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At least 1,693 records · Page 94Linked to original sources
PubMed2002

The study of long-term HIV dynamics using semi-parametric non-linear mixed-effects models.

Modelling HIV dynamics has played an important role in understanding the pathogenesis of HIV infection in the past several years. Non-linear parametric models, derived from the mechanisms of HIV infection and drug action, have been used to fit short-term clinical data from AIDS clinical trials. However, it is found that the parametric models may not be adequate to fit long-term HIV dynamic data. To preserve the meaningful interpretation of the short-term HIV dynamic models as well as to characterize the long-term dynamics, we introduce a class of semi-parametric non-linear mixed-effects (NLME) models. The models are non-linear in population characteristics (fixed effects) and individual variations (random effects), both of which are modelled semi-parametrically. A basis-based approach is proposed to fit the models, which transforms a general semi-parametric NLME model into a set of standard parametric NLME models, indexed by the bases used. The bases that we employ are natural cubic splines for easy implementation. The resulting standard NLME models are low-dimensional and easy to solve. Statistical inferences that include testing parametric against semi-parametric mixed-effects are investigated. Innovative bootstrap procedures are developed for simulating the empirical distributions of the test statistics. Small-scale simulation and bootstrap studies show that our bootstrap procedures work well. The proposed approach and procedures are applied to long-term HIV dynamic data from an AIDS clinical study.

Acquired Immunodeficiency Syndrome↗
PubMed1997

Conduction block and chaotic dynamics in an asymmetrical model of coupled cardiac cells.

The initiation and propagation of the cardiac impulse depends on intrinsic properties of cells, geometrical arrangements, and intercellular coupling resistances. To address the issue of the interplay between these factors in a simple way, we have used a system, based on the van Capelle and Dürrer model, including a pacemaker and a non-pacemaker cell linked by an ohmic coupling resistance. The influence of asymmetrical cell sizes and electronic load was investigated by using numerical simulations and continuation-bifurcation techniques. The loading of a small pacemaker cell by a large non-pacemaker one (pacemaker: non-pacemaker size ratio = 0.3) was expressed as a pronounced early repolarization in the pacemaker cell and a quite long latency for the impulse propagation. Using coupling resistance as the continuation parameter, three behavioral zones were detected from low to high coupling resistance values: a zone of total quiescence (0:0), a zone of effective entertainment (1:1), and a zone of total block (1:0 pattern). At the boundary between 1:1 and 1:0 patterns, for relatively high coupling resistance values, a cascade of period doubling bifurcations emerged, corresponding to discrete changes of propagation patterns leading into irregular dynamics. Another route to irregular dynamics was also observed in the parameter space. The high sensitivity of the detected irregular dynamics to initial conditions and the positive value of the maximum Lyapunov exponent allowed us to identify these dynamics as being chaotic. Since neither intermediate block patterns nor irregular dynamics were observed with larger size ratios, we suggest that the interplay between resting membrane conductance of the non-pacemaker cell and intercellular coupling may bring about these rhythmic disturbances.

Animals↗
PubMed2001

The influence of predator--prey population dynamics on the long-term evolution of food web structure.

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.

Animals↗
PubMed1996

Identification of the nonlinear state-space dynamics of the action-perception cycle for visually induced postural sway.

Human subjects standing in a sinusoidally moving visual environment display postural sway with characteristic dynamical properties. We analyzed the spatiotemporal properties of this sway in an experiment in which the frequency of the visual motion was varied. We found a constant gain near 1, which implies that the sway motion matches the spatial parameters of the visual motion for a large range of frequencies. A linear dynamical model with constant parameters was compared quantitatively with the data. Its failure to describe correctly the spatiotemporal properties of the system led us to consider adaptive and nonlinear models. To differentiate between possible alternative structures we directly fitted nonlinear differential equations to the sway and visual motion trajectories on a trial-by-trial basis. We found that the eigenfrequency of the fitted model adapts strongly to the visual motion frequency. The damping coefficient decreases with increasing frequency. This indicates that the system destabilizes its postural state in the inertial frame. This leads to a faster internal dynamics which is capable of synchronizing posture with fast-moving visual environments. Using an algorithm which allows the identification of essentially nonlinear terms of the dynamics we found small nonlinear contributions. These nonlinearities are not consistent with a limit-cycle dynamics, accounting for the robustness of the amplitude of postural sway against frequency variations. We interpret out results in terms of active generation of postural sway specified by sensory information. We derive also a number of conclusions for a behavior-oriented analysis of the postural system.

