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The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD model forecasts. Despite its widespread use and utility, DMD can fail to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD’s first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD’s performance is demonstrated in numerical and experimental fluids examples. In particular, in the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques. Further, TDMD extracts modes that reveal detailed spatial structures missed by standard DMD.

Speech perception is mediated by both left and right auditory cortices but with differential sensitivity to specific acoustic information contained in the speech signal. A detailed description of this functional asymmetry is missing, and the underlying models are widely debated. We analyzed cortical responses from 96 epilepsy patients with electrode implantation in left or right primary, secondary, and/or association auditory cortex (AAC). We presented short acoustic transients to noninvasively estimate the dynamical properties of multiple functional regions along the auditory cortical hierarchy. We show remarkably similar bimodal spectral response profiles in left and right primary and secondary regions, with evoked activity composed of dynamics in the theta (around 4-8 Hz) and beta-gamma (around 15-40 Hz) ranges. Beyond these first cortical levels of auditory processing, a hemispheric asymmetry emerged, with delta and beta band (3/15 Hz) responsivity prevailing in the right hemisphere and theta and gamma band (6/40 Hz) activity prevailing in the left. This asymmetry is also present during syllables presentation, but the evoked responses in AAC are more heterogeneous, with the co-occurrence of alpha (around 10 Hz) and gamma (>25 Hz) activity bilaterally. These intracranial data provide a more fine-grained and nuanced characterization of cortical auditory processing in the 2 hemispheres, shedding light on the neural dynamics that potentially shape auditory and speech processing at different levels of the cortical hierarchy.

The number of fluorescent labels that can unambiguously be distinguished in a single image when acquired through band pass filters is severely limited by the spectral overlap of available fluorophores. The recent development of spectral microscopy and the application of linear unmixing algorithms to spectrally recorded image data have allowed simultaneous imaging of fluorophores with highly overlapping spectra. However, the number of distinguishable fluorophores is still limited by the unavoidable decrease in signal to noise ratio when fluorescence signals are fractionated over multiple wavelength bins. Here we present a spectral image analysis algorithm to greatly expand the number of distinguishable objects labeled with binary combinations of fluorophores. Our algorithm utilizes a priori knowledge about labeled specimens and imposes a binary label constraint on the unmixing solution. We have applied our labeling and analysis strategy to identify microbes labeled by fluorescence in situ hybridization and here demonstrate the ability to distinguish 120 differently labeled microbes in a single image.

Sexual desire discrepancy is one of the most frequently reported sexual concerns for individuals and couples and has been shown to be negatively associated with sexual and relationship satisfaction. Sexual desire has increasingly been examined as a state-like construct that ebbs and flows, but little is known about whether there are patterns in the fluctuation of sexual desire. Utilizing spectral and cross-spectral analysis, we transformed 30 days of dyadic daily diary data for perceived levels of sexual desire for a non-clinical sample of 133 couples (266 individuals) into the frequency domain to identify shared periodic state fluctuations in sexual desire. Spectral analysis is a technique commonly used in physics and engineering that allows time series data to be analyzed for the presence of regular cycles of fluctuation. Cross-spectral analysis allows for dyadic data to be analyzed for shared rates of fluctuation between partners as well as the degree of (a)synchrony (or phase shift) between these fluctuations. Men and women were found to exhibit fluctuations in sexual desire at various frequencies including rates of once and twice per month, and to have sexual desire that was unlikely to fluctuate over periods of three days or less and therefore exhibited persistence. Similar patterns of fluctuation were exhibited within couples and these patterns were found to be largely synchronous. While instances of desire discrepancy may arise due to differences in rates of sexual desire fluctuation and random fluctuations, such instances may be normal for romantic relationships. The results have important implications for researchers, clinicians, and educators in that they corroborate the supposition that sexual desire ebbs and flows and suggest that it does so with predictable regularity.

