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PubMed1994

Scientific methodology in temporomandibular disorders. Part III: Diagnostic reasoning.

Temporomandibular disorders (TMD), as a cluster of individual diseases and disorders, pose new intellectual challenges to the diagnostic skills of dentists. New technologies enable dentists to avail themselves of paraclinical data such that diagnosis can and should be disease specific or etiology specific. The importance of logic in diagnostic reasoning is discussed. Studies of the reasoning process of doctors with reputations for having good clinical judgement have resulted in protocols of diagnostic reasoning. Three specific strategies are presented and discussed-probabilistic, causal and deterministic. The difference between intellectual and managerial decisions are explained relative to utility of the strategies.

Algorithms↗
PubMed1992

Extending the stochastic two-stage model of carcinogenesis to include self-regulation of the nonmalignant cell population.

One of the challenges of introducing greater biological realism into stochastic models of cancer induction is to find a way to represent the homeostatic control of the normal cell population over its own size without complicating the analysis too much to obtain useful results. Current two-stage models of carcinogenesis typically ignore homeostatic control. Instead, a deterministic growth path is specified for the population of "normal" cells, while the population of "initiated" cells is assumed to grow randomly according to a birth-death process with random immigrations from the normal population. This paper introduces a simple model of homeostatically controlled cell division for mature tissues, in which the size of the nonmalignant population remains essentially constant over time. Growth of the nonmalignant cell population (normal and initiated cells) is restricted by allowing cells to divide only to fill the "openings" left by cells that die or differentiate, thus maintaining the constant size of the nonmalignant cell population. The fundamental technical insight from this model is that random walks, rather than birth-and-death processes, are the appropriate stochastic processes for describing the kinetics of the initiated cell population. Qualitative and analytic results are presented, drawn from the mathematical theories of random walks and diffusion processes, that describe the probability of spontaneous extinction and the size distribution of surviving initiated populations when the death/differentiation rates of normal and initiated cells are known. The constraint that the nonmalignant population size must remain approximately constant leads to much simpler analytic formulas and approximations, flowing directly from random walk theory, than in previous birth-death models.(ABSTRACT TRUNCATED AT 250 WORDS)

Cell Death↗
PubMed2004

Phasic spike patterning in rat supraoptic neurones in vivo and in vitro.

In vivo, most vasopressin cells of the hypothalamic supraoptic nucleus fire action potentials in a 'phasic' pattern when the systemic osmotic pressure is elevated, while most oxytocin cells fire continuously. The phasic firing pattern is believed to arise as a consequence of intrinsic activity-dependent changes in membrane potential, and these have been extensively studied in vitro. Here we analysed the discharge patterning of supraoptic nucleus neurones in vivo, to infer the characteristics of the post-spike sequence of hyperpolarization and depolarization from the observed spike patterning. We then compared patterning in phasic cells in vivo and in vitro, and we found systematic differences in the interspike interval distributions, and in other statistical parameters that characterized activity patterns within bursts. Analysis of hazard functions (probability of spike initiation as a function of time since the preceding spike) revealed that phasic firing in vitro appears consistent with a regenerative process arising from a relatively slow, late depolarizing afterpotential that approaches or exceeds spike threshold. By contrast, in vivo activity appears to be dominated by stochastic rather than deterministic mechanisms, and appears consistent with a relatively early and fast depolarizing afterpotential that modulates the probability that random synaptic input exceeds spike threshold. Despite superficial similarities in the phasic firing patterns observed in vivo and in vitro, there are thus fundamental differences in the underlying mechanisms.

Action Potentials↗
PubMed1995

Active mutation in self-reproducing networks of machines and tapes.

Self-reproduction via description is discussed in a network model of machines and description tapes. Tapes consist of bit strings, which encode the machines' function A tape is replicated when it is read by adequate machines. Generally, a machine rewrites a tape without doing correct replication. The variation in a reproduced tape is taken as mutation. Because this mutation is caused by a machine's program, we call it active mutation. Which machine is translated from a given tape is dependent on what kind of a machine reads the tape. External noise is introduced in a machine's reading process to make errors. A new reaction pathway is induced by external noise via a machine's error action. We find that the induced pathways will be mimicked deterministically in an emerging core structure. This core structure will remain stable after turning off external noise. Low external noise develops a core structure of a minimal self-replicative loop. When external noise is elevated, a more complex network evolves. Machines containing a complex core network, which has been bred in high external noise, will actively rewrite tapes rather than just replicate them. Self-replication not as an individual but as a network now becomes important.