Humans↗
PubMed2005

On the relations between single cell activity in the motor cortex and the direction and magnitude of three-dimensional dynamic isometric force.

The role of the motor cortex in the control of both the direction and magnitude of dynamic force, when both are allowed to vary in 3D, is not known. We recorded the activity of 504 cells in the motor cortex of two monkeys during a behavioral task in which the subjects used a manipulandum to vary both the direction and magnitude of isometric force in 3D space. The majority (86%) of cells active in the task related to the direction, a tiny number (2.5%) to the magnitude, and a moderate number (11.5%) to both the direction and magnitude of dynamic force output. Finally, we compared neural activity in the same population of neurons during dynamic and static force output and found that the relations to direction and magnitude were very similar in both epochs. Our results indicate that during dynamic force production, cells in the motor cortex are primarily concerned with specifying the direction of force. The magnitude signal is not prominent in motor cortex neurons, and in general, magnitude and direction of force are specified together. Furthermore, the data suggest that the control of static and dynamic motor systems is based, to a great extent, on a common control process.

Action Potentials↗
PubMed2002

Density-dependent birth rate, birth pulses and their population dynamic consequences.

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos.

Animals↗
PubMed2006

The effect of irradiance, vertical mixing and temperature on spring phytoplankton dynamics under climate change: long-term observations and model analysis.

Spring algal development in deep temperate lakes is thought to be strongly influenced by surface irradiance, vertical mixing and temperature, all of which are expected to be altered by climate change. Based on long-term data from Lake Constance, we investigated the individual and combined effects of these variables on algal dynamics using descriptive statistics, multiple regression models and a process-oriented dynamic simulation model. The latter considered edible and less-edible algae and was forced by observed or anticipated irradiance, temperature and vertical mixing intensity. Unexpectedly, irradiance often dominated algal net growth rather than vertical mixing for the following reason: algal dynamics depended on algal net losses from the euphotic layer to larger depth due to vertical mixing. These losses strongly depended on the vertical algal gradient which, in turn, was determined by the mixing intensity during the previous days, thereby introducing a memory effect. This observation implied that during intense mixing that had already reduced the vertical algal gradient, net losses due to mixing were small. Consequently, even in deep Lake Constance, the reduction in primary production due to low light was often more influential than the net losses due to mixing. In the regression model, the dynamics of small, fast-growing algae was best explained by vertical mixing intensity and global irradiance, whereas those of larger algae were best explained by their biomass 1 week earlier. The simulation model additionally revealed that even in late winter grazing may represent an important loss factor during calm periods when losses due to mixing are small. The importance of losses by mixing and grazing changed rapidly as it depended on the variable mixing intensity. Higher temperature, lower global irradiance and enhanced mixing generated lower algal biomass and primary production in the dynamic simulation model. This suggests that potential consequences of climate change may partly counteract each other.

Climate↗
PubMed2005

Photosynthesis in dynamic light: systems biology of unconventional chlorophyll fluorescence transients in Synechocystis sp. PCC 6803.

Photosynthetic organisms live in a dynamic environment where light typically fluctuates around a mean level that is slowly drifting during the solar day. We show that the far-from-equilibrium photosynthesis occurring in a rapidly fluctuating light differs vastly from the stationary-flux photosynthesis attained in a constant or slowly drifting light. Photosynthetic organisms in a static or slowly drifting light can be characterized by a steady-state quantum yield of chlorophyll fluorescence emission F' that is changing linearly with small and slow variations of the incident irradiance I+DeltaI(t): F'(I+DeltaI(t)) approximately Fmean '(dF)/(dI).DeltaI(t). In Synechocystis sp. PCC 6803, the linear approximation holds for an extended interval covering largely the static irradiance range experienced by the cyanobacteria in nature. The photosynthetic dynamism and, consequently, the dynamism of the chlorophyll fluorescence emission change dramatically when exposing the organism to a fluctuating irradiance. Harmonically-modulated irradiance I+DeltaI . sin(2pit/T), T approximately 1-25 s induces perpetual, far-from-equilibrium forced oscillations that are strongly non-linear, exhibiting significant hysteresis with multiple fluorescence levels corresponding to a single instantaneous level of the incident irradiance. We propose that, in nature, the far-from-equilibrium dynamic phenomena represent a significant correction to the steady-state photosynthetic activity that is typically investigated in laboratory. Analysis of the forced oscillations by the tools of systems biology suggests that the dynamism of photosynthesis observed in fluctuating light can be explained by a delayed action of regulatory agents.

