Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes' method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.

BackgroundSexual dimorphisms are well recognized in various cardiac diseases such as ischemic cardiomyopathy (ICM), hypertrophic cardiomyopathy (HCM) and dilated cardiomyopathy (DCM). Thorough understanding of the underlying genetic programs is crucial to optimize treatment strategies specified for each gender. By performing meta-analysis and microarray analysis, we sought to comprehensively characterize the sexual dimorphisms in the healthy and diseased heart at the level of both mRNA and miRNA transcriptome.ResultsExisting mRNA microarray data of both mouse and human heart were integrated, identifying dozens/ hundreds of sexually dimorphic genes in healthy heart, ICM, HCM, and DCM. These sexually dimorphic genes overrepresented gene ontologies (GOs) important for cardiac homeostasis. Further, microarray of miRNA, isolated from mouse sham left ventricle (LV) (n = 6 & n = 5 for male & female) and chronic MI LV (n = 19 & n = 19) and from human normal LV (n = 6 & n = 6) and ICM LV (n = 4 & n = 5), was conducted. This revealed that 13 mouse miRNAs are sexually dimorphic in MI and 6 in normal heart. In human, 3 miRNAs were sexually dimorphic in ICM and 15 in normal heart. These data revealed miRNA-mRNA networks that operate in a sexually-biased fashion.ConclusionsmRNA and miRNA transcriptome of normal and disease heart show significant sex differences, which might impact the cardiac homeostasis. Together this study provides the first comprehensive picture of the genome-wide program underlying the heart sexual dimorphisms, laying the foundation for gender specific treatment strategies.

Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.

We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate Normal model with known covariance matrices. Introduced priors are superharmonic and put more weight on matrices with smaller singular values. They are a natural generalization of the Stein prior. Bayes estimators and Bayesian predictive densities based on introduced priors are minimax and dominate those based on the uniform prior in finite samples. The risk reduction is large when the true value of the parameter has small singular values. In particular, introduced priors perform stably well in the low rank case. We apply this result to multivariate linear regression problems by considering priors depending on the future samples. Introduced priors are compatible with reduced-rank regression.