Gaussian White Noise Input Research Articles

Sufficient condition for reliable logic operations in an over damped bistable system driven by Gaussian white noise.

In this paper, we investigate an overdamped bistable system subject to Gaussian white noise and logical inputs. By solving and estimating the steady distribution of the corresponding Fokker-Planck equation and considering the two essential features of the reliable logic operations (RLOs)-initial value independence and sign invariance-we establish the sufficient condition for RLO occurrence and identify parametric resonance phenomena in the system. Our numerical simulations confirm the reliability and accuracy of the theoretical results. This work offers insights into enhancing the accuracy of stochastic systems, particularly in the realm of logical stochastic resonance, thereby contributing to advancements in understanding and controlling stochastic dynamical systems.

Input-size dependence of the baroreflex neural arc transfer characteristics during Gaussian white noise inputs.

Although Gaussian white noise (GWN) inputs offer a theoretical framework for identifying higher-order nonlinearity, an actual application to the data of the neural arc of the carotid sinus baroreflex did not succeed in fully predicting the well-known sigmoidal nonlinearity. In the present study, we assumed that the neural arc can be approximated by a cascade of a linear dynamic (LD) component and a nonlinear static (NS) component. We analyzed the data obtained using GWN inputs with a mean of 120 mmHg and standard deviations (SDs) of 10, 20, and 30 mmHg for 15 min each in anesthetized rats (n = 7). We first estimated the linear transfer function from carotid sinus pressure to sympathetic nerve activity (SNA) and then plotted the measured SNA against the linearly predicted SNA. The predicted and measured data pairs exhibited an inverse sigmoidal distribution when grouped into 10 bins based on the size of the linearly predicted SNA. The sigmoidal nonlinearity estimated via the LD-NS model showed a midpoint pressure (104.1 ± 4.4 mmHg for SD of 30 mmHg) lower than that estimated by a conventional stepwise input (135.8 ± 3.9 mmHg, P < 0.001). This suggests that the NS component is more likely to reflect the nonlinearity observed during pulsatile inputs that are physiological to baroreceptors. Furthermore, the LD-NS model yielded higher R2 values compared with the linear model and the previously suggested second-order Uryson model in the testing dataset.NEW & NOTEWORTHY We examined the input-size dependence of the baroreflex neural arc transfer characteristics during Gaussian white noise inputs. A linear dynamic-static nonlinear model yielded higher R2 values compared with a linear model and captured the well-known sigmoidal nonlinearity of the neural arc, indicating that the nonlinear dynamics contributed to determining sympathetic nerve activity. Ignoring such nonlinear dynamics might reduce our ability to explain underlying physiology and significantly limit the interpretation of experimental data.

Sampling Gaussian stationary random fields: A stochastic realization approach

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the difficulty of being computationally expensive, which is even more serious when the dimension of the random field is large. This paper proposes an efficient stochastic realization approach for sampling Gaussian stationary random fields from a systems and control point of view. Specifically, we take the exponential and squared exponential covariance functions as examples and make a decoupling assumption when there are multiple dimensions. Then a rational spectral density is constructed in each dimension using techniques from covariance extension, and the corresponding autoregressive moving-average (ARMA) model is obtained via spectral factorization. As a result, samples of the random field with a specific covariance function can be generated very efficiently in the space domain by implementing the ARMA recursion using a Gaussian white noise input. Such a procedure is computationally cheap due to the fact that the constructed ARMA model has a low order. Furthermore, the same method is integrated to multiscale simulations where interpolations of the generated samples are achieved when one zooms into finer scales. Both theoretical analysis and simulation results show that our approach performs favorably compared with covariance matrix decomposition methods.

An Optimized Zero-Attracting LMS Algorithm for the Identification of Sparse System

This paper introduces an optimized zero-attractor to improve the performance of least mean square (LMS)-based algorithms for the identification of sparse system. Compared with previous LMS-based algorithms for sparse system identification, the performance of the proposed optimized zero-attracting LMS (OZ-LMS) is much less sensitive to the tuning parameters and measurement noise power, and performs much better for sparse system. Comprehensive performance analysis of the mean-square deviation (MSD) of OZ-LMS is derived in detail. Moreover, the parameter selection rules for optimal steady-state MSD are discussed. Simulation results, using white Gaussian noise and speech input signals, show improved performance over existing methods. Furthermore, we show that the numerical results of OZ-LMS agree with the theoretical predictions.

