Regional synchrony in full-scale activated sludge bioreactors due to deterministic microbial community assembly

PubMed Central

Griffin, James S; Wells, George F

2017-01-01

Seasonal community structure and regionally synchronous population dynamics have been observed in natural microbial ecosystems, but have not been well documented in wastewater treatment bioreactors. Few studies of community dynamics in full-scale activated sludge systems facing similar meteorological conditions have been done to compare the importance of deterministic and neutral community assembly mechanisms. We subjected weekly activated sludge samples from six regional full-scale bioreactors at four wastewater treatment plants obtained over 1 year to Illumina sequencing of 16S ribosomal RNA genes, resulting in a library of over 17 million sequences. All samples derived from reactors treating primarily municipal wastewater. Despite variation in operational characteristics and location, communities displayed temporal synchrony at the individual operational taxonomic unit (OTU), broad phylogenetic affiliation and community-wide scale. Bioreactor communities were dominated by 134 abundant and highly regionally synchronized OTU populations that accounted for over 50% of the total reads. Non-core OTUs displayed abundance-dependent population synchrony. Alpha diversity varied by reactor, but showed a highly reproducible and synchronous seasonal fluctuation. Community similarity was dominated by seasonal changes, but individual reactors maintained minor stable differences after 1 year. Finally, the impacts of mass migration driven by direct biomass transfers between reactors was investigated, but had no significant effect on community similarity or diversity in the sink community. Our results show that population dynamics in activated sludge bioreactors are consistent with niche-driven assembly guided by seasonal temperature fluctuations. PMID:27996980

Hybrid deterministic/stochastic simulation of complex biochemical systems.

PubMed

Lecca, Paola; Bagagiolo, Fabio; Scarpa, Marina

2017-11-21

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose, computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the time elapsing between data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due to the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We introduce a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, the MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between the stochastic model and the deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as a stochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagents' abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and that of the software tool.

Scale-invariance underlying the logistic equation and its social applications

NASA Astrophysics Data System (ADS)

Hernando, A.; Plastino, A.

2013-01-01

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series

NASA Astrophysics Data System (ADS)

Sugihara, George; May, Robert M.

1990-04-01

An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Synchronisation of chaos and its applications

NASA Astrophysics Data System (ADS)

Eroglu, Deniz; Lamb, Jeroen S. W.; Pereira, Tiago

2017-07-01

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order. We survey the main theory behind complete, generalised and phase synchronisation phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.

Antibiotic-induced population fluctuations and stochastic clearance of bacteria

PubMed Central

Le, Dai; Şimşek, Emrah; Chaudhry, Waqas

2018-01-01

Effective antibiotic use that minimizes treatment failures remains a challenge. A better understanding of how bacterial populations respond to antibiotics is necessary. Previous studies of large bacterial populations established the deterministic framework of pharmacodynamics. Here, characterizing the dynamics of population extinction, we demonstrated the stochastic nature of eradicating bacteria with antibiotics. Antibiotics known to kill bacteria (bactericidal) induced population fluctuations. Thus, at high antibiotic concentrations, the dynamics of bacterial clearance were heterogeneous. At low concentrations, clearance still occurred with a non-zero probability. These striking outcomes of population fluctuations were well captured by our probabilistic model. Our model further suggested a strategy to facilitate eradication by increasing extinction probability. We experimentally tested this prediction for antibiotic-susceptible and clinically-isolated resistant bacteria. This new knowledge exposes fundamental limits in our ability to predict bacterial eradication. Additionally, it demonstrates the potential of using antibiotic concentrations that were previously deemed inefficacious to eradicate bacteria. PMID:29508699

Phenotypic switching of populations of cells in a stochastic environment

NASA Astrophysics Data System (ADS)

Hufton, Peter G.; Lin, Yen Ting; Galla, Tobias

2018-02-01

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise-deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.

Evidence for deterministic chaos in aperiodic oscillations of acute lymphoblastic leukemia cells in long-term culture

NASA Astrophysics Data System (ADS)

Lambrou, George I.; Chatziioannou, Aristotelis; Vlahopoulos, Spiros; Moschovi, Maria; Chrousos, George P.

Biological systems are dynamic and possess properties that depend on two key elements: initial conditions and the response of the system over time. Conceptualizing this on tumor models will influence conclusions drawn with regard to disease initiation and progression. Alterations in initial conditions dynamically reshape the properties of proliferating tumor cells. The present work aims to test the hypothesis of Wolfrom et al., that proliferation shows evidence for deterministic chaos in a manner such that subtle differences in the initial conditions give rise to non-linear response behavior of the system. Their hypothesis, tested on adherent Fao rat hepatoma cells, provides evidence that these cells manifest aperiodic oscillations in their proliferation rate. We have tested this hypothesis with some modifications to the proposed experimental setup. We have used the acute lymphoblastic leukemia cell line CCRF-CEM, as it provides an excellent substrate for modeling proliferation dynamics. Measurements were taken at time points varying from 24h to 48h, extending the assayed populations beyond that of previous published reports that dealt with the complex dynamic behavior of animal cell populations. We conducted flow cytometry studies to examine the apoptotic and necrotic rate of the system, as well as DNA content changes of the cells over time. The cells exhibited a proliferation rate of nonlinear nature, as this rate presented oscillatory behavior. The obtained data have been fit in known models of growth, such as logistic and Gompertzian growth.

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stich, Michael; Ribó, Josep M.; Blackmond, Donna G., E-mail: blackmond@scripps.edu

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the autocatalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reversemore » reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.« less

Changing contributions of stochastic and deterministic processes in community assembly over a successional gradient.

PubMed

Måren, Inger Elisabeth; Kapfer, Jutta; Aarrestad, Per Arild; Grytnes, John-Arvid; Vandvik, Vigdis

2018-01-01

Successional dynamics in plant community assembly may result from both deterministic and stochastic ecological processes. The relative importance of different ecological processes is expected to vary over the successional sequence, between different plant functional groups, and with the disturbance levels and land-use management regimes of the successional systems. We evaluate the relative importance of stochastic and deterministic processes in bryophyte and vascular plant community assembly after fire in grazed and ungrazed anthropogenic coastal heathlands in Northern Europe. A replicated series of post-fire successions (n = 12) were initiated under grazed and ungrazed conditions, and vegetation data were recorded in permanent plots over 13 years. We used redundancy analysis (RDA) to test for deterministic successional patterns in species composition repeated across the replicate successional series and analyses of co-occurrence to evaluate to what extent species respond synchronously along the successional gradient. Change in species co-occurrences over succession indicates stochastic successional dynamics at the species level (i.e., species equivalence), whereas constancy in co-occurrence indicates deterministic dynamics (successional niche differentiation). The RDA shows high and deterministic vascular plant community compositional change, especially early in succession. Co-occurrence analyses indicate stochastic species-level dynamics the first two years, which then give way to more deterministic replacements. Grazed and ungrazed successions are similar, but the early stage stochasticity is higher in ungrazed areas. Bryophyte communities in ungrazed successions resemble vascular plant communities. In contrast, bryophytes in grazed successions showed consistently high stochasticity and low determinism in both community composition and species co-occurrence. In conclusion, stochastic and individualistic species responses early in succession give way to more niche-driven dynamics in later successional stages. Grazing reduces predictability in both successional trends and species-level dynamics, especially in plant functional groups that are not well adapted to disturbance. © 2017 The Authors. Ecology, published by Wiley Periodicals, Inc., on behalf of the Ecological Society of America.

Numerical modeling of the transmission dynamics of drug-sensitive and drug-resistant HSV-2

NASA Astrophysics Data System (ADS)

Gumel, A. B.

2001-03-01

A competitive finite-difference method will be constructed and used to solve a modified deterministic model for the spread of herpes simplex virus type-2 (HSV-2) within a given population. The model monitors the transmission dynamics and control of drug-sensitive and drug-resistant HSV-2. Unlike the fourth-order Runge-Kutta method (RK4), which fails when the discretization parameters exceed certain values, the novel numerical method to be developed in this paper gives convergent results for all parameter values.

A Simple Mechanism for Cooperation in the Well-Mixed Prisoner's Dilemma Game

NASA Astrophysics Data System (ADS)

Perc, Matjaž

2008-11-01

I show that the addition of Gaussian noise to the payoffs is able to stabilize cooperation in well-mixed populations, where individuals play the prisoner's dilemma game. The impact of stochasticity on the evolutionary dynamics can be expressed deterministically via a simple small-noise expansion of multiplicative noisy terms. In particular, cooperation emerges as a stable noise-induced steady state in the replicator dynamics. Due to the generality of the employed theoretical framework, presented results should prove valuable in various scientific disciplines, ranging from economy to ecology.

Stochastic evolution in populations of ideas

PubMed Central

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games. PMID:28098244

Stochastic evolution in populations of ideas

NASA Astrophysics Data System (ADS)

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.

Spectral analysis of a two-species competition model: Determining the effects of extreme conditions on the color of noise generated from simulated time series

NASA Astrophysics Data System (ADS)

Golinski, M. R.

2006-07-01

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since natural populations do not live in isolation, the present paper simulates a discrete-time two-species competition model with environmental noise to determine the type of colored population noise generated by extreme conditions in the long-term population dynamics of competing populations. Discrete Fourier analysis is applied to the simulation results and the calculated Hurst exponent ( H) is used to determine how the color of population noise for the two species corresponds to extreme conditions in population dynamics. To interpret the biological meaning of the color of noise generated by the two-species model, the paper determines the color of noise generated by three reference models: (1) A two-dimensional discrete-time white noise model (0⩽ H<1/2); (2) A two-dimensional fractional Brownian motion model (H=1/2); and (3) A two-dimensional discrete-time model with noise for unbounded growth of two uncoupled species (1/2< H⩽1).

Bridging the Timescales of Single-Cell and Population Dynamics

NASA Astrophysics Data System (ADS)

Jafarpour, Farshid; Wright, Charles S.; Gudjonson, Herman; Riebling, Jedidiah; Dawson, Emma; Lo, Klevin; Fiebig, Aretha; Crosson, Sean; Dinner, Aaron R.; Iyer-Biswas, Srividya

2018-04-01

How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a data-validated theoretical framework that accounts for observables at both single-cell and population scales. We derive exact analytical complete time-dependent solutions to cell-age distributions and population growth rates as functionals of the underlying interdivision time distributions, for symmetric and asymmetric cell division. These results provide insights into the surprising implications of stochastic single-cell dynamics for population growth. Using our results for asymmetric division, we deduce the time to transition from the reproductively quiescent (swarmer) to the replication-competent (stalked) stage of the Caulobacter crescentus life cycle. Remarkably, population numbers can spontaneously oscillate with time. We elucidate the physics leading to these population oscillations. For C. crescentus cells, we show that a simple measurement of the population growth rate, for a given growth condition, is sufficient to characterize the condition-specific cellular unit of time and, thus, yields the mean (single-cell) growth and division timescales, fluctuations in cell division times, the cell-age distribution, and the quiescence timescale.

A kinetic theory for age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Chou, Tom; Greenman, Chris

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

NASA Astrophysics Data System (ADS)

Constable, George W. A.; McKane, Alan J.

2018-07-01

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

NASA Astrophysics Data System (ADS)

Constable, George W. A.; McKane, Alan J.

2017-11-01

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.

Reactive strategies in indirect reciprocity.

PubMed

Ohtsuki, Hisashi

2004-04-07

Evolution of reactive strategy of indirect reciprocity is discussed, where individuals interact with others through the one-shot Prisoner's Dilemma game, changing their partners in every round. We investigate all of the reactive strategies that are stochastic, including deterministic ones as special cases. First we study adaptive dynamics of reactive strategies by assuming monomorphic population. Results are very similar to the corresponding evolutionary dynamics of direct reciprocity. The discriminating strategy, which prescribes cooperation only with those who cooperated in the previous round, cannot be an outcome of the evolution. Next we examine the case where the population includes a diversity of strategies. We find that only the mean 'discriminatoriness' in the population is the parameter that affects the evolutionary dynamics. The discriminating strategy works as a promoter of cooperation there. However, it is again not the end point of the evolution. This is because retaliatory defection, which was prescribed by the discriminating strategy, is regarded as another defection toward the society. These results caution that we have to reconsider the role of retaliatory defection much more carefully.

Spread of a disease and its effect on population dynamics in an eco-epidemiological system

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Roy, Parimita

2014-12-01

In this paper, an eco-epidemiological model with simple law of mass action and modified Holling type II functional response has been proposed and analyzed to understand how a disease may spread among natural populations. The proposed model is a modification of the model presented by Upadhyay et al. (2008) [1]. Existence of the equilibria and their stability analysis (linear and nonlinear) has been studied. The dynamical transitions in the model have been studied by identifying the existence of backward Hopf-bifurcations and demonstrated the period-doubling route to chaos when the death rate of predator (μ1) and the growth rate of susceptible prey population (r) are treated as bifurcation parameters. Our studies show that the system exhibits deterministic chaos when some control parameters attain their critical values. Chaotic dynamics is depicted using the 2D parameter scans and bifurcation analysis. Possible implications of the results for disease eradication or its control are discussed.

Extinction in neutrally stable stochastic Lotka-Volterra models

NASA Astrophysics Data System (ADS)

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Extinction in neutrally stable stochastic Lotka-Volterra models.

PubMed

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1992-01-01

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes.

PubMed

Sardanyés, Josep; Arderiu, Andreu; Elena, Santiago F; Alarcón, Tomás

2018-05-01

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called 'stamping machine replication' (SMR) and 'geometric replication' (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication. © 2018 The Author(s).

Quantitative investigations of the epidemiology of phocine distemper virus (PDV) in European common seal populations.

PubMed

Grenfell, B T; Lonergan, M E; Harwood, J

1992-04-20

This paper uses simple mathematical models to examine the long-term dynamic consequences of the 1988 epizootic of phocine distemper virus (PDV) infection in Northern European common seal populations. In a preliminary analysis of single outbreaks of infection deterministic compartmental models are used to estimate feasible ranges for the transmission rate of the infection and the level of disease-induced mortality. These results also indicate that the level of transmission in 1988 was probably sufficient to eradicate the infection throughout the Northern European common seal populations by the end of the first outbreak. An analysis of longer-term infection dynamics, which takes account of the density-dependent recovery of seal population levels, corroborates this finding. It also indicates that a reintroduction of the virus would be unlikely to cause an outbreak on the scale of the 1988 epizootic until the seal population had recovered for at least 10 years. The general ecological implications of these results are discussed.

