Statistical Analysis of Motor Unit Firing Patterns in a Human Skeletal Muscle

A statistical analysis of the firing pattern of single motor units in the human brachial biceps muscle is presented. Single motor unit spike trains are recorded and analyzed. The statistical treatment of these spike trains is as stochastic point processes, the theory of which is briefly discussed. Evidence is presented that motor unit spike trains may be modelled by a renewal process with an underlying gaussian probability density. Statistical independence of successive interspike intervals is shown using scatter diagrams; the hypothesis of a gaussian distribution is accepted at the 99th percentile confidence limit, chi-square test, in 90% of the units tested. A functional relationship between the mean and standard deviation is shown and discussed; its implications in obtaining sample size are presented in an appendix.The results of higher order analysis in the form of autocorrelograms and grouped interval histograms are presented. Grouped interval histograms are discussed in the context of motor unit data, and used to confirm the hypothesis that a stable probability density function does not represent a good model of the data at this level of analysis.     

Stochastic radial basis functions

Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.     

Performance of four ordination techniques assuming three different non-linear species response models

Summary The performances of four ordination techniques (reciprocal averaging, parametric mapping, gaussian ordination and non-metric multidimensional scaling) are evaluated using artificial data based on three vegetation models: the gaussian response curve, -function curves, and an ecological response model. No technique performs well with the artificial data not based on a gaussian model. Non-metric multidimensional scaling seemed marginally better than other techniques. Some of the implications of this failure are discussed.     

The perception of a dotted line in noise: a model of good continuation and some experimental results

A formal model is proposed, describing how the perceptual interpretation of dot figures is guided by the Gestalt rule of good continuation. The algorithm will be restricted to figures with a collinear dot array (line) embedded in a background of randomly placed dots. The model, CODE-2, is an elaboration of the model, CODE-1, of grouping dots on the basis of the Gestalt rule of (relative) proximity, and consists of the introduction of non-circular symmetric gaussian distribution functions for the representation of the orientation dependent strength of interaction between collinear dots. Supra-threshold contours of the function, resulting from a superposition on each dot of the gaussian functions, are assumed to predict the perceptual grouping of the dots. A quantitative measure for the perceptual salience of dotted lines was defined as the contrast between the internal coherence of the line dots, and their interference with the noise dots. For 20 stimuli the CODE-2 grouping of the dots is reported, together with the results of a line-in-noise latency experiment. There was a significant correlation between the predicted saliences and the experimental results. The results support the usefulness of representing good continuation between collinear dots by non-circular symmetric gaussian distribution functions.     

Radial migration of DNA molecules in cylindrical flow. III. Circles and the effect of non-gaussian polymer statistics.

We have previously shown that DNA will migrate radially inward in a concentric-cylinder shear flow apparatus. We assumed gaussian chain statistics, and we considered only linear molecules. In this paper, we extend the analysis to closed circular molecules, and we consider non-gaussian statistics for both linears and circles. We find that, in good solvents, the inward radial migration velocity is more sensitive to the molecular weight than M5/2, which we previously reported for gaussian chains. Furthermore, linears migrate radially inward 8 times faster than do circles of the same molecular weight. This suggests the possibility of separating linear from circular DNA in solution.     

Geometric and many-particle aspects of transmitter binding.

We investigate the various reactivity patterns possible when several transmitter molecules, released at one side of a synaptic gap, diffuse and bind reversibly to a single receptor at the other end. In the framework of a one-dimensional approximation, the complete time, reactivity, concentration and gap-width dependence are determined, using a rigorous theoretical and computational approach to the many-body aspects of this problem. The time dependence of the survival probability is found to consist of up to four phases. These include a short delay followed by gaussian, power-law, and exponential decay phases. A rigorous expression is derived for the long-time exponent and approximate expressions are obtained for describing the short-time gaussian phase.     

Comparison of gaussian and t-distribution densities for modeling fluorescence dispersion in flow cytometric DNA histograms

In this paper, we have analyzed, on an experimental basis, the behaviour of the standardized t-distribution with three degrees of freedom versus the gaussian model, when employed for describing the fluorescence dispersion effect in flow cytometric DNA measurements. The comparison has been performed by employing two different objective criteria based on a computer analysis for fitting DNA histograms and on a parameter related to the peak distribution shape. The results indicate that, when the peak variance is not particularly small, the two models are substantially equivalent. In the case of experimental data with very sharp peaks, the t-distribution performs better than the gaussian density.     

Monte Carlo generation of polypeptide random coil conformations; the persistence vector and the chain vector distribution

Polypeptide random coil conformations of various chain lenghts (N = 5, 10, 20, 40, 80 peptide units) are generated by a Monte Carlo procedure. The characteristic ratio obtained for the sets of generated conformations is identical with the exact value calculated with the average transformation matrix procedure, indicating the equivalence of the two treatments. On the basic of the generated sets of conformations the length and direction of the persistence vector (the averaged chain vector expressed in the reference frame of the first two skeletal bonds) are investigated for various chain lengths. The radial distribution function for the chain vector shows the length of the chain vector for small polypeptides (N = 5, 10) not to deviate far from its most probable value. Also for larger chains up to chains of 80 peptide units very significant deviations from a gaussian distribution are observed.The distribution of the length of the vector connecting the remote end of the chain with the end of the persistence vector exhibited behavior much doser to the gaussian approximation, an improvement especially significant for the short chains.     

