Theoretical Relationship Between Two Measures of Spike Synchrony: Correlation Index and Vector Strength

Information processing in the nervous system critically relies on temporally precise spiking activity. In the auditory system, various degrees of phase-locking can be observed from the auditory nerve to cortical neurons. The classical metric for quantifying phase-locking is the vector strength (VS), which captures the periodicity in neuronal spiking. More recently, another metric, called the correlation index (CI), was proposed to quantify the temporally reproducible response characteristics of a neuron. The CI is defined as the peak value of a normalized shuffled autocorrelogram (SAC). Both VS and CI have been used to investigate how temporal information is processed and propagated along the auditory pathways. While previous analyses of physiological data in cats suggested covariation of these two metrics, general characterization of their connection has never been performed. In the present study, we derive a rigorous relationship between VS and CI. To model phase-locking, we assume Poissonian spike trains with a temporally changing intensity function following a von Mises distribution. We demonstrate that VS and CI are mutually related via the so-called concentration parameter that determines the degree of phase-locking. We confirm that these theoretical results are largely consistent with physiological data recorded in the auditory brainstem of various animals. In addition, we generate artificial phase-locked spike sequences, for which recording and analysis parameters can be systematically manipulated. Our analysis results suggest that mismatches between empirical data and the theoretical prediction can often be explained with deviations from the von Mises distribution, including skewed or multimodal period histograms. Furthermore, temporal relations of spike trains across trials can contribute to higher CI values than predicted mathematically based on the VS. We find that, for most applications, a SAC bin width of 50 ms seems to be a favorable choice, leading to an estimated error below 2.5% for physiologically plausible conditions. Overall, our results provide general relations between the two measures of phase-locking and will aid future analyses of different physiological datasets that are characterized with these metrics.

Neuron particles capture network topology and behavior from single units

While networks of neurons, glia and vascular systems enable and support brain functions, to date, mathematical tools to decode network dynamics and structure from very scarce and partially observed neuronal spiking behavior remain underdeveloped. Large neuronal networks contribute to the intrinsic neuron transfer function and observed neuronal spike trains encoding complex causal information processing, yet how this emerging causal fractal memory in the spike trains relates to the network topology is not fully understood. Towards this end, we propose a novel statistical physics inspired neuron particle model that captures the causal information flow and processing features of neuronal spiking activity. Relying on synthetic comprehensive simulations and real-world neuronal spiking activity analysis, the proposed fractional order operators governing the neuronal spiking dynamics provide insights into the memory and scale of the spike trains as well as information about the topological properties of the underlying neuronal networks. Lastly, the proposed model exhibits superior predictions of animal behavior during multiple cognitive tasks.

Supervised Learning Algorithm for Multilayer Spiking Neural Networks with Long-Term Memory Spike Response Model

As a new brain-inspired computational model of artificial neural networks, spiking neural networks transmit and process information via precisely timed spike trains. Constructing efficient learning methods is a significant research field in spiking neural networks. In this paper, we present a supervised learning algorithm for multilayer feedforward spiking neural networks; all neurons can fire multiple spikes in all layers. The feedforward network consists of spiking neurons governed by biologically plausible long-term memory spike response model, in which the effect of earlier spikes on the refractoriness is not neglected to incorporate adaptation effects. The gradient descent method is employed to derive synaptic weight updating rule for learning spike trains. The proposed algorithm is tested and verified on spatiotemporal pattern learning problems, including a set of spike train learning tasks and nonlinear pattern classification problems on four UCI datasets. Simulation results indicate that the proposed algorithm can improve learning accuracy in comparison with other supervised learning algorithms.

Synaptic Interactions in Scorpion Peg Sensilla Appear to Maintain Chemosensory Neurons within Dynamic Firing Range

Scorpions have elaborate chemo-tactile organs called pectines on their ventral mesosoma. The teeth of the comb-like pectines support thousands of minute projections called peg sensilla (a.k.a. “pegs”), each containing approximately 10 chemosensory neurons. Males use pectines to detect pheromones released by females, and both sexes apparently use pectines to find prey and navigate to home retreats. Electrophysiological recordings from pegs of Paruroctonus utahensis reveal three spontaneously active cells (A1, A2, and B), which appear to interact synaptically. We made long-term extracellular recordings from the bases of peg sensilla and used a combination of conditional cross-interval and conditional interspike-interval analyses to assess the temporal dynamics of the A and B spike trains. Like previous studies, we found that A cells are inhibited by B cells for tens of milliseconds. However, after normalizing our records, we also found clear evidence that the A cells excite the B cells. This simple local circuit appears to maintain the A cells in a dynamic firing range and may have important implications for tracking pheromonal trails and sensing substrate chemistry for navigation.

