On the parameter estimation for diffusion models of single neuron's activities

 For the Ornstein-Uhlenbeck neuronal model a quantitative method is proposed for the estimation of the two parameters characterizing the unkown input process, namely the neuron’s mean input per unit time μ and the infinitesimal standard deviation per unit time σ. This method is based on the experimentally observed first- and second-order moments of interspike intervals. The dependence of the estimates μ^ and σ^ on the moments of the observed interspike intervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables are included in which the displayed values of μ^ and σ^ have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applied to interspike interval data recorded from neurons in the mesencephalic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage. Received: 10 October 1994/Accepted in revised form: 21 March 1995     

A stochastic model of multistable visual perception

 Multistability in vision is an intriguing phenomenon that is currently not well understood. In this paper, we present a new, stochastic model for multistable visual perception. It is based on results of time series analysis of experimental data, yielding evidence for it being a linear, stochastic process. This is the outcome of testing for unstable periodic orbits and comparing the correlation dimension of the data to that of white noise. In the model, all degrees of freedom but one can be determined by general knowledge, thus resulting in a high degree of parsimony. The remaining parameter is used to model the individual characteristics that vary between subjects. Fitting simulations to the experimental data proves the parameter to be in a physiologically highly plausible range. Received: 12 September 2000 / Accepted in revised form: 17 May 2001     

Marker-based adjustment of the additive relationship matrix for estimation of genetic parameters��an example using Eucalyptus cladocalyx

The effects of adjusting additive (numerator) relationship matrices (A) for inbreeding estimates taken from molecular markers were investigated using a small, model population of Eucalyptus cladocalyx. A number of individual-tree, mixed-models were compared, incorporating estimates of population- and family-level selfing and ancestral inbreeding applied either as average values to the entire population or as variable estimates for subpopulation and family groups. The consequences of ignoring inbreeding were inflated additive genetic variance estimates and underestimation of residual variance, with resulting inflation of heritability. We found models that correct for differential inbreeding at the subpopulation level give similar results to more complex ones including family-level estimates. Our analysis indicates that the commonly applied coefficient of relationship for first-generation eucalypt progeny of ρ = 1/2.5 appears to be quite suitable for correcting variance component and heritability estimates. However, if inbreeding is not specifically corrected for by adjustment of A, some minor rank changes of individual breeding values can occur, especially where levels of inbreeding vary among families, and some suboptimal selections and loss of genetic gain may ensue.     

Detection of sinusoidal gratings by pattern-specific detectors: further evidence for the correlation principle in human vision

 The detection of compound sinusoidal gratings of various spatial frequency separations and four different grating sizes has been studied using the summation-to-threshold paradigm. Contrast interrelation functions have been measured and spatial frequency tuning estimates, based on the slope of the contrast interrelation function at two definite points, were derived using the “negative gradient technique” proposed by Logvinenko [Logvinenko (1995) Biol Cybern 73: 547–552]. It is shown that compound grating detection can be modelled by assuming pattern-specific sensory mechanisms for each of the spatial frequency components, which adapt to the periodicity and the size of the stimulus but not to its envelope function. Further, it is shown that relative sensitivity for a given spatial frequency separation can be predicted with good accuracy by the correlation of the grating components used for superposition. It is suggested that the most plausible implementation of the pattern correlation principle in human grating detection is the “grating cell” model. Received: 10 March 2000 / Accepted in revised form: 4 December 2000     

Noise-induced transition in excitable neuron models

 We studied the influence of noisy stimulation on the Hodgkin-Huxley neuron model. Rather than examining the noise-related variability of the discharge times of the model – as has been done previously – our study focused on the effect of noise on the stationary distributions of the membrane potential and gating variables of the model. We observed that a gradual increase in the noise intensity did not result in a gradual change of the distributions. Instead, we could identify a critical intermediate noise range in which the shapes of the distributions underwent a drastic qualitative change. Namely, they moved from narrow unimodal Gaussian-like shapes associated with low noise intensities to ones that spread widely at large noise intensities. In particular, for the membrane potential and the sodium activation variable, the distributions changed from unimodal to bimodal. Thus, our investigation revealed a noise-induced transition in the Hodgkin-Huxley model. In order to further characterize this phenomenon, we considered a reduced one-dimensional model of an excitable system, namely the active rotator. For this model, our analysis indicated that the noise-induced transition is associated with a deterministic bifurcation of approximate equations governing the dynamics of the mean and variance of the state variable. Finally, we shed light on the possible functional importance of this noise-induced transition in neuronal coding by determining its effect on the spike timing precision in models of neuronal ensembles. Received: 19 September 2000 / Accepted in revised form: 4 March 2001     

