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PubMed1996

Waveform estimation techniques for event-related bioelectric signals: a study of performance.

Many bioelectric signals result from the electrical response of a physiological system to an impulse that can be internal (ECG signals) or external (evoked potentials). A comparative study of performance of seven waveform estimation techniques used for event-related signals that are time-locked to a stimulus is presented in this paper. Computer generate 1 signals and noise for several signal-to-noise ratios (SNRs) are used to make ensembles of simulated noisy waveforms. The performance of each technique is numerically investigated using the root-mean-squared error and two well known SNR estimators. The results show that an adaptive impulse correlated filter performs the best. It is capable of estimating the deterministic component of the signal and removes the noise uncorrelated with stimulus even if this noise is colored and without the need for prealignment.

Computer Simulation↗

PubMed2003

A chaotic approach to maintain the population diversity of genetic algorithm in network training.

The concept of chaos being radically different from statistical randomness is introduced into chemometrics research. The chaotic system that is deterministic with underlying patterns and inherent ability in searching the space of interest has been employed to improve the performance of chemometric algorithms. In this paper, a chaotic mutation is introduced into the genetic algorithm (GA) which is used for artificial neural network (ANN) training. The chaotic algorithm is very efficient in maintaining the population diversity during the evolution process of GA. The proposed algorithm CGANN has been testified by prediction of vibrational frequencies of octahedral hexahalides from some selected molecular parameters.

Algorithms↗

PubMed2004

A machine learning method for extracting symbolic knowledge from recurrent neural networks.

Neural networks do not readily provide an explanation of the knowledge stored in their weights as part of their information processing. Until recently, neural networks were considered to be black boxes, with the knowledge stored in their weights not readily accessible. Since then, research has resulted in a number of algorithms for extracting knowledge in symbolic form from trained neural networks. This article addresses the extraction of knowledge in symbolic form from recurrent neural networks trained to behave like deterministic finite-state automata (DFAs). To date, methods used to extract knowledge from such networks have relied on the hypothesis that networks' states tend to cluster and that clusters of network states correspond to DFA states. The computational complexity of such a cluster analysis has led to heuristics that either limit the number of clusters that may form during training or limit the exploration of the space of hidden recurrent state neurons. These limitations, while necessary, may lead to decreased fidelity, in which the extracted knowledge may not model the true behavior of a trained network, perhaps not even for the training set. The method proposed here uses a polynomial time, symbolic learning algorithm to infer DFAs solely from the observation of a trained network's input-output behavior. Thus, this method has the potential to increase the fidelity of the extracted knowledge.

Algorithms↗

PubMed1999

A method for estimating pharmacokinetic risks of concentration-dependent drug interactions from preclinical data.

This article evaluates a novel approach for estimating the pharmacokinetic risks associated with drug interactions in populations. Preclinical pharmacokinetic and metabolism data are analyzed with a stochastic differential equation-based pharmacokinetic model that recognizes that the risks associated with known drug interactions involve deterministic and stochastic components. Specifically, a Bernoulli jump-diffusion pharmacokinetic model that accounts for the pharmacokinetics, the variability inherent in the pharmacokinetics, and the idiosyncratic nature of the possibility of drug interactions is proposed. In addition, the variability inherent in the extent of drug interaction is explicitly accounted for. The approach provides useful mechanistic insights into the stochastic processes that "drive" drug interactions in populations because it yields analytical results. The validity of the model predictions was tested with experimental data from two previously investigated systems: N-1 and N-3 caffeine demethylation in populations with smokers and in the terfenadine-ketoconazole system.

Dose-Response Relationship, Drug↗

PubMed1968

The dynamics of malaria.

