Dynamics of the vocal imitation process: how a zebra finch learns its song.

Song imitation in birds provides good material for studying the basic biology of vocal learning. Techniques were developed for inducing the rapid onset of song imitation in young zebra finches and for tracking trajectories of vocal change over a 7-week period until a match to a model song was achieved. Exposure to a model song induced the prompt generation of repeated structured sounds (prototypes) followed by a slow transition from repetitive to serial delivery of syllables. Tracking this transition revealed two phenomena: (i) Imitations of dissimilar sounds can emerge from successive renditions of the same prototype, and (ii) developmental trajectories for some sounds followed paths of increasing acoustic mismatch until an abrupt correction occurred by period doubling. These dynamics are likely to reflect underlying neural and articulatory constraints on the production and imitation of sounds.

Studying the song development process: rationale and methods.

Current technology makes it possible to measure song development continuously throughout a vocal ontogeny. Here we briefly review some of the problems involved and describe experimental and analytic methods for automatic tracing of vocal changes. These techniques make it possible to characterize the specific methods the bird uses to imitate sounds: an automated song recognition procedure allows continuous song recording, followed by automated sound analysis that partition the song to syllables, extract acoustic features of each syllable, and summarize the entire song development process over time into a single database. The entire song development is then presentable in the form of images or movie clips. These Dynamic Vocal Development (DVD) maps show how each syllable type emerges, and how the bird manipulates syllable features to eventually approximate the model song. Most of the experimental and analytic methods described here have been organized into a software package, which also allows combined neural and sound recording to monitor changes in brain activity as vocal learning occurs. The software is available at http://ofer.sci.ccny.cuny.edu.

Song development: in search of the error-signal.

Song development provides an opportunity to study the mechanisms of vocal learning dynamically at molecular, cellular and systems levels, and across time scales ranging from minutes to months. To exploit these opportunities one needs to identify appropriate units, types and time scales of vocal change in nearly real time. The previous chapter by Tchernikovski et al. in this volume described techniques that make this research strategy feasible by allowing us to observe the song learning process through a "temporal microscope" with variable degrees of resolution. In this chapter we summarize some of the new observations and raise hypotheses about the learning strategy of the bird. We focus on inferences that can be drawn from behavioral observations to the nature and complexity of the instructive signal that guides the vocal change (error-signal). We examine two effects: i) the emergence of syllable types and ii) changes in features within a syllable type. We found that different features of the same syllable change during different and sometimes disjointed developmental windows. We discuss the possibility that song imitation is achieved by correcting partial errors, and that features of those partial errors change adaptively during development, perhaps concurrently with changes in perception and in motor proficiency. Those hypotheses can be best examined by across levels investigation, starting from identifying critical moments in song development and recording of articulatory dynamics and neural patterns when only a few features of specific syllables undergo rapid changes. Such investigation could relate behavioral events to brain mechanisms that guide song learning from moment-to-moment and across extended periods.

Automatic sorting of multiple unit neuronal signals in the presence of anisotropic and non-Gaussian variability.

Neuronal noise sources and systematic variability in the shape of a spike limit the ability to sort multiple unit waveforms recorded from nervous tissue into their single neuron constituents. Here we present a procedure to efficiently sort spikes in the presence of noise that is anisotropic, i.e., dominated by particular frequencies, and whose amplitude distribution may be non-Gaussian, such as occurs when spike waveforms are a function of interspike interval. Our algorithm uses a hierarchical clustering scheme. First, multiple unit records are sorted into an overly large number of clusters by recursive bisection. Second, these clusters are progressively aggregated into a minimal set of putative single units based on both similarities of spike shape as well as the statistics of spike arrival times, such as imposed by the refractory period. We apply the algorithm to waveforms recorded with chronically implanted micro-wire stereotrodes from neocortex of behaving rat. Natural extension of the algorithm may be used to cluster spike waveforms from records with many input channels, such as those obtained with tetrodes and multiple site optical techniques.