Water temperature and mixing depth affect timing and magnitude of events during spring succession of the plankton

Individual-level diet variation can be easily quantified by gut-content analysis. However, because gut contents are a ‘snapshot’ of individuals’ feeding habits, such cross-sectional data can be subject to sampling error and lead one to overestimate levels of diet variation. In contrast, stable isotopes reflect an individual’s long-term diet, so isotope variation among individuals can be interpreted as diet variation. Nevertheless, population isotope variances alone cannot be directly compared among populations, because they depend on both the level of diet variation and the variance of prey isotope ratios. We developed a method to convert population isotope variances into a standardized index of individual specialization (WIC/TNW) that can be compared among populations, or to gut-content variation. We applied this method to diet and carbon isotope data of four species of frogs of the Brazilian savannah. Isotopes showed that gut contents provided a reliable measure of diet variation in three populations, but greatly overestimated diet variation in another population. Our method is sensitive to incomplete sampling of the prey and to among-individual variance in fractionation. Therefore, thorough sampling of prey and estimates of fractionation variance are desirable. Otherwise, the method is straightforward and provides a new tool for quantifying individual-level diet variation in natural populations that combines both gut-content and isotope data. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Wide-field, motion-sensitive neurons and matched filters for optic flow fields

 The receptive field organization of a class of visual interneurons in the fly brain (vertical system, or VS neurons) shows a striking similarity to certain self-motion-induced optic flow fields. The present study compares the measured motion sensitivities of the VS neurons (Krapp et al. 1998) to a matched filter model for optic flow fields generated by rotation or translation. The model minimizes the variance of the filter output caused by noise and distance variability between different scenes. To that end, prior knowledge about distance and self-motion statistics is incorporated in the form of a “world model”. We show that a special case of the matched filter model is able to predict the local motion sensitivities observed in some VS neurons. This suggests that their receptive field organization enables the VS neurons to maintain a consistent output when the same type of self-motion occurs in different situations. Received: 14 June 1999 / Accepted in revised form: 20 March 2000     

Exact sampling formulas for multi-type Galton-Watson processes

 Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution. It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions. Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction. Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25 Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA     

Annual pattern of micro- and mesozooplankton abundance and biomass in a subtropical estuary

The pattern of biomass and abundance of microzooplankton andmesozooplankton were studied over an annual cycle in the NuecesEstuary, Texas. Zooplankton samples and associated hydrographicdata were collected at four locations at biweekly intervalsfrom September 1987 through October 1988. This is a broad, shallowbay system with an average depth of 2.4 m. The concentrationof chlorophyll a in the surface waters averaged 7.4 µgl^–1with 85% passing through a 20 µ mesh. Microzooplankton(20–200 µ in length) were extremely abundant throughoutthis study. Abundances of ciliates (including both aloricateciliates and tintinnids) ranged from 5000 to 400 000 l^–,with a mean of 38 000 l^–1 of seawater over the entirecourse of the study. Mesozooplankton (200–2000 µmin length) abundance averaged 6100 m^–3 for samples collectedduring the day and 10 100 m^–3 for samples collected atnight. Mesozooplankton were dominated by Acartia tonsa whichmade up {small tilde}50% of the total. Biomass estimates formicrozooplankton (based on volume estimates) were often higherthan measured biomass of mesozooplankton. Given the shortergeneration times and higher metabolic rate of microzooplanktoncompared to mesozooplankton, microzooplankton should have agreater effect on the trophic dynamics of the Nueces Estuarythan mesozooplankton.     

