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PubMed1991

Asymmetric Boltzmann machines.

We study asymmetric stochastic networks from two points of view: combinatorial optimization and learning algorithms based on relative entropy minimization. We show that there are non trivial classes of asymmetric networks which admit a Lyapunov function L under deterministic parallel evolution and prove that the stochastic augmentation of such networks amounts to a stochastic search for global minima of L. The problem of minimizing L for a totally antisymmetric parallel network is shown to be associated to an NP-complete decision problem. The study of entropic learning for general asymmetric networks, performed in the non equilibrium, time dependent formalism, leads to a Hebbian rule based on time averages over the past history of the system. The general algorithm for asymmetric networks is tested on a feed-forward architecture.

Algorithms↗
PubMed2002

Quantifying physiological data with Lempel-Ziv complexity--certain issues.

The oscillations observed in physiological data can be attributed largely to the presence of either a nonlinear deterministic or a nondeterministic component. The Lempel-Ziv complexity and its variants have been used successfully to quantify the regularity of these oscillations. The decrease in the complexity can be observed in the case of nontrivial deterministic patterns as well as correlated noise. Thus, any conclusion on the nature of the pattern based solely on the value of the Lempel-Ziv complexity is incomplete. In this paper, the use of the surrogate data technique is suggested to avoid spurious interpretation of this measure of complexity. The data sets considered include the uterine contraction obtained during active labor. The surrogates are generated using the amplitude adjusted fourier transform and the iterated amplitude adjusted fourier transform. The approximate entropy is used as an alternate measure to verify the results obtained.

Cluster Analysis↗
PubMed1997

Population dynamics, demographic stochasticity, and the evolution of cooperation.

A basic evolutionary problem posed by the Iterated Prisoner's Dilemma game is to understand when the paradigmatic cooperative strategy Tit-for-Tat can invade a population of pure defectors. Deterministically, this is impossible. We consider the role of demographic stochasticity by embedding the Iterated Prisoner's Dilemma into a population dynamic framework. Tit-for-Tat can invade a population of defectors when their dynamics exhibit short episodes of high population densities with subsequent crashes and long low density periods with strong genetic drift. Such dynamics tend to have reddened power spectra and temporal distributions of population size that are asymmetric and skewed toward low densities. The results indicate that ecological dynamics are important for evolutionary shifts between adaptive peaks.

Biological Evolution↗
PubMed1999

Non-linear time series analysis of intracranial EEG recordings in patients with epilepsy--an overview.

Deterministic chaos offers a striking explanation for apparently irregular behavior, a characteristic feature of brain electrical activity. The framework of the theory of non-linear dynamics provides new concepts and powerful algorithms to analyze such time series. However, different influencing factors render the use of non-linear measures in a strict sense problematic. Nevertheless, if interpreted with care, particularly the correlation dimension or the Lyapunov-exponents provide a means to reliably characterize different states of normal and pathological brain function. This overview summarizes recent findings applying this concept in the field of epileptology that promise to be important for clinical practice. Non-linear measures extracted from the intra-cranially recorded EEG allow (a) localization of epileptogenic areas in different cerebral regions even during seizure-free intervals, (b) investigation of the influence of anticonvulsive drugs and (c) detection of features predictive of imminent seizure activity. Moreover, particularly the dimensional complexity proves a valuable parameter reflecting spatially distributed neuronal activity during verbal learning and memory processes. Specific changes in time of this non-linear measure allow the prediction of memory performance and, in addition, represent an estimate of the recruitment potency in the anterior mesial temporal lobes. Thus, the application of non-linear time series analysis to brain electrical activity offers new information about the dynamics of the underlying neuronal networks.

Electroencephalography↗
PubMed1999

Linked insurance-tumor registry database for health services research.

