Noise Titration Research Articles

Backdoor Federated Learning-Based mmWave Beam Selection

Federated learning (FL) is an emerging paradigm for distributed machine learning that uses the data and the computational power of user devices while maintaining user privacy (e.g., position and motion track). It has been proved a promising way to help the learning-based millimeter wave (mmWave) system achieve efficient link configuration. However, FL systems have an inherent vulnerability to backdoor attacks during training, and this has not received attention in current FL-based beam selection research. The goal of a backdoor attacker is to implant a backdoor in the model such that at test time, the model will mispredict a certain family of inputs, and corrupt the performance of the trained model on specific sub-tasks. We study backdoor attacks in an FL-based beam selection system based on a deep neural network that utilizes user location information. Specifically, we propose a backdoor attack scheme that can be configured in the real world. The attacker’s trigger is an obstacle placed in certain locations. When the model encounters an input with these obstacles, the backdoor will be triggered, and the model will output the beam specified by the attacker. Through experiments, we show that the proposed attack can achieve a high attack success rate in a system without a defense mechanism. Moreover, we show that the traditional norm-clipping defense method cannot effectively defend against our attack. Furthermore, we propose a new backdoor attack defense method and verify the effectiveness of this scheme through experiments. In addition, we propose a backdoor detection method: the federated noise titration method, which can diagnose whether the model has a backdoor. Overall, our work explored backdoor attacks, defenses, and detection of the FL-based mmWave beam selection system.

Testing for nonlinearity and chaos in economic time series with noise titration

Recently, a new test for nonlinearity and chaos was proposed, the noise titration technique. I discuss in this paper its relevance for the case of economic time series. I apply the test on two relevant datasets for which previous assessments exist, both simulated and real data. Compared to other tests for nonlinearity and chaos I find that this approach performs relatively well.

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Distinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the problems identified.

Long-Term Tracking of a Patient’s Health Condition Based on Pulse Rate Dynamics During Sleep

This article proposed a method to track the changes in health condition of a patient after coronary stenting over seven successive seasons based on daily pulse rate (PR). The pulse signal was recorded by an unconstrained monitoring system during sleep. Seasonal PR dynamics were evaluated by both linear measures, including time domain and frequency domain indexes, and nonlinear measures such as noise limit (NL), detection rate (DR), sample entropy (SampEn), and Poincaré plots. NL and DR were derived using the noise titration method. Significant changes in seasonal indexes of the patient were evaluated statistically. The results show that an overall downward trend of the PR dynamics corresponds to changes in the patient's health condition that began in winter and developed in spring and worsened most seriously in the following summer. The monthly and seasonal orbits of PR nonlinearity of the patient were plotted and observed to follow different trajectory compared with a healthy subject. These results indicate the feasibility of applying dynamics of PR as a potential prognostic tool for detecting early changes in a patient's health condition and also for understanding the temporal transition of health condition over a long-term period.

Nonlinear heart rate dynamics: Circadian profile and influence of age and gender

Heart rate variability (HRV) is used as a marker of autonomic modulation of heart rate. Nonlinear HRV parameters providing information about the scaling behaviour or the complexity of the cardiac system were included. In addition, the chaotic behaviour was quantified by means of the recently developed numerical noise titration technique. 24 h Holter recordings of a large healthy population ( N = 276, 141 males, 18–71 years of age) were available. The goal was to investigate the influence of gender, age and day–night variation on these nonlinear HRV parameters. Numerical titration yielded similar information as other nonlinear HRV parameters do. However, it does not require long and cleaned data and therefore applicable on short (5 min) noisy time series. A higher nonlinear behaviour was observed during the night (NLdr; day: 50.8 ± 19.6%, night: 59.1 ± 19.5%; P < 0.001) while nonlinear heart rate fluctuations decline with increasing age (NLdr; Pearson correlation coefficient r between −0.260 and −0.319 dependent on gender and day or night, all P < 0.01). A clear circadian profile could be found for almost every parameter, showing in particular which changes occur during the transition phases of waking up and going to sleep. Our results support the involvement of the autonomic nervous system in the generation of nonlinear and complex heart rate dynamics.