Random median sampling to enhance the precision of population estimates

We describe the characteristics of a sampling procedure called random median sampling that was proposed to enhance the precision of population estimates. In performing random median sampling, we first select a sampling item at random from the sampling area. We roughly compare the abundance of individuals in the selected item with that of the adjacent two items in order to identify the item that has median abundance, i.e., the item that has the second largest abundance among the three items. We count the number of individuals of the item having the median abundance. This procedure is repeated n times in the sampling area (i = 1, 2, ..., n). Let m _i be the ith median abundance. The estimates of the mean abundance per sampling item and the variance of estimates are given by Σm _i /n and Σ(m _i –Σm _i /n)²/n(n – 1), respectively. This method is a local application of the median ranked set sampling that was proposed by Muttlak (J Appl Stat Sci 6:245–255, 1997). Random median sampling is effective when the correlation coefficient between adjacent items is small. If the correlation coefficient is close to zero, random median sampling reduces the variance of estimates to 45 or 32% of that in simple random sampling when the distribution follows a normal distribution or a Laplace distribution, respectively. The sample size required to achieve a given precision of estimate decreases accordingly. The effectiveness of random median sampling, however, is small if the correlation coefficient is large. The condition in which random median sampling is superior to simple random sampling is also discussed.     

Using sensory weighting to model the influence of canal,otolith and visual cues on spatial orientation and eye movements

 The sensory weighting model is a general model of sensory integration that consists of three processing layers. First, each sensor provides the central nervous system (CNS) with information regarding a specific physical variable. Due to sensor dynamics, this measure is only reliable for the frequency range over which the sensor is accurate. Therefore, we hypothesize that the CNS improves on the reliability of the individual sensor outside this frequency range by using information from other sensors, a process referred to as “frequency completion.” Frequency completion uses internal models of sensory dynamics. This “improved” sensory signal is designated as the “sensory estimate” of the physical variable. Second, before being combined, information with different physical meanings is first transformed into a common representation; sensory estimates are converted to intermediate estimates. This conversion uses internal models of body dynamics and physical relationships. Third, several sensory systems may provide information about the same physical variable (e.g., semicircular canals and vision both measure self-rotation). Therefore, we hypothesize that the “central estimate” of a physical variable is computed as a weighted sum of all available intermediate estimates of this physical variable, a process referred to as “multicue weighted averaging.” The resulting central estimate is fed back to the first two layers. The sensory weighting model is applied to three-dimensional (3D) visual–vestibular interactions and their associated eye movements and perceptual responses. The model inputs are 3D angular and translational stimuli. The sensory inputs are the 3D sensory signals coming from the semicircular canals, otolith organs, and the visual system. The angular and translational components of visual movement are assumed to be available as separate stimuli measured by the visual system using retinal slip and image deformation. In addition, both tonic (“regular”) and phasic (“irregular”) otolithic afferents are implemented. Whereas neither tonic nor phasic otolithic afferents distinguish gravity from linear acceleration, the model uses tonic afferents to estimate gravity and phasic afferents to estimate linear acceleration. The model outputs are the internal estimates of physical motion variables and 3D slow-phase eye movements. The model also includes a smooth pursuit module. The model matches eye responses and perceptual effects measured during various motion paradigms in darkness (e.g., centered and eccentric yaw rotation about an earth-vertical axis, yaw rotation about an earth-horizontal axis) and with visual cues (e.g., stabilized visual stimulation or optokinetic stimulation). Received: 20 September 2000 / Accepted in revised form: 28 September 2001     

Chaos and population disappearances in simple ecological models

A class of truncated unimodal discrete-time single species models for which low or high densities result in extinction in the following generation are considered. A classification of the dynamics of these maps into five types is proven: (i) extinction in finite time for all initial densities, (ii) semistability in which all orbits tend toward the origin or a semi-stable fixed point, (iii) bistability for which the origin and an interval bounded away from the origin are attracting, (iv) chaotic semistability in which there is an interval of chaotic dynamics whose compliment lies in the origin’s basin of attraction and (v) essential extinction in which almost every (but not every) initial population density leads to extinction in finite time. Applying these results to the Logistic, Ricker and generalized Beverton-Holt maps with constant harvesting rates, two birfurcations are shown to lead to sudden population disappearances: a saddle node bifurcation corresponding to a transition from bistability to extinction and a chaotic blue sky catastrophe corresponding to a transition from bistability to essential extinction. Received: 14 February 2000 / Revised version: 15 August 2000 / Published online: 16 February 2001     

Determination of the precision of spike timing in the visual cortex of anaesthetised cats

 Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by chance production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4–1.4 ms (a result evidently at variance with a simple ‘integrate and fire’ model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the ‘spontaneous’ and ‘evoked’ responses. Received: 3 April 1995/Accepted in revised form: 11 July 1995     