Flexural band gaps and vibration control of a periodic railway track

Periodic structures exhibit unique band gap characteristics by virtue of which they behave as vibro-acoustic filters thereby allowing only waves within a certain frequency range to pass through. In this paper, lateral and vertical flexural wave propagation and vibration control of a railway track periodically supported on rigid sleepers using fastenings are studied in depth. The dispersion relations in both lateral and vertical directions are obtained using the Floquet-Bloch theorem and the resulting dispersion curves are verified using finite element models. Afterwards, tuned mass dampers (TMDs) with different mass ratios are designed to control vibrations of the examined rail in both the directions. Moreover, the influence of damping of rail and resonators on band gap characteristics is investigated. As a replacement to the conventional TMD, a novel possibility to control vibration relies on using another existing rail as a lateral distributed resonator (LDR). Although the effectiveness of LDR is lower than that of localized resonators, the former represents a simple and promising way to control vibrations. Efficacy of the proposed control methods is finally verified by applying a random Gaussian white noise input. The study presented here is useful to understand the propagation and attenuation behavior of flexural waves and to develop efficient and novel vibration control strategies for track structures.

Kernel Extreme Learning Machine based Cluster Sparse Proportionate Affine Projection Algorithm for Echo Cancellation

The performance of kernel extreme learning machine based CSPAPA (KELM-CSPAPA) is proposed and studied. An adaptive density-based clustering algorithm (ADBC) is used to decompose the training dataset into multiple subsets. Furthermore, the improved flower pollination optimization algorithm (IFPA) is used to optimize the parameters of the KELM model. Initially, the performance of the ADBC algorithm is studied to estimate the optimal number of clusters using three different inputs. Then the KELM model is assessed with different machine learning models using various statistical indices. The time consumption of KELM for the colored noise and speech signal inputs are less compared to the white Gaussian noise input. Finally, a performance comparison of KELM-CSPAPA is presented with three benchmark algorithms: PAPA, block sparse PAPA (BS-PAPA), and CS-PAPA. The result shows that the proposed method outperformed existing algorithms. The simulation results demonstrate that KELM-CSPAPA fully exploits the sparsity and handled the clustered-sparse signal.

Modal parameter identification of time-varying systems via wavelet-based frequency response function

Modal parameter identification of systems, structures and machines with variable physical parameters is an important task for their damage diagnosis, maintenance and repair, and life cycle management, especially when time-varying vibration modes are involved. The paper proposes a new combined, two-step, i.e., estimated wavelet-based frequency response function (FRF) and least-squares iterative algorithm, modeling approach in order to determine time-varying vibration modes based on Gaussian white noise input excitation. The time-varying wavelet-based FRF is estimated based on output noise estimation model $$H_1$$ ; the second step identifies time-varying modal parameters based on estimated wavelet-based FRF with the use of least-squares iterative algorithm. Estimated wavelet-based FRF can reveal the dynamic characteristics of the system correctly similar to the theoretical FRF by single degree of freedom (SDOF). The combined method is demonstrated using system identification analysis based on the simulated stiffness-varying and mass-varying multiple-degree-of-freedom (MDOF) system subjected to random Gaussian white noise excitation. The results show that the proposed combined method accurately identifies modal parameter of the time-invariant analyzed structure, and correctly captures modal parameter of the time-varying analyzed structure. The modal frequency and shape agree with theoretical results well. The analysis results also indicate that the proposed combined method is sensitive to the position of input excitation. The estimation accuracy wavelet-based FRF can be improved by selecting the average number of times and wavelet parameters.

Centrality Measures in Linear Consensus Networks With Structured Network Uncertainties

We propose new insights into the network centrality based not only on the network graph, but also on a more structured model of network uncertainties. The focus of this paper is on the class of uncertain linear consensus networks in continuous time, where the network uncertainty is modeled by structured additive Gaussian white noise input on the update dynamics of each agent. The performance of the network is measured by the expected dispersion of its states in steady state. This measure is equal to the square of the $\mathcal {H}_2$ -norm of the network, and it quantifies the extent by which its state deviates away from the consensus state in steady state. We show that this performance measure can be explicitly expressed as a function of the Laplacian matrix of the network and the covariance matrix of the noise input. We investigate several structures for noise input and provide engineering insights on how each uncertainty structure can be relevant in real-world settings. Then, a new centrality index is defined in order to assess the influence of each agent or link on the network performance. For each noise structure, the value of the centrality index is calculated explicitly, and it is shown how it depends on the network topology as well as the noise structure. Our results assert that agents or links can be ranked according to this centrality index, and their rank can drastically change from the lowest to the highest, or vice versa, depending on the noise structure. This fact hints at emergence of fundamental tradeoffs on network centrality in the presence of multiple concurrent network uncertainties with different structures.