Hierarchical spatiotemporal matrix models for characterizing invasions

USGS Publications Warehouse

Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew

2007-01-01

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.

Hierarchical spatiotemporal matrix models for characterizing invasions

USGS Publications Warehouse

Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew

2007-01-01

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing. ?? 2006, The International Biometric Society.

Complex Population Dynamics and the Coalescent Under Neutrality

PubMed Central

Volz, Erik M.

2012-01-01

Estimates of the coalescent effective population size Ne can be poorly correlated with the true population size. The relationship between Ne and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of Ne such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics. PMID:22042576

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Modelling the effect of an alternative host population on the spread of citrus Huanglongbing

NASA Astrophysics Data System (ADS)

d'A. Vilamiu, Raphael G.; Ternes, Sonia; Laranjeira, Francisco F.; de C. Santos, Tâmara T.

2013-10-01

The objective of this work was to model the spread of citrus Huanglongbing (HLB) considering the presence of a population of alternative hosts (Murraya paniculata). We developed a compartmental deterministic mathematical model for representing the dynamics of HLB disease in a citrus orchard, including delays in the latency and incubation phases of the disease in the plants and a delay period on the nymphal stage of Diaphorina citri, the insect vector of HLB in Brazil. The results of numerical simulations indicate that alternative hosts should not play a crucial role on HLB dynamics considering a typical scenario for the Recôncavo Baiano region in Brazil . Also, the current policy of removing symptomatic plants every three months should not be expected to significantly hinder HLB spread.

A Mathematical Model for Alternation of Polygamy and Parthenogenesis: Stability Versus Efficiency and Analogy with Parasitism.

PubMed

Sanchez-Palencia, Evariste; Lherminier, Philippe; Françoise, Jean-Pierre

2016-12-01

The present work is a contribution to the understanding of the sempiternal problem of the "burden of factor two" implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually born males. This instability implies evolution of the system towards an attractor involving both (sexual and asexual) populations (which does not imply optimality of the population). We also exhibit the analogy with a parasite/host system.

Evolutionary suicide through a non-catastrophic bifurcation: adaptive dynamics of pathogens with frequency-dependent transmission.

PubMed

Boldin, Barbara; Kisdi, Éva

2016-03-01

Evolutionary suicide is a riveting phenomenon in which adaptive evolution drives a viable population to extinction. Gyllenberg and Parvinen (Bull Math Biol 63(5):981-993, 2001) showed that, in a wide class of deterministic population models, a discontinuous transition to extinction is a necessary condition for evolutionary suicide. An implicit assumption of their proof is that the invasion fitness of a rare strategy is well-defined also in the extinction state of the population. Epidemic models with frequency-dependent incidence, which are often used to model the spread of sexually transmitted infections or the dynamics of infectious diseases within herds, violate this assumption. In these models, evolutionary suicide can occur through a non-catastrophic bifurcation whereby pathogen adaptation leads to a continuous decline of host (and consequently pathogen) population size to zero. Evolutionary suicide of pathogens with frequency-dependent transmission can occur in two ways, with pathogen strains evolving either higher or lower virulence.

Methods For Self-Organizing Software

DOEpatents

Bouchard, Ann M.; Osbourn, Gordon C.

2005-10-18

A method for dynamically self-assembling and executing software is provided, containing machines that self-assemble execution sequences and data structures. In addition to ordered functions calls (found commonly in other software methods), mutual selective bonding between bonding sites of machines actuates one or more of the bonding machines. Two or more machines can be virtually isolated by a construct, called an encapsulant, containing a population of machines and potentially other encapsulants that can only bond with each other. A hierarchical software structure can be created using nested encapsulants. Multi-threading is implemented by populations of machines in different encapsulants that are interacting concurrently. Machines and encapsulants can move in and out of other encapsulants, thereby changing the functionality. Bonding between machines' sites can be deterministic or stochastic with bonding triggering a sequence of actions that can be implemented by each machine. A self-assembled execution sequence occurs as a sequence of stochastic binding between machines followed by their deterministic actuation. It is the sequence of bonding of machines that determines the execution sequence, so that the sequence of instructions need not be contiguous in memory.

Non-Deterministic Dynamic Instability of Composite Shells

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2004-01-01

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics, and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties, in that order.

Stochasticity and determinism in models of hematopoiesis.

PubMed

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Hidden order in crackling noise during peeling of an adhesive tape.

PubMed

Kumar, Jagadish; Ciccotti, M; Ananthakrishna, G

2008-04-01

We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive Lyapunov exponent in a midrange of traction velocities. The results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick-slip dynamics.

Hpm of Estrogen Model on the Dynamics of Breast Cancer

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Balamuralitharan, S.; Sundaresan, T.

2018-04-01

We enhance a deterministic mathematical model involving universal dynamics on breast cancer with immune response. This is population model so includes Normal cells class, Tumor cells, Immune cells and Estrogen. The eects regarding Estrogen are below incorporated in the model. The effects show to that amount the arrival of greater Estrogen increases the danger over growing breast cancer. Furthermore, approximate solution regarding nonlinear differential equations is arrived by Homotopy Perturbation Method (HPM). Hes HPM is good and correct technique after solve nonlinear differential equation directly. Approximate solution learnt with the support of that method is suitable same as like the actual results in accordance with this models.

A model for a spatially structured metapopulation accounting for within patch dynamics.

PubMed

Smith, Andrew G; McVinish, Ross; Pollett, Philip K

2014-01-01

We develop a stochastic metapopulation model that accounts for spatial structure as well as within patch dynamics. Using a deterministic approximation derived from a functional law of large numbers, we develop conditions for extinction and persistence of the metapopulation in terms of the birth, death and migration parameters. Interestingly, we observe the Allee effect in a metapopulation comprising two patches of greatly different sizes, despite there being decreasing patch specific per-capita birth rates. We show that the Allee effect is due to the way the migration rates depend on the population density of the patches. Copyright © 2013 Elsevier Inc. All rights reserved.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Effects of Lead Exposure, Environmental Conditions, and Metapopulation Processes on Population Dynamics of Spectacled Eiders.

USGS Publications Warehouse

Flint, Paul L.; Grand, James B.; Petersen, Margaret; Rockwell, Robert F.

2016-01-01

Spectacled eider Somateria fischeri numbers have declined and they are considered threatened in accordance with the US Endangered Species Act throughout their range. We synthesized the available information for spectacled eiders to construct deterministic, stochastic, and metapopulation models for this species that incorporated current estimates of vital rates such as nest success, adult survival, and the impact of lead poisoning on survival. Elasticities of our deterministic models suggested that the populations would respond most dramatically to changes in adult female survival and that the reductions in adult female survival related to lead poisoning were locally important. We also examined the sensitivity of the population to changes in lead exposure rates. With the knowledge that some vital rates vary with environmental conditions, we cast stochastic models that mimicked observed variation in productivity. We also used the stochastic model to examine the probability that a specific population will persist for periods of up to 50 y. Elasticity analysis of these models was consistent with that for the deterministic models, with perturbations to adult female survival having the greatest effect on population projections. When used in single population models, demographic data for some localities predicted rapid declines that were inconsistent with our observations in the field. Thus, we constructed a metapopulation model and examined the predictions for local subpopulations and the metapopulation over a wide range of dispersal rates. Using the metapopulation model, we were able to simulate the observed stability of local subpopulations as well as that of the metapopulation. Finally, we developed a global metapopulation model that simulates periodic winter habitat limitation, similar to that which might be experienced in years of heavy sea ice in the core wintering area of spectacled eiders in the central Bering Sea. Our metapopulation analyses suggested that no subpopulation is independent and that future management actions may be improved through a metapopulation framework. For example, management actions could include displacement of breeding females from"sink" areas that reduce the growth potential of the population as a whole. However, this action is contingent upon dispersal among local populations, for which there is limited information. Thus, we recommend that researchers examine dispersal behavior among areas on the Yukon-Kuskokwim Delta in western Alaska. The metapopulation framework could also be applied at the rangewide scale to address the density-dependent limitation of available polynya habitat during winter that may limit the recovery of small subpopulations, such as that on the Yukon-Kuskokwim Delta. Reductions in other subpopulations may be necessary to ensure an increase in the Yukon-Kuskokwim Delta population. Thus, we recommend that managers consider the interpopulation dynamics of spectacled eiders at different spatial scales in future management actions.

Dynamical signatures of isometric force control as a function of age, expertise, and task constraints.

PubMed

Vieluf, Solveig; Sleimen-Malkoun, Rita; Voelcker-Rehage, Claudia; Jirsa, Viktor; Reuter, Eva-Maria; Godde, Ben; Temprado, Jean-Jacques; Huys, Raoul

2017-07-01

From the conceptual and methodological framework of the dynamical systems approach, force control results from complex interactions of various subsystems yielding observable behavioral fluctuations, which comprise both deterministic (predictable) and stochastic (noise-like) dynamical components. Here, we investigated these components contributing to the observed variability in force control in groups of participants differing in age and expertise level. To this aim, young (18-25 yr) as well as late middle-aged (55-65 yr) novices and experts (precision mechanics) performed a force maintenance and a force modulation task. Results showed that whereas the amplitude of force variability did not differ across groups in the maintenance tasks, in the modulation task it was higher for late middle-aged novices than for experts and higher for both these groups than for young participants. Within both tasks and for all groups, stochastic fluctuations were lowest where the deterministic influence was smallest. However, although all groups showed similar dynamics underlying force control in the maintenance task, a group effect was found for deterministic and stochastic fluctuations in the modulation task. The latter findings imply that both components were involved in the observed group differences in the variability of force fluctuations in the modulation task. These findings suggest that between groups the general characteristics of the dynamics do not differ in either task and that force control is more affected by age than by expertise. However, expertise seems to counteract some of the age effects. NEW & NOTEWORTHY Stochastic and deterministic dynamical components contribute to force production. Dynamical signatures differ between force maintenance and cyclic force modulation tasks but hardly between age and expertise groups. Differences in both stochastic and deterministic components are associated with group differences in behavioral variability, and observed behavioral variability is more strongly task dependent than person dependent. Copyright © 2017 the American Physiological Society.

Demographic noise can reverse the direction of deterministic selection

PubMed Central

Constable, George W. A.; Rogers, Tim; McKane, Alan J.; Tarnita, Corina E.

2016-01-01

Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviors will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when demographic stochasticity is accounted for, selection can in fact act in the reverse direction to that predicted deterministically, instead favoring cooperative behaviors that appreciably increase the carrying capacity of the population. Populations that exist in larger numbers experience a selective advantage by being more stochastically robust to invasions than smaller populations, and this advantage can persist even in the presence of reproductive costs. We investigate this general effect in the specific context of public goods production and find conditions for stochastic selection reversal leading to the success of public good producers. This insight, developed here analytically, is missed by the deterministic analysis as well as by standard game theoretic models that enforce a fixed population size. The effect is found to be amplified by space; in this scenario we find that selection reversal occurs within biologically reasonable parameter regimes for microbial populations. Beyond the public good problem, we formulate a general mathematical framework for models that may exhibit stochastic selection reversal. In this context, we describe a stochastic analog to r−K theory, by which small populations can evolve to higher densities in the absence of disturbance. PMID:27450085

Modeling seasonal measles transmission in China

NASA Astrophysics Data System (ADS)

Bai, Zhenguo; Liu, Dan

2015-08-01

A discrete-time deterministic measles model with periodic transmission rate is formulated and studied. The basic reproduction number R0 is defined and used as the threshold parameter in determining the dynamics of the model. It is shown that the disease will die out if R0 < 1 , and the disease will persist in the population if R0 > 1 . Parameters in the model are estimated on the basis of demographic and epidemiological data. Numerical simulations are presented to describe the seasonal fluctuation of measles infection in China.

Stochastic oscillations in models of epidemics on a network of cities

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.; McKane, A. J.

2011-11-01

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of n cities. In the model a fraction fjk of individuals from city k commute to city j, where they may infect, or be infected by, others. Starting from a continuous-time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: A unique nontrivial fixed point always exists and has the feature that the fraction of susceptible, infected, and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent

USGS Publications Warehouse

Leirs, H.; Stenseth, N.C.; Nichols, J.D.; Hines, J.E.; Verhagen, R.; Verheyen, W.

1997-01-01

Ecology has long been troubled by the controversy over how populations are regulated. Some ecologists focus on the role of environmental effects, whereas others argue that density-dependent feedback mechanisms are central. The relative importance of both processes is still hotly debated, but clear examples of both processes acting in the same population are rare. Keyfactor analysis (regression of population changes on possible causal factors) and time-series analysis are often used to investigate the presence of density dependence, but such approaches may be biased and provide no information on actual demographic rates. Here we report on both density-dependent and density-independent effects in a murid rodent pest species, the multimammate rat Mastomys natalensis (Smith, 1834), using statistical capture-recapture models. Both effects occur simultaneously, but we also demonstrate that they do not affect all demographic rates in the same way. We have incorporated the obtained estimates of demographic rates in a population dynamics model and show that the observed dynamics are affected by stabilizing nonlinear density-dependent components coupled with strong deterministic and stochastic seasonal components.

Deterministic generation of multiparticle entanglement by quantum Zeno dynamics.

PubMed

Barontini, Giovanni; Hohmann, Leander; Haas, Florian; Estève, Jérôme; Reichel, Jakob

2015-09-18

Multiparticle entangled quantum states, a key resource in quantum-enhanced metrology and computing, are usually generated by coherent operations exclusively. However, unusual forms of quantum dynamics can be obtained when environment coupling is used as part of the state generation. In this work, we used quantum Zeno dynamics (QZD), based on nondestructive measurement with an optical microcavity, to deterministically generate different multiparticle entangled states in an ensemble of 36 qubit atoms in less than 5 microseconds. We characterized the resulting states by performing quantum tomography, yielding a time-resolved account of the entanglement generation. In addition, we studied the dependence of quantum states on measurement strength and quantified the depth of entanglement. Our results show that QZD is a versatile tool for fast and deterministic entanglement generation in quantum engineering applications. Copyright © 2015, American Association for the Advancement of Science.

Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects

NASA Technical Reports Server (NTRS)

Sachs, Rainer K.; Shuryak, Igor; Brenner, David; Fakir, Hatim; Hahnfeldt, Philip

2007-01-01

When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend treatment gaps during radiotherapy, apart from decreasing the probability of eradicating the primary cancer, substantially increase the risk of later second cancers.

Influence of body condition on the population dynamics of Atlantic salmon with consideration of the potential impact of sea lice.

PubMed

Susdorf, R; Salama, N K G; Lusseau, D

2017-11-21

Atlantic salmon Salmo salar is an iconic species of high conservation and economic importance. At sea, individuals typically are subject to sea lice infestation, which can have detrimental effects on their host. Over recent decades, the body condition and marine survival in NE Atlantic stocks have generally decreased, reflected in fewer adults returning to rivers, which is partly attributable to sea lice. We developed a deterministic stage-structured population model to assess condition-mediated population dynamics resulting in changing fecundity, age at sexual maturation and marine survival rate. The model is parameterized using data from the North Esk system, north-east Scotland. Both constant and density-dependent juvenile survival rates are considered. We show that even small sea lice-mediated changes in mean body condition of MSW can cause substantial population declines, whereas 1SW condition is less influential. Density dependence alleviates the condition-mediated population effect. The resilience of the population to demographic perturbations declines as adult condition is reduced. Indirect demographic changes in salmonid life-history traits (e.g., body condition) are often considered unimportant for population trajectory. The model shows that Atlantic salmon population dynamics can be highly responsive to sea lice-mediated effects on adult body condition, thus highlighting the importance of non-lethal parasitic long-term effects. © 2017 The Authors Journal of Fish Diseases Published by John Wiley & Sons Ltd.

Modeling the within-host dynamics of cholera: bacterial-viral interaction.

PubMed

Wang, Xueying; Wang, Jin

2017-08-01

Novel deterministic and stochastic models are proposed in this paper for the within-host dynamics of cholera, with a focus on the bacterial-viral interaction. The deterministic model is a system of differential equations describing the interaction among the two types of vibrios and the viruses. The stochastic model is a system of Markov jump processes that is derived based on the dynamics of the deterministic model. The multitype branching process approximation is applied to estimate the extinction probability of bacteria and viruses within a human host during the early stage of the bacterial-viral infection. Accordingly, a closed-form expression is derived for the disease extinction probability, and analytic estimates are validated with numerical simulations. The local and global dynamics of the bacterial-viral interaction are analysed using the deterministic model, and the result indicates that there is a sharp disease threshold characterized by the basic reproduction number [Formula: see text]: if [Formula: see text], vibrios ingested from the environment into human body will not cause cholera infection; if [Formula: see text], vibrios will grow with increased toxicity and persist within the host, leading to human cholera. In contrast, the stochastic model indicates, more realistically, that there is always a positive probability of disease extinction within the human host.

Stochastic foundations in nonlinear density-regulation growth

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Assaf, Michael; Horsthemke, Werner; Campos, Daniel

2017-08-01

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

Stochastic dynamics and logistic population growth

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Assaf, Michael; Campos, Daniel; Horsthemke, Werner

2015-06-01

The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic parameters. In addition, we derive the conditions for extinction or persistence of the population by employing either the momentum-space spectral theory or the real-space Wentzel-Kramers-Brillouin approximation to determine the probability distribution function and the mean time to extinction of the population. Our analytical results agree well with numerical simulations.

Early signatures of regime shifts in gene expression dynamics

NASA Astrophysics Data System (ADS)

Pal, Mainak; Pal, Amit Kumar; Ghosh, Sayantari; Bose, Indrani

2013-06-01

Recently, a large number of studies have been carried out on the early signatures of sudden regime shifts in systems as diverse as ecosystems, financial markets, population biology and complex diseases. The signatures of regime shifts in gene expression dynamics are less systematically investigated. In this paper, we consider sudden regime shifts in the gene expression dynamics described by a fold-bifurcation model involving bistability and hysteresis. We consider two alternative models, models 1 and 2, of competence development in the bacterial population B. subtilis and determine some early signatures of the regime shifts between competence and noncompetence. We use both deterministic and stochastic formalisms for the purpose of our study. The early signatures studied include the critical slowing down as a transition point is approached, rising variance and the lag-1 autocorrelation function, skewness and a ratio of two mean first passage times. Some of the signatures could provide the experimental basis for distinguishing between bistability and excitability as the correct mechanism for the development of competence.

Learning to generate combinatorial action sequences utilizing the initial sensitivity of deterministic dynamical systems.

PubMed

Nishimoto, Ryu; Tani, Jun

2004-09-01

This study shows how sensory-action sequences of imitating finite state machines (FSMs) can be learned by utilizing the deterministic dynamics of recurrent neural networks (RNNs). Our experiments indicated that each possible combinatorial sequence can be recalled by specifying its respective initial state value and also that fractal structures appear in this initial state mapping after the learning converges. We also observed that the sequences of mimicking FSMs are encoded utilizing the transient regions rather than the invariant sets of the evolved dynamical systems of the RNNs.

A white-box model of S-shaped and double S-shaped single-species population growth

PubMed Central

Kalmykov, Lev V.

2015-01-01

Complex systems may be mechanistically modelled by white-box modeling with using logical deterministic individual-based cellular automata. Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models). Most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka–Volterra models. In black-box models, the individual-based (mechanistic) mechanisms of population dynamics remain hidden. Here we mechanistically model the S-shaped and double S-shaped population growth of vegetatively propagated rhizomatous lawn grasses. Using purely logical deterministic individual-based cellular automata we create a white-box model. From a general physical standpoint, the vegetative propagation of plants is an analogue of excitation propagation in excitable media. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We have investigated mechanisms of the single-species population growth limited by habitat size, intraspecific competition, regeneration time and fecundity of individuals in two types of boundary conditions and at two types of fecundity. Besides that, we have compared the S-shaped and J-shaped population growth. We consider this white-box modeling approach as a method of artificial intelligence which works as automatic hyper-logical inference from the first principles of the studied subject. This approach is perspective for direct mechanistic insights into nature of any complex systems. PMID:26038717

Stochastic mixed-mode oscillations in a three-species predator-prey model

NASA Astrophysics Data System (ADS)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

Hybrid stochastic and deterministic simulations of calcium blips.

PubMed

Rüdiger, S; Shuai, J W; Huisinga, W; Nagaiah, C; Warnecke, G; Parker, I; Falcke, M

2007-09-15

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

NASA Astrophysics Data System (ADS)

Han, Jiang; Chen, Ye-Hwa; Zhao, Xiaomin; Dong, Fangfang

2018-04-01

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.

Using stochastic models to incorporate spatial and temporal variability [Exercise 14

Treesearch

Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke

2003-01-01

To this point, our analysis of population processes and viability in the western prairie fringed orchid has used only deterministic models. In this exercise, we conduct a similar analysis, using a stochastic model instead. This distinction is of great importance to population biology in general and to conservation biology in particular. In deterministic models,...

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

Epidemic spreading on adaptively weighted scale-free networks.

PubMed

Sun, Mengfeng; Zhang, Haifeng; Kang, Huiyan; Zhu, Guanghu; Fu, Xinchu

2017-04-01

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

Towards a Population Dynamics Theory for Evolutionary Computing: Learning from Biological Population Dynamics in Nature

NASA Astrophysics Data System (ADS)

Ma, Zhanshan (Sam)

In evolutionary computing (EC), population size is one of the critical parameters that a researcher has to deal with. Hence, it was no surprise that the pioneers of EC, such as De Jong (1975) and Holland (1975), had already studied the population sizing from the very beginning of EC. What is perhaps surprising is that more than three decades later, we still largely depend on the experience or ad-hoc trial-and-error approach to set the population size. For example, in a recent monograph, Eiben and Smith (2003) indicated: "In almost all EC applications, the population size is constant and does not change during the evolutionary search." Despite enormous research on this issue in recent years, we still lack a well accepted theory for population sizing. In this paper, I propose to develop a population dynamics theory forEC with the inspiration from the population dynamics theory of biological populations in nature. Essentially, the EC population is considered as a dynamic system over time (generations) and space (search space or fitness landscape), similar to the spatial and temporal dynamics of biological populations in nature. With this conceptual mapping, I propose to 'transplant' the biological population dynamics theory to EC via three steps: (i) experimentally test the feasibility—whether or not emulating natural population dynamics improves the EC performance; (ii) comparatively study the underlying mechanisms—why there are improvements, primarily via statistical modeling analysis; (iii) conduct theoretical analysis with theoretical models such as percolation theory and extended evolutionary game theory that are generally applicable to both EC and natural populations. This article is a summary of a series of studies we have performed to achieve the general goal [27][30]-[32]. In the following, I start with an extremely brief introduction on the theory and models of natural population dynamics (Sections 1 & 2). In Sections 4 to 6, I briefly discuss three categories of population dynamics models: deterministic modeling with Logistic chaos map as an example, stochastic modeling with spatial distribution patterns as an example, as well as survival analysis and extended evolutionary game theory (EEGT) modeling. Sample experiment results with Genetic algorithms (GA) are presented to demonstrate the applications of these models. The proposed EC population dynamics approach also makes survival selection largely unnecessary or much simplified since the individuals are naturally selected (controlled) by the mathematical models for EC population dynamics.

Stochastic population dynamics of a montane ground-dwelling squirrel.

PubMed

Hostetler, Jeffrey A; Kneip, Eva; Van Vuren, Dirk H; Oli, Madan K

2012-01-01

Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1) for 9 out of 18 years. The stochastic population growth rate λ(s) was 0.92, suggesting a declining population; however, the 95% CI on λ(s) included 1.0 (0.52-1.60). Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years) probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.

Stochastic Population Dynamics of a Montane Ground-Dwelling Squirrel

PubMed Central

Hostetler, Jeffrey A.; Kneip, Eva; Van Vuren, Dirk H.; Oli, Madan K.

2012-01-01

Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990–2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1) for 9 out of 18 years. The stochastic population growth rate λs was 0.92, suggesting a declining population; however, the 95% CI on λs included 1.0 (0.52–1.60). Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years) probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration. PMID:22479616

Positive dwell time algorithm with minimum equal extra material removal in deterministic optical surfacing technology.

PubMed

Li, Longxiang; Xue, Donglin; Deng, Weijie; Wang, Xu; Bai, Yang; Zhang, Feng; Zhang, Xuejun

2017-11-10

In deterministic computer-controlled optical surfacing, accurate dwell time execution by computer numeric control machines is crucial in guaranteeing a high-convergence ratio for the optical surface error. It is necessary to consider the machine dynamics limitations in the numerical dwell time algorithms. In this paper, these constraints on dwell time distribution are analyzed, and a model of the equal extra material removal is established. A positive dwell time algorithm with minimum equal extra material removal is developed. Results of simulations based on deterministic magnetorheological finishing demonstrate the necessity of considering machine dynamics performance and illustrate the validity of the proposed algorithm. Indeed, the algorithm effectively facilitates the determinacy of sub-aperture optical surfacing processes.

WKB theory of large deviations in stochastic populations

NASA Astrophysics Data System (ADS)

Assaf, Michael; Meerson, Baruch

2017-06-01

Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics—such as those determining population extinction, fixation or switching between different states—are presently in a focus of attention of statistical physicists. We review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation allows one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and multiple, but also briefly consider populations on heterogeneous networks and spatial populations. The spatial setting also allows one to study large fluctuations of the speed of biological invasions. Finally, we briefly discuss possible directions of future work.

Implementation speed of deterministic population passages compared to that of Rabi pulses

NASA Astrophysics Data System (ADS)

Chen, Jingwei; Wei, L. F.

2015-02-01

Fast Rabi π -pulse technique has been widely applied to various coherent quantum manipulations, although it requires precise designs of the pulse areas. Relaxing the precise pulse designs, various rapid adiabatic passage (RAP) approaches have been alternatively utilized to implement various population passages deterministically. However, the usual RAP protocol could not be implemented desirably fast, as the relevant adiabatic condition should be robustly satisfied during the passage. Here, we propose a modified shortcut to adiabaticity (STA) technique to accelerate significantly the desired deterministic quantum state population passages. This transitionless technique is beyond the usual rotating wave approximation (RWA) performed in the recent STA protocols, and thus can be applied to deliver various fast quantum evolutions wherein the relevant counter-rotating effects cannot be neglected. The proposal is demonstrated specifically with the driven two- and three-level systems. Numerical results show that with the present STA technique beyond the RWA the usual Stark-chirped RAPs and stimulated Raman adiabatic passages could be significantly speeded up; the deterministic population passages could be implemented as fast as the widely used fast Rabi π pulses, but are insensitive to the applied pulse areas.

Evolutionary dynamics of the traveler's dilemma and minimum-effort coordination games on complex networks.

PubMed

Iyer, Swami; Killingback, Timothy

2014-10-01

The traveler's dilemma game and the minimum-effort coordination game are social dilemmas that have received significant attention resulting from the fact that the predictions of classical game theory are inconsistent with the results found when the games are studied experimentally. Moreover, both the traveler's dilemma and the minimum-effort coordination games have potentially important applications in evolutionary biology. Interestingly, standard deterministic evolutionary game theory, as represented by the replicator dynamics in a well-mixed population, is also inadequate to account for the behavior observed in these games. Here we study the evolutionary dynamics of both these games in populations with interaction patterns described by a variety of complex network topologies. We investigate the evolutionary dynamics of these games through agent-based simulations on both model and empirical networks. In particular, we study the effects of network clustering and assortativity on the evolutionary dynamics of both games. In general, we show that the evolutionary behavior of the traveler's dilemma and minimum-effort coordination games on complex networks is in good agreement with that observed experimentally. Thus, formulating the traveler's dilemma and the minimum-effort coordination games on complex networks neatly resolves the paradoxical aspects of these games.