Formation of unilamellar vesicles by repetitive freeze-thaw cycles: characterization by electron microscopy and 31P-nuclear magnetic resonance

 It has been reported that repetitive freeze-thaw cycles of aqueous suspensions of dioleoylphosphatidylcholine form vesicles with a diameter smaller than 200 nm. We have applied the same treatment to a series of phospholipid suspensions with particular emphasis on dioleoylphosphatidylcholine/dioleoylphosphatidic acid (DOPC/DOPA) mixtures. Freeze-fracture electron microscopy revealed that these unsaturated lipids form unilamellar vesicles after 10 cycles of freeze-thawing. Both electron microscopy and broad-band ³¹P NMR spectra indicated a disparity of the vesicle sizes with a highest frequency for small unilamellar vesicles (diameters ≤30 nm) and a population of larger vesicles with a frequency decreasing exponentially as the diameter increases. From ³¹P NMR investigations we inferred that the average diameter of DOPC/DOPA vesicles calculated on the basis of an exponential size distribution was of the order of 100 nm after 10 freeze-thaw cycles and only 60 nm after 50 cycles. Fragmentation by repeated freeze-thawing does not have the same efficiency for all lipid mixtures. As found already by others, fragmentation into small vesicles requires the presence of salt and does not take place in pure water. Repetitive freeze-thawing is also efficient to fragment large unilamellar vesicles obtained by filtration. If applied to sonicated DOPC vesicles, freeze-thawing treatment causes fusion of sonicated unilamellar vesicles into larger vesicles only in pure water. These experiments show the usefulness of NMR as a complementary technique to electron microscopy for size determination of lipid vesicles. The applicability of the freeze-thaw technique to different lipid mixtures confirms that this procedure is a simple way to obtain unilamellar vesicles. Received: 2 September 1999 / Revised version: 27 February 2000 / Accepted: 27 February 2000     

Bioremediation of polychlorinated biphenyl-contaminated soil using carvone and surfactant-grown bacteria

Partial bioremediation of polychlorinated biphenyl (PCB)-contaminated soil was achieved by repeated applications of PCB-degrading bacteria and a surfactant applied 34 times over an 18-week period. Two bacterial species, Arthrobacter sp. strain B1B and Ralstonia eutrophus H850, were induced for PCB degradation by carvone and salicylic acid, respectively, and were complementary for the removal of different PCB congeners. A variety of application strategies was examined utilizing a surfactant, sorbitan trioleate, which served both as a carbon substrate for the inoculum and as a detergent for the mobilization of PCBs. In soil containing 100 μg Aroclor 1242 g⁻¹ soil, bioaugmentation resulted in 55–59% PCB removal after 34 applications. However, most PCB removal occurred within the first 9 weeks. In contrast, repeated addition of surfactant and carvone to non-inoculated soil resulted in 30–36% PCB removal by the indigenous soil bacteria. The results suggest that bioaugmentation with surfactant-grown, carvone-induced, PCB-degrading bacteria may provide an effective treatment for partial decontamination of PCB-contaminated soils. Received: 9 March 2000 / Received revision: 27 June 2000 / Accepted: 16 July 2000     

Genetics of tassel branch number in maize and its implications for a selection program for small tassel size

Summary Tassel branch numbers of six crosses of maize (Zea mays L.) were analyzed to determine inheritance of this trait. Generation mean analyses were used to estimate genetic effects, and additive and nonadditive components of variance were calculated and evaluated for bias due to linkage. Both narrow-sense and broad-sense heritabilities were estimated. Additive genetic variance estimates were significant in five of the six crosses, whereas estimates of variance due to nonadditive components were significant in only three crosses. Additionally, estimates of additive variance components usually were larger than corresponding nonadditive components. There was no evidence for linkage bias in these estimates. Estimates of additive genetic effects were significant in four of six crosses, but significant dominance, additive × additive and additive × dominance effects also were detected. Additive, dominance, and epistatic gene action, therefore, all influenced the inheritance of tassel branch number, but additive gene action was most important. Both narrow-sense and broadsense heritability estimates were larger than those reported for other physiological traits of maize and corroborated conclusions concerning the importance of additive gene action inferred from analyses of genetic effects and variances. We concluded that selection for smalltasseled inbreds could be accomplished most easily through a mass-selection and/or pedigree-selection system. Production of a small-tasseled hybrid would require crossing of two small-tasseled inbreds. We proposed two genetic models to explain unexpected results obtained for two crosses. One model involved five interacting loci and the other employed two loci displaying only additive and additive × additive gene action.Journal Paper No. J-9231 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa 50011. Project No. 2152     

