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This work deals with the problem of online differentiation of noisy signals. In this context, several types of differentiators including linear, sliding-mode based, adaptive, Kalman, and ALIEN differentiators are studied through mathematical analysis and numerical experiments. To resolve the drawbacks of the exact differentiators, new implicit and semi-implicit discretization schemes are proposed in this work to suppress the digital chattering caused by the wrong time-discretization of set-valued functions as well as providing some useful properties, e.g., finite-time convergence, invariant sliding-surface, exactness. A complete comparative analysis is presented in the manuscript to investigate the behavior of the discrete-time differentiators in the presence of several types of noises, including white noise, sinusoidal noise, and bell-shaped noise. Many details such as quantization effect and realistic sampling times are taken into account to provide useful information based on practical conditions. Many comments are provided to help the engineers to tune the parameters of the differentiators.

Purpose A high-precision rotated elliptical beam profiling method based on pixel ion chamber is proposed in this paper. This method aims to improve the accuracy by modeling the transverse profile of rotated beam as an ellipse with additional correlation coefficient and eliminating the fitting error due to the volume averaging effect of pixel ion chamber. Methods In pencil beam scanning (PBS) proton therapy systems, the transverse beam profile model is generally represented as a standard Gaussian distribution. Considering the elliptical spots, two-dimensional (2D) joint Gaussian distribution characterized with the correlation coefficient ρ is adopted in this study. Gaussian-type particle distribution with white noise was generated and processed in MATLAB to simulate the secondary particle collection in the pixel ion chamber. The simulated pixel ion chamber is a commercially available ion chamber which consists of 12 × 12 small square pixels (3.75 × 3.75 mm2 ) with a 0.05 mm interval. The simulated signals were preprocessed by filtering with the noise threshold and extracting the maximum simply connected domain (MSCD) of the signal. Then, five geometric parameters that identify the transverse beam profiles were fitted under different signal-to-noise ratio (SNR) conditions: the center of the beam (x0 , y0 ), the spot size (σmajor , σminor ), and the rotation angle θ formed between the major axes of elliptical spot and the x axes of the ion chamber. First, the simulated signals were preprocessed by filtering with the noise threshold and extracting the MSCD of the signal. Second, a rectification curve of systematic error in fitted spot size versus the prescribed spot size was used to predict the systematic error due to the volume averaging effect. Finally, the effects of fitting errors on therapeutic dose were evaluated in terms of gamma index and relative dose difference. Results When the SNR is not less than 20 dB, the relative fitting error of spot size and the absolute fitting error of angle θ are less than 1% and 6.1°, respectively. The fitting error of beam center increases with spot size and will not exceed 0.22 mm when spot size reaches up to 12 mm. At a SNR equal to 20 dB, neither cold nor hot spots were presented in dose distribution calculated with the fitted spot parameters. Conclusion The improved Gaussian fitting algorithm performs well when SNR is not less than 20 dB. This method can effectively distinguish the nominal beam and rotated elliptical beam. An ideal systematic error curve can be predicted and used to correct the fitted spot size, thus eliminating the systematic error due to the volume averaging effect of the pixel ion chamber. The fitting error of spot size cannot be fully corrected, but it is negligible and shows little effect on the overall therapeutic dose.

In this paper, we investigate the numerical approximation of stochastic convection-reaction-diffusion equations using two explicit exponential integrators. The stochastic partial differential equation (SPDE) is driven by additive Wiener process. The approximation in space is done via a combination of the standard finite element method and the Galerkin projection method. Using the linear functional of the noise, we construct two accelerated numerical methods, which achieve higher convergence orders. In particular, we achieve convergence rates approximately $1$ for trace class noise and $\frac{1}{2}$ for space-time white noise. These convergences orders are obtained under less regularities assumptions on the nonlinear drift function than those used in the literature for stochastic reaction-diffusion equations. Numerical experiments to illustrate our theoretical results are provided

