Progress 10/01/98 to 09/30/06

Outputs
Progress was made in several areas during this period. One project involved the spectral analysis of sequence variability in Basic-Helix-Loop-Helix (bHLH) protein domains. This was joint work with Drs. Bill Atchley and Zhi Wang. A manuscript on this work has been accepted for publication pending minor revisions. Boltzmann-Shannon entropy profiles were used to represent the variation in alphabetic amino acids.Factor score profiles were used to represent the variance in the underlying physiochemical attributes such as polarity/hydrophobicity, secondary structure, molecular volume, codon composition and electrostatic charge. THe spectral analysis results indicate that the periodicity of the bHLH entropy profile corresponds well with its alpha helix secondary structure, namely 3.6 amino acids per turn of the helix. Several of the physiochemical properties also had a close correspondence to the 3.6 amino acid period. The second project involved the selection of compunds for a toxicological study of skin adsorption in pigs. Target compounds were selected from a large candidiate population based by trying several transformations of the chenical and biophysical properties of the compounds. The equidistant sampling of the first four principal components seems to work the best among the methods examined. Further work with Dr. Budsaba related to mixture compunds was also initiated.

Impacts
The description of the variability pattern and the underlying physiochemical attributes of proteins are important in molecular evolutionary research. The periodicity analysis of nucleic acids and prpteins by our methods allow one to obtain meaningful information about their structure function and evolution. The complex demodulation method is a promising approach for the detection of the boundary of functional regions of protein sequences. This approach is also been used a component in multivariate sequence analysis projects. In the compound selection project, the sampling procedure in the principal components space has potential use for experimental design in other toxicological studies.

Publications

• No publications reported this period

Progress 10/01/04 to 09/30/05

Outputs
Progress was made in several areas during this period. One project involved the spectral analysis of sequence variability in Basic-Helix-Loop-Helix (bHLH) protein domains. This was joint work with Drs. Bill Atchley and Zhi Wang. Boltzmann-Shannon entropy profiles were used to represent the variation in alphabetic amino acids.Factor score profiles were used to represent the variance in the underlying physiochemical attributes such as polarity/hydrophobicity, secondary structure, molecular volume, codon composition and electrostatic charge. THe spectral analysis results indicate that the periodicity of the bHLH entropy profile corresponds well with its alpha helix secondary structure, namely 3.6 amino acids per turn of the helix. Several of the physiochemical properties also had a close correspondence to the 3.6 amino acid period. The second project involved the selection of compunds for a toxicological study of skin adsorption in pigs. Target compounds were selected from a large candidiate population based by trying several transformations of the chenical and biophysical properties of the compounds. The equidistant sampling of the first four principal components seems to work the best among the methods examined.

Impacts
The description of the variability pattern and the underlying physiochemical attributes of proteins are important in molecular evolutionary research. The periodicity analysis of nucleic acids and prpteins by our methods allow one to obtain meaningful information about their structure function and evolution. The complex demodulation method is a promising approach for the detection of the boundary of functional regions of protein sequences. In the compound selection project, the sampling procedure in the principal components space has potential use for experimental design in other toxicological studies.

Publications

• No publications reported this period

Progress 10/01/03 to 09/30/04

Outputs
Progress was made in several areas this year. Testing whether random effects are needed in a statistical model of repeated measurement response data is a concern in many biological areas. The application investigated was in cutaneous pharmacology and toxicology, but the methodology is applicable to many other areas as well. To test whether random effects are needed in a nonlinear mixed effects model, we proposed a test statistic, approximately an F random variable, from the fixed parameter approach which compares the residual sum of squares from the full model and the reduced model. The difference of exponentials model is commonly used in cutaneous pharmacology studies so we examined pig skin transport data and did simulations to examine the behaviour of our procedure. The empirical size of the test is slightly higher than the nominal alpha level, however the test offers very good power for detection. In another area, further applications of our previous work on compass plots to other toxicological applications were examined. Further analysis of chemical mixtures in dermal skin adsorption was done to try to compare effects in skin flaps to a newly developed experimental procedure using membrane coated fibers as well as diffusion cells. Statistically this can be viewed as a multivariate calibration problem. The underlying hypothesis is that chemical absorption and distribution via passive diffusion in a biological system are governed by the relative molecular interaction strengths of the chemicals within the biological membrane and the overlying medium. These strengths are detectable by using a set of probe compounds in membrane coated fibers and an adequately characterized multiple membrane system in vitro.

