Temporal Signal Analysis Research Articles

The emergence and circulation of human immunodeficiency virus (HIV)-1 subtype C.

Introduction. Human immunodeficiency virus (HIV)-1 subtype C is the most prevalent globally and is thought to have originated in non-human primates in the Democratic Republic of Congo.Hypothesis/Gap Statement. Although the global dominance of HIV-1 subtype C is well established, a thorough understanding of its evolutionary history and transmission dynamics across various risk populations remains elusive. The current knowledge is insufficient to fully capture the global diversification and dissemination of this subtype.Aim. We for the first time sought to investigate the global evolutionary history and spatiotemporal dynamics of HIV-1 subtype C using a selection of maximum-likelihood-based phylodynamic approaches on a total of 1210 near full-length genomic sequences sampled from 32 countries, collected in 4 continents, with sampling dates between 1986-2019 among various risk groups were analysed.Methodology. We subsampled the HIV-1 subtype C genomic datasets based on continent and risk group traits, and performed nucleotide substitution model selection analysis, maximum likelihood (ML) phylogenetic reconstruction, phylogenetic tree topology similarity analysis, temporal signal analysis and traced the timings of viral spread both geographically and by risk group.Results. Based on the phylodynamic analyses of four datasets (full1210, locrisk626, loc562 and risk393), we inferred the time to the most recent common ancestor (TMRCA) in the 1930s and an evolutionary rate of 0.0023 substitutions per site per year. The total number of introduction events of HIV-1 subtype C between continents and between risk groups is estimated to be 71 and 115, respectively. The largest number of introductions occurred from Africa to Europe (n=32), from not-recorded to heterosexual (n=40) and from heterosexual to not-recorded (n=51) risk groups.Conclusion. Our results emphasize that HIV subtype C has mainly spread from Africa to Europe, likely through heterosexual transmission.

SVD-Based Mind-Wandering Prediction from Facial Videos in Online Learning.

This paper presents a novel approach to mind-wandering prediction in the context of webcam-based online learning. We implemented a Singular Value Decomposition (SVD)-based 1D temporal eye-signal extraction method, which relies solely on eye landmark detection and eliminates the need for gaze tracking or specialized hardware, then extract suitable features from the signals to train the prediction model. Our thorough experimental framework facilitates the evaluation of our approach alongside baseline models, particularly in the analysis of temporal eye signals and the prediction of attentional states. Notably, our SVD-based signal captures both subtle and major eye movements, including changes in the eye boundary and pupil, surpassing the limited capabilities of eye aspect ratio (EAR)-based signals. Our proposed model exhibits a 2% improvement in the overall Area Under the Receiver Operating Characteristics curve (AUROC) metric and 7% in the F1-score metric for 'not-focus' prediction, compared to the combination of EAR-based and computationally intensive gaze-based models used in the baseline study These contributions have potential implications for enhancing the field of attentional state prediction in online learning, offering a practical and effective solution to benefit educational experiences.

ShinyTempSignal: an R shiny application for exploring temporal and other phylogenetic signals

The molecular clock model is fundamental for inferring species divergence times from molecular sequences. However, its direct application may introduce significant biases due to sequencing errors, recombination events, and inaccurately labeled sampling times. Improving accuracy necessitates rigorous quality control measures to identify and remove potentially erroneous sequences. Furthermore, while not all branches of a phylogenetic tree may exhibit a clear temporal signal, specific branches may still adhere to the assumptions, with varying evolutionary rates. Supporting a relaxed molecular clock model better aligns with the complexities of evolution. The root-to-tip regression method has been widely used to analyze the temporal signal in phylogenetic studies and can be generalized for detecting other phylogenetic signals. Despite its utility, there remains a lack of corresponding software implementations for broader applications. To address this gap, we present shinyTempSignal, an interactive web application implemented with the shiny framework, available as an R package and publicly accessible at https://github.com/YuLab-SMU/shinyTempSignal. This tool facilitates the analysis of temporal and other phylogenetic signals under both strict and relaxed models. By extending the root-to-tip regression method to diverse signals, shinyTempSignal helps in the detection of evolving features or traits, thereby laying the foundation for deeper insights and subsequent analyses.

