Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “deterministic processes”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,243 records · Page 69Linked to original sources

On the cumulants of population size for the stochastic power law logistic model.

The deterministic power law logistic model is used to describe density-dependent population growth in cases where the ordinary logistic model is insufficient. This paper investigates an analogous stochastic power law logistic model. The exact (unconditional) population size distributions and the cumulant functions for this stochastic model are intractable for large population sizes. Approximating cumulant functions are derived for populations of any size, and are illustrated with examples of assumed Africanized honey bee population dynamics. Outstanding among the findings is that the approximations for the cumulant functions are very accurate for these examples. The stochastic power law logistic model is very general and may be applied to describe the growth of many other natural populations.

Animals↗

Radiation risk during long-term spaceflight.

Cosmonauts' exposure to cosmic rays during long-term spaceflight can cause unfavorable effects in health and risk for the crew members' lives. All unfavorable effects induced by exposure should be taken into consideration for the risk estimation. They should include both the acute deterministic effects and delayed effects called stochastic. On the ground the limitation of unfavorable consequences of acute exposure is achieved by means of establishing dose limits. But in space applications this approach can't be acceptable. Establishing a fixed dose limit is adequate to introducing indefinite reserve coefficient and therefore ineffective usage of spacecraft resource. The method of radiation risk calculation caused by acute and delayed effects of cosmonauts' exposure is discussed and substantiated in the report. Peculiarities of the impact of permanent radiation sources (galactic cosmic rays and trapped radiation) and the variable one (solar cosmic rays) are taken into consideration.

Aerospace Medicine↗

Scaling of mesoscale simulations of polymer melts with the bare friction coefficient.

Both the Rouse and reptation model predict that the dynamics of a polymer melt scale inversely proportional with the Langevin friction coefficient xi. Mesoscale Brownian dynamics simulations of polyethylene validate these scaling predictions, providing the reptational friction xi(R)=xi+xi(C) is used, where xi(C) reflects the fundamental difference between a deterministic and a stochastic propagator even in the limit of xi to zero. The simulations have been performed with Langevin background friction and with pairwise friction, as in dissipative particle dynamics. Both simulation methods lead to equal scaling behavior with xi(C) having almost the same value in both cases. The scaling is tested for the diffusion g(t), the shear relaxation modulus G(t), and the Rouse mode autocorrelations of melts of C(120)H(242), C(400)H(802), and C(1000)H(2002). The derived dynamical scaling procedure is very useful to reduce run-time in mesoscale computer simulations, especially if pairwise friction is applied.

Chemistry, Physical↗

Stochastic finite element analysis of biological systems: comparison of a simple intervertebral disc model with experimental results.

Statistical methods allow the effects of uncertainty to be incorporated into finite element models. This has potential benefits for the analysis of biological systems where natural variability can give rise to substantial uncertainty in both material and geometrical properties. In this study, a simple model of the intervertebral disc under compression was created and analysed as both a deterministic and a stochastic system. Factorial analysis was used to determine the important parameters to be included in the stochastic analysis. The predictions from the model were compared to experimental results from 21 sheep discs. The size and shape of the distribution of the axial deformations predicted by the model was consistent with the experimental results given that the number of model solutions far exceeded the number of experimental results. Stochastic models could be valuable in determining the range and most likely value of stress in a tissue or implant.

Animals↗

[Deterministic and stochastic identification of neurophysiologic systems].

The paper deals with deterministic and stochastic identification methods applied to the concrete neurophysiological systems. The deterministic identification was carried out for the system: efferent fibres-muscle. The obtained transition characteristics demonstrated dynamic nonlinearity of the system. Identification of the neuronal model and the "afferent fibres-synapses-neuron" system in mollusc Planorbis corneus was carried out using the stochastic methods. For these purpose the Wiener method of stochastic identification was expanded for the case of pulse trains as input and output signals. The weight of the nonlinear component in the Wiener model and accuracy of the model prediction were quantitatively estimated. The results obtained proves the possibility of using these identification methods for various neurophysiological systems.

Animals↗

Mechanisms underlying ventricular tachycardia and its transition to ventricular fibrillation in the structurally normal heart.