The auditory system is highly sensitive to recurring patterns in the acoustic input - even in otherwise unstructured material, such as white noise or random tonal sequences. Electroencephalography (EEG) research revealed a characteristic negative potential to periodically recurring auditory patterns - a response, which has been interpreted as memory trace-related and specific, rather than as a sign of periodicity-driven entrainment. Here, we aim to disentangle these two possible contributions by investigating the influence of a periodic sound sequence's inherent temporal regularity on event-related potentials. Participants were presented continuous sequences of short tones of random pitch, with some sequences containing a recurring pattern, and asked to indicate whether they heard a repetition. Patterns were either spaced equally across the random sequence (isochronous condition) or with a temporal jitter (jittered condition), which enabled us to differentiate between event-related potentials (and thus processing operations associated with a memory trace for a repeated pattern) and the periodic nature of the repetitions. A negative recurrence-related component could be observed independently of temporal regularity, was pattern-specific, and modulated by across trial repetition of the pattern. Critically, isochronous pattern repetition induced an additional early periodicity-related positive component, which started to build up already before the pattern onset and which was elicited undampedly even when the repeated pattern was occasionally not presented. This positive component likely reflects a sensory driven entrainment process that could be the foundation of a behavioural benefit in detecting temporally regular repetitions.

In 1929, Fisher proposed a test for periodicity based on the largest periodogram ordinate. If the true frequency lies between two consecutive Fourier frequencies and the signal to noise ratio is low, the test may conclude that there is no periodicity. This loss of power was noted by Whittle in 1952, as well as the necessary assumption that the noise be white. Whittle and subsequent authors suggested remedies for the white noise assumption. This paper proposes simple tests, based on the Fourier coefficients, that is, the Fourier transforms at the Fourier frequencies, that have good power properties at all frequencies.

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and state filters for each mode, our algorithm relies on the ability to find the most probable model as a mode estimate, which we show is possible with input and state filters by identifying a key property, that a particular residual signal we call generalized innovation is a Gaussian white noise. We also provide an asymptotic analysis for the proposed algorithm and provide sufficient conditions for asymptotically achieving convergence to the true model (consistency), or to the 'closest' model according to an information-theoretic measure (convergence). A simulation example of intention-aware vehicles at an intersection is given to demonstrate the effectiveness of our approach., Comment: Submitted to SIAM Journal on Control and Optimization

In this short note, we prove an asymptotic expansion for the ratio of the Dirichlet density to the multivariate normal density with the same mean and covariance matrix. The expansion is then used to derive an upper bound on the total variation between the corresponding probability measures and rederive the asymptotic variance of the Dirichlet kernel estimators introduced by Aitchison & Lauder (1985) and studied theoretically in Ouimet (2020). Another potential application related to the asymptotic equivalence between the Gaussian variance regression problem and the Gaussian white noise problem is briefly mentioned but left open for future research., 12 pages, 6 figures

[Abstract Not Available]

Seismically derived amplitude‐versus‐angle attributes along with well constraints are the base inputs into inverting seismic into subsurface properties. Conditioning the common image gathers is a common workflow in quantitative inversion and leads to a more accurate inversion product due to the removal of post‐migration artefacts. Here, we apply a neural network to condition the post‐migration gathers. The network is a cycle generative adversarial network, CycleGAN, which was designed for image‐to‐image translation. This can be considered the same problem as translating an artefact rich seismic gather to an artefact free seismic gather. To assess the feasibility of applying the network to pre‐stack conditioning, synthetic data sets were generated to train different networks for different tasks. The networks were trained to remove white noise, residual de‐multiples, gather flattening and a combination of the above for conditioning. The results show that a trained network was able remove white noise providing a more robust amplitude‐versus‐offset calculation. Another network trained using synthetic gathers with and without multiples assisted in multiple removal. However, instability around primary preservation has been observed so the network works better as a residual de‐multiple method. For gather conditioning, a network was trained with the unpaired artefact‐rich and artefact‐free training data where the artefacts included complex moveout, noise and multiples. When applied to the test data sets, the networks cleaned the artefact‐rich test data and translated complex moveout into flat gathers whilst preserving the amplitude response. Finally, two networks are applied to real data where a gather based on the well logs is used to quantify the match between the conditioned gathers and the raw gathers. The first network used synthetic data to train the network and, when applied to real data, provided a better tie with the well. The second network was trained with synthetic gathers whose properties were constrained by real seismic gathers from near the well. As anticipated, the network trained on the representative training data outperforms the network trained using the unconstrained data. However, the ability of the first network to condition the gather indicates that a sweep of networks can be trained without the need for real data and applied in a manner analogous to the way parameters are adjusted in traditional geophysical methods. The results show that the different neural networks can offer an alternative or augmentation to the existing geophysical workflow for conditioning pre‐stack seismic gathers.

