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Techniques for modeling of a stochastic activity of neurons are briefly reviewed. Our model is proposed, some experimental results with input Gaussian stochastic processes are discussed, and the concept of e-curves is introduced.
Techniques for modeling of a stochastic activity of neurons are briefly reviewed. Our model is proposed, some experimental results with input Gaussian stochastic processes are discussed, and the concept of e-curves is introduced.
The authors describe a hybrid computer neurone model intended for the investigation of stochastic transformations effected by neurones in correlation to some of their physiological parameters. The model is designed so as to give the best possible characterization of the internal dynamics of a neurone with minimum limiting conditions. It allows the generation of suitable input stochastic processes or operates with input processes obtained experimentally in the living neurone and it carries out basic statistical tests of the output stochastic process.
- MeSH
- hybridní počítače * MeSH
- lidé MeSH
- modely neurologické * MeSH
- neurony fyziologie MeSH
- pravděpodobnost * MeSH
- stochastické procesy * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.
- Klíčová slova
- mathematical modelling, placental development, placental shape, spiral artery, stochastic dynamics,
- MeSH
- arteriae umbilicales fyziologie MeSH
- biologické modely * MeSH
- embryonální vývoj fyziologie MeSH
- fyziologická neovaskularizace fyziologie MeSH
- kyslík metabolismus MeSH
- lidé MeSH
- organogeneze fyziologie MeSH
- placenta embryologie MeSH
- placentace * MeSH
- počítačová simulace MeSH
- statistické modely MeSH
- stochastické procesy MeSH
- těhotenství MeSH
- Check Tag
- lidé MeSH
- těhotenství MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Názvy látek
- kyslík MeSH
A stochastic differential equation describing the process of drug dissolution is presented. This approach generalizes the classical deterministic first-order model. Instead of assuming a constant fractional dissolution rate, it is considered here that the rate is corrupted by a white noise. The half-dissolution time is investigated for the model. The maximum likelihood and Bayes methods for the estimation of the parameters of the model are developed. The method is illustrated on experimental data. As expected, due to the nonlinear relationship between the fractional dissolution rate and the dissolution time, the estimates of the dissolution rate obtained from this stochastic model are systematically lower than the rate calculated from the deterministic model.
- MeSH
- algoritmy MeSH
- Bayesova věta MeSH
- kinetika MeSH
- léčivé přípravky chemie MeSH
- rozpustnost * MeSH
- statistické modely MeSH
- stochastické procesy MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Názvy látek
- léčivé přípravky MeSH
This article presents a stochastic model of binaural hearing in the medial superior olive (MSO) circuit. This model is a variant of the slope encoding models. First, a general framework is developed describing the elementary neural operations realized on spike trains in individual parts of the circuit and how the neurons converging onto the MSO are connected. Random delay, coincidence detection of spikes, divergence and convergence of spike trains are operations implemented by the following modules: spike generator, jitter generator, and coincidence detector. Subsequent processing of spike trains computes the sound azimuth in the circuit. The circuit parameters that influence efficiency of slope encoding are studied. In order to measure the overall circuit performance the concept of an ideal observer is used instead of a detailed model of higher relays in the auditory pathway. This makes it possible to bridge the gap between psychophysical observations in humans and recordings taken of small rodents. Most of the results are obtained through numerical simulations of the model.
- MeSH
- akční potenciály fyziologie MeSH
- akustická stimulace metody MeSH
- lidé MeSH
- modely neurologické * MeSH
- nervová síť * fyziologie MeSH
- nucleus olivaris caudalis * fyziologie MeSH
- sluchová dráha * fyziologie MeSH
- stochastické procesy MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.
- Klíčová slova
- gene regulatory networks, high-dimensional computation, parametric analysis, stochastic modelling,
- MeSH
- stochastické procesy MeSH
- teoretické modely * MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
The authors describe the effects of changes in excitatory and inhibitory synapse weight on the number of spikes generated in the presence of constant absolute refractory phase and threshold level values. Input stochastic processes with Gaussian distributions were presumed. The problem was resolved in a hybrid computer model of stochastic neuronal activity. The results are given in the form of "e-curves", "i-curves" and gradient fields. It was shown that, in a set of paired values of the two weights, zones could be found in which the number of generated spikes depended mainly on just one of them. It was also shown that, in a given neurone with a fixed synapse morphology, the effect of the individual synapses on the number of generated spikes altered with changes in input stochastic processes to the synapses.
- MeSH
- akční potenciály MeSH
- hybridní počítače MeSH
- lidé MeSH
- modely neurologické * MeSH
- neurony fyziologie MeSH
- pravděpodobnost * MeSH
- stochastické procesy * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
Interaural time differences (ITDs), the differences of arrival time of the sound at the two ears, provide a major cue for low-frequency sound localization in the horizontal plane. The first nucleus involved in the computation of ITDs is the medial superior olive (MSO). We have modeled the neural circuit of the MSO using a stochastic description of spike timing. The inputs to the circuit are stochastic spike trains with a spike timing distribution described by a given probability density function (beta density). The outputs of the circuit reproduce the empirical firing rates found in experiment in response to the varying ITD. The outputs of the computational model are calculated numerically and these numerical simulations are also supported by analytical calculations. We formulate a simple hypothesis concerning how sound localization works in mammals. According to this hypothesis, there is no array of delay lines as in the Jeffress' model, but the inhibitory input is shifted in time as a whole. This is consistent with experimental observations in mammals.
A new stochastic model for the residence time distribution of a drug injected instantaneously into the circulatory system is proposed and analyzed. The properties of the residence time are derived from the assumptions made about the cycle time distribution and the rule for elimination. This rule is given by the probability distribution of the number of cycles needed for elimination of a randomly selected molecule of the drug. Only the geometric distribution has been previously used for this purpose. Its transformation is applied here to get a boundary for the residence time. Other discrete distributions are applied with a view to describing different experimental situations. Suitable continuous probability distributions for the cycle time description are discussed.
