodic signals. BIO_CYCLE estimates which signals are periodic in high-throughput circadian experiments, producing estimates of amplitudes, periods, phases, as well as several statistical significance measures. BIO_CYCLE is particulary useful to address several other related circadian problems, such as analyzing periodicity in high-throughput circadian proteomic data, or inferring sample time in different species.

A machine learning method to detect molecular species that oscillate in high-throughput circadian experiments. BIO_CLOCK estimates the time at which a particular single-time-point transcriptomic experiment was carried. In most cases, BIO_CLOCK can reliably predict time, within approximately 1 h, using the expression levels of only a small number of core clock genes. BIO_CLOCK is used to annotate most mouse experiments found in the Gene Expression Omnibus database with an inferred time stamp.

Compares a collection of diurnal/circadian models against microarray time course data to identify cycling genes. HAYSTACK uses least-square linear regression for each gene against all model cycling patterns with 24 possible phases. A series of statistical tests were used to identify the best-fit model, phase-of-expression, and to estimate a p-value and false discovery rate for each gene. The Web version of HAYSTACK can be used to compare any large-scale dataset representing at least three data points against a set of user-supplied model patterns.

Simulates a model of the post-translational Kai circadian clock. KMC-KaiC is a dedicated Kinetic Monte Carlo (KMC) algorithm that allows to simulate the Kai system at the level of individual KaiC hexamers and monomers and explicitly tracks the turnover of every ATP nucleotide. All the reaction rates in the simulation strictly obey detailed balance.

Checks hypothesis that dynamic changes in the concentrations of both adenosine molecules and receptors can account for changes in cognitive performance. CSR model can link the sleep homeostatic process, cognitive performance, and sleep patterns to an underlying physiological and molecular biological mechanism. It can serve for generation of one-step predictions of both sleep and performance.

Identifies and characterizes cycling variables in large datasets. JTK_CYCLE applies the JTK algorithm to alternative hypothesized group orderings corresponding to a range of user-defined period lengths and phases. JTK_CYCLE can be used to identify cycling variables within a broad range of quantitative datasets, which suggests a role for JTK_CYCLE in such diverse fields as cell division, physiology, metabolism, and population biology.

Detects rhythms of any period and makes few assumptions about wave forms. RAIN uses non-parametric methods to detect rhythms in time series. RAIN deals with outliers, missing values and is optimized for time series comprising 10-100 measurements.

Incorporates prior knowledge into the analysis of periodic data. PSEA offers the ability to compare gene expression results to a nonuniform background distribution and offers the fast, dynamic computation of statistical significance. It identifies biologically related gene sets showing temporally coordinated expression. PSEA evaluates each selected gene set for evidence of temporally coordinated transcription. It provides summary statistics describing these gene sets and produces summary diagrams depicting the results. PSEA enables biologists to analyze their own periodic data and it facilitates the interpretation of rhythmic biological data at the genome scale.

Serves for wavelet analysis and visualization of oscillatory signals. WAVOS has many features to simplify analysis with the discrete wave- let transform (DWT) and continuous wavelet transform (CWT), including: both command-line and graphical user interfaces; automatic processing of multiple time series simultaneously; or interfaces to multiple standard file formats. It provides several options for managing the implicit periodization and corresponding boundary effects.

Enables detection of gene-wise differential rhythmicity and differential expression in circadian or otherwise rhythmic transcriptome data. LimoRhyde provides a framework for assessing how rhythmic biological systems respond to genetic and environmental perturbations. The software is inspired by cosinor regression. It can be applied to data from any experimental design that can be described by a linear model.

Obsolete

A general-purpose robust testing procedure for finding periodic sequences in multiple time series data. Robustperiodic is based on a spectral estimator which is incorporated into the hypothesis testing framework using a so-called g-statistic together with correction for multiple testing. This results in a robust testing procedure which is insensitive to heavy contamination of outliers, missing-values, short time series, nonlinear distortions, and is completely insensitive to any monotone nonlinear distortions.

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