Reentrant ventricular tachycardia (VT) is the most common sustained arrhythmia leading to ventricular fibrillation (VF). However, despite more than a century of research, the mechanism(s) of the conversion from reentrant VT to VF have not been elucidated. Based on their different electrocardiographic appearance, reentrant VT and VF have traditionally been thought of as resulting from two widely different mechanisms. Whereas VT is seen as a rapid but well organized process whereby the excitation wave rotates about a single well-defined circuit, fibrillation has been described as turbulent cardiac electrical activity, resulting from the random and aperiodic propagation of multiple independent wavelets throughout the cardiac muscle. Recently, the application of concepts derived from the theory of non-linear dynamics to the problem of wave propagation in the heart and the advent of modern high-resolution mapping techniques, have led some investigators to view VT and VF in terms of a single mechanism, whereby the self-organization of electrical waves forms 'rotors' that give rise to rapidly rotating spiral waves and results in either VT or VF, depending on the frequency of rotation and on the interaction of wave fronts with the cardiac muscle. As such, monomorphic VT is thought to result from a stationary rotor, whose frequency of rotation is within a range that allows 1:1 excitation of both ventricles. On the other hand, VF is thought to result from either a single rapidly drifting rotor, or a stationary rotor whose frequency of excitation is exceedingly high, thus resulting in multiple areas of intermittent block and giving rise to complex patterns of propagation with both deterministic and stochastic components. This article reviews the prevailing theories for the maintenance of VF, and discusses recently proposed mechanisms underlying transitions between VT and VF.

Death, Sudden, Cardiac↗

Intraoperative and postoperative evaluation of cavitation in mechanical heart valve patients.

BACKGROUND: Cavitation has been claimed partly responsible for the increased risk of thromboembolic complications, hemolysis, and fatal valve failure seen in mechanical heart valve patients. In vivo studies have investigated cavitation using high-pass filtering of the high-frequency pressure fluctuations with the root mean square values as an assessment of intensities. In vitro studies have shown that this well-known method may not be ideal owing to loss of data as a consequence of filtering, and because it requires a priori knowledge of the valve resonance pattern. Therefore, a new method has been developed, which decomposes the signal into nondeterministic (cavitation) and deterministic (valve resonance) signal components, and hence decreases data loss. This study aimed to evaluate cavitation in patients with mechanical, biological, and native heart valves both intraoperatively and postoperatively using the new method. METHODS: High-frequency pressure fluctuations were measured by a hydrophone intraoperatively and postoperatively in 14 patients with mechanical valves, 10 patients with normal aortic valves, and 5 patients with bioprosthesis. The total signal energy was evaluated as nondeterministic and deterministic energies. RESULTS: Nondeterministic energies were verified both intraoperatively and postoperatively in all patients who had a mechanical valve; this finding confirms the cavitation potential of mechanical valves. None of the data recorded in patients with bioprosthetic or native valves contained nondeterministic energy. CONCLUSIONS: The study confirms the presence of cavitation in mechanical heart valve patients using the nondeterministic energy of high-frequency pressure fluctuations as a quantitative measure of cavitation both intraoperatively and postoperatively.

Acoustics↗

Modelling the variability of lag times and the first generation times of single cells of E. coli.

A mathematical model combining deterministic and stochastic elements describes the growth and division of single cells. Its deterministic part is based on the model of Baranyi and Roberts [International Journal of Food Microbiology 23 (1994) 277] modelling the gradual adjustment of the cells to a new environment. The stochastic part assumes a random threshold size for the division of a single cell, which accounts for the variability of the individual generation times. Experimental results of the first division times of thousands of single cells using a microscopic flow system could be reproduced with this model, and it has the potential to be used to study the effects of different stress and environmental factors on the distribution of the lag and generation times of individual cells.

Cell Division↗

Transition from stochastic to deterministic behavior in calcium oscillations.

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.

Adenosine Triphosphate↗

Predicting temporal fluctuations in an intracellular signalling pathway.