Impacts
Dermal risk assessment of individual chemicals is based on the knowledge of the permeability characteristics of specific chemicals through skin, with extrapolations being made to potential absorption in humans. The ongoing experimental and statistical studies using the combination of animal dermal absorption with chemical mixtures and membrane coated fibers in vitro will aid the appropriate risk determination for the more realistic situation of exposure to chemical mixtures.

Publications

• Budsaba, K., Smith, C.E. 2004. Testing the need for a random effects model in a two compartment model. Thammasat Int. J. Sc. Tech. 9: 1-9.

Progress 10/01/02 to 09/30/03

Outputs
Progress was made in several areas. The mathematical foundations of the methods used for the stochastic ordering of level crossings and first passage times for stochastic processes of the diffusion type were examined and a manuscript submitted with Dr. Sacerdote of Univ. of Torino. Applications of this methodology for studies in models of firings of single neurons was published previously with Dr. Sacerdote. A review article with Drs. Doi and Inoue on the essential nonlinear dynamics and signal transfer characteristics of neurons was prepared including an introduction to dynamical system theory and bifurcations, as well as the responses of simple neural models to stochastic inputs and stochastic phase locking.

Impacts
The stochastic ordering methology provides another method for sensitivity analysis in neural, ecological and population growth models. The review article should be useful to other areas of computational biology as well such as stochastic models of gene regulation.

Publications

• No publications reported this period

Progress 10/01/01 to 09/30/02

Outputs
Progress was made in several areas this year. The jet fuel JP-8 causes more dermal problems upon exposure than comerical jet fuel Jet-A. A factorial study to examine the effects of the performance additives, DIEGME, 8Q21 and Stadis450, was performed on skin flaps. Various combinations of these 3 performance additives in JP-8 can potentially alter the dermal disposition of aromatic and aliphatic fuel components in skin. Products of two-factor interactions were not predictable from single-factor exposures. In another study on skin absorption methyl salicylate was used to simulate the exposure to a very toxic compund sulfur mustard. Flux profiles, area under the curve, peak flux and time to peak flux were determined for pig skin flaps and support the use of methyl salicylate as a dermal simulant for sulfur mustard exposure. Finally preliminary studies were done on additional biological applications of stochastic orderings for first passage times of diffusion process models.

Impacts
The use of nontoxic compounds to mimic the percutaneous absorption of toxic compounds for labatory studies provides a safer method for the experimental studies on skin to design more effective protective suits and barriers. Likewise the decompositions of JP-8 into its components and a factorial design on their dermal diaposition provides a model for analyzing other chemical mixtures.

Publications

• Baynes, R.E., Brooks, J.D., Budsaba, K.,Smith, C.E., and Riviere, J.E. 2001. Mixture effects of JP-8 dditives on the dermal disposition of jet fuel components. Toxicology and Applied Pharmacology 175: 269-281.
• Riviere, J.E., Smith, C.E., Budsaba, K., Brooks, J.D., Olajos, E.J., Salem, H., and Monteiro-Riviere, N.A. 2001. Use of methyl salicylate as a simulant to predict the percutaneous absorption of sulfur mustard. J. Applied Toxicology 21:91-99.

Progress 10/01/00 to 09/30/01

Outputs
Progress was made in several areas this year. Further progress was made on stochastic ordering of distributions resulting from first passage times of neural diffusion process models. A new graphical procedure, compass plots was developed to examine significant inetractions in multifactor experiments. An application in skin adsorption for pigs was examined as a model for adsorption in human forearm. Finally a sensitivity and variabilty analyses was performed in a physiologically based pharmacokinetic model for the toxicologically relevant compound, methyl tert-butyl ether.

Impacts
The compass plot approach should be useful in other areas besides tocicology for visually assessing statistically significant interactions in multifactor experiments. The sensitivity and variability analyses can be used in other pharmacokinetic experiments as well. The stochastic ordering approach to first passage times for diffusion processes is applicable in a variety of situations such as tumor growth and ecology models.

