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PubMed2005

Testing for directed influences among neural signals using partial directed coherence.

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity. When applying multivariate time series analysis techniques to neural signals, detection of directed relationships, which can be described in terms of Granger-causality, is of particular interest. Partial directed coherence has been introduced for a frequency domain analysis of linear Granger-causality based on modeling the underlying dynamics by vector autoregressive processes. We discuss the statistical properties of estimates for partial directed coherence and propose a significance level for testing for nonzero partial directed coherence at a given frequency. The performance of this test is illustrated by means of linear and non-linear model systems and in an application to electroencephalography and electromyography data recorded from a patient suffering from essential tremor.

Algorithms↗
PubMed2006

Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks.

The process of infection during an epidemic can be envisaged as being transmitted via a network of routes represented by a contact network. Most differential equation models of epidemics are mean-field models. These contain none of the underlying spatial structure of the contact network. By extending the mean-field models to pair-level, some of the spatial structure can be contained in the model. Some networks of transmission such as river or transportation networks are clearly asymmetric, whereas others such as airborne infection can be regarded as symmetric. Pair-level models have been developed to describe symmetric contact networks. Here we report on work to develop a pair-level model that is also applicable to asymmetric contact networks. The procedure for closing the model at the level of pairs is discussed in detail. The model is compared against stochastic simulations of epidemics on asymmetric contact networks and against the predictions of the symmetric model on the same networks.

Communicable Diseases↗
PubMed1985

Differentiation and frequency distributions of body weights in plants and animals.

The basic and simplest system that one can consider in ecology is a group of individuals of equal age and representing one species, that is, a cohort. This paper is an attempt to show that analysis of such a system may be of great importance to understanding basic ecological problems, such as, intraspecific competition and the dynamics of a single population. It is easy to observe that in even-aged populations individuals differ in weights. A close look can show that weight distributions in even-aged populations may have different skewness. Most common are distributions with coefficients of skewness greater than zero. Sometimes weight distributions are symmetrical or with skewness coefficients less than zero. In a cohort of growing individuals the coefficient of skewness changes with time: most often starting from zero (symmetrical distribution), it increases in time; sometimes after an initial increase it can decrease in the final stage of growth, which is related to an increased mortality of individuals. The rate of change in skewness, and the skewness itself depend on the density of individuals in a cohort and on food conditions. They are greater at higher densities and increase with deteriorating food conditions. Weight distributions are symmetrical at low densities and optimal food conditions. The differences in individual weights measured by variance of weight distributions or coefficient of variation follow the same pattern, but observed changes with time, density and food conditions are not so clear. These conclusions rest upon the review of numerous papers concerning both plants and animals, which is presented in this paper. In the past, the properties of weight distributions in even-aged populations were explained not by interactions between individuals, but rather as a natural outcome of the growth process of non-interacting individuals. The exponential equation of growth, with relative growth rate having a normal distribution in populations, was used to support this hypothesis. Obtained weight distributions were of positive skewness; however, this model, which in fact is able to describe the growth process only in its initial stage, cannot explain the changes of skewness of weight distributions with density and food conditions. A model has been developed which includes competitive interactions among members of even-aged populations to explain observed properties of weight distributions in them. The basic assumption is that intraspecific competition leads to uneven partitioning of resources, which are the object of competition. Functions describing resource partitioning among individuals are included into the model.(ABSTRACT TRUNCATED AT 400 WORDS)

Aging↗
PubMed1994

Statistical analysis of aberrant crypt assays for colon cancer promotion studies.

The size of aberrant crypt foci in rodent colons is a short-term assay for the promotion of colon carcinogenesis. An approximate model for the number of aberrant crypts in a focus is derived by assuming a branching process with a gamma lifetime. Maximum likelihood estimation can be implemented using symbolic manipulation packages. Although in most cases the model provides a reasonable fit for the distribution of the number of aberrant crypts per focus, there is some evidence of lack of fit. A more robust analysis can be based on summarizing the data for each animal by their mean number of aberrant crypts per focus. The branching process with gamma lifetime is used to obtain expressions for the functional relation between the variance of the number of aberrant crypts per focus and their mean. It is shown that in most cases this relation is quadratic. The quadratic relation also holds for other lifetime distributions. The parameters of the quadratic relation can be estimated by pseudolikelihood. An experiment for assessing the promotional effect of the compound HMF is used for illustration.

Analysis of Variance↗
PubMedDate not supplied

Broth recycling to reduce process noise resulting from concentrated substrate addition in fed-batch cultivation of Escherichia coli.

In this work feed hardware for fed-batch cultivation is presented (broth recycle feed injection system or BRFIS). BRFIS proved superior to conventional submerged or dripped feed systems in reducing dissolved oxygen (DO) oscillations during Escherichia coli fed-batch cultivation (5 min coefficient of variation of 0.7% for BRFIS as compared to 26% or greater for conventional feeding hardware in a 2 L test reactor). Hence, BRFIS is useful for fed-batch cultivation systems where the DO signal is used in measurement or control.

