Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.
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Biological Transport↗
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The use of operational modeling of HIV/AIDS in a systems approach to public health decision making.
Compartmental models of infectious diseases readily represent known biological and epidemiological processes, are easily understood in flow-chart form by administrators, are simple to adjust to new information, and lend themselves to routine statistical analysis such as parameter estimation and model fitting. Technical results are immediately interpretable in epidemiological and public health terms. Deterministic models are easily stochasticized where this is important for practical purposes. With HIV/AIDS, serial data on both HIV prevalence and AIDS morbidity have been available from San Francisco. Assuming the distribution of the incubation period to be biologically stable, statistical analysis is quite feasible in other regions, even those with no reliable HIV data. Transmission rates must be estimated locally. It is also often possible to estimate the effective size of a population subgroup at risk, from population data on AIDS morbidity only. Computer simulation provides estimates of the evolving pattern of both HIV prevalence and AIDS morbidity. Some public health questions can be answered only by appropriately formulated stochastic models.
Decision Making↗
Deterministic nonlinear chaos in brain function and borderline psychopathological phenomena.
There exists a fundamental overall property of the brain which monitors, modulates, and ensures a smoothness of function and which further determines elegance and grace in functioning. This property also imparts a quality of, or a sense of proportion among all other faculties of the brain. It is postulated in this paper that such a property/function, up to now almost taken for granted, is maintained/exercised by a nonlinear deterministic chaotic mode of brain function. If this is the case, borderline psychopathological phenomena, when they flare up, can be explained as resulting from sudden reduction of such a deterministic chaotic mode and the emergence of a pathological order, as the system becomes an oscillating one.
Borderline Personality Disorder↗
A critical examination of perceptual and cognitive effects attributed to full-spectrum fluorescent lighting.
Full-spectrum fluorescent lighting (FSFL) has been credited with causing dramatic improvements in vision, perception and cognitive performance as compared with other fluorescent lamp types. These effects are hypothesized to occur because of similarity between FSFL emissions and daylight, which is said to have evolutionary superiority over other light sources. This review, covering 1945-98, critically considers the evidence for these claims. In general, poor-quality research has resulted in an absence of simple deterministic effects that can be confidently attributed to fluorescent lamp type. Promising avenues for lighting behaviour research include investigations of cognitive mediators of lighting-behaviour relationships, and flicker rates and colour rendering effects on visual processing, appearance judgements and affect. Good lighting solutions are more complex than lamp type specification.
Cognition↗
Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA.
Computer simulations of the supercoiling of DNA, largely limited to stochastic search techniques, can offer important information to complement analytical models and experimental data. Through association of an energy function, minimum-energy supercoiled conformations, fluctuations about these states, and interconversions among forms may be sought. In theory, the observation of such large-scale conformational changes is possible, but modeling and numerical considerations limit the picture obtained in practice. A new computational approach is reported that combines an idealized elastic energy model, a compact B-spline representation of circular duplex DNA, and deterministic minimization and molecular dynamics algorithms. A trefoil knotting result, made possible by a large time-step dynamics scheme, is described. The simulated strand passage supports and details a supercoiled-directed knotting mechanism. This process may be associated with collective bending and twisting motions involved in supercoiling propagation and interwound branching. The results also demonstrate the potential effectiveness of the Langevin/implicit-Euler dynamics scheme for studying biomolecular folding and reactions over biologically interesting time scales.
Chemical Phenomena↗
Modelling wastewater transformation in sewers based on ASM3.
A deterministic model for wastewater transformations in the sewer that includes activity in the wastewater and in the sewer wall biofilm was developed. It is based on the Activated Sludge Model No. 3 (ASM3). The mass transfer processes in the biofilm were modelled with the effectiveness approach. This approach allowed for fast calculation, required only a limited number of parameters and gave good results. The ASM3 related parameters were calibrated and validated with laboratory experiments. An equation for the aeration of the wastewater through the water surface was determined with a method based on the inert gas sulphur hexafluoride. The other model parameters such as wall roughness, attachment of particles to the biofilm and biofilm erosion were calibrated and validated with field experiments in a main sewer. The resulting model described the oxygen concentration and wastewater respiration well. It can be easily linked for integrated urban hydrology modelling with the WWTP Activated Sludge Model and the newly proposed River Water Quality Model No. 1.