Working conditions for safe detection of nonlinearity and noise titration

Even if noise titration cannot be satisfactorily used to prove the presence of chaos, it can still be used to detect nonlinear component in dynamics. Nevertheless, since the technique have the use of nonlinear models for one-step-ahead predictions, it requires an acute choice of modeling parameters, i.e., the number of terms and the nonlinearity degree of the models. Based on illustrative examples, we propose conditions under which the method of noise titration can be reliably applied to characterize nonlinearity in the time series. It is thus possible to compare different time series and state which one is governed by the strongest nonlinearity. For instance, it is shown that, when there is a single nonlinear term in the equations describing the system, the variable on which it acts can be identified among the others.

Ventilatory chaos is impaired in carotid atherosclerosis.

Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%), 23 with moderate stenosis (<70%), and 25 controls. Chaos was characterized by the noise titration method, the correlation dimension and the largest Lyapunov exponent. Baroreflex sensitivity was estimated in the frequency domain. In the control group, 92% of the time series exhibit nonlinear deterministic chaos with positive noise limit, whereas only 68% had a positive noise limit value in the stenoses groups. Ventilatory chaos was impaired in the groups with carotid stenoses, with significant parallel decrease in the noise limit value, correlation dimension and largest Lyapunov exponent, as compared to controls. In multiple regression models, the percentage of carotid stenosis was the best in predicting the correlation dimension (p<0.001, adjusted R2: 0.35) and largest Lyapunov exponent (p<0.001, adjusted R2: 0.6). Baroreflex sensitivity also predicted the correlation dimension values (p = 0.05), and the LLE (p = 0.08). Plaque removal after carotid surgery reversed the loss of ventilatory complexity. To conclude, ventilatory chaos is impaired in carotid atherosclerosis. These findings depend on the severity of the stenosis, its localization, plaque surface and morphology features, and is independently associated with baroreflex sensitivity reduction. These findings should help to understand the determinants of ventilatory complexity and breathing control in pathological conditions.

Neurally Adjusted Ventilatory Assist Increases Respiratory Variability and Complexity in Acute Respiratory Failure

Neurally adjusted ventilatory assist (NAVA) is a partial ventilatory support mode where positive pressure is provided in relation to diaphragmatic electrical activity (EAdi). Central inspiratory activity is normally not monotonous, but it demonstrates short-term variability and complexity. The authors reasoned that NAVA should produce a more "natural" or variable breathing pattern than other modes. This study compared respiratory variability and complexity during pressure support ventilation (PSV) and NAVA. Flow and EAdi were recorded during routine PSV (tidal volume approximately 6-8 ml/kg) and four NAVA levels (1-4 cm H2O/microVEAdi) in 12 intubated patients. Breath-by-breath variability of flow and EAdi-related variables was quantified by the coefficient of variation (CV) and autocorrelation analysis. Complexity of flow and EAdi was described using noise titration, largest Lyapunov exponent, Kolmogorov-Sinai entropy, and three-dimensional phase portraits. Switching from PSV to NAVA increased the CV and decreased the autocorrelation for most flow-related variables in a dose-dependent manner (P < 0.05, partial eta for the CV of mean inspiratory flow 0.642). The changes were less marked for EAdi. A positive noise limit was consistently found for flow and EAdi. Largest Lyapunov exponent and Kolmogorov-Sinai entropy for flow were greater during NAVA than PSV and increased with NAVA level (P < 0.05, partial eta 0.334 and 0.312, respectively). Largest Lyapunov exponent and Kolmogorov-Sinai entropy for EAdi were not influenced by ventilator mode. Compared with PSV, NAVA increases the breathing pattern variability and complexity of flow, whereas the complexity of EAdi is unchanged. Whether this improves clinical outcomes remains to be determined.

Uncovering chaotic structure in mechanomyography signals of fatigue biceps brachii muscle

The mechanomyography (MMG) signal reflects mechanical properties of limb muscles that undergo complex phenomena in different functional states. We undertook the study of the chaotic nature of MMG signals by referring to recent developments in the field of nonlinear dynamics. MMG signals were measured from the biceps brachii muscle of 5 subjects during fatigue of isometric contraction at 80% maximal voluntary contraction (MVC) level. Deterministic chaotic character was detected in all data by using the Volterra–Wiener–Korenberg model and noise titration approach. The noise limit, a power indicator of the chaos of fatigue MMG signals, was 22.20±8.73. Furthermore, we studied the nonlinear dynamic features of MMG signals by computing their correlation dimension D 2, which was 3.35±0.36 across subjects. These results indicate that MMG is a high-dimensional chaotic signal and support the use of the theory of nonlinear dynamics for analysis and modeling of fatigue MMG signals.

