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A stochastic model for the development of an AIDS epidemic in a heterosexual population.

A non-age-dependent model, describing the evolution of a bisexual population, is developed in this paper and applied to projecting an AIDS epidemic in a heterosexual population. Included in the formulation are frequency- and non-frequency-dependent rules of partnership formation as well as five states of HIV disease, affecting the probability of infection per sexual contact. Results from computer experiments, designed to study the development of an AIDS epidemic in a heterosexual population fed by single males with a 50% prevalence of HIV infection prior to becoming active in heterosexual partnerships, are reported. In these experiments, the only source of HIV infection for females was sexual contacts with infected males within partnerships. Data on the probability of infection per sexual contact with an infected partner and the number of sexual contacts per month were incorporated into the model. However, the numbers used for the initial population of singles, couples, and those becoming sexually active per month were hypothetical. Even though the prevalence of HIV infection among males entering heterosexual partnerships was high, after 30 years the projected prevalence of HIV infection among females ranged from about 10 to 15% depending in part on the expected duration of partnerships and on whether the frequency- or non-frequency-dependent model was used. In these experiments, solutions of the embedded, nonlinear, deterministic equations for the incidence of HIV infection and the cumulative number of deaths due to AIDS proved to be good measures of central tendency for the sample functions of the stochastic population process.

Acquired Immunodeficiency Syndrome

Cytophotometric analysis of basic nuclear proteins during gametogenesis in the free-living nematode Panagrellus silusiae.

The cytochemical staining characteristics of basic nuclear proteins during gametogenesis in both sexes of the free-living nematode Panagrellus silusiae were monitored by absorption microspectrophotometry. During spermatogenesis, the levels of both of the nuclear-bound Sakaguchi and 1-fluoro-2, 4-dinitrobenzene (FDNB) reagents per Feulgen-DNA content increase prior to meiosis and subsequently drop off during spermiogenesis. During oogenesis, the amount of Sakaguchi-protein to DNA ratio rises slightly whereas the FDNB-protein to DNA ratio undergoes a meagre decline. Since the oocyte of Panagrellus accumulates DNA in excess of a 4C DNA equivalent, the relative constancy of the ratio of basic nuclear protein content to DNA amount during oogenesis signifies that these proteins are being continously produced during oocyte maturation. After treatment with alkaline fast green (pH 8.1) the cytoplasmic and nuclear regions of the gonocytes of both sexes yield such an intense reaction that microspectrophotometric measurements could not be taken. The basis of the cytoplasmic staining reaction to the fast green (pH 8.1) dye was not determined. The rapid, highly deterministic programme of embryogenesis in Panagrellus may require a substantial stockpiling of basic nuclear proteins during oogenesis.

Animals

Impact of diffuse nitrate pollution sources on groundwater quality--some examples from Czechoslovakia.

In several regions of Czechoslovakia with intensive agricultural production, the correlation between the amount of nitrogen fertilizer applied and the nitrate content in groundwater has been recognized. Nitrate pollution of groundwater is considered to be the most serious source of nonpoint pollution in Czechoslovakia. A program of research into the effects of farming activities on groundwater quality in Czechoslovakia is under way on experimental fields (20 to 30 hectares) and, simultaneously, in regions in which shallow, vulnerable aquifers occur. The importance of the soil organic matter's stability for maintaining the groundwater quality is emphasized. Research based on nitrogen and organic carbon balance has shown that the restoration of a soil-groundwater system is a complicated process that usually requires changes in the extent and intensity of agricultural activities and consistent attention to the effects produced by natural conditions. Regional investigation of the impact of farming on shallow aquifers in the fluvial deposits of the Elbe River in Bohemia has proved the hydrochemical instability and vertical hydrochemical heterogeneity of these aquifers. The WASTEN deterministic model was used for modeling the transport and transformation of various types of inorganic fertilizers. The input data is based on laboratory and field measurements. Special topics are the verification of model calculations and the time and spatial variability of input data with respect to the unsaturated zone. The research results are being used for making regional and national agro-groundwater managerial schemes more precise, as well as for decision-making.

Agriculture

Computerized electrocardiogram diagnosis: fuzzy approach.

This paper investigates the computerized analysis of electrocardiographic signals. The biological variability, the lack of standards in the definition of measurements and of diagnostic criteria make the classification problem a complex task. Two basic methods of the diagnostic process are described: the statistical model and the deterministic approach. In particular, a model for ECG classification will be illustrated where the imprecise knowledge of the state of cardiac system and the vague definition of the pathological classes are taken care of by means of the fuzzy set formalism.