Previous studies on dynamic systems of transmission of malaria, and of eradication of infection following the interruption of transmission, have now been adapted for advanced techniques using the facilities offered by computers.The computer programmes have been designed for a deterministic model suitable for a large community and also for a stochastic model relevant to small populations in which infections reach very low finite numbers. In this model, new infections and recoveries are assessed by the daily inoculation rate and are subject to laws of chance. Such a representation is closer than previous models to natural happenings in the process of malaria eradication. Further refinements of the new approach include the seasonal transmission and simulation of mass chemotherapy aimed at a cure of P. falciparum infections.These programmes present models on which the actual or expected results of changes due to various factors can be studied by the analysis of specific malaria situations recorded in the field. The value of control methods can also be tested by the study of such hypothetical epidemiological models and by trying out various procedures.Two specific malaria situations (in a pilot project in Northern Nigeria and in an outbreak in Syria) were studied by this method and provided some interesting results of operational value. The attack measures in the pilot project in Northern Nigeria were carried out according to the theoretical model derived from the basic data obtained in the field.

Disease Outbreaks↗

PubMed1988

The adaptation ability of neuronal models subject to a current step stimulus.

Three neuronal models of the spike initiating process were investigated with respect to their ability to show adaptation to a current step: (i) the perfect integrator model (PIM), (ii) the leaky integrator model (LIM), and (iii) the Hodgkin-Huxley (HH)-model. It was found that although each neuronal model will generate different response spike trains to a given stimulus, all responses fulfilled the criteria of a deterministic neural response (Awiszus 1988). The results show that both PIM and LIM are unable to show adaptation regardless of the choice of model parameters whereas the HH-model shows a clear rate of discharge adaptation. The reason for this adaptation lies in the fact that there are conditions for the HH-model where a step stimulus is highly effective. These conditions are investigated by means of a phase plane analysis. Consequences of these results for the explanation of neuronal adaptation and the validity of the neuronal models investigated are discussed.

Action Potentials↗

PubMed1983

A stochastic approach for the interpretation of single pulse experiments in morphological multicompartments of renewing and exponentially growing cell populations.

A general approach for the interpretation of single pulse experiments in multicompartment systems is presented. It allows an extension of the classical single compartment Barret's methodology, and has been detailed in the pipeline model case to show its capabilities. FLM, FLC, grain count curves, labelling indices and compartment size ratios of each compartment, are fitted into a coherent scheme that fully describes the statistical aspects of the phase durations including possible losses. It is shown that if the compartments are identical, irrespective of the feedback coupling between them, the system may be treated as a single compartment. It is also shown that the FLC information is necessary to identify the existence of losses in the system, and how to correct the "apparent" transit times if losses are present. The pipeline model is treated and a suggestion is made to reconcile the "British" and "American" interpretations of the erythroid system. As a corollary, simple formulae are derived in the deterministic case through a coupling matrix describing the interaction between compartments. Computer codes are described and have been implemented in the J.E.N. Thermoecology Laboratory.

Cell Count↗

PubMedDate not supplied

Microemboli detection using ultrasound backscatter.

Microemboli detection and characterisation have recently received great attention due to its clinical importance in the management of cerebrovascular disease. The new method presented in this paper is directly based on the idea that the ultrasound (US) backscattered signal from flowing blood is chaotic (El-Brawany and Nassiri 2002). The detection technique involves building a nonlinear model of the deterministic characteristics of the chaotic backscatter signal from blood, and the use of this model to look at the prediction error as a primary decision-making criterion for the microemboli detector. A complementary feature to the prediction error, namely, the degree of coherence between the US excitation pulse and the prediction error signal is used to enhance the detection process. The detector has been built using a feed-forward neural network with error back-propagation. The detection technique is tested successfully using a vascular flow phantom with solid spheres and bubbles of known sizes introduced in the flow circuit to mimic solid and gaseous emboli. Receiver operating characteristic (ROC) curve is used to assess the performance of the detection process. The total classification rate ranges from 88% to 96%.

Blood Flow Velocity↗

PubMed2004

Consistency of nonlinear system response to complex drive signals.

The consistency of a nonlinear system's response to a repeated complex waveform drive signal is an important consideration in classical and quantum systems as diverse as lasers, neuronal networks, and manufacturing plants. We show from a consideration of different characteristic waveforms that there is typically an optimal drive amplitude for the most consistent response; internal noise sources dominate for small amplitude driving while deterministic system nonlinearity reduces consistency for large amplitudes. We test this general concept and its measurement experimentally and numerically on the specific example of a laser system.