The aim of time-varying heart rate variability spectral analysis is to detect and quantify changes in the heart rate variability spectrum components during nonstationary events. Of the methods available, the nonparametric short-time Fourier Transform and parametric time-varying autoregressive modeling are the most commonly employed. The current study (1) compares short-time Fourier Transform and autoregressive modeling methods influence on heart rate variability spectral characteristics over time and during an experimental ozone exposure in mature adult spontaneously hypertensive rats, (2) evaluates the agreement between short-time Fourier Transform and autoregressive modeling method results, and (3) describes the advantages and disadvantages of each method. Although similar trends were detected during ozone exposure, statistical comparisons identified significant differences between short-time Fourier Transform and autoregressive modeling analysis results. Significant differences were observed between methods for LF power ( p ≤ 0.014); HF power ( p ≤ 0.011); total power ( p ≤ 0.027); and normalized HF power ( p = 0.05). Furthermore, inconsistencies between exposure-related observations accentuated the lack of agreement between short-time Fourier Transform and autoregressive modeling overall. Thus, the short-time Fourier Transform and autoregressive modeling methods for time-varying heart rate variability analysis could not be considered interchangeable for evaluations with or without interventions that are known to affect cardio-autonomic activity.

Background Nonnegative matrix factorization (NMF) has been successfully used for electroencephalography (EEG) spectral analysis. Since NMF was proposed in the 1990s, many adaptive algorithms have been developed. However, the performance of their use in EEG data analysis has not been fully compared. Here, we provide a comparison of four NMF algorithms in terms of accuracy of estimation, stability (repeatability of the results) and time complexity of algorithms with simulated data. In the practical application of NMF algorithms, stability plays an important role, which was an emphasis in the comparison. A Hierarchical clustering algorithm was implemented to evaluate the stability of NMF algorithms. Results In simulation-based comprehensive analysis of fit, stability, accuracy of estimation and time complexity, hierarchical alternating least squares (HALS) low-rank NMF algorithm (lraNMF_HALS) outperformed the other three NMF algorithms. In the application of lraNMF_HALS for real resting-state EEG data analysis, stable and interpretable features were extracted. Conclusion Based on the results of assessment, our recommendation is to use lraNMF_HALS, providing the most accurate and robust estimation.

Post-myocardial infarction (MI) remodeling contributes to increased electrophysiological and structural heterogeneity and arrhythmogenesis. Utilising the post-infarct ovine model our aim was to determine unipolar electrogram frequency characteristics consequent to this remodeling and the development of Ventricular Tachycardia (VT). Mapping studies were performed on 14 sheep at >1 month post-MI induction. Sheep were divided into VT inducible (n = 7) and non-inducible (n = 7) groups. Multielectrode needles (n = 20) were deployed within and surrounding ventricular scar for electrophysiological assessment of electrogram amplitude and width. Spectral analysis of electrograms was undertaken using wavelet and fast fourier transformations (WFFT) to calculate root mean square (RMS) power intervals spanning 0-300Hz in 20Hz intervals. Quantitative assessment between electrophysiological and histological parameters including collagen density, and structural organization of the myocardium was performed. Increasing myocardial scar density resulted in attenuation of electrogram amplitude and RMS values. (all p<0.01). Between groups there were no differences in electrogram amplitude (p = 0.37), however WFFT analysis revealed significantly higher RMS values in the VT group (p<0.05) in association with high frequency fractional components of the electrogram. As scar density increased, greater between-group differences in RMS were observed spanning this high frequency (200-280Hz) spectrum and which were proportionally dependent on the degree of structural disorganisation of the myocardium (p<0.001) and number of extrastimuli required to induce VT (p<0.05). High frequency unipolar electrogram spectral characteristics were quantitatively co-influenced by the presence of fibrosis and degree of myocardial structural dissorganisation and were associated with the propensity for development of VT.

