Low-frequency Correlation Research Articles

Daily fluctuations in COVID-19 infection rates under Tokyo's epidemic prevention measures - new evidence from adaptive Fourier decomposition.

The COVID-19 pandemic has witnessed widespread infections and variants. Particularly, Tokyo faced the challenge of seven waves of COVID-19, during which government interventions played a pivotal role. Therefore, gaining a comprehensive understanding of government control measures is of paramount importance, which is beneficial for health authorities in the policy development process. Our study analysis the daily change data of the daily COVID-19 infection count in Tokyo from January 16, 2020 to September 30, 2022. We utilized adaptive Fourier decomposition (AFD) for analyzing the temporal trends within COVID-19 data. It extends the conventional AFD approach by constructing new components base on multiple individual components at various time-frequency scales. Furthermore, we conducted Pearson correlation assessments of the first to third-order synthesis results, along with comparative analyses against other signal analysis techniques. Ultimately, these new components are integrated with policy data spanning different time periods for a comprehensive analysis. The analysis of daily COVID-19 data in Tokyo using AFD reveals how various government policies impacted infection rates across seven distinct fluctuation periods. In the decomposition results, the reduction of business hours policy correlated with high-frequency components in the first four waves, while the low-frequency components for the sixth wave suggested a decline in its relevance. The vaccination policy initially displayed a mid-frequency correlation with the fifth wave and continued with a low-frequency correlation in the last wave. Moreover, our statistical analysis (value of p < 0.05) demonstrated that 75% of the third-order AFD components exhibited significant positive correlations with the original infections, while the correlation coefficients of most components in EMD and VMD did not attain significance. In the time-frequency domain, AFD demonstrates superior performance compared to EMD and VMD in capturing crucial data related to epidemic control measures. The variations in daily COVID-19 infection counts during these seven periods under various policies are evident in distinct third-order AFD components. These findings guide the formulation of future public health policies and social measures.

Application of Neural Network Algorithm Based on Principal Component Image Analysis in Band Expansion of College English Listening.

With the development of information technology, band expansion technology is gradually applied to college English listening teaching. This technology aims to recover broadband speech signals from narrowband speech signals with a limited frequency band. However, due to the limitations of current voice equipment and channel conditions, the existing voice band expansion technology often ignores the high-frequency and low-frequency correlation of the audio, resulting in excessive smoothing of the recovered high-frequency spectrum, too dull subjective hearing, and insufficient expression ability. In order to solve this problem, a neural network model PCA-NN (principal components analysis-neural network) based on principal component image analysis is proposed. Based on the nonlinear characteristics of the audio image signal, the model reduces the dimension of high-dimensional data and realizes the effective recovery of the high-frequency detailed spectrum of audio signal in phase space. The results show that the PCA-NN, i.e., neural network based on principal component analysis, is superior to other audio expansion algorithms in subjective and objective evaluation; in log spectrum distortion evaluation, PCA-NN algorithm obtains smaller LSD. Compared with EHBE, Le, and La, the average LSD decreased by 2.286 dB, 0.51 dB, and 0.15 dB, respectively. The above results show that in the image frequency band expansion of college English listening, the neural network algorithm based on principal component analysis (PCA-NN) can obtain better high-frequency reconstruction accuracy and effectively improve the audio quality.

Low-Frequency Noise Correlation in Current-Mode Magnetic Transducers: The CHOPFET Case

This paper is about low-frequency noise correlation in current-mode magnetic field transducers. The analysis methodology specifically focuses on the chopper-stabilized MAGFET (CHOPFET), a magnetotransistor that is compatible with the spinning current technique for low-frequency noise and offset cancelation. Experiments performed on a prototype circuit fabricated in the Austria Mikro Systeme 0.35 $\mu \text{m}$ CMOS process show a minimum value of 0.75 noise correlation between the two consecutive switching phases on an arbitrary-chosen terminal and whatever the operation region of the CHOPFET. This includes the contributions of uncorrelated sources, which cannot be separated from the correlated ones in the analysis process.