We used a newly developed stochastic-based program to predict the fluctuations in numbers of molecules in a chemotactic signalling pathway of coliform bacteria. Specifically, we examined temporal changes in molecules of CheYp, a cytoplasmic protein known to influence the direction of rotation of the flagellar motor. Signalling molecules in the vicinity of a flagellar motor were represented as individual software objects interacting according to probabilities derived from experimentally-observed concentrations rate constants. The simulated CheYp molecules were found to undergo random fluctuations in number about an average corresponding to the deterministically calculated concentration. Both the relative amplitude of the fluctuations, as a proportion of the total number of molecules, and their average duration, increased as the simulated volume was reduced. In a simulation corresponding to 10% of the volume of a bacterium, the average duration of fluctuations was found to be 80.7 ms, which is much shorter than the observed alternations between clockwise and counter clockwise rotations of tethered bacteria (typically 2.6 s). Our results are therefore not in agreement with a simple threshold-crossing model for motor switching. However, it is possible to filter the CheYp fluctuations to produce temporal distributions closer to the observed swimming behaviour and we discuss the possible implications for the control of motor rotation.

Escherichia coli↗

Single subject image analysis using the complex general linear model--an application to functional magnetic resonance imaging with multiple inputs.

A linear time invariant model is applied to functional fMRI blood flow data. Based on traditional time series analysis, this model assumes that the fMRI stochastic output sequence can be determined by a constant plus a linear filter (hemodynamic response function) of several fixed deterministic inputs and an error term assumed stationary with zero mean. The input function consists of multiple exponential distributed (time delay between images) visual stimuli consisting of negative and erotic images. No a priori assumptions are made about the hemodynamic response function that, in essence, is calculated at each spatial position from the data. The sampling rate for the experiment is 400 ms in order to allow for filtering out higher frequencies associated with the cardiac rate. Since the statistical analysis is carried out in the Fourier domain, temporal correlation problems associated with inference in the time domain are avoided. This formal model easily lends itself to further development based on previously developed statistical techniques.

Adult↗

Accuracy of telemetry signals in the post-implantation monitoring of electrograms sensed by pacemakers.

Monitoring of electrograms (EGMs) sensed by pacemakers (PMs) during their lifetime is the utmost importance, since changes of these signals, due to modifications of the electrode-myocardial interface may occur compromising the proper functioning of the PM. Since after implantation these intracardiac signals are accessible only by means of a telemetry system, it is necessary to ascertain how faithfully the telemetric signals reproduce the direct ones. To this aim we devised an accurate method, based on linear system theory, which allows the estimation of the transfer function of the PM-telemetry system and the comparison of a set of time and frequency domain parameters (wave amplitude, slew rate, frequency at the spectrum peak and bandwidth) computed on both direct and telemetric signals. To overcome the problem that these two signals cannot be recorded simultaneously, an appropriate model of the input and output signals of the PM-telemetry system and of their interrelationship was identified. This model relies on a set of reasonable assumptions about the nature of the direct signal (supposed to have a fixed morphology within a predefined analysis window) and of noise sources corrupting both the direct and telemetric signals. Owing to the involvement of deterministic and stochastic signals, the theory of quasi-stationary signals was employed to obtain the system transfer function. To test our method, direct and telemetric recordings were performed on 12 patients with atrial sensing carrying Medtronic Pacemakers (Mod Elite 7077/7086, programmer Mod 9760) with unipolar steroid eluting leads (Medtronic Capsure 4523). The results we obtained demonstrate that the specific system considered acts as a low-pass filter with a -3 dB frequency at about 90 Hz this ensures that the telemetric signal contains almost all the information of the direct one and can be used to monitor the changes of the signals sensed by the PM.

Aged↗

Nonlinear stochastic modeling of aphid population growth.

This paper develops a stochastic population size model for the black-margined pecan aphid. Prajneshu [Prajneshu, A nonlinear statistical model for aphid population growth. J. Indian Soc. Agric. Statist. 51 (1998), p. 73] proposes a novel nonlinear deterministic model for aphid abundance. The per capita death rate in his model is proportional to the cumulative population size, and the solution is a symmetric analytical function. This paper fits Prajneshu's deterministic model to data. An analogous stochastic model, in which both the current and the cumulative aphid counts are state variables, is then proposed. The bivariate solution of the model, with parameter values suggested by the data, is obtained by solving a large system of Kolmogorov equations. Differential equations are derived for the first and second order cumulants, and moment closure approximations are obtained for the means and variances by solving the set of only five equations. These approximations, which are simple for ecologists to calculate, are shown to give accurate predictions of the two endpoints of applied interest, namely (1) the peak aphid count and (2) the final cumulative aphid count.

