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At least 847 records · Page 47Linked to original sources

Discrete stochastic modeling of calcium channel dynamics.

We propose a discrete stochastic model for calcium dynamics in living cells. A set of probabilities for the opening/closing of calcium channels is assumed to depend on the calcium concentration. We study this model in one dimension, analytically in the limit of a large number of channels per site N, and numerically for small N. As the number of channels per site is increased, the transition from a nonpropagating region of activity to a propagating one changes from one described by directed percolation to that of deterministic depinning in a spatially discrete system. Also, for a small number of channels a propagating calcium wave can leave behind a novel fluctuation-driven state.

Calcium Channels↗

Nonhomogeneous local atrial activity during acute atrial fibrillation: spectral and dynamic analysis.

Atrial fibrillation (A Fib) has been categorized into four different types (I-IV) based on the morphology of the epicardial bipolar electrogram. In the present study, we hypothesized that these same types of A Fib also exist at endocardial sites. Simultaneous high, mid, and low right atrial endocardial bipolar electrograms were analyzed during acute A Fib induced by a rapid train of stimuli (20-40 Hz) for 1-3 seconds in anesthetized closed-chest dogs (N = 7, total of 72 episodes). A Fib lasted between 3 seconds and a few minutes (22.3 +/- 22.8 sec). During A Fib, bipolar electrograms (0.5-500 Hz) were both discrete (types I and II) on electrograms recorded at one site and at the same time irregular (type III) on electrograms recorded at another site. The three simultaneously recorded electrograms encompassed all combinations of the four types of A Fib. When A Fib had a discrete electrogram morphology (types I and/or II), the mean rate of the A Fib was 494 +/- 93 beats/min. At a given site, electrogram morphology also changed type over time. Fast Fourier transform (FFT) of the digitized electrograms (8-10 sec, 800 Hz digitization) showed peaks mostly below 15 Hz (range 0-30 Hz), that were either discrete (narrow band) with clear harmonic components, or had continuous (broad band) spectra, that changed in a time and site dependent manner. Phase plane plots (PPP), a plot of voltage versus rate of change of voltage, varied with respect to time and location. However, the morphology of these PPP often inscribed well defined structure suggesting dynamics compatible with deterministic chaos, rather than random dynamics.(ABSTRACT TRUNCATED AT 250 WORDS)

Acute Disease↗

The engineering of gene regulatory networks.

The rapid accumulation of genetic information and advancement of experimental techniques have opened a new frontier in biomedical engineering. With the availability of well-characterized components from natural gene networks, the stage has been set for the engineering of artificial gene regulatory networks with sophisticated computational and functional capabilities. In these efforts, the ability to construct, analyze, and interpret qualitative and quantitative models is becoming increasingly important. In this review, we consider the current state of gene network engineering from a combined experimental and modeling perspective. We discuss how networks with increased complexity are being constructed from simple modular components and how quantitative deterministic and stochastic modeling of these modules may provide the foundation for accurate in silico representations of gene regulatory network function in vivo.

Animals↗

A p-Adic model for the process of thinking disturbed by physiological and information noise.

We develop a model of the process of thinking in the presence of noise (which is produced by the simultaneous action of a huge number of neurons in the brain as well as by external information and internal cognitive processes). Our model is based on Freud's idea on the splitting of cognitive processes into two (closely connected) domains: consciousness and subconsciousness. We represent the process of thinking as a random dynamical process in a space of ideas endowed with a non-Euclidean geometry (which differs extremely from the ordinary Euclidean geometry of spatial location of neurons in the brain). The so-called p-adic geometry on a space of ideas describes the ability of cognitive systems to form associations. We show that random dynamical thinking systems on a p -adic space of ideas still generate only deterministic ideas. We also study positive and negative effects of noise (in particular, creativeness and stress).

Brain↗

Attractor reliability reveals deterministic structure in neuronal spike trains.

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewal-like processes with the same spike-time histogram.

Action Potentials↗

The simple perfection of quantum correlation in human vision.