Influence of Following, Regular, and Irregular Long Waves on Wind-Wave Growth with Fetch: An Experimental Study

AbstractA series of experiments were conducted in a wind-wave tank facility in Marseilles (France) to study the effects of preexisting swell conditions (represented by long mechanically generated waves) on wind-wave growth with fetch. Both monochromatic and irregular (JONSWAP-type) long-wave conditions with different values of wave steepness have been generated in the presence of a constant wind forcing, for several wind velocities. A spectral analysis of temporal wave signals combined with airflow measurements allowed for the study of the evolution of both wave systems with the aim of identifying the interaction mechanisms transportable to prototype scale. In particular, a specific method is used to separate the two wave systems in the measured bimodal spectra. In fetch-limited conditions, pure wind-wave growth is in accordance with anterior experiments, but differs from the prototype scale in terms of energy and frequency variations with fetch. Monochromatic long waves are shown to reduce the energy of the wind-waves significantly, as it was observed in anterior laboratory experiments. The addition of JONSWAP-type long waves instead results in a downshift of the wind-wave peak frequency but no significant energy reduction. Overall, it is observed that the presence of long waves affects the wind-wave energy and frequency variations with fetch. Finally, in the presence of JONSWAP-type long waves, variations of wind-wave energy and peak frequency with fetch appear in close agreement with the wind-wave growth observed at prototype scale both in terms of variations and nondimensional magnitude.

Quantitative and qualitative analysis of fetal temporal lobe T2 signal in cytomegalovirus infected fetuses and normal controls.

Temporal lobe T2 hyperintensity has been described in association with prenatal cytomegalovirus (CMV) infection on fetal MRI. However, these findings are often perplexing with high inter-observer variability. Our objective was to evaluate temporal lobe T2 signal quantitatively in prenatal CMV infection. In this retrospective study, 119 fetuses, of which 51 fetuses with suspected CMV exposure (29-36 weeks of gestation) based on maternal seroconversion and age-matched 68 normal controls, were included. Mean and maximal temporal lobe T2 signal were evaluated quantitatively by measuring the T2 signal in the temporal lobes relative to the amniotic fluid's signal. Intra-observer, inter-observer variability and diagnostic performance were assessed. The occurrence of neonatal sensorineural hearing loss (SNHL) was recorded. Relative temporal lobe T2 signal did not change along with the examined gestational age. Of our suspected CMV cohort, 29 fetuses were positive for fetal CMV infection on polymerase chain reaction (PCR) analysis. There were no statistically significant differences in the relative mean or maximal temporal lobes T2 signal between CMV positive, CMV negative fetuses, or normal controls. No correlation was found between neonatal SNHL and temporal lobe T2 signal. When temporal lobe T2 signal is analyzed quantitatively, CMV infected fetuses do not present an increased signal than age-matched controls. Thus, reported subjective temporal T2 hyperintensities should be interpreted carefully and should have a limited effect on pregnancy management, especially as an isolated finding. Our study illustrates the importance of quantitative imaging in diagnostic neuroradiology.

INVESTIGATION OF LPG SOOTING DIFFUSION FLAME BY RAINBOW SCHLIEREN DEFLECTOMETRY

Rainbow schlieren deflectometry was employed to characterize the flame structure of unsteady laminar liquefied petroleum gas (LPG) jet diffusion flame. The schlieren images were acquired at 4000 Hz sampling rate for sooting LPG flame at Re = 500, and Abel inversion was employed to estimate local field refractive index difference. The a priori relationship between the refractive index difference and temperature was established using the opposed flow flame reactor concept. The peak temperature observed in the near-field region varies with axial location from 1000 K to 1700 K, which falls in the range of typical sooting flame. The sooting flame has depicted a typical flicker behavior of the unsteady laminar diffusion flame. Flicker behavior and flame puff formation could be attributed to the interaction of buoyancy-sustained outer vortical structure with the flame surface. It was observed that additional air entrainment during puff formation leads to higher temperatures in the puff (1700 K), which leads to better oxidation of carbon soot and its precursors at down-stream locations, a unique feature of sooting flames. Irrespective of whether space–time evolution at any axial location or frequency spectrum analysis of temporal signal of hue at any spatial location or the amplitude–time signal of decomposed mode from proper orthogonal decomposition (POD) analysis of color schlieren images, is employed the global unique flicker frequency of 13.33 Hz was observed in the near-field LPG diffusion flame. Interestingly the first two dominant energy modes of POD analysis correspond to flow features indicating strong ambient air entrainment pointing towards the role of outer vortical structures on flame flickering phenomena.

