PubMed · 3567326
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J A Schellman. 1987. Selective binding and solvent denaturation.. https://doi.org/10.1002/bip.360260408
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A stochastic model for transport of radionuclides in soil is presented. It is based on probability density functions of solute displacements, which are interpreted as impulse response functions of a linear dynamic system. Two transport models are discussed: (1) a convective-stochastic approach which takes into account spatial variability of flow and sorption and leads to a lognormal probability distribution of displacements, and (2) the conventional convective-dispersive model with a constant retardation coefficient. To compare their applicability, both models were applied to depth distributions of 90Sr and 137Cs fallout measured in an Orthic Podsol. The convective-stochastic approach was found to provide a better representation of the observed depth distributions. Using this model, migration rates of the radionuclides were calculated.
The addition of noise to a system can sometimes improve its ability to transfer information reliably. This phenomenon--known as stochastic resonance--was originally proposed to account for periodicity in the Earth's ice ages, but has now been shown to occur in many systems in physics and biology. Recent experimental and theoretical work has shown that the simplest system exhibiting 'stochastic resonance' consists of nothing more than signal and noise with a threshold-triggered device (when the signal plus noise exceeds the threshold, the system responds momentarily, then relaxes to equilibrium to await the next triggering event). Here we introduce a class of non-dynamical and threshold-free systems that also exhibit stochastic resonance. We present and analyse a general mathematical model for such systems, in which a sequence of pulses is generated randomly with a probability (per unit time) that depends exponentially on an input. When this input is a sine-wave masked by additive noise, we observe an increase in the output signal-to-noise ratio as the level of noise increases. This result shows that stochastic resonance can occur in a broad class of thermally driven physico-chemical systems, such as semiconductor p-n junctions, mesoscopic electronic devices and voltage-dependent ion channels, in which reaction rates are controlled by activation barriers.
A comparison is made between two methods of parameter estimation for analysis of dynamic experiments in which the input function is noisy. Noise in the input function leads to uncertainties in the calculated model-predicted values, and therefore the covariance matrix of the residuals is a function of the model parameters. Statistical uncertainties in the model-predicted values significantly change the nature of the fitting process and the quality of the results. The initial method uses a weighted least-squares criterion where the weighting matrix is the inverse of the full covariance matrix of the residuals, incorporating both the noise in the output data and the noise in the input function. The methodology was applied to dynamic emission tomography studies of the heart, where the blood (input) and tissue (output) tracer concentrations at each time are derived from two regions of interest in the same tomographic section. The second method introduces additional parameters to describe the input function, and adds terms to the weighted sum of squares which comprise the criterion. Instead of only summing the weighted terms to account for differences between the model and the output function, there is a second set of terms to account for the differences between the model and the input function. The two methods have different theoretical bases and appear to optimize different criteria, but it is shown here that they are equivalent to one another. The criterion which they minimize is the same under certain matrix invertibility constraints, which must be satisfied to ensure the stability of either method.