Chlorophyll↗
PubMed1994

Non-linear forecasting measurements of multichannel EEG dynamics.

This work presents a new method for studying the underlying dynamics of multichannel EEG on the basis of the mathematical theory of dynamical systems. It computes the local loss of predictability and Kolmogorov entropy of the dynamics reconstructed from brain electrical activity. This reconstruction uses multichannel recordings in order to quantify an equivalent of spatio-temporal mapping. Five experimental conditions have been studied: closed eyes at rest, closed eyes and counting even numbers, staring at a spotlight, passive and active auditive odd-ball tasks. The entropy is positive for all the experimental conditions which proves that the underlying EEG dynamics are chaotic. Moreover, on the basis of the dynamical signature it is possible to differentiate 3 types of EEG activity: the rest closed eyes activity, the task closed eyes activity (counting and odd-ball tasks) and the open eyes activity (staring at a spotlight). It is inferred that this index could characterize task-related changes in brain activity.

Adult↗
PubMed1995

Computing with dynamic attractors in neural networks.

In this paper we report on some new architectures for neural computation, motivated in part by biological considerations. One of our goals is to demonstrate that it is just as easy for a neural net to compute with arbitrary attractors--oscillatory or chaotic--as with the more usual asymptotically stable fixed points. The advantages (if any) of such architectures are currently being investigated; but it seems reasonable that the much richer dynamics of recurrent networks, so obvious in recordings of brain activity, must be useful for something. On the other hand, the constraints of computing with biological wet-ware may make chaotic dynamics unavoidable in complex nervous systems. We hypothesize also that the as yet unrivaled capabilities of the human brain derive from an ability to integrate both analog intuitive pattern recognition operations, and digital symbolic logical operations at the ground level of its hardware. To investigate these possibilities, we have constructed a parallel distributed processing architecture inspired by the structure and dynamics of cerebral cortex. The construction assumes that cortex is a set of coupled associative memories with dynamic attractors. It is guided also by a particular concept of the physical structure required of macroscopic computational systems in general for reliable computation in the presence of noise. Our challenge is to accomplish real tasks that brains can do, using ordinary differential equations, in networks that are as faithful as possible to the known anatomy and dynamics of cortex.

Algorithms↗
PubMed2004

On time-space of nonlinear phenomena with Gompertzian dynamics.

This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.

Animals↗
PubMed2004

Time delay as a key factor of model plankton dynamics.

Studies of the mechanisms underlying complex dynamics of ecological systems at various spatial and time scales bring increasing awareness that complexity is an intrinsic feature of ecological functioning. This paper is to investigate the role of such an ecologically significant parameter as the time delay due to maturation processes in the complex plankton dynamics. We show that the time lag T1, associated with the zooplankton maturation period can lead to essential changes in the plankton dynamics. Particularly, we show that the coexistence of limit cycle and chaotic attractor we have recently found to be typical of the system at T1 = 0 [A.B. Medvinsky, I.A. Tikhonova, R.R. Aliev, B.-L. Li, Z.-S. Lin, H. Malchow, Patchy environment as a factor of complex plankton dynamics, Phys. Rev. E 64 (2001) 021915] is replaced by pure chaotic plankton dynamics as T1 becomes more than a critical value. The results obtained imply that chaos is a rather common phenomenon in the plankton functioning.

Animals↗
PubMed2005

Spatial dynamics of invasion: the geometry of introduced species.

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

Animal Migration↗
PubMed2006

Frequency flows and the time-frequency dynamics of multivariate phase synchronization in brain signals.

The quantification of phase synchrony between brain signals is of crucial importance for the study of large-scale interactions in the brain. Current methods are based on the estimation of the stability of the phase difference between pairs of signals over a time window, within successive frequency bands. This paper introduces a new approach to study the dynamics of brain synchronies, Frequency Flows Analysis (FFA). It allows direct tracking and characterization of the nonstationary time-frequency dynamics of phase synchrony among groups of signals. It is based on the use of the one-to-one relationship between frequency locking and phase synchrony, which applies when the concept of phase synchrony is not taken in an extended 'statistical' sense of a bias in the distribution of phase differences, but in the sense of a continuous phase difference conservation during a short period of time. In such a case, phase synchrony implies identical instantaneous frequencies among synchronized signals, with possible time varying frequencies of synchronization. In this framework, synchronous groups of signals or neural assemblies can be identified as belonging to common frequency flows, and the problem of studying synchronization becomes the problem of tracking frequency flows. We use the ridges of the analytic wavelet transforms of the signals of interest in order to estimate maps of instantaneous frequencies and reveal sustained periods of common instantaneous frequency among groups of signal. FFA is shown to track complex dynamics of synchrony in coupled oscillator models, reveal the time-frequency and spatial dynamics of synchrony convergence and divergence in epileptic seizures, and in MEG data the large-scale ongoing dynamics of synchrony correlated with conscious perception during binocular rivalry.