Readability Analysis Based on Cognitive Assessment Using Physiological Sensing

For a given individual, the readability of a content determines the amount of cognitive load experienced during the reading. Among many physiological parameters, the brain signals provide direct information about the cognitive load. In this paper, for a silent reading scenario, electroencephalogram (EEG) signal and pupillary response are used to address both global and localized analysis of a content. The global analysis is done using the EEG data collected from a target group of readers on whether the overall content is easy or difficult to understand. The entropy analysis of left temporal brain signals is found to grossly differentiate the texts. Detailed analysis is done using the pupil dilation to localize certain difficult segments in the content. The oscillatory behavior of the pupil dilation reveals detailed characteristics of the effect of the texts on each individual. To carry out the experiment, two types (easy and difficult) of textual contents are considered which are calibrated using standard natural language processing parameters. The proposed work presents a methodology for global and detailed analysis of a content which helps in preparing the reading materials. Furthermore, the methodology provides the insights into the reading characteristics of the individuals.

STORI Plots Enable Accurate Tracking of Individual Ion Signals.

Charge detection mass spectrometry (CDMS) of low-level signals is currently limited to the analysis of individual ions that generate a persistent signal during the entire observation period. Ions that disintegrate during the observation period produce reduced frequency domain signal amplitudes, which lead to an underestimation of the ion charge state, and thus the ion mass. The charge assignment can only be corrected through an accurate determination of the time of ion disintegration. The traditional mechanisms for temporal signal analysis have severe limitations for temporal resolution, spectral resolution, and signal-to-noise ratios. Selective Temporal Overview of Resonant Ions (STORI) plots provide a new framework to accurately analyze low-level time domain signals of individual ions. STORI plots allow for complete correction of intermittent signals, the differentiation of single and multiple ions at the same frequency, and the association of signals that spontaneously change frequency.

Characteristics of counter-current gas-liquid two-phase flow and its limitations in vertical annuli

This paper aims to characterise the complex flow behaviour of counter-current gas-liquid flows in concentric vertical annuli over a wide range of gas and liquid flowrates. The experiments were performed with air and water in two different annulus sizes: (a) a 100 mm hydraulic diameter annulus with a 170 mm diameter outer pipe and a 70 mm diameter inner pipe; and (b) a 19 mm hydraulic diameter annulus between 44 mm and 25 mm pipes, to investigate the effect of flow geometry on flow structure. Flow regimes were identified quantitatively by applying fast Fourier transform (FFT) on the associated pressure fluctuation signals, collected at 10 Hz and 100 Hz frequency. Video images captured at 4,000 fps with a high-speed camera were used in a visual analysis of the flow regimes to verify the FFT results. Furthermore, flow regime transitions and their underlying mechanisms were determined by their associated pressure gradient and void fractions, as well as analysis of temporal pressure signals. The commonly described slug flow regime, consisting of stable Taylor bubbles traversing the length of the channel, was not observed in the larger annulus. However, the FFT of the pressure signals indicate that unstable Taylor bubbles form as a result of bubble coalescence but collapse due to instability at the gas-liquid interface, known as Rayleigh-Taylor instability. Therefore, the apparent slug-churn flow regime was classified as a highly turbulent heterogeneous flow, developing at superficial gas velocities from 0.265 to 3.968 m/s and superficial liquid velocities from 0.004 to 0.147 m/s. Interestingly, annular flow regime did not develop in either of the tested small and large annuli. The onsets of counter-current flow limitations, or flooding, were identified in the 100 mm hydraulic diameter annulus with gas flooding due to very high gas flow rates and liquid flooding due to very high liquid flow rates. The mechanism that initiates gas flooding was observed to be the formation of large waves flowing upward near the water inlet point, with counter-current flow observed below the water inlet point at the onset of gas flooding. Clarity was also provided on the concepts of flooding and zero liquid penetration for the cases of flow in a water filled channel and a falling film, and a new empirical correlation for the onset of flooding was developed.