We investigated the global structure of intrinsic cross-frequency dynamics by systematically examining power-based temporal associations among a broad range of oscillation frequencies both within and across EEG-based current sources (sites). We focused on power-based associations that could reveal unique timescale dependence independently of interacting frequencies. Large spectral-power fluctuations across all sites occurred at two characteristic timescales, sub-second and seconds, yielding distinct patterns of cross-frequency associations. On the fast sub-second timescale, within-site (local) associations were consistently between pairs of β-γ frequencies differing by a constant Δf (particularly Δf ~ 10 Hz at posterior sites and Δf ~ 16 Hz at lateral sites) suggesting that higher-frequency oscillations are organized into Δf amplitude-modulated packets, whereas cross-site (long-distance) associations were all within-frequency (particularly in the >30 Hz and 6-12 Hz ranges, suggestive of feedforward and feedback interactions). On the slower seconds timescale, within-site (local) associations were characterized by a broad range of frequencies selectively associated with ~10 Hz at posterior sites and associations among higher (>20 Hz) frequencies at lateral sites, whereas cross-site (long-distance) associations were characterized by a broad range of frequencies at posterior sites selectively associated with ~10 Hz at other sites, associations among higher (>20 Hz) frequencies among lateral and anterior sites, and prevalent associations at ~10 Hz. Regardless of timescale, within-site (local) cross-frequency associations were weak at anterior sites indicative of frequency-specific operations. Overall, these results suggest that the fast sub-second-timescale coordination of spectral power is limited to local amplitude modulation and insulated within-frequency long-distance interactions (likely feedforward and feedback interactions), while characteristic patterns of cross-frequency interactions emerge on the slower seconds timescale. The results also suggest that the occipital α oscillations play a role in organizing higher-frequency oscillations into ~10 Hz amplitude-modulated packets to communicate with other regions. Functional implications of these timescale-dependent cross-frequency associations await future investigations.

Interference signals in coherence scanning interferometry at high numerical apertures and narrow bandwidth illumination are spectrally broadened. This enables phase analysis within a spectral range much wider than the spectral distribution of the light emitted by the light source. Consequently, different surface features can be resolved depending on the wavelength used for phase analysis of the interference signals. In addition, the surface topography itself affects the spectral composition of interference signals in different ways. Signals related to tilted surfaces or step height structures show special spectral characteristics. Thus, spectral amplitude and phase analysis enables a better understanding of the underlying physical mechanisms and gives hints how to improve the measurement accuracy.

Spectral ripple discrimination (SRD) has been widely used to evaluate the spectral resolution in cochlear implant (CI) recipients based on its strong correlation with speech perception performance. However, despite its usefulness for predicting speech perception outcomes, SRD performance exhibits large across-subject variabilities even among subjects implanted with the same CIs and sound processors. The potential factors of this observation include current spread, nerve survival, and CI mapping. Previous studies have found that the spectral resolution reduces with increasing distance of the stimulation electrode from the auditory nerve fibers (ANFs), attributable to increasing current spread. However, it remains unclear whether the spread of excitation is the only cause of the observation, or whether other factors such as temporal interaction also contribute to it. In this study, we used a computational model to investigate channel interaction upon non-simultaneous stimulation with respect to the electrode-ANF distance, and evaluated the SRD performance for five electrode-ANF distances. The SRD performance was determined based on the similarity between two neurograms in response to standard and inverted stimuli and used to evaluate the spectral resolution in the computational model. The spread of excitation was observed to increase with increasing electrode-ANF distance, consistent with previous findings. Additionally, the preceding pulses delivered from neighboring channels induced a channel interaction that either inhibited or facilitated the neural responses to subsequent pulses depending on the electrode-ANF distance. The SRD performance was also found to decrease with increasing electrode-ANF distance. The findings of this study suggest that variation of the neural responses (inhibition or facilitation) with the electrode-ANF distance in CI users may cause spectral smearing, and hence poor spectral resolution. A computational model such as that used in this study is a useful tool for understanding the neural factors related to CI outcomes, such as cannot be accomplished by behavioral studies alone.