A Comprehensive Account of Sound Sequence Imitation in the Songbird

The amazing imitation capabilities of songbirds show that they can memorize sensory sequences and transform them into motor activities which in turn generate the original sound sequences. This suggests that the bird's brain can learn 1.) to reliably reproduce spatio-temporal sensory representations and 2.) to transform them into corresponding spatio-temporal motor activations by using an inverse mapping. Neither the synaptic mechanisms nor the network architecture enabling these two fundamental aspects of imitation learning are known. We propose an architecture of coupled neuronal modules that mimick areas in the song bird and show that a unique synaptic plasticity mechanism can serve to learn both, sensory sequences in a recurrent neuronal network, as well as an inverse model that transforms the sensory memories into the corresponding motor activations. The proposed membrane potential dependent learning rule together with the architecture that includes basic features of the bird's brain represents the first comprehensive account of bird imitation learning based on spiking neurons

Theta rhythmicity enhances learning in adaptive STDP

The classical STDP window captures changes of a synaptic weight in response to the relative timing of a pre and a postsynaptic spike (see e.g. Bi and Poo, 1998). Due to its static nature, however, it cannot account for nonlinear interactions between spikes. Several theoretical studies offer dynamic formulations for STDP, for example by modulating the synaptic weight change by variables like synaptic calcium concentration (Shouval et al., 2002) or somatic depolarisation (Clopath et al., 2010), or by introducing spike triplet interactions (Pfister and Gerstner, 2006). Here, we propose a new model which is formulated as a set of differential equations (Schmiedt et al., 2010). The weight change is given by a differential Hebbian learning rule, which reproduces the STDP window for spike pairs. To account for the effects of repeated neuronal firing on the synaptic weight, we introduce modulations of the spike impact, which act on exponential traces of the spiking activity. We found that this model captures a series of experiments on STDP with complex spike pattern in cortex (Froemke et al., 2006) and hippocampus (Wang et al., 2005). When applied to continuous firing rates, our approach allows us to analyze the effects of given time courses of firing rates on the synaptic weight change, i.e. the filter properties of STDP. For sinusoidal modulations of baseline firing rates we find the strongest weight changes for modulation frequencies in the theta band, which plays a key role in learning. Furthermore, weight modifications in the hippocampus are predicted to be most prominent for baseline rates of around 5Hz in striking agreement with experimental findings.
This suggests that STDP-dependent learning is mediated by theta oscillations and modulated by the background firing rate which are both testable predictions of our theory

Self-Organized Critical Noise Amplification in Human Closed Loop Control

When humans perform closed loop control tasks like in upright standing or while balancing a stick, their behavior exhibits non-Gaussian fluctuations with long-tailed distributions. The origin of these fluctuations is not known. Here, we investigate if they are caused by self-organized critical noise amplification which emerges in control systems when an unstable dynamics becomes stabilized by an adaptive controller that has finite memory. Starting from this theory, we formulate a realistic model of adaptive closed loop control by including constraints on memory and delays. To test this model, we performed psychophysical experiments where humans balanced an unstable target on a screen. It turned out that the model reproduces the long tails of the distributions together with other characteristic features of the human control dynamics. Fine-tuning the model to match the experimental dynamics identifies parameters characterizing a subject's control system which can be independently tested. Our results suggest that the nervous system involved in closed loop motor control nearly optimally estimates system parameters on-line from very short epochs of past observations

Limited profit in predictable stock markets

It has been assumed that arbitrage profits are not possible in efficient markets, because future prices are not predictable. Here we show that predictability alone is not a sufficient measure of market efficiency. We instead propose to measure inefficiencies of markets in terms of the maximal profit an ideal trader can take out from a market. In a stock market model with an evolutionary selection of agents this method reveals that the mean relative amount of realizable profits $P$ is very limited and we find that it decays with rising number of agents in the markets. Our results show that markets may self-organize their collective dynamics such that it becomes very sensitive to profit attacks which demonstrates that a high degree of market efficiency can coexist with predictability.Comment: 4 pages, 4 figure