Power Spectral Density Parameters Research Articles

Stochastic prior for non-parametric star-formation histories

ABSTRACT The amount of power contained in the variations in galaxy star-formation histories (SFHs) across a range of time-scales encodes key information about the physical processes which modulate star formation. Modelling the SFHs of galaxies as stochastic processes allows the relative importance of different time-scales to be quantified via the power spectral density (PSD). In this paper, we build upon the PSD framework and develop a physically motivated, ‘stochastic’ prior for non-parametric SFHs in the spectral energy distribution (SED)-modelling code prospector. We test this prior in two different regimes: (1) massive, $z = 0.7$ galaxies with both photometry and spectra, analogous to those observed with the LEGA-C survey, and (2) $z = 8$ galaxies with photometry only, analogous to those observed with NIRCam on JWST. We find that it is able to recover key galaxy parameters (e.g. stellar mass, stellar metallicity) to the same level of fidelity as the commonly used continuity prior. Furthermore, the realistic variability information incorporated by the stochastic SFH model allows it to fit the SFHs of galaxies more accurately and precisely than traditional non-parametric models. In fact, the stochastic prior is $\gtrsim 2\times$ more accurate than the continuity prior in measuring the recent star-formation rates (log SFR$_{100}$ and log SFR$_{10}$) of both the $z = 0.7$ and $z = 8$ mock systems. While the PSD parameters of individual galaxies are difficult to constrain, the stochastic prior implementation presented in this work allows for the development of hierarchical models in the future, i.e. simultaneous SED-modelling of an ensemble of galaxies to measure their underlying PSD.

BEYONDPLANCK

We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BEYONDPLANCKGibbs sampling framework, which we applied toPlanckLow Frequency Instrument (LFI) time-ordered data. Following previous works in the literature, we initially adopted a 1/fmodel for the noise power spectral density (PSD), but we found the need for an additional lognormal component in the noise model in the 30 and 44 GHz bands. We implemented an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then used this procedure to both estimate the gapless correlated noise in the time-domain,ncorr, and to sample the noise PSD parameters,ξn = {σ0, fknee, α, Ap}. In contrast to previousPlanckanalyses, we assumed piecewise stationary noise only within each pointing period (PID), and not throughout the full mission, but we adopted the LFI Data Processing Center results as priors onαandfknee. We generally found best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results has revealed many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/fmodel appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise that is not described by a 1/fmodel in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/fat the 2–3σlevel in each one-hour pointing period, motivating the addition of the lognormal noise component for these bands. For certain periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/fprofile is not adequate for obtaining a full characterization of thePlanckLFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with thePlanckLFI data and the current work is a first attempt at understanding and mitigating these issues.

Seismic reliability analysis using a multi-fidelity surrogate model: Example of base-isolated buildings

An approach is presented for conducting simulation-based seismic reliability analysis using a multi-fidelity surrogate model. To illustrate the approach, a base-isolated building is considered comprising a reinforced concrete frame for primary building and lead-rubber bearings for isolation devices. The high-fidelity model is a nonlinear finite-element model used in time history analysis. Ground motions are generated from a parametric power spectral density function that is compatible with a target response spectrum at the site of interest. The low-fidelity model uses a linear-elastic stick model for the superstructure, while stochastic linearization is used to capture the nonlinearity of the base isolation. Cokriging is used as a multi-fidelity surrogate model for fusing a large number of low-fidelity model evaluations with few high-fidelity model evaluations, in order to attain high-fidelity model accuracy while mitigating the computational cost. After training the Cokriging model, Monte Carlo simulation is carried out by sampling the cheap multi-fidelity surrogate, and the probability of failure is subsequently evaluated for different response thresholds. The relative error in failure probability prediction of Cokriging is shown to be in the range of 6% with a maximum of 10%, for a critical range of sample response variable threshold values, in contrast to errors as high as 60% provided by the low-fidelity model.