Bioreactors↗
PubMed1992

Levels of aggregation and the generalized matching law.

Concurrent operant behavior is often described using molar response tendencies measured over many sessions. In contrast, other models relate the allocation of behavior to momentary or molecular processes that operate over shorter periods. In this article, a formal model of the statistical properties of molecular behavioral matching is developed. Molar matching is the result when many individual bouts of responding are aggregated. However, behavioral allocation at the molecular level will differ from the molar result. The model indicates that aggregation effects should be controlled in analyses of matching and that the comparison of molecular theories of concurrent operant behavior with molecular models of matching performance affords ideographic analyses of choice behavior.

Animals↗
PubMed2006

Learning by operant conditioning as a nonlinear self-organized process.

Responses of individuals have been rewarded in fixed ratio operant conditioning experiments throughout the last 5 years. The long numerical series of performance rates so obtained have been analyzed by using Fourier spectra, obtaining 1/f noise, and wavelet techniques for the analysis of local variability. These techniques reveal that the evolution of data in each individual is nonlinear but it fluctuates showing self-organized patterns in successive time scales, which leads to a long term logarithmic growth. Based on these observations a model has been developed. It can simulate with a great accuracy the rate of response exhibited by our subjects in all time scales.

Conditioning, Operant↗
PubMed1989

Detection of feedback in the central nervous system using system identification techniques.

An analysis method to detect the presence of feedback between biological signals, particularly those associated with the central nervous system, is presented. The technique is based on recent results in the system identification literature involving the concept of a feedback free process. It may be applied to volume conducted signals such as EEG and EMG, as well as to neuronal spike trains through the use of a data transformation procedure. The utility of the technique is then demonstrated in a study of the relationship between Parkinsonian tremor and certain tremor cells found in the thalamus of Parkinsonian patients, using data collected during thalamotomies. The results obtained suggest that feedback mechanisms may be an important factor contributing to Parkinsonian tremor.

Biofeedback, Psychology↗
PubMed2004

DNA-protein interactions under random jump conditions.

We model the site-specific association of a protein molecule with DNA as a random walk with random jumps. Results show that the simultaneous occurrence of processes such as sliding, hopping, and intersegmental transfer can facilitate the diffusion-controlled site-specific association rate. We have also shown that sliding would dominate at lower DNA length, whereas at higher lengths hopping and intersegmental transfer would dominate. Apart from this, we predict that the association rate is directly proportional to the size of nonspecific DNA that flanks the specific site. These results are consistent with the experimental observations.

Binding Sites↗
PubMed1986

The time course of repair of ultraviolet-induced DNA damage; implications for the structural organisation of repair.

Alternative molecular mechanisms can be envisaged for the cellular repair of UV-damaged DNA. In the "random collision" model, DNA damage distributed throughout the genome is recognised and repaired by a process of random collision between DNA damage and repair enzymes. The other model assumes a "processive" mechanism, whereby DNA is scanned for damage by a repair complex moving steadily along its length. These two models give different predictions concerning the time course of repair. Random collision should result in a declining rate of repair with time as the concentration of lesions in the DNA falls; but the processive model predicts a constant rate of repair until scanning is complete. We have examined the time course of DNA repair in human fibroblasts given low (generally sublethal) doses of UV light. Using 3 distinct assays, we find no sign of a constant repair rate after 4 J/m2 or less, even when the first few hours after irradiation are examined. Thus DNA repair is likely to depend on random collision. The implications of this finding for the structural organisation of repair are discussed.

DNA Ligases↗
PubMed2001

Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis.

This paper is concerned with modern approaches to mechanistic modeling of the process of cancer detection. Measurements of tumor size at diagnosis represent a valuable source of information to enrich statistical inference on the processes underlying tumor latency. One possible way of utilizing this information is to model cancer detection as a quantal response variable. In doing so, one relates the chance of detecting a tumor to its current size. We present various theoretical results emerging from this approach and illustrate their usefulness with numerical examples and analyses of epidemiological data. An alternative approach based on a threshold type mechanism of tumor detection is briefly described.

Computer Simulation↗
PubMed1991

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↗
PubMed2000

Threshold modeling of autonomic control of heart rate variability.

Even in the absence of external perturbation to the human cardiovascular system, measures of cardiac function, such as heart rate, vary with time in normal physiology. The primary source of the variation is constant regulation by a complex control system which modulates cardiac function through the autonomic nervous system. Here, we present methods of characterizing the statistical properties of the underlying processes that result in variations in ECG R-wave event times within the framework of an integrate-and-fire model. We first present techniques for characterizing the noise processes that result in heart rate variability even in the absence of autonomic input. A relationship is derived that relates the spectrum of R-R intervals to the spectrum of the underlying noise process. We then develop a technique for the characterization of the dynamic nature of autonomically related variability resulting from exogenous inputs, such as respiratory-related modulation. A method is presented for the estimation of the transfer function that relates the respiratory-related input to the variations in R-wave event times. The result is a very direct analysis of autonomic control of heart rate variability through noninvasive measures, which provides a method for assessing autonomic function in normal and pathological states.