Evolutionary dynamics of the traveler's dilemma and minimum-effort coordination games on complex networks

NASA Astrophysics Data System (ADS)

Iyer, Swami; Killingback, Timothy

2014-10-01

The traveler's dilemma game and the minimum-effort coordination game are social dilemmas that have received significant attention resulting from the fact that the predictions of classical game theory are inconsistent with the results found when the games are studied experimentally. Moreover, both the traveler's dilemma and the minimum-effort coordination games have potentially important applications in evolutionary biology. Interestingly, standard deterministic evolutionary game theory, as represented by the replicator dynamics in a well-mixed population, is also inadequate to account for the behavior observed in these games. Here we study the evolutionary dynamics of both these games in populations with interaction patterns described by a variety of complex network topologies. We investigate the evolutionary dynamics of these games through agent-based simulations on both model and empirical networks. In particular, we study the effects of network clustering and assortativity on the evolutionary dynamics of both games. In general, we show that the evolutionary behavior of the traveler's dilemma and minimum-effort coordination games on complex networks is in good agreement with that observed experimentally. Thus, formulating the traveler's dilemma and the minimum-effort coordination games on complex networks neatly resolves the paradoxical aspects of these games.

Coevolutionary dynamics in large, but finite populations

NASA Astrophysics Data System (ADS)

Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph

2006-07-01

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.

Dynamics of the double-crested cormorant population on Lake Ontario

USGS Publications Warehouse

Blackwell, Bradley F.; Stapanian, Martin A.; Weseloh, D.V. Chip

2002-01-01

After nearly 30 years of recolonization and expansion across North America, the double-crested cormorant (Phalacrocorax auritus) occupies the role of a perceived and, in some situations, realized threat to fish stocks and other resources. However, population data necessary to plan, defend, and implement management of this species are few. Our purpose was to gain insight into the relative contribution of various population parameters to the overall rate of population growth and identify data needs critical to improving our understanding of the dynamics of double-crested cormorant populations. We demonstrated the construction of a biologically reasonable representation of cormorant population growth on Lake Ontario (1979-2000) by referencing literature values for fertility, age at first breeding, and survival. These parameters were incorporated into a deterministic stage-classified matrix model. By calculating the elasticity of matrix elements (i.e., statgspecific fertility and survival), we found that cormorant population growth on Lake Ontario was most sensitive to survival of birds about to turn age 3 and older. Finally, we demonstrated how this information could be used to evaluate management scenarios and direct future research by simulating potential environmental effects on fertility and survival, as well as a 5-year egg-oiling program. We also demonstrated that survival of older birds exerts more effective population control than changes in fertility.

A van der Waals-like Transition Between Normal and Cancerous Phases in Cell Populations Dynamics of Colorectal Cancer

NASA Astrophysics Data System (ADS)

Qiu, Kang; Wang, Li-Fang; Shen, Jian; Yousif, Alssadig A. M.; He, Peng; Shao, Dan-Dan; Zhang, Xiao-Min; Kirunda, John B.; Jia, Ya

2016-11-01

Based on a deterministic continuous model of cell populations dynamics in the colonic crypt and in colorectal cancer, we propose four combinations of feedback mechanisms in the differentiations from stem cells (SCs) to transit cells (TCs) and then to differentiated cells (DCs), the four combinations include the double linear (LL), the linear and saturating (LS), the saturating and linear (SL), and the double saturating (SS) feedbacks, respectively. The relative fluctuations of the population of SCs, TCs, and DCs around equilibrium states with four feedback mechanisms are studied by using the Langevin method. With the increasing of net growth rate of TCs, it is found that the Fano factors of TCs and DCs go to a peak in a transient phase, and then increase again to infinity in the cases of LS and SS feedbacks. The “up-down-up” characteristic on the Fano factor (like the van der Waals loop) demonstrates that there exists a transient phase between the normal and cancerous phases, our novel findings suggest that the mathematical model with LS or SS feedback might be better to elucidate the dynamics of a normal and abnormal (cancerous) phases.

Decreasing stochasticity through enhanced seasonality in measles epidemics.

PubMed

Mantilla-Beniers, N B; Bjørnstad, O N; Grenfell, B T; Rohani, P

2010-05-06

Seasonal changes in the environment are known to be important drivers of population dynamics, giving rise to sustained population cycles. However, it is often difficult to measure the strength and shape of seasonal forces affecting populations. In recent years, statistical time-series methods have been applied to the incidence records of childhood infectious diseases in an attempt to estimate seasonal variation in transmission rates, as driven by the pattern of school terms. In turn, school-term forcing was used to show how susceptible influx rates affect the interepidemic period. In this paper, we document the response of measles dynamics to distinct shifts in the parameter regime using previously unexplored records of measles mortality from the early decades of the twentieth century. We describe temporal patterns of measles epidemics using spectral analysis techniques, and point out a marked decrease in birth rates over time. Changes in host demography alone do not, however, suffice to explain epidemiological transitions. By fitting the time-series susceptible-infected-recovered model to measles mortality data, we obtain estimates of seasonal transmission in different eras, and find that seasonality increased over time. This analysis supports theoretical work linking complex population dynamics and the balance between stochastic and deterministic forces as determined by the strength of seasonality.

Human brain detects short-time nonlinear predictability in the temporal fine structure of deterministic chaotic sounds

NASA Astrophysics Data System (ADS)

Itoh, Kosuke; Nakada, Tsutomu

2013-04-01

Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.

Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

NASA Astrophysics Data System (ADS)

Choustova, Olga

2007-02-01

We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

A Model for the Epigenetic Switch Linking Inflammation to Cell Transformation: Deterministic and Stochastic Approaches

PubMed Central

Gérard, Claude; Gonze, Didier; Lemaigre, Frédéric; Novák, Béla

2014-01-01

Recently, a molecular pathway linking inflammation to cell transformation has been discovered. This molecular pathway rests on a positive inflammatory feedback loop between NF-κB, Lin28, Let-7 microRNA and IL6, which leads to an epigenetic switch allowing cell transformation. A transient activation of an inflammatory signal, mediated by the oncoprotein Src, activates NF-κB, which elicits the expression of Lin28. Lin28 decreases the expression of Let-7 microRNA, which results in higher level of IL6 than achieved directly by NF-κB. In turn, IL6 can promote NF-κB activation. Finally, IL6 also elicits the synthesis of STAT3, which is a crucial activator for cell transformation. Here, we propose a computational model to account for the dynamical behavior of this positive inflammatory feedback loop. By means of a deterministic model, we show that an irreversible bistable switch between a transformed and a non-transformed state of the cell is at the core of the dynamical behavior of the positive feedback loop linking inflammation to cell transformation. The model indicates that inhibitors (tumor suppressors) or activators (oncogenes) of this positive feedback loop regulate the occurrence of the epigenetic switch by modulating the threshold of inflammatory signal (Src) needed to promote cell transformation. Both stochastic simulations and deterministic simulations of a heterogeneous cell population suggest that random fluctuations (due to molecular noise or cell-to-cell variability) are able to trigger cell transformation. Moreover, the model predicts that oncogenes/tumor suppressors respectively decrease/increase the robustness of the non-transformed state of the cell towards random fluctuations. Finally, the model accounts for the potential effect of competing endogenous RNAs, ceRNAs, on the dynamics of the epigenetic switch. Depending on their microRNA targets, the model predicts that ceRNAs could act as oncogenes or tumor suppressors by regulating the occurrence of cell transformation. PMID:24499937

Kinetic theory of age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Ecological drivers of guanaco recruitment: variable carrying capacity and density dependence.

PubMed

Marino, Andrea; Pascual, Miguel; Baldi, Ricardo

2014-08-01

Ungulates living in predator-free reserves offer the opportunity to study the influence of food limitation on population dynamics without the potentially confounding effects of top-down regulation or livestock competition. We assessed the influence of relative forage availability and population density on guanaco recruitment in two predator-free reserves in eastern Patagonia, with contrasting scenarios of population density. We also explored the relative contribution of the observed recruitment to population growth using a deterministic linear model to test the assumption that the studied populations were closed units. The observed densities increased twice as fast as our theoretical populations, indicating that marked immigration has taken place during the recovery phase experienced by both populations, thus we rejected the closed-population assumption. Regarding the factors driving variation in recruitment, in the low- to medium-density setting, we found a positive linear relationship between recruitment and surrogates of annual primary production, whereas no density dependence was detected. In contrast, in the high-density scenario, both annual primary production and population density showed marked effects, indicating a positive relationship between recruitment and per capita food availability above a food-limitation threshold. Our results support the idea that environmental carrying capacity fluctuates in response to climatic variation, and that these fluctuations have relevant consequences for herbivore dynamics, such as amplifying density dependence in drier years. We conclude that including the coupling between environmental variability in resources and density dependence is crucial to model ungulate population dynamics; to overlook temporal changes in carrying capacity may even mask density dependence as well as other important processes.

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model

PubMed Central

Nené, Nuno R.; Dunham, Alistair S.; Illingworth, Christopher J. R.

2018-01-01

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. PMID:29500183

The role of population inertia in predicting the outcome of stage-structured biological invasions.

PubMed

Guiver, Chris; Dreiwi, Hanan; Filannino, Donna-Maria; Hodgson, Dave; Lloyd, Stephanie; Townley, Stuart

2015-07-01

Deterministic dynamic models for coupled resident and invader populations are considered with the purpose of finding quantities that are effective at predicting when the invasive population will become established asymptotically. A key feature of the models considered is the stage-structure, meaning that the populations are described by vectors of discrete developmental stage- or age-classes. The vector structure permits exotic transient behaviour-phenomena not encountered in scalar models. Analysis using a linear Lyapunov function demonstrates that for the class of population models considered, a large so-called population inertia is indicative of successful invasion. Population inertia is an indicator of transient growth or decline. Furthermore, for the class of models considered, we find that the so-called invasion exponent, an existing index used in models for invasion, is not always a reliable comparative indicator of successful invasion. We highlight these findings through numerical examples and a biological interpretation of why this might be the case is discussed. Copyright © 2015. Published by Elsevier Inc.

Moving forward in circles: challenges and opportunities in modelling population cycles.

PubMed

Barraquand, Frédéric; Louca, Stilianos; Abbott, Karen C; Cobbold, Christina A; Cordoleani, Flora; DeAngelis, Donald L; Elderd, Bret D; Fox, Jeremy W; Greenwood, Priscilla; Hilker, Frank M; Murray, Dennis L; Stieha, Christopher R; Taylor, Rachel A; Vitense, Kelsey; Wolkowicz, Gail S K; Tyson, Rebecca C

2017-08-01

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer-resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research. © 2017 John Wiley & Sons Ltd/CNRS.

Moving forward in circles: Challenges and opportunities in modeling population cycles

USGS Publications Warehouse

Barraquand, Frederic; Louca, Stilianos; Abbott, Karen C; Cobbold, Christina A; Cordoleani, Flora; DeAngelis, Donald L.; Elderd, Bret D; Fox, Jeremy W; Greenwood, Priscilla; Hilker, Frank M; Murray, Dennis; Stieha, Christopher R; Taylor, Rachel A; Vitense, Kelsey; Wolkowicz, Gail; Tyson, Rebecca C

2017-01-01

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.

Stochastic simulations on a model of circadian rhythm generation.

PubMed

Miura, Shigehiro; Shimokawa, Tetsuya; Nomura, Taishin

2008-01-01

Biological phenomena are often modeled by differential equations, where states of a model system are described by continuous real values. When we consider concentrations of molecules as dynamical variables for a set of biochemical reactions, we implicitly assume that numbers of the molecules are large enough so that their changes can be regarded as continuous and they are described deterministically. However, for a system with small numbers of molecules, changes in their numbers are apparently discrete and molecular noises become significant. In such cases, models with deterministic differential equations may be inappropriate, and the reactions must be described by stochastic equations. In this study, we focus a clock gene expression for a circadian rhythm generation, which is known as a system involving small numbers of molecules. Thus it is appropriate for the system to be modeled by stochastic equations and analyzed by methodologies of stochastic simulations. The interlocked feedback model proposed by Ueda et al. as a set of deterministic ordinary differential equations provides a basis of our analyses. We apply two stochastic simulation methods, namely Gillespie's direct method and the stochastic differential equation method also by Gillespie, to the interlocked feedback model. To this end, we first reformulated the original differential equations back to elementary chemical reactions. With those reactions, we simulate and analyze the dynamics of the model using two methods in order to compare them with the dynamics obtained from the original deterministic model and to characterize dynamics how they depend on the simulation methodologies.

Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

PubMed Central

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

Increased persistence via asynchrony in oscillating ecological populations with long-range interaction

NASA Astrophysics Data System (ADS)

Gupta, Anubhav; Banerjee, Tanmoy; Dutta, Partha Sharathi

2017-10-01

Understanding the influence of the structure of a dispersal network on the species persistence and modeling a realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the persistence of interacting ecological systems was studied [M. D. Holland and A. Hastings, Nature (London) 456, 792 (2008), 10.1038/nature07395], where it was shown that a randomization of the structure of a dispersal network in a metapopulation model of prey and predator increases the species persistence via clustering, prolonged transient dynamics, and amplitudes of population fluctuations. In this paper, by contrast, we show that a deterministic network topology in a metapopulation can also favor asynchrony and prolonged transient dynamics if species dispersal obeys a long-range interaction governed by a distance-dependent power law. To explore the effects of power-law coupling, we take a realistic ecological model, namely, the Rosenzweig-MacArthur model in each patch (node) of the network of oscillators, and show that the coupled system is driven from synchrony to asynchrony with an increase in the power-law exponent. Moreover, to understand the relationship between species persistence and variations in power-law exponent, we compute a correlation coefficient to characterize cluster formation, a synchrony order parameter, and median predator amplitude. We further show that smaller metapopulations with fewer patches are more vulnerable to extinction as compared to larger metapopulations with a higher number of patches. We believe that the present work improves our understanding of the interconnection between the random network and the deterministic network in theoretical ecology.

Deterministic and stochastic CTMC models from Zika disease transmission

NASA Astrophysics Data System (ADS)

Zevika, Mona; Soewono, Edy

2018-03-01

Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.

Games of multicellularity.

