Using interspike intervals to quantify noise effects on spike trains in temperature encoding neurons

Mutual information measure of visual perception based on noisy spiking neural networks

Note that images of low-illumination are weak aperiodic signals, while mutual information can be used as an effective measure for the shared information between the input stimulus and the output response of nonlinear systems, thus it is possible to develop novel visual perception algorithm based on the principle of aperiodic stochastic resonance within the frame of information theory. To confirm this, we reveal this phenomenon using the integrate-and-fire neural networks of neurons with noisy binary random signal as input first. And then, we propose an improved visual perception algorithm with the image mutual information as assessment index. The numerical experiences show that the target image can be picked up with more easiness by the maximal mutual information than by the minimum of natural image quality evaluation (NIQE), which is one of the most frequently used indexes. Moreover, the advantage of choosing quantile as spike threshold has also been confirmed. The improvement of this research should provide large convenience for potential applications including video tracking in environments of low illumination.

Coupling between fast and slow oscillator circuits in Cancer borealis is temperature-compensated

Coupled oscillatory circuits are ubiquitous in nervous systems. Given that most biological processes are temperature-sensitive, it is remarkable that the neuronal circuits of poikilothermic animals can maintain coupling across a wide range of temperatures. Within the stomatogastric ganglion (STG) of the crab, Cancer borealis, the fast pyloric rhythm (~1 Hz) and the slow gastric mill rhythm (~0.1 Hz) are precisely coordinated at ~11°C such that there is an integer number of pyloric cycles per gastric mill cycle (integer coupling). Upon increasing temperature from 7°C to 23°C, both oscillators showed similar temperature-dependent increases in cycle frequency, and integer coupling between the circuits was conserved. Thus, although both rhythms show temperature-dependent changes in rhythm frequency, the processes that couple these circuits maintain their coordination over a wide range of temperatures. Such robustness to temperature changes could be part of a toolbox of processes that enables neural circuits to maintain function despite global perturbations.

Dynamical analysis of periodic bursting in piece-wise linear planar neuron model

A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.

Measuring effects of different noises in a model using ISI-distance methods

This paper examines the effects of current and conductance noises in a minimal Hodgkin–Huxley type model of a cold receptor neuron. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Compared with common used interspike interval method, ISI-distance is a simple complementary approach to measure the different effects of current and conductance noises. ISI-distance extracts information from the interspike intervals by evaluating the ratio of instantaneous firing rates, which is parameter-free, time scale-independent and easy to visualize. Simulation results show that the most significant differences between different noise implementations in a pacemaker-like tonic firing regime at the transition to chaotic burst discharges.

Stimulus detection after interruption of the feedforward response in a backward masking paradigm

In backward masking, a target stimulus is rendered invisible by the presentation of a second stimulus, the mask. When the mask is effective, neural responses to the target are suppressed. Nevertheless, weak target responses sometimes may produce a behavioural response. It remains unclear whether the reduced target response is a purely feedforward response or that it includes recurrent activity. Using a feedforward neural network of biological plausible spiking neurons, we tested whether a transient spike burst is sufficient for face categorization. After training the network, the system achieved face/non-face categorization for sets of grayscale images. In a backward masking paradigm, the transient burst response was cut off thereby reducing the feedforward target response. Despite the suppressed feedforward responses stimulus classification remained robust. Thus according to our model data stimulus detection is possible with purely, suppressed feedforward responses.

Firing pattern and synchronization property analysis in a network model of the olfactory bulb

In the olfactory system, both the temporal spike structure and spatial distribution of neuronal activity are important for processing odor information. In this paper, a biophysically-detailed, spiking neuronal model is used to simulate the activity of olfactory bulb. It is shown that by varying some key parameters such as maximal conductances of Ks and Nap the spike train of single neuron can exhibit various firing patterns. Synchronization in coupled neurons is also investigated as the coupling strength varying in the situation of two neurons and network. It is illustrated that the coupled neurons can exhibit different types of pattern when the coupling strength varies. These results may be instructive to understand information transmission in olfactory system.

Noise-induced spatiotemporal patterns in Hodgkin-Huxley neuronal network

The effect of noise on the pattern selection in a regular network of Hodgkin-Huxley neurons is investigated, and the transition of pattern in the network is measured from subexcitable to excitable media. Extensive numerical results confirm that kinds of travelling wave such as spiral wave, circle wave and target wave could be developed and kept alive in the subexcitable network due to the noise. In the case of excitable media under noise, the developed spiral wave and target wave could coexist and new target-like wave is induced near to the border of media. The averaged membrane potentials over all neurons in the network are calculated to detect the periodicity of the time series and the generated traveling wave. Furthermore, the firing probabilities of neurons in networks are also calculated to analyze the collective behavior of networks.

