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PubMed2005

Correlated firing in a feedforward network with Mexican-hat-type connectivity.

We report on deterministic and stochastic evolutions of firing states through a feedforward neural network with Mexican-hat-type connectivity. The prevalence of columnar structures in a cortex implies spatially localized connectivity between neural pools. Although feedforward neural network models with homogeneous connectivity have been intensively studied within the context of the synfire chain, the effect of local connectivity has not yet been studied so thoroughly. When a neuron fires independently, the dynamics of macroscopic state variables (a firing rate and spatial eccentricity of a firing pattern) is deterministic from the law of large numbers. Possible stable firing states, which are derived from deterministic evolution equations, are uniform, localized, and nonfiring. The multistability of these three states is obtained where the excitatory and inhibitory interactions among neurons are balanced. When the presynapse-dependent variance in connection efficacies is incorporated into the network, the variance generates common noise. Then the evolution of the macroscopic state variables becomes stochastic, and neurons begin to fire in a correlated manner due to the common noise. The correlation structure that is generated by common noise exhibits a nontrivial bimodal distribution. The development of a firing state through neural layers does not converge to a certain fixed point but keeps on fluctuating.

Artifacts↗
PubMed2006

A model for detection of individual cow mastitis based on an indicator measured in milk.

A dynamic deterministic biological model was developed that generates, for a given cow on a given day, a value for her risk of having mastitis. The model combines real-time information from a mastitis indicator measured in milk with additional factors that are other known risk factors of mastitis but that are not reflected in the indicator. l-Lactate dehydrogenase (LDH), an enzyme whose activity is increased because of mastitis, is used as an example of a mastitis indicator. The additional factors incorporated in the model are days from calving, breed, parity, milk yield, udder characteristics, other disease records, electrical conductivity, and herd characteristics. The model is designed to run each time a new LDH value is recorded and can run in the absence of the additional factors. Electrical conductivity measurements and disease records, where available, also trigger the model to run. As an input, milk LDH activity values (micromol/min per L) are multiplied by milk yield (L) to produce the amount of LDH (micromol/min) and are then smoothed using an extended Kalman filter before being processed by the biological model. The output comprises a risk of acute mastitis and a relative degree of chronic mastitis. The model also produces a days-to-next sample value that allows sampling frequency to be either increased or reduced depending on the risk of mastitis. The days-to-next sample value was designed to make the best use of opportunities afforded by automated, inline sampling technology. The model functionality was investigated using simulated data, and real-farm data of naturally occurring mastitis were then used to validate the model. The results demonstrated that the model is robust to sampling frequency and random noise in the LDH measurements. It was able to detect mastitis reasonably well: Using a threshold mastitis risk of 0.7, sensitivity for detecting clinical mastitis was 82%. Specificity, that is, the ability to avoid misclassifying healthy observations as mastitis, was 99%.

Acute Disease↗
PubMed2004

Chaotic dynamics of a behavior-based miniature mobile robot: effects of environment and control structure.

To study the regularity and complexity of autonomous behavior, the flow of sensory information obtained in autonomous mobile robots under various conditions was analyzed as a complex system. Sensory information time series Xn was collected from a miniature mobile robot during free navigation, and plotted on the return map, the graph of X(n+tau) vs. Xn. The plot exhibited a characteristic trajectory, representing the regularity of the time series. Correlation integral and Lyapunov exponent analysis also showed properties of deterministic chaos; the presence of fractal dimension and positive Lyapunov exponent. Analysis of sensory information obtained in the robot with three different neural controllers revealed that the autonomous robot behaves in such a way that the flow of sensory information is governed by a deterministic rule, and this pattern is unique to each controller. Furthermore, the analysis in various environments exhibited that transitions from one trajectory to another on the return map occur during the course of autonomous behavior. The fractal and Lyapunov dimensions calculated in various conditions indicate that these dimension could be utilized to quantify the complexity of autonomous behavior and the relative difficulty of tasks. Analyses at different evolutionary stage revealed that behavioral performance correlates with fractal dimension. These studies using a miniature mobile robot that allowed to idealize the experimental conditions demonstrated firmly that the complex analysis could be utilized in evaluation and optimization of autonomous systems and the behavior.

Behavior↗
PubMed2005

Reactive clusters on a membrane.