Publications

• Budsaba, K., Smith, C.E. and Riviere, J.E. 2000. Compass plots: A combination of star plot and analysis of means to visualize significant interactions in complex toxicolgy studies. Toxicology Methods 10:313-332.
• Licata, A.M., Dekant, W., Smith, C.E. and Borghoff, S.J. 2001. A physiologically based pharmacokinetic model for methyl tert-butyl ether in humans: implementing sensitivity and variability analyses. Toxicological sciences 62:191-204.
• Sacerdote, L. and Smith, C.E. 2000. New parameter relationships determined via stochastic ordering for spike activity in a reversal potential neural model. Biosystems 58:59-65.
• Sacerdote, L. and Smith, C.E. 2000. A qualitative comparison of some diffusion models for neural activity via stochastic ordering. Biological Cybernetics 83:543-551.

Progress 10/01/99 to 09/30/00

Outputs
Progress was made in several areas this year. The first pasage time problem for neural diffusion models was examined via the method of stochastic orderings of distributions. This was applied to the Ornstein Unhlenbeck model, Feller process model and also to a reversal potential model. Using the comparision theorem for diffusion processes, one can use these results to say which sets of parameter will produce faster firing times in one model versus the other. The method also allows one to say which function or invariant will produce identical firing time distributions. A spatial temporal version of the neural firing problem and a theorem about stable encoding in networks with lateral inhibition appeared during this year. Also another application area that produced published results was the use of compartmental model of pig skin to compare the absorption of various jet fuels in terms of their absorption.

Impacts
This research provides new graphical methods and analysis methods for handling the transport and disposition of chemical mixtures in the skin.

Publications

• Riviere, J.E., Brooks, J.B., Monterio-Riviere, N.A., Budsaba, K.,Smith, C.E. 1999. Dermal absorption and distribution of topically dosed jet fuels Jet-A, JP-8, and JP8(100). Tox. Appl. Pharm. 160:60-75.
• Gutkin, B. S., Smith, C.E. 2000. Noise reduction and stable encoding of spatial structure by a lateral inhibition recurrent neural network". Biological Cybernetics 82:469-475.

Progress 10/01/98 to 09/30/99

Outputs
Progress was made in several areas this year. The problem of ordering the first passage time distributions was addressed in several publications. Using the Skorohod comaprison theorem, the relationship among the biophysical parameters in several commonly used neural models (Ornstein-Uhlenbeck and Feller process) was made clearer in terms of their effects on the shape of the distribution as well as the mean and variance. The passage time and disposition of chemical mixtures through the pig skin preparation was examined for comerical and military jet fuels. A new graphical method for presenting the results of ANOVA analysis, compass plots, was developed for comparing the effects of different design factors in different skin layers. The role of noise on stable encoding in model neural networks by a lateral inhibition network was examined by simulation and analytical results for the mean and covariance. The specificity of receptor types in a branching neuron was examined for hair cell inputs and suggested that the slower more regularly discharging receptor needed to have a high degree of stimulus specificity.

Impacts
This research provides new graphical methods and analysis methods for handling the transport and disposition of chemical mixtures in the skin.

Publications

• RIVIERE, J. E., BROOKS, J.D., MONTEIRO-RIVIERE, N. A., BUDSABA, K., SMITH, C. E. (1999). Dermal Absorption and Distribution of Topically Dosed Jet Fuels Jet-A, JP-8, and JP-8(100). Toxicology and Applied Pharmacology 160:60-75
• SACERDOTE, L., SMITH, C.E. (1999). A qualitative comparison of some diffusion models for neural activity via stochastic ordering. Biological Cybernetics, in press.
• GUTKIN, B. S. and SMITH, C.E. (1999). Noise reduction and stable encoding of spatial structure by a lateral inhibition recurrent neural network. Biological Cybernetics (in press).
• BUDSABA, K., SMITH, C.E., RIVIERE, J.E. (1999). Compass Plots: A Joint Graphical Representation of the Factorial Design, Treatment Means and Fitted Effects.Submitted to Journal of Computational and Graphical Statistics.

Progress 01/01/98 to 12/31/98

Outputs
The past year has produced results in several areas. The effects of membrane noise on the responses to a model neuron subject to periodic stimulation were examined with regard to the phaselocking behaviour of the output spike train. Another area with neurophysiological applications was further refinement of the Laguerre series density approximation. The region in the parameter space where the approximation will produce a nonnegative approximation for the density for the three and four term Laguerre series was determined. In this region maximum likelihood estimates for the parameters were determined numerically and a Hessian based method determined approximate confidence regions. Both simulations and single unit neurophysiological data were used to test the methodology.