Quantitative Characterization Method for Rock Surface Roughness with Different Scale Fluctuation

Quantitative characterization of the surface roughness plays a vital role in the field of rock mechanics. The objectives of this study were to propose a new index that can describe the various morphological characteristics with different scale fluctuation. The power spectral density (PSD) parameters and conventional statistical parameters were used to analyze the roughness of meso-scale grind surfaces, intermediate-scale synthesis surfaces, and macro-scale shear surfaces. The results showed that the PSD parameters (slope k, intercept b, spectral moment λ0, and spectral shape parameters ω1 and ω2) and conventional statistical parameters (RMS and Z2) have evident uniqueness and uniformity in characterizing the roughness with different scale fluctuation. It is necessary to appropriately use the correct parameters for classifying and quantifying the roughness. For this purpose, a new characterization index SLA was proposed based on the spectral shape parameter ω1, spectral moment λ0, slope k, and angle fractal index C.

Proposal of a pseudo‐electrocardiogram model incorporating heart rate variability and QT‐interval variability, and its application

In this work, we propose a model that incorporates QT‐interval variability (QTV) by extending the synthetic electrocardiogram (ECG) model including heart rate variability (HRV). The model consists of three modified coupled ordinary differential equations and an equation to incorporate QTV by shifting the position of the T‐wave; in addition, RR and QT tachograms that have frequency characteristics composed of multiple Gaussian distribution peaks are used. An ECG signal can be generated by adapting a certain ECG waveform and by giving the means, standard deviations, and power spectral density parameters of HRV and QTV. This proposed model may reveal the neurophysiological mechanisms underlying the relationship between QTV and HRV and/or the autonomic activity, and it may solve problems in the measurement of QT‐interval. In conclusion, this proposed model is a very useful tool in medical education and experimental simulation. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Application of intraoperative electrocorticography in bypass surgery for adult moyamoya disease: a preliminary study.

Postoperative complications of surgical revascularization in moyamoya disease (MMD) are difficult to predict because of poor knowledge of the underlying pathophysiological process. Since the aim of surgery is to improve brain dynamics by increasing regional blood flow, we hypothesize that postoperative complications are closely related to aberrant electrophysiological changes. Thus, we evaluated the clinical significance of intraoperative electrocorticography (iECoG) in bypass surgery for adult MMD. Ninety-one adult patients operated on by the same neurosurgeon in our institute were involved (26 in the iECoG group, 65 in the traditional group). Two 1 × 6 subdural electrode grids were placed parallel to the middle frontal gyrus and superior temporal gyrus to record ECoG data continuously during the procedure in the iECoG group. Selected from several M4 candidate arteries, the recipient artery was determined to be closer to the cortex with lower power spectral density (PSD) in the beta band. The PSD parameter we used was the (delta+theta)/(alpha+beta) (DTAB) ratio (DTABR). Next, the pre- and post-bypass PSD values were evaluated, and correlations between post-/pre-bypass PSD parameter ratios and neurological/neuropsychological performance (in terms of changes in National Institutes of Health Stroke Scale [NIHSS] and Mini-Mental State Examination [MMSE] scores) were analyzed. Postoperative complications (transient neurological events) in the iECoG group were significantly lower than those in the traditional group (p = 0.046). In the iECoG group, the post-/pre-bypass DTABR ratio in the bypass area was significantly correlated with postoperative NIHSS (p = 0.002, r2 = 0.338) and MMSE changes (p = 0.007, r2 = 0.266). In the nonbypass area, neither postoperative NIHSS nor MMSE changes showed a significant correlation with the post-/pre-bypass DTABR ratio (p > 0.05). Additionally, patients with postoperative complications exhibited significantly higher DTABR (1.67 ± 0.33 vs. 0.95 ± 0.08, p = 0.003) and PSD of the theta band (1.54 ± 0.21 vs. 1.13 ± 0.08, p = 0.036). This study is the first to explain and guide surgical revascularization from the perspective of electrophysiology. Intraoperative ECoG is not only sensitive in reflecting and predicting postoperative neurological and cognitive performance but also usable as a reference for recipient artery selection.