We investigate the reaction dynamics of diffusive molecules with immobile binding partners. The fixed reactants build clusters that are comprised of just a few tens of molecules, which leads to small cluster sizes. These molecules participate in the reaction only if they are activated. The dynamics of activation is mapped to a time-dependent size of an active region within the cluster. We focus on the deterministic description of the dynamics of a single cluster. The spatial setup accounts for one of the most important determinants of the dynamics of a cluster, i.e. diffusional transport of reaction partners towards or away from the active region of the cluster. We provide numerical and analytical evidence that diffusion influences decisively the dynamic regimes of the reactions. The application of our methods to intracellular Ca2+ dynamics shows that large local concentrations saturate the Ca2+ feedback to the channel state control. It eliminates oscillations depending on this feedback.

Animals↗
PubMed1996

Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia.

Chaotic regimes in a mathematical model of pacemaker activity in the bursting neurons of a snail Helix pomatia, have been investigated. The model includes a slow-wave generating mechanism, a spike-generating mechanism, an inward Ca current, intracellular Ca ions, [Ca2+]in, their fast buffering and uptake by intracellular Ca stores, and a [Ca2+]in-inhibited Ca current. Chemosensitive voltage-activated conductance, gB*, responsible for termination of the spike burst, and chemosensitive sodium conductance, gNa*, responsible for the depolarization phase of the slow-wave, were used as control parameters. These conductances in intact snail bursting neuron are regulated by neuropeptides. Time courses of the membrane potential and [Ca2+]in were employed to analyse different regimes in the model. Histograms of interspike intervals, autocorrelograms, spectral characteristics, one-dimensional return maps, phase plane trajectories, positive Lyapunov exponent and especially cascades of period-doubling bifurcations demonstrate that approaches to chaos were generated. The bifurcation diagram as a function of gB* and the ([Ca2+]in-V) phase diagram of initial conditions reveal fractal features. It has been observed that a short-lasting depolarizing current of elevation of [Ca2+]in may evoke transformation of chaotic activity into a regular bursting one. These kinds of transitions do not require any changes in the parameters of the model. The results demonstrate that chaotic regimes of neuronal activity modulated by neuropeptides may play a relevant role in information processing and storage at the level of a single neuron.

Animals↗
PubMed1999

Estimation of the dynamics of event-related desynchronisation changes in electroencephalograms.

A method for the estimation of medium rate transitions of non-stationary electroencephalograms (EEG) is proposed. The method is applicable to such EEG dynamics that are between (a) fast transitions for which segmentation procedures are used and (b) slow transitions for which adaptive filters work properly. The estimation of the transition dynamics is based on a novel time-varying autoregressive model. This model belongs to the class of deterministic regression time-varying autoregressive models and its parametrisation allows only simultaneous transitions in all coefficient evolutions. Data from 22 patients was analysed. The performance of the method is first evaluated with realistic simulations of known transition dynamics and it is shown to be able to track medium-rate transitions. The method is then applied to the estimation of the dynamics of event related desynchronisation. It is shown that the proposed method is able to estimate the transitions which are less apparent, such as from a multi-infarct patient.

Algorithms↗
PubMed1993

Use of a new mathematical model in fitting survivorship curves of Drosophila treated with the antioxidant thiazolidine carboxylic acid.

We have recently proposed a mathematical model of survival mortality kinetics. It is based on biological and statistical hypotheses and is able to fit survivorship curves even at advanced ages, where other models fail. The mathematical function contains two parameters, omega and So, related to deterministic and stochastic factors, respectively. In the present paper the model has been applied to a set of survival curves of Drosophila melanogaster. The different curves derived from populations of flies treated with different doses of the antioxidant thiazolidine carboxylic acid (TCA). The treatment induced a significant progressive increase of mean and maximum lifespan up to the TCA dietary concentration of 0.3%. Higher doses of TCA, on the contrary, were toxic, reducing both mean and maximum lifespan. An interpretation of the differential TCA effects has been attempted on the basis of the values assumed by the two model parameters.

Aging↗
PubMed1998

Radiation protection recommendations as applied to the disposal of long-lived solid radioactive waste. A report of The International Commission on Radiological Protection.