Impacts
(N/A)

Publications

• DOI, S., INOUE, J., SATO, S., Smith, C. E. 1998. Response characteristics of a simplified neuron model to a periodic input in presence of membrane noise. Chapter 16 in Modelling in the Neurosciecnes: From Ionic Channels to Neural Networks, Ed. Roman Poznanski, Gordon and Breach Science Publishers.

Progress 01/01/97 to 12/31/97

Outputs
The past year has produced results in several areas. One continuing area was the use of Laguerre series density approximations to model the interspike interval histograms of several types of neurons: auditory, olfactory, and sleep waking cycle neurons. Conditions for the positivity of the density approximation were determined and used to implement numerical maximum likelihood estimation for the two, three and four parameter cases. A likelihood ratio test was used to distinguish among the number of parameters. A Laguerre series was a better fit by this criterion for the auditory and sleep waking cycle neurons but not for the first order olfactory neurons. Laguerre series approximations were also used to extend our previous results for the residence time distributions in a stochastic model for circulatory transport to a larger class of cycle time distributions.

Impacts
(N/A)

Publications

• SMITH, C.E., LANSKY P. and LUNG T.H. 1997. Cycle Time and Residence Time Density Approximations in a Stochastic Model for Circulatory Transport. Bulletin of Mathematical Biology 59:1-22.

Progress 01/01/96 to 12/30/96

Outputs
The past year has produced results in several areas. One continuing area was thefurther examination of compartmental models of skin transport. Using a dominant eigenvalues approach, the number of parameters in the model could be reduced considerably and allowed sensitivity analysis in terms of the original biological rate constants. This approach will help to pinpoint the biological source of variability in models and provide a more tractable framework for the analysis of mixtures of compounds applied to the skin. Another area was the use of Laguerre series to model the interspike interval histograms of several types of neurons: auditory, olfactory, and sleep-waking cycle neurons. Conditions for the positivity of the density approximation were determined and two parameter estimation procedures were tested. Laguerre series approximations were also used to model the residence time distributions in a stochastic model for circulatory transport.

Impacts
(N/A)

Publications

• LUNG, T. H. and SMITH, C. E. 1996. Moment plots for positively skewed distributions:confidence contours, density approximations and biological applications. Proceedings of the Biometric Section, American Statistical Association, pp. 189-194 SMITH, C.
• E., WILLIAMS, P. L. and RIVIERE, J. E. 1996. Compartmental models of skin transport: dominant eigenvalues approach. Proceedings of the Biometric Section, American Statistical Association, pp. 449-454.

Progress 01/01/95 to 12/30/95

Outputs
The past year has produced results in several areas. One continuing area was the further examination of diagnostic methods for characterizing serial dependence in neural pont process data. The publication with C. J. Liu presented the use of conditional interval plots to determine negative serial dependence due to changes in location, scale or shape of the conditional distributions. This method was illustrated on both auditory nerve data at three stimulus levels and on stimulated data. The publication with Gutkin provides a framework for analyzing the variability seen in labeled glucose measurements of neural activity in somatosensory cortex. The practical implication of both studies is that variability in single neuron and in population studies can be analyzed through statistical modeling and the results may help pinpoint biophysical sources of the variability. Other areas of research include: the development of a dominant eigenvalue approach for skin transport compartment models, the use of Laguerre series with linear combinations of order statistics to model interspike interval histograms of neurons, and approximation methods for bursting behavior in pancreatic Beta cells.

Impacts
(N/A)

Publications

• GUTKIN, B. S. and SMITH, C. E. 1995. On the stochastic stability of a neural network model of somatosensory information processing. The Neurobiology of Computation. pp. 221-226. Ed. J. M. Bower. Kluwer Academic Publishers.
• SMITH, C.E. and LIU, C.J. 1995. Serial dependency in neural spike trains. J. Society of Instrument and Control Engineers. 34:901-906.

Progress 01/01/94 to 12/30/94

Outputs
The past year has produced results in several areas. Preliminary results on applying the stochastic approximation methods used on neural firing times to the timing of bursts in pancreatic beta cells indicate that the times between burst onsets are well approximated by an iterative conditional probability analysis. Simulations show that this method was better than an inverse Gaussian distribution method and a Jacobian based method. The rapid spiking portion of the response requires a negative binomial approximation since it corresponds to the fast manifold in the phase plane. Another project examined the role of rate independent serial dependence in neural spike trains. In addition to reducing the variance of the short time estimate of the mean, a form of temporal scaling is also required. Finally the use of L-moments to represent neural spike train densities has continued through simulation studies. Confidence contours show the order statistics approach has better sampling properties than the Pearson plot method examined previously.