Disentangling seasonal and interannual legacies from inferred patterns of forest water and carbon cycling using tree-ring stable isotopes.

Tree-ring carbon and oxygen isotope ratios have been used to understand past dynamics in forest carbon and water cycling. Recently, this has been possible for different parts of single growing seasons by isolating anatomical sections within individual annual rings. Uncertainties in this approach are associated with correlated climate legacies that can occur at a higher frequency, such as across successive seasons, or a lower frequency, such as across years. The objective of this study was to gain insight into how legacies affect cross-correlation in the δ13 C and δ18 O isotope ratios in the earlywood (EW) and latewood (LW) fractions of Pinus ponderosa trees at thirteen sites across a latitudinal gradient influenced by the North American Monsoon (NAM) climate system. We observed that δ13 C from EW and LW has significant positive cross-correlations at most sites, whereas EW and LW δ18 O values were cross-correlated at about half the sites. Using combined statistical and mechanistic models, we show that cross-correlations in both δ13 C and δ18 O can be largely explained by a low-frequency (multiple-year) mode that may be associated with long-term climate change. We isolated, and statistically removed, the low-frequency correlation, which resulted in greater geographical differentiation of the EW and LW isotope signals. The remaining higher-frequency (seasonal) cross-correlations between EW and LW isotope ratios were explored using a mechanistic isotope fractionation-climate model. This showed that lower atmospheric vapor pressure deficits associated with monsoon rain increase the EW-LW differentiation for both δ13 C and δ18 O at southern sites, compared to northern sites. Our results support the hypothesis that dominantly unimodal precipitation regimes, such as near the northern boundary of the NAM, are more likely to foster cross-correlations in the isotope signals of EW and LW, potentially due to greater sharing of common carbohydrate and soil water resource pools, compared to southerly sites with bimodal precipitation regimes.

Cerebrovascular Reactivity Measured by Near-Infrared Spectroscopy

The pressure reactivity index (PRx) describes cerebral vessel reactivity by correlation of slow waves of intracranial pressure (ICP) and arterial blood pressure. In theory, slow changes in the relative total hemoglobin (rTHb) measured by near-infrared spectroscopy are caused by the same blood volume changes that cause slow waves of ICP. Our objective was to develop a new index of vascular reactivity, the hemoglobin volume index (HVx), which is a low-frequency correlation of arterial blood pressure and rTHb measured with near-infrared spectroscopy. Gradual hypotension was induced in piglets while cortical laser-Doppler flux was monitored. ICP was monitored, and rTHb was measured continuously using reflectance near-infrared spectroscopy. The HVx was recorded as a moving linear correlation between slow waves (20 to 300 seconds) of arterial blood pressure and rTHb. Autoregulation curves were constructed by averaging values of the PRx or HVx in 5-mm Hg bins of cerebral perfusion pressure. The laser-Doppler flux-determined lower limit of autoregulation was 29.4+/-6.7 mm Hg (+/-SD). Coherence between rTHb and ICP was high at low frequencies. HVx was linearly correlated with PRx. The PRx and HVx both showed higher values below the lower limit of autoregulation and lower values above the lower limit of autoregulation. Areas under the receiver operator characteristic curves were 0.88 and 0.85 for the PRx and HVx, respectively. Coherence between the rTHb and ICP waveforms at the frequency of slow waves suggests that slow waves of ICP are related to blood volume changes. The HVx has potential for further development as a noninvasive alternative to the PRx.

