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PubMed1979

A time series approach to forecasting Australian total live-births.

The relationship between classical demographic deterministic forecasting models, stochastic structural econometric models and time series models is discussed. Final equation autoregressive moving average (ARMA) models for Australian total live-births are constructed. Particular attention is given to the problem of transforming the time series to stationarity (and Gaussianity) and the properties of the forecasts are analyzed. Final form transfer function models linking births to females in the reproductive age groups are also constructed and a comparison of actual forecast performance using the various models is made. Long-run future forecasts are generated and compared with available projections based on the deterministic cohort model after which some policy implications of the analysis are considered.

Australia↗
PubMed1994

A clarification of the phi mixing model.

The authors review a deterministic model proposed for the analysis of two-way contingency tables that arise in counts of pairwise interactions. This model decomposes the table into the sum of two matrices with special forms: in one the contacts are distributed selectively, in the other they are distributed at random. We show that this model has several inherent problems. The decomposition is not unique, which compromises estimation and interpretation of the parameters; the deterministic framework provides no basis for estimation or hypothesis testing; and the assumption of decomposibility is supported by neither empirical evidence nor theoretical considerations. We show that generalized linear models provide a suitable alternative once the probability process is specified and the overparameterization is removed.

Animals↗
PubMed1995

Measuring "chaos" in the brain: a tutorial review of EEG dimension estimation.

The technique of dimension estimation is currently a leading application of nonlinear dynamics (popularly termed "chaos theory") to EEG analysis. A tutorial review of this technique is presented along with some elementary background concepts from nonlinear dynamics. Practical aspects of applying dimension estimation to EEG data are also reviewed, and the possible role of deterministic chaos in brain function is discussed.

Brain↗
PubMed1985

Possible forms for dwell-time histograms from single-channel current records.

Certain macromolecules embedded in the cell membranes of a variety of cells behave as gated ion-selective pores or channels. The length of time that a channel remains open or closed is not deterministic in nature and must be described in terms of relative probabilities. If channels act independently of each other and appropriate experimental conditions can be maintained, the behavior of a channel can be described by a homogeneous Markov process. Using this representation, the relative probability of observing openings (or closings) of various durations can be described by a sum of discrete components which are related to the underlying model of the kinetic behavior of the channel. Generally, these discrete components are taken to be simple decaying exponentials; however, exponentially decaying oscillatory components (as well as certain others which are discussed) are consistent with the Markov process representation. The presence of components other than simple decaying exponentials is shown to imply the violation of detailed balance in the steady-state (which requires energy), and thus, the presence of cyclic pathways in models which accurately represent the kinetic behavior of the channel. Oscillatory components, if present, will in general decay at a faster rate than the slowest decaying component, which, except under a very restricted set of conditions, will be a simple exponential.

Cell Membrane Permeability↗
PubMed1996

Computing marginal expectations for large compartmentalized models with application to AIDS evolution in a prison system.

The customary models for the AIDS epidemic are compartmentalized according to criteria such as risk factors, sexual habits, gender, race, age, and HIV status and stage. Hitherto, with very few exceptions, investigators have resorted to deterministic approximations or to simulation for the computational investigation of such models, which do not yield to purely analytic methods. The present paper describes a numerical technique, not dependent on Monte Carlo simulations, for such compartmentalized Markov population processes. Analytic error bounds and computational evidence suggest that this technique is quite accurate. The study is motivated and illustrated by a model for a prison system, with ten interrelated prisons, twenty compartments, and thousands of individuals. This model is of increasing interest in itself because the HIV/AIDS epidemic is particularly virulent among prison populations, where the environment offers special opportunities to investigate various prevention and educational programmes quantitatively. Our computational techniques are shown to be effective for the analysis of such a prison system, even though the resulting Markov process is an order of magnitude more complicated than other stochastic epidemic models currently being investigated. The modelling approach and numerical device appear to be applicable to a wide variety of population processes involving migration between population patches.

Acquired Immunodeficiency Syndrome↗
PubMed1995

The D-1 dopamine receptor: past, present and future an idiosyncratic review.

