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PubMed1999

Analysis of the stabilizing effect of Rom on the genetic network controlling ColE1 plasmid replication.

A stochastic model of ColE1 plasmid replication is presented. It is implemented by using UltraSAN, a simulation tool based on an extension of stochastic Petri nets (SPNs). It allows an exploration of the variation in plasmid number per bacterium, which is not possible using a deterministic model. In particular, the rate at which plasmid-free bacteria arise during bacterial division is explored in some detail since spontaneous plasmid loss is a widely observed empirical phenomenon. The rate of spontaneous plasmid loss provides an evolutionary explanation for the maintainance of Rom protein. The presence of Rom acts to reduce variance in plasmid copy number, thereby reducing the rate of plasmid loss at bacterial division. The ability of stochastic models to link biochemical function with evolutionary considerations is discussed.

Cell Division↗

PubMed2003

Which future for the French Pyrenean brown bear (Ursus arctos) population? An approach using stage-structured deterministic and stochastic models.

The Pyrenean brown bear (Ursus arctos) population is considered as one of the most seriously threatened with extinction in Western Europe. To assess its viability and possible needs of augmentation, we develop deterministic and stochastic stage-structured demographic models. The deterministic model reveals that a bear population cannot have a high annual growth rate and is particularly sensitive to breeder survival. High demographic parameters appear to be crucial to population persistence, especially for a small population that remains vulnerable to demographic and environmental stochasticities. The Pyrenean population cannot therefore be considered as viable. Successful conservation strategies for this population would require releasing more bears in both sub-populations in the near future.

Animals↗

PubMed2003

Community dynamics in a university environment.

Scholars have characterized academic communities of faculty, administration, and students in U.S. universities as "organized anarchies." In contrast, we offer evidence that the community structures of two representative public university systems are notably systematic by applying empirical phase-diagram techniques from the nonlinear dynamics literature to reconstruct low-dimensional deterministic behavior from historic data on the coevolution of faculty, administration, and student populations in each system. Ecological community models, fit with population data for each university, reproduce the essence of this behavior. The models offer novel explanations of how university resources obtained from enrollments and other sources are systematically partitioned among faculty, administration, and student populations interacting in shifting and well-defined community roles. This work offers empirical evidence that ecological principles, typically reserved for characterizing nonhuman interactions in biological systems, can shed light on human interactions in social systems.

Group Processes↗

PubMed2004

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Algorithms↗

PubMed2003

Climate variation and regional gradients in population dynamics of two hole-nesting passerines.

Latitudinal gradients in population dynamics can arise through regional variation in the deterministic components of the population dynamics and the stochastic factors. Here, we demonstrate an increase with latitude in the contribution of a large-scale climate pattern, the North Atlantic Oscillation (NAO), to the fluctuations in size of populations of two European hole-nesting passerine species. However, this influence of climate induced different latitudinal gradients in the population dynamics of the two species. In the great tit the proportion of the variability in the population fluctuations explained by the NAO increased with latitude, showing a larger impact of climate on the population fluctuations of this species at higher latitudes. In contrast, no latitudinal gradient was found in the relative contribution of climate to the variability of the pied flycatcher populations because the total environmental stochasticity increased with latitude. This shows that the population ecological consequences of an expected climate change will depend on how climate affects the environmental stochasticity in the population process. In both species, the effects will be larger in those parts of Europe where large changes in climate are expected.

Animals↗

PubMed1999

A stochastic model of the electrically stimulated auditory nerve: single-pulse response.

Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.

Action Potentials↗

PubMed2003

Effect of environmental fluctuations on the dynamic composition of engineered cartilage: a deterministic model in stochastic environment.

Dynamics of extracellular matrix (ECM) deposition and scaffold degradation in cell-polymer constructs have been studied in a random fluctuating environment created due to the applications of growth factors into the in vitro generation of cartilaginous constructs. Existing models of cell-polymer constructs for the design of engineered cartilage have been discussed and then a new deterministic scheme in random environment proposed taking into account the effects of growth factors as the environmental variability in the form of Gaussian white noise. Steady-state probability distribution of each individual component of the ECM in its homeostasis is found explicitly. The computer-simulated results of the model have been discussed and then compared with the data from a variety of scaffold systems and culture conditions.

Animals↗

PubMed2000

Biological effects of cosmic radiation: deterministic and stochastic.