Algorithms↗

PubMedDate not supplied

The ontogeny of phonological categories and the primacy of lexical learning in linguistic development.

In this paper, we draw on recent developments in several areas of cognitive science that suggest that the lexicon is at the core of grammatical generalizations at several different levels of representation. Evidence comes from many sources, including recent studies on language processing in adults and on language acquisition in children. Phonological behavior is influenced very early by pattern frequency in the lexicon of the ambient language, and we propose that phonological acquisition might provide the initial bootstrapping into grammatical generalization in general. The phonological categories over which pattern frequencies are calculated, however, are neither transparently available in the audiovisual signal nor deterministically fixed by the physiological and perceptual capacities of the species. Therefore, we need several age-appropriate models of how the lexicon can influence a child's interactions with the ambient language over the course of phonological acquisition.

Child↗

PubMed1992

Modelling survivorship kinetics: a two-parameter model.

A mathematical model of survivorship kinetics is presented. It takes into account both deterministic and stochastic aspects of survival curves. Earlier reports [Piantanelli: Arch Gerontol Geriatr 1986;5:107-118; Piantanelli: Ann NY Acad Sci 1988; 521:99-109] described a model capable of making distinct predictions on the mean and standard deviation of an index of physiological function, fitting data even in the tail of survivorship curves, and accounting for the selection of the cohort at advanced ages. However, it contains four parameters whose biological interpretation is unclear. In the present paper we propose a modification of the model which maintains the main characteristics of the previous one and, in addition, results in two significant improvements. First, the number of free parameters is reduced to only two, making much easier both their estimation and interpretation, particularly when the model is applied to data from various animal groups manipulated in different ways. Second, it is possible to relate the parameters to well-defined deterministic and stochastic factors: specifically, a deterministic component describing the environmental and genetic influence on physiological functions, and a stochastic component representing the fluctuating interactions of the living organism and its environment.

Aging↗

PubMed2004

Growth cone pathfinding: a competition between deterministic and stochastic events.

BACKGROUND: Growth cone migratory patterns show evidence of both deterministic and stochastic search modes. RESULTS: We quantitatively examine how these two different migration modes affect the growth cone's pathfinding response, by simulating growth cone contact with a repulsive cue and measuring the resultant turn angle. We develop a dimensionless number, we call the determinism ratio Psi, to define the ratio of deterministic to stochastic influences driving the growth cone's migration in response to an external guidance cue. We find that the growth cone can exhibit three distinct types of turning behaviors depending on the magnitude of Psi. CONCLUSIONS: We conclude, within the context of these in silico studies, that only when deterministic and stochastic migration factors are in balance (i.e. Psi ~ 1) can the growth cone respond constructively to guidance cues.

Algorithms↗

PubMed2002

Combinatorial and cross-fiber averaging transform muscle electrical responses with a large stochastic component into deterministic contractions.

Pyloric muscles of the stomatogastric neuromuscular system of the lobster Panulirus interruptus produce highly deterministic (range, less than +/- 6% of mean amplitude) contractions in response to motor nerve stimulation with unchanging spike bursts containing physiological (5-10) spike numbers. Intracellular recordings of extrajunctional potentials (EJPs) evoked in these muscles by motor nerve stimulation revealed a large, apparently stochastic amplitude variation (range, +/- 36% of mean amplitude). These observations raised the question of how do electrical responses with a large amplitude variation give rise to deterministic muscle output? We show here that this question is likely resolved by (1) combinatorial averaging within individual muscle fibers of the multiple EJPs that occur in motor neuron bursts, and (2) averaging across muscle fibers whose electrical responses are uncorrelated. Synapses with high inherent variability are also present in vertebrate CNSs. Combinatorial averaging in multispike inputs would also reduce variation in postsynaptic response at these synapses. The data reported here provide further support that bursting presynaptic activity could make such synapses functionally deterministic as well.

Action Potentials↗

PubMed2007

Process and meaning: nonlinear dynamics and psychology in visual art.

Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life.

Art↗

PubMed1997

[Data organization in statistics applied to biology].