Biofilms↗
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↗
An iterative sequential mixed-integer approach to automated prostate brachytherapy treatment plan optimization.
Conventional treatment planning for interstitial prostate brachytherapy is generally a 'trial and error' process in which improved treatment plans are generated by iteratively changing, via expert judgement, the configuration of sources within the target volume in order to achieve a satisfactory dose distribution. We have utilized linear mixed-integer programming (MIP) and the branch-and-bound method, a deterministic search algorithm, to generate treatment plans. The rapidity of dose falloff from an interstitial radioactive source requires fine sampling of the space in which dose is calculated. This leads to a large and complex model that is difficult to solve as a single 3D problem. We have therefore implemented an iterative sequential approach that optimizes pseudo-independent 2D slices to achieve a fine-grid 3D solution. Using our approach, treatment plans can be generated in 20-45 min on a 200 MHz processor. A comparison of our approach with the manual 'trial and error' approach shows that the optimized plans are generally superior. The dose to the urethra and rectum is usually maintained below harmful levels without sacrificing target coverage. In the event that the dose to the urethra is undesirably high, we present a refined optimization approach that lowers urethra dose without significant loss in target coverage. An analysis of the sensitivity of the optimized plans to seed misplacement during the implantation process is also presented that indicates remarkable stability of the dose distribution in comparison with manual treatment plans.
Algorithms↗
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↗
Rule-based programming paradigm: a formal basis for biological, chemical and physical computation.
A rule-based programming paradigm is described as a formal basis for biological, chemical and physical computations. In this paradigm, the computations are interpreted as the outcome arising out of interaction of elements in an object space. The interactions can create new elements (or same elements with modified attributes) or annihilate old elements according to specific rules. Since the interaction rules are inherently parallel, any number of actions can be performed cooperatively or competitively among the subsets of elements, so that the elements evolve toward an equilibrium or unstable or chaotic state. Such an evolution may retain certain invariant properties of the attributes of the elements. The object space resembles Gibbsian ensemble that corresponds to a distribution of points in the space of positions and momenta (called phase space). It permits the introduction of probabilities in rule applications. As each element of the ensemble changes over time, its phase point is carried into a new phase point. The evolution of this probability cloud in phase space corresponds to a distributed probabilistic computation. Thus, this paradigm can handle tor deterministic exact computation when the initial conditions are exactly specified and the trajectory of evolution is deterministic. Also, it can handle probabilistic mode of computation if we want to derive macroscopic or bulk properties of matter. We also explain how to support this rule-based paradigm using relational-database like query processing and transactions.
Algorithms↗
Continuously varying critical exponents in a sandpile model with internal disorder.
A sandpile model with an internal disorder is presented. The updating of critical sites is done according to a stochastic rule (with a probabilistic toppling q). Using a unified mean-field theory and numerical simulations, we have shown that the criticality is ensured for any value of q. The static critical exponents have been calculated and found to be the same as those obtained for the deterministic sandpile model, which is a particular case of the stochastic model. They have a universal q-independent behavior. In the limit of slow driving, we have developed a relation between our model and the branching process in order to compute the size exponent tau. It presents a continuous variation with the parameter of toppling q.
Journal Article↗
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↗
The importance of I.P. Pavlov for the development of neuroscience.
By his experimental and theoretical work on the physiology and pathophysiology of the higher nervous activity I.P. Pavlov significantly influenced the development of Neuroscience. During the 1950 Pavlovian Conference in Moscow, Stalin and the Communist Party tried to dogmatize his and his pupils' fundamental theories. But the Pavlovian ideas were developed by his pupils in open discussions with representatives of other schools in a very creative way, opening the doors for a systemic approach to understanding the integrative functional systems of brain and behavior. Pavlov emphasized the high plasticity of the central nervous system, investigated the complex functional systems within the brain and between the organism and its environment, and designed models for pathological deviations of the higher nervous activity. During his last years, he freed himself from the strong deterministic view and characterized the organism and its environment as a self-organizing system.
History, 19th Century↗
Human exposure to large solar particle events in space.