Evaluation of Sensory Pathways in Spinal Cord by Comparison of fMRI Methodologies

Introduction: Today, clinicians and neuroscientists need to have a comprehensive survey of neurological pathologies and injuries. For the First-time, SEEP contrast and Spin-Echo pulse sequences was used for functional imaging of the Lumbar spinal cord. This method used by several research groups for Spinal cord mapping, but other researchers tried to improve BOLD fMRI to Spinal cord imaging simultaneously. Here, we present a comparison between useful imaging methods and finally use of certain procedure for Spinal cord mapping with sensory stimulation. Materials and Methods: We planned two imaging protocols on Siemens 3T magnetom trio scanner: HASTE/SSFP, TE/TR: 76mS/6750mS for 9 sagittal slices with 2 mm thickness, FOV= 280×210mm, and Gradient Echo EPI, TE/TR: 30S/3000mS for 21 axial slices with 5mm thickness, FOV= 64×64mm. These image acquisition procedures performed on All 5 subjects (male, Age: 24.6±2.05), stimulated by 60g von Frey filament. Stimulations were used in the block design, 8 blocks with time 40.5 S for SE protocol and 42 S for GRE protocol and performed on right foot L4 dermatome. We entered each subject’s data sets into an individual first-level statistical analysis. Then we calculated signal changes in the mask that generated in the statistical analysis and amount of temporal Signal to Noise Ratio (tSNR). Other subjects group (5 males, Age 25.3±1.5) was imaged with same protocol as GE-EPI and T2W anatomic images (3D-FSE Isotropic, TR/TE:1500/430 ms, FOV= 256×60 mm, slice-thickness: 1mm). Data sets were processed with GLM and Finally, all first-level analysis results are entered in Higher-level analysis as group analysis and obtained statistical maps for spinal cord functions. Results: We observed different tSNR in two separated datasets, 2.619 ± 0.440 for SE-HASTE images and 4.901 ± 0.762 for GRE-EPI. After statistical analysis of images and obtaining signal change in the spinal cord. We comprised them and measured signal change was 1.737 ± 1.252 for SE-EPI and 2.554 ± 1.327 for GE-EPI. Based on these results we decided to use GE- EPI for spinal cord functional imaging. We stimulated L4 dermatome and this localized activation was observed in the T9-T1. The activation maps show ipsilateral synapse and tracks in the dorsal higher than ventral horn. Conclusion: At the first step evaluation of imaging methods show GRE-EPI can more efficient for Lumbar functional MRI and detection of BOLD signal change in the spinal cord. This research demonstrates the benefits of spinal cord fMRI for mapping of sensory stimulation. The resulting activity maps show primarily in ipsilateral dorsal regions and in some ventral regions, consistent with the spinal cord anatomy. These data also illustrate details of the sensory organization of the spinal cord, as well as anatomical detail of the spinous processes and positions of nerve roots.

Improved spectral resolution in time-varying interferometry

In this work, we present a procedure that allows increasing the resolution of dynamic length measurements made by spectral interferometry. The proposed scheme leads to obtaining a compact photonic instrument with the ability to measure distances, variations on positions and vibrations with a very high resolution. This measurement system includes a superluminescent source (SLED), a digital spectrometer and a Fizeau interferometer. Spectral data is processed by applying Fourier domain techniques previously applied in optical coherence tomography. The resolution of the spectral measurement system is determined by the spectrometer bandwidth and the light source employed. A signal is obtained by analysing the time evolution of a single pixel from the spectrometer CCD sensor, which is later analysed using time domain interferometry (TDI) techniques. This procedure works by detecting changes in the optical path below those that can be detected by spectral analysis. The original resolution obtained with the solely spectral techniques was 2.2 µm but was improved to 40 nm by complementary analysis of temporal signals.

Analysis of Temporal Signals of Climate

The dynamics of carbon dioxide in the atmosphere is analyzed and it is shown that the Pinatubo eruption in 1991 had a noticeable effect on these dynamics. The growth rate slowed down. Moreover, analyzing the year-on-year CO2 growth data, we can see an an-thropogenic footprint, possibly due to the burning of fossil fuels. On top of this anthropo-genic contribution is a natural contribution that is of similar magnitude, and that closely follows the ocean surface temperature (influenced by ENSO, El Ni&ntildeo Southern Oscilla-tion). This latter fact is consistent with the hypothesis of the correlation of global temper-atures and carbon-dioxide in the atmosphere being governed by Henry’s Law, in which carbon dioxide variations are the result of, rather than the cause of, temperature changes. This latter being the so-called “greenhouse effect”, sometimes mentioned as responsible for (anthropogenic) climate changes, and that cannot explain the observed phenomena described here. Similar conclusions are drawn on monthly data of carbon dioxide and temperature as well.