" Trend Breaks, Long-Run Restrictions, and the Contractionary Effects of Technology Improvements"

Do hours worked rise or fall following an increase in the level of technology? Empirical results from structural VARs with long-run restrictions are often sensitive to whether hours worked enters the VAR in loglevels or in growth rates. However, this paper finds that once one allows for (statistically and economically plausible) trend breaks in labor productivity, the treatment of hours is relatively unimportant: Even with hours worked in levels, hours fall on impact following a technology improvement. Indeed, encompassing tests suggest that the specification with breaks can easily “explain” (or encompass) the large positive apparent response when the breaks are omitted; in contrast, the no-breaks specification has more difficulty explaining the negative response when breaks are included. The issue is the common low frequency high-low-high pattern of hours per capita and productivity growth in the post-world-war II period. Simple analytics plus simulations demonstrate that such low-frequency correlation almost inevitably implies a positive estimated impulse response, regardless of whether the low-frequency correlation is actually causal.This suggests the need for caution in interpreting the results of estimated responses with long-run restrictions, since results may be driven by effects other than those you think you are identifying. I thank Shanthi Ramnath, David Kang, Stephanie Wang, and Andrew McCallum for superb research assistance. I also thank Toni Braun, Susanto Basu, Jeff Campbell, Larry Christiano, Martin Eichenbaum, Jon Faust, Jonas Fisher, Neville Francis, Jordi Gali, Valerie Ramey, John Williams, and Rob Vigfusson for helpful conversations. I thank Valerie Ramey and Rob Vigfusson for providing computer code. The views expressed in this paper are my own and do not necessarily reflect the views of anyone else affiliated with the Federal Reserve System. JEL Codes E24, E32, O47, keywords Technology shocks, business cycles, structural change.

Trend Breaks, Long-Run Restrictions, and the Contractionary Effects of Technology Improvements

Structural vector-autoregressions with long-run restrictions are extraordinarily sensitive to low-frequency correlations. This paper explores this sensitivity analytically and via simulations, focusing on the contentious issue of whether hours worked rise or fall when technology improves. Recent literature finds that when hours per person enter the VAR in levels, hours rise; when they enter in differences, hours fall. However, once we allow for (statistically and economically plausible) trend breaks in productivity, the treatment of hours is relatively unimportant: Hours fall sharply on impact following a technology improvement. The issue is the common high-low-high pattern of hours per capita and productivity growth since World-War II. Such low-frequency correlation almost inevitably implies a positive estimated impulse response. The trend breaks control for this correlation. In addition, the specification with breaks can easily 'explain' (or encompass) the positive estimated response when the breaks are omitted; in contrast, the no-breaks specification has more difficulty explaining the negative response when breaks are included. More generally, this example suggests a need for care in applying the long-run-restrictions approach.

Trend breaks, long-run restrictions, and contractionary technology improvements

Structural vector autoregressions with long-run restrictions are extraordinarily sensitive to low-frequency correlations. Recent literature finds that the estimated effects of technology shocks are sensitive to how one treats hours per capita. However, after allowing for (statistically and economically significant) trend breaks in productivity, results are much less sensitive: hours fall when technology improves. The issue is that the common high–low–high pattern of productivity growth and hours (i.e., the low-frequency correlation) inevitably leads to a positive estimated response. The trend breaks control for this correlation. This example suggests a practical need for care in using long-run restrictions.

Is M82 X-1 Really an Intermediate-Mass Black Hole? X-Ray Spectral and Timing Evidence

Ultraluminous X-ray sources (ULXs) with apparent luminosities up to hundreds of times the Eddington luminosity for a neutron star have been discovered in external galaxies. The existence of intermediate-mass black holes has been proposed to explain these sources. We present evidence for an intermediate-mass black hole in the ULX M82 X-1 based on the spectral features and timing (quasi-periodic oscillation [QPO]) properties of the X-radiation from this source. We revisited XMM-Newton and Rossi X-Ray Timing Explorer (RXTE) data for M82 X-1 obtained in 2001 and 1997 for XMM and RXTE, respectively. We show for these observations that the source is either in transition or in a high/soft state with photon spectral indices 2.1 and 2.7, respectively. We confirm the early determination of the QPO frequency nu approx. = 55 mHz in this source by Strohmayer & Mushotzky and identify this as the low-frequency QPO for the source. We apply a new method to determine the black hole mass of M82 X-1. The method uses the index-QPO low-frequency correlation that has been recently established in Galactic black hole candidates GRS 1915+105, XTE JI550-564, 4U 1630-47, and others. Using scaling arguments and the correlation derived from the consideration of Galactic black holes, we conclude that M82 X-1 is an intermediate black hole with a mass of the order of 1000 solar mass,.