Heart rate variability during REM and non-REM sleep in preterm neonates with and without abnormal cardiorespiratory events

Aim Analyse heart rate variability (HRV) of preterm neonates undergoing a polysomnography in relation to the occurrence of abnormal cardiorespiratory events on one hand and the type of sleep states on the other hand. Methods To quantify nonlinear HRV, the numerical noise titration technique is used, adapted to neonatal heart rate data. HRV is calculated for 30 preterm neonates with mean post-conceptional age of 36.4 weeks, divided into three groups according to the occurrence of abnormal events during the polysomnographies and the eventual home monitoring. Results Periods of non-REM sleep have lower noise limit values and can be distinguished significantly from periods of REM sleep and from the total recording period. The presence of abnormal events does not influence this finding. Significant differences between groups are only found during non-REM segments by means of the noise limit value computed via numerical noise titration while the linear HRV parameters were not able to discriminate. Conclusion ECG measurement of a relatively short non-REM sleep period without specific abnormal events is sufficient to define a mature cardiorespiratory pattern in preterm infants.

Failure in distinguishing colored noise from chaos using the “noise titration” technique

Identifying chaos in experimental data-noisy data-remains a challenging problem for which conclusive arguments are still very difficult to provide. In order to avoid problems usually encountered with techniques based on geometrical invariants (dimensions, Lyapunov exponent, etc.), Poon and Barahona introduced a numerical titration procedure which compares one-step-ahead predictions of linear and nonlinear models [Proc. Natl. Acad. Sci. U.S.A. 98, 7107 (2001)]. We investigate the aformentioned technique in the context of colored noise or other types of nonchaotic behaviors. The main conclusion is that in several examples noise titration fails to distinguish such nonchaotic signals from low-dimensional deterministic chaos.

Chaotic dynamics of cardioventilatory coupling in humans: effects of ventilatory modes

Cardioventilatory coupling (CVC), a transient temporal alignment between the heartbeat and inspiratory activity, has been studied in animals and humans mainly during anesthesia. The origin of the coupling remains uncertain, whether or not ventilation is a main determinant in the CVC process and whether the coupling exhibits chaotic behavior. In this frame, we studied sedative-free, mechanically ventilated patients experiencing rapid sequential changes in breathing control during ventilator weaning during a switch from a machine-controlled assistance mode [assist-controlled ventilation (ACV)] to a patient-driven mode [inspiratory pressure support (IPS) and unsupported spontaneous breathing (USB)]. Time series were computed as R to start inspiration (RI) and R to the start of expiration (RE). Chaos was characterized with the noise titration method (noise limit), largest Lyapunov exponent (LLE) and correlation dimension (CD). All the RI and RE time series exhibit chaotic behavior. Specific coupling patterns were displayed in each ventilatory mode, and these patterns exhibited different linear and chaotic dynamics. When switching from ACV to IPS, partial inspiratory loading decreases the noise limit value, the LLE, and the correlation dimension of the RI and RE time series in parallel, whereas decreasing intrathoracic pressure from IPS to USB has the opposite effect. Coupling with expiration exhibits higher complexity than coupling with inspiration during mechanical ventilation either during ACV or IPS, probably due to active expiration. Only 33% of the cardiac time series (RR interval) exhibit complexity either during ACV, IPS, or USB making the contribution of the cardiac signal to the chaotic feature of the coupling minimal. We conclude that 1) CVC in unsedated humans exhibits a complex dynamic that can be chaotic, and 2) ventilatory mode has major effects on the linear and chaotic features of the coupling. Taken together these findings reinforce the role of ventilation in the CVC process.

Chaotic Signatures of Heart Rate Variability and Its Power Spectrum in Health, Aging and Heart Failure

