We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model’s validity using time-rescaling and density evolution techniques. Paninski et al., November 30, 2004 2 1

Neural spike train decoding algorithms and techniques to compute Shannon mutual information are important methods for analyzing how neural systems represent biological signals.Decoding algorithms are also one of several strategies being used to design controls for brain-machine interfaces. Developing optimal strategies to desig n decoding algorithms and compute mutual information are therefore important problems in computational neuroscience. We present a general recursive Žlter decoding algorithm based on a point process model of individual neuron spiking activity and a linear stochastic state-space model of the biological signal. We derive from the algorithm new instantaneous estimates of the entropy, entropy rate, and the mutual information between the signal and the ensemble spiking activity. We assess the accuracy of the algorithm by computing, along with the decoding error, the true coverage probability of the approximate 0.95 conŽdence regions for the individual signal estimates. We illustrate the new algorithm by reanalyzing the position and ensemble neural spiking activity of CA1 hippocampal neurons from two rats foraging in an open circular environment. We compare the performance of this algorithm with a linear Žlter constructed by the widely used reverse correlation method. The median decoding error for Animal 1 (2) during 10 minutes of open foraging was 5.9 (5.5) cm, the median entropy was 6.9 (7.0) bits, the median information was 9.4 (9.4) bits, and the true coverage probability for 0.95 conŽdence regions was 0.67 (0.75) using 34 (32) neurons. These Žndings improve signiŽcantly on our previous results and suggest an integrated approach to dynamically reading neural codes, measuring their properties, and quantifying the accuracy with which encoded information is extracted.

Foundation under Grant No. 9978318. The authors thank Larry Bradshaw at the USDA Forest Service for providing the weather station data as well as LADPW and LACFD (esp. Mike Takeshita and Frank Vidales) for generously sharing their data and expertise. 1 Numerical indices are commonly used as tools for assisting in wildfire management and haz-ard assessment. While the usage of such indices is widespread, assessment of these indices in their respective regions of application is rare. We evaluate the effectiveness of the Burning Index (BI) for predicting wildfire occurrences in Los Angeles County, California using space-time point process models. The models are based on an additive decomposition of the conditional intensity, with separate terms to describe spatial and seasonal variability as well as contributions from the BI. The models are fit to wildfire and BI data from the years 1976–2000 using a combination of nonparametric kernel smoothing methods and parametric maximum likelihood. In addition to using AIC to compare competing models, new multi-dimensional residual methods based on approximate random thinning and rescaling are employed to detect departures from the models

We demonstrate the efficacy of a new spike-sorting method based on a Markov Chain Monte Carlo (MCMC) algorithm by applying it to real data recorded from Purkinje cells (PCs) in young rat cerebellar slices. This algorithm is unique in its capability to estimate and make use of the firing statistics as well as the spike amplitude dynamics of the recorded neurons. PCs exhibit multiple discharge states, giving rise to multimodal interspike interval (ISI) histograms and to correlations between successive ISIs. The amplitude of the spikes generated by a PC in an “active ” state decreases, a feature typical of many neurons from both vertebrates and invertebrates. These two features constitute a major and recurrent problem for all the presently available spike-sorting methods. We first show that a Hidden Markov Model with 3 log-Normal states provides a flexible and satisfying description of the complex firing of single PCs. We then incorporate this model into our previous MCMC based spikesorting algorithm [31, Pouzat et al, 2004, J. Neurophys. 91, 2910-2928] and test this new algorithm on multi-unit recordings of bursting PCs. We show that our method successfully classifies the bursty spike trains fired by PCs by using an independent single unit recording from a patch-clamp pipette. 1 1

The activity of neurons in the brain often varies systematically with some quantitative feature of a stimulus or action. A well-known example is the tendency of the firing rates of neurons in the primary motor cortex to vary with the direction of a subject’s arm or wrist movement. When this movement is constrained to vary in only two dimensions, the direction of movement may be characterized by an angle, and the neuronal firing rate can be written as a function of this angle. The firing rate function has traditionally been fit with a cosine, but recent evidence suggests that departures from cosine tuning occur frequently. We report here a new nonparametric regression method for fitting periodic functions and demonstrate its application to the fitting of neuronal data. The method is an extension of Bayesian Adaptive Regression Splines (BARS) and applies both to normal and non-normal data, including Poisson data, which commonly arise in neuronal applications. We compare the new method to a periodic version of smoothing splines and some parametric alternatives and find the new method to be especially valuable when the smoothness of the periodic function varies unevenly across its domain.