PubMed

Kaveh, Kamran; Veller, Carl; Nowak, Martin A

2016-08-21

Evolutionary game dynamics are often studied in the context of different population structures. Here we propose a new population structure that is inspired by simple multicellular life forms. In our model, cells reproduce but can stay together after reproduction. They reach complexes of a certain size, n, before producing single cells again. The cells within a complex derive payoff from an evolutionary game by interacting with each other. The reproductive rate of cells is proportional to their payoff. We consider all two-strategy games. We study deterministic evolutionary dynamics with mutations, and derive exact conditions for selection to favor one strategy over another. Our main result has the same symmetry as the well-known sigma condition, which has been proven for stochastic game dynamics and weak selection. For a maximum complex size of n=2 our result holds for any intensity of selection. For n≥3 it holds for weak selection. As specific examples we study the prisoner's dilemma and hawk-dove games. Our model advances theoretical work on multicellularity by allowing for frequency-dependent interactions within groups. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling sandhill crane population dynamics

USGS Publications Warehouse

Johnson, D.H.

1979-01-01

The impact of sport hunting on the Central Flyway population of sandhill cranes (Grus canadensis) has been a subject of controversy for several years. A recent study (Buller 1979) presented new and important information on sandhill crane population dynamics. The present report is intended to incorporate that and other information into a mathematical model for the purpose of assessing the long-range impact of hunting on the population of sandhill cranes.The model is a simple deterministic system that embodies density-dependent rates of survival and recruitment. The model employs four kinds of data: (1) spring population size of sandhill cranes, estimated from aerial surveys to be between 250,000 and 400,000 birds; (2) age composition in fall, estimated for 1974-76 to be 11.3% young; (3) annual harvest of cranes, estimated from a variety of sources to be about 5 to 7% of the spring population; and (4) age composition of harvested cranes, which was difficult to estimate but suggests that immatures were 2 to 4 times as vulnerable to hunting as adults.Because the true nature of sandhill crane population dynamics remains so poorly understood, it was necessary to try numerous (768 in all) combinations of survival and recruitment functions, and focus on the relatively few (37) that yielded population sizes and age structures comparable to those extant in the real population. Hunting was then applied to those simulated populations. In all combinations, hunting resulted in a lower asymptotic crane population, the decline ranging from 5 to 54%. The median decline was 22%, which suggests that a hunted sandhill crane population might be about three-fourths as large as it would be if left unhunted. Results apply to the aggregate of the three subspecies in the Central Flyway; individual subspecies or populations could be affected to a greater or lesser degree.

Down to the roughness scale assessment of piston-ring/liner contacts

NASA Astrophysics Data System (ADS)

Checo, H. M.; Jaramillo, A.; Ausas, R. F.; Jai, M.; Buscaglia, G. C.

2017-02-01

The effects of surface roughness in hydrodynamic bearings been accounted for through several approaches, the most widely used being averaging or stochastic techniques. With these the surface is not treated “as it is”, but by means of an assumed probability distribution for the roughness. The so called direct, deterministic or measured-surface simulation) solve the lubrication problem with realistic surfaces down to the roughness scale. This leads to expensive computational problems. Most researchers have tackled this problem considering non-moving surfaces and neglecting the ring dynamics to reduce the computational burden. What is proposed here is to solve the fully-deterministic simulation both in space and in time, so that the actual movement of the surfaces and the rings dynamics are taken into account. This simulation is much more complex than previous ones, as it is intrinsically transient. The feasibility of these fully-deterministic simulations is illustrated two cases: fully deterministic simulation of liner surfaces with diverse finishings (honed and coated bores) with constant piston velocity and load on the ring and also in real engine conditions.

GAPPARD: a computationally efficient method of approximating gap-scale disturbance in vegetation models

NASA Astrophysics Data System (ADS)

Scherstjanoi, M.; Kaplan, J. O.; Thürig, E.; Lischke, H.

2013-09-01

Models of vegetation dynamics that are designed for application at spatial scales larger than individual forest gaps suffer from several limitations. Typically, either a population average approximation is used that results in unrealistic tree allometry and forest stand structure, or models have a high computational demand because they need to simulate both a series of age-based cohorts and a number of replicate patches to account for stochastic gap-scale disturbances. The detail required by the latter method increases the number of calculations by two to three orders of magnitude compared to the less realistic population average approach. In an effort to increase the efficiency of dynamic vegetation models without sacrificing realism, we developed a new method for simulating stand-replacing disturbances that is both accurate and faster than approaches that use replicate patches. The GAPPARD (approximating GAP model results with a Probabilistic Approach to account for stand Replacing Disturbances) method works by postprocessing the output of deterministic, undisturbed simulations of a cohort-based vegetation model by deriving the distribution of patch ages at any point in time on the basis of a disturbance probability. With this distribution, the expected value of any output variable can be calculated from the output values of the deterministic undisturbed run at the time corresponding to the patch age. To account for temporal changes in model forcing (e.g., as a result of climate change), GAPPARD performs a series of deterministic simulations and interpolates between the results in the postprocessing step. We integrated the GAPPARD method in the vegetation model LPJ-GUESS, and evaluated it in a series of simulations along an altitudinal transect of an inner-Alpine valley. We obtained results very similar to the output of the original LPJ-GUESS model that uses 100 replicate patches, but simulation time was reduced by approximately the factor 10. Our new method is therefore highly suited for rapidly approximating LPJ-GUESS results, and provides the opportunity for future studies over large spatial domains, allows easier parameterization of tree species, faster identification of areas of interesting simulation results, and comparisons with large-scale datasets and results of other forest models.

Production scheduling and rescheduling with genetic algorithms.

PubMed

Bierwirth, C; Mattfeld, D C

1999-01-01

A general model for job shop scheduling is described which applies to static, dynamic and non-deterministic production environments. Next, a Genetic Algorithm is presented which solves the job shop scheduling problem. This algorithm is tested in a dynamic environment under different workload situations. Thereby, a highly efficient decoding procedure is proposed which strongly improves the quality of schedules. Finally, this technique is tested for scheduling and rescheduling in a non-deterministic environment. It is shown by experiment that conventional methods of production control are clearly outperformed at reasonable run-time costs.

Autonomous choices among deterministic evolution-laws as source of uncertainty

NASA Astrophysics Data System (ADS)

Trujillo, Leonardo; Meyroneinc, Arnaud; Campos, Kilver; Rendón, Otto; Sigalotti, Leonardo Di G.

2018-03-01

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these pseudo-random dynamical systems. Each chaotic system in this family exhibits a sensitivity to initial conditions that encompasses the sequence of choices of the evolution rule in some collection of maps. This opens a possibility to extend current theories of complex behaviors on the basis of intrinsic uncertainty in deterministic chaos.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure

NASA Astrophysics Data System (ADS)

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure.

PubMed

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

Population dynamics in the presence of quasispecies effects and changing environments

NASA Astrophysics Data System (ADS)

Forster, Robert Burke

2006-12-01

This thesis explores how natural selection acts on organisms such as viruses that have either highly error-prone reproduction or face variable environmental conditions or both. By modeling population dynamics under these conditions, we gain a better understanding of the selective forces at work, both in our simulations and hopefully also in real organisms. With an understanding of the important factors in natural selection we can forecast not only the immediate fate of an existing population but also in what directions such a population might evolve in the future. We demonstrate that the concept of a quasispecies is relevant to evolution in a neutral fitness landscape. Motivated by RNA viruses such as HIV, we use RNA secondary structure as our model system and find that quasispecies effects arise both rapidly and in realistically small populations. We discover that the evolutionary effects of neutral drift, punctuated equilibrium and the selection for mutational robustness extend to the concept of a quasispecies. In our study of periodic environments, we consider the tradeoffs faced by quasispecies in adapting to environmental change. We develop an analytical model to predict whether evolution favors short-term or long-term adaptation and validate our model through simulation. Our results bear directly on the population dynamics of viruses such as West Nile that alternate between two host species. More generally, we discover that a selective pressure exists under these conditions to fuse or split genes with complementary environmental functions. Lastly, we study the general effects of frequency-dependent selection on two strains competing in a periodic environment. Under very general assumptions, we prove that stable coexistence rather than extinction is the likely outcome. The population dynamics of this system may be as simple as stable equilibrium or as complex as deterministic chaos.

Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters

PubMed Central

Li, Fangting

2017-01-01

The notion of an attractor has been widely employed in thinking about the nonlinear dynamics of organisms and biological phenomena as systems and as processes. The notion of a landscape with valleys and mountains encoding multiple attractors, however, has a rigorous foundation only for closed, thermodynamically non-driven, chemical systems, such as a protein. Recent advances in the theory of nonlinear stochastic dynamical systems and its applications to mesoscopic reaction networks, one reaction at a time, have provided a new basis for a landscape of open, driven biochemical reaction systems under sustained chemostat. The theory is equally applicable not only to intracellular dynamics of biochemical regulatory networks within an individual cell but also to tissue dynamics of heterogeneous interacting cell populations. The landscape for an individual cell, applicable to a population of isogenic non-interacting cells under the same environmental conditions, is defined on the counting space of intracellular chemical compositions x = (x1,x2, … ,xN) in a cell, where xℓ is the concentration of the ℓth biochemical species. Equivalently, for heterogeneous cell population dynamics xℓ is the number density of cells of the ℓth cell type. One of the insights derived from the landscape perspective is that the life history of an individual organism, which occurs on the hillsides of a landscape, is nearly deterministic and ‘programmed’, while population-wise an asynchronous non-equilibrium steady state resides mostly in the lowlands of the landscape. We argue that a dynamic ‘blue-sky’ bifurcation, as a representation of Waddington's landscape, is a more robust mechanism for a cell fate decision and subsequent differentiation than the widely pictured pitch-fork bifurcation. We revisit, in terms of the chemostatic driving forces upon active, living matter, the notions of near-equilibrium thermodynamic branches versus far-from-equilibrium states. The emergent landscape perspective permits a quantitative discussion of a wide range of biological phenomena as nonlinear, stochastic dynamics. PMID:28490602

BatTool: an R package with GUI for assessing the effect of White-nose syndrome and other take events on Myotis spp. of bats

PubMed Central

2014-01-01

Background Myotis species of bats such as the Indiana Bat and Little Brown Bat are facing population declines because of White-nose syndrome (WNS). These species also face threats from anthropogenic activities such as wind energy development. Population models may be used to provide insights into threats facing these species. We developed a population model, BatTool, as an R package to help decision makers and natural resource managers examine factors influencing the dynamics of these species. The R package includes two components: 1) a deterministic and stochastic model that are accessible from the command line and 2) a graphical user interface (GUI). Results BatTool is an R package allowing natural resource managers and decision makers to understand Myotis spp. population dynamics. Through the use of a GUI, the model allows users to understand how WNS and other take events may affect the population. The results are saved both graphically and as data files. Additionally, R-savvy users may access the population functions through the command line and reuse the code as part of future research. This R package could also be used as part of a population dynamics or wildlife management course. Conclusions BatTool provides access to a Myotis spp. population model. This tool can help natural resource managers and decision makers with the Endangered Species Act deliberations for these species and with issuing take permits as part of regulatory decision making. The tool is available online as part of this publication. PMID:24955110

BatTool: an R package with GUI for assessing the effect of White-nose syndrome and other take events on Myotis spp. of bats

USGS Publications Warehouse

Erickson, Richard A.; Thogmartin, Wayne E.; Szymanski, Jennifer A.

2014-01-01

Background: Myotis species of bats such as the Indiana Bat and Little Brown Bat are facing population declines because of White-nose syndrome (WNS). These species also face threats from anthropogenic activities such as wind energy development. Population models may be used to provide insights into threats facing these species. We developed a population model, BatTool, as an R package to help decision makers and natural resource managers examine factors influencing the dynamics of these species. The R package includes two components: 1) a deterministic and stochastic model that are accessible from the command line and 2) a graphical user interface (GUI). Results: BatTool is an R package allowing natural resource managers and decision makers to understand Myotis spp. population dynamics. Through the use of a GUI, the model allows users to understand how WNS and other take events may affect the population. The results are saved both graphically and as data files. Additionally, R-savvy users may access the population functions through the command line and reuse the code as part of future research. This R package could also be used as part of a population dynamics or wildlife management course. Conclusions: BatTool provides access to a Myotis spp. population model. This tool can help natural resource managers and decision makers with the Endangered Species Act deliberations for these species and with issuing take permits as part of regulatory decision making. The tool is available online as part of this publication.

BatTool: an R package with GUI for assessing the effect of White-nose syndrome and other take events on Myotis spp. of bats.

PubMed

Erickson, Richard A; Thogmartin, Wayne E; Szymanski, Jennifer A

2014-01-01

Myotis species of bats such as the Indiana Bat and Little Brown Bat are facing population declines because of White-nose syndrome (WNS). These species also face threats from anthropogenic activities such as wind energy development. Population models may be used to provide insights into threats facing these species. We developed a population model, BatTool, as an R package to help decision makers and natural resource managers examine factors influencing the dynamics of these species. The R package includes two components: 1) a deterministic and stochastic model that are accessible from the command line and 2) a graphical user interface (GUI). BatTool is an R package allowing natural resource managers and decision makers to understand Myotis spp. population dynamics. Through the use of a GUI, the model allows users to understand how WNS and other take events may affect the population. The results are saved both graphically and as data files. Additionally, R-savvy users may access the population functions through the command line and reuse the code as part of future research. This R package could also be used as part of a population dynamics or wildlife management course. BatTool provides access to a Myotis spp. population model. This tool can help natural resource managers and decision makers with the Endangered Species Act deliberations for these species and with issuing take permits as part of regulatory decision making. The tool is available online as part of this publication.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

PubMed

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model.

PubMed

Nené, Nuno R; Dunham, Alistair S; Illingworth, Christopher J R

2018-05-01

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. Copyright © 2018 Nené et al.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Invasion of cooperators in lattice populations: linear and non-linear public good games.

PubMed

Vásárhelyi, Zsóka; Scheuring, István

2013-08-01

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open. Here we examined the dynamics of individual based stochastic models of the NVD. We analyze the dynamics in well-mixed and viscous populations. We show in both cases that coexistence between cooperators and defectors is possible; moreover, spatial aggregation of types in viscous populations can easily lead to pure cooperation. Furthermore we analyze the invasion of cooperators in populations consisting predominantly of defectors. In accordance with analytical results, in deterministic systems, we found the invasion of cooperators successful in the well-mixed case only if their initial concentration was higher than a critical threshold, defined by the replicator dynamics of the NVD. In the viscous case, however, not the initial concentration but the initial number determines the success of invasion. We show that even a single mutant cooperator can invade with a high probability, because the local density of aggregated cooperators exceeds the threshold defined by the game. Comparing the results to models using different benefit functions (linear or sigmoid), we show that the role of the benefit function is much more important in the well-mixed than in the viscous case. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Taking Control: Stealth Assessment of Deterministic Behaviors within a Game-Based System

ERIC Educational Resources Information Center

Snow, Erica L.; Likens, Aaron D.; Allen, Laura K.; McNamara, Danielle S.

