Seismic and auditory tuning curves from bullfrog saccular and amphibian papular axons

We present seismic and auditory frequency tuning curves of individual bullfrog, Rana catesbeiana, saccular and amphibian papilla axons that responded to both seismic and auditory stimuli. In this study we found: 1) most saccular axons respond well to auditory stimuli with moderate signal strength (50-70 dB SPL) as well as to seismic stimuli; 2) most amphibian papilla axons respond well to seismic stimuli as well as to auditory stimuli, and their seismic sensitivities are comparable to those of saccular axons (responding to sinusoidal stimuli with peak accelerations in the range 0.001 to 0.1 cm/S2); 3) the responses to both seismic and auditory stimuli from both saccule and amphibian papilla are tuned, i.e. the strength of the response varies with the frequency of the stimulus; and this tuning is clearly not the result of second order resonance; 4) in individual axons the tuning properties for seismic stimuli often are not the same as those for auditory stimuli, a fact that may provide clues about how the stimulus signal energy is transferred to the hair cells in each case.     

Decoding cortical neuronal signals: Network models,information estimation and spatial tuning

We have studied the encoding of spatial pattern information by complex cells in the primary visual cortex of awake monkeys. Three models for the conditional probabilities of different stimuli, given the neuronal response, were fit and compared using cross-validation. For our data, a feed-forward neural network proved to be the best of these models.The information carried by a cell about a stimulus set can be calculated from the estimated conditional probabilities. We performed a spatial spectroscopy of the encoding, examining how the transmitted information varies with both the average coarseness of the stimulus set and the coarseness differences within it. We find that each neuron encodes information about many features at multiple scales. Our data do not appear to allow a characterization of these variations in terms of the detection of simple single features such as oriented bars.     

Systematic tuning of parameters in support vector clustering

Clustering algorithms divide a set of observations into groups so that members of the same group share common features. In most of the algorithms, tunable parameters are set arbitrarily or by trial and error, resulting in less than optimal clustering. This paper presents a global optimization strategy for the systematic and optimal selection of parameter values associated with a clustering method. In the process, a performance criterion for the optimization model is proposed and benchmarked against popular performance criteria from the literature (namely, the Silhouette coefficient, Dunn's index, and Davies-Bouldin index). The tuning strategy is illustrated using the support vector clustering (SVC) algorithm and simulated annealing. In order to reduce the computational burden, the paper also proposes an alternative to the adjacency matrix method (used for the assignment of cluster labels), namely the contour plotting approach. Datasets tested include the iris and the thyroid datasets from the UCI repository, as well as lymphoma and breast cancer data. The optimal tuning parameters are determined efficiently, while the contour plotting approach leads to significant reductions in computational effort (CPU time) especially for large datasets. The performance criteria comparisons indicate mixed results. Specifically, the Silhouette coefficient and the Davies-Bouldin index perform better, while the Dunn's index is worse on average than the proposed performance index.     

Orientation tuning of motion-sensitive neurons shaped by vertical-horizontal network interactions

We measured the orientation tuning of two neurons of the fly lobula plate (H1 and H2 cells) sensitive to horizontal image motion. Our results show that H1 and H2 cells are sensitive to vertical motion, too. Their response depended on the position of the vertically moving stimuli within their receptive field. Stimulation within the frontal receptive field produced an asymmetric response: upward motion left the H1/H2 spike frequency nearly unaltered while downward motion increased the spike frequency to about 40% of their maximum responses to horizontal motion. In the lateral parts of their receptive fields, no such asymmetry in the responses to vertical image motion was found. Since downward motion is known to be the preferred direction of neurons of the vertical system in the lobula plate, we analyzed possible interactions between vertical system cells and H1 and H2 cells. Depolarizing current injection into the most frontal vertical system cell (VS1) led to an increased spike frequency, hyperpolarizing current injection to a decreased spike frequency in both H1 and H2 cells. Apart from VS1, no other vertical system cell (VS2-8) had any detectable influence on either H1 or H2 cells. The connectivity of VS1 and H1/H2 is also shown to influence the response properties of both centrifugal horizontal cells in the contralateral lobula plate, which are known to be postsynaptic to the H1 and H2 cells. The vCH cell receives additional input from the contralateral VS2-3 cells via the spiking interneuron V1.     

An empirical function for the description of root growth

Vertical growth of young cress roots (Lepidium sativum L.) which have not yet attained their steady state is analyzed in terms of the relative elemental rate of elongation (RELEL). To this end, an empirical model function is suggested which describes, by means of six parameters, the movement of marker particles on the root surface. These parameters are interpreted as morphological and physiological quantities. Their determination by independent measurements is in good agreement with that obtained by fitting the model function to the experimental data. The RELEL is then evaluated analytically, so that numerical smoothing and differentiating algorithms with all their problems are avoided. The result demonstrates that—apart from the root cap—nearly the whole root is elongating, including the root hair region and part of the basal portion beyond it. This explains the basal curvature component that is observed during the graviresponse of cress roots.     