Stochastic response of a fractional vibroimpact system

The paper proposes a method to investigate the stochastic dynamics of a vibroimpact single-degree-of-freedom fractional system under a Gaussian white noise input. It is assumed that the system has a hard type impact against a one-sided motionless barrier, which is located at the system’s equilibrium position; furthermore, the system under study is endowed with an element modeled with fractional derivative. The proposed method is based on stochastic averaging technique and overcome the particular difficulty due to the presence of fractional derivative of an absolute value function; particularly an analytical expression for the system’s mean squared response amplitude is presented and compared with results obtained by numerical simulations.

A reanalysis of “Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons”

Neuronal activity in the central nervous system varies strongly in time and across neuronal populations. It is a longstanding proposal that such fluctuations generically arise from chaotic network dynamics. Various theoretical studies predict that the rich dynamics of rate models operating in the chaotic regime can subserve circuit computation and learning. Neurons in the brain, however, communicate via spikes and it is a theoretical challenge to obtain similar rate fluctuations in networks of spiking neuron models. A recent study investigated spiking balanced networks of leaky integrate and fire (LIF) neurons and compared their dynamics to a matched rate network with identical topology, where single unit input-output functions were chosen from isolated LIF neurons receiving Gaussian white noise input. A mathematical analogy between the chaotic instability in networks of rate units and the spiking network dynamics was proposed. Here we revisit the behavior of the spiking LIF networks and these matched rate networks. We find expected hallmarks of a chaotic instability in the rate network: For supercritical coupling strength near the transition point, the autocorrelation time diverges. For subcritical coupling strengths, we observe critical slowing down in response to small external perturbations. In the spiking network, we found in contrast that the timescale of the autocorrelations is insensitive to the coupling strength and that rate deviations resulting from small input perturbations rapidly decay. The decay speed even accelerates for increasing coupling strength. In conclusion, our reanalysis demonstrates fundamental differences between the behavior of pulse-coupled spiking LIF networks and rate networks with matched topology and input-output function. In particular there is no indication of a corresponding chaotic instability in the spiking network.

A reanalysis of "Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons".

Neuronal activity in the central nervous system varies strongly in time and across neuronal populations. It is a longstanding proposal that such fluctuations generically arise from chaotic network dynamics. Various theoretical studies predict that the rich dynamics of rate models operating in the chaotic regime can subserve circuit computation and learning. Neurons in the brain, however, communicate via spikes and it is a theoretical challenge to obtain similar rate fluctuations in networks of spiking neuron models. A recent study investigated spiking balanced networks of leaky integrate and fire (LIF) neurons and compared their dynamics to a matched rate network with identical topology, where single unit input-output functions were chosen from isolated LIF neurons receiving Gaussian white noise input. A mathematical analogy between the chaotic instability in networks of rate units and the spiking network dynamics was proposed. Here we revisit the behavior of the spiking LIF networks and these matched rate networks. We find expected hallmarks of a chaotic instability in the rate network: For supercritical coupling strength near the transition point, the autocorrelation time diverges. For subcritical coupling strengths, we observe critical slowing down in response to small external perturbations. In the spiking network, we found in contrast that the timescale of the autocorrelations is insensitive to the coupling strength and that rate deviations resulting from small input perturbations rapidly decay. The decay speed even accelerates for increasing coupling strength. In conclusion, our reanalysis demonstrates fundamental differences between the behavior of pulse-coupled spiking LIF networks and rate networks with matched topology and input-output function. In particular there is no indication of a corresponding chaotic instability in the spiking network.

Simulation of Wide-Sense Stationary Random Time-Series With Specified Spectral Densities

In this paper, an effective approach to the simulation of wide-sense stationary random time-series, defined by its power spectral density (PSD) is presented. This approach is based on approximating the sample paths of target random process by finite series of sample functions of random processes, obtained as the outputs of suitably chosen set of second-order linear filters to independent limited band Gaussian white noise inputs. Thus, the Gaussian distribution of simulated time-series is obtained without applying the central limit theorem. Also, the Fourier spectra of the simulated sample paths are not discrete functions, as in the case of the multisine random time-series representation used by most classical simulation methods. The method can be applied to any analytical or nonparametric representation of the specified PSD. The proposed approach is applied to simulation of road input sample paths, compatible with PSDs described by analytical forms that can or cannot be derived by linear shape filters. The method is validated by comparison of spectral response of a half-car model to the input induced by a measured road profile with that obtained for the simulated road input. This input is derived from the nonparametric PSD, determined by third-octave filtering of the measured profile. The advantages of the proposed approach are highlighted by its comparison with a conventional method, based on the representation of simulated road input by a sum of harmonics with random phases.