Machine learning application to detect light echoes around black holes

ABSTRACT X-ray reverberation has become a powerful tool to probe the disc-corona geometry near black holes. Here, we develop machine learning (ML) models to extract the X-ray reverberation features imprinted in the power spectral density (PSD) of active galactic nucleus (AGN). The machine is trained using simulated PSDs in the form of a simple power-law encoded with the relativistic echo features. Dictionary learning and sparse coding algorithms are used for the PSD reconstruction, by transforming the noisy PSD to a representative sparse version. Then, the support vector machine is employed to extract the interpretable reverberation features from the reconstructed PSD that holds the information of the source height. The results show that the accuracy of predicting the source height, h, is genuinely high and the misclassification is only found when h > 15rg. When the test PSD has a bending power-law shape, which is completely new to the machine, the accuracy is still high. Therefore, the ML model does not require the intrinsic shape of the PSD to be determined in advance. By focusing on the PSD parameter space observed in real AGN data, classification for h ≤ 10rg can be determined with 100 per cent accuracy, even using a PSD in an energy band that contains a reflection flux as low as $10{{\ \rm per\ cent}}$ of the total flux. For h > 10rg, the data, if misclassified, will have small uncertainties of Δh ∼ 2–4rg. This work shows, as a proof of concept, that the ML technique could shape new methodological directions in the X-ray reverberation analysis.

Vibration Analysis of a Bus’s Air Spring Suspension Subjected to Random Road Profile

Vehicle dynamics model in type of 1/4 is used for vibration analysis under the effect of random road profile with different grades. The mathematical model to describe the used random road profile is able to change the type of investigated road grades by selecting the corresponding power spectral density parameter of the road grade according to the ISO 8608 standard. Random road profile is ivestigated in the range of frequency domain from 0 to 50 (Hz). The air spring stiffness and the damping coefficience are determined on the basis of reference to the practical vehicle. The variation of relative displacement amplitude of the suspension in the range of investigation domain is small, the air spring stiffness used in the calculation is constant. The obtained results corresponding to different grades of road surface roughness including displacement and acceleration parameters. Relative displacement is a parameter that aims to verify the ability to ensure safe working of the suspension, namely rattle spacing. Acceleration is used to evaluate the vehicle's comfort. Calculation results are analyzed as the basis for evaluating the influence of the air spring stiffness and road surface conditions on the comfort of the vehicle, as the basis for changing the air spring stiffness in accordance with adjusting the pressure of it according to the type of road profile quality.

Thermal loading effect on P-wave form and power spectral density in crystalline and non-crystalline rocks

Geomechanical properties of rocks change considerably when subjected to thermal loading. In some cases, the damage induced by thermal loading is advantageous for geotechnical activities such as geothermal reservoir and hydraulic fracturing, and it is non-beneficial for other activities including stability of underground spaces and rock slopes; therefore, this paper deals with parameters such as P-wave form and power spectral density (PSD) as indexes for considering the degree of damage induced by thermal loading in rocks. In this regard, 7 types of rocks in 3 categories including igneous, sedimentary, and metamorphic were selected and heated up to 500 °C at furnace for 5 h; then, the specimens were cooled down immediately, and subsequently, P-wave velocity and P-wave form were measured. The results showed that thermal loading has no significant impact on the frequency component of different rocks; however, PSD parameter decreases dramatically after heating at 500 °C. In addition, the effect of thermal loading at 500 °C on the P-wave form for crystalline and non-crystalline rocks is variable. For crystalline rocks at room temperature, the peak of PSD parameter reduces more than non-crystalline rocks; in other words, in crystalline rocks, the dissipation of energy is greater than non-crystalline rocks. Microscopic observations were also provided in order to investigate the effect of thermal loading on PSD parameter in detail. It can be concluded that the mechanism of intergranular and intragranular microcracks in crystalline rocks and also the mechanism of disintegrated background cement in non-crystalline rocks could be attributed to the reduction in peak of PSD parameter.

Ambient Seismic Noise Analysis Associated with the 2010 Eruption of Merapi Volcano Using Temporal Variations of Randomness and Background Noise

We present the combination of permutation entropy (PE) and power spectral density (PSD) analysis on continuous seismic data recorded by short-period seismic stations during the 2010 Merapi volcano eruption. The calculation of PE aims at characterizing the randomness level in seismic noise, while the PSD parameters use to detect the background noise level in various frequency bands. It was previously observed that a significant reduction of randomness before the volcano eruption could be indicated as one of the short-term precursors due to the lack of high frequencies (>1 Hz) in the noise wave-field caused by high absorption losses as the hot magma uprises to the upper crust. The results show no significant reduction in signal randomness before the eruption series. The characteristic of events during the preeruptive period and the crisis tends to be chaotic (PE in the range 0.9 to 1). Further calculations show that the standard deviation in PE decreased in four days before the first eruption onset on 26 October. PE was stable at the highest values (very close to 1) and gradually returned to the previous fluctuation after the eruption onset. The level of background noise in the low- and high-frequency bands appeared to have the same tendency. The two main eruptions correspond to the two highest peaks of noise levels.

