A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This approach consists of sifting an ensemble white noise-added signal (data) and treats the mean as final true result. Finite, not infinitesimal, amplitude noise necessary to force exhaust all possible solutions in process, thus making different scale signals collate proper intrinsic mode functions (IMF) dictated by dyadic filter banks. As EEMD a time–space analysis method, added averaged out with sufficient number trials;...

Based on numerical experiments white noise using the empirical mode decomposition (EMD) method, we find empirically that EMD is effectively a dyadic filter, intrinsic function (IMF) components are all normally distributed, and Fourier spectra of IMF identical cover same area semi–logarithmic period scale. Expanding from these findings, further deduce product energy density its corresponding averaged constant, energy–density chi–squared distributed. Furthermore, derive spread components....

Determining trend and implementing detrending operations are important steps in data analysis. Yet there is no precise definition of "trend" nor any logical algorithm for extracting it. As a result, various ad hoc extrinsic methods have been used to determine facilitate operation. In this article, simple given nonlinear nonstationary time series as an intrinsically determined monotonic function within certain temporal span (most often that the span), or which can be at most one extremum...

Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through Hilbert transform. This paper offers an overview of difficulties involved in using AS, two new methods to overcome computing IF. The first approach compute quadrature (defined here as a simple 90° shift phase angle) directly. second designated normalized transform (NHT), which consists applying empirically...

This article addresses data-driven time-frequency (T-F) analysis of multivariate signals, which is achieved through the empirical mode decomposition (EMD) algorithm and its noise assisted extensions, ensemble EMD (EEMD) (MEMD). Unlike standard approaches that project data onto predefined basis functions (harmonic, wavelet) thus coloring representation blurring interpretation, bases for are derived from can be nonlinear nonstationary. For data, we show how MEMD aligns intrinsic joint...

The Earth has warmed at an unprecedented pace in the decades of 1980s and 1990s (IPCC Climate change 2007: scientific basis, Cambridge University Press, Cambridge, 2007). In Wu et al. (Proc Natl Acad Sci USA 104:14889–14894, 2007) we showed that rapidity warming late twentieth century was a result concurrence secular trend phase multidecadal (~65-year period) oscillatory variation estimated contribution former to be about 0.08°C per decade since ~1980. Here demonstrate robustness those...

A multi-dimensional ensemble empirical mode decomposition (MEEMD) for data (such as images or solid with variable density) is proposed here. The based on the applications of (EEMD) to slices in each and every dimension involved. final reconstruction corresponding intrinsic function (IMF) a comparable minimal scale combination principle. For two-dimensional spatial images, f(x,y), we consider (or image) collection one-dimensional series both x-direction y-direction. Each decomposed through...

Pathologic states are associated with a loss of dynamical complexity. Therefore, therapeutic interventions that increase physiologic complexity may enhance health status. Using multiscale entropy analysis, we show the postural sway dynamics healthy young and elderly subjects more complex than history falls. Application subsensory noise to feet has been demonstrated improve stability in elderly. We next this therapy significantly increases fluctuations subjects. Quantification changes...

Empirical Mode Decomposition (EMD) has been widely used to analyze non-stationary and nonlinear signal by decomposing data into a series of intrinsic mode functions (IMFs) trend function through sifting processes. For lack firm mathematical foundation, the implementation EMD is still empirical ad hoc. In this paper, we prove mathematically that EMD, as practiced now, only gives an approximation true envelope. As result, there potential conflict between strict definition IMF its natural cubic...

In climate science, an anomaly is the deviation of a quantity from its annual cycle. There are many ways to define Traditionally, this cycle taken be exact repeat itself year after year. This stationary may not reflect well intrinsic nonlinearity system, especially under external forcing. paper, we re-examine reference frame for anomalies by re-examining We propose alternative anomalies, modulated (MAC) that allows change year, defining anomalies. order useful, need able instantaneous cycle:...

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional and give a full informational representation nonlinear non-stationary data. It uses nested empirical mode decomposition Hilbert–Huang transform (HHT) approach identify intrinsic amplitude frequency modulations often present in systems. Comparisons are first made with spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions...

