Smooth Entropy in Axiomatic Thermodynamics

Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including very small systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. Transformations among microcanonical states are characterised by the Boltzmann entropy

Stimulus-dependent maximum entropy models of neural population codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. To be able to infer a model for this distribution from large-scale neural recordings, we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. The model is able to capture the single-cell response properties as well as the correlations in neural spiking due to shared stimulus and due to effective neuron-to-neuron connections. Here we show that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. As a result, the SDME model gives a more accurate account of single cell responses and in particular outperforms uncoupled models in reproducing the distributions of codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like surprise and information transmission in a neural population.Comment: 11 pages, 7 figure

NeuroGrid: recording action potentials from the surface of the brain.

Recording from neural networks at the resolution of action potentials is critical for understanding how information is processed in the brain. Here, we address this challenge by developing an organic material-based, ultraconformable, biocompatible and scalable neural interface array (the 'NeuroGrid') that can record both local field potentials(LFPs) and action potentials from superficial cortical neurons without penetrating the brain surface. Spikes with features of interneurons and pyramidal cells were simultaneously acquired by multiple neighboring electrodes of the NeuroGrid, allowing for the isolation of putative single neurons in rats. Spiking activity demonstrated consistent phase modulation by ongoing brain oscillations and was stable in recordings exceeding 1 week's duration. We also recorded LFP-modulated spiking activity intraoperatively in patients undergoing epilepsy surgery. The NeuroGrid constitutes an effective method for large-scale, stable recording of neuronal spikes in concert with local population synaptic activity, enhancing comprehension of neural processes across spatiotemporal scales and potentially facilitating diagnosis and therapy for brain disorders

Nobody Is Perfect: ERP Effects Prior to Performance Errors in Musicians Indicate Fast Monitoring Processes

Background: One central question in the context of motor control and action monitoring is at what point in time errors can be detected. Previous electrophysiological studies investigating this issue focused on brain potentials elicited after erroneous responses, mainly in simple speeded response tasks. In the present study, we investigated brain potentials before the commission of errors in a natural and complex situation. Methodology/Principal Findings: Expert pianists bimanually played scales and patterns while the electroencephalogram (EEG) was recorded. Event-related potentials (ERPs) were computed for correct and incorrect performances. Results revealed differences already 100 ms prior to the onset of a note (i.e., prior to auditory feedback). We further observed that erroneous keystrokes were delayed in time and pressed more slowly. Conclusions: Our data reveal neural mechanisms in musicians that are able to detect errors prior to the execution of erroneous movements. The underlying mechanism probably relies on predictive control processes that compare the predicted outcome of an action with the action goal

Encoding of brain state changes in local field potentials modulated by motor behaviors

Local field potentials (LFPs) measure aggregate neural activity resulting from the coordinated firing of neurons within a local network. We hypothesized that state parameters associated with the underlying brain dynamics may be encoded in LFPs but may not be directly measurable in the signal temporal and spectral contents. Using the Kalman filter we estimated latent state changes in LFPs recorded in monkey motor cortical areas during the execution of a visually instructed reaching task, under different applied force conditions. Prior to the estimation, matched filtering was performed to decouple behavior-relevant signals (Stamoulis and Richardson, J Comput Neurosci, 2009) from unrelated background oscillations. State changes associated with baseline oscillations appeared insignificant. In contrast, state changes estimated from LFP components associated with the execution of movement were significant. Approximately direction-invariant state vectors were consistently observed. Their patterns appeared invariant also to force field conditions, with a peak in the first 200 ms of the movement interval, but exponentially decreasing to the zero state approximately 200 ms from movement onset, also the time at which movement velocity reached its peak. Thus, state appeared to be modulated by the dynamics of movement but neither by movement direction nor by the mechanical environment. Finally, we compared state vectors estimated using the Kalman filter to the basis functions obtained through Principal Component Analysis. The pattern of the estimated state vector was very similar to that of the first PCA component, further suggesting that LFPs may directly encode brain state fluctuations associated with the dynamics of behavior.National Institutes of Health (U.S.) (NIH 5T32NS048005-05)National Institutes of Health (U.S.) (NIH 1UL1RR025758-01)National Institutes of Health (U.S.) (NS-044393