Temporal filters in response to presynaptic spike trains: Interplay of cellular, synaptic and short-term plasticity time scales

Temporal filters, the ability of postsynaptic neurons to preferentially select certain presynaptic input patterns, have been shown to be associated with the notion of information filtering and coding of sensory inputs. Their properties can be dynamically characterized as the transient responses to periodic presynaptic inputs. Short-term plasticity (STP) has been proposed to be an important player in the generation of temporal filters, but the response of postsynaptic neurons to presynaptic inputs depends on a collection of time scales in addition to STP's, which conspire to create temporal filters: the postsynaptic time scales generated by the cellular intrinsic currents and the presynaptic time scales captured by the ISI distribution patterns. The mechanisms by which these time scales and the processes giving rise to them interact to produce temporal filters in response to presynaptic input spike trains are not well understood. We carry out a systematic modeling and computational analysis to understand how the postsynaptic low-, high- and band-pass temporal filters are generated in response to periodic presynaptic spike trains in the presence STP, and how the dynamic properties of these filters depend on the interplay of a hierarchy of processes: arrival of the presynaptic spikes, the activation of STP and its effect on the synaptic connection efficacy, and the response of the postsynaptic cell. The time scales associated with each of these processes operate at the short-term, single-event level (they are activated at the arrival of each presynaptic spike) and collectively produce the long-term time scales that determine the shape and properties of the filters. We develop a series of mathematical tools to address these issues for a relatively simple model where depression and facilitation interact only at the level of the synaptic efficacy change as time progresses and we extend our results and tools to account for more complex models that involve interactions at the STP level and multiple STP time scales. We use these tools to understand the mechanisms of generation of temporal filters in the postsynaptic cells in terms of the properties and dynamics of the interacting building blocks.

Acceleration of the SPADE Method Using a Custom-Tailored FP-Growth Implementation

The SPADE (spatio-temporal Spike PAttern Detection and Evaluation) method was developed to find reoccurring spatio-temporal patterns in neuronal spike activity (parallel spike trains). However, depending on the number of spike trains and the length of recording, this method can exhibit long runtimes. Based on a realistic benchmark data set, we identified that the combination of pattern mining (using the FP-Growth algorithm) and the result filtering account for 85–90% of the method's total runtime. Therefore, in this paper, we propose a customized FP-Growth implementation tailored to the requirements of SPADE, which significantly accelerates pattern mining and result filtering. Our version allows for parallel and distributed execution, and due to the improvements made, an execution on heterogeneous and low-power embedded devices is now also possible. The implementation has been evaluated using a traditional workstation based on an Intel Broadwell Xeon E5-1650 v4 as a baseline. Furthermore, the heterogeneous microserver platform RECS|Box has been used for evaluating the implementation on two HiSilicon Hi1616 (Kunpeng 916), an Intel Coffee Lake-ER Xeon E-2276ME, an Intel Broadwell Xeon D-D1577, and three NVIDIA Tegra devices (Jetson AGX Xavier, Jetson Xavier NX, and Jetson TX2). Depending on the platform, our implementation is between 27 and 200 times faster than the original implementation. At the same time, the energy consumption was reduced by up to two orders of magnitude.

Sparse connectivity for MAP inference in linear models using sister mitral cells

Sensory processing is hard because the variables of interest are encoded in spike trains in a relatively complex way. A major goal in studies of sensory processing is to understand how the brain extracts those variables. Here we revisit a common encoding model in which variables are encoded linearly. Although there are typically more variables than neurons, this problem is still solvable because only a small number of variables appear at any one time (sparse prior). However, previous solutions require all-to-all connectivity, inconsistent with the sparse connectivity seen in the brain. Here we propose an algorithm that provably reaches the MAP (maximum a posteriori) inference solution, but does so using sparse connectivity. Our algorithm is inspired by the circuit of the mouse olfactory bulb, but our approach is general enough to apply to other modalities. In addition, it should be possible to extend it to nonlinear encoding models.

Fokker–Planck approach to neural networks and to decision problems

We review applications of the Fokker–Planck equation for the description of systems with event trains in computational and cognitive neuroscience. The most prominent example is the spike trains generated by integrate-and-fire neurons when driven by correlated (colored) fluctuations, by adaptation currents and/or by other neurons in a recurrent network. We discuss how for a general Gaussian colored noise and an adaptation current can be incorporated into a multidimensional Fokker–Planck equation by Markovian embedding for systems with a fire-and-reset condition and how in particular the spike-train power spectrum can be determined by this equation. We then review how this framework can be used to determine the self-consistent correlation statistics in a recurrent network in which the colored fluctuations arise from the spike trains of statistically similar neurons. We then turn to the popular drift-diffusion models for binary decisions in cognitive neuroscience and demonstrate that very similar Fokker–Planck equations (with two instead of only one threshold) can be used to study the statistics of sequences of decisions. Specifically, we present a novel two-dimensional model that includes an evidence variable and an expectancy variable that can reproduce salient features of key experiments in sequential decision making.