A Time-Dependent Intrinsic Correlation (TDIC) method is introduced. This new approach includes both auto- and cross-correlation analysis designed especially to analyze, capture track the local correlations between nonlinear nonstationary time series pairs. The based on Empirical Mode Decomposition (EMD) decompose data into their intrinsic mode functions (IMFs) uses instantaneous periods of IMFs determine a set sliding window sizes for computation running correlation coefficients multi-scale...

The empirical mode decomposition (EMD) based time-frequency analysis has been used in many scientific and engineering fields. mathematical expression of EMD the time-frequency-energy domain appears to be a generalization Fourier transform (FT), which leads speculation that latter may special case former. On other hand, is also known behave like dyadic filter bank when decompose white noise. These two observations seem contradict each other. In this paper, we study filtering properties EMD,...

Abstract Climate change is not only reflected in the changes annual means of climate variables but also their cycles (seasonality), especially regions outside tropics. In this study, ensemble empirical mode decomposition (EEMD) method applied to investigate nonlinear trend amplitude cycle (which contributes 96% total variance) China’s daily mean surface air temperature for period 1961–2007. The results show that variation and are significant, with a peak-to-peak 13% (1.8°C) its significant...

High-mobility group AT-hook1 (HMGA1, formerly HMG-I/Y), an architectural transcription factor, participates in a number of tumor biological processes. However, its effect on cervical cancer remains largely indistinct. In this study, we found that HMGA1 was generally overexpressed tissues and positively correlated with lymph node metastasis advanced clinical stage. Via exogenously increasing or decreasing the expression HMGA1, showed affected proliferation, colony formation, migration...

Abstract Trans-Pacific transport of enhanced ozone plumes has been mainly attributed to fossil fuel combustion in Asia spring, but less attention paid vegetation fires Asia. Here we show that the El Niño-Southern Oscillation (ENSO)-modulated Southeast Asia, rather than Asian plumes, dominate interannual variability springtime trans-Pacific across entire North Pacific Ocean. During Niño springs, intensified from both Indochinese Peninsula and Indonesia, together with large-scale circulation...

Abstract. Eastern China (27–41∘ N, 110–123∘ E) is heavily polluted by nitrogen dioxide (NO2), particulate matter with aerodynamic diameter below 2.5 µm (PM2.5), and other air pollutants. These pollutants vary on a variety of temporal spatial scales, many scales that are nonperiodic nonstationary, challenging proper quantitative characterization visualization. This study uses newly compiled EOF–EEMD analysis visualization package to evaluate the spatiotemporal variability ground-level NO2,...

Abstract It is believed that the continuing change in Earth’s climate will affect viral activity and transmission of influenza over coming decades. However, a consensus severity risk an epidemic warming has not been reached. was previously reported warmer winter can reduce caused mortality, but this relation cannot explain deadly many countries northern mid-latitudes 2017–2018, one warmest winters recent Here, we reveal widely spread 2017–2018 be attributed to abnormally strong rapid weather...

In this paper, the circulations driven by deep heating and shallow are investigated through analytically solving a set of linear equations examining simulated dry primitive equation model. Special emphasis is placed on low-level mass (moisture) convergence associated with forced circulation maintenance heat sources. It found that more likely to be trapped horizontally near area but relatively extended in vertical. As consequence, diabatic cannot balance adiabatic cooling due upward motion....

Abstract This study investigates changes in the frequency of ENSO, especially prolonged 1990–95 El Niño event, context secular annual cycle, ENSO interannual variability, and background mean state tropical eastern Pacific sea surface temperature (SST). The ensemble empirical mode decomposition (EEMD) method is applied to isolate those components from Niño-3 SST index for period 1880–2008. It shown that cycle [referred as a refined modulated (MAC)] has strong modulation change both amplitude...

As the original definition on Hilbert spectrum was given in terms of total energy and amplitude, there is a mismatch between traditional Fourier spectrum, which defined density. Rigorous definitions amplitude spectra are density time-frequency space. Unlike spectral analysis, where resolution fixed once data length sampling rate given, could be arbitrarily assigned analysis (HSA). Furthermore, HSA also provide zooming ability for detailed examination specific frequency range with all power....