Large-scale species delimitation method for hyperdiverse groups.

Accelerating the description of biodiversity is a major challenge as extinction rates increase. Integrative taxonomy combining molecular, morphological, ecological and geographical data is seen as the best route to reliably identify species. Classic molluscan taxonomic methodology proposes primary species hypotheses (PSHs) based on shell morphology. However, in hyperdiverse groups, such as the molluscan family Turridae, where most of the species remain unknown and for which homoplasy and plasticity of morphological characters is common, shell-based PSHs can be arduous. A four-pronged approach was employed to generate robust species hypotheses of a 1000 specimen South-West Pacific Turridae data set in which: (i) analysis of COI DNA Barcode gene is coupled with (ii) species delimitation tools GMYC (General Mixed Yule Coalescence Method) and ABGD (Automatic Barcode Gap Discovery) to propose PSHs that are then (iii) visualized using Klee diagrams and (iv) evaluated with additional evidence, such as nuclear gene rRNA 28S, morphological characters, geographical and bathymetrical distribution to determine conclusive secondary species hypotheses (SSHs). The integrative taxonomy approach applied identified 87 Turridae species, more than doubling the amount previously known in the Gemmula genus. In contrast to a predominantly shell-based morphological approach, which over the last 30 years proposed only 13 new species names for the Turridae genus Gemmula, the integrative approach described here identified 27 novel species hypotheses not linked to available species names in the literature. The formalized strategy applied here outlines an effective and reproducible protocol for large-scale species delimitation of hyperdiverse groups.

Extraction of the average and differential dynamical response in stimulus-locked experimental data.

In optical imaging experiments of primary visual cortex, visual stimuli evoke a complicated dynamics. Typically, any stimulus with sufficient contrast evokes a response. Much of the response is the same regardless of which stimulus is presented. For instance, when oriented drifting gratings are presented to the visual system, over 90% of the response is the same from orientation to orientation. Small differences may be seen, however, between the responses to different orientations. A problem in the analysis of optical measurements of the response to stimulus in cortical tissue is the distinction of the 'global' or 'non-specific' response from the 'differential' or 'stimulus-specific' response. This problem arises whenever the signal of interest is the difference in response to various stimuli and is evident in many kinds of uni- and multivariate data. To this end, we present enhancements to a frequency-based method that we previously introduced called the periodic stacking method. These enhancements allow us to separately estimate the dynamics of both the average signal across all stimuli (the 'global' response) and deviations from the average amongst the various stimuli (the 'stimulus-specific' response) evoked in response to a set of stimuli. We also discuss improvements in the signal-to-noise ratio, relative to standard trial averaging methods, that result from the data-adaptive smoothing in our method.

Spatiotemporal analysis of optical imaging data.

Previous methods for analyzing optical imaging data have relied heavily on temporal averaging. However, response dynamics are rich sources of information. Here, we develop and present a method that combines principal component analysis and multitaper harmonic analysis to extract the statistically significant spatial and temporal response from optical imaging data. We apply the method to both simulated data and experimental optical imaging data from the cat primary visual cortex.

A population study of integrate-and-fire-or-burst neurons.

Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the bursting behavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate-and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population model and study a population of such LGN cells. This population model, the first simulation of its kind evolving in a two-dimensional phase space, is used to study the behavior of bursting populations in response to diverse stimulus conditions.

An optimization approach to signal extraction from noisy multivariate data.

We consider a problem of blind signal extraction from noisy multivariate data, in which each datum represents a system's response, observed under a particular experimental condition. Our prototype example is multipixel functional images of brain activity in response to a set of prescribed experimental stimuli. We present a novel multivariate analysis technique, which identifies the different activity patterns (signals) that are attributable to specific experimental conditions, without a priori knowledge about the signal or the noise characteristics. The extracted signals, which we term the generalized indicator functions, are optimal in the sense that they maximize a weighted difference between the signal variance and the noise variance. With an appropriate choice of the weighting parameter, the method returns a set of images whose signal-to-noise ratios satisfy some user-defined level of significance. We demonstrate the performance of our method in optical intrinsic signal imaging of cat cortical area 17. We find that the method performs effectively and robustly in all tested data, which include both real experimental data and numerically simulated data. The method of generalized indicator functions is related to canonical variate analysis, a multivariate analysis technique that directly solves for the maxima of the signal-to-noise ratio, but important theoretical and practical differences exist, which can make our method more appropriate in certain situations.

A population approach to cortical dynamics with an application to orientation tuning.

A typical functional region in cortex contains thousands of neurons, therefore direct neuronal simulation of the dynamics of such a region necessarily involves massive computation. A recent efficient alternative formulation is in terms of kinetic equations that describe the collective activity of the whole population of similar neurons. A previous paper has shown that these equations produce results that agree well with detailed direct simulations. Here we illustrate the power of this new technique by applying it to the investigation of the effect of recurrent connections upon the dynamics of orientation tuning in the visual cortex. Our equations express the kinetic counterpart of the hypercolumn model from which Somers et al (Somers D, Nelson S and Sur M 1995 J. Neurosci. 15 5448-65) computed steady-state cortical responses to static stimuli by direct simulation. We confirm their static results. Our method presents the opportunity to simulate the data-intensive dynamical experiments of Ringach et al (Ringach D, Hawken M and Shapley R 1997 Nature 387 281-4), in which 60 randomly oriented stimuli were presented each second for 15 min, to gather adequate statistics of responses to multiple presentations. Without readjustment of the previously defined parameters. our simulations yield substantial agreement with the experimental results. Our calculations suggest that differences in the experimental dynamical responses of cells in different cortical layers originate from differences in their recurrent connections with other cells. Thus our method of efficient simulation furnishes a variety of information that is not available from experiment alone.