Diagnosis, Computer-Assisted

The scalp distribution of the fractal dimension of the EEG and its variation with mental tasks.

The insights gained by the concept of deterministic chaos for the EEG is that this seemingly disordered process may be governed by relatively few simple laws which could be determined. One of the quantitative measures of a complex dynamical system is that of its dimension. The term 'dimension' refers to the ability of a space to contain a set of points. We estimated the correlational dimension of the EEG and compared the outcome to traditional Fourier analyses. In addition, we tested the hypothesis that the EEG can be described as filtered noise. Data from 15 electrode sites and 31 subjects are reported in the present study. We have utilized a variety of tasks that cut across sensory modalities including touch, vision, and imagery which reflect neuropsychological processes that differentially engage areas of the cortex in the first part of the study. In the second part, the differences between the perception of an object and the imagination of the same object were evaluated. The outcome shows variations between scalp sites for all measures and also variations between tasks in terms of dimensionality of the EEG. The hypothesis of a higher dimensionality ("complexity") of imagery compared to actual perceptual processing was confirmed. A statistical comparison between the maps generated by means of the various measures shows that different informations are extracted when using the different measures. There is also statistical evidence that the EEG cannot completely be described by the model of filtered noise.

Adult

Chaotic dynamics in autonomic nervous system activity of a patient during a psychotherapy session.

Chaos theory and nonlinear dynamical modeling have been applied successfully in a variety of scientific fields ranging from the physical sciences to population biology. More recently, investigators have modeled long-term psychological processes by applying this paradigm to subjective measures. Yet, mathematically rigorous dynamical modeling of transient psychodynamic processes remains uncharted. Human behaviors and intrapsychic processes often defy prediction, yet psychodynamic theory views these as fundamentally deterministic. We postulate that a nonlinear dynamical analysis of mental states and mental control processes may help reconcile the paradox that seemingly random mental states are thought ultimately to result from deterministic, rather than stochastic, psychological processes. As an initial empirical approach, we examined spontaneously occurring autonomic activity of a patient during 1 hr of psychotherapy and illustrate that cardiac responses associated with psychologically meaningful events possess nonlinear characteristics indicative of chaos. Such nonlinear analyses may shed light on fundamental issues of psychological functioning.

Adult

A statistical analysis of the ECG measurements used in computerized interpretation of acute anterior myocardial infarction with applications to interpretive criteria development.

Computerized interpretation of the electrocardiogram (ECG) for detection of acute myocardial infarction (AMI) has been an area of active investigation for the past few years. Advances in the development of criteria for increased accuracy have resulted through the use of clinically correlated databases. Previously, using such databases, the sensitivity for interpretation of AMI in the Marquette 12SL ECG analysis program has increased from 21% to 65% with specificity remaining unchanged (99%). This study attempted to find measurements of the QRS and ST-segment from 7 of the 12 standard ECG leads to increase the sensitivity of detection of anterior AMI to the level of a trained physician while maintaining the current level of specificity. Regression analyses were performed on the measurements to see which ones could improve sensitivity and what effect they had on specificity. There was no clear separation of the individual measurements between the normal database or the true positive and true negative anterior AMI databases for maintaining high specificity. In a parallel study of the same data, deterministic criteria combining both ST and T wave information increased the sensitivity of the 12SL analysis program for detection of anterior AMI to 71% on a clinically correlated anterior AMI database and 75% on a physician interpreted anterior AMI database while maintaining the specificity at 99%.

Adult

The reproducibility of forced expiratory wheezes.

Previous work has shown forced expiratory wheezes (FEW) to be associated with onset of flow limitation and to have spectral characteristics similar to wheezes heard in patients with obstructive lung diseases. This study was designed to determine whether the acoustic characteristics of FEW are reproducible under controlled lung volume and flow conditions. Six healthy, nonsmoking young adults 28 to 37 yr of age were studied. They performed FVC maneuvers through a set of round apertures (diameters, 14, 12, 10, 8, 6, 4, 2, and 1 mm). Flow, measured with a pneumotachograph, and tracheal lung sounds, recorded with a Hewlett-Packard HP20510A contact sensor, were recorded simultaneously on magnetic tape and analyzed off-line. For each subject, data from three different aperture sizes, measured in triplicates, were analyzed (total of 54 runs); 199 different wheezes were identified (mean, 3.7 wheezes/run), and 56.7 +/- 5.1% (mean +/- SEM) of wheezes found in a certain run (range, 41.7 to 77.8%) were identical to wheezes found in the other two runs of the same aperture size (i.e., same flow rate). In 17 of the 18 sets of triplicate runs analyzed, at least one major wheeze was identical in all three runs of the set. In three of the sets, two different identical wheezes were found. These findings support a deterministic mechanism of generation of wheezes and is in line with the predictions of the "flutter theory."