Acupuncture at the auricular branch of the vagus nerve enhances heart rate variability in humans: An exploratory study.

BackgroundRecent animal and human studies have shown antiarrhythmic effects inhibiting inducibility of atrial fibrillation through low-level transcutaneous electrical stimulation at the auricular branch of the vagus nerve (ABVN).ObjectiveThe present study investigated effects of acupuncture at the ABVN on the autonomic cardiac nervous system in humans through analysis of heart rate and heart rate variability (HRV) parameters.MethodsWe enrolled 24 healthy male volunteers and compared acupuncture at the ABVN to placebo-acupuncture performed at the Ma-35 point (an acupuncture point used in traditional Chinese medicine to treat pain caused by gonarthrosis). An additional measurement without acupuncture served as control. We analyzed the following heart rate and HRV parameters: standard deviation of normal-to-normal intervals (SDNN), root mean square of successive R-R interval differences (RMSSD), high frequency (HF), low frequency (LF), LF/HF ratio.ResultsIn comparison to placebo acupuncture, acupuncture at the ABVN led to a significant reduction in heart rate (approximately 4%–6%, P < .05) and an increase in overall HRV demonstrated by SDNN (approximately 19%, P < .05). RMSSD and power spectral density parameters (HF, LF, LF/HF) showed statistical trends (P < .1) induced by auricular acupuncture in favor of vagal tone. No relevant difference was shown between control and placebo group.ConclusionAcupuncture of the region innervated by the ABVN may activate the parasympathetic nervous system, as suggested by reduction in heart rate and increase in SDNN. However, given the lack of clear significant changes in other HRV parameters, this effect seems modest and its evaluation requires further investigation.

Unsupervised joint deconvolution and segmentation method for textured images: a Bayesian approach and an advanced sampling algorithm

The paper tackles the problem of joint deconvolution and segmentation of textured images. The images are composed of regions containing a patch of texture that belongs to a set of K possible classes. Each class is described by a Gaussian random field with parametric power spectral density whose parameters are unknown. The class labels are modelled by a Potts field driven by a granularity coefficient that is also unknown. The method relies on a hierarchical model and a Bayesian strategy to jointly estimate the labels, the K textured images in addition to hyperparameters: the signal and the noise levels as well as the texture parameters and the granularity coefficient. The capability to estimate the latter is an important feature of the paper. The estimates are designed in an optimal manner as a risk minimizer that yields the marginal posterior maximizer for the labels and the posterior mean for the rest of the unknowns. They are computed based on a convergent procedure from samples of the posterior obtained through an advanced MCMC algorithm: Perturbation-Optimization step and Fisher Metropolis-Hastings step within a Gibbs loop. Various numerical evaluations provide encouraging results despite the strong difficulty of the problem.

Speech-based Class Attendance

In the department of engineering, students are required to fulfil at least 80 percent of class attendance. Conventional method requires student to sign his/her initial on the attendance sheet. However, this method is prone to cheating by having another student signing for their fellow classmate that is absent. We develop our hypothesis according to a verse in the Holy Qur’an (95:4), “We have created men in the best of mould”. Based on the verse, we believe each psychological characteristic of human being is unique and thus, their speech characteristic should be unique. In this paper we present the development of speech biometric-based attendance system. The system requires user’s voice to be installed in the system as trained data and it is saved in the system for registration of the user. The following voice of the user will be the test data in order to verify with the trained data stored in the system. The system uses PSD (Power Spectral Density) and Transition Parameter as the method for feature extraction of the voices. Euclidean and Mahalanobis distances are used in order to verified the user’s voice. For this research, ten subjects of five females and five males were chosen to be tested for the performance of the system. The system performance in term of recognition rate is found to be 60% correct identification of individuals.