2016-01-01

Game-based environments frequently afford students the opportunity to exert agency over their learning paths by making various choices within the environment. The combination of log data from these systems and dynamic methodologies may serve as a stealth means to assess how students behave (i.e., deterministic or random) within these learning…

Taking Control: Stealth Assessment of Deterministic Behaviors within a Game-Based System

ERIC Educational Resources Information Center

Snow, Erica L.; Likens, Aaron D.; Allen, Laura K.; McNamara, Danielle S.

2015-01-01

Game-based environments frequently afford students the opportunity to exert agency over their learning paths by making various choices within the environment. The combination of log data from these systems and dynamic methodologies may serve as a stealth means to assess how students behave (i.e., deterministic or random) within these learning…

Langevin approach to a chemical wave front: Selection of the propagation velocity in the presence of internal noise

NASA Astrophysics Data System (ADS)

Lemarchand, A.; Lesne, A.; Mareschal, M.

1995-05-01

The reaction-diffusion equation associated with the Fisher chemical model A+B-->2A admits wave-front solutions by replacing an unstable stationary state with a stable one. The deterministic analysis concludes that their propagation velocity is not prescribed by the dynamics. For a large class of initial conditions the velocity which is spontaneously selected is equal to the minimum allowed velocity vmin, as predicted by the marginal stability criterion. In order to test the relevance of this deterministic description we investigate the macroscopic consequences, on the velocity and the width of the front, of the intrinsic stochasticity due to the underlying microscopic dynamics. We solve numerically the Langevin equations, deduced analytically from the master equation within a system size expansion procedure. We show that the mean profile associated with the stochastic solution propagates faster than the deterministic solution at a velocity up to 25% greater than vmin.

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

Analysis of stochastic model for non-linear volcanic dynamics

NASA Astrophysics Data System (ADS)

Alexandrov, D.; Bashkirtseva, I.; Ryashko, L.

2014-12-01

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Influence of demographic changes on the impact of vaccination against varicella and herpes zoster in Germany - a mathematical modelling study.

PubMed

Horn, Johannes; Damm, Oliver; Greiner, Wolfgang; Hengel, Hartmut; Kretzschmar, Mirjam E; Siedler, Anette; Ultsch, Bernhard; Weidemann, Felix; Wichmann, Ole; Karch, André; Mikolajczyk, Rafael T

2018-01-09

Epidemiological studies suggest that reduced exposure to varicella might lead to an increased risk for herpes zoster (HZ). Reduction of exposure to varicella is a consequence of varicella vaccination but also of demographic changes. We analyzed how the combination of vaccination programs and demographic dynamics will affect the epidemiology of varicella and HZ in Germany over the next 50 years. We used a deterministic dynamic compartmental model to assess the impact of different varicella and HZ vaccination strategies on varicella and HZ epidemiology in three demographic scenarios, namely the projected population for Germany, the projected population additionally accounting for increased immigration as observed in 2015/2016, and a stationary population. Projected demographic changes alone result in an increase of annual HZ cases by 18.3% and a decrease of varicella cases by 45.7% between 1990 and 2060. Independently of the demographic scenario, varicella vaccination reduces the cumulative number of varicella cases until 2060 by approximately 70%, but also increases HZ cases by 10%. Unlike the currently licensed live attenuated HZ vaccine, the new subunit vaccine candidate might completely counteract this effect. Relative vaccine effects were consistent across all demographic scenarios. Demographic dynamics will be a major determinant of HZ epidemiology in the next 50 years. While stationary population models are appropriate for assessing vaccination impact, models incorporating realistic population structures allow a direct comparison to surveillance data and can thus provide additional input for immunization decision-making and resource planning.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

PubMed Central

Cotter, C. J.

2017-01-01

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316

Rare event computation in deterministic chaotic systems using genealogical particle analysis

NASA Astrophysics Data System (ADS)

Wouters, J.; Bouchet, F.

2016-09-01

In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in deterministic dynamical systems. We demonstrate that genealogical particle analysis algorithms can be successfully applied to a toy model of atmospheric dynamics, the Lorenz ’96 model. We furthermore use the Ornstein-Uhlenbeck system to illustrate a number of implementation issues. We also show how a time-dependent objective function based on the fluctuation path to a high threshold can greatly improve the performance of the estimator compared to a fixed-in-time objective function.

ShinyGPAS: interactive genomic prediction accuracy simulator based on deterministic formulas.

PubMed

Morota, Gota

2017-12-20

Deterministic formulas for the accuracy of genomic predictions highlight the relationships among prediction accuracy and potential factors influencing prediction accuracy prior to performing computationally intensive cross-validation. Visualizing such deterministic formulas in an interactive manner may lead to a better understanding of how genetic factors control prediction accuracy. The software to simulate deterministic formulas for genomic prediction accuracy was implemented in R and encapsulated as a web-based Shiny application. Shiny genomic prediction accuracy simulator (ShinyGPAS) simulates various deterministic formulas and delivers dynamic scatter plots of prediction accuracy versus genetic factors impacting prediction accuracy, while requiring only mouse navigation in a web browser. ShinyGPAS is available at: https://chikudaisei.shinyapps.io/shinygpas/ . ShinyGPAS is a shiny-based interactive genomic prediction accuracy simulator using deterministic formulas. It can be used for interactively exploring potential factors that influence prediction accuracy in genome-enabled prediction, simulating achievable prediction accuracy prior to genotyping individuals, or supporting in-class teaching. ShinyGPAS is open source software and it is hosted online as a freely available web-based resource with an intuitive graphical user interface.

A stochastic model for correlated protein motions

NASA Astrophysics Data System (ADS)

Karain, Wael I.; Qaraeen, Nael I.; Ajarmah, Basem

2006-06-01

A one-dimensional Langevin-type stochastic difference equation is used to find the deterministic and Gaussian contributions of time series representing the projections of a Bovine Pancreatic Trypsin Inhibitor (BPTI) protein molecular dynamics simulation along different eigenvector directions determined using principal component analysis. The deterministic part shows a distinct nonlinear behavior only for eigenvectors contributing significantly to the collective protein motion.

Deterministic generation of remote entanglement with active quantum feedback

DOE PAGES

Martin, Leigh; Motzoi, Felix; Li, Hanhan; ...

2015-12-10

We develop and study protocols for deterministic remote entanglement generation using quantum feedback, without relying on an entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can bemore » modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Lastly, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.« less

Optimal Vaccination in a Stochastic Epidemic Model of Two Non-Interacting Populations

DTIC Science & Technology

2015-02-17

of diminishing returns from vacci- nation will generally take place at smaller vaccine allocations V compared to the deterministic model. Optimal...take place and small r0 values where it does not is illustrat- ed in Fig. 4C. As r0 is decreased, the region between the two instances of switching...approximately distribute vaccine in proportion to population size. For large r0 (r0 ≳ 2.9), two switches take place . In the deterministic optimal solution, a

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

PubMed Central

2018-01-01

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the properties of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Last, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site. PMID:29386401

Dynamics of stochastic SEIS epidemic model with varying population size

NASA Astrophysics Data System (ADS)

Liu, Jiamin; Wei, Fengying

2016-12-01

We introduce the stochasticity into a deterministic model which has state variables susceptible-exposed-infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Itô's formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.

Importance sampling with imperfect cloning for the computation of generalized Lyapunov exponents

NASA Astrophysics Data System (ADS)

Anteneodo, Celia; Camargo, Sabrina; Vallejos, Raúl O.

2017-12-01

We revisit the numerical calculation of generalized Lyapunov exponents, L (q ) , in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then L (q ) is obtained by taking the limit noise-amplitude → 0 after the calculation. We focus on a particular method that involves periodic cloning and pruning of a set of trajectories. However, instead of considering a noisy dynamics, we implement an imperfect (noisy) cloning. This alternative method is compared with the standard one and, when possible, with analytical results. As a workbench we use the asymmetric tent map, the standard map, and a system of coupled symplectic maps. The general conclusion of this study is that the imperfect-cloning method performs as well as the standard one, with the advantage of preserving the deterministic dynamics.

Improvement and empirical research on chaos control by theory of "chaos + chaos = order".

PubMed

Fulai, Wang

2012-12-01

This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.

Estimating golden-cheeked warbler immigration: Implications for the spatial scale of conservation

USGS Publications Warehouse

Duarte, A.; Weckerly, F.W.; Schaub, M.; Hatfield, Jeffrey S.

2016-01-01

Understanding the factors that drive population dynamics is fundamental to species conservation and management. Since the golden-cheeked warbler Setophaga chrysoparia was first listed as endangered, much effort has taken place to monitor warbler abundance, occupancy, reproduction and survival. Yet, despite being directly related to local population dynamics, movement rates have not been estimated for the species. We used an integrated population model to investigate the relationship between immigration rate, fledging rate, survival probabilities and population growth rate for warblers in central Texas, USA. Furthermore, using a deterministic projection model, we examined the response required by vital rates to maintain a viable population across varying levels of immigration. Warbler abundance fluctuated with an overall positive trend across years. In the absence of immigration, the abundance would have decreased. However, the population could remain viable without immigration if both adult and juvenile survival increased by almost half or if juvenile survival more than doubled. We also investigated the response required by fledging rates across a range of immigration in order to maintain a viable population. Overall, we found that immigration was required to maintain warbler target populations, indicating that warbler conservation and management programs need to be implemented at larger spatial scales than current efforts to be effective. This study also demonstrates that by using limited data within integrated population models, biologists are able to monitor multiple key demographic parameters simultaneously to gauge the efficacy of strategies designed to maximize warbler viability in a changing landscape.

Health safety nets can break cycles of poverty and disease: a stochastic ecological model.

PubMed

Plucinski, Mateusz M; Ngonghala, Calistus N; Bonds, Matthew H

2011-12-07

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a 'safety net', defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium.

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography

NASA Astrophysics Data System (ADS)

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography.

PubMed

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

The spreading dynamics of sexually transmitted diseases with birth and death on heterogeneous networks

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde; Alsaedi, Ahmed; Hayat, Tasawar

2017-02-01

In this paper, we formulate a deterministic model by including the vacant sites, which represent inactive individuals or potential contacts, to investigate the spreading dynamics of sexually transmitted diseases in heterogeneous networks. We first analytically derive the basic reproduction number R 0, which completely determines global dynamics of the system in the long run. Specifically, if R 0  <  1, the disease-free equilibrium is globally asymptotically stable, i.e. disease disappears from the network irrespective of initial infected numbers and distributions, whereas if R 0  >  1, the system is uniformly persistent around a unique endemic equilibrium, i.e. disease persists in the network. Furthermore, by using a suitable Lyapunov function the global stability of endemic equilibrium for low/high-risk infected individuals only is proved. Finally, the effects of three immunization schemes are studied and compared, and extensive numerical simulations are performed to investigate the effect of network topology and population turnover on disease spread. Our results suggest that population turnover could have great impact on the sexually transmitted disease system in heterogeneous networks, including the basic reproduction number and infection prevalence.

Expansion Under Climate Change: The Genetic Consequences.

PubMed

Garnier, Jimmy; Lewis, Mark A

2016-11-01

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically, the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

Population Dynamics of Early Human Migration in Britain

PubMed Central

Vahia, Mayank N.; Ladiwala, Uma; Mahathe, Pavan; Mathur, Deepak

2016-01-01

Background Early human migration is largely determined by geography and human needs. These are both deterministic parameters when small populations move into unoccupied areas where conflicts and large group dynamics are not important. The early period of human migration into the British Isles provides such a laboratory which, because of its relative geographical isolation, may allow some insights into the complex dynamics of early human migration and interaction. Method and Results We developed a simulation code based on human affinity to habitable land, as defined by availability of water sources, altitude, and flatness of land, in choosing the path of migration. Movement of people on the British island over the prehistoric period from their initial entry points was simulated on the basis of data from the megalithic period. Topographical and hydro-shed data from satellite databases was used to define habitability, based on distance from water bodies, flatness of the terrain, and altitude above sea level. We simulated population movement based on assumptions of affinity for more habitable places, with the rate of movement tempered by existing populations. We compared results of our computer simulations with genetic data and show that our simulation can predict fairly accurately the points of contacts between different migratory paths. Such comparison also provides more detailed information about the path of peoples’ movement over ~2000 years before the present era. Conclusions We demonstrate an accurate method to simulate prehistoric movements of people based upon current topographical satellite data. Our findings are validated by recently-available genetic data. Our method may prove useful in determining early human population dynamics even when no genetic information is available. PMID:27148959

Finite-size effects and switching times for Moran process with mutation.

PubMed

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

Complex dynamic in ecological time series

Treesearch

Peter Turchin; Andrew D. Taylor

1992-01-01

Although the possibility of complex dynamical behaviors-limit cycles, quasiperiodic oscillations, and aperiodic chaos-has been recognized theoretically, most ecologists are skeptical of their importance in nature. In this paper we develop a methodology for reconstructing endogenous (or deterministic) dynamics from ecological time series. Our method consists of fitting...

Host Resistance, Population Structure and the Long-Term Persistence of Bubonic Plague: Contributions of a Modelling Approach in the Malagasy Focus

PubMed Central

Gascuel, Fanny; Choisy, Marc; Duplantier, Jean-Marc; Débarre, Florence; Brouat, Carine

2013-01-01

Although bubonic plague is an endemic zoonosis in many countries around the world, the factors responsible for the persistence of this highly virulent disease remain poorly known. Classically, the endemic persistence of plague is suspected to be due to the coexistence of plague resistant and plague susceptible rodents in natural foci, and/or to a metapopulation structure of reservoirs. Here, we test separately the effect of each of these factors on the long-term persistence of plague. We analyse the dynamics and equilibria of a model of plague propagation, consistent with plague ecology in Madagascar, a major focus where this disease is endemic since the 1920s in central highlands. By combining deterministic and stochastic analyses of this model, and including sensitivity analyses, we show that (i) endemicity is favoured by intermediate host population sizes, (ii) in large host populations, the presence of resistant rats is sufficient to explain long-term persistence of plague, and (iii) the metapopulation structure of susceptible host populations alone can also account for plague endemicity, thanks to both subdivision and the subsequent reduction in the size of subpopulations, and extinction-recolonization dynamics of the disease. In the light of these results, we suggest scenarios to explain the localized presence of plague in Madagascar. PMID:23675291

Host resistance, population structure and the long-term persistence of bubonic plague: contributions of a modelling approach in the Malagasy focus.