Independent Noise Enhances Synchronization in Heterogeneous Systems

We investigated effects of noise inputs on synchronous firing in a simple model neuron system with electrophysiological heterogeneity. The system consists of two leaky integrate-and-fire (LIF) neurons with different membrane time constants. They are uncoupled and driven by Gaussian white noise inputs. We found that correlation between spike trains of two LIF neurons was maximized at input correlation slightly smaller than one. The same result was obtained for a more realistic system consisting of two non-identical Hodgkin–Huxley neurons. We also revealed the mechanism underlying the effect.

A New Spectrum Sensing Method Using Output Analysis of the PFD

In this brief, a new blind spectrum sensing method is proposed based on frequency comparison using a phase frequency detector (PFD). The PFD output patterns are utilized in a way to sense the spectrum with no knowledge of incoming signals, noise, or channel parameters. The detection and false alarm error probabilities are analytically calculated for additive white Gaussian noise and sine-wave input and are simulated for different inputs. It is shown that the required detection and false alarm probabilities can be achieved by changing the system parameters. The results show that the proposed method has lower complexity and outperforms the previous single-antenna blind method over flat fading channel.

SU-E-I-96: Realistic Synthetic CT Imaging of Small Numerical Lesions with Simple CT Simulation Model Incorporating Equipment MTF.

Quantitative analysis in CT imaging often requires image data set of lesions with ground truth, which is practically impossible in general. This study presents a simple CT simulation model which enables to create realistic synthetic CT images of numerical voxel phantoms for small lesionswith various shape and sizes. Basic CT parameters were acquired from DICOM header of target CT data, and were used in the CT simulator. Frequency response of forward and backward projectors were determined by measuring NPS of reconstructed image from white Gaussian noise input data, which were then used to iteratively calibrate those projectors so as to produce white Gaussian NPS output. Then, the MTF of target equipment were measured and incorporated into the sinogram filter before back projection in order to reflect focal spot blurring and vendor specific recon kernel. For validation, physical and numerical phantoms with rod and tube shape of 2mm ∼ 10mm were created and imaged with a real CT (Sensation 16, Siemens) and the proposed simulated CT, respectively. Images were reconstructed with 8 different kernels (B10 ∼ B80) in both CT imaging technique, and their line profiles were compared. Synthesized and physically scanned CT images of phantoms with different shape, sizes, and recon kernels agreed well in visual assessment, size measurement, and line profile comparison. Proposed method could produce realistic synthetic CT images of numerical phantoms highly mimicking in visual appearance and quantitative comparison, which has a potential for use as ground truth data set in quantitative image analysis.

Inhibition of Oscillation in a Neural Oscillator Model for Sound Therapy of Tinnitus

Perception of continuous or intermittent sounds ringing in the ears without any external source is referred to as tinnitus. For the management of tinnitus one of the most effective approaches is sound therapy. Previously, we demonstrated a conceptual and computational plastic neural oscillator model for the mechanisms of tinnitus generation and the clinical effects of sound therapy on tinnitus. The proposed model has a stable oscillatory state and a stable equilibrium (non-oscillatory) state. It can be hypothesized that the oscillation state corresponds to the generation of tinnitus and the equilibrium state corresponds to the state in which the tinnitus is inhibited. Through numerical simulations of this model it was found that the oscillation can be inhibited by supplying band-pass noise (BN) stimuli, which clinically has been used as a stimulus for treatment of tinnitus (i.e., sound therapy). The current paper describes the inhibition of the oscillation by yet two different types of noise stimuli: Gaussian white noise (GWN) and additive uniform noise (AUN). This investigation shows that only smaller RMS value of GWN input could inhibit the oscillation. When larger RMS values of GWN were employed the inhibition of oscillation was not frequent. It was observed that AUN can inhibit the oscillation with higher possibility than GWN or BN. It is an interesting result although it does not directly suggest that AUN is better than GWN or BN in clinic.