OBJECTIVE: Breast cancer screening and treatment data are often limited to restricted populations, including women older than 65 years old. The goal of this project was to develop procedures to link tumor registry and insurance claims databases on women younger than 65 years old with breast cancer and to assess the accuracy and validity of the linked dataset. METHODS: Iowa Cancer Registry (ICR) and Wellmark Blue Cross/Blue Shield of Iowa (BC/BS) membership files of women with incident in situ or invasive breast cancer from 1989 to 1996 were linked. An automated deterministic match was followed with visual inspection from three independent reviewers applying a matching protocol. Matched and overall registry data were compared to assess population representativeness. Claims from BC/BS for incident cases during 1994 were examined for coding of a recent breast cancer diagnosis or treatment. RESULTS: The final dataset included 4,397 matched cases of patients aged 21 years and older from 1989 to 1996. The sociodemographic and tumor characteristics of the ICR population younger than 65 years old (n = 7,469) with breast cancer or carcinoma in situ were nearly identical with those of the matched patients younger than 65 years old (n = 3,449). Nearly all (96%) of the 445 matched incident cases in 1994 had claims data (CPT, DRG, or ICD-9 code) indicative of breast cancer. Treatment patterns varied by data source, with agreement ranging from 76% to 82%. CONCLUSIONS: The validity and generalizability of these data demonstrate their potential for further health services research among younger insured women with breast cancer. Additionally, the process outlined may be useful for developing other datasets to study other cancers in the population younger than 65 years old.

Adult↗
PubMedDate not supplied

A deterministic and stochastic simulation model for intra-herd paratuberculosis transmission.

In France, the considerable economic losses due to paratuberculosis introduction in cattle herds may justify the development of a herd-level certification procedure. For a cost/benefit analysis purpose, a simple deterministic and stochastic simulation model for intra-herd paratuberculosis transmission has been developed to evaluate the economic consequences of the purchase of a single infected heifer in a French average herd. The values of the epidemiological parameters were provided by a panel of French paratuberculosis experts. The results were in adequacy with field observations. A sensitivity analysis was conducted. The model was however difficult to validate rigorously, since few data on the intra-herd paratuberculosis true prevalence level are currently available.

Age Factors↗
PubMedDate not supplied

[Shared surveillance: meningococcal disease vs influenza].

OBJECTIVE: To analyse the association between the behavior of meningococcal disease and influenza, using for this purpose population statistics for Spain for the period of 1964 to 1997. METHODS: Ecological study of the incidence of meningococcal disease and influenza in Spain from 1964 to 1997, inclusive. The study used weekly statistical data for these diseases supplied by the Compulsory Disease Reporting System (Enfermedades de Declaración Obligatoria, EDO). The deterministic component of the meningococcal disease and influenza series was studied by means of spectral analysis based on the Fast Fourier Transformation, and the non-deterministic component was studied using the ARIMA model. The Box-Jenkins method was used for pre-bleaching the series, and a cross-correlation was subsequently established between the residuals in order to detect the presence of any significant correlations between the meningococcal disease and influenza series. RESULTS: During the period from 1964 to 1997, the week that showed, on average, the greatest number of cases for the season was week 7 in the case of meningococcal disease and week 6 in the case of influenza. Spectral analysis of the meningococcal disease and influenza series clearly demonstrated the annual periodicity of both series, and periodicity of nearly 11 years for meningococcal disease and slightly over 10 years for influenza. When cross-correlation is established after prebleaching the series, positive correlations are obtained in the results of lags 0, 1, 2, and 3. Introducing influenza as an exogenous variable in the multivariate model of meningococcal disease corroborates these results. There was a statistically significant relationship between the two processes during the same week and with a three-week lapse. CONCLUSIONS: By means of a methodology not previously applied to this subject, and by the use of prolonged time-span, country-comprehensive population statistics (which includes several epidemics waves), an association was shown to exist between meningococcal disease and influenza. This suggests the need for the surveillance of the two processes in an interrelated manner.

Disease Outbreaks↗
PubMed2006

Stochastic and deterministic simulations of heterogeneous cell population dynamics.

A Monte Carlo algorithm, which can accurately simulate the dynamics of entire heterogeneous cell populations, was developed. The algorithm takes into account the random nature of cell division as well as unequal partitioning of cellular material at cell division. Moreover, it is general in the sense that it can accommodate a variety of single-cell, deterministic reaction kinetics as well as various stochastic division and partitioning mechanisms. The validity of the algorithm was assessed through comparison of its results with those of the corresponding deterministic cell population balance model in cases where stochastic behavior is expected to be quantitatively negligible. Both algorithms were applied to study: (a) linear intracellular kinetics and (b) the expression dynamics of a genetic network with positive feedback architecture, such as the lac operon. The effects of stochastic division as well as those of different division and partitioning mechanisms were assessed in these systems, while the comparison of the stochastic model with a continuum model elucidated the significance of cell population heterogeneity even in cases where only the prediction of average properties is of primary interest.