Many flexible extensions of the Cox proportional hazards model incorporate time-dependent (TD) and/or nonlinear (NL) effects of time-invariant covariates. In contrast, little attention has been given to the assessment of such effects for continuous time-varying covariates (TVCs). We propose a flexible regression B-spline-based model for TD and NL effects of a TVC. To account for sparse TVC measurements, we added to this model the effect of time elapsed since last observation (TEL), which acts as an effect modifier. TD, NL, and TEL effects are estimated with the iterative alternative conditional estimation algorithm. Furthermore, a simulation extrapolation (SIMEX)-like procedure was adapted to correct the estimated effects for random measurement errors in the observed TVC values. In simulations, TD and NL estimates were unbiased if the TVC was measured with a high frequency. With sparse measurements, the strength of the effects was underestimated but the TEL estimate helped reduce the bias, whereas SIMEX helped further to correct for bias toward the null due to "white noise" measurement errors. We reassessed the effects of systolic blood pressure (SBP) and total cholesterol, measured at two-year intervals, on cardiovascular risks in women participating in the Framingham Heart Study. Accounting for TD effects of SBP, cholesterol and age, the NL effect of cholesterol, and the TEL effect of SBP improved substantially the model's fit to data. Flexible estimates yielded clinically important insights regarding the role of these risk factors. These results illustrate the advantages of flexible modeling of TVC effects.

Improving the seismic time–frequency resolution is a crucial step for identifying thin reservoirs. In this paper, we propose a new high‐precision time–frequency analysis algorithm, synchroextracting generalized S‐transform, which exhibits superior performance at characterizing reservoirs and detecting hydrocarbons. This method first calculates time–frequency spectra using generalized S‐transform; then, it squeezes all but the most smeared time–frequency coefficients into the instantaneous frequency trajectory and finally obtains highly accurate and energy‐concentrated time–frequency spectra. We precisely deduce the mathematical formula of the synchroextracting generalized S‐transform. Synthetic signal examples testify that this method can correctly decompose a signal and provide a better time–frequency representation. The results of a synthetic seismic signal and real seismic data demonstrate that this method can identify some reservoirs with thincknesses smaller than a quarter wavelength and can be successfully applied for hydrocarbon detection. In addition, examples of synthetic signals with different levels of Gaussian white noise show that this method can achieve better results under noisy conditions. Hence, the synchroextracting generalized S‐transform has great application prospects and merits in seismic signal processing and interpretation.

International audience; Discretization of continuous time autoregressive (AR) processes driven by a Brownian motion and embedding of discrete time AR sequences driven by a Gaussian white noise are classical issues. The article aims at establishing and using such discretization and embedding formulae between extended AR continuous time processes and discrete time sequences. The continuous-time processes are driven by either Brownian or jump processes, and may have random coefficients depending on time; Levy-driven processes are also considered. The innovation of the discrete time processes may be of many types - including Gaussian. In one way, observing the continuous time AR process at discrete times leads the AR dynamics of the discretized process to be characterized. The other way round, AR sequences can be embedded, in the almost sure sense, into continuous time AR processes with the same dynamics. Illustration is provided through many examples and simulation.

We give a construction allowing to construct local renormalised solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalising the recent results of [BDH16,FG16,OW16]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [Hai14,BHZ16,CH16] applies, including in particular one-dimensional systems with KPZ-type nonlinearities driven by space-time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalisation procedure are given by local functionals of the solution. The main feature of our construction is that it allows to exploit a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small., Comment: 20 pages

Noise is one of the main factors that can influence the processes of sound communication across a wide range of animal groups. Although the effects of ambient noise on animal communication, including anthropogenic noise, have received increasing attention, few studies have examined changes in the fine structure of acoustic signals produced by vocalizing species in constantly noisy environments. Here, we used natural recordings to determine the associations between stream noise and call parameters in the little torrent frog (Amolops torrentis). We also used playbacks of stream noise recorded in natural habitats and playbacks of white noise to examine how male vocal signals change with increasing noise levels. The results show that noise intensity has a significant effect on male call frequency, but not on call amplitude or other call characteristics. Based on this evidence, we suggest that in streamside species stream noise drives males to alter call frequency and call as loudly as possible in order to improve discriminability. These findings provide insights into the role played by ecological selection in the evolution of noise‐dependent anuran vocal plasticity.