Prediction of Beck Depression Inventory (BDI-II) Score Using Acoustic Measurements in a Sample of Iium Engineering Students

Psychiatrist currently relies on questionnaires and interviews for psychological assessment. These conservative methods often miss true positives and might lead to death, especially in cases where a patient might be experiencing suicidal predisposition but was only diagnosed as major depressive disorder (MDD). With modern technology, an assessment tool might aid psychiatrist with a more accurate diagnosis and thus hope to reduce casualty. This project will explore on the relationship between speech features of spoken audio signal (reading) in Bahasa Malaysia with the Beck Depression Inventory scores. The speech features used in this project were Power Spectral Density (PSD), Mel-frequency Ceptral Coefficients (MFCC), Transition Parameter, formant and pitch. According to analysis, the optimum combination of speech features to predict BDI-II scores include PSD, MFCC and Transition Parameters. The linear regression approach with sequential forward/backward method was used to predict the BDI-II scores using reading speech. The result showed 0.4096 mean absolute error (MAE) for female reading speech. For male, the BDI-II scores successfully predicted 100% less than 1 scores difference with MAE of 0.098437. A prediction system called Depression Severity Evaluator (DSE) was developed. The DSE managed to predict one out of five subjects. Although the prediction rate was low, the system precisely predict the score within the maximum difference of 4.93 for each person. This demonstrates that the scores are not random numbers.

Use of generated artificial road profiles in road roughness evaluation

In the evaluation of road roughness and its effects on vehicles response in terms of ride quality, loads induced on pavement, drivers’ comfort, etc., it is very common to generate road profiles based on the equation provided by ISO 8608 standard, according to which it is possible to group road surface profiles into eight different classes. However, real profiles are significantly different from the artificial ones because of the non-stationary feature of the first ones and the not full capability of the ISO 8608 equation to correctly describe the frequency content of real road profiles. In this paper, the international roughness index, the frequency-weighted vertical acceleration awz according to ISO 2631, and the dynamic load index are applied both on artificial and real profiles, highlighting the different results obtained. The analysis carried out in this work has highlighted some limitation of the ISO 8608 approach in the description of performance and conditions of real pavement profiles. Furthermore, the different sensitivity of the various indices to the fitted power spectral density parameters is shown, which should be taken into account when performing analysis using artificial profiles.

Drinking functional coherent mineral water accompanies a strengthening of the very low frequency impact on heart rate variability, and mono and multifractal heart rhythm dynamics in healthy humans

Background: Research on functional water has revealed its physiological functions and health-beneficial effects. Accordingly, this study explored the effects of drinking an average dietary volume of functional coherent mineral water (FCMW) on blood pressure, short-term cardiovascular variables, fractal heart rhythm dynamics, and salivary immunoglobulin A. Methods: Fifteen healthy subjects were randomized in a pre-post crossover design, selected the morning after an overnight fast. Short-term electrocardiography (ECG) was measured before and after drinking either control mineral water (CMW) or FCMW on two separate occasions. Saliva was collected for four minutes before the start of each ECG measurement. Blood pressure was monitored in five-minute intervals for one hour. Results: Drinking 100 ml of FCMW temporarily increased arterial blood pressure at 20 to 25 minutes in the 60 minutes post-drinking. Drinking CMW led to a significant reduction in the heart rate, while all-time domain and Power Spectral Density parameters (PSD) were unaffected. Consumption of FCMW resulted in a highly significant difference and decrease in heart rate, and an increase in NN interbeat intervals, and in two of the PSD parameters. A large increase in total power had a significant increasing effect on 2–3-minute oscillations of the very low frequency (VLF) power, indicating a specific change in the heartʼs intrinsic cardiac rhythm that is fundamental to health and well-being. An extension in mono and multifractal scaling of heart rate dynamics defines a healthy function and non-local adaptability, indicating a higher capacity to respond to unpredictable stimuli and stresses, a function which improves autonomic stability. The effect on the heart rate and VLF power suggest an efficient cellular metabolism and a stabilizing effect on mucosal immunoglobulin A. Conclusions: Functional coherent mineral water with an apparent non-local electromagnetic identity triggered in healthy subjects a sustainable sympathetic response in cardiac VLF power, which is considered an intrinsic health-promoting rhythm produced by the heart itself that accompanies adaptive mono and multifractal heart rhythm dynamics. Keywords: functional water, VLF-power, heart rate variability, fractal scaling, health improvement

