Enhancing the Resolution of a Sensor Via Negative Correlation: A Biologically Inspired Approach

Abstract

We demonstrate that a neuronal system, underpinned by "fire-then-reset" dynamics, can display an enhanced resolution R~T(ob)(-1) where T(ob) is the observation time of the measurement; this occurs when the interspike intervals are negatively correlated and T(ob)<Δ/ε, where ε is a parameter characterizing the level of correlation between interspike intervals and Δ is the average interspike interval. We also show that by introducing negative correlations into the time domain response of a nonlinear dynamical sensor it is possible to replicate this enhanced scaling of the resolution. Thus, we demonstrate the potential for designing a novel class of biomimetic sensors that afford improved signal resolution by functionally utilizing negative correlations.

Patterns of interval correlations in neural oscillators with adaptation

“…There is experimental evidence accumulating that the spiking in many cases is not a renewal process, i.e., a spike train with mutually independent ISIs, but that intervals are typically correlated over a few lags (Lowen and Teich, 1992; Ratnam and Nelson, 2000; Neiman and Russell, 2001; Nawrot et al, 2007; Engel et al, 2008) [further reports are reviewed in (Farkhooi et al, 2009; Avila-Akerberg and Chacron, 2011)]. These correlations are a basic statistics of any spike train with important implications for information transmission and signal detection in neural systems (Ratnam and Nelson, 2000; Chacron et al, 2001, 2004; Avila-Akerberg and Chacron, 2011) and man-made signal detectors (Nikitin et al, 2012). They are often characterized by the serial correlation coefficient (SCC) ${\rho }_k=\frac{\langle \left(T_i-\langle T_i\rangle \right)\left(T_{i+k}-\langle T_{i+k}\rangle \right)\rangle }{\langle {(T_i-\langle T_i\rangle )}^2\rangle },$ where T i and T i + k are two ISIs lagged by an integer k and 〈·〉 denotes ensemble averaging.…”

Enhanced Signal Detection by Adaptive Decorrelation of Interspike Intervals

“…Such negative serial correlations are commonly observed in many cell types and organisms (Perkel, Gerstein, & Moore, 1967;Nawrot et al, 2007;Farkhooi, Strube-Bloss, & Nawrot, 2009;Berry & Meister, 1998). They reduce spike count variability and enhance the detection of rate changes relative to comparable renewal interval sequences (Chacron, Longtin, & Maler, 2001;Chacron, Lindner, & Longtin, 2004;Chacron, Maler, & Bastian, 2005;Lüdtke & Nelson, 2006;Nawrot et al, 2007;Maimon & Assad, 2009;Farkhooi et al, 2009Farkhooi et al, , 2011Avila-Akerberg & Chacron, 2011;Nikitin, Stocks, & Bulsara, 2012).…”

“…An important related question is whether this quasi-IID representation of the spike pattern could provide additional information about an input that is not available in firing rate statistics (Gussin, Benda, & Maler, 2007). As stated above, numerous studies have established that negative serial ISI correlations reduce the variance of firing rate, making firing rate changes more statistically discriminable relative to comparable renewal ISI spike trains (Chacron et al, 2001(Chacron et al, , 2004Chacron, Maler, & Bastian, 2005;Lüdtke & Nelson, 2006;Nawrot et al, 2007;Maimon & Assad, 2009;Farkhooi et al, 2009Farkhooi et al, , 2011Avila-Akerberg & Chacron, 2011;Nikitin et al, 2012). This variance-reduction phenomenon defines the rate coding performance benchmark for spike trains with negative serial interval correlations.…”

Interspike interval correlations in networks of inhibitory integrate-and-fire neurons

“…In particular, it is now possible to compute, in some cases even analytically, the SCC for single-neuron models in the presence of spike-frequency adaptation [4], colored noise [5] and time-dependent deterministic or stochastic firing thresholds [6]. Recently, it was also shown that, at short observation times, negative ISI correlations can enhance the resolution of a nonlinear dynamical sensor whose design was inspired by a simple non-renewal neuron model [7]. There also have been recent efforts to characterize the patterning of ISI sequences using ordinal analysis, revealing parameter sets that maximize the probability of certain patterns [8].…”