Capacities and efficient computation of first-passage probabilities.

A reversible diffusion process is initialized at position x_{0} and run until it first hits any of several targets. What is the probability that it terminates at a particular target? We propose a computationally efficient approach for estimating this probability, focused on those situations in which it takes a long time to hit any target. In these cases, direct simulation of the hitting probabilities becomes prohibitively expensive. On the other hand, if the timescales are sufficiently long, then the system will essentially "forget" its initial condition before it encounters a target. In these cases the hitting probabilities can be accurately approximated using only local simulations around each target, obviating the need for direct simulations. In empirical tests, we find that these local estimates can be computed in the same time it would take to compute a single direct simulation, but that they achieve an accuracy that would require thousands of direct simulation runs.

Base-pair ambiguity and the kinetics of RNA folding.

BACKGROUND: A pairings of nucleotide sequences. Given this forbidding free-energy landscape, mechanisms have evolved that contribute to a directed and efficient folding process, including catalytic proteins and error-detecting chaperones. Among structural RNA molecules we make a distinction between "bound" molecules, which are active as part of ribonucleoprotein (RNP) complexes, and "unbound," with physiological functions performed without necessarily being bound in RNP complexes. We hypothesized that unbound molecules, lacking the partnering structure of a protein, would be more vulnerable than bound molecules to kinetic traps that compete with native stem structures. We defined an "ambiguity index"-a normalized function of the primary and secondary structure of an individual molecule that measures the number of kinetic traps available to nucleotide sequences that are paired in the native structure, presuming that unbound molecules would have lower indexes. The ambiguity index depends on the purported secondary structure, and was computed under both the comparative ("gold standard") and an equilibrium-based prediction which approximates the minimum free energy (MFE) structure. Arguing that kinetically accessible metastable structures might be more biologically relevant than thermodynamic equilibrium structures, we also hypothesized that MFE-derived ambiguities would be less effective in separating bound and unbound molecules. RESULTS: We have introduced an intuitive and easily computed function of primary and secondary structures that measures the availability of complementary sequences that could disrupt the formation of native stems on a given molecule-an ambiguity index. Using comparative secondary structures, the ambiguity index is systematically smaller among unbound than bound molecules, as expected. Furthermore, the effect is lost when the presumably more accurate comparative structure is replaced instead by the MFE structure. CONCLUSIONS: A statistical analysis of the relationship between the primary and secondary structures of non-coding RNA molecules suggests that stem-disrupting kinetic traps are substantially less prevalent in molecules not participating in RNP complexes. In that this distinction is apparent under the comparative but not the MFE secondary structure, the results highlight a possible deficiency in structure predictions when based upon assumptions of thermodynamic equilibrium.

Transsacadic Information and Corollary Discharge in Local Field Potentials of Macaque V1.

Approximately three times per second, human visual perception is interrupted by a saccadic eye movement. In addition to taking the eyes to a new location, several lines of evidence suggest that the saccades play multiple roles in visual perception. Indeed, it may be crucial that visual processing is informed about movements of the eyes in order to analyze visual input distinctly and efficiently on each fixation and preserve stable visual perception of the world across saccades. A variety of studies has demonstrated that activity in multiple brain areas is modulated by saccades. The hypothesis tested here is that these signals carry significant information that could be used in visual processing. To test this hypothesis, local field potentials (LFPs) were simultaneously recorded from multiple electrodes in macaque primary visual cortex (V1); support vector machines (SVMs) were used to classify the peri-saccadic LFPs. We find that LFPs in area V1 carry information that can be used to distinguish neural activity associated with fixations from saccades, precisely estimate the onset time of fixations, and reliably infer the directions of saccades. This information may be used by the brain in processes including visual stability, saccadic suppression, receptive field (RF) remapping, fixation amplification, and trans-saccadic visual perception.

Ambiguity and nonidentifiability in the statistical analysis of neural codes.

Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.

Visual Turing test for computer vision systems.

