Recognition of nonlinearities in the neuronal encoding of repetitive spike trains has generated a number of models to explain this behavior. Here we develop the mathematics and a set of tests for two such models: the leaky integrator and the variable-gamma model. Both of these are nearly sufficient to explain the dynamic behavior of a number of repetitively firing, sensory neurons. Model parame...

We examine the effect of the phase-resetting curve on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy superthreshold stimulation. We use linear-response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem and contrast the results for type I vs type II models and across ...

We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1) -dimensional kinetic moment equations from a Boltzmann-like equation descri...

We develop a method from semiparametric statistics (Cox, 1972) for the purpose of tracking links and connection strengths over time in a neuronal network from spike train data. We consider application of the method as implemented in Masud and Borisyuk (2011), and evaluate its use on data generated independently of the Cox model hypothesis, in particular from a spiking model of Izhikevich in fou...

Covariations in neuronal latency or excitability can lead to peaks in spike train covariograms that may be very similar to those caused by spike timing synchronization (see companion article). Two quantitative methods are described here. The first is a method to estimate the excitability component of a covariogram, based on trial-by-trial estimates of excitability. Once estimated, this componen...

There are two basic problems in the statistical analysis of neural data. The "encoding" problem concerns how information is encoded in neural spike trains: can we predict the spike trains of a neuron (or population of neurons), given an arbitrary stimulus or observed motor response? Conversely, the "decoding" problem concerns how much information is in a spike train, in particular, how well can...

high speed trains are an indispensable part of rapid transportation systems in many countries. as the fastest means of transport on the ground, these trains are extremely sensitive to the terrain and track conditions. geometrical irregularities and mechanical characteristics of the track, together with inconsistencies in the lane (including bridges that support the track) are considered importa...