Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Online Control of Voice Intensity in Late Bilinguals' First and Second Language Speech Production: Evidence From Unexpected and Brief Noise Masking

Purpose Speech production requires the combined efforts of feedforward control and feedback control subsystems. The primary purpose of this study is to explore whether the relative weighting of auditory feedback control is different between the first language (L1) and the second language (L2) production for late bilinguals. The authors also make an exploratory investigation into how bilinguals' speech fluency and speech perception relate to their auditory feedback control. Method Twenty Chinese–English bilinguals named Chinese or English bisyllabic words, while being exposed to 30- or 60-dB unexpected brief masking noise. Variables of language (L1 or L2) and noise condition (quiet, weak noise, or strong noise) were manipulated in the experiment. L1 and L2 speech fluency tests and an L2 perception test were also included to measure bilinguals' speech fluency and auditory acuity. Results Peak intensity analyses indicated that the intensity increases in the weak noise and strong noise conditions were larger in L2-English than L1-Chinese production. Intensity contour analysis showed that the intensity increases in both languages had an onset around 80–140 ms, a peak around 220–250 ms, and persisted till 400 ms post vocalization onset. Correlation analyses also revealed that poorer speech fluency or L2 auditory acuity was associated with larger Lombard effect. Conclusions For late bilinguals, the reliance on auditory feedback control is heavier in L2 than in L1 production. We empirically supported a relation between speech fluency and the relative weighting of auditory feedback control, and provided the first evidence for the production–perception link in L2 speech motor control.

Noise Robust Projection Rule for Klein Hopfield Neural Networks

Multistate Hopfield models, such as complex-valued Hopfield neural networks (CHNNs), have been used as multistate neural associative memories. Quaternion-valued Hopfield neural networks (QHNNs) reduce the number of weight parameters of CHNNs. The CHNNs and QHNNs have weak noise tolerance by the inherent property of rotational invariance. Klein Hopfield neural networks (KHNNs) improve the noise tolerance by resolving rotational invariance. However, the KHNNs have another disadvantage of self-feedback, a major factor of deterioration in noise tolerance. In this work, the stability conditions of KHNNs are extended. Moreover, the projection rule for KHNNs is modified using the extended conditions. The proposed projection rule improves the noise tolerance by a reduction in self-feedback. Computer simulations support that the proposed projection rule improves the noise tolerance of KHNNs.

Tumor Stabilization Induced by T-Cell Recruitment Fluctuations

The influence of random fluctuations on the recruitment of effector cells towards a tumor is studied by means of a stochastic mathematical model. Aggressively growing tumors are confronted against varying intensities of the cell-mediated immune response for which chaotic and periodic oscillations coexist together with stable tumor dynamics. A thorough parametric analysis of the noise-induced transition from this oscillatory regime to complete tumor dominance is carried out. A hysteresis phenomenon is uncovered, which stabilizes the tumor at its carrying capacity and drives the healthy and the immune cell populations to their extinction. Furthermore, it is shown that near a crisis bifurcation, such transitions occur under weak noise intensities. Finally, the corresponding noise-induced chaos-order transformation is analyzed and discussed in detail.

Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions

<p>For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one; the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such instability is the ice-albedo feedback. Following an idea developed by Eckhardt and co. for the investigation of multistable turbulent flows, we study the global instability giving rise to the snowball/warm multistability in the climate system by identifying the climatic Melancholia state, a saddle embedded in the boundary between the two basins of attraction of the stable climates. We then introduce random perturbations as modulations to the intensity of the incoming solar radiation. We observe noise-induced transitions between the competing basins of attractions. In the weak noise limit, large deviation laws define the invariant measure and the statistics of escape times. By empirically constructing the instantons, we show that the Melancholia states are the gateways for the noise-induced transitions in the weak-noise limit. In the region of multistability, in the zero-noise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. Finally, we propose a new method for constructing Melancholia states from direct numerical simulations, thus bypassing the need to use the edge-tracking algorithm.</p><p>Refs.</p><p>V. Lucarini, T. Bodai, Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions, Nonlinearity 30, R32 (2017)</p><p>V. Lucarini, T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122,158701 (2019)</p>