Adult

Time-series analysis. Use of autocorrelation as an analytic strategy for describing pattern and change.

Although graphic representation of time-series data is one method to describe patterns of phenomena, autocorrelations, correlograms, and plots of the autocorrelation function provide descriptive and statistical methods that reveal the structure of a deterministic cycle component within the time-series. The autocorrelation function provides a method for the investigator to test hypotheses about the nature and pattern of relationships between measured and latent variables. Patterns of phenomena can be analyzed statistically using objectively provided criteria. The autocorrelation function can also be used to understand the change in response or behavioral patterns following an experimental intervention. Traditional group comparison designs, using cross-sectional data collection strategies cannot identify differences within the individual nor can they identify patterns of behavior or structural patterns within the data. Autocorrelation and cross-correlation become threats to statistical validity when conventional methods are used; however, in time-series analysis, autocorrelation allows close scrutiny of the pattern of response within an individual across a time-dimension.

Data Interpretation, Statistical

Possible detection of turbulent blood flow using multiparametric encoding gradients in MRI.

Magnetic resonance imaging (MRI) has significant potential as a highly accurate noninvasive flow measurement technique. Presented here is an approach to the imaging of turbulence in the velocity profiles. Recent publications have presented multiparametric encoding gradient methods, which are based on a deterministic rather than a statistical approach to spin motion. Following these methods of building up a general gradient from a basic set of gradients, the effects of turbulence and undetermined moments of motion on the image are discussed. Image blurring due to the nondeterministic behavior of spins (e.g., diffusion, turbulence) is not removed by these techniques, and this fact may be useful in identifying regions of turbulent flow, which are of importance in the clinical observation of cardiac and vascular haemodynamics. Due to its random nature, the elimination of turbulent effects by the use of a deterministic method is bound to fail. On the other hand, regions of turbulent flow may be identified due to signal decrease from those regions, provided one is careful to remove all the causes of nonturbulent signal reduction present due to nonturbulent flow moments. In the multiparametric phase encoding method, gradient amplitude tends to increase with higher moments of motion. The temporal behavior of these gradients is discussed, and it is suggested that the increase in their duration will enhance the encoding of higher motion terms at the expense of imaging time.

Blood Flow Velocity

Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series.

An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.

Animals

Adaptive realtime compensatory feedback to open the light-pupil reflex loop.

Integrity of the visual pathway is often clinically determined from response of the pupil to light. The need for more quantitative measurement of pupillary response has led engineers to investigate the light-pupil reflex with systems analysis techniques. The results have made the light-pupil reflex a model of the application of the principles of control theory to physiologic mechanisms. This analysis required that the system be rendered open loop by focusing the stimulus at the center of the pupil. Patients may not be able to restrict their head and eye movement well enough to permit the feedback loop to be rendered open loop optically. Thus, clinical applications of the technique have been limited. A means of opening the feedback loop by using a realtime deterministic autoregressive moving average prediction algorithm integrated into a computer based television pupillometer has been developed. It employs a model reference adaptive scheme to identify the physiologic system, then predicts future values of pupil area to compensate for delays in the measuring apparatus. A computer driven liquid crystal display shutter controls retinal illuminance to render the light-pupil reflex open loop. This technique reduced the mean square error of retinal illuminance by about 75% compared to uncompensated pupil responses.

Algorithms

Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm.

A method is presented for identifying functional expansion and difference equation representations for nonlinear systems. The method relies on an orthogonal approach which does not require explicit creation of orthogonal functions. This greatly reduces computing time, so that 15-fold increases in speed of estimating kernels or difference equation coefficients are readily obtainable, compared with a previous orthogonal technique. In addition, storage requirements are considerably diminished. A wide variety of input excitation, both random and deterministic, can be used, and the method is not limited to inputs which are Gaussian, white or lengthy. A model of the peripheral auditory system is simulated to show kernel measurement is free of artifacts using the present method, in contrast to the crosscorrelation approach.