Impacts
(N/A)

Publications

• SMITH, C. E. and LANSKY, P. 1994. A reliability application of a mixture of inverse Gaussian distributions. Applied Stochastic Models and Data Analysis. 10:61-69.
• LANSKA, V., LANSKY, P., and SMITH, C.E. 1994. Synaptic transmission in a diffusion model for neural activity. J. Theoretical Biology. 166:393-406.

Progress 01/01/93 to 12/30/93

Outputs
The past year has produced results in several areas. One continuing area was thefurther refinement of diagnostic methods for examining serial dependence in neural point process data. The conditional interval plots used previously were based on binning the conditioning interspike intervals into successive five percentile bins. This method can obscure synchronization or phase locking in auditory nerve spike train data in the 1 to 5 kHz range. Equal time binwidths were used to redo previous analysis of both auditory nerve and model simulation data. Small periodicities were revealed at the higher stimulus levels in the experimental data. The practical implication is that the equal binning method should first be applied to the data and sample size weighted regressions be used on the conditional moment plots. If no evidence of periodicities are found in the residuals, then our previous methodolgy can be applied. Other areas of research include the development of a bivariate inverse Gaussian distribution simulation method that produces marginal distributions that coincide with the standard univariate method and the use of neural firing time approximation methods for bursting behaviour in pancreatic Beta cells.

Impacts
(N/A)

Publications

• BAILEY, B., LIU, C.J., and SMITH, C.E. 1993. Conditional plots for nonrenewal neural spike train data. 1992 Proceedings of the Section on Statistical Education, American Stat. Assoc. pp. 224-229.
• LANSKY, P. and SMITH, C.E. 1992. A one-dimensional neuronal diffusion model with reversal potentials. J. Mathematical and Physical Sciences 25:472-477.

Progress 01/01/92 to 12/30/92

Outputs
The fifth year has produced results in several areas. One major area was the further development of diagnostic methods for examining serial dependence in neural point process data. The methodology was applied to simulations of a stochastic afterhyperpolarization model. The procedure produced an estimation of the intensity function of the underlying process, even though the amount of negative serial dependence increased with increasing firing rate. Practically the work suggests a protocol of increasing stimulus levels to determine the presence of underlying cumulative recovery mechanisms in the nerve. For experimental data from cat auditory nerve, graphical methods for smoothing joint interval data along with normalizing transformations provide a method for detecting 'phase locking' or synchrony that appears to be more sensitive than the Fourier analysis methods currently used by neurophysiologists. Said another way, the firing pattern of the nerve in response to a single tone has sinusoidal modulations in its temporal pattern at a lower sound level than that required to produce an increase in the mean firing rate. Other areas of research include: the development of other models for afterhyperpolarization via simulations and approximation methods; Laguerre series approximations to probability densities for pharmacokinetic residence time data.

Impacts
(N/A)

Publications

• LANSKY, P., MUSILA, M. and SMITH, C.E. 1992. Effects of afterhyperpolarization on neuronal firing. Biosystems 27:25-38.
• SMITH, C.E. 1992. A note on neuronal firing and input variability. J. Theor. Biology 154:271-275.
• SMITH, C.E. 1992. A heuristic approach to stochastic models of single neurons. Single Neuron Computation, edited by T. McKenna, J. Davis, S. F. Zornetzer. Boston, MA., Academic Press, Inc. pp.561-588.

Progress 01/01/91 to 12/30/91

Outputs
The fourth year has produced results in several areas. One major area was the development of diagnostic methods for examining serial dependence in neural point process data. The work concentrated on graphical and statistical methods for determining the presence or absence of serial dependence in stationary spike trains, and the order and type of the dependence. The successive steps of characterizing the dependence lead to a resultant renewal process, and is called a whitening procedure somewhat analogous to those in AR time series. The technique was applied to simulated neural model data and to data from cat auditory nerve in response to tonal and harmonic stimuli. The whitening procedure alters the location, scale and shape parameters of the conditional interspike interval distribution. One practical use is the prediction of nonstationary responses from a characterization of the serial dependence in the background discharge. The motivation is that a negative serial dependence between interspike intervals may reflect an underlying biophysical mechanism, e.g., cumulative afterhyperpolarization, as well as alter the cells information coding capability. Another major effort was on Laguerre series approximations to probability densities used to model neural interspike intervals and pharmacokinetic data.