Effect of degree of uniformity on predicted visual cortical response tuning curves

 The different cortical visual cells exhibit a large repertoire of responses to sinusoidal gratings, depending on their receptive field structure and the stimulation parameters. It has been shown previously that the tuning curves and histogram shapes of cell responses are affected by subunit distances. One receptive field model (Spitzer and Hochstein 1985b) incorporated subunit distance but assigned it as a constant parameter, for ease of calculation. Here we investigate different tuning curve properties of various primary cortical cell types during testing of 10 deg of nonuniform distances of the receptive fields’ subunits. The effect of nonuniformity was compared for average responses, tuning curve shapes, maximum peak responses, and bandwidths across four cell types of different sizes. The shapes and other properties of tuning curves are usually found to be retained also when the degree of uniformity is not very high for most of the cell types. In addition, the effect of uniformity is compared across these different response properties. The maximum peak responses of the tuning curve are found to display a lower coefficient of variation than the bandwidth, for all cell types, for most degrees of uniformity. Received: 15 June 1993/Accepted in revised form: 5 August 1994     

Resampling-based empirical prediction: an application to small area estimation

Best linear unbiased prediction is well known for its wide rangeof applications including small area estimation. While the theoryis well established for mixed linear models and under normalityof the error and mixing distributions, the literature is sparsefor nonlinear mixed models under nonnormality of the error distributionor of the mixing distributions. We develop a resampling-basedunified approach for predicting mixed effects under a generalizedmixed model set-up. Second-order-accurate nonnegative estimatorsof mean squared prediction errors are also developed. Giventhe parametric model, the proposed methodology automaticallyproduces estimators of the small area parameters and their meansquared prediction errors, without requiring explicit analyticalexpressions for the mean squared prediction errors.     

Determination of proliferative parameters from growth curves

Data on total cell numbers and proportions of non-proliferative cells during the development of a tissue can be obtained by experiment. This paper shows, via a simple mathematical model, that data collected over a period of time determine the time profile of two proliferative parameters. These are the rate per proliferative cell per day at which cells divide and the average number of proliferative daughters which result from the division of a proliferative cell. One dataset alone does not provide sufficient information to determine either time profile. The findings are applicable where there is no significant cell death during the growth period. The mathematical model is fitted to data from chick neural retina.     

Determination of proliferative parameters from growth curves

Abstract. Data on total cell numbers and proportions of non-proliferative cells during the development of a tissue can be obtained by experiment. This paper shows, via a simple mathematical model, that data collected over a period of time determine the time profile of two proliferative parameters. These are the rate per proliferative cell per day at which cells divide and the average number of proliferative daughters which result from the division of a proliferative cell. One dataset alone does not provide sufficient information to determine either time profile. The findings are applicable where there is no significant cell death during the growth period. The mathematical model is fitted to data from chick neural retina.     

Hamilton goes empirical: estimation of inclusive fitness from life-history data

Hamilton's theory of kin selection is one of the most important advances in evolutionary biology since Darwin. Central to the kin-selection theory is the concept of inclusive fitness. However, despite the importance of inclusive fitness in evolutionary theory, empirical estimation of inclusive fitness has remained an elusive task. Using the concept of individual fitness, I present a method for estimating inclusive fitness and its components for diploid organisms with age-structured life histories. The method presented here: (i) allows empirical estimation of inclusive fitness from life-history data; (ii) simultaneously considers all components of fitness, including timing and magnitude of reproduction; (iii) is consistent with Hamilton's definition of inclusive fitness; and (iv) adequately addresses shortcomings of existing methods of estimating inclusive fitness. I also demonstrate the application of this new method for testing Hamilton's rule.     

LAMARC 2.0: maximum likelihood and Bayesian estimation of population parameters

We present a Markov chain Monte Carlo coalescent genealogy sampler, LAMARC 2.0, which estimates population genetic parameters from genetic data. LAMARC can co-estimate subpopulation Theta = 4N(e)mu, immigration rates, subpopulation exponential growth rates and overall recombination rate, or a user-specified subset of these parameters. It can perform either maximum-likelihood or Bayesian analysis, and accomodates nucleotide sequence, SNP, microsatellite or elecrophoretic data, with resolved or unresolved haplotypes. It is available as portable source code and executables for all three major platforms. AVAILABILITY: LAMARC 2.0 is freely available at http://evolution.gs.washington.edu/lamarc     

A statistical analysis of natural images matches psychophysically derived orientation tuning curves.