Algorithms

Dimensional analysis of the human EEG and intelligence.

The purpose of this study was the determination of the relationship between the dimensional complexity of the electroencephalogam (EEG) and the level of intelligence in humans. In two experiments 34 male subjects were divided into two groups, with high and low levels of intelligence (as measured by the intelligence quotient (IQ)). During a resting phase and various mental imagery conditions the EEG was recorded from several scalp sites. Nonlinear analysis, based on the theory of deterministic chaos, revealed that subjects with high IQs demonstrate higher dimensional complexity of the EEG attractors than subjects with low IQs only during resting conditions. During performance of the imagery tasks the less intelligent subjects increase the complexity of electrical brain dynamics such that IQ-dependency vanishes. The gross (mass) neuronal manifestation of general intelligence seems to depend on task conditions and may be related to the individual brain dynamics only when no specific task is present.

Adult

Neural perspectives of cerebral correlates of giftedness.

Giftedness is defined as some special endowment or propensity for creativity, skill, and eminent achievement, found in relatively few individuals among the population. A high order of mental power (IQ), creativity, and motivation (task commitment) appear to be the most universally recognized attributes of the gifted. This report summarizes current knowledge of the cerebral correlates of intelligence and creativity, including physiological measures of EEG, cortical power spectrum, brain evoked potentials, and positron emission tomography. Controversy, debates, contentions, formal hypotheses, and research issues are considered. We are especially interested in the formulation of the deterministic function of EEG-brain dynamics. A CHAOS modeling on hierarchy of cognitive organization and cerebral processing in the gifted is suggested.

Adaptation, Psychological

Persistence in population models with demographic fluctuations.

A persistence and extinction theory is developed through analytical studies of deterministic population models. Under hypotheses that require demographic parameters to fluctuate temporally, the populations may or may not oscillate. Extinction, when it occurs, is asymptotic. An hierarchy of persistence criteria, based upon fluctuations measured by time average means, is derived. In some situations a threshold value is found to separate persistent population models from those that tend to extinction. Application of the persistence-extinction theory is to the problem of assessing effects of a toxic substance on a population when toxicant inputs to the environment and to resources are oscillatory.

Demography

A methodological study of a nonlinear stochastic model of an AIDS epidemic with recruitment.

A nonlinear stochastic model of an AIDS epidemic with recruitment of infectives, susceptibles, and AIDS cases into a randomly mixing population of male homosexuals was formulated and studied from a methodological point of view through intensive computer experimentation. Probability generating functions were used to formulate a model for the monthly probability that a susceptible individual becomes infected with HIV, under the assumption that the probability of infection per sexual contact varies as a function of the duration of infection. A method for taking into account the use of condoms to prevent infection with HIV was also introduced. Nonlinear difference equations, resembling deterministic epidemic models, were embedded in the stochastic population process by iterating an initial conditional expectation. Examples of Monte Carlo experiments are presented, illustrating that solutions of these nonlinear difference equations are not always good measures of central tendency for variations in the sample functions of the process. Two important substantive conclusions drawn from the Monte Carlo experiments were that efforts should be made to collect quantitative information on the probability of infection per sexual contact as a function of duration of infection and the frequency of condom use within and among risk categories in a population.

Acquired Immunodeficiency Syndrome

On the description of neuronal output properties using spike train data.

Neuronal output properties for input stimuli that evoke a deterministic response can be efficiently described by the interspike-interval function (Awiszus 1988a). It is shown in this paper that there are stimuli for which both the Hodgkin-Huxley (HH-) model of an action potential encoding membrane (Hodgkin and Huxley 1952) and a muscle spindle primary afferent generate responses which violate the conditions for a deterministic one. Instead of being stochastic these responses follow systematic rules, namely those for a semi-deterministic response, a class of neuronal responses established in this paper that includes the deterministic one. Instead of being stochastic these output properties are best described by the interspike-interval curve. A phase plane analysis of the internal properties of the HH-model underlying such responses shows that it is reasonable to assume that responses of an HH-model and consequently, all neurons for which an HH-model is a valid description of the action potential encoding process, always fall into the class of semi-deterministic responses, regardless of the input current density time course as long as it is large enough to maintain spike activity. Consequences of this assumption for the analysis of neuronal output properties are discussed with respect to output measures and efficient input stimuli.

Action Potentials