The approach of a neuron population firing rate to a new equilibrium: an exact theoretical result.

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.

On the simulation of large populations of neurons.

The dynamics of large populations of interacting neurons is investigated. Redundancy present in subpopulations of cortical networks is exploited through the introduction of a probabilistic description. A derivation of the kinetic equations for such subpopulations, under general transmembrane dynamics, is presented. The particular case of integrate-and-fire membrane dynamics is considered in detail. A variety of direct simulations of neuronal populations, under varying conditions and with as many as O(10(5)) neurons, is reported. Comparison is made with analogous kinetic equations under the same conditions. Excellent agreement, down to fine detail, is obtained. It is emphasized that no free parameters enter in the comparisons that are made.

A principal components-based method for the detection of neuronal activity maps: application to optical imaging.

We present a novel analysis technique for the extraction of neuronal activity patterns from functional imaging data. We illustrate this technique on data from optical imaging. Optical imaging of the mammalian visual cortex probe the patterns in which the neuronal responses to various aspects of the visual world, such as orientation and color, are spatially organized within the cortex. Recovering these patterns from the image data is a challenging problem as the neuronal response signal is extremely weak in comparison to the background vegetative processes (e.g., circulation and respiration). The proposed technique obtains the neuronal activity pattern using a combination of principal component analysis and statistical significance testing. The performance of this method is compared with the results of existing analysis techniques. The comparison shows the new method to be more sensitive than previous methods.

Representation of spatial frequency and orientation in the visual cortex.

Knowledge of the response of the primary visual cortex to the various spatial frequencies and orientations in the visual scene should help us understand the principles by which the brain recognizes patterns. Current information about the cortical layout of spatial frequency response is still incomplete because of difficulties in recording and interpreting adequate data. Here, we report results from a study of the cat primary visual cortex in which we employed a new image-analysis method that allows improved separation of signal from noise and that we used to examine the neurooptical response of the primary visual cortex to drifting sine gratings over a range of orientations and spatial frequencies. We found that (i) the optical responses to all orientations and spatial frequencies were well approximated by weighted sums of only two pairs of basis pictures, one pair for orientation and a different pair for spatial frequency; (ii) the weightings of the two pictures in each pair were approximately in quadrature (1/4 cycle apart); and (iii) our spatial frequency data revealed a cortical map that continuously assigns different optimal spatial frequency responses to different cortical locations over the entire spatial frequency range.

Separating spatially distributed response to stimulation from background. I. Optical imaging.

We consider the problem of estimating a small stimulus-induced response to stimulation that is masked by a fluctuating background when measurements of the background in the absence of stimulation are available, as is common in optical imaging of the cortex and in many other experimental situations. Two related methods based on the Karhunen-Loève procedure are discussed. One seeks the function, an indicator function, that is most parallel to the response data and most orthogonal to the background data. The second removes the subspace spanned by the background from the response. Numerical investigations on simulated optical imaging data show that the first method is generally superior. Connections between the two methods and techniques for assessing the quality of the result are discussed.

Low-dimensional procedure for the characterization of human faces.

A method is presented for the representation of (pictures of) faces. Within a specified framework the representation is ideal. This results in the characterization of a face, to within an error bound, by a relatively low-dimensional vector. The method is illustrated in detail by the use of an ensemble of pictures taken for this purpose.

Characteristic patterns of an inhomogeneous imaging system with an application to vision.

We examine consequences of image-forming inhomogeneity in the form of a point-spread function that changes with position on the image plane. The familiar self-replicating sinusoids, which a homogeneous system simply multiplies by its spatial modulation-transfer function, generalize to eigenfunctions, which the system multiplies by eigenvalues. We give a way to calculate the eigenfunctions and eigenvalues from the variable point-spread function. We illustrate this with data from the visual system and show that these lead to a discrete set of most-sensitive eigenfunctions, which we construct.

The eigenfunction problem in higher dimensions: Exact results.

A hermitian integral kernel in N-space may be mapped to a corresponding Hamiltonian in 2N-space by the Wigner transformation. Linear simplectic transformation on the phase space of the Hamiltonian yields a new kernel whose spectrum is unchanged and whose eigenfunctions follow from an explicit unitary transformation. If an integral kernel has a Wigner transform whose surfaces of constant value are concentric ellipsoids, then the Wigner transform yields exact results to the eigenfunction problem. Such behavior is asymptotically generic near extrema of the Wigner transform, from which follow simple and robust asymptotic results for the ends of the eigenvalue spectrum and for the corresponding eigenfunctions.

The eigenfunction problem in higher dimensions: Asymptotic theory.

The spectral problem for linear operators on fully infinite domains is considered. A transformation first introduced by Wigner is used to show a number of asymptotic results. The method leads to a WKB (Wentzel-Kromers-Brillouin) theory for operators in more than one dimension. This includes practical tools for the approximate evaluation of spectra and eigenfunctions. Several general examples are developed.