PubMed

Gascuel, Fanny; Choisy, Marc; Duplantier, Jean-Marc; Débarre, Florence; Brouat, Carine

2013-01-01

Although bubonic plague is an endemic zoonosis in many countries around the world, the factors responsible for the persistence of this highly virulent disease remain poorly known. Classically, the endemic persistence of plague is suspected to be due to the coexistence of plague resistant and plague susceptible rodents in natural foci, and/or to a metapopulation structure of reservoirs. Here, we test separately the effect of each of these factors on the long-term persistence of plague. We analyse the dynamics and equilibria of a model of plague propagation, consistent with plague ecology in Madagascar, a major focus where this disease is endemic since the 1920s in central highlands. By combining deterministic and stochastic analyses of this model, and including sensitivity analyses, we show that (i) endemicity is favoured by intermediate host population sizes, (ii) in large host populations, the presence of resistant rats is sufficient to explain long-term persistence of plague, and (iii) the metapopulation structure of susceptible host populations alone can also account for plague endemicity, thanks to both subdivision and the subsequent reduction in the size of subpopulations, and extinction-recolonization dynamics of the disease. In the light of these results, we suggest scenarios to explain the localized presence of plague in Madagascar.

Automated Flight Routing Using Stochastic Dynamic Programming

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Morando, Alex; Grabbe, Shon

2010-01-01

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

A random walk on water (Henry Darcy Medal Lecture)

NASA Astrophysics Data System (ADS)

Koutsoyiannis, D.

2009-04-01

Randomness and uncertainty had been well appreciated in hydrology and water resources engineering in their initial steps as scientific disciplines. However, this changed through the years and, following other geosciences, hydrology adopted a naïve view of randomness in natural processes. Such a view separates natural phenomena into two mutually exclusive types, random or stochastic, and deterministic. When a classification of a specific process into one of these two types fails, then a separation of the process into two different, usually additive, parts is typically devised, each of which may be further subdivided into subparts (e.g., deterministic subparts such as periodic and aperiodic or trends). This dichotomous logic is typically combined with a manichean perception, in which the deterministic part supposedly represents cause-effect relationships and thus is physics and science (the "good"), whereas randomness has little relationship with science and no relationship with understanding (the "evil"). Probability theory and statistics, which traditionally provided the tools for dealing with randomness and uncertainty, have been regarded by some as the "necessary evil" but not as an essential part of hydrology and geophysics. Some took a step further to banish them from hydrology, replacing them with deterministic sensitivity analysis and fuzzy-logic representations. Others attempted to demonstrate that irregular fluctuations observed in natural processes are au fond manifestations of underlying chaotic deterministic dynamics with low dimensionality, thus attempting to render probabilistic descriptions unnecessary. Some of the above recent developments are simply flawed because they make erroneous use of probability and statistics (which, remarkably, provide the tools for such analyses), whereas the entire underlying logic is just a false dichotomy. To see this, it suffices to recall that Pierre Simon Laplace, perhaps the most famous proponent of determinism in the history of philosophy of science (cf. Laplace's demon), is, at the same time, one of the founders of probability theory, which he regarded as "nothing but common sense reduced to calculation". This harmonizes with James Clerk Maxwell's view that "the true logic for this world is the calculus of Probabilities" and was more recently and epigrammatically formulated in the title of Edwin Thompson Jaynes's book "Probability Theory: The Logic of Science" (2003). Abandoning dichotomous logic, either on ontological or epistemic grounds, we can identify randomness or stochasticity with unpredictability. Admitting that (a) uncertainty is an intrinsic property of nature; (b) causality implies dependence of natural processes in time and thus suggests predictability; but, (c) even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon, we may shape a stochastic representation of natural processes that is consistent with Karl Popper's indeterministic world view. In this representation, probability quantifies uncertainty according to the Kolmogorov system, in which probability is a normalized measure, i.e., a function that maps sets (areas where the initial conditions or the parameter values lie) to real numbers (in the interval [0, 1]). In such a representation, predictability (suggested by deterministic laws) and unpredictability (randomness) coexist, are not separable or additive components, and it is a matter of specifying the time horizon of prediction to decide which of the two dominates. An elementary numerical example has been devised to illustrate the above ideas and demonstrate that they offer a pragmatic and useful guide for practice, rather than just pertaining to philosophical discussions. A chaotic model, with fully and a priori known deterministic dynamics and deterministic inputs (without any random agent), is assumed to represent the hydrological balance in an area partly covered by vegetation. Experimentation with this toy model demonstrates, inter alia, that: (1) for short time horizons the deterministic dynamics is able to give good predictions; but (2) these predictions become extremely inaccurate and useless for long time horizons; (3) for such horizons a naïve statistical prediction (average of past data) which fully neglects the deterministic dynamics is more skilful; and (4) if this statistical prediction, in addition to past data, is combined with the probability theory (the principle of maximum entropy, in particular), it can provide a more informative prediction. Also, the toy model shows that the trajectories of the system state (and derivative properties thereof) do not resemble a regular (e.g., periodic) deterministic process nor a purely random process, but exhibit patterns indicating anti-persistence and persistence (where the latter statistically complies with a Hurst-Kolmogorov behaviour). If the process is averaged over long time scales, the anti-persistent behaviour improves predictability, whereas the persistent behaviour substantially deteriorates it. A stochastic representation of this deterministic system, which incorporates dynamics, is not only possible, but also powerful as it provides good predictions for both short and long horizons and helps to decide on when the deterministic dynamics should be considered or neglected. Obviously, a natural system is extremely more complex than this simple toy model and hence unpredictability is naturally even more prominent in the former. In addition, in a complex natural system, we can never know the exact dynamics and we must infer it from past data, which implies additional uncertainty and an additional role of stochastics in the process of formulating the system equations and estimating the involved parameters. Data also offer the only solid grounds to test any hypothesis about the dynamics, and failure of performing such testing against evidence from data renders the hypothesised dynamics worthless. If this perception of natural phenomena is adequately plausible, then it may help in studying interesting fundamental questions regarding the current state and the trends of hydrological and water resources research and their promising future paths. For instance: (i) Will it ever be possible to achieve a fully "physically based" modelling of hydrological systems that will not depend on data or stochastic representations? (ii) To what extent can hydrological uncertainty be reduced and what are the effective means for such reduction? (iii) Are current stochastic methods in hydrology consistent with observed natural behaviours? What paths should we explore for their advancement? (iv) Can deterministic methods provide solid scientific grounds for water resources engineering and management? In particular, can there be risk-free hydraulic engineering and water management? (v) Is the current (particularly important) interface between hydrology and climate satisfactory?. In particular, should hydrology rely on climate models that are not properly validated (i.e., for periods and scales not used in calibration)? In effect, is the evolution of climate and its impacts on water resources deterministically predictable?

Maxwell Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Boyd, Alexander B.; Crutchfield, James P.

2016-05-01

We introduce a deterministic chaotic system—the Szilard map—that encapsulates the measurement, control, and erasure protocol by which Maxwellian demons extract work from a heat reservoir. Implementing the demon's control function in a dynamical embodiment, our construction symmetrizes the demon and the thermodynamic system, allowing one to explore their functionality and recover the fundamental trade-off between the thermodynamic costs of dissipation due to measurement and those due to erasure. The map's degree of chaos—captured by the Kolmogorov-Sinai entropy—is the rate of energy extraction from the heat bath. Moreover, an engine's statistical complexity quantifies the minimum necessary system memory for it to function. In this way, dynamical instability in the control protocol plays an essential and constructive role in intelligent thermodynamic systems.

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

PubMed

Sakai, Kenshi; Upadhyaya, Shrinivasa K; Andrade-Sanchez, Pedro; Sviridova, Nina V

2017-03-01

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

NASA Astrophysics Data System (ADS)

Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

2014-09-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

Terminal Model Of Newtonian Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Yen Ting; Buchler, Nicolas E.

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the propertiesmore » of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.« less

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

DOE PAGES

Lin, Yen Ting; Buchler, Nicolas E.

2018-01-31

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the propertiesmore » of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.« less

Dynamical Motor Control Learned with Deep Deterministic Policy Gradient

PubMed Central

2018-01-01

Conventional models of motor control exploit the spatial representation of the controlled system to generate control commands. Typically, the control command is gained with the feedback state of a specific instant in time, which behaves like an optimal regulator or spatial filter to the feedback state. Yet, recent neuroscience studies found that the motor network may constitute an autonomous dynamical system and the temporal patterns of the control command can be contained in the dynamics of the motor network, that is, the dynamical system hypothesis (DSH). Inspired by these findings, here we propose a computational model that incorporates this neural mechanism, in which the control command could be unfolded from a dynamical controller whose initial state is specified with the task parameters. The model is trained in a trial-and-error manner in the framework of deep deterministic policy gradient (DDPG). The experimental results show that the dynamical controller successfully learns the control policy for arm reaching movements, while the analysis of the internal activities of the dynamical controller provides the computational evidence to the DSH of the neural coding in motor cortices. PMID:29666634

Dynamical Motor Control Learned with Deep Deterministic Policy Gradient.

PubMed

Shi, Haibo; Sun, Yaoru; Li, Jie

2018-01-01

Conventional models of motor control exploit the spatial representation of the controlled system to generate control commands. Typically, the control command is gained with the feedback state of a specific instant in time, which behaves like an optimal regulator or spatial filter to the feedback state. Yet, recent neuroscience studies found that the motor network may constitute an autonomous dynamical system and the temporal patterns of the control command can be contained in the dynamics of the motor network, that is, the dynamical system hypothesis (DSH). Inspired by these findings, here we propose a computational model that incorporates this neural mechanism, in which the control command could be unfolded from a dynamical controller whose initial state is specified with the task parameters. The model is trained in a trial-and-error manner in the framework of deep deterministic policy gradient (DDPG). The experimental results show that the dynamical controller successfully learns the control policy for arm reaching movements, while the analysis of the internal activities of the dynamical controller provides the computational evidence to the DSH of the neural coding in motor cortices.

GAPPARD: a computationally efficient method of approximating gap-scale disturbance in vegetation models

NASA Astrophysics Data System (ADS)

Scherstjanoi, M.; Kaplan, J. O.; Thürig, E.; Lischke, H.

2013-02-01

Models of vegetation dynamics that are designed for application at spatial scales larger than individual forest gaps suffer from several limitations. Typically, either a population average approximation is used that results in unrealistic tree allometry and forest stand structure, or models have a high computational demand because they need to simulate both a series of age-based cohorts and a number of replicate patches to account for stochastic gap-scale disturbances. The detail required by the latter method increases the number of calculations by two to three orders of magnitude compared to the less realistic population average approach. In an effort to increase the efficiency of dynamic vegetation models without sacrificing realism, and to explore patterns of spatial scaling in forests, we developed a new method for simulating stand-replacing disturbances that is both accurate and 10-50x faster than approaches that use replicate patches. The GAPPARD (approximating GAP model results with a Probabilistic Approach to account for stand Replacing Disturbances) method works by postprocessing the output of deterministic, undisturbed simulations of a cohort-based vegetation model by deriving the distribution of patch ages at any point in time on the basis of a disturbance probability. With this distribution, the expected value of any output variable can be calculated from the output values of the deterministic undisturbed run at the time corresponding to the patch age. To account for temporal changes in model forcing, e.g., as a result of climate change, GAPPARD performs a series of deterministic simulations and interpolates between the results in the postprocessing step. We integrated the GAPPARD method in the forest models LPJ-GUESS and TreeM-LPJ, and evaluated these in a series of simulations along an altitudinal transect of an inner-alpine valley. With GAPPARD applied to LPJ-GUESS results were insignificantly different from the output of the original model LPJ-GUESS using 100 replicate patches, but simulation time was reduced by approximately the factor 10. Our new method is therefore highly suited rapidly approximating LPJ-GUESS results, and provides the opportunity for future studies over large spatial domains, allows easier parameterization of tree species, faster identification of areas of interesting simulation results, and comparisons with large-scale datasets and forest models.

Population density equations for stochastic processes with memory kernels

NASA Astrophysics Data System (ADS)

Lai, Yi Ming; de Kamps, Marc

2017-06-01

We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

Modeling the role of environmental variables on the population dynamics of the malaria vector Anopheles gambiae sensu stricto

PubMed Central

2012-01-01

Background The impact of weather and climate on malaria transmission has attracted considerable attention in recent years, yet uncertainties around future disease trends under climate change remain. Mathematical models provide powerful tools for addressing such questions and understanding the implications for interventions and eradication strategies, but these require realistic modeling of the vector population dynamics and its response to environmental variables. Methods Published and unpublished field and experimental data are used to develop new formulations for modeling the relationships between key aspects of vector ecology and environmental variables. These relationships are integrated within a validated deterministic model of Anopheles gambiae s.s. population dynamics to provide a valuable tool for understanding vector response to biotic and abiotic variables. Results A novel, parsimonious framework for assessing the effects of rainfall, cloudiness, wind speed, desiccation, temperature, relative humidity and density-dependence on vector abundance is developed, allowing ease of construction, analysis, and integration into malaria transmission models. Model validation shows good agreement with longitudinal vector abundance data from Tanzania, suggesting that recent malaria reductions in certain areas of Africa could be due to changing environmental conditions affecting vector populations. Conclusions Mathematical models provide a powerful, explanatory means of understanding the role of environmental variables on mosquito populations and hence for predicting future malaria transmission under global change. The framework developed provides a valuable advance in this respect, but also highlights key research gaps that need to be resolved if we are to better understand future malaria risk in vulnerable communities. PMID:22877154

Dynamic Probabilistic Instability of Composite Structures

NASA Technical Reports Server (NTRS)

Chamis, Christos C.

2009-01-01

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties in that order.

Two-strain competition in quasineutral stochastic disease dynamics.