A paradox regarding the classic power spectral analysis of heart rate variability (HRV) is whether the characteristic high- (HF) and low-frequency (LF) spectral peaks represent stochastic or chaotic phenomena. Resolution of this fundamental issue is key to unraveling the mechanisms of HRV, which is critical to its proper use as a noninvasive marker for cardiac mortality risk assessment and stratification in congestive heart failure (CHF) and other cardiac dysfunctions. However, conventional techniques of nonlinear time series analysis generally lack sufficient sensitivity, specificity and robustness to discriminate chaos from random noise, much less quantify the chaos level. Here, we apply a ‘litmus test’ for heartbeat chaos based on a novel noise titration assay which affords a robust, specific, time-resolved and quantitative measure of the relative chaos level. Noise titration of running short-segment Holter tachograms from healthy subjects revealed circadian-dependent (or sleep/wake-dependent) heartbeat chaos that was linked to the HF component (respiratory sinus arrhythmia). The relative ‘HF chaos’ levels were similar in young and elderly subjects despite proportional age-related decreases in HF and LF power. In contrast, the near-regular heartbeat in CHF patients was primarily nonchaotic except punctuated by undetected ectopic beats and other abnormal beats, causing transient chaos. Such profound circadian-, age- and CHF-dependent changes in the chaotic and spectral characteristics of HRV were accompanied by little changes in approximate entropy, a measure of signal irregularity. The salient chaotic signatures of HRV in these subject groups reveal distinct autonomic, cardiac, respiratory and circadian/sleep-wake mechanisms that distinguish health and aging from CHF.

Nonlinear nature of spectral components in heart rate variability

We proposed a new hybrid method combining the band-phase-randomized surrogate data with noise titration to discern the influence of spectral components on heartbeat chaos. The results demonstrate that the chaotic strength of phase-randomized surrogate data in the high frequency band (HF) of heart rate variability (HRV) is reduced significantly, which indicates that the frequency components of spectral analysis involve intrinsic chaotic information. The hybrid method proposed in this study is effective to distinguish the different contributions of spectral components to chaotic strength of the test data. This method is applicable not only to HRV but also to other deterministic signals.

Effects of inspiratory loading on the chaotic dynamics of ventilatory flow in humans

Human ventilation at rest exhibits complexity and chaos. The aim of this study was to determine whether suprapontine interferences with the automatic breathing control could contribute to ventilatory chaos. We conducted a post hoc analysis of a previous study performed in awake volunteers exhibiting cortical pre-motor potentials during inspiratory loading. In eight subjects, flow was recorded at rest, while breathing against inspiratory threshold loads (median 21.5 cm H(2)O) and resistive loads (50 cm H(2)Ol(-1)s(-1)) loads, and while inhaling 7% CO(2)-93% O(2). Chaos was identified through noise titration (noise limit, NL) and the sensitivity to initial conditions was assessed through the largest Lyapunov exponent (LLE). Breath-by-breath variability was evaluated using the coefficient of variation of several ventilatory variables. Chaos was consistently present in ventilatory flow recordings, but mechanical loading did not alter NL, LLE, or variability. In contrast, CO(2) altered chaos and reduced variability. In conclusion, inspiratory loading - and any resultant respiratory-related cortical activity - were not associated with changes in ventilatory chaos in this study, arguing against suprapontine contributions to ventilatory complexity.

Source of human ventilatory chaos: Lessons from switching controlled mechanical ventilation to inspiratory pressure support in critically ill patients

Ventilatory flow measured at the airway opening in humans exhibits a complex dynamics that has the features of chaos. Currently available data point to a neural origin of this feature, but the role of respiratory mechanics has not been specifically assessed. In this aim, we studied 17 critically ill mechanically ventilated patients during a switch form an entirely machine-controlled assistance mode (assist-controlled ventilation ACV) to a patient-driven mode (inspiratory pressure support IPS). Breath-by-breath respiratory variability was assessed with the coefficient of variation of tidal volume, total cycle time, inspiratory time, expiratory time, mean inspiratory flow, duty cycle. The detection of chaos was performed with the noise titration technique. When present, chaos was characterized with numerical indexes (correlation dimension, irregularity; largest Lyapunov exponent, sensitivity to initial conditions). Expectedly, the coefficients of variations of the respiratory variables were higher during IPS than during ACV. During ACV, noise titration failed to detect nonlinearities in 12 patients who did not exhibit signs of spontaneous respiratory activity. This indicates that the mechanical properties of the respiratory system were not sufficient to produce ventilatory chaos in the presence of a nonlinear command (ventilator clock). A positive noise limit was found in the remaining 5 cases, but these patients exhibited signs of active expiratory control (highly variable expiratory time, respiratory frequency higher than the set frequency). A positive noise limit was also observed in 16/17 patients during IPS (p<0.001). These observations suggest that ventilatory chaos predominantly has a neural origin (intrinsic to the respiratory central pattern generators, resulting from their perturbation by respiratory afferents, or both), with little contribution of respiratory mechanics, if any.