(79) Waste, by definition, has no benefit. It should be viewed as one aspect of the beneficial practice that gave rise to it. Furthermore, radioactive waste management should be placed in the context of the management of society's waste in general. (80) A major issue in evaluating the acceptability of a disposal system for long-lived solid radioactive waste is that doses or risks may arise from exposures in the distant future. There is uncertainty surrounding any estimate of these doses or risks due to lack of knowledge about future conditions. Such exposures are treated as potential exposures as their magnitude depends on future processes and conditions that have probabilities associated with them. (81) Nevertheless, the Commission recognises a basic principle that individuals and populations in the future should be afforded at least the same level of protection from the action of disposing of radioactive waste today as is the current generation. This implies use of the current quantitative dose and risk criteria derived from considering associated health detriment. Therefore, protection of future generations should be achieved by applying these dose or risk criteria to the estimated future doses or risks in appropriately defined critical groups. These estimates should not be regarded as measures of health detriment beyond times of around several hundreds of years into the future. In the case of these longer time periods, they represent indicators of the protection afforded by the disposal system. (82 Constrained optimisation is the central approach to evaluating the radiological acceptability of a waste disposal system; dose or risk constraints are used rather than dose or risk limits. By this transition from limitation to optimisation, the needs of practical application of the radiological protection system to the disposal of long-lived solid waste disposal are met: determination of acceptability now for exposures that may occur in the distant future. Optimisation should be applied in an iterative manner during the disposal system development process and should particularly cover both site selection and repository design. (83) Two broad categories of exposure situations should be considered: natural processes and human intrusion. The latter only refers to intrusion that is inadvertent. The radiological implications of deliberate intrusion into a repository are the responsibility of the intruder. Assessed doses or risks arising from natural processes should be compared with a dose constraint of 0.3 mSv per year or its risk equivalent of around 10(-5) per year. With regard to human intrusion, the consequences from one or more plausible stylized scenarios should be considered in order to evaluate the resilience of the repository to such events. (84) The Commission considers that in circumstances where human intrusion could lead to doses to those living around the site sufficiently high that intervention on current criteria would almost always be justified, reasonable efforts should be made at the repository development stage to reduce the probability of human intrusion or to limit its consequences. In this respect, the Commission has previously advised that an existing annual dose of around 10 mSv per year may be used as a generic reference level below which intervention is not likely to be justifiable. Conversely, an existing annual dose of around 100 mSv per year may be used as a generic reference level above which intervention should be considered almost always justifiable. Similar considerations apply in situations where the thresholds for deterministic effects in relevant organs are exceeded. (85) Compliance with the constraints can be assessed by utilising either an aggregated risk-oriented approach, with a risk constraint, or a disaggregated dose/probability approach, with a dose constraint, or a combination of both. A similar level of protection can be achieved by any of these approaches; however, more information may

Hazardous Waste↗
PubMed1989

Comparison of the effects of enteral feeding with continuous and intermittent parenteral nutrition on hepatic triglyceride secretion in human beings.

Plasma triglyceride turnover was measured during steady-state conditions in 22 postoperative patients. Nine had received nutritional support with an enteral regimen, seven had received an equivalent regimen as continuous parenteral nutrition, and six received the same parenteral regimen as a cyclical infusion. After 5 days of nutritional support, each patient received an intravenous bolus of tritiated glycerol. Plasma radiolabeled triglyceride content was measured during the subsequent 24 hours. The data were analyzed by means of a simple deterministic model of plasma triglyceride kinetics and compared with the results obtained by stochastic analysis. The rates of hepatic triglyceride secretion obtained by deterministic analysis were higher than those obtained by the stochastic approach. However, the mode of delivery of the nutritional regimen did not affect the rate of hepatic triglyceride secretion regardless of the method of analysis. The results suggest that neither complete nutritional bypass of the gastrointestinal tract nor interruption of parenteral nutrition in an attempt to mimic normal eating has any effect on hepatic triglyceride secretion. Any beneficial effect that enteral feeding or cyclical parenteral nutrition may have on liver dysfunction associated with standard parenteral nutrition appears to be unrelated to changes in hepatic triglyceride secretion.

Aged↗
PubMed2005

Coupled map lattice approximations for spatially explicit individual-based models of ecology.

Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction-diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models.

Animals↗
PubMed1997

Detection of chaotic determinism in time series from randomly forced maps.

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Algorithms↗
PubMed2002

Nonlinear analysis of irregular animal vocalizations.

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.

Animals↗
PubMed2006

Deterministic and stochastic regimes of asexual evolution on rugged fitness landscapes.

We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length L. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance d(eff) up to which the population can spread in genotype space. For d(eff) = L, the deterministic quasi-species theory operates while for d(eff) < 1, the evolution is completely stochastic. Between these two limiting cases, the dynamics are described by a local quasi-species theory below a crossover time T(x) while above T(x) the population gets trapped at a local fitness peak and manages to find a better peak via either stochastic tunneling or double mutations. In the stochastic regime d(eff) < 1, we identify two subregimes associated with clonal interference and uphill adaptive walks, respectively. We argue that our findings are relevant to the interpretation of evolution experiments with microbial populations.

Adaptation, Biological↗
PubMed2001

Designer gene networks: Towards fundamental cellular control.