Probing the structure of porous media using NMR spin echoes.

The NMR pulsed field gradient spin-echo (PFGSE) amplitude M(k,t) is a direct measure of the diffusion propagator of the molecules of a fluid diffusing in the pores of a porous medium. For small values of k = gamma g delta, where g is the gradient strength, delta is the duration of the gradient pulse, and gamma the gyromagnetic ratio, the PFGSE amplitude gives the diffusion coefficient D(t). The exact short-time diffusion coefficient, D(t)/D0 = 1-(4 square root of D0tS)/(9 Vp square root of pi)-D0tHS/(12Vp) + rho tS/6Vp, provides an important method for determining the surface to pore-volume ratio S/Vp. Here the mean surface curvature H = <1/R1 + 1/R2>. Combining early D(t) with the magnetization decay one obtains the surface relaxivity rho. The long-time effective diffusion constant derived from PFGSE gives information on the tortuosity of the connected space. The diffusion coefficient measured by PFGSE equals that derived from electrical conductivity only when rho = 0. Exact solutions with partially absorbing boundary conditions for a periodic structure are used to illustrate the influence of rho on the diffusion coefficient. M(k,t) can be well represented by a convolution of the structure factor of the connected pore space with an appropriate Gaussian propagator. This ansatz provides a model-independent way of obtaining the structure factor.

Simulations of pulsed field gradient spin-echo measurements in porous media.

Under ideal conditions, in an isotropic homogeneous system, pulsed field gradient spin-echo (PFGSE) experiments measure the probability P(R,t), that a diffusing water molecule will travel a root mean square distance, R, in a time interval of length t. We will show that random walk simulations on model porous media provide valuable insight to the sensitivity of this measurement to (1) complex pore geometries and (2) enhanced relaxation at the pore-grain interface.

Self-diffusion in periodic porous media: a comparison of numerical simulation and eigenvalue methods.

Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.

Schrödinger equation with a spatially and temporally random potential: effects of cross-phase modulation in optical communication.

We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrödinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribution of the input and output optical fields. We use these results to determine the amplitude and timing jitter of a signal pulse and to estimate the system capacity in analog communication.

Laboratory evolution of adenylyl cyclase independent learning in Drosophila and missing heritability.

Gene interactions are acknowledged to be a likely source of missing heritability in large-scale genetic studies of complex neurological phenotypes. However, involvement of rare variants, de novo mutations, genetic lesions that are not easily detected with commonly used methods and epigenetic factors also are possible explanations. We used a laboratory evolution study to investigate the modulatory effects of background genetic variation on the phenotypic effect size of a null mutation with known impact on olfactory learning. To accomplish this, we first established a population that contained variation at just 23 loci and used selection to evolve suppression of the learning defect seen with null mutations in the rutabaga adenylyl cyclase. We thus biased the system to favor relatively simplified outcomes by choosing a Mendelian trait and by restricting the genetic variation segregating in the population. This experimental design also assures that the causal effects are among the known 23 segregating loci. We observe a robust response to selection that requires the presence of the 23 variants. Analyses of the underlying genotypes showed that interactions between more than two loci are likely to be involved in explaining the selection response, with implications for the missing heritability problem.

Sampling properties of the spectrum and coherency of sequences of action potentials.

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This article begins with a review of these quantities, their interpretation, and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented that builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low-variance gaussian process. It is found that in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus. Although the material discussed is of general applicability to point processes, attention will be confined to sequences of neuronal action potentials (spike trains), the motivation for this work.

Nonlinear limits to the information capacity of optical fibre communications.