In health statistics data collection may be associated or not to the variable time, that is the moment of data acquisition. The variable may be necessary, if the characteristics of the statistics problem require it. It may be a useful information, particularly in the study of multivariable systems, in order to increase the selectivity of the mutual relations between the variables involved. The main subject is the relation between presumed pathogenous agents and biological damage. In order to identify a mathematical model of a system when variations in the time are present, drawn the distinction between deterministic an statistics methods, an intepretation of significance, validity, and applicability of statististical methods is proposed. For the purpose of showing affinities, the model is compared with other models, that is linear regression and cohort studies. The quantity of data, the frequency and the length in time of the sampling are considered. Characteristics and qualifications of a software for data processing are discussed. The importance of sampling, transmission and organization protocols of the data is also shown.

Biometry↗

PubMed1994

A theoretical study of the socioecology of ungulates. II. A dynamic programming study of the stochastic formulation.

We develop a stochastic version of a previously discussed model of optimal herd size selection in ungulates. We assume that a large herd size confers to the animals a high level of protection against predators, but reduces the amount of food which can be eaten by each individual; on the contrary animals belonging to small herds would have access to large amounts of food but would bear a high risk of being killed by predators. Employing a dynamic programming approach we analyze the optimal trade-off between starvation and predation risks under the hypothesis that the animals would try to maximize their expected reproductive fitness during the incoming breeding period. We compare the optimal strategy in environments described by different kinds of stochastic food distributions (including the deterministic limit) for different values of predation pressure and of overall food availability. We obtain general information about the effect of the level of randomness of food distribution on the mean individual fitness and on the number of reproducers (the animals which survive to the beginning of the reproductive season). Moreover we discuss how a certain number of behavioral and ecological processes--which have been often described in natural populations of ungulates and which are usually explained in terms of phenological variations of the ecological landscape--may be interpreted as caused by intrinsic variations of the animals' strategy.

Animal Nutritional Physiological Phenomena↗

PubMed2006

Timescales of population rarity and commonness in random environments.

This is a mathematical study of the interactions between non-linear feedback (density dependence) and uncorrelated random noise in the dynamics of unstructured populations. The stochastic non-linear dynamics are generally complex, even when the deterministic skeleton possesses a stable equilibrium. There are three critical factors of the stochastic non-linear dynamics; whether the intrinsic population growth rate (lambda) is smaller than, equal to, or greater than 1; the pattern of density dependence at very low and very high densities; and whether the noise distribution has exponential moments or not. If lambda < 1, the population process is generally transient with escape towards extinction. When lambda > or = 1, our quantitative analysis of stochastic non-linear dynamics focuses on characterizing the time spent by the population at very low density (rarity), or at high abundance (commonness), or in extreme states (rarity or commonness). When lambda >1 and density dependence is strong at high density, the population process is recurrent: any range of density is reached (almost surely) in finite time. The law of time to escape from extremes has a heavy, polynomial tail that we compute precisely, which contrasts with the thin tail of the laws of rarity and commonness. Thus, even when lambda is close to one, the population will persistently experience wide fluctuations between states of rarity and commonness. When lambda = 1 and density dependence is weak at low density, rarity follows a universal power law with exponent -3/2. We provide some mathematical support for the numerical conjecture [Ferriere, R., Cazelles, B., 1999. Universal power laws govern intermittent rarity in communities of interacting species. Ecology 80, 1505-1521.] that the -3/2 power law generally approximates the law of rarity of 'weakly invading' species with lambda values close to one. Some preliminary results for the dynamics of multispecific systems are presented.

Ecology↗

PubMed2000

Ratchet driven by quasimonochromatic noise

The currents generated by noise-induced activation processes in a periodic potential are investigated analytically, by digital simulation and by performing analog experiments. The noise is taken to be quasimonochromatic and the potential to be a smoothed sawtooth. Two analytic approaches are studied. The first involves a perturbative expansion in inverse powers of the frequency characterizing quasimonochromatic noise and the second is a direct numerical integration of the deterministic differential equations obtained in the limit of weak noise. These results, together with the digital and analog experiments, show that the system does indeed give rise, in general, to a net transport of particles. All techniques also show that a current reversal exists for a particular value of the noise parameters.

Journal Article↗