Adult↗
PubMed2004

Competitive coexistence in a dynamic landscape.

This paper investigates the effect of a dynamic landscape on the persistence of many interacting species. We develop a multi-species community model with an evolving landscape in which the creation and destruction of habitat are dynamic and local in space. Species interactions are also local involving hierarchical competitive trade-offs. We show that dynamic landscapes can reverse the trend of increasing species richness with higher fragmentation observed in static landscapes. The increase in the species-area exponent from a homogeneous to a fragmented landscape does not occur when dynamics are turned on. Thus, temporal aspects of the processes that generate and destroy habitat appear dominant relative to spatial characteristics. We also demonstrate, however, that temporal and spatial aspects interact to influence the persistence time of individual species, and therefore, rank-abundance curves. Specifically, persistence in the model increases in habitats with faster local turnover because of the presence of dynamic corridors.

Animals↗
PubMed2006

Evolutionary game dynamics in finite populations with strong selection and weak mutation.

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expected motion in our model resembles the standard replicator dynamics when the population is large, but is qualitatively different when the population is small. Our analysis shows that even in large finite populations the behavior of a replicator-like system can be different from that of the standard replicator dynamics. As an application, we consider selective language dynamics. We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics.

Biological Evolution↗
PubMed2026

Estradiol dynamics during superovulation are associated with oocyte quantity and maturation stage in cynomolgus macaques.

OBJECTIVE: To examine whether dynamic changes in circulating estradiol during ovarian stimulation are associated with the number and maturation status of oocytes recovered in cynomolgus macaques. DESIGN: Observational study based on retrospective analysis of ovarian stimulation cycles. SUBJECTS: Sixty-six ovarian stimulation cycles from adult female cynomolgus macaques (Macaca fascicularis) housed at the Primate Resources Center. EXPOSURE: Animals underwent a standardized gonadotropin-based ovarian stimulation protocol. Circulating estradiol concentrations were measured at multiple time points during the late follicular phase before oocyte recovery, and estradiol dynamics were defined as the difference between the maximum and minimum values observed across these measurements. MAIN OUTCOME MEASURES: Total number of oocytes recovered per stimulation cycle, number of mature oocytes at the metaphase two stage, and proportional distribution of oocyte maturation stages. RESULTS: Dynamic changes in estradiol concentrations were positively associated with the total number of oocytes recovered per cycle (correlation coefficient 0.45). A similar but weaker association was observed with the number of mature oocytes recovered (correlation coefficient 0.36). In contrast, estradiol dynamics were not associated with the proportional distribution of oocyte maturation stages. Donor age and body weight were not significantly associated with oocyte recovery outcomes. CONCLUSION: Dynamic changes in circulating estradiol during ovarian stimulation primarily reflect the quantitative dimension of ovarian response in cynomolgus macaques, with limited relevance for the maturation stage composition of recovered oocytes.

Animals↗
PubMed1998

Consequences of population models for the dynamics of food chains.

A class of bioenergetic ecological models is studied for the dynamics of food chains with a nutrient at the base. A constant influx rate of the nutrient and a constant efflux rate for all trophic levels is assumed. Starting point is a simple model where prey is converted into predator with a fixed efficiency. This model is extended by the introduction of maintenance and energy reserves at all trophic levels, with two state variables for each trophic level, biomass and reserve energy. Then the dynamics of each population are described by two ordinary differential equations. For all models the bifurcation diagram for the bi-trophic food chain is simple. There are three important regions; a region where the predator goes to extinction, a region where there is a stable equilibrium and a region where a stable limit cycle exists. Bifurcation diagrams for tritrophic food chains are more complicated. Flip bifurcation curves mark regions where complex dynamic behaviour (higher periodic limit cycles as well as chaotic attractors) can occur. We show numerically that Shil'nikov homoclinic orbits to saddle-focus equilibria exists. The codimension 1 continuations of these orbits form a 'skeleton' for a cascade of flip and tangent bifurcations. The bifurcation analysis facilitates the study of the consequences of the population model for the dynamic behaviour of a food chain. Although the predicted transient dynamics of a food chain may depend sensitively on the underlying model for the populations, the global picture of the bifurcation diagram for the different models is about the same.

Animals↗