Graph spectral characterization of the XY model on complex networks.

There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

A Temporal and Spatial Analysis Approach to Automated Segmentation of Microbubble Signals in Contrast-Enhanced Ultrasound Images: Application to Quantification of Active Vascular Density in Human Lower Limbs

Contrast-enhanced ultrasound (CEUS) using microbubble contrast agents has shown great promise in visualising and quantifying active vascular density. Most existing approaches for vascular density quantification using CEUS are calculated based on image intensity and are susceptible to confounding factors and imaging artefact. Poor reproducibility is a key challenge to clinical translation. In this study, a new automated temporal and spatial signal analysis approach is developed for reproducible microbubble segmentation and quantification of contrast enhancement in human lower limbs. The approach is evaluated in vitro on phantoms and in vivo in lower limbs of healthy volunteers before and after physical exercise. In this approach, vascular density is quantified based on the relative areas microbubbles occupy instead of their image intensity. Temporal features of the CEUS image sequences are used to identify pixels that contain microbubble signals. A microbubble track density (MTD) measure, the ratio of the segmented microbubble area to the whole tissue area, is calculated as a surrogate for active capillary density. In vitro results reveal a good correlation (r2 = 0.89) between the calculated MTD measure and the known bubble concentration. For in vivo results, a significant increase (129% in average) in the MTD measure is found in lower limbs of healthy volunteers after exercise, with excellent repeatability over a series of days (intra-class correlation coefficient = 0.96). This compares to the existing state-of-the-art approach of destruction and replenishment analysis on the same patients (intra-class correlation coefficient ≤0.78). The proposed new approach shows great potential as an accurate and highly reproducible clinical tool for quantification of active vascular density.

Dynamic decomposition of spatiotemporal neural signals.

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals.

Functional Laterality of Task-Evoked Activation in Sensorimotor Cortex of Preterm Infants: An Optimized 3 T fMRI Study Employing a Customized Neonatal Head Coil.

BackgroundFunctional magnetic resonance imaging (fMRI) in neonates has been introduced as a non-invasive method for studying sensorimotor processing in the developing brain. However, previous neonatal studies have delivered conflicting results regarding localization, lateralization, and directionality of blood oxygenation level dependent (BOLD) responses in sensorimotor cortex (SMC). Amongst the confounding factors in interpreting neonatal fMRI studies include the use of standard adult MR-coils providing insufficient signal to noise, and liberal statistical thresholds, compromising clinical interpretation at the single subject level.Patients / methodsHere, we employed a custom-designed neonatal MR-coil adapted and optimized to the head size of a newborn in order to improve robustness, reliability and validity of neonatal sensorimotor fMRI.Thirteen preterm infants with a median gestational age of 26 weeks were scanned at term-corrected age using a prototype 8-channel neonatal head coil at 3T (Achieva, Philips, Best, NL). Sensorimotor stimulation was elicited by passive extension/flexion of the elbow at 1 Hz in a block design. Analysis of temporal signal to noise ratio (tSNR) was performed on the whole brain and the SMC, and was compared to data acquired with an ‘adult’ 8 channel head coil published previously. Task-evoked activation was determined by single-subject SPM8 analyses, thresholded at p < 0.05, whole-brain FWE-corrected.ResultsUsing a custom-designed neonatal MR-coil, we found significant positive BOLD responses in contralateral SMC after unilateral passive sensorimotor stimulation in all neonates (analyses restricted to artifact-free data sets = 8/13). Improved imaging characteristics of the neonatal MR-coil were evidenced by additional phantom and in vivo tSNR measurements: phantom studies revealed a 240% global increase in tSNR; in vivo studies revealed a 73% global and a 55% local (SMC) increase in tSNR, as compared to the ‘adult’ MR-coil.ConclusionsOur findings strengthen the importance of using optimized coil settings for neonatal fMRI, yielding robust and reproducible SMC activation at the single subject level. We conclude that functional lateralization of SMC activation, as found in children and adults, is already present in the newborn period.

