Are the input parameters of white-noise-driven integrate-and-fire neurons uniquely determined by rate and CV?

Integrate-and-fire (IF) neurons have found widespread applications in computational neuroscience. Particularly important are stochastic versions of these models where the driving consists of a synaptic input modeled as white Gaussian noise with mean $\mu$ and noise intensity $D$. Different IF models have been proposed, the firing statistics of which depends nontrivially on the input parameters $\mu$ and $D$. In order to compare these models among each other, one must first specify the correspondence between their parameters. This can be done by determining which set of parameters ($\mu$, $D$) of each model is associated to a given set of basic firing statistics as, for instance, the firing rate and the coefficient of variation (CV) of the interspike interval (ISI). However, it is not clear {\em a priori} whether for a given firing rate and CV there is only one unique choice of input parameters for each model. Here we review the dependence of rate and CV on input parameters for the perfect, leaky, and quadratic IF neuron models and show analytically that indeed in these three models the firing rate and the CV uniquely determine the input parameters

Fluctuation-dissipation relations for spiking neurons

Spontaneous fluctuations and stimulus response are essential features of neural functioning but how they are connected is poorly understood. I derive fluctuation-dissipation relations (FDR) between the spontaneous spike and voltage correlations and the firing rate susceptibility for i) the leaky integrate-and-fire (IF) model with white noise; ii) an IF model with arbitrary voltage dependence, an adaptation current, and correlated noise. The FDRs can be used to derive correlation statistics or to infer the system's response from observations of its spontaneous activity

Towards a Unification of Supercomputing, Molecular Dynamics Simulation and Experimental Neutron and X-ray Scattering Techniques

Molecular dynamics simulation has become an essential tool for scientific discovery and investigation. The ability to evaluate every atomic coordinate for each time instant sets it apart from other methodologies, which can only access experimental observables as an outcome of the atomic coordinates. Here, the utility of molecular dynamics is illustrated by investigating the structure and dynamics of fundamental models of cellulose fibers. For that, a highly parallel code has been developed to compute static and dynamical scattering functions efficiently on modern supercomputing architectures. Using state of the art supercomputing facilities, molecular dynamics code and parallelization strategies, this work also provides insight into the relationship between cellulose crystallinity and cellulose-lignin aggregation by performing multi-million atom simulations. Finally, this work introduces concepts to augment the ability of molecular dynamics to interpret experimental observables with the help of Markov modeling, which allows for a convenient description of complex molecule dynamics as transitions between well defined conformations. The work presented here suggests that molecular dynamics will continue to evolve and integrate with experimental techniques, like neutron and X-ray scattering, and stochastic models, like Markov modeling, to yield unmatched descriptions of molecule dynamics and interpretations of experimental data, facilitated by the growing computational power available to scientists