Whenever energetic solar protons produced by solar particle events traverse bulk matter, they undergo various nuclear and atomic collision processes which significantly alter the physical characteristics and biologically important properties of their transported radiation fields. These physical interactions and their effect on the resulting radiation field within matter are described within the context of a recently developed deterministic, coupled neutron-proton space radiation transport computer code (BRYNTRN). Using this computer code, estimates of human exposure in interplanetary space, behind nominal (2 g/cm2) and storm shelter (20 g/cm2) thicknesses of aluminum shielding, are made for the large solar proton event of August 1972. Included in these calculations are estimates of cumulative exposures to the skin, ocular lens, and bone marrow as a function of time during the event. Risk assessment in terms of absorbed dose and dose equivalent is discussed for these organs. Also presented are estimates of organ exposures for hypothetical, worst-case flare scenarios. The rate of dose equivalent accumulation places this situation in an interesting region of dose rate between the very low values of usual concern in terrestrial radiation environments and the high dose rate values prevalent in radiation therapy.
Bone Marrow↗
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↗
Kinetics of initiation, propagation, and termination for the [rac-(C(2)H(4)(1-indenyl)(2))ZrMe][MeB(C(6)F(5))(3)]-catalyzed polymerization of 1-hexene.
Metallocene-catalyzed polymerization of 1-alkenes offers fine control of critical polymer attributes such as molecular weight, polydispersity, tacticity, and comonomer incorporation. Enormous effort has been expended on the synthesis and discovery of new catalysts and activators, but elementary aspects of the catalytic processes remain unclear. For example, it is unclear how the catalyst is distributed among active and dormant sites and how this distribution influences the order in monomer for the propagation rates, for which widely varying values are reported. Similarly, although empirical relationships between average molecular weights and monomer have been established for many systems, the underlying mechanisms of chain termination are unclear. Another area of intense interest concerns the role of ion-pairing in controlling the activity and termination mechanisms of metallocene-catalyzed polymerizations. Herein we report the application of quenched-flow kinetics, active site counting, polymer microstructure analysis, and molecular weight distribution analysis to the determination of fundamental rate laws for initiation, propagation, and termination for the polymerization of 1-hexene in toluene solution as catalyzed by the contact ion-pair, [rac-(C(2)H(4)(1-indenyl)(2))ZrMe][MeB(C(6)F(5))(3)] (1) over the temperature range of -10 to 50 degrees C. Highly isotactic (>99% mmmm) poly-1-hexene is produced with no apparent enchained regioerrors. Initiation and propagation processes are first order in the concentrations of 1-hexene and 1 but independent of excess borane or the addition of the contact ion-pair [PhNMe(3)][MeB(C(6)F(5))(3)]. Active site counting and the reaction kinetics provide no evidence of catalyst accumulation in dormant or inactive sites. Initiation is slower than propagation by a factor of 70. The principal termination process is the formation of unsaturates of two types: vinylidene end groups that arise from termination after a 1,2 insertion and vinylene end groups that follow 2,1 insertions. The rate law for the former termination process is independent of the 1-hexene concentration, whereas the latter is first order. Analysis of (13)C-labeled polymer provides support for a mechanism of vinylene end group formation that is not chain transfer to monomer. Deterministic modeling of the molecular weight distributions using the fundamental rate laws and kinetic constants demonstrates the robustness of the kinetic analysis. Comparisons of insertion frequencies with estimated limits on the rates of ion-pair symmetrization obtained by NMR suggest that ion-pair separation prior to insertion is not required, but the analysis requires assumptions that cannot be validated.
Alkenes↗
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↗
On the comparative static properties of the expected population density in the presence of stochastic fluctuations.
We consider the impact of increased stochastic fluctuations on the expected density of an unstructured population evolving according to a regular diffusion process subject to a concave expected growth rate. By relying on the flow nature of the solutions of stochastic differential equations and Girsanov's theorem, we demonstrate that typically increased volatility decreases the expected future population density. As a consequence, we are able to characterize the sensitivity of the expected population density with respect to changes in the diffusion coefficient measuring the size of the stochastic fluctuations. We provide both qualitative and quantitative information about the consequences of a mis-specified volatility structure and, especially, of a deterministic approximation to stochastic population growth. We also consider the effect of uncertainty in the initial density and demonstrate that the sign of the relationship between the expected population density and initial uncertainty is unambiguosly negative.
Animals↗