The exponential growth in the rate at which information can be communicated through an optical fibre is a key element in the 'information revolution'. However, as for all exponential growth laws, physical limits must be considered. The nonlinear nature of the propagation of light in optical fibre has made these limits difficult to elucidate. Here we use a key simplification to investigate the theoretical limits to the information capacity of an optical fibre arising from these nonlinearities. The success of our approach lies in relating the nonlinear channel to a linear channel with multiplicative noise, for which we are able to obtain analytical results. In fundamental distinction to linear channels with additive noise, the capacity of a nonlinear channel does not grow indefinitely with increasing signal power, but has a maximal value. The ideas presented here may have broader implications for other nonlinear information channels, such as those involved in sensory transduction in neurobiology. These have been often examined using additive noise linear channel models but, as we show here, nonlinearities can change the picture qualitatively.

Towards quantification of vocal imitation in the zebra finch.

The transition from an amorphous subsong into mature song requires a series of vocal changes. By tracing song elements during development, we have shown that the imitation trajectory to the target could not be predicted based on monotonic progression of vocal changes, indicating an internal component that imposes constraints on song development. Here we further examine the nature of constraints on song imitation in the zebra finch. We first present techniques for identifying and tracing distinctive vocal changes, and then we examine how sequences of vocal change are expressed and coordinated. Examples suggest two types of constraints on song imitation, based on the nature of the temporal context. Developmentally diachronic constraints are imposed by sequential dependencies between vocal changes as a function of developmental time, whereas developmentally synchronic constraints are given by the acoustic context of notes within the song. Finally, we show that the tendency of birds to copy certain sounds in the song model before others might be related to such constraints. We suggest that documenting the full range of distinctive vocal changes and the coordination of their expression would be useful for testing mechanisms of vocal imitation.

Distributions of singular values for some random matrices.

The singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of singular values of low-rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic and saddle point integration techniques, we extend these results to heterogeneous and correlated noise sources. We also provide perturbative estimates of error bars on the reconstructed low-rank matrix obtained by truncating a singular value decomposition.

Analysis of dynamic brain imaging data.

Modern imaging techniques for probing brain function, including functional magnetic resonance imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this paper we develop appropriate techniques for analysis and visualization of such imaging data to separate the signal from the noise and characterize the signal. The techniques developed fall into the general category of multivariate time series analysis, and in particular we extensively use the multitaper framework of spectral analysis. We develop specific protocols for the analysis of fMRI, optical imaging, and MEG data, and illustrate the techniques by applications to real data sets generated by these imaging modalities. In general, the analysis protocols involve two distinct stages: "noise" characterization and suppression, and "signal" characterization and visualization. An important general conclusion of our study is the utility of a frequency-based representation, with short, moving analysis windows to account for nonstationarity in the data. Of particular note are 1) the development of a decomposition technique (space-frequency singular value decomposition) that is shown to be a useful means of characterizing the image data, and 2) the development of an algorithm, based on multitaper methods, for the removal of approximately periodic physiological artifacts arising from cardiac and respiratory sources.

Fluctuation analysis of motor protein movement and single enzyme kinetics.

We studied fluctuations in the displacement of silica beads driven by single molecules of the motor protein kinesin, moving under low mechanical loads at saturating ATP concentrations. The variance in position was significantly smaller than expected for the case of stepwise movement along a regular lattice of positions with exponentially distributed intervals. The small variance suggests that two or more sequential processes with comparable reaction rates dominate the biochemical cycle. The low value is inconsistent with certain recently proposed thermal ratchet models for motor movement as well as with scenarios where the hydrolysis of a single ATP molecule leads to a cluster of several steps. Fluctuation analysis is a potential powerful tool for studying kinetic behavior whenever the output of a single enzyme can be monitored.

Scalable architecture in mammalian brains.