A marine seismic method based on continuous source and receiver wavefields has been developed. The method requires continuous recording of the seismic data. The source that may consist of multiple source elements can emit signals continuously while moving. The ideal source wavefield to be used with this method should be as white as possible both in a temporal and a spatial sense to avoid deep notches in the spectrum enabling a stable multi-dimensional deconvolution. White noise has such properties. However, equipment that can generate white noise does not exist. In order to generate a continuous source wavefield that is approaching the properties of white noise using existing equipment onboard marine seismic vessels, individual air-guns can be triggered with short randomized time intervals in a near-continuous fashion. The main potential benefits with the method are to reduce the environmental impact of marine seismic surveys and to improve acquisition efficiency. The peak sound pressure levels are significantly reduced by triggering one air-gun at a time compared to conventional marine seismic sources. Sound exposure levels are also reduced in most directions. Since the method is based on continuous recording of seismic data and the air-guns are triggered based on time and not based on position, there are less vessel speed limitations compared to conventional marine seismic data acquisition. Also, because the source wavefield is spread out in time, the wavefields emitted from source elements in different cross-line positions can be designed such that the emitted wavefield is spatially white in this direction. This means that source elements in multiple cross-line positions can be operated simultaneously, potentially improving the cross-line sampling and/or the acquisition efficiency.

Partial discharge (PD) detection is useful to the online monitoring of high-voltage cables, which are affected by periodic narrowband interference and random white noise. To suppress the influence of complex noise signals on the measurement of PD signals, a novel noise reduction method based on improved empirical wavelet transform (IEWT) and kurtosis for the PD signals of high-voltage cables is proposed. First, empirical wavelet function (EWF) signals arranged in order of frequency are obtained by decomposing the signal with IEWT. Then, the kurtosis criterion is introduced, and the reconstructed inherent modal function is adaptively screened. Finally, the improved threshold function is used in eliminating residual noise information in the reconstructed signal. Compared with the noise reduction methods based on EWT and EMD, the proposed noise reduction method can effectively suppress noise information in PD and has good practicability.

The paper discusses the identification of the empirical, partially intelligible white noise processes generated by deterministic numerical algorithms. The introduced fuzzy‐random complemen...

Let Xn = (xij) be a k×n data matrix with complex‐valued, independent and standardized entries satisfying a Lindeberg‐type moment condition. We consider simultaneously R sample covariance matrices Bnr=1nQrXnXn∗Qr⊤,1≤r≤R, where the Qr's are non‐random real matrices with common dimensions p×k(k≥p). Assuming that both the dimension p and the sample size n grow to infinity, the limiting distributions of the eigenvalues of the matrices {Bnr} are identified, and as the main result of the paper, we establish a joint central limit theorem (CLT) for linear spectral statistics of the R matrices {Bnr}. Next, this new CLT is applied to the problem of testing a high‐dimensional white noise in time series modelling. In experiments, the derived test has a controlled size and is significantly faster than the classical permutation test, although it does have lower power. This application highlights the necessity of such joint CLT in the presence of several dependent sample covariance matrices. In contrast, all the existing works on CLT for linear spectral statistics of large sample covariance matrices deal with a single sample covariance matrix (R = 1).

The single-photon quantum filtering problems have been investigated recently with applications in quantum computing. In practice, the detector responds with a quantum efficiency of less than unity since there exists some mode mismatch between the detector and the system and the single-photon signal may be corrupted by quantum white noise. Consequently, quantum filters based on multiple measurements are designed in this paper to improve estimation performance. More specifically, the filtering equations for a 2-level quantum system driven by a single-photon input state and under multiple measurements are presented in this paper. Four scenarios, ie, (1) 2 diffusive measurements with Q-P quadrature form, (2) 2 diffusive measurements with Q-Q quadrature form, (3) diffusive plus Poissonian measurements, and (4) 2 Poissonian measurements, are considered. It is natural to compare the filtering results, ie, measuring a single channel or both channels, which one is better? By the simulation where we use a single photon to excite an atom, it seems that multiple measurements enable us to excite the atom with higher probability than only measuring a single channel. In addition, a measurement back-action phenomenon is revealed by the simulation results.