Our basic understanding of the biological responses to cosmic radiations comes in large part from an international series of ground-based laboratory studies, where accelerators have provided the source of representative charged particle radiations. Most of the experimental studies have been performed using acute exposures to a single radiation type at relatively high doses and dose rates. However, most exposures in flight occur from low doses of mixed radiation fields at low-dose rates. This paper provides a brief overview of existing pertinent clinical and biological radiation data and the limitations associated with data available from specific components of the radiation fields in airflight and space travel.

Chromosome Aberrations↗

PubMed1997

Alpha rhythms: noise, dynamics and models.

Alpha rhythms appear as sinusoidal-like oscillations in the electroencephalogram (EEG) within the frequency range 8-12 Hz that waxe and wane in a more or less irregular way. The irregularity may have various origins. It may be due to noise or the oscillations may have an intrinsic irregular character, e.g. they may be generated by chaotic processes [Jansen (1991) Quantitative analysis of electroencephalograms: is there chaos in the future? Int. J. Biomed. Comput., 27: 95-123; Pradham, N. and Dutt, D.N. (1993) A nonlinear perspective in understanding the neurodynamics of EEG. Comput. Biol. Med., 23: 425-442; Pritchard et al. (1995) Dimensional analysis of resting human EEG II: Surrogate-data testing indicates nonlinearily but not low-dimensional chaos. Psychophysiology. 32: 486]. The term noise is often used in neurophysiology with different connotations as pointed out by Bullock (1990), either meaning an unwanted signal from the point of view of the receiver of a message, or a signal with intrinsic random fluctuations, i.e. with a stochastic character. Here we consider noise in this sense, as random or quasi-random neural activity. In this overview, we concentrate on the question of whether alpha rhythms should be considered generated in neuronal networks (1) as forms of filtered noise, (2) as deterministic oscillations influenced by noise or (3) as the result of chaotic dynamics. A clear answer to this question can have theoretical value because it may lead to a general model of the generation of this important EEG signal. Such a model, of course, would be a macroscopic one, since it would primarily account for the properties of the alpha rhythms at the neuronal network level. A translation of these properties to the microscopic, i.e. neuronal, level will not be easy to achieve without more direct knowledge of the membrane and synaptic basic properties of the neurons involved. Here we consider the question formulated above by presenting some relevant experimental evidence and theoretical arguments. The consideration whether alpha rhythms may have noise or chaotic sources implies examining how and where such sources can occur in the neuronal networks of the brain. Therefore we present, first, some basic data regarding the possible origin of noise and of chaos in neuronal networks. Second, the signal analysis methods that have to be applied in order to discriminate between filtered noise activities and chaotic oscillations are introduced. Third, the implications of these signal analyses regarding the possible answer to the initial question are discussed.

Alpha Rhythm↗

PubMed2003

Nonspiking and spiking proprioceptors in the crab: white noise analysis of spiking CB-chordotonal organ afferents.

The proprioceptors that signal the position and movement of the first two joints of crustacean legs provide an excellent system for comparison of spiking and nonspiking (graded) information transfer and processing in a simple motor system. The position, velocity, and acceleration of the first two joints of the crab leg are monitored by both nonspiking and spiking proprioceptors. The nonspiking thoracic-coxal muscle receptor organ (TCMRO) spans the TC joint, while the coxo-basal (CB) joint is monitored by the spiking CB chordotonal organ (CBCTO) and by nonspiking afferents arising from levator and depressor elastic strands. The response characteristics and nonlinear models of the input-output relationship for CB chordotonal afferents were determined using white noise analysis (Wiener kernel) methods. The first- and second-order Wiener kernels for each of the four response classes of CB chordotonal afferents (position, position-velocity, velocity, and acceleration) were calculated and the gain function for each receptor determined by taking the Fourier transform of the first-order kernel. In all cases, there was a good correspondence between the response of an afferent to deterministic stimulation (trapezoidal movement) and the best-fitting linear transfer function calculated from the first-order kernel. All afferents also had a nonlinear response component and second-order Wiener kernels were calculated for afferents of each response type. Models of afferent responses based on the first- and second-order kernels were able to predict the response of the afferents with an average accuracy of 86%.

Action Potentials↗

PubMedDate not supplied

GLARE: a new approach for filtering large reagent lists in combinatorial library design using product properties.