Animals↗

Prostate cancer: progression of prostate-specific antigen after external beam irradiation.

This paper is concerned with the development of a stochastic path of prostate-specific antigen (PSA) level after radiation treatment for prostate cancer. PSA is a biomarker for prostate cancer, higher levels of which indicate the seriousness of the cancer progression. Following the deterministic modeling of the data by the previous authors, Cox et al., this paper is concerned with the theoretical knowledge that could be gained by the stochastic modeling in discrete form of the PSA path over time. The expected value of the PSA level is computed and compared with the deterministic model and it is found that they are the same for about the first year after radiation therapy. The American Society for Therapeutic Radiology has set a consensus panel definition of biochemical failure following radiation therapy: the rise in three consecutive levels of PSA is considered to be a failure of the radiation therapy. Knowledge of the path of PSA presented in this paper would be useful in the management of the radiation treatment and in particular assessing quantitatively any clinically based policy for defining recurrence after radiation therapy. Application of the model is illustrated by fitting it to clinical data available in the University of Michigan cancer center.

Humans↗

Disease contact tracing in random and clustered networks.

The efficacy of contact tracing, be it between individuals (e.g. sexually transmitted diseases or severe acute respiratory syndrome) or between groups of individuals (e.g. foot-and-mouth disease; FMD), is difficult to evaluate without precise knowledge of the underlying contact structure; i.e. who is connected to whom? Motivated by the 2001 FMD epidemic in the UK, we determine, using stochastic simulations and deterministic 'moment closure' models of disease transmission on networks of premises (nodes), network and disease properties that are important for contact tracing efficiency. For random networks with a high average number of connections per node, little clustering of connections and short latency periods, contact tracing is typically ineffective. In this case, isolation of infected nodes is the dominant factor in determining disease epidemic size and duration. If the latency period is longer and the average number of connections per node small, or if the network is spatially clustered, then the contact tracing performs better and an overall reduction in the proportion of nodes that are removed during an epidemic is observed.

Communicable Disease Control↗

From local interactions to population dynamics in site-based models of ecology.

A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation.

Competitive Behavior↗

A fuzzy-based approach to remove clock skew and reset from one-way delay measurement.

One-way delay (OWD) traces are important measurements for analyzing end-to-end performance on the Internet. It is still a great challenge to provide a scalable solution for large-scale OWD measurement. Because the clocks at end systems are usually not synchronized, the OWD measurements are often inaccurate. For the more challenging case with clock resets to some reference times during the measurement, the OWD measurements are more inaccurate. Furthermore, the measurement data often exhibit considerable network-induced noise when the network is heavily loaded. All the existing OWD measurement techniques, such as linear programming and convex-hull approach (CHA), try to solve this problem by deterministic mathematics model. However, they often fail to distinguish clock resets from temporary Internet congestion. Based on the fuzzy-clustering analysis, this paper proposes a new algorithm to estimate and remove the clock skews and resets from measurement results. This algorithm has been implemented as a tool called fuzzy-based OWD corrector (FOC). The paper then presents OWD measurements of several Internet paths using FOC. Numerical experiments demonstrate that FOC is more accurate and robust than the existing techniques. FOCs computation complexity O(N) is similar to that of CHA and its computing time is much less than that of convex-hull technique.

Algorithms↗

Noise reduction for vocal pathologies.

A noise reduction scheme, particularly suited for the correction of vocal pathologies, is proposed. The filter makes use of concepts originated within the theory of dynamical systems and deterministic chaos. In particular, the idea of embedding scalar data in order to reconstruct a phase space is of fundamental importance here. Furthermore, the concept of an attractor as a result of dynamical constraints is exploited. In order to perform noise reduction one needs redundancy and the human voice provides it even within a phoneme, namely the smallest structural unit of speech. Due to several repetitions of a pattern called pitch inside a phoneme, separation between the pure voice signal and the noise is possible, provided the latter is uncorrelated with the former. With a proper parameter tuning, different kinds of noise can be removed. We describe the idea behind the noise reduction algorithm and present applications to vocal pathologies.

Algorithms↗