Interhemispheric phase synchrony and amplitude correlation of spontaneous beta oscillations in human subjects: a magnetoencephalographic study.

Interhemispheric phase synchrony and amplitude correlation of beta oscillations were studied with MEG in a resting condition. The left and right hemisphere beta oscillations exhibited phase-locking with a phase-lag near zero degrees. The index of synchronization was strongest when these oscillations had large amplitude. Functionally, we interpret the phase synchrony on the basis of bilaterality of movement organization. A positive interhemispheric correlation was also found for the amplitude of spontaneous beta oscillations over long time intervals (> 1 s). The low-frequency correlation of spontaneous rhythmic activity may be the source of the low-frequency correlations of the hemodynamic responses in homologous areas that have been reported previously and have been interpreted as functional connectivity between these areas.

The long time tail of molecular velocity correlation in a confined fluid: observation by modulated gradient spin-echo NMR

In addition to the fast correlation for local stochastic motion the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time tail decay [1,2]. This article presents a study by the NMR modulated gradient spin-echo method (MGSE) [3] on a system of water trapped in the space between the closely packed polystyrene beads. The results prove that the obtained dependence of spin-echo attenuation on time, gradient strength and modulation frequency nicely corresponds to the recently developed NMR approach, which is able to describe the effects of arbitrarily shaped gradient pulse sequence on the spin-echo attenuation [4,5]. With an MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin-phase, giving the spin-echo attenuation proportional to a value of the velocity correlation spectrum at the modulation frequency. It enables to extract the low-frequency correlation spectrum of confined water molecules. The function exhibits a negative long time tail characteristic (a low-frequency decay of the spectrum), that can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay).

Temporal correlations in low frequency BOLD fluctuations reveal functional networks

Introduction It has been demonstrated that very low frequency temporal fluctuations in rapidly sampled blood oxygenation level dependent (BOLD) weighted echoplanar imaging data are phase-locked between many right and left-hemisphere symmetric functional cortices such as precentral gyrus (i.e. motor cortex) in human subjects at rest (1, 2). It has been postulated by the authors that these correlations in lowfrequency fluctuations are a reflection of functional connectivity. It has also been shown that Resting-state acquisitions are, in fact, timeseries acquisitions in which the subject is asked to refrain from overt activity. The “state” of the brain is otherwise uncontrolled. A recent experiment by Franson et al showed residual effects of BOLD signal lasting several tens of seconds after very brief neuronal stimulation(3). Thus, a possible explanation of the a posterion’ observations of low-frequency temporal correlation between functionally connected anatomic regions is that uncontrolled brain activity excites these connected regions and subsequent filtering isolates the long-term effects from higher frequency noise fluctuations, which are non-specific to function (e.g. cardiac and respiratory-related BOLD fluctuations). As a further test of this, we designed an experiment in which subjects continuously performed a cognitive task, which excites a network of brain regions. The task is performed at a rate of 0.4Hz. The data are then filtered to remove fluctuations above 0.08Hz (corresponding to a period of 12.5 seconds). If low frequency fluctuations are a measure of functional connectivity, then the correlations between brain regions in the filtered data should reflect the network of brain regions involved in the task.

Modeling noise correlation behavior in dual-collector magnetotransistors using small signal equivalent circuit analysis

We present a distributed small signal equivalent circuit model based on hybrid-/spl pi/ for modeling of the low-frequency noise correlation behavior in dual-collector magnetotransistors (MTs). The model is based on the assumption that the noise sources at the emitter-base junction of the transistor are spatially correlated; the degree of spatial correlation in noise sources being limited by the intrinsic base spreading resistance. This gives rise to a degradation in correlation of terminal collector noise currents at high current, or injection, levels due to nonuniformities in the dc bias current distribution.

