Enhanced cochlear implant coding using multiplicative noise (Invited Paper)

The stable state properties and mean first-passage time of tristable system driven by non-correlated additive and multiplicative non-Gaussian noise

In this paper, we consider the Schlogl model with time-delayed feedback to study the switching behavior of a bistable chemical reaction system in the presence of cross-correlated multiplicative and additive noise sources. Our results show that (i) the multiplicative noise (or additive noise) can induce the switch from high (or low) concentration state to low (or high) concentration one; (ii) the mean first passage time (MFPT) of switch from high concentration state to the low concentration one as functions of the noise strengths exhibits a maximum, which is the signature of the noise enhanced stability (NES) phenomenon for the high concentration state; and (iii) as the value of cross-correlation strength λ, time delay τ, or strength K of the feedback loop increases, the maximum in the MFPT increases, i.e., λ, τ, or K can enhance stability of the high concentration state.

We derive an optimum filter function to detect a target degraded by multiplicative noise and additive overlapping noise and placed in background noise. The filter is designed to maximize the metric peak-to-output energy, which is the ratio of the expected value squared of the output peak at the target position to the expected value of the average output energy. The optimum filter provides improved discrimination as well as robustness to input noise. One advantage of the filter described here over the homomorphic filters is that the additional preprocess on the input image, that is, the input logarithmic operation, is not required for reducing the effects of multiplicative noise. The performance of the filter is examined in terms of discrimination against background noise and robustness to multiplicative and additive input noise. Both multiplicative amplitude noise and multiplicative complex noise are considered.

Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances

Current reversal in a continuously periodic system driven by an additive noise and a multiplicative noise

The issues are considered, associated with the estimation of the measurement accuracy of the information parameters of the useful signal in the conditions of simultaneous action of multiplicative and additive noise, which in general have non-Gaussian character of the distribution. Two approaches to representation of the multiplicative noise are analyzed. It is shown that when considering of multiplicative noise in the form of deterministic or quasideterministic process the measurement accuracy is affected as non-Gaussian nature of the additive noise and average power of the multiplicative noise. It is shown that with the increase of the average power of the multiplicative noise effect of non-Gaussian nature of the additive noise on the measurement accuracy is reduced. It is shown that if the multiplicative noise is a random process, then the potential measurement accuracy under its influence can be reduced by more than an order of magnitude. Accounting non-Gaussian character of equivalent noise formed by additive noise and a multiplicative part, leads to a significant reduction in the potential loss of measurement accuracy.

During early development, peripheral sensory systems generate physiological activity prior to exposure to normal environmental stimuli. This activity is thought to facilitate maturation of these neurons and their connections, perhaps even promoting efficacy or modifying downstream circuitry. In the mammalian auditory system, initial connections form at embryonic ages, but the functional characteristics of these early neural connections have not been assayed. We investigated processes of embryonic auditory development using a whole-head slice preparation that preserved connectivity between peripheral and brainstem stations of the auditory pathway. Transgenic mice expressing fluorescent protein provided observation of spiral ganglion and cochlear nucleus neurons to facilitate targeted electrophysiological recording. Here we demonstrate an apparent peripheral-to-central order for circuit maturation. Spiral ganglion cells acquire action potential-generating capacity at embryonic day 14 (E14), the earliest age tested, and action potential waveforms begin to mature in advance of comparable states for neurons of the ventral cochlear nucleus (VCN) and medial nucleus of the trapezoid body (MNTB). In accordance, auditory nerve synapses in the VCN are functional at E15, prior to VCN connectivity with the MNTB, which occurs at least 1 day later. Spiral ganglion neurons exhibit spontaneous activity at least by E14 and are able to drive third-order auditory brainstem neurons by E17. This activity precedes cochlear-generated wave activity by 4 days and ear canal opening by at least 2 weeks. Together, these findings reveal a previously unknown initial developmental phase for auditory maturation, and further implicate the spiral ganglion as a potential controlling centre in this process.

Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

In this study, we investigate the dynamic mechanisms of tumor progression in response to fluctuations and uncertainties within the tumor-immune microenvironment. Utilizing temporal single-cell data, we develop a novel stochastic reaction-convection model that captures the spatiotemporal dynamics of macrophage responses to tumor cells subjected to both multiplicative and additive noise generated by non-homologous microenvironmental fluctuations. We prove the existence and uniqueness of a global positive solution for the proposed stochastic model. Then, by combining the stochastic Lyapunov analysis and the comparison theorem, we explore the moment boundaries for cell populations, as well as the asymptotic behavior at the boundary equilibrium points; sufficient conditions for driving sustained tumor growth and clearance are derived by employing the ergodicity theorem and are interestingly found to be only related to multiplicative noise. Furthermore, we employ an upwind finite difference scheme to simulate the effects of different noise types on a cell population distribution and the persistence of tumor growth. Results show that while additive noise influences the multimodal distribution of early tumor cell phenotypes, it has minimal impact on the mean density of tumor cells, indicating that additive noise acts primarily as a diffusion factor. In contrast, increasing multiplication noise effectively inhibits the development without altering the number of peaks in a phenotypic distribution. Interestingly, when additive and multiplicative noises are correlated, stronger additive noise can have dual effects on the steady-state distribution of tumor cells, with increased correlation positively influencing tumor cell elimination. These results provide novel insight into the tumor-immune microenvironment dynamics.

The problem of distributed parameter estimation from binary quantized observations is studied when the unquantized observations are corrupted by combined multiplicative and additive Gaussian noise. These results are applicable to sensor networks where the sensors observe a parameter in combined additive and nonadditive noise and to a case where dispersed receivers are employed with analog communication over fading channels where the receivers employ binary quantization before noise-free digital communications to a fusion center. We first discuss the case in which all the quantizers use an identical threshold. The parameter identifiability condition is given, and, surprisingly, it is shown that unless the common threshold is chosen properly and the parameter lies in an open interval, the parameter will not generally be identifiable, in contrast to the additive noise case. The best achievable mean square error (MSE) performance is characterized by deriving the corresponding Cramer-Rao Lower Bound (CRLB). A closed-form expression describing the corresponding maximum likelihood (ML) estimator is presented. The stability of the performance of the ML estimators is improved when a nonidentical threshold strategy is utilized to estimate the unknown parameter. The thresholds are designed by maximizing the minimum asymptotic relative efficiency (ARE) between quantized and unquantized ML estimators. Although the ML estimation problem is nonconvex, it is shown that one can relax the optimization to make it convex. The solution to the relaxed problem is used as an initial solution in a gradient algorithm to solve the original problem. Next, the case where both the variances of the additive noise and multiplicative noise are unknown is studied. The corresponding CRLB is obtained, and the ML estimation problem is transformed to a convex optimization, which can be solved efficiently. Finally, numerical simulations are performed to substantiate the theoretical analysis.

Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise

Tails in the probability distribution of stochastic processes with power law multiplicative noise

Aims: Hearing loss is the most common form of sensory impairment in humans. Short impulses of a high intensity noise can trigger sudden hearing loss, which is generally irreversible and associated with structural tissue damage of the cochlea and auditory nerve. It is well established that myelination is essential for the rapid propagation of action potentials along axons, and that Schwann cells are responsible for myelin sheath production in the peripheral nervous system. In the cochlea, spiral ganglion neuron axons are myelinated by Schwann cells. This myelin contributes to axonal protection and allows for efficient action potential transmission along the auditory nerve. For this reason, here we studie the morphological changes on cochlear hair cells and myelin sheaths of the auditory nerve, directly linked to hearing impairment induced by acoustic trauma.Material and methods: To study the auditory functions, auditory brainstem responses and distortion products were measured at baseline, 2 days, and 21 days after trauma in rats. Then, scanning and transmission electron microscopy techniques were performed to analyze cochleae and the auditory nerve at 21 days after trauma.Results: We observed that acoustic trauma induced cochlear outer hair cell loss and fusion of inner hair cell stereocilia. We also observed an axonal loss and myelin sheath disorganization of the auditory nerve.Conclusions: These data confirm that a strong acoustic trauma induced histological changes in the cochlea and auditory nerve, leading to permanent hearing loss.

In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

In this paper, the localization accuracy of range-only sensors is investigated. Being different from most previous studies, we consider a more general measurement model with both additive and multiplicative noise other than with only additive noise. The main contributions lie in twofold. First, a CRLB(Cramer-Rao Lower Bound)-based metric is proposed to evaluate the localization accuracy. In addition, the analytical relationships between target-sensor distance and localization accuracy, and between noise and localization accuracy are derived. Second, numerical analysis is executed to evaluate the localization accuracy for three important regular patterns of sensor deployment, i.e., triangle, square and hexagon. Two aspects have been examined and discussed, including (a) the geometric distribution of localization accuracy, (b) the average localization accuracy. Both theoretical and numerical results show that the multiplicative noise will influence significantly the localization accuracy. This study also provides important guidelines for optimal sensor deployment.