Effects of hypercapnia and hypocapnia on ventilatory variability and the chaotic dynamics of ventilatory flow in humans

In humans, lung ventilation exhibits breath-to-breath variability and dynamics that are nonlinear, complex, sensitive to initial conditions, unpredictable in the long-term, and chaotic. Hypercapnia, as produced by the inhalation of a CO(2)-enriched gas mixture, stimulates ventilation. Hypocapnia, as produced by mechanical hyperventilation, depresses ventilation in animals and in humans during sleep, but it does not induce apnea in awake humans. This emphasizes the suprapontine influences on ventilatory control. How cortical and subcortical commands interfere thus depend on the prevailing CO(2) levels. However, CO(2) also influences the variability and complexity of ventilation. This study was designed to describe how this occurs and to test the hypothesis that CO(2) chemoreceptors are important determinants of ventilatory dynamics. Spontaneous ventilatory flow was recorded in eight healthy subjects. Breath-by-breath variability was studied through the coefficient of variation of several ventilatory variables. Chaos was assessed with the noise titration method (noise limit) and characterized with numerical indexes [largest Lyapunov exponent (LLE), sensitivity to initial conditions; Kolmogorov-Sinai entropy (KSE), unpredictability; and correlation dimension (CD), irregularity]. In all subjects, under all conditions, a positive noise limit confirmed chaos. Hypercapnia reduced breathing variability, increased LLE (P = 0.0338 vs. normocapnia; P = 0.0018 vs. hypocapnia), increased KSE, and slightly reduced CD. Hypocapnia increased variability, decreased LLE and KSE, and reduced CD. These results suggest that chemoreceptors exert a strong influence on ventilatory variability and complexity. However, complexity persists in the quasi-absence of automatic drive. Ventilatory variability and complexity could be determined by the interaction between the respiratory central pattern generator and suprapontine structures.

Chaos in Atomic Force Microscopy

Chaotic oscillations of microcantilever tips in dynamic atomic force microscopy (AFM) are reported and characterized. Systematic experiments performed using a variety of microcantilevers under a wide range of operating conditions indicate that softer AFM microcantilevers bifurcate from periodic to chaotic oscillations near the transition from the noncontact to the tapping regimes. Careful Lyapunov exponent and noise titration calculations of the tip oscillation data confirm their chaotic nature. AFM images taken by scanning the chaotically oscillating tips over the sample show small, but significant metrology errors at the nanoscale due to this "deterministic" uncertainty.

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

The mammalian ventilatory behaviour exhibits nonlinear dynamics as reflected by certain nonlinearity or complexity indicators (e.g. correlation dimension, approximate entropy, Lyapunov exponents, etc.) but this is not sufficient to determine its possible chaotic nature. To address this, we applied the noise titration technique, previously shown to discern and quantify chaos in short and noisy time series, to ventilatory flow recordings obtained in quietly breathing normal humans. Nine subjects (8 men and 1 woman, 24-42 years) were studied during 15-min epochs of ventilatory steady-state (10.1+/-3.0 breaths/min, tidal volume 0.63+/-0.2 L). Noise titration applied to the unfiltered signals subsampled at 5 Hz detected nonlinearity in all cases (noise limit 20.2+/-12.5%). Noise limit values were weakly correlated to the correlation dimension and the largest Lyapunov exponent of the signals. This study shows that the noise titration approach evidences a chaotic dimension to the behavior of ventilatory flow over time in normal humans during tidal breathing.

Behavioral and EEG measures of sleeping and waking in the preterm period

Analyse heart rate variability (HRV) of preterm neonates undergoing a polysomnography in relation to the occurrence of abnormal cardiorespiratory events on one hand and the type of sleep states on the other hand.To quantify nonlinear HRV, the numerical noise titration technique is used, adapted to neonatal heart rate data. HRV is calculated for 30 preterm neonates with mean post-conceptional age of 36.4 weeks, divided into three groups according to the occurrence of abnormal events during the polysomnographies and the eventual home monitoring.Periods of non-REM sleep have lower noise limit values and can be distinguished significantly from periods of REM sleep and from the total recording period. The presence of abnormal events does not influence this finding. Significant differences between groups are only found during non-REM segments by means of the noise limit value computed via numerical noise titration while the linear HRV parameters were not able to discriminate.ECG measurement of a relatively short non-REM sleep period without specific abnormal events is sufficient to define a mature cardiorespiratory pattern in preterm infants.