A theory is presented that specifies the amount of light that is needed for the perception of any stimulus that is defined in space, time and color. For detection and discrimination mechanistic neural elements with deterministic procedures exist. Twin pairs of red and green cones are ordered in three sets along clockwise and counter clockwise revolving spirals and along circles around the center of the fovea. In the rod-free fovea the red pairs are ordered along the spirals and the green along the circles. Each cone is accompanied by--dependent on retinal eccentricity--up to 100 satellite rods. For the retinal signal processing such a receptor group constitutes a space-quantum in analogy with time-quanta of about 0.04 s. In the peripheral retina the red and green twin pairs of space-quanta are roughly ordered along and at random distributed over the spirals and circles. Over each time-quantum, the cone and rods of a space-quantum sum their responses in a common nerve circuit of the luminosity channel. The summation's results from twin pairs of the same set of space-quanta are correlated by two-fold spatio-temporal coincidence mechanisms in the retina. Their outcome signals the perception of light, movement and edge. In the fused binocular visual field the movement and edge signals of the three sets from both eyes perfectly join vectorially together, provided the responding pairs of space-quanta are binocularly in perfect register as they normally are. The receptor's Weber gain control makes the receptor an all-or-none-system. The space-quantum's De Vries gain control makes its sensitivity equal to the average of the poisson fluctuations in quantum absorption per time-quantum. The controls are based on, respectively, arithmetically feed forward and backward inhibitive nerve mechanisms. The thermal noise of the photo-pigment resets the controls. The response to the second quantum absorption in a time-quantum in the individual rod, red or green cone has accession to the white, red or green nerve color circuit, respectively, and produces there a corresponding color signal. Already a single absorption in a blue cone is for a blue signal. In the retina, for the generation of yellow signals, the color circuits of individual red and green cones of each mixed entwined triple of red and green twin pairs of space-quanta are cross-connected through a nerve opponent color circuit. In the lateral geniculate nucleus in groups of seven neighboring triples, through two nerve opponent color circuits that are common for the two eyes together, the red and green signals as well as the yellow and blue mutually annihilate each other's color. White signals remain. In anomalous trichromacy, the space-quanta of some pairs have different cones or in one of them the cone is missing. In dichromacy, all pairs have different cones or one type of cones is missing. For perceptive resolution the periodic scanning of the retinal image by the eye tremor in synchrony with the time-quanta, overrules the limit of optical resolution as set by diffraction in the eye optics. Dependent on pupil diameter the scanning contributes up to a factor of about 30 to resolution. The action potentials of the Purkinje cells in the myocardium generate the time-quanta of the central nervous system as well as the mechanical scanning of the retinal image through the synchronic periodic variation of the tonus in the eye muscles.

Adaptation, Ocular↗

Non-linear prediction for oesophageal voice analysis.

Herein, non-linear prediction methods are applied to oesophageal voice analysis. The research aims to investigate normal and pathological subjects, in order to improve knowledge of the oesophageal voice behaviour. Analysis is performed in the reconstructed phase space, using both non-linear prediction with local linear approximation and the S-Map method. Preliminary results seem to confirm that in normal subjects a non-linear stable deterministic behaviour takes place, while in pathological subjects the non-linear contribution reduces while the time series becomes unstable.

Adult↗

Deterministic numerical model for treating the three elastic constants in nematic liquid-crystalline polymers.

In this paper, a deterministic model, which considers the three Frank elastic constants, is introduced. It is based on a lattice model and a director is used to represent the orientation of the liquid crystals in each cell. A tensor expression of the so-called "texture field" is deduced so that the nematic symmetry is conserved automatically. In the current model, the evolution of the director field can be viewed as a process towards the state of zero elastic torque. The model forms the basis for an improved understanding of the mesoscale structures and rheological phenomena of nematic liquid-crystalline polymers. It has been tested in its ability to reproduce the Fréedericksz transitions, and simulations of thin liquid crystalline polymer films clearly show the effect of unequal elastic constants on the director microstructure evolution.

Journal Article↗

Uncertain numbers and uncertainty in the selection of input distributions--consequences for a probabilistic risk assessment of contaminated land.

Risks from exposure to contaminated land are often assessed with the aid of mathematical models. The current probabilistic approach is a considerable improvement on previous deterministic risk assessment practices, in that it attempts to characterize uncertainty and variability. However, some inputs continue to be assigned as precise numbers, while others are characterized as precise probability distributions. Such precision is hard to justify, and we show in this article how rounding errors and distribution assumptions can affect an exposure assessment. The outcome of traditional deterministic point estimates and Monte Carlo simulations were compared to probability bounds analyses. Assigning all scalars as imprecise numbers (intervals prescribed by significant digits) added uncertainty to the deterministic point estimate of about one order of magnitude. Similarly, representing probability distributions as probability boxes added several orders of magnitude to the uncertainty of the probabilistic estimate. This indicates that the size of the uncertainty in such assessments is actually much greater than currently reported. The article suggests that full disclosure of the uncertainty may facilitate decision making in opening up a negotiation window. In the risk analysis process, it is also an ethical obligation to clarify the boundary between the scientific and social domains.

Body Weight↗

ArcEGMO-URBAN--hydrological model for point sources in river basins.

The new model ArcEGMO-URBAN aims at deterministic and spatiotemporal modelling of water, nitrogen and phosphorus fluxes from all urbanised areas of a river basin considering all potential sources. Pollution loads are calculated for discrete urban patches and balanced on the level of hydrological subbasins. Modelling results can be defined by the user of any level of spatial and/or temporal aggregation, e.g. matter balances for river basins or river sections and years or months, respectively. To process spatial data, a Geographic Information System is linked to the model. Information on urban land use and general characteristics of river basins is based on digital coverages, partly generated from remote-sensing data. Moreover, statistical data, e.g. on population, sewer systems, wastewater treatment plants etc. are included. Stormwater runoff from impervious surfaces is calculated as one input to the sewer network. Wastewater is considered with its main sewer system, pumping stations and treatment plants. Finally, the discharge is balanced for discrete river sections. Modelling results attest ArcEGMO-URBAN its ability to realistically quantify matter fluxes and major pollution sources as well as their seasonal variation. This makes the model an applicable tool for the analysis of scenarios with e.g. varying population distribution or climatic and technological conditions.

Geographic Information Systems↗

The interpretation of time-varying data with DIAMON-1.

Applying the methods of Artificial Intelligence to clinical monitoring requires some kind of signal-to-symbol conversion as a prior step. Subsequent processing of the derived symbolic information must also be sensitive to history and development, as the failure to address temporal relationships between findings invariably leads to inferior results. DIAMON-1, a framework for the design of diagnostic monitors, provides two methods for the interpretation of time-varying data: one for the detection of trends based on classes of courses, and one for the tracking of disease histories modelled through deterministic automata. Both methods make use of fuzzy set theory taking account of the elasticity of medical categories and allowing discrete disease models to mirror the patient's continuous progression through the stages of illness.

Artificial Intelligence↗

Sustainable pattern analysis of a publicly owned Material Recovery Facility in a fast-growing urban setting under uncertainty.

Sustainable development goals are achievable through the installation of Material Recovery Facilities (MRFs) in certain solid waste management systems, especially those in rapidly expanding multi-district urban areas. MRFs are a cost-effective alternative when curbside recycling does not demonstrate long-term success. Previous capacity planning uses mixed integer programming optimization for the urban center of the city of San Antonio, Texas to establish that a publicly owned material recovery facility is preferable to a privatized facility. As a companion study, this analysis demonstrates that a MRF alleviates economic, political, and social pressures facing solid waste management under uncertainty. It explores the impact of uncertainty in decision alternatives in an urban environmental system. From this unique angle, waste generation, incidence of recyclables in the waste stream, routing distances, recycling participation, and other planning components are taken as intervals to expand upon previous deterministic integer-programming models. The information incorporated into the optimization objectives includes economic impacts for recycling income and cost components in waste management. The constraint set consists of mass balance, capacity limitation, recycling limitation, scale economy, conditionality, and relevant screening restrictions. Due to the fragmented data set, a grey integer programming modeling approach quantifies the consequences of inexact information as it propagates through the final solutions in the optimization process. The grey algorithm screens optimal shipping patterns and an ideal MRF location and capacity. Two case settings compare MRF selection policies where optimal solutions exemplify the value of grey programming in the context of integrated solid waste management.

Algorithms↗

The dynamics of a neuronal culture of dissociated cortical neurons of neonatal rats.

Neuronal networks of dissociated cortical neurons from neonatal rats were cultured over a multielectrode dish with 64 active sites, which were used both for recording the electrical activity and for stimulation. After about 4 weeks of culture, a dense network of neurons had developed and their electrical activity was studied. When a brief voltage pulse was applied to one extracellular electrode, a clear electrical response was evoked over almost the entire network. When a strong voltage pulse was used, the response was composed of an early phase, terminating within 25 ms, and a late phase which could last several hundreds of milliseconds. Action potentials evoked during the early phase occurred with a precise timing with a small jitter and the electrical activity initiated by a localized stimulation diffused significantly over the network. In contrast, the late phase was characterized by the occurrence of clusters of electrical activity with significant spatio-temporal fluctuations. The late phase was suppressed by adding small amounts of D(-)-2-amino-5-phosphonovaleric acid to the extracellular medium, or by increasing the amount of extracellular Mg2+. The electrical activity of the network was substantially increased by the addition of bicuculline to the extracellular medium. The results presented here show that the neuronal network may exist in two different dynamical states: one state in which the neuronal network behaves as a non-chaotic deterministic system and another state where the system exhibits large spatio-temporal fluctuations, characteristic of stochastic or chaotic systems.

Action Potentials↗

Approximating the long-term behaviour of a model for parasitic infection.

In a companion paper two stochastic models, useful for the initial behaviour of a parasitic infection, were introduced. Now we analyse the long term behaviour. First a law of large numbers is proved which allows us to analyse the deterministic analogues of the stochastic models. The behaviour of the deterministic models is analogous to the stochastic models in that again three basic reproduction ratios are necessary to fully describe the information needed to separate growth from extinction. The existence of stationary solutions is shown in the deterministic models, which can be used as a justification for simulation of quasi-equilibria in the stochastic models. Host-mortality is included in all models. The proofs involve martingale and coupling methods.

Animals↗

An agent-based approach for modeling molecular self-organization.

Agent-based modeling is a technique currently used to simulate complex systems in computer science and social science. Here, we propose its application to the problem of molecular self-assembly. A system is allowed to evolve from a separated to an aggregated state following a combination of stochastic, deterministic, and adaptive rules. We consider the problem of packing rigid shapes on a lattice to verify that this algorithm produces more nearly optimal aggregates with less computational effort than comparable Monte Carlo simulations.

Algorithms↗

Time-frequency plane Wiener filtering of the high-resolution ECG: development and application.

The time-frequency plane Wiener (TFPW) filter is a new method, based on a posteriori Wiener filtering principles, to enhance the performance of ensemble averaging. This paper develops the mathematical aspects of the TFPW filter, and assesses its performance with elementary signals, such as sine waves and chirps, and authentic high-resolution electrocardiogram (HRECG) ensembles. The principal feature of the TFPW filter is its use of the time-frequency plane to accommodate signal nonstationarity. Using a posteriori computed statistics of the ensemble, the filter matches itself to the time-frequency structure of the signals to be estimated. The method is sufficiently general to be applicable to any class of repetitive signal with a deterministic time-frequency structure and additive noise in the ensemble. It is concluded that significant improvements in both estimated signal fidelity and noise reduction are possible with the TFPW filter, compared to conventional ensemble averaging.

Electrocardiography↗

Optimal stopover decisions under wind influence: the effects of correlated winds.

Wind speed and direction have a significant effect on a flying bird's ground speed. Migrants are therefore expected to be sensitive to wind conditions and this should have consequences for optimal strategies of stopover and refuelling. Based on an earlier model of time-minimizing migration which includes wind condition, we investigate the consequences of the temporal correlation of wind conditions. Day-to-day changes in wind conditions are modelled with a two-state Markov process and an expression for the expected speed of migration is derived. The policy of the migrants is described by two parameters: a day t(g) when the birds start to leave whenever favourable conditions occur and a later day t(b)when they leave even in unfavourable winds. The model predicts that in most cases departures should be close to the date which is predicted by a wind-free deterministic model and that the birds should never leave without wind assistance. Only if the probability that the condition remains the same on the following day is close to 1 should the birds leave even in unfavourable conditions shortly after the deterministic optimal date. If the transition matrix is highly asymmetrical, i.e. if it is very probable that unfavourable conditions remain and that favourable conditions will change into unfavourable, then the birds are predicted to start using good winds several days before the deterministic optimal date. An analysis of six years of wind data from two sites in Sweden shows that wind directions on successive days are in fact correlated in all years.

Animals↗

A deterministic algorithm for constrained enumeration of transmembrane protein folds.

A deterministic algorithm for enumeration of transmembrane protein folds is presented. Using a set of sparse pairwise atomic distance constraints (such as those obtained from chemical cross-linking, FRET, or dipolar EPR experiments), the algorithm performs an exhaustive search of secondary structure element packing conformations distributed throughout the entire conformational space. The end result is a set of distinct protein conformations, which can be scored and refined as part of a process designed for computational elucidation of transmembrane protein structures.

Algorithms↗