Algorithms↗
PubMed2003

Parameter estimation in biochemical pathways: a comparison of global optimization methods.

Here we address the problem of parameter estimation (inverse problem) of nonlinear dynamic biochemical pathways. This problem is stated as a nonlinear programming (NLP) problem subject to nonlinear differential-algebraic constraints. These problems are known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based) local optimization methods fail to arrive at satisfactory solutions. To surmount this limitation, the use of several state-of-the-art deterministic and stochastic global optimization methods is explored. A case study considering the estimation of 36 parameters of a nonlinear biochemical dynamic model is taken as a benchmark. Only a certain type of stochastic algorithm, evolution strategies (ES), is able to solve this problem successfully. Although these stochastic methods cannot guarantee global optimality with certainty, their robustness, plus the fact that in inverse problems they have a known lower bound for the cost function, make them the best available candidates.

Algorithms↗
PubMed2003

Robust parameter estimation techniques for stochastic within-host macroparasite models.

We present a stochastic model of the within-host population dynamics of lymphatic filariasis, and use a simulated goodness-of-fit (GOF) method to estimate immunological parameters and their confidence intervals from experimental data. A variety of deterministic moment closure approximations to the stochastic system are explored and compared with simulation results. For the maximum GOF parameter estimates, none of the methods of closure accurately reproduce the behaviour of the stochastic model. However, direct analysis of the stochastic model demonstrates that the high levels of variation observed in the data can be reproduced without requiring parameters to vary between hosts. This indicates that the observed aggregation of parasite load may be dynamically generated by random variation in the development of an effective immune response against parasite larvae.

Animals↗
PubMed2000

DNA computing on surfaces.

DNA computing was proposed as a means of solving a class of intractable computational problems in which the computing time can grow exponentially with problem size (the 'NP-complete' or non-deterministic polynomial time complete problems). The principle of the technique has been demonstrated experimentally for a simple example of the hamiltonian path problem (in this case, finding an airline flight path between several cities, such that each city is visited only once). DNA computational approaches to the solution of other problems have also been investigated. One technique involves the immobilization and manipulation of combinatorial mixtures of DNA on a support. A set of DNA molecules encoding all candidate solutions to the computational problem of interest is synthesized and attached to the surface. Successive cycles of hybridization operations and exonuclease digestion are used to identify and eliminate those members of the set that are not solutions. Upon completion of all the multistep cycles, the solution to the computational problem is identified using a polymerase chain reaction to amplify the remaining molecules, which are then hybridized to an addressed array. The advantages of this approach are its scalability and potential to be automated (the use of solid-phase formats simplifies the complex repetitive chemical processes, as has been demonstrated in DNA and protein synthesis). Here we report the use of this method to solve a NP-complete problem. We consider a small example of the satisfiability problem (SAT), in which the values of a set of boolean variables satisfying certain logical constraints are determined.

Computing Methodologies↗
PubMed1983

On some stochastic formulations and related statistical moments of pharmacokinetic models.

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

Animals↗
PubMed2006

Stochastic model of transcription factor-regulated gene expression.

We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes, gene A and gene B, which synthesize the TFs and the target gene proteins, respectively. We show through analytic calculations that the TF fluctuations have a significant effect on the distribution of the target gene protein levels when the mean TF level falls in the highest sensitive region of the dose-response curve. We further study the effect of reducing the copy number of gene A from two to one. The enhanced TF fluctuations yield results different from those in the deterministic case. The probability that the target gene protein level exceeds a threshold value is calculated with the knowledge of the probability density functions associated with the TF and target gene protein levels. Numerical simulation results for a more detailed stochastic model are shown to be in agreement with those obtained through analytic calculations. The relevance of these results in the context of the genetic disorder haploinsufficiency is pointed out. Some experimental observations on the haploinsufficiency of the tumour suppressor gene, Nkx 3.1, are explained with the help of the stochastic model of TF-regulated gene expression.

Computer Simulation↗
PubMed1994

Austere military medical care: a graded response.