1. Key events in the experimental investigation of the D-1 dopamine receptor are reviewed. 2. The efficacy of D-1 receptor agonists in the treatment of experimental parkinsonism in MPTP-treated primates is demonstrated. The diminished dyskinetic liability of D-1 agonists is discussed. 3. The significance of the dopa-induced dyskinesias is discussed from the perspective of deterministic chaos. The unpredictibility and irreproducibility of dyskinetic movements is highlighted and compared with features of the logistic equation. 4. The authors propose that the dopa-induced dyskinesias should be considered to be a manifestation of a chaotic process within the basal ganglia. The loss of the dopaminergic innervation and the subsequent repeated exposure to dopamine (derived from the exogenous dopa administered to the subjects) alters the response properties of the basal ganglia circuitry so that stimulation of dopamine receptors now elicits the dyskinetic movements.

Animals↗
PubMed1993

Time series analysis of complex dynamics in physiology and medicine.

A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.

Animals↗
PubMed1993

Recurrence plots of neuronal spike trains.

The recently developed qualitative method of diagnosis of dynamical systems-recurrence plots-has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as significant deviations from randomness in serial ordering of intervals. Recurring episodes of alike, quasi-deterministic firing patterns suggest the spontaneous modulation of the dynamical complexity of the trajectories of observed neurons. These modulations are associated with changing dynamical properties of a neuronal spike-train-generating system. Their existence is compatible with the information processing paradigm of attractor neural networks.

Action Potentials↗
PubMed1980

System-theoretical analysis of the Clare Bishop Area in the cat.

The Clare Bishop Area (CBA) is a retinotopically organized cortical area in the cat brain connected to a great variety of visual areas in a very complex way (Fig. 1). Experimental analysis is difficult because of the following aspects: 1. As the distance from the retina increases, the signal combinations necessary to analyse the system become more and more specific. 2. Feedback loops cannot be opened, so an unequivocal identification of CBA cell properties is impossible. 3. The nonlinear character seems to have a great influence on signal processing. To circumvent these problems, specific signal combinations leading to a separation of input subsystems have been developed (Hoffmann and v. Seelen, 1979). On grounds of practical experience and theoretic considerations, the signal combinations are usually restricted to combinations of deterministic and stochastic signals when analysing the CBA. The different methods of measurement are applied successively, the linearizing ones being used first so that a rough classification is possible. If the nonlinear features of the system have little efect, they can be linearized in the theoretical description, if not, a model consisting of a sequence of a linear dynamic system and a nonlinear one with a static, polynomial feature must be used for analysis by parameter estimation. The experimental part of this publication deals with the determination of a number of cell properties. Some hypotheses on the function of the CBA are tested. THe results lead to the conclusion that further experiments, such as are discussed below, are necessary in the input subsystems, area 18 and 19. The experimental results of some other authors (Hubel and Wiesel, 1969; Turlejski, 1975; Turlejski and Michalski, 1975; Smith and Bauman, 1979; SPera and Bauman, 1979) are confirmed by the implicaions of the present results.

Animals↗
PubMed1989

Optimal input design: case study of the metabolic process.

An optimal input of nutrients into the metabolic process of the individual subject so as to effect desired therapeutic results is particularly important for the critically ill. A patient-related, individualized nutrients optimization procedure is proposed here. The procedure is applicable to any time-invariant and deterministic metabolic model that is bound by one or more quantitative limiting criteria. As a case in hand, the procedure is used to optimize the individual metabolic needs of critically ill patients. The results indicate that, given a proper metabolic model, the patient may be treated on an individual appropriateness basis rather than on the traditional statistical intuitive approach.

Critical Care↗
PubMed1994

Artificial neural networks for the diagnosis of atrial fibrillation.

Different forms of artificial intelligence have been applied to pattern recognition in medicine. Recently, however, a relatively new technique involving software-based neural networks has become more readily available. Deterministic logic is currently applied to rhythm analysis in computer-assisted ECG interpretation methods developed in the University of Glasgow. The aim of the present study is to compare an artificial neural network with deterministic logic for separating sinus rhythm (SR) with supraventricular extrasystoles (SVEs) and/or ventricular extra-systoles (VEs) from atrial fibrillation (AF) at a particular point in the diagnostic logic of the Glasgow Program. A total of 2363 ECGs with 1495 AF and 868 SR + (SVEs and/or VEs) are used for training and testing a variety of neural networks, and the optimum design is selected. Methods for combining the results of the neural-network classification and the deterministic interpretation are also developed. A further 717 ECGs are used to test the selected network. The results show that the use of an artificial neural network can improve the sensitivity of reporting AF from 88.5% using the deterministic approach to 92%, without sacrificing specificity (92.3%).

