Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments

We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal filtering of the functionals. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal linear filtering of the functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

Estimating Excitatory and Inhibitory Synaptic Conductances from Spike Trains using a Recursive Bayesian Approach

Inference of excitatory and inhibitory synaptic conductances (SCs) from the spike trains is poorly addressed in the literature due to the complexity of the problem. As recent technological advancements make recording spikes from multiple (neighbor) neurons of a behaving animal (in some rare cases from humans) possible, this paper tackles the problem of estimating SCs solely from the recorded spike trains. Given an ensemble of spikes corresponding to population of neighbor neurons, we aim to infer the average excitatory and inhibitory SCs underlying the shared neural activity. In this paper, we extended our previously established Kalman filtering (KF)–based algorithm to incorporate the voltage-to-spike nonlinearity (mapping from membrane potential to spike rate). Having estimated the instantaneous spike rate using optimal linear filtering (Gaussian kernel), our proposed algorithm uses KF followed by expectation maximization (EM) algorithm in a recursive fashion to infer the average SCs. As the dynamics of SCs and membrane potential is included in our model, the proposed algorithm, unlike other related works, considers different sources of stochasticity, i.e., the variabilities of SCs, membrane potential, and spikes. Moreover, it is worth mentioning that our algorithm is blind to the external stimulus, and it performs only based on observed spikes. We validate the accuracy and practicality of our technique through simulation studies where leaky integrate and fire (LIF) model is used to generate spikes. We show that the estimated SCs can precisely track the original ones. Moreover, we show that the performance of our algorithm can be further improved given enough number of trials (spikes). As a rule of thumb, 50 trials of neurons with the average firing rate of 5 Hz can guarantee the accuracy of our proposed algorithm.

Real-time decoding of bladder pressure from pelvic nerve activity

Real time algorithms for decoding physiological signals from peripheral nerve recordings form an important component of closed loop bioelectronic medicine (electroceutical) systems. As a feasibility demonstration, we considered the problem of decoding bladder pressure from pelvic nerve electroneurograms. We extracted power spectral density of the nerve signal across a band optimised for Shannon Mutual Information, followed by linearization via piece-wise linear regression, and finally decoded signal reconstruction through optimal linear filtering. We demonstrate robust and effective reconstruction of bladder pressure, both prior to and following pharmacological manipulation.