Impacts
(N/A)

Publications

• LIU, C.J. 1991. Parameter estimation of continuous-time point processes: serial dependence and neural applications. Ph.D. Thesis. North Carolina State Univ., Raleigh, NC, 186p.
• SMITH, C.E. 1991. A Laguerre series approximation to the probability density of the first passage time of the Ornstein Uhlenbeck process. Proceedings of the 1991 International Conference on Noise in Physical Systems and.

Progress 01/01/90 to 12/30/90

Outputs
The third year has produced results in several areas. A critical review was madeof first passage time problems resulting from stochastic neural models of the spike initiation site. The review focused on one compartment diffusion models for the subthreshold membrane potential. New results and generalizations of the Wiener process and Ornstein Uhlenbeck models were summarized along with remarks about their biophysical interpretation. Limitations of these models were addressed by using a nonconstant infinitesimal variance. The form of this nonlinearity can represent several physiologically relevant processes such as reversal potentials, nonlinear summation of postsynaptic potentials, and shunting inhibition. The practical benefit of this review was a collection of statistical and modeling results from a range of sources (biological, engineering, probability and statistics) in a cogent, physiologically oriented summary. Progress was also made on the properties of the first passage time for the Ornstein Uhlenbeck process with a nonzero initial condition. Approximations and moment properties were examined and contrasted to the case with a zero initial condition. One practical result is that a postspike hyperpolarization produces a greater positive skew for a given coefficient of variation in the interspike intervals.

Impacts
(N/A)

Publications

• LANSKY, P., SMITH, C. E., and RICCIARDI, L. M. 1990. One-dimensional stochastic diffusion models of neuronal activity and related first passage time problems. Trends in Biological Cybernetics 1:153-162.

Progress 01/01/89 to 12/30/89

Outputs
The second year has produced results in several areas. Approximation methods forthe first passage time of the Ornstein Uhlenbeck process, a continuous time analog of an AR1 time series model, were examined in the limit of small noise and low thresholds. A generalization of Stein's method by including higher order moments compares well with previously published results that used singular perturbation theory and matched asymptotic expansions. The mean passage time is slightly overestimated, while the first-order term in the variance is identical in the two methods. A lower bound for the mean passage time was obtained from an approximation by a Wiener process with linear drift. The practical result is that these bounds are simple to calculate and can be used as a prelude to the more detailed analysis of perturbation theory. More complicated models for the nerve membrane and the related first passage time problem were critically surveyed in an invited review article with Drs. Lansky and Ricciardi. The approximation methods mentioned above are useful in these more realistic models as well. Finally, some progress has been made in analysis of nonrenewal neural point process data. The lack of dependence between neural events can be characterized by regressions on conditional mean and median plots of the times between events. The practical result is that stationary data from nonstimulus conditions can be used to predict some statistics of nonstationary stimulus driven point process data.

Impacts
(N/A)

Publications

• LANSKY, P. and SMITH, C. E. 1989. The effect of a random initial value in neural first passage time models. Mathematical Biosciences 93:191-215.

Progress 04/01/88 to 12/30/88

Outputs
The first year has concentrated on the effects of a random initial condition on first passage time distributions of neural firing time models. In collaboration with Dr. Lansky, a random initial value was used in three models: A singular first order process, Wiener process with linear drift, and the Ornstein Uhlenbeck process. The results show that several commonly observed distributions of interspike intervals can be produced by the first model with the proper choice of initial condition. Some parameter estimation procedures were developed for the second model which has a mixture of inverse Gaussian distributions for the interspike intervals. The third model with a truncated normal as the initial condition retains several key features of the fixed initial case, namely a coefficient of variation (CV) greater than one, and approaches an exponential distribution as the threshold becomes large. The practical result is that the effect of a random, vs fixed, initial condition is most pronounced at high firing rates of the neuron. The other main results were on calculating standard errors for several moment relationships commonly plotted for interspike intervals such as skewness vs CV or excess vs skewness. The experimentally important result is that a weighted least squares fit should be used for summarizing these plots as the errors are quite heteroscedastic.

Impacts
(N/A)

Publications

• LANSKY, P. and SMITH, C.E. 1988. First passage time problem etc. Proceedings of Fourth Conference of the International Organization of Psychophysiology, Prague, (Eds. T. Radil, Z. Bohdanecky), p. 161. ABSTRACT.