Biological Evolution↗
PubMed2005

Does god play dice with schizophrenia? A probabilistic model for the understanding of causation in mental illness.

While the pure sciences have moved over the XX century from the certainties of the Laplacian mechanistic models to probabilistic ones, such as quantum physics, the attempts to explain the causation in mental illness are still stuck to deterministic frameworks which are deceptively reassuring, but also too simplistic to approach problems of such a complexity. The deterministic approach has led to several false leads that have affected research in the aetiology in mental illness, especially schizophrenia, and only moving to probabilistic models will allow an understanding of the causal processes. In this paper is challenged the almost universally accepted assumption that, to explain the lack of complete concordance amongst identical twins in schizophrenia, there is the need to resort to environmental aetiological agents. It is described instead how, using a probabilistic framework, a polygenic model without threshold can satisfactorily explain the data available so far without having to resort to environmental factors. The genes predisposing to schizophrenia, probably through a derailment of the neurodevelopment, would have a normal distribution in the general population, while the liability for the illness will increase exponentially with the number of risk genes, with a small minority of the population being at high risk. The average genetic liability to develop schizophrenia in individuals who later are affected by the disorder is around 50%. The adoption of a probabilistic model for the understanding of the inheritance of schizophrenia has therefore far reaching consequences, revolutionizing the interpretation of the twin studies, allowing a consistent model which does not require environmental interventions in the aetiology of schizophrenia and offering a framework to make sense of findings from the epidemiological research which are not satisfactorily explained by the deterministic models adopted so far.

Genetic Predisposition to Disease↗
PubMed2000

Stochastic modelling of environmental variation for biological populations.

We examine stochastic effects, in particular environmental variability, in population models of biological systems. Some simple models of environmental stochasticity are suggested, and we demonstrate a number of analytic approximations and simulation-based approaches that can usefully be applied to them. Initially, these techniques, including moment-closure approximations and local linearization, are explored in the context of a simple and relatively tractable process. Our presentation seeks to introduce these techniques to a broad-based audience of applied modellers. Therefore, as a test case, we study a natural stochastic formulation of a non-linear deterministic model for nematode infections in ruminants, proposed by Roberts and Grenfell (1991). This system is particularly suitable for our purposes, since it captures the essence of more complicated formulations of parasite demography and herd immunity found in the literature. We explore two modes of behaviour. In the endemic regime the stochastic dynamic fluctuates widely around the non-zero fixed points of the deterministic model. Enhancement of these fluctuations in the presence of environmental stochasticity can lead to extinction events. Using a simple model of environmental fluctuations we show that the magnitude of this system response reflects not only the variance of environmental noise, but also its autocorrelation structure. In the managed regime host-replacement is modelled via periodic perturbation of the population variables. In the absence of environmental variation stochastic effects are negligible, and we examine the system response to a realistic environmental perturbation based on the effect of micro-climatic fluctuations on the contact rate. The resultant stochastic effects and the relevance of analytic approximations based on simple models of environmental stochasticity are discussed.

Animals↗
PubMed2004

Estimating variability in models for recurrent epidemics: assessing the use of moment closure techniques.

The major role played by demographic stochasticity in determining the dynamics and persistence of childhood diseases, such as measles, chickenpox and pertussis, has long been realized. Techniques which can be used to estimate the magnitude of this stochastic effect are of clear importance. In this study, we assess and compare the use of two moment closure approximations to estimate the variability seen about the average behavior of stochastic models for the recurrent epidemics seen in childhood diseases. The performance of the approximations are assessed using analytic techniques available for the simplest epidemiological model and using numerical simulations in more complex settings. We also present epidemiologically important extensions of previous work, considering variability in the SEIR model and in situations for which there is seasonal variation in disease transmission. Important implications of stochastic effects for the dynamics of childhood diseases are highlighted, including serious deficiencies of deterministic descriptions of dynamical behavior.

Demography↗
PubMed1998

Nonlinear feedforward networks with stochastic outputs: infomax implies redundancy reduction.

We prove that maximization of mutual information between the output and the input of a feedforward neural network leads to full redundancy reduction under the following sufficient conditions: (i) the input signal is a (possibly nonlinear) invertible mixture of independent components; (ii) there is no input noise; (iii) the activity of each output neuron is a (possibly) stochastic variable with a probability distribution depending on the stimulus through a deterministic function of the inputs (where both the probability distributions and the functions can be different from neuron to neuron); (iv) optimization of the mutual information is performed over all these deterministic functions. This result extends that obtained by Nadal and Parga (1994) who considered the case of deterministic outputs.