Key points Rodents explore their immediate environment using their whiskers. Such exploration leads to micromotions, which contain many high-frequency (50-200 Hz) components. High-frequency whisker motion is represented faithfully in the temporal structure of the spike trains of trigeminal neurons. However, the representation of high-frequency sensory inputs in cortex is not fully understood. By combining extracellular and intracellular recordings in the rat somatosensory cortex and thalamus, we show that high-frequency sensory inputs, either sinusoidal or white noise, elicit internally generated gamma (20-60 Hz) band oscillations in cortical networks. Gamma oscillations modulate cortical spike probability while preserving sub-millisecond phase relations with high-frequency sensory inputs. Consequently, our results indicate that millisecond precision stimulus-locked spiking activity and sensory-induced gamma oscillation can constitute independent multiplexed coding schemes at the single-cell level. Abstract In the natural environment, tactile exploration often leads to high-frequency vibrations at the level of the sensory organs. Single-unit recordings of cortical neurons have pointed towards either a rate or a temporal code for representing high-frequency tactile signals. In cortical networks, sensory processing results from the interaction between feedforward inputs relayed from the thalamus and internally generated activity. However, how the emergent activity represents high-frequency sensory input is not fully understood. Using multisite single-unit, local field potential and intracellular recordings in the somatosensory cortex and thalamus of lightly sedated male rats, we measured neuronal responses evoked by sinusoidal and band-pass white noise whisker stimulation at frequencies that encompass those observed during texture exploration (50-200 Hz). We found that high-frequency sensory inputs relayed from the thalamus elicit both sub-millisecond stimulus-locked responses and internally generated gamma (20-60 Hz) band oscillations in cortical networks. Gamma oscillations modulate spike probability while preserving sub-millisecond phase relations with sensory inputs. Therefore, precise stimulus-locked spiking activity and sensory-induced gamma oscillations can constitute independent multiplexed coding schemes at the single-cell level.

PURPOSE Range errors constrain treatment planning by limiting choice of ion beam angles and requiring large margins. Ionoacoustic range verification requires recovering the location of an acoustic source from low frequency signals. A priori information is applied to stably overcome resolution limits of inverse acoustic source imaging in this simulation study. In particular, the accuracy and robustness of ionoacoustic range verification for lateral and oblique delivery of high-energy protons to the prostate is examined. METHODS Dose maps were computed using GEANT4 Monte Carlo simulations via the TOPAS user interface. Thermoacoustic pulses were propagated using k-Wave software, with initial pressures corresponding to instantaneous dose deposition and piecewise constant maps of tissue properties derived from the planning CT. A database of dose maps with corresponding thermoacoustic emissions and Bragg peak locations, referred to as "control points," were precomputed. Corresponding thermoacoustic emissions were also precomputed. Pulses were recorded at four coplanar locations corresponding to the outer surface of a virtual transrectal array. To model experimental beam delivery, k-Wave results were convolved in time with a Gaussian envelope to account for noninstantaneous proton delivery by a synchrocyclotron. Thermoacoustic pulses were bandlimited below 150 kHz, and amplitudes were directly proportional to charge delivered. To test robustness of our method, white noise was added. Range was estimated in a two-step process. The first step obtained a preliminary range estimate by one-way beamforming. The second step was taken using data corresponding to the "control point" nearest to the preliminary range estimate. For each receiver, the time of flight difference, ∆t, between the measured and control thermoacoustic signals were accurately estimated by applying the Fourier shift theorem. Receiver-Bragg peak distance was then estimated by adding vs ∆t to the known distance of the control point, where vs is soundspeed. A linear system of equations based upon all receiver locations and distances was solved to recover the Bragg peak location. All simulations were performed relative to the planning CT. Because ultrasound (US) images were not available, results were overlaid onto the planning CT. RESULTS Beamformed estimates from noise-free data tracked all beam locations within 1 cm. Final estimates for oblique and lateral beams were accurate to within 1.0 and 1.6 mm respectively. Average errors of final range estimates for oblique beams from data with SNR = 0 dB were no greater than 2.0 mm. CONCLUSIONS Ionoacoustic range verification may improve current practice. Ionoacoustic range estimates can be inherently co-registered to ultrasound images of underlying anatomy. To ensure estimates are robust in clinical practice, dose maps based upon the planning CT should be overlaid onto ultrasound volumes acquired at time of treatment and acoustic simulations re-computed to provide a database of control points and corresponding thermoacoustic emissions. Computation times for beamformed estimates are already fast enough for online range verification, but are not accurate enough for a measurement aperture limited to the surface of a transrectal ultrasound probe. Accelerated acoustic simulations will be required to enable online two-stage correction, but offline calculation is already suitable for adaptive planning.