Critical behavior of sliding charge-density waves in 4-ε dimensions

The critical dynamics of charge-density waves (CDW's) just above the threshold for steady-state sliding motion are studied via a renormalization-group expansion in 4-\ensuremath{\epsilon} dimensions. This necessitates the simultaneous treatment of the long-wavelength low-frequency dynamics as well as the singular behavior associated with the jumps of local regions during which the local velocities become large. Scaling forms are obtained for response and correlation functions in the critical region, and exponent identities are derived. To leading order in \ensuremath{\epsilon}, the exponent \ensuremath{\zeta} of the CDW current ${\mathit{I}}_{\mathrm{CDW}}$\ensuremath{\sim}(V-${\mathit{V}}_{\mathit{T}}$${)}^{\mathrm{\ensuremath{\zeta}}}$ just above the threshold voltage ${\mathit{V}}_{\mathit{T}}$ is found to be \ensuremath{\zeta}=1-\ensuremath{\epsilon}/6+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$), in reasonable agreement with recent numerical simulations in two and three dimensions. The spatial correlations in the local velocities of the CDW decay exponentially with a correlation length, which diverges with an exponent \ensuremath{\nu} exactly equal to 1/2. Nevertheless, finite-size scaling of many quantities will be determined by a different exponent ${\ensuremath{\nu}}_{\mathrm{FS}}$=1/2+\ensuremath{\epsilon}/8+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$)=2/d+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). The other exponents are related to \ensuremath{\zeta}, \ensuremath{\nu}, and ${\ensuremath{\nu}}_{\mathrm{FS}}$. Simple forms of long-wavelength low-frequency correlation and response functions in the moving phase are obtained to all orders in perturbation theory.

A dynamical treatment of the spin glass transition

Closed non-linear equations are derived through mode-coupling approximations for the correlation functions and susceptibilities for the Edwards-Anderson model of a classical Heisenberg system with nearest-neighbour random exchange couplings. These equations, which exhibit full dynamical stability, lead to a self-consistent treatment of spin-density propagation and spin-current relaxation. They are found to describe a transition from a paramagnetic to a spin glass phase, which is viewed as one where the dynamics changes from ergodic to a non-ergodic behaviour. Near the critical temperature Tc the low-frequency correlation functions are obtained as dynamical scaling laws governed by a critical frequency omega c, which slows down proportionally to epsilon 2, with epsilon =(T-Tc)/Tc. Approaching the critical point from the paramagnetic side the diffusivity vanishes linearly with epsilon . The susceptibility exhibits a symmetric cusp. The drastic changes of the spin dynamics at the transition point show up most clearly for the spin-current spectra. The numerical solution of the equations is discussed.

Low-frequency correlation functions in case of nonlinear dynamics of fluctuations

A method is developed for calculating low-frequency asymptotic correlation functions of basic operators “ â m ” which correspond to gross variables describing a nonequibliriium state of a system. We have introduced a Weyl operator, its nonequilibrium average value being considered as a quantum distribution function of gross variables. The generalized Fokker-Planck equation is then derived for the distribution function. This equation is used for obtaining a chain of equations for asymptotic correlation functions containing only Weyl operator functions of “ â m ”. The kinetic coefficients and self-energy are expressed in terms of irreducible correlation functions which correspond to effects of nonlinear dynamics of fluctuations. It is shown in our approach that hydrodynamic modes may be considered as a zero order approximation. As an application of the formalism the generalized mode-mode coupling approximation is investigated.

S Matrix and Low Energy Theorem in the Theory of Correlation Functions

We have examined the current correlation functions is statistical mechanics from a scattering theory viewpoint. In the light of low energy theorems, we study the connection between the long wavelength, low-frequency correlation functions of conserved currents and the on-shell scattering matrix elements which describe the collision processes taking place in the thermodynamical system of interest. Explicit general formulas are derived for the leading correction terms to the ideal gas correlation functions. These correction terms include the effect of two-body scatterings and double scatterings in three-body events. They are expressed in terms of two-body cross section, time delay, and the quantum analog of the distance of closest approach. Their connection to the second virial coefficient is established through sum rules. Relationship between our results and the Boltzmann equation is discussed.