In war, there has always been a dichotomy between health care needs and resources, and until the mid 18th century, this was an accepted fact of military medicine. However, since then, health care has made remarkable progress based on a belief that a linear periodic deterministic approach will provide solutions to problems. The dichotomy between needs and resources has been recognized or accepted only in disaster or mass casualty medicine, and then only to a limited degree. While degradation to dyssymmetry or chaos and unpredictability is accepted in other scientific disciplines, it has been ignored in medicine. The unpredictability and dissonance inherent in providing military medical care exists, and requires an acceptance of chaos as normal and inevitable. Accordingly, graded responses or austere levels of treatment care plans should be developed that will provide for improved care, particularly in austere military situations.

Health Care Rationing↗
PubMedDate not supplied

Evidence of deterministic chaos in the myoelectric signal.

Our aim was to study whether the myoelectric signals can be better modelled as outputs of a nonlinear dynamic system rather than as random stochastic signals. Both the nonlinear predictability and the dimensionality of the signals were studied using methods of nonlinear dynamics. The signals were measured from the biceps brachii muscle during both fatiguing and non-fatiguing isometric contractions at low load levels. The myoelectric signals were found to be nonlinear and to have a structure statistically distinguishable from random noise. The correlation dimension describing the dimensionality of the myoelectric signal decreased during local muscular fatigue. The results support the use of the theory of nonlinear dynamics for the modelling of the myoelectric signals.

Adult↗
PubMed1999

Conditionally Selective Dependence of Random Variables on External Factors.

Selective influence of experimental factors upon observable or hypothetical random variables is a key concept in the analysis of processing architectures and response time decompositions. This paper deals with the notion of conditionally selective influence, defined as follows. Let {X1, em leader, Xn} be stochastically interdependent random variables (e.g., hypothetical components of response time), and let Phi be a set of external factors affecting the joint distribution of {X1, em leader, Xn}. A subset of factors &Lambdai conditionally selectively influences Xi if at any fixed values of the remaining random variables the conditional distribution of Xi only depends on factors inside &Lambdai. The notion of conditional selectivity generalizes the relationship between factors and random variables described in Townsend (1984) as "indirect nonselectivity." This paper establishes the structure of the joint distribution of {X1, em leader, Xn} that is necessary and sufficient for {X1, em leader, Xn} to be conditionally selectively influenced by (not necessarily disjoint) factor subsets {&Lambda1, em leader, Gamman}, respectively. The notion of conditional selectivity is compared to that of unconditional selectivity, defined as follows. A subset of factors &Gammai unconditionally selectively influences Xi if the latter can be presented as a deterministic function of &Gammai and of some random variables (the same for all Xi, i=1, em leader, n) whose joint distribution does not depend on any factors from Phi. The two forms of selective influence are generally incompatible. Copyright 1999 Academic Press.

Journal Article↗
PubMed1995

Filtering noncorrelated noise in impedance cardiography.

Impedance cardiography (ICG) may be altered by noises as respiration and movement artifacts, mainly during exercise. In this work, a scaled Fourier linear combiner (SFLC) event-related to the R-R interval of ECG is proposed. It estimates the deterministic component of the impedance cardiographic signal and removes the noises uncorrelated to this interval. The impedance cardiographic signal is modeled as Fourier series with the coefficients estimated by the least mean square (LMS) algorithm. Simulations have been carried out to evaluate the filter performance for different noise conditions. Moreover, the method capability to remove uncorrelated noises was also examined in physiological data obtained in rest and exercise, by synchronizing respiration and pedaling with a metronome. Analyzing the ICG power spectrum, it was concluded that the proposed filter could remove the noises that are not synchronized with heart rate.

Algorithms↗
PubMed2005

A method for segmentation of switching dynamic modes in time series.

A method to identify switching dynamics in time series, based on Annealed Competition of Experts algorithm (ACE), has been developed by Kohlmorgen et al. Incorrect selection of embedding dimension and time delay of the signal significantly affect the performance of the ACE method, however. In this paper, we utilize systematic approaches based on mutual information and false nearest neighbor to determine appropriate embedding dimension and time delay. Moreover, we obtained further improvements to the original ACE method by incorporating a deterministic annealing approach as well as phase space closeness measure. Using these improved implementations, we have enhanced the performance of the ACE algorithm in determining the location of the switching of dynamic modes in the time series. The application of the improved ACE method to heart rate data obtained from rats during control and administration of double autonomic blockade conditions indicate that the improved ACE algorithm is able to segment dynamic mode changes with pinpoint accuracy and that its performance is superior to the original ACE algorithm.

Algorithms↗