Summary This paper addresses the problem of designing robust Kalman estimators for uncertain systems with mixed uncertainties including the same uncertain-variance multiplicative noise in state and measurement matrices, missing measurements, and uncertain-variance linearly correlated measurement and process white noise. By introducing fictitious noise to compensate for multiplicative noise, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, on the basis of the worst-case system with known conservative upper bounds of uncertain variances, the minimax robust time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady-state Kalman estimators are also presented, and 3 modes of convergence in a realization among the time-varying and steady-state robust Kalman estimators for the time-varying and time-invariant systems are presented and proved by the dynamic error system analysis method. A simulation example with application to autoregressive signal processing is also given to show the effectiveness and correctness of the proposed results.

Noisy, unpredictable sounds are often present in the vocalizations of fearful and stressed animals across many taxa. A variety of structural characteristics, called nonlinear acoustic phenomena, that include subharmonics, rapid frequency modulations, and deterministic chaos are responsible for the harsh sound quality of these vocalizations. Exposure to nonlinear sound can elicit increased arousal in birds and mammals. Past experiments have used white noise to test for effects of deterministic chaos on perceivers. However, deterministic chaos differs structurally from white noise (i.e., random signal with equal energy at all frequencies), and unlike white noise, may differ dramatically depending on how it is produced. In addition, the subtle structural variation of chaos may not be distinguishable in the environment due to the attenuation and degradation of sound over distance and different habitat types. We designed two experiments to clarify whether American robins (Turdus migratorius) and warbling vireos (Vireo gilvus) discriminate between white noise and deterministic chaos. We broadcast and re-recorded white noise and two exemplars of deterministic chaos—one generated with a Chua oscillator and the other generated using a logistic equation—at 1, 10, 20, 30, 40, and 80 m across open and forested habitat and used spectrogram correlations to compare stimuli along this degradational gradient. We found that sounds degraded similarly in both habitats when compared to a reference distance of 1 m. Comparing pairs of stimuli across distances suggested that Chua chaos was more easily distinguishable from noise and logistic chaos. In addition, all stimuli became more distinctive over increased distance. The second experiment tested behavioral responses of robins and warbling vireos to control sounds of tropical kingbird (Quiscalus mexicanus), white noise, and two exemplars of deterministic chaos (Chua and logistic). Neither American robins nor warbling vireos responded differently to at least two types of deterministic chaos and white noise, validating previous playback studies that used white noise as a surrogate for deterministic chaos. Uniform responses to a variety of nonlinear features in these birds possibly reflect error management in alarm signal detection.

We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the L2-distance between the spectral density operator and its best (L2-)approximation by a spectral density operator corresponding to a white noise process. The estimation of this distance can be easily accomplished by sums of periodogram kernels, and it is shown that an appropriately standardized version of the estimator is asymptotically normal distributed under the null hypothesis (of functional white noise) and under the alternative. As a consequence, we obtain a very simple test (using the quantiles of the normal distribution) for the hypothesis of a white noise functional process. In particular, the test does not require either the estimation of a long-run variance (including a fourth order cumulant) or resampling procedures to calculate critical values. Moreover, in contrast to all other methods proposed in the literature, our approach also allows testing for ‘relevant’ deviations from white noise and constructing confidence intervals for a measure that measures the discrepancy of the underlying process from a functional white noise process.

This paper investigates the robust model predictive control (RMPC) problem for a class of linear discrete-time systems subject to saturated inputs and randomly occurring uncertainties (ROUs). Due to limited bandwidth of the network channels, the networked transmission would inevitably lead to incomplete measurements and subsequently unavoidable network-induced phenomenon that include saturated inputs as a special case. The saturated inputs are assumed to be sector-bounded in the underlying system. In addition, the ROUs are taken into account to reflect the difficulties in precise system modelling, where the norm-bounded uncertainties are governed by certain uncorrelated Bernoulli-distributed white noise sequences with known conditional probabilities. Based on the invariant set theory, a sufficient condition is derived to guarantee the robust stability in the mean-square sense of the closed-loop system. By employing the convex optimization technique, the controller gain is obtained by solving an optimization problem with some inequality constraints. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed RMPC scheme.

In this paper, we investigate the dynamics of a multigroup disease propagation model with distributed delays and nonlinear incidence rates, which accounts for the relapse of recovered individuals. The main concern is the stability of the equilibria, sufficient conditions for global stability being obtained by applying Lyapunov-LaSalle invariance principle and using Lyapunov functionals, which are constructed using their single-group counterparts. The situation in which the deterministic model is subject to perturbations of white noise type is also investigated from a stability viewpoint.