Feedback↗
PubMed1998

Stability analysis of the FitzHugh-Nagumo differential equations driven by impulses: applied to the electrical firing of magnocellular neurons.

A stability analysis is carried out for a mathematical model which describes the electrical firing of a single vasopressin neuron. The model used in a FitzHugh-Nagumo-type system which is driven by impulses. The analysis is based on recent developments in the stability theory of impulsive differential equations. Conditions are derived under which the system of differential equations is stable at two of its equilibrium points. Biologically this bistability represents the cell alternating between periods of electrical activity and silence. The conditions for stability are specified in terms of the amplitude and frequency of the impulses perturbing the system. Both stochastic and deterministic impulses are considered.

Action Potentials↗
PubMed2004

Developing complex signaling models using GENESIS/Kinetikit.

The development of biologically realistic models of signaling pathways is a demanding process, involving computational challenges as well as those arising from the complexity of detailed pathway models. We have developed the General Neural Simulation System (GENESIS) and Kinetikit (GENESIS/Kinetikit), a graphical simulation environment for modeling biochemical signaling pathways using deterministic and stochastic methods. A library of models of several common signaling pathways complements the software. This combination of numerical computation engines, graphical modeling tools, and library of models is designed to build on the cumulative development of models and techniques from many sources. The complete simulation environment and demonstration models are available from (http://stke.sciencemag.org/cgi/content/full/sigtrans;2004/219/pl4/DC1; also at http://www.ncbs.res.in/~bhalla/kkit/download.html). The associated library of signaling pathways is based on published experimental and simulation studies and is curated to ensure that the simulation outcomes match published results. Models in the library are maintained in a database (http://doqcs.ncbs.res.in). Individual pathway models can be combined to build complex signaling network simulations. The overall goal of this process is to attain sufficient biological realism in models to directly compare their outcomes with experiments and to improve our understanding of complex signaling.

Computational Biology↗
PubMed2004

Efficient algorithm for computation of the second-order moment of the subpixel-edge position.

Subpixel-edge detection is the first stage in processing many high-level vision algorithms. However, the study of the statistical properties of such data has remained incomplete in most research. We present a method for estimating the second-order moments of the subpixel-edge position, computed by a deterministic algorithm based on three quadratic interpolations. The algorithm is tested on different types of noise (Gaussian, impulse, colored) and compared with two methods in the literature. The results show that this approach remains accurate even at high noise levels.

Algorithms↗
PubMed1985

Decision making under uncertainty: a comparison of simple scalability, fixed-sample, and sequential-sampling models.

The purpose of this article is to investigate the learning and memory processes involved in decision making under uncertainty. In two different experiments, subjects were given a choice between a certain alternative that produced a single known payoff and an uncertain alternative that produced a normal distribution of payoffs. Initially this distribution was unknown, and in the first experiment it was learned through feedback from past decisions, whereas in the second experiment it was learned by observing sample outcomes. In the first experiment, a response deadline was used to limit the amount of time available for making a decision. In the second experiment, an observation cost was used to limit the number of samples that could be purchased. The mean and variance of the uncertain alternative and the value of the certain alternative were factorially manipulated to study their joint effects on choice probability, choice response time (Experiment 1), and number of observations purchased (Experiment 2). Algebraic-deterministic theories developed for decision making with simple gambles fail to explain the present results. Two new models are developed and tested--fixed- and sequential-sampling models--that attempt to describe the learning and memory processes involved in decision making under uncertainty.

Adult↗
PubMed2005

The dual klepsydra model of internal time representation and time reproduction.

We present a model of the internal representation and reproduction of temporal durations, the 'dual klepsydra' model (DKM). Unlike most contemporary models operating on a 'pacemaker-counter' scheme, the DKM does not assume an oscillatory process as the internal time-base. It is based on irreversible, dissipative processes in inflow/outflow systems (leaky klepsydrae), whose states are continuously compared; if their states are equal, durations are subjectively perceived as equal. Model-based predictions fit experimental time reproduction data with good accuracy, and show qualitative features not accounted for by other models. The deterministic model is characterized by two parameters, kappa (outflow rate coefficient) and eta (ratio of inflow rates). A stochastic version of the model (SDKM) assumes randomly fluctuating inflows, involves two more parameters, and accounts for intra-individual variance of reproduced durations. Analysis of the SDKM leads to non-trivial problems in the stochastic theory, briefly sketched here. Methods of parameter estimation for both deterministic and stochastic versions are given. Applying the DKM to the subjective experience of time passage, we show how subjective measure of elapsed time is constituted. Finally, essential features of the model and its possible neurophysiological interpretation are discussed.