We present a novel computer algorithm, called GLARE (Global Library Assessment of REagents), that addresses the issue of optimal reagent selection in combinatorial library design. This program reduces or eliminates the time a medicinal chemist spends examining reagents which a priori cannot be part of a "good" library. Our approach takes the large reagent sets returned by standard chemical database queries and produces often considerably reduced reagent sets that are well-behaved with respect to a specific template. The pruning enforces "goodness" constraints such as the Lipinski rule of five on the product properties such that any reagent selection from the resulting sets produces only "good" products. The algorithm we implemented has three important features: (i) As opposed to genetic algorithms or other stochastic algorithms, GLARE uses a deterministic greedy procedure that smoothly filters out nonviable reagents. (ii) The pruning method can be biased to produce reagent sets with a balanced size, conserving proportionally more reagents in smaller sets. (iii) For very large combinatorial libraries, a partitioning scheme allows libraries as large as 10(12) to be evaluated in 0.25 s on an IBM AMD Opteron processor. This algorithm is validated on a diverse set of 12 libraries. The results that we obtained show an excellent compliance to the product property requirements and very fast timings.

Algorithms↗

PubMed2006

Detecting and characterizing phase synchronization in nonstationary dynamical systems.

We propose a general framework for detecting and characterizing phase synchronization from noisy, nonstationary time series. For detection, we propose to use the average phase-synchronization time and show that it is extremely sensitive to parameter changes near the onset of phase synchronization. To characterize the degree of temporal phase synchronization, we suggest to monitor the evolution of phase diffusion from a moving time window and argue that this measure is practically useful as it can be enhanced by increasing the size of the window. While desynchronization events can be caused by either a lack of sufficient deterministic coupling or noise, we demonstrate that the time scales associated with the two mechanisms are quite different. In particular, noise-induced desynchronization events tend to occur on much shorter time scales. This allows for the effect of noise on phase synchronization to be corrected in a practically doable manner. We perform a control study to substantiate these findings by constructing and investigating a prototype model of nonstationary dynamical system that consists of coupled chaotic oscillators with time-varying coupling parameter.

Algorithms↗

PubMed2002

Nonlinear nonstationary Wiener model of infant EEG seizures.

This paper presents the estimation of a nonstationary nonlinear model of seizures in infants based on parallel Wiener structures. The model comprises two parts and is partly derived from the Roessgen et al. seizure model. The first part consists of a nonlinear Wiener model of the pure background activity, and the second part in a nonlinear Wiener model of the pure seizure activity with a time-varying deterministic input signal. The two parts are then combined in a parallel structure. The Wiener model consists of an autoregressive moving average filter followed by a nonlinear shaping function to take into account the non-Gaussian statistical behavior of the data. Model estimation was performed on 64 infants of whom four showed signs of clinical and electrical seizures. Model validation is performed using time-frequency-based entropy distance and shows an averaged improvement of 50% in modeling performance compared with the Roessgen model.

Electroencephalography↗

PubMed2006

The time course of binocular rivalry reveals a fundamental role of noise.

When our two eyes view incongruent images, we experience binocular rivalry: An ongoing cycle of dominance periods of either image and transition periods when both are visible. Two key forces underlying this process are adaptation of and inhibition between the images' neural representations. Models based on these factors meet the constraints posed by data on dominance periods, but these are not very stringent. We extensively studied contrast dependence of dominance and transition durations and that of the occurrence of return transitions: Occasions when an eye loses and regains dominance without intervening dominance of the other eye. We found that dominance durations and the incidence of return transitions depend similarly on contrast; transition durations show a different dependence. Regarding dominance durations, we show that the widely accepted rule known as Levelt's second proposition is only valid in a limited contrast range; outside this range, the opposite of the proposition is true. Our data refute current models, based solely on adaptation and inhibition, as these cannot explain the long and reversible transitions that we find. These features indicate that noise is a crucial force in rivalry, frequently dominating the deterministic forces.

Adaptation, Physiological↗

PubMed2001

An approach to the complexity of the brain.