Autonomic Nervous System↗
PubMed1998

Simulation of prokaryotic genetic circuits.

Biochemical and genetic approaches have identified the molecular mechanisms of many genetic reactions, particularly in bacteria. Now a comparably detailed understanding is needed of how groupings of genes and related protein reactions interact to orchestrate cellular functions over the cell cycle, to implement preprogrammed cellular development, or to dynamically change a cell's processes and structures in response to environmental signals. Simulations using realistic, molecular-level models of genetic mechanisms and of signal transduction networks are needed to analyze dynamic behavior of multigene systems, to predict behavior of mutant circuits, and to identify the design principles applicable to design of genetic regulatory circuits. When the underlying design rules for regulatory circuits are understood, it will be far easier to recognize common circuit motifs, to identify functions of individual proteins in regulation, and to redesign circuits for altered functions.

Bacteria↗
PubMed1991

GAMEES: a probabilistic environment for expert systems.

This paper describes GAMEES (Graphical Modelling Environment for Expert Systems), an interactive graphical environment for building and processing Belief Networks and Influence Diagrams. We review the existing systems designed for analogous purposes, and, after a brief introduction to Belief Networks and Influence Diagrams, we describe the graphical interface, discuss algorithms for probabilistic inference on these networks and illustrate the current implementation of GAMEES. The system has been designed for being integrated within wider expert systems and actually it is part of the Therapy Advisor module within an expert system for the management of anemic patients.

Algorithms↗
PubMed1999

Declining survival probability threatens the North Atlantic right whale.

The North Atlantic northern right whale (Eubalaena glacialis) is considered the most endangered large whale species. Its population has recovered only slowly since the cessation of commercial whaling and numbers about 300 individuals. We applied mark-recapture statistics to a catalog of photographically identified individuals to obtain the first statistically rigorous estimates of survival probability for this population. Crude survival decreased from about 0.99 per year in 1980 to about 0.94 in 1994. We combined this survival trend with a reported decrease in reproductive rate into a branching process model to compute population growth rate and extinction probability. Population growth rate declined from about 1. 053 in 1980 to about 0.976 in 1994. Under current conditions the population is doomed to extinction; an upper bound on the expected time to extinction is 191 years. The most effective way to improve the prospects of the population is to reduce mortality. The right whale is at risk from entanglement in fishing gear and from collisions with ships. Reducing this human-caused mortality is essential to the viability of this population.

Animals↗
PubMed2004

Control of cardiac function and noise from a decaying power spectrum.

Evidence is presented that adds to the debate surrounding the question: To what extent does neural control of cardiac output exploit noise? The transduction capability of cardiac afferent neurons, situated in and adjacent to the heart, is vital to feedback in control of cardiac function. An analysis of in situ cardiac afferent activity shows evidence of independent and exponentially distributed interspike intervals. An anatomical basis for such memoryless interspike intervals ultimately derives from the fact that each afferent neuron is associated with a field of sensory neurites, or bare nerve endings, that transduce local chemical and mechanical stimuli in a many-to-one fashion. As such, cardiac afferent neurons and their sensory neurite inputs are respectively modeled here by the Hodgkin-Huxley equations forced by "red" noise (decaying power spectrum) perturbing an otherwise constant subthreshold input. A variable barrier competition model is derived from these equations in order to address the question: How are noisy inputs being processed by sensory neurons to cause each spike? It is found that ion channels are responsible for significant input "whitening" (increased spectral power at higher frequency) through differentiation of the inputs. Such whitening is a means to distinguish low-frequency control signals from otherwise red noise fluctuations. Furthermore, spiking occurs when backward moving averages of the whitened inputs, over a window of the order of the sodium activation time scale, exceed an approximately constant barrier.

Action Potentials↗
PubMed2004

Time domain system identification of unknown initial conditions.

System identification is a method for using measured data to create or improve a mathematical model of the object being tested. From the measured data however, noise is noticed at the beginning of the response. One solution to avoid this noise problem is to skip the noisy data and then use the initial conditions as active parameters, to be found by using the system identification process. This paper describes the development of the equations for setting up the initial conditions as active parameters. The simulated data and response data from actual shear buildings were used to prove the accuracy of both the algorithm and the computer program, which include the initial conditions as active parameters. The numerical and experimental model analysis showed that the value of mass, stiffness and frequency were very reasonable and that the computed acceleration and measured acceleration matched very well.

Algorithms↗