Understanding how stimulus information is encoded in spike trains is a central problem in computational neuroscience. Decoding methods provide an important tool for addressing this problem, by allowing us to explicitly read out the information contained in spike responses. Here we introduce several decoding methods based on point-process neural encoding models (i.e. “forward ” models that predict spike responses to novel stimuli). These models have concave log-likelihood functions, allowing for efficient fitting via maximum likelihood. Moreover, we may use the likelihood of the observed spike trains under the model to perform optimal decoding. We present: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus — the most probable stimulus to have generated the observed single- or multiple-spike train response, given some prior distribution over the stimulus; (2) a Gaussian approximation to the posterior distribution, which allows us to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the response; and (4) a framework for the detection of change-point times (e.g. the time at which the stimulus undergoes a change in mean or variance), by marginalizing over the posterior distribution of stimuli. We show several examples illustrating the performance of these estimators with simulated data. 1

We analyze several recent schemes for watermarking network flows based on splitting the flow into intervals. We show that this approach creates time dependent correlations that enable an attack that combines multiple watermarked flows. Such an attack can easily be mounted in nearly all applications of network flow watermarking, both in anonymous communication and stepping stone detection. The attack can be used to detect the presence of a watermark, recover the secret parameters, and remove the watermark from a flow. The attack can be effective even if different the watermarks in different flows carry different messages. We analyze the efficacy of our attack using a probabilistic model and a Markov-modulated Poisson process (MMPP) model of interactive traffic. We also implement our attack and test it using both synthetic and real-world traces, showing that our attack is effective with as few as 10 watermarked flows. Finally, we propose a countermeasure that defeats the attack by using multiple watermark positions. 1

Cortical neurons in vivo had been regarded as Poisson spike generators that convey no information other than the rate of random firing. Recently, using a metric for analyzing local variation of interspike intervals, researchers have found that individual neurons express specific patterns in generating spikes, which may symbolically be termed regular, random, or bursty, rather invariantly in time. In order to study the dynamics of firing patterns in greater detail, we propose here a Bayesian method for estimating firing irregularity and the firing rate simultaneously for a given spike sequence, and we implement an algorithm that may render the empirical Bayesian estimation practicable for data comprising a large number of spikes. Application of this method to electrophysiological data revealed a subtle correlation between the degree of firing irregularity and the firing rate for individual neurons. Irregularity of firing did not deviate greatly around the low degree of dependence on the firing rate and remained practically unchanged for individual neurons in the cortical areas V1 and MT, whereas it fluctuated greatly in the lateral geniculate nucleus of the thalamus. This indicates the presence and absence of autocontrolling mechanisms for maintaining patterns of firing in the cortex and thalamus, respectively.

Brain-driven interfaces depend on estimation procedures to convert neural signals to inputs for prosthetic devices that can assist individuals with severe motor deficits. Previous estimation procedures were developed on an application-specific basis. Here we report a coherent estimation framework that unifies these procedures and motivates new applications of prosthetic devices driven by action potentials, local field potentials (LFP), electrocorticography (ECoG), electroencephalography (EEG), electromyography (EMG), or optical methods. The brain-driven interface is described as a probabilistic relationship between neural activity and components of a prosthetic device that may take on discrete or continuous values. A new estimation procedure is developed for action potentials, and a corresponding procedure is described for field potentials and optical measurements.

A nonparametric approach is developed to extract information from interspike interval data. In terms of Expectation-Maximization (EM) algorithm, interspike interval data from experiments and simulations are first approximated by a mixture of various probability distributions, including Gamma, inverse Gaussian, log-normal, and the interspike interval distribution of the leaky integrate-and-fire model. We demonstrate that our approach is successful when fitting benchmark data which failed to be fitted in the literature. Also, an approach to fit mixture distributions to censored data, collected naturally in trial-to-trial or multi-electrode array experiments, is presented. The software to perform above computations is available at