A neural net method is used to extract principal components from real-world images. The initial components are a Gaussian followed by horizontal and vertical operators, starting with the first derivative and moving to successively higher orders. Two of the components are 'bar-detectors'. Their measured orientation selectivity is similar to that suggested by Foster & Ward (Proc. R. Soc. Lond. B 243, 75 (1991] to account for brief-exposure psychophysical data. In tests with noise images, the ratio of sensitivity between the two components is controlled by the degree of anisotropy in the image.     

Auditory sensitivity and psychophysical tuning curves in the elephant nose fish,Gnathonemus petersii

Summary Hearing sensitivity and psychophysical tuning curves were determined for the mormyridGnathonemus petersii. Pure tone hearing thresholds were determined from 100 Hz to 2,500 Hz, with best sensitivity being about –31 dB (re: 1 dyne/ cm²) from 300 Hz to 1,000 Hz. In order to determine frequency tuning of the auditory system, psychophysical tuning curves (PTC's) were measured with the masker presented simultaneously with, or just ahead of, the 500 Hz test signal. The sound level for different frequencies needed to just mask the test tone were determined from 100 to 800 Hz. Maximum masking occurred in both forward and simultaneous conditions when the masker and the test tone were at the same frequency. As the masker was moved in frequency from 500 Hz, higher sound levels of maskers were needed to afford masking of the test tone. The data were similar in simultaneous and forward masking, with theQ _{10 dB}, a measure of sharpness of tuning, being about 5 in both cases. Data were compared for other species for which behavioral thresholds and PTC's are available.Gnathonemus hears about as wide a range of frequencies as the goldfish,Carassius auratus, although the PTC's for the two species are strikingly different. The PTC's forGnathonemus resemble those determined in a forward-masking paradigm for the clown knife fish,Notopterus chitala, even thoughGnathonemus has a wider hearing bandwidth.Abbreviations AM amplitude modulated - EOD electric organ discharge - PTC psychophysical tuning curve     

Regression with empirical variable selection: description of a new method and application to ecological datasets

Despite recent papers on problems associated with full-model and stepwise regression, their use is still common throughout ecological and environmental disciplines. Alternative approaches, including generating multiple models and comparing them post-hoc using techniques such as Akaike''s Information Criterion (AIC), are becoming more popular. However, these are problematic when there are numerous independent variables and interpretation is often difficult when competing models contain many different variables and combinations of variables. Here, we detail a new approach, REVS (Regression with Empirical Variable Selection), which uses all-subsets regression to quantify empirical support for every independent variable. A series of models is created; the first containing the variable with most empirical support, the second containing the first variable and the next most-supported, and so on. The comparatively small number of resultant models (n = the number of predictor variables) means that post-hoc comparison is comparatively quick and easy. When tested on a real dataset – habitat and offspring quality in the great tit (Parus major) – the optimal REVS model explained more variance (higher R²), was more parsimonious (lower AIC), and had greater significance (lower P values), than full, stepwise or all-subsets models; it also had higher predictive accuracy based on split-sample validation. Testing REVS on ten further datasets suggested that this is typical, with R² values being higher than full or stepwise models (mean improvement = 31% and 7%, respectively). Results are ecologically intuitive as even when there are several competing models, they share a set of “core” variables and differ only in presence/absence of one or two additional variables. We conclude that REVS is useful for analysing complex datasets, including those in ecology and environmental disciplines.     

Response histogram shapes and tuning curves: The predicted responses of several cortical cell types to drifting gratings stimuli

The responses to visual stimuli of simple cortical cells show linear spatial summation within and between their receptive field subunits. Complex cortical cells do not show this linearity. We analyzed the simulated responses to drifting sinusoidal grating stimuli of simple and of several types of complex cells. The complex cells, whose responses are seen to be half-wave rectified before pooling, have receptive fields consisting of two or more DOG (difference-of-Gaussians) shaped subunits. In both cases of stimulation by contrast-reversal gratings or drifting gratings, the cells' response as a function of spatial frequency is affected by the subunit distances 2 and the stimulation frequency . Furthermore, an increased number of subunits (a larger receptive field) yields a narrower peak tuning curve with decreased modulation depth for many of the spatial frequencies. The average and the peak response tuning curves are compared for the different receptive field types.     

Inequality constrained estimation of genetic parameters

Summary A method is presented for computing estimates of genetic parameters under linear inequality constraints such that solutions are within theoretical limits. The method produces biased estimators, yet a small scale numerical study, also presented, shows that the inequality constrained estimators have a small mean squared error of prediction than the best of unbiased estimators. The increase in efficiency of estimation is particularly useful for traits where heritability is near the boundary values of zero or one.