Noise destroys feedback enhanced figure-ground segmentation but not feedforward figure-ground segmentation

Figure-ground (FG) segmentation is the separation of visual information into background and foreground objects. In the visual cortex, FG responses are observed in the late stimulus response period, when neurons fire in tonic mode, and are accompanied by a switch in cortical state. When such a switch does not occur, FG segmentation fails. Currently, it is not known what happens in the brain on such occasions. A biologically plausible feedforward spiking neuron model was previously devised that performed FG segmentation successfully. After incorporating feedback the FG signal was enhanced, which was accompanied by a change in spiking regime. In a feedforward model neurons respond in a bursting mode whereas in the feedback model neurons fired in tonic mode. It is known that bursts can overcome noise, while tonic firing appears to be much more sensitive to noise. In the present study, we try to elucidate how the presence of noise can impair FG segmentation, and to what extent the feedforward and feedback pathways can overcome noise. We show that noise specifically destroys the feedback enhanced FG segmentation and leaves the feedforward FG segmentation largely intact. Our results predict that noise produces failure in FG perception.

Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns

Period-doubling bifurcation to chaos were discovered in spontaneous firings of Onchidium pacemaker neurons. In this paper, we provide three cases of bifurcation processes related to period-doubling bifurcation cascades to chaos observed in the spontaneous firing patterns recorded from an injured site of rat sciatic nerve as a pacemaker. Period-doubling bifurcation cascades to period-4 (π(2,2)) firstly, and then to chaos, at last to a periodicity, which can be period-5, period-4 (π(4)) and period-3, respectively, in different pacemakers. The three bifurcation processes are labeled as case I, II and III, respectively, manifesting procedures different to those of period-adding bifurcation. Higher-dimensional unstable periodic orbits (UPOs) can be detected in the chaos, built close relationships to the periodic firing patterns. Case III bifurcation process is similar to that discovered in the Onchidium pacemaker neurons and simulated in theoretical model-Chay model. The extra-large Feigenbaum constant manifesting in the period-doubling bifurcation process, induced by quasi-discontinuous characteristics exhibited in the first return maps of both ISI series and slow variable of Chay model, shows that higher-dimensional periodic behaviors appeared difficult within the period-doubling bifurcation cascades. The results not only provide examples of period-doubling bifurcation to chaos and chaos with higher-dimensional UPOs, but also reveal the dynamical features of the period-doubling bifurcation cascades to chaos.

Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model

The dynamics of neurons is characterized by a variety of different spiking patterns in response to external stimuli. One of the most important transitions in neuronal response patterns is the transition from tonic firing to burst discharges, i.e., when the neuronal activity changes from single spikes to the grouping of spikes. An increased number of interspike-interval sequences of specific temporal correlations was detected in anticipation of temperature induced tonic-to-bursting transitions in both, experimental impulse recordings from hypothalamic brain slices and numerical simulations of a stochastic model. Analysis of the modelling data elucidates that the appearance of such patterns can be related to particular system dynamics in the vicinity of the period-doubling bifurcation. It leads to a nonlinear response on de- and hyperpolarizing perturbations introduced by noise. This explains why such particular patterns can be found as reliable precursors of the neurons' transition to burst discharges.

Synchronization study in ring-like and grid-like neuronal networks

In this paper, we study the synchronization status of both two gap-junction coupled neurons and neuronal network with two different network connectivity patterns. One of the network connectivity patterns is a ring-like neuronal network, which only considers nearest-neighbor neurons. The other is a grid-like neuronal network, with all nearest neighbor couplings. We show that by varying some key parameters, such as the coupling strength and the external current injection, the neuronal network will exhibit various patterns of firing synchronization. Different types of firing synchronization are diagnosed by means of a mean field potential, a bifurcation diagram, a correlation coefficient and the ISI-distance method. Numerical simulations demonstrate that the synchronization status of multiple neurons is much dependent on the network patters, when the number of neurons is the same. It is also demonstrated that the synchronization status of two coupled neurons is similar with the grid-like neuronal network, but differs radically from that of the ring-like neuronal network. These results may be instructive in understanding synchronization transitions in neuronal systems.