PubMed

Kogan, Oleg; Khasin, Michael; Meerson, Baruch; Schneider, David; Myers, Christopher R

2014-10-01

We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.

Rare events in stochastic populations under bursty reproduction

NASA Astrophysics Data System (ADS)

Be'er, Shay; Assaf, Michael

2016-11-01

Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise—uncertainty in the step size of the reaction—on the dynamics of stochastic populations. This was done by investigating the effect of bursty influx on the switching dynamics of stochastic populations. Here we extend this formalism to account for bursty reproduction processes, and improve the accuracy of the formalism to include subleading-order corrections. Bursty reproduction appears in various contexts, where notable examples include bursty viral production from infected cells, and reproduction of mammals involving varying number of offspring. The main question we quantitatively address is how bursty reproduction affects the overall fate of the population. We consider two complementary scenarios: population extinction and population survival; in the former a population gets extinct after maintaining a long-lived metastable state, whereas in the latter a population proliferates despite undergoing a deterministic drift towards extinction. In both models reproduction occurs in bursts, sampled from an arbitrary distribution. Using the WKB approach, we show in the extinction problem that bursty reproduction broadens the quasi-stationary distribution of population sizes in the metastable state, which results in a drastic reduction of the mean time to extinction compared to the non-bursty case. In the survival problem, it is shown that bursty reproduction drastically increases the survival probability of the population. Close to the bifurcation limit our analytical results simplify considerably and are shown to depend solely on the mean and variance of the burst-size distribution. Our formalism is demonstrated on several realistic distributions which all compare well with numerical Monte-Carlo simulations.

On the number of different dynamics in Boolean networks with deterministic update schedules.

PubMed

Aracena, J; Demongeot, J; Fanchon, E; Montalva, M

2013-04-01

Deterministic Boolean networks are a type of discrete dynamical systems widely used in the modeling of genetic networks. The dynamics of such systems is characterized by the local activation functions and the update schedule, i.e., the order in which the nodes are updated. In this paper, we address the problem of knowing the different dynamics of a Boolean network when the update schedule is changed. We begin by proving that the problem of the existence of a pair of update schedules with different dynamics is NP-complete. However, we show that certain structural properties of the interaction diagraph are sufficient for guaranteeing distinct dynamics of a network. In [1] the authors define equivalence classes which have the property that all the update schedules of a given class yield the same dynamics. In order to determine the dynamics associated to a network, we develop an algorithm to efficiently enumerate the above equivalence classes by selecting a representative update schedule for each class with a minimum number of blocks. Finally, we run this algorithm on the well known Arabidopsis thaliana network to determine the full spectrum of its different dynamics. Copyright © 2013 Elsevier Inc. All rights reserved.

Uniqueness of Nash equilibrium in vaccination games.

PubMed

Bai, Fan

2016-12-01

One crucial condition for the uniqueness of Nash equilibrium set in vaccination games is that the attack ratio monotonically decreases as the vaccine coverage level increasing. We consider several deterministic vaccination models in homogeneous mixing population and in heterogeneous mixing population. Based on the final size relations obtained from the deterministic epidemic models, we prove that the attack ratios can be expressed in terms of the vaccine coverage levels, and also prove that the attack ratios are decreasing functions of vaccine coverage levels. Some thresholds are presented, which depend on the vaccine efficacy. It is proved that for vaccination games in homogeneous mixing population, there is a unique Nash equilibrium for each game.

Deterministic chaos in an ytterbium-doped mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Mélo, Lucas B. A.; Palacios, Guillermo F. R.; Carelli, Pedro V.; Acioli, Lúcio H.; Rios Leite, José R.; de Miranda, Marcio H. G.

2018-05-01

We experimentally study the nonlinear dynamics of a femtosecond ytterbium doped mode-locked fiber laser. With the laser operating in the pulsed regime a route to chaos is presented, starting from stable mode-locking, period two, period four, chaos and period three regimes. Return maps and bifurcation diagrams were extracted from time series for each regime. The analysis of the time series with the laser operating in the quasi mode-locked regime presents deterministic chaos described by an unidimensional Rossler map. A positive Lyapunov exponent $\\lambda = 0.14$ confirms the deterministic chaos of the system. We suggest an explanation about the observed map by relating gain saturation and intra-cavity loss.

Ada programming guidelines for deterministic storage management

NASA Technical Reports Server (NTRS)

Auty, David

1988-01-01

Previous reports have established that a program can be written in the Ada language such that the program's storage management requirements are determinable prior to its execution. Specific guidelines for ensuring such deterministic usage of Ada dynamic storage requirements are described. Because requirements may vary from one application to another, guidelines are presented in a most-restrictive to least-restrictive fashion to allow the reader to match appropriate restrictions to the particular application area under investigation.

Thermal treatment of the minority game

NASA Astrophysics Data System (ADS)

Burgos, E.; Ceva, Horacio; Perazzo, R. P.

2002-03-01

We study a cost function for the aggregate behavior of all the agents involved in the minority game (MG) or the bar attendance model (BAM). The cost function allows us to define a deterministic, synchronous dynamic that yields results that have the main relevant features than those of the probabilistic, sequential dynamics used for the MG or the BAM. We define a temperature through a Langevin approach in terms of the fluctuations of the average attendance. We prove that the cost function is an extensive quantity that can play the role of an internal energy of the many-agent system while the temperature so defined is an intensive parameter. We compare the results of the thermal perturbation to the deterministic dynamics and prove that they agree with those obtained with the MG or BAM in the limit of very low temperature.

Thermal treatment of the minority game.

PubMed

Burgos, E; Ceva, Horacio; Perazzo, R P J

2002-03-01

We study a cost function for the aggregate behavior of all the agents involved in the minority game (MG) or the bar attendance model (BAM). The cost function allows us to define a deterministic, synchronous dynamic that yields results that have the main relevant features than those of the probabilistic, sequential dynamics used for the MG or the BAM. We define a temperature through a Langevin approach in terms of the fluctuations of the average attendance. We prove that the cost function is an extensive quantity that can play the role of an internal energy of the many-agent system while the temperature so defined is an intensive parameter. We compare the results of the thermal perturbation to the deterministic dynamics and prove that they agree with those obtained with the MG or BAM in the limit of very low temperature.

Characterizing the dynamics of rubella relative to measles: the role of stochasticity

PubMed Central

Rozhnova, Ganna; Metcalf, C. Jessica E.; Grenfell, Bryan T.

2013-01-01

Rubella is a completely immunizing and mild infection in children. Understanding its behaviour is of considerable public health importance because of congenital rubella syndrome, which results from infection with rubella during early pregnancy and may entail a variety of birth defects. The recurrent dynamics of rubella are relatively poorly resolved, and appear to show considerable diversity globally. Here, we investigate the behaviour of a stochastic seasonally forced susceptible–infected–recovered model to characterize the determinants of these dynamics and illustrate patterns by comparison with measles. We perform a systematic analysis of spectra of stochastic fluctuations around stable attractors of the corresponding deterministic model and compare them with spectra from full stochastic simulations in large populations. This approach allows us to quantify the effects of demographic stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the recurrent patterns exhibited by these diseases. We discuss the implications of our findings in the context of vaccination and changing birth rates as well as the persistence of these two childhood infections. PMID:24026472

Improving Deterministic Reserve Requirements for Security Constrained Unit Commitment and Scheduling Problems in Power Systems

NASA Astrophysics Data System (ADS)

Wang, Fengyu

Traditional deterministic reserve requirements rely on ad-hoc, rule of thumb methods to determine adequate reserve in order to ensure a reliable unit commitment. Since congestion and uncertainties exist in the system, both the quantity and the location of reserves are essential to ensure system reliability and market efficiency. The modeling of operating reserves in the existing deterministic reserve requirements acquire the operating reserves on a zonal basis and do not fully capture the impact of congestion. The purpose of a reserve zone is to ensure that operating reserves are spread across the network. Operating reserves are shared inside each reserve zone, but intra-zonal congestion may block the deliverability of operating reserves within a zone. Thus, improving reserve policies such as reserve zones may improve the location and deliverability of reserve. As more non-dispatchable renewable resources are integrated into the grid, it will become increasingly difficult to predict the transfer capabilities and the network congestion. At the same time, renewable resources require operators to acquire more operating reserves. With existing deterministic reserve requirements unable to ensure optimal reserve locations, the importance of reserve location and reserve deliverability will increase. While stochastic programming can be used to determine reserve by explicitly modelling uncertainties, there are still scalability as well as pricing issues. Therefore, new methods to improve existing deterministic reserve requirements are desired. One key barrier of improving existing deterministic reserve requirements is its potential market impacts. A metric, quality of service, is proposed in this thesis to evaluate the price signal and market impacts of proposed hourly reserve zones. Three main goals of this thesis are: 1) to develop a theoretical and mathematical model to better locate reserve while maintaining the deterministic unit commitment and economic dispatch structure, especially with the consideration of renewables, 2) to develop a market settlement scheme of proposed dynamic reserve policies such that the market efficiency is improved, 3) to evaluate the market impacts and price signal of the proposed dynamic reserve policies.

Deterministic Factors Overwhelm Stochastic Environmental Fluctuations as Drivers of Jellyfish Outbreaks.

PubMed

Benedetti-Cecchi, Lisandro; Canepa, Antonio; Fuentes, Veronica; Tamburello, Laura; Purcell, Jennifer E; Piraino, Stefano; Roberts, Jason; Boero, Ferdinando; Halpin, Patrick

2015-01-01

Jellyfish outbreaks are increasingly viewed as a deterministic response to escalating levels of environmental degradation and climate extremes. However, a comprehensive understanding of the influence of deterministic drivers and stochastic environmental variations favouring population renewal processes has remained elusive. This study quantifies the deterministic and stochastic components of environmental change that lead to outbreaks of the jellyfish Pelagia noctiluca in the Mediterranen Sea. Using data of jellyfish abundance collected at 241 sites along the Catalan coast from 2007 to 2010 we: (1) tested hypotheses about the influence of time-varying and spatial predictors of jellyfish outbreaks; (2) evaluated the relative importance of stochastic vs. deterministic forcing of outbreaks through the environmental bootstrap method; and (3) quantified return times of extreme events. Outbreaks were common in May and June and less likely in other summer months, which resulted in a negative relationship between outbreaks and SST. Cross- and along-shore advection by geostrophic flow were important concentrating forces of jellyfish, but most outbreaks occurred in the proximity of two canyons in the northern part of the study area. This result supported the recent hypothesis that canyons can funnel P. noctiluca blooms towards shore during upwelling. This can be a general, yet unappreciated mechanism leading to outbreaks of holoplanktonic jellyfish species. The environmental bootstrap indicated that stochastic environmental fluctuations have negligible effects on return times of outbreaks. Our analysis emphasized the importance of deterministic processes leading to jellyfish outbreaks compared to the stochastic component of environmental variation. A better understanding of how environmental drivers affect demographic and population processes in jellyfish species will increase the ability to anticipate jellyfish outbreaks in the future.

3D Dynamic Rupture Simulations along Dipping Faults, with a focus on the Wasatch Fault Zone, Utah

NASA Astrophysics Data System (ADS)

Withers, K.; Moschetti, M. P.

2017-12-01

We study dynamic rupture and ground motion from dip-slip faults in regions that have high-seismic hazard, such as the Wasatch fault zone, Utah. Previous numerical simulations have modeled deterministic ground motion along segments of this fault in the heavily populated regions near Salt Lake City but were restricted to low frequencies ( 1 Hz). We seek to better understand the rupture process and assess broadband ground motions and variability from the Wasatch Fault Zone by extending deterministic ground motion prediction to higher frequencies (up to 5 Hz). We perform simulations along a dipping normal fault (40 x 20 km along strike and width, respectively) with characteristics derived from geologic observations to generate a suite of ruptures > Mw 6.5. This approach utilizes dynamic simulations (fully physics-based models, where the initial stress drop and friction law are imposed) using a summation by parts (SBP) method. The simulations include rough-fault topography following a self-similar fractal distribution (over length scales from 100 m to the size of the fault) in addition to off-fault plasticity. Energy losses from heat and other mechanisms, modeled as anelastic attenuation, are also included, as well as free-surface topography, which can significantly affect ground motion patterns. We compare the effect of material structure and both rate and state and slip-weakening friction laws have on rupture propagation. The simulations show reduced slip and moment release in the near surface with the inclusion of plasticity, better agreeing with observations of shallow slip deficit. Long-wavelength fault geometry imparts a non-uniform stress distribution along both dip and strike, influencing the preferred rupture direction and hypocenter location, potentially important for seismic hazard estimation.

Taking chances and making mistakes: non-genetic phenotypic heterogeneity and its consequences for surviving in dynamic environments

PubMed Central

van Boxtel, Coco; van Heerden, Johan H.; Nordholt, Niclas; Schmidt, Phillipp

2017-01-01

Natural selection has shaped the strategies for survival and growth of microorganisms. The success of microorganisms depends not only on slow evolutionary tuning but also on the ability to adapt to unpredictable changes in their environment. In principle, adaptive strategies range from purely deterministic mechanisms to those that exploit the randomness intrinsic to many cellular and molecular processes. Depending on the environment and selective pressures, particular strategies can lie somewhere along this continuum. In recent years, non-genetic cell-to-cell differences have received a lot of attention, not least because of their potential impact on the ability of microbial populations to survive in dynamic environments. Using several examples, we describe the origins of spontaneous and induced mechanisms of phenotypic adaptation. We identify some of the commonalities of these examples and consider the potential role of chance and constraints in microbial phenotypic adaptation. PMID:28701503

A data-driven model for influenza transmission incorporating media effects.

PubMed

Mitchell, Lewis; Ross, Joshua V

2016-10-01

Numerous studies have attempted to model the effect of mass media on the transmission of diseases such as influenza; however, quantitative data on media engagement has until recently been difficult to obtain. With the recent explosion of 'big data' coming from online social media and the like, large volumes of data on a population's engagement with mass media during an epidemic are becoming available to researchers. In this study, we combine an online dataset comprising millions of shared messages relating to influenza with traditional surveillance data on flu activity to suggest a functional form for the relationship between the two. Using this data, we present a simple deterministic model for influenza dynamics incorporating media effects, and show that such a model helps explain the dynamics of historical influenza outbreaks. Furthermore, through