Radial migration of DNA molecules in cylindrical flow. II. The non-draining model and possible application to fractionation

The radial-migration calculation of the preceding paper is extended to the non-draining polymer. The results show an inward radial velocity that depends on the 5/2 power of the molecular weight, assuming gaussian statistics for the chain. This sensitivity to size serves as the basis for a method of separating DNA molecules in solution according to their size. Normal stress (Weissenberg) effects are also discussed.     

Polymorphism of acetylcholinesterase and identification of new molecular forms after sedimentation analysis

Acetylcholinesterase (AChE) is composed of several distinct molecular forms, which are identified and partly resolved by velocity sedimentation analysis on sucrose gradients. We made the assumption that each AChE form sediments as a peak of activity with a gaussian shape in the continuous sucrose gradient. We experimentally demonstrate that the complex AChE profiles can be decomposed in gaussian distributions of separate molecular entities. We performed a high salt-detergent extraction of AChE from mouse skeletal muscle and isolated fractions enriched in each particular from. These fractions were then submitted to a second sedimentation, to assess the stability and to further characterize each AChE form. Then, we calculated the statistical significance level of each AChE form and identified up to 9 separate molecular specifies in mouse adult muscle. These forms are the major "4 S", "6.5 S", "10 S", "12 S" and "16 S" and minor molecular active components of AChE. These results suggest complex structural interactions between catalytic and non catalytic subunits of AChE and do not simply fit the tailed asymmetric globular model of AChE with six molecular species.     

Proton NMR bandshape studies of lamellar liquid crystals and gel phases containing lecithins and cholesterol.

Proton NMR spectra for gel and liquid crystalline samples, composed of dimyristoyl and/or dipalmitoyl lecithin, cholesterol and water, can be consistently interpreted in terms of mesophase symmetry and molecular diffusion according to a model proposed by Wennerstrom (Wennerstrom, H. (1973) Chem. Phys. Lett. 18, 41-44). It is shown by computer simulation that the characteristic "super-lorentzian" bandshape of the lamellar mesophase can be described by the superposition of three gaussian curves. The NMR signal of the gel phase can be simulated by the superposition of two gaussian curves with widths at half height of 2.5 kHz and 19 kHz. An upper limit of the lateral diffusion coefficient of the lecithin molecules in the gel phase is calculated to be about 5-10(-15) m-2/s. It is therefore concluded that the static intermolecular dipolar couplings average to zero in the lamellar mesophase. An estimation of the order parameter of the liquid crystalline phase is made from experimental data and a calculated "rigid lattice" linewidth. A two phase system is shown to exist in the temperature range 28-34 degrees C for a mesophase of a mixture of dimyristoyl and dipalmitoyl lecithin. The presence of cholesterol results in enhanced lateral diffusion of the lecithin molecules at temperatures below the Chapman transition point.     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.     

Fumarase activity in skeletal muscle of man

Soluble extracts of human skeletal muscle have a fumarase activity of 31.2 +/- 7.27 (M. vastus lateralis quadricipitis) or 30.9 +/- 8.0 U/g wet weight at 37 degrees C (M. deltoideus). The distribution of activities in the 36 muscle samples studies is not gaussian. There is a significant correlation between the activities of citrate synthase and fumarase (r = + 0.881; p less than 0.001) in all investigated muscles, excepting M. vastus lateralis quadricipitis.     

Enaminones 11. An examination of some ethyl ester enaminone derivatives as anticonvulsant agents

In this paper, we investigated the previously synthesized anticonvulsant enaminone ethyl ester analogs using the computational gaussian 03 programs. The significant chemical features of the enaminone compounds that lead to positive anticonvulsant activity were identified. From our analyses, we believe that the neutrality of the phenyl ring may be important for binding in the hydrophobic pocket of the active site and that the binding of the phenyl substituent is the main reason why some analogs are active and others are inactive.     

Detection Theory Applied to the Absolute Sensitivity of Sensory Systems

Mainly the skin senses touch and warmth have been investigated. It is shown that the decision model describes the experimental data better than the threshold model. The experiments lead to the assumption that an internal noise exists, which is a neural activity being undistinguishable from the neural activity caused by small stimuli and which adds to the neural activity caused by the stimulus. The probability distribution of this internal noise can be considered to be gaussian. The relation between stimulus and neural activity is alinear for the touch sense. The question of whether noise of a multiplicative nature must be assumed is discussed.     

Stochastic resonance in the LIF models with input or threshold noise

In this paper, two stochastic versions of the LIF neural model are considered: one with the noise signal applied to the firing threshold, the other having it added to the input current. Then, adopting a discontinuous stepwise noise whose innovations are uncorrelated and gaussian distributed, the behaviours of the two models pertaining to the stochastic resonance (SR) are analysed and compared. Furthermore, it is shown that introducing a suitable time correlation into the noise signal brings us from the first model to the second one.     

Coding DNA sequences: statistical distributions

The base distributions in coding DNA sequences (CDS) are investigated. We explore the scaling properties of the 4-dimensional directed random walk and compare them with that for the DNA sequences. Inference from these observation are, however, contradicted by alternate analysis using factorial moments. To resolve this conflict we look directly at the nucleotide base distributions. In all the cases the base distributions change from gaussian to non-gaussian as the scale size is increased. The CDS, therefore, have nucleotide distributions different from the random.