The prediction of EEG signals using a feedback-structured adaptive rational function filter

 In this article, we present a feedback-structured adaptive rational function filter based on a recursive modified Gram-Schmidt algorithm and apply it to the prediction of an EEG signal that has nonlinear and nonstationary characteristics. For the evaluation of the prediction performance, the proposed filter is compared with other methods, where a single-step prediction and a multi-step prediction are considered for a short-term prediction, and the prediction performance is assessed in normalized mean square error. The experimental results show that the proposed filter shows better performance than other methods considered for the short-term prediction of EEG signals. Received: 22 September 1998 / Accepted in revised form: 29 February 2000     

Existence of traveling wave solutions in a diffusive predator-prey model

 We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R ⁴ and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R ⁴ . The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem. Received: 25 May 2001 / Revised version: 5 August 2002 / Published online: 19 November 2002 RID="*" ID="*" Research was supported by the National Natural Science Foundations (NNSF) of China. RID="*" ID="*" Research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. On leave from the Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada. Mathematics Subject Classification (2000): 34C35, 35K57 Key words or phrases: Traveling wave solution – Wazewski set – Shooting argument – Hopf bifurcation Acknowledgements. We would like to thank the two referees for their careful reading and helpful comments.     

Topographic analysis of dimension estimates of EEG and filtered rhythms in epileptic patients with complex partial seizures

Nonlinear dynamic properties were analyzed on the EEG and filtered rhythms recorded from healthy subjects and epileptic patients with complex partial seizures. Estimates of correlation dimensions of control EEG, interictal EEG and ictal EEG were calculated. The values were demonstrated on topograms. The delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz) and gamma (30–40 Hz) components were obtained and considered as signals from the cortex. Corresponding surrogate data was produced. Firstly, the influence of sampling parameters on the calculation was tested. The dimension estimates of the signals from the frontal, temporal, parietal and occipital regions were computed and compared with the results of surrogate data. In the control subjects, the estimates between the EEG and surrogate data did not differ (P > 0.05). The interictal EEG from the frontal region and occipital region, as well as its theta component from the frontal region, and temporal region, showed obviously low dimensions (P < 0.01). The ictal EEG exhibited significantly low-dimension estimates across the scalp. All filtered rhythms from the temporal region yielded lower results than those of the surrogate data (P < 0.01). The dimension estimates of the EEG and filtered components markedly changed when the neurological state varied. For each neurological state, the dimension estimates were not uniform among the EEG and frequency components. The signal with a different frequency range and in a different neurological state showed a different dimension estimate. Furthermore, the theta and alpha components demonstrated the same estimates not only within each neurological state, but also among the different states. These results indicate that the theta and alpha components may be caused by similar dynamic processes. We conclude that the brain function underlying the ictal EEG has a simple mechanism. Several heterogeneous dynamic systems play important roles in the generation of EEG. Received: 10 December 1999 / Accepted in revised form: 8 May 2000     

Clustered restricted mean survival time regression

For multicenter randomized trials or multilevel observational studies, the Cox regression model has long been the primary approach to study the effects of covariates on time-to-event outcomes. A critical assumption of the Cox model is the proportionality of the hazard functions for modeled covariates, violations of which can result in ambiguous interpretations of the hazard ratio estimates. To address this issue, the restricted mean survival time (RMST), defined as the mean survival time up to a fixed time in a target population, has been recommended as a model-free target parameter. In this article, we generalize the RMST regression model to clustered data by directly modeling the RMST as a continuous function of restriction times with covariates while properly accounting for within-cluster correlations to achieve valid inference. The proposed method estimates regression coefficients via weighted generalized estimating equations, coupled with a cluster-robust sandwich variance estimator to achieve asymptotically valid inference with a sufficient number of clusters. In small-sample scenarios where a limited number of clusters are available, however, the proposed sandwich variance estimator can exhibit negative bias in capturing the variability of regression coefficient estimates. To overcome this limitation, we further propose and examine bias-corrected sandwich variance estimators to reduce the negative bias of the cluster-robust sandwich variance estimator. We study the finite-sample operating characteristics of proposed methods through simulations and reanalyze two multicenter randomized trials.