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a single-gene network. Bistability in the steady-state protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven around the hysteresis loop. We highlight the frequency dependence on the tunable parameter values, and discuss design plausibility. We emphasize how the model equations can be used to develop design criteria for robust oscillations, and illustrate this point with parameter plots illuminating the oscillatory regions for given parameter values. We then turn to the utilization of an intrinsic cellular process as a means of controlling the oscillations. We consider a network design which exhibits self-sustained oscillations, and discuss the driving of the oscillator in the context of synchronization. Then, as a second design, we consider a synthetic network with parameter values near, but outside, the oscillatory boundary. In this case, we show how resonance can lead to the induction of oscillations and amplification of a cellular signal. Finally, we construct a toggle switch from positive regulatory elements, and compare the switching properties for this network with those of a network constructed using negative regulation. Our results demonstrate the utility of model analysis in the construction of synthetic gene regulatory networks. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2001

Noisy clockwork: time series analysis of population fluctuations in animals.

Both biotic interactions and abiotic random forcing are crucial influences on population dynamics. This frequently leads to roughly equal importance of deterministic and stochastic forces. The resulting tension between noise and determinism makes ecological dynamics unique, with conceptual and methodological challenges distinctive from those in other dynamical systems. The theory for stochastic, nonlinear ecological dynamics has been developed alongside methods to test models. A range of dynamical components has been considered-density dependence, environmental and demographic stochasticity, and climatic forcing-as well as their often complex interactions. We discuss recent advances in understanding ecological dynamics and testing theory using long-term data and review how dynamical forces interact to generate some central field and laboratory time series.

Animals↗
PubMed2001

A stochastic, molecular model of the fission yeast cell cycle: role of the nucleocytoplasmic ratio in cycle time regulation.

We propose a stochastic version of a recently published, deterministic model of the molecular mechanism regulating the mitotic cell cycle of fission yeast, Schizosaccharomyces pombe. Stochasticity is introduced in two ways: (i) by considering the known asymmetry of cell division, which produces daughter cells of slightly different sizes; and (ii) by assuming that the nuclear volumes of the two newborn cells may also differ. In this model, the accumulation of cyclins in the nucleus is proportional to the ratio of cytoplasmic to nuclear volumes. We have simulated the cell-cycle statistics of populations of wild-type cells and of wee1(-) mutant cells. Our results are consistent with well known experimental observations.

Algorithms↗
PubMed1998

Determining the number of independent sources of the EEG: a simulation study on information criteria.

The separation of signal and noise is an important problem in the analysis of EEG and MEG data. Furthermore, many source localisation strategies need the number of independent signal components as input parameter (e.g., dipole fit, multiple signal classification). Information criteria offer a relatively objective way to separate the space spanned by the principal components of the data covariance matrix into a signal and a noise part. Eighteen such criteria were extensively tested by simulations. They differ with respect to the statistical model of the data, the assumptions on the noise, and the correction term. In the simulations, different dipole sources were used to generate EEG, which was then distorted by Gaussian correlated or uncorrelated noise. The noise level, the accuracy of the noise covariance matrix used by the criteria, the numbers of channels and time samples, and the stochastic or deterministic nature of the source waveforms were varied. The performance of the criteria was very variable. For each criterion, limits for the noise level and the relative inaccuracy of the noise covariance matrix could be established. Taking more channels or time steps did increase the criteria's ability to tolerate noise, but at the same time, made them more vulnerable to inaccuracies in the (estimated) noise covariance matrices. Out of the eighteen criteria investigated, we recommend two criteria that are best suited for the cases of (1) high noise and accurate covariances and (2) low noise and less accurate covariances.

Artifacts↗
PubMed2005

Learning deterministic finite automata with a smart state labeling evolutionary algorithm.

Learning a Deterministic Finite Automaton (DFA) from a training set of labeled strings is a hard task that has been much studied within the machine learning community. It is equivalent to learning a regular language by example and has applications in language modeling. In this paper, we describe a novel evolutionary method for learning DFA that evolves only the transition matrix and uses a simple deterministic procedure to optimally assign state labels. We compare its performance with the Evidence Driven State Merging (EDSM) algorithm, one of the most powerful known DFA learning algorithms. We present results on random DFA induction problems of varying target size and training set density. We also studythe effects of noisy training data on the evolutionary approach and on EDSM. On noise-free data, we find that our evolutionary method outperforms EDSM on small sparse data sets. In the case of noisy training data, we find that our evolutionary method consistently outperforms EDSM, as well as other significant methods submitted to two recent competitions.

Algorithms↗