Today, computer vision systems are tested by their accuracy in detecting and localizing instances of objects. As an alternative, and motivated by the ability of humans to provide far richer descriptions and even tell a story about an image, we construct a "visual Turing test": an operator-assisted device that produces a stochastic sequence of binary questions from a given test image. The query engine proposes a question; the operator either provides the correct answer or rejects the question as ambiguous; the engine proposes the next question ("just-in-time truthing"). The test is then administered to the computer-vision system, one question at a time. After the system's answer is recorded, the system is provided the correct answer and the next question. Parsing is trivial and deterministic; the system being tested requires no natural language processing. The query engine employs statistical constraints, learned from a training set, to produce questions with essentially unpredictable answers-the answer to a question, given the history of questions and their correct answers, is nearly equally likely to be positive or negative. In this sense, the test is only about vision. The system is designed to produce streams of questions that follow natural story lines, from the instantiation of a unique object, through an exploration of its properties, and on to its relationships with other uniquely instantiated objects.

Invariance in the recurrence of large returns and the validation of models of price dynamics.

Starting from a robust, nonparametric definition of large returns ("excursions"), we study the statistics of their occurrences, focusing on the recurrence process. The empirical waiting-time distribution between excursions is remarkably invariant to year, stock, and scale (return interval). This invariance is related to self-similarity of the marginal distributions of returns, but the excursion waiting-time distribution is a function of the entire return process and not just its univariate probabilities. Generalized autoregressive conditional heteroskedasticity (GARCH) models, market-time transformations based on volume or trades, and generalized (Lévy) random-walk models all fail to fit the statistical structure of excursions.

Conditional modeling and the jitter method of spike resampling.

The existence and role of fine-temporal structure in the spiking activity of central neurons is the subject of an enduring debate among physiologists. To a large extent, the problem is a statistical one: what inferences can be drawn from neurons monitored in the absence of full control over their presynaptic environments? In principle, properly crafted resampling methods can still produce statistically correct hypothesis tests. We focus on the approach to resampling known as jitter. We review a wide range of jitter techniques, illustrated by both simulation experiments and selected analyses of spike data from motor cortical neurons. We rely on an intuitive and rigorous statistical framework known as conditional modeling to reveal otherwise hidden assumptions and to support precise conclusions. Among other applications, we review statistical tests for exploring any proposed limit on the rate of change of spiking probabilities, exact tests for the significance of repeated fine-temporal patterns of spikes, and the construction of acceptance bands for testing any purported relationship between sensory or motor variables and synchrony or other fine-temporal events.

A rate and history-preserving resampling algorithm for neural spike trains.

Resampling methods are popular tools for exploring the statistical structure of neural spike trains. In many applications, it is desirable to have resamples that preserve certain non-Poisson properties, like refractory periods and bursting, and that are also robust to trial-to-trial variability. Pattern jitter is a resampling technique that accomplishes this by preserving the recent spiking history of all spikes and constraining resampled spikes to remain close to their original positions. The resampled spike times are maximally random up to these constraints. Dynamic programming is used to create an efficient resampling algorithm.

Spike count reliability and the Poisson hypothesis.

The variability of cortical activity in response to repeated presentations of a stimulus has been an area of controversy in the ongoing debate regarding the evidence for fine temporal structure in nervous system activity. We present a new statistical technique for assessing the significance of observed variability in the neural spike counts with respect to a minimal Poisson hypothesis, which avoids the conventional but troubling assumption that the spiking process is identically distributed across trials. We apply the method to recordings of inferotemporal cortical neurons of primates presented with complex visual stimuli. On this data, the minimal Poisson hypothesis is rejected: the neuronal responses are too reliable to be fit by a typical firing-rate model, even allowing for sudden, time-varying, and trial-dependent rate changes after stimulus onset. The statistical evidence favors a tightly regulated stimulus response in these neurons, close to stimulus onset, although not further away.

Invariance and selectivity in the ventral visual pathway.

Pattern recognition systems that are invariant to shape, pose, lighting and texture are never sufficiently selective; they suffer a high rate of "false alarms". How are biological vision systems both invariant and selective? Specifically, how are proper arrangements of sub-patterns distinguished from the chance arrangements that defeat selectivity in artificial systems? The answer may lie in the nonlinear dynamics that characterize complex and other invariant cell types: these cells are temporarily more receptive to some inputs than to others (functional connectivity). One consequence is that pairs of such cells with overlapping receptive fields will possess a related property that might be termed functional common input. Functional common input would induce high correlation exactly when there is a match in the sub-patterns appearing in the overlapping receptive fields. These correlations, possibly expressed as a partial and highly local synchrony, would preserve the selectivity otherwise lost to invariance.