Atrial Fibrillation↗
PubMed1988

Ventricular fibrillation-defibrillation in the toad Bufo paracnemis.

Fibrillation is more likely to occur in animals showing a high degree of cellular differentiation. Lower species, with cardiac tissue histologically and electrophysiologically more uniform, very rarely, if ever, can fall into this uncoordinated activity. We describe experiments during which two specimens of the South American toad, Bufo paracnemis (body weights, 363 g and 297 g; ventricular weights, 1.8 g and 1.4 g, respectively), were repeatedly fibrillated and defibrillated almost at will. However, we failed when we tried a series of experiments in a given number of animals. Over a total of 16 fibrillation-defibrillation episodes, a fibrillation threshold of about 3.8 mA/g was estimated. The lowest defibrillation values were, respectively, 43 mA/g and 507 mA/g, using rectangular pulses (less than 7 msec pulses width). There were also a few spontaneous reversals before and after defibrillation shocks. These cases point to our still poor understanding of the mechanisms involved in the process. It is suggested that reentry or multiple ectopic foci might not be the basic mechanisms, as traditionally accepted. Rather, it might well be a new behavior of the cells or group of cells like that predicted by the theory of deterministic chaos.

Animals↗
PubMed1979

A mathematical model for the 1973 cholera epidemic in the European Mediterranean region.

For the cholera epidemic that occurred in the European Mediterranean region in the summer of 1973, a simple deterministic mathematic model is proposed; it consists of a system of two ordinary differential equations which concern the evolution of the human infective population in a town community and of bacteria population in the sea. It is conjectured that the infection process obeys a non linear saturation-type law. A phase space analysis is performed for the system of equations. Conclusions are drawn which concern the evolution of the epidemic and which suggest some indications for the selection of public health policies. The validity of the model is compared with the available data for the town of Bari (Italy).

Cholera↗
PubMed1996

A mathematical model for fibro-proliferative wound healing disorders.

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsen et al., J. theor. Biol. 177, 113-128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states-a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.

Adult↗
PubMed1995

Application of the correlation integral to respiratory data of infants during REM sleep.

Non-linear time sequence analysis has been performed on infant sleep measurement data in order to obtain more information about the respiratory processes. As a first step, respiration data during REM sleep were analysed with methods from non-linear dynamics, especially, the correlation integral and the slope of its log-log plot, representing the correlation dimension. Before calculation of the correlation integral, a special kind of filtering has to be applied to the data. This filtering algorithm is a state space and singular value decomposition-based noise reduction method, and it is used to separate the noise and signal subspaces. The dynamics of a signal (in our case data from the respiratory process) and its degrees of freedom can be characterised by the correlation integral and by the correlation dimension, respectively. The main result of this study is that the highly irregular-looking breathing patterns during REM sleep could be described by a deterministic system, and finally the physiological significance of this finding is discussed.

Electroencephalography↗
PubMed1974

A note on the balance between random sampling and population size. (On the 30th anniversary of G. Malécot's paper).

Wright's model for the effects of random fluctuations in gene frequency in a population of fixed size is generalized to randomly fluctuating population size, and treated from the viewpoint of G. Malécot, using a martingale convergence theorem. The gene frequency approaches a limit, whose value depends on the actual realization, or history, of the process; that is, convergence is with probability one (or: almost surely) in statistical language. The limit does not necessarily represent a state of fixation of either allele; in particular, the limiting probability distribution is not necessarily trivial. For the special case of deterministically varying population size, a necessary and sufficient condition for such non-triviality is given.

Alleles↗
PubMed1978

Size variations and correlation of different cell cycle events in slow-growing Escherichia coli.

Cell lengths have been determined at which cycle events occur in the slow-growing Escherichia coli B/r substrains A, K, and F26. The radioautographic and electron microscope analyses allowed determination of the variations in length at birth, initiation and termination of DNA replication, and initiation of the constriction process and of cell separation. In all three substrains the standard deviation increased between cell birth and initiation of DNA replication. From there on, the standard deviation remained relatively constant until cell separation. These observations are consistent with the presence of a deterministic phase during the cell cycle in which the cell sizes at initation of DNA replication and at cell division are correlated.

Cell Cycle↗