The Two-Dimensional Power Spectral Density: A Connection Between 2-D Rational Functions and Linear Systems

A derivation of the power spectral density (PSD) matrix of a continuous-time, linear, constant-coefficient system with white Gaussian noise input is given. The assumption of wide-sense stationarity is not made. By transforming the two-dimensional (2-D) autocorrelation function (ACF), a 2-D spectral density is obtained that takes the system's transient behavior into account. The 2-D PSD is a non-separable rational function. The results are applicable to second-order Volterra series representations of nonlinear systems. Simulations are presented for a fourth order system that compare the 2-D PSD amplitude (both theoretical and empirical) with its 1-D counterpart on 50 realizations of a short data segment containing an initial transient.

Equilibrium and Response Properties of the Integrate-and-Fire Neuron in Discrete Time.

The integrate-and-fire neuron with exponential postsynaptic potentials is a frequently employed model to study neural networks. Simulations in discrete time still have highest performance at moderate numerical errors, which makes them first choice for long-term simulations of plastic networks. Here we extend the population density approach to investigate how the equilibrium and response properties of the leaky integrate-and-fire neuron are affected by time discretization. We present a novel analytical treatment of the boundary condition at threshold, taking both discretization of time and finite synaptic weights into account. We uncover an increased membrane potential density just below threshold as the decisive property that explains the deviations found between simulations and the classical diffusion approximation. Temporal discretization and finite synaptic weights both contribute to this effect. Our treatment improves the standard formula to calculate the neuron's equilibrium firing rate. Direct solution of the Markov process describing the evolution of the membrane potential density confirms our analysis and yields a method to calculate the firing rate exactly. Knowing the shape of the membrane potential distribution near threshold enables us to devise the transient response properties of the neuron model to synaptic input. We find a pronounced non-linear fast response component that has not been described by the prevailing continuous time theory for Gaussian white noise input.

Beyond linear perturbation theory: the instantaneous response of the integrate-and-fire model

Event Abstract Back to Event Beyond linear perturbation theory: the instantaneous response of the integrate-and-fire model Moritz Helias1*, Moritz Deger2, Stefan Rotter2 and Markus Diesmann1 1 RIKEN Brain Science Institute, Japan 2 Bernstein Center for Computational Neuroscience, Germany The integrate-and-fire neuron model with exponential postsynaptic potentials is widely used in analytical work and in simulation studies of neural networks alike. For Gaussian white noise input currents, the membrane potential distribution is known exactly [1]. The linear response properties of the model have successfully been calculated and applied to the dynamics of recurrent networks in this diffusion limit [2]. However, the diffusion approximation assumes the effect of each synapse on the membrane potential to be infinitesimally small. Here we present a novel hybrid theory that takes finite synaptic weights into account. We show, that this considerably alters the absorbing boundary condition at the threshold: the probability density increases just below threshold. As a result, the response of the neuron to a fast transient input is enhanced much in the same way as found for the case of synaptic filtering [3]. However, in contrast to this earlier work relying on linear perturbation theory [4], we quantify to all orders an instantaneous response that is asymmetric for excitatory and inhibitory transients and exhibits a non-linear dependence on positive perturbation amplitudes. Furthermore we demonstrate that in the pooled response of two neuronal populations to antisymmetric transients the linear components exactly cancel. In this scenario the macroscopic network dynamics is dominated by the instantaneous non-linear components of the response. These results suggest that the linear response approach neglects important features of the rectifying nature of threshold units with finite jumps even for small perturbations. We provide an analytical framework to go beyond [5]. Partially funded by BMBF Grant 01GQ0420 to BCCN Freiburg, EU Grant 15879 (FACETS), DIP F1.2, Helmholtz Alliance on Systems Biology, and Next-Generation Supercomputer Project of MEXT.

A Class of Sparseness-Controlled Algorithms for Echo Cancellation

In the context of acoustic echo cancellation (AEC), it is shown that the level of sparseness in acoustic impulse responses can vary greatly in a mobile environment. When the response is strongly sparse, convergence of conventional approaches is poor. Drawing on techniques originally developed for network echo cancellation (NEC), we propose a class of AEC algorithms that can not only work well in both sparse and dispersive circumstances, but also adapt dynamically to the level of sparseness using a new sparseness-controlled approach. Simulation results, using white Gaussian noise (WGN) and speech input signals, show improved performance over existing methods. The proposed algorithms achieve these improvement with only a modest increase in computational complexity.