Multi-Point Disturbance Detection and High-Precision Positioning of Polarization-Sensitive Optical Time-Domain Reflectometry

Compared with its counterparts, polarization sensitive optical time-domain reflectometry (P-OTDR) has two typical problems in terms of multi-point disturbance detection and high precision positioning, which restrict its practical applications. In this paper, we propose a novel method by using two-dimensional (2-D) image processing and statistical clustering. In place of the traditional spatial or temporal signal analysis way, the idea employs the temporally and the spatially uneven/inconsistent evolving patterns induced by the multiple individual events, and the proposed method is carried out to accumulate the temporally differentiated OTDR traces and then build up a 2-D temporal-spatial evolving graph, by using edge detection and automatic clustering to distinguish different disturbing points with precise locations. Through series of multi-point disturbance tests, the proposed method has been proved to have better performance than the conventional direct differentiation method and the fast Fourier transform spectrum analysis.

Novel Two-Dimensional Singular Spectrum Analysis for Effective Feature Extraction and Data Classification in Hyperspectral Imaging

Feature extraction is of high importance for effective data classification in hyperspectral imaging (HSI). Considering the high correlation among band images, spectral-domain feature extraction is widely employed. For effective spatial information extraction, a 2-D extension to singular spectrum analysis (2D-SSA), which is a recent technique for generic data mining and temporal signal analysis, is proposed. With 2D-SSA applied to HSI, each band image is decomposed into varying trends, oscillations, and noise. Using the trend and the selected oscillations as features, the reconstructed signal, with noise highly suppressed, becomes more robust and effective for data classification. Three publicly available data sets for HSI remote sensing data classification are used in our experiments. Comprehensive results using a support vector machine classifier have quantitatively evaluated the efficacy of the proposed approach. Benchmarked with several state-of-the-art methods including 2-D empirical mode decomposition (2D-EMD), it is found that our proposed 2D-SSA approach generates the best results in most cases. Unlike 2D-EMD that requires sequential transforms to obtain detailed decomposition, 2D-SSA extracts all components simultaneously. As a result, the execution time in feature extraction can be also dramatically reduced. The superiority in terms of enhanced discrimination ability from 2D-SSA is further validated when a relatively weak classifier, i.e., the k-nearest neighbor, is used for data classification. In addition, the combination of 2D-SSA with 1-D principal component analysis (2D-SSA-PCA) has generated the best results among several other approaches, demonstrating the great potential in combining 2D-SSA with other approaches for effective spatial-spectral feature extraction and dimension reduction in HSI.

Acoustic Gaits: Gait Analysis With Footstep Sounds.

We describe the acoustic gaits-the natural human gait quantitative characteristics derived from the sound of footsteps as the person walks normally. We introduce the acoustic gait profile, which is obtained from temporal signal analysis of sound of footsteps collected by microphones and illustrate some of the spatio-temporal gait parameters that can be extracted from the acoustic gait profile by using three temporal signal analysis methods-the squared energy estimate, Hilbert transform and Teager-Kaiser energy operator. Based on the statistical analysis of the parameter estimates, we show that the spatio-temporal parameters and gait characteristics obtained using the acoustic gait profile can consistently and reliably estimate a subset of clinical and biometric gait parameters currently in use for standardized gait assessments. We conclude that the Teager-Kaiser energy operator provides the most consistent gait parameter estimates showing the least variation across different sessions and zones. Acoustic gaits use an inexpensive set of microphones with a computing device as an accurate and unintrusive gait analysis system. This is in contrast to the expensive and intrusive systems currently used in laboratory gait analysis such as the force plates, pressure mats and wearable sensors, some of which may change the gait parameters that are being measured.

Crackle: The Homology of Noise

We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates the vertices, the homology of these complexes can either become trivial as the number $$n$$n of vertices grows, or can contain more and more complex structures. The different behaviours are consequences of different underlying distributions for the generation of vertices, and we consider three illustrative examples, when the vertices are sampled from Gaussian, exponential, and power-law distributions in $${\mathbb {R}}^d$$Rd. We also discuss consequences of our results for manifold learning with noisy data, describing the topological phenomena that arise in this scenario as crackle, in analogy to audio crackle in temporal signal analysis.