Animals↗
PubMed1977

A mechanistic model of the aerobic growth of Saccharomyces cerevisiae.

A two-stage deterministic model of the growth of Saccharomyces cerevisiae is presented. The cell cycle of this organism was used to suggest the basic model structure. The model represents the preparatory processes of substrate uptake and conversion separately from replication and division. The regulation of the fraction of the culture devoted to each of these broad areas of metabolism, and the overall growth rate, is related to the nature and availability of the energy substrate. The simulation of respiration and glycolysis is achieved by including two alternative energy producing pathways. The regulation of these pathways is described in terms of the postulated primary regulation of the proportion of the culture required for substrate uptake and conversion, and the overall kinetic constants for each pathway. This regulation is dictated primarily by the growth rate rather than the nature or concentration of the energy substrate. The model successfully describes both batch and continuous growth of S. cerevisiae under conditons of glucose limitation and oxygen excess. A preliminary assessment indicates that adjustment of the relevant parameters will allow the model to describe the growth of S. cerevisiae on other sugars and under oxygen limitation. Similarly the model could be expected to describe the growth characteristics of other yeast species.

Aerobiosis↗
PubMed2003

Wave nucleation rate in excitable systems in the low noise limit.

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially extended nonpotential pair of equations driven by thermal (i.e., white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other nonequilibrium pattern-forming processes.

Journal Article↗
PubMed2000

Can varying concepts of susceptibility in risk assessment affect particulate matter standards?

The Clean Air Act mandates that sensitive subpopulations be considered in setting standards to protect the public's health. The purposes of this paper are to point out different conceptualizations of susceptibility, examine how it is approached in risk-related processes, and recommend ways it may be more explicitly framed for risk assessment and management purposes. We studied the traditional risk assessment paradigm, the U.S. Environmental Protection Agency (EPA) guidelines and revised PM standard, discussions from recent interdisciplinary meetings, and peer-reviewed literature. Areas of controversy include what factors intrinsic and extrinsic to the host should be incorporated in susceptibility, what health endpoints are of concern, whether susceptibility is deterministic or stochastic, and whether it should be defined on an individual or population scale. Recent discussions about susceptibility applied to PM indicate that it needs to be more clearly defined and evaluated for scientific and policy purposes. We conclude that varying concepts of susceptibility can affect risk-related processes such as PM standard setting. We recommend that susceptibility be clearly defined in the problem statement of risk assessments and be addressed in a specific subsection of risk characterization, integrating all susceptibility findings from the prior three steps in the risk assessment paradigm.

Air Pollution↗
PubMed2001

Using a continuous time hidden Markov process, with covariates, to model bed occupancy of people aged over 65 years.

Previously, the application of a continuous time hidden Markov model with discrete states was used to model geriatric inpatient behaviour. This was itself built on research using a discrete deterministic model to represent the flow of geriatric patients around departments of geriatric medicine. This paper uses the continuous time hidden Markov models and includes the effect of covariates, age and sex, in the model. Fitting the models we can visually see that the two compartment models provides estimates that are much closer to those observed in the data. The addition of covariates provides us with evidence of a difference in length of stay between men and women. However, even significant alterations to the mean age of patients in the model does not effect the length of stay.

Age Factors↗
PubMed2006

A truce with neutral theory: local deterministic factors, species traits and dispersal limitation together determine patterns of diversity in stream invertebrates.

1. Studies seeking to explain local patterns of diversity have typically relied on niche explanations, reflected in correlations with local environmental conditions, or neutral theory, invoking dispersal processes and speciation. 2. We used macroinvertebrate community data from 10 streams that varied independently in local ecological conditions and spatial proximity. Neutral theory predicts that similarity in communities will be negatively associated with distance between sites, while niche theory suggests that community similarity will be positively associated with similarity in local ecological conditions. 3. Similarity in total invertebrate, grazer and predator assemblages showed negative relationships with distance and, for grazers and predators, positive relationships with local ecological conditions. However, the best model predicting community similarity in all three cases included aspects of both local ecological conditions and distance between sites. 4. When assemblages were analysed according to dispersal ability, high-dispersal species were shown to be freely accessing all sites and community similarity was not well predicted by either local ecology or spatial separation. Assemblages of species with low and moderate dispersal ability were best predicted by combined models, including distance between sites and local ecological factors. 5. The results suggest that the perceived dichotomy between neutral and local environmental processes in determining local patterns of diversity may not be useful. Neutral and niche processes structured these communities differentially depending on trophic level and species traits. 6. We emphasize the potential for both dispersal processes and local environmental conditions to explain local patterns of diversity.

Animals↗