MODELING THE POWER SPECTRA OF ACTIVE GALACTIC NUCLEI WITH MARKOV CHAIN MONTE CARLO

We present a new method for calculating the power spectral density (PSD) of a light curve using Markov Chain Monte Carlo principles. This method allows for a faster estimation of PSD parameters, along with more robust estimates of the uncertainties for each parameter. We show that this technique is valid by applying it to a simulated light curve, where it correctly estimates the PSD parameters. We then analyze the light curves of two nearby AGNs, NGC 4593 and Mkn 79. Breaks in the PSD are detected at timescales of and days, respectively. These values agree with the predicted breaks based on scaling relationships with other AGNs and galactic black hole binary systems. The break timescale for each object agrees with the viscous timescale for a geometrically thick accretion disk, supporting the idea that a propagating fluctuation model may be responsible for variations in the X-ray flux.

Roughness-Induced Pavement–Vehicle Interactions

Pavement roughness affects rolling resistance and thus vehicle fuel consumption. When a vehicle travels at constant speed on an uneven road surface, the mechanical work dissipated in the vehicle's suspension system is compensated by vehicle engine power and results in excess fuel consumption. This dissipation depends on both road roughness and vehicle dynamic characteristics. This paper proposes, calibrates, and implements a mechanistic model for roughness-induced dissipation. The distinguishing feature of the model is its combination of a thermodynamic quantity (energy dissipation) with results from random vibration theory to identify the governing parameters that drive the excess fuel consumption caused by pavement roughness, namely, the international roughness index (IRI) and the waviness number, w (a power spectral density parameter). It is shown through sensitivity analysis that the sensitivity of model output, that is, excess fuel consumption, to the waviness number is significant and comparable to that of IRI. Thus, introducing the waviness number as a second roughness index, in addition to IRI, allows a more accurate quantification of the impact of surface characteristics on vehicle fuel consumption and the corresponding greenhouse gas emissions. This aspect is illustrated by application of the roughness–fuel consumption model to two road profiles extracted from FHWA's Long-Term Pavement Performance database.

Numerical simulation of non-Gaussian wind load

Compared with Gaussian wind loads, there is a higher probability of strong suction fluctuations occurrence for non-Gaussian wind pressures. These instantaneous and intermittent fluctuations are the initial cause of local damage to roof structures, particularly at the edges and corners of long-span roofs. Thus, comparative errors would occur if a Gaussian model is used to describe a non-Gaussian wind load, and structural security would not be guaranteed. This paper presents a simplified method based on the inverse fast Fourier transform (IFFT), in which the amplitude spectrum is established via a target power spectrum. Also, the phase spectrum is constructed by introducing the exponential peak generation (EPG) model. Finally, a random process can be generated via IFFT that meets the specified power spectral density (PSD), skewness and kurtosis. In contrast to a wind tunnel experiment, this method can avoid the coupled relation between the non-Gaussian and the power spectrum characteristics, and lead to the desired computational efficiency. Its fitting accuracy is not affected by phase spectrum. Moreover, the fitting precision of the kurtosis and PSD parameters can be guaranteed. In a few cases, the fitting precision of the skewness parameter is fairly poor, but kurtosis is more important than skewness in the description of the non-Gaussian characteristics. Above all, this algorithm is simple and stable and would be an effective method to simulate a non-Gaussian signal.

Cyclic Seesaw Process for Optimization and Identification

A known approach to optimization is the cyclic (or alternating or block coordinate) method, where the full parameter vector is divided into two or more subvectors and the process proceeds by sequentially optimizing each of the subvectors, while holding the remaining parameters at their most recent values. One advantage of such a scheme is the preservation of potentially large investments in software, while allowing for an extension of capability to include new parameters for estimation. A specific case of interest involves cross-sectional data that is modeled in state–space form, where there is interest in estimating the mean vector and covariance matrix of the initial state vector as well as certain parameters associated with the dynamics of the underlying differential equations (e.g., power spectral density parameters). This paper shows that, under reasonable conditions, the cyclic scheme leads to parameter estimates that converge to the optimal joint value for the full vector of unknown parameters. Convergence conditions here differ from others in the literature. Further, relative to standard search methods on the full vector, numerical results here suggest a more general property of faster convergence for seesaw as a consequence of the more “aggressive” (larger) gain coefficient (step size) possible.