Comparison of mammalian brain parts has often focused on differences in absolute size, revealing only a general tendency for all parts to grow together. Attempts to find size-independent effects using body weight as a reference variable obscure size relationships owing to independent variation of body size and give phylogenies of questionable significance. Here we use the brain itself as a size reference to define the cerebrotype, a species-by-species measure of brain composition. With this measure, across many mammalian taxa the cerebellum occupies a constant fraction of the total brain volume (0.13 +/- 0.02), arguing against the hypothesis that the cerebellum acts as a computational engine principally serving the neocortex. Mammalian taxa can be well separated by cerebrotype, thus allowing the use of quantitative neuroanatomical data to test evolutionary relationships. Primate cerebrotypes have progressively shifted and neocortical volume fractions have become successively larger in lemurs and lorises, New World monkeys, Old World monkeys, and hominoids, lending support to the idea that primate brain architecture has been driven by directed selection pressure. At the same time, absolute brain size can vary over 100-fold within a taxon, while maintaining a relatively uniform cerebrotype. Brains therefore constitute a scalable architecture.

Tripling the capacity of wireless communications using electromagnetic polarization.

Wireless communications are a fundamental part of modern information infrastructure. But wireless bandwidth is costly, prompting a close examination of the data channels available using electromagnetic waves. Classically, radio communications have relied on one channel per frequency, although it is well understood that the two polarization states of planar waves allow two distinct information channels; techniques such as 'polarization diversity' already take advantage of this. Recent work has shown that environments with scattering, such as urban areas or indoors, also possess independent spatial channels that can be used to enhance capacity greatly. In either case, the relevant signal processing techniques come under the heading of 'multiple-input/multiple-output' communications, because multiple antennae are required to access the polarization or spatial channels. Here we show that, in a scattering environment, an extra factor of three in channel capacity can be obtained, relative to the conventional limit using dual-polarized radio signals. The extra capacity arises because there are six distinguishable electric and magnetic states of polarization at a given point, rather than two as is usually assumed.

The nature of spatiotemporal changes in cerebral hemodynamics as manifested in functional magnetic resonance imaging.

The nature of changes in rapidly acquired magnetic resonance images of the brain was studied by using a denoising method and spectral techniques optimally suited to short time series. It was found that the stimulus related changes have a complex spatiotemporal structure even for simple visual stimuli. Apart from a low frequency window, the non-stimulus-related changes were found to correspond in detail to either breathing or heartbeat, although these two sources show different patterns of spatial coherence in the image. At low frequencies, oscillations with frequencies around 0.1 Hz were observed, also with nontrivial space-time structure, which are likely to be vasomotor in origin.

Variability of extracellular spike waveforms of cortical neurons.

1. Here we study the variability in extracellular records of action potentials. Our work is motivated, in part, by the need to construct effective algorithms to classify single-unit waveforms from multiunit recordings. 2. We used microwire electrode pairs (stereotrodes) to record from primary somatosensory cortex of awake, behaving rat. Our data consist of continuous records of extracellular activity and segmented records of extracellular spikes. Spectral and principal component techniques are used to analyze mean single-unit wave-forms, the variability between different instances of a single-unit waveform, and the underlying background activity. 3. The spectrum of the variability between different instances of a single-unit waveforms is not white, and falls off above 1 kHz with a frequency dependence of roughly f-2. This spectrum is different from that of the mean spike waveforms, which falls off roughly as f-4, but is essentially identical with the spectrum of background activity. The spatial coherence of the variability on the 10-micron scale also falls off at high frequencies. 4. The variability between different instances of a single-unit waveform is dominated by a relatively small number of principal components. As a consequence, there is a large anisotropy in the cluster of the spike waveforms. 5. The background noise cannot be represented as a stationary Gaussian random process. In particular, we observed that the spectrum changes significantly between successive 20-ms intervals. Furthermore, the total power in the background activity exhibits larger fluctuations than is consistent with a stationary Gaussian random process. 6. Roughly half of the single-unit spike waveforms exhibit systematic changes as a function of the interspike interval. Although this results in a non-Gaussian distribution in the space of waveforms, the distribution can be modeled by a scalar function of the interspike interval. 7. We use a set of 44 mean single-unit waveforms to define the space of differences between spike waveforms. This characterization, together with that of the background activity, is used to construct a filter that optimizes the detection of differences between single-unit waveforms. Further, an information theoretic measure is defined that characterizes the detectability.