The establishment of ordered neuronal connections is supposed to take place under the control of specific cell adhesion molecules (CAM) which guide neuroblasts and axons to their appropriate destination. The extreme complexity of the nervous system does not provide a favorable medium for the development of deterministic connections. Simon's [112] theorems offer a mean to approach the high level of complexity of the nervous system. The basic tenet is that complex systems are hierarchically organized and decomposable. Such systems can arise by selective trial and error mechanisms. Subsystems in complex systems only interact in an aggregate manner, and no significant information is lost if the detail of aggregate interactions is ignored. A number of nervous activities, which qualify for these requirements, are shown. The following sources of selection are considered: internal and external feedbacks, previous experience, plasticity in simple structures, and the characteristic geometry of dendrites. The role played by CAMs and other membrane-associated molecules is discussed in the sense that they are either inductor molecules that turn on different homeobox genes, or downstream products of genes, or both. These molecules control cellular and tissular differentiation in the developing brain creating sources of selection required for the trial and error process in the organization of the nervous tissue.

Animals↗

PubMed1999

A new structurally dissolvable self-reproducing loop evolving in a simple cellular automata space.

We constructed a simple evolutionary system, "evoloop," on a deterministic nine-state five-neighbor cellular automata (CA) space by improving the structurally dissolvable self-reproducing loop we had previously contrived [14] after Langton's self-reproducing loop [7]. The principal role of this improvement is to enhance the adaptability (a degree of the variety of situations in which structures in the CA space can operate regularly) of the self-reproductive mechanism of loops. The experiment with evoloop met with the intriguing result that, though no mechanism was explicitly provided to promote evolution, the loops varied through direct interaction of their phenotypes, smaller individuals were naturally selected thanks to their quicker self-reproductive ability, and the whole population gradually evolved toward the smallest ones. This result gives a unique example of evolution of self-replicators where genotypical variation is caused by precedent phenotypical variation. Such interrelation of genotype and phenotype would be one of the important factors driving the evolutionary process of primitive life forms that might have actually occurred in ancient times.

Artificial Intelligence↗

PubMed2000

Horizontal versus vertical transmission of parasites in a stochastic spatial model.

A number of pathogens may be transmitted from parent to child at or before birth (vertically) or from one individual to another by contact (horizontally). A natural deterministic and non-spatial model, introduced by Lipsitch et al. [Proc. Roy. Soc. London Ser. B 260 (1995) 3211 shows that an epidemic is possible if the vertical transmission or the horizontal transmission is high enough. In contrast, we introduce a stochastic spatial model that shows that, on a particular graph, if the vertical transmission is not high enough, then the infected individuals disappear even for very high horizontal transmission. This illustrates the fact that introducing space may greatly change the qualitative behavior of a model.

Disease Transmission, Infectious↗

PubMedDate not supplied

Deterministic and stochastic models for the seasonal variability of measles transmission.

Fine and Clarkson used a discrete-time epidemic model with variable transmission parameter to analyze measles data for England and Wales for 1950-1965, during the time of biennial epidemics. Their model seems to provide a convincing fit when its parameters are estimated from these data. In particular, they obtained nearly equal estimates for the variable transmission parameter from the widely different data for epidemic and nonepidemic years. They did not, however, study the dynamics of their model. In this paper we make such a study, and find that the model is unsatisfactory in some important respects. It has a unique equilibrium (to be exact, a solution showing only seasonal variation), and neutrally stable oscillations around this equilibrium are possible, but with period approximately 3 years, not 2. (The model also has an exact 3-year cycle, while for intermediate initial values it shows unstable "chaotic" behavior.) If we vary the amount of variation in the transmission parameter, from no variation to 2.5 times the observed amount, the main periodicity remains approximately 3 years, though the complexity of behavior changes, increasing as the amount of variation increases. A continuous-time version of the model also has an equilibrium and a 3-year cycle, the main difference being that these are stable rather than neutrally stable. A stochastic version shows that simulations starting close to either the equilibrium or the 3-year cycle have a high probability of remaining close to the corresponding deterministic solutions for at least 20-30 years. The oscillatory features of the model are thus reasonably robust against stochastic fluctuations. We conclude that the simple homogeneous mixing model cannot be adapted to provide an adequate fit to the data, especially in explaining the observed biennial cycles. It seems likely that the pattern of seasonal variation found by Fine and Clarkson is essentially correct, but for accurate modeling of measles we need also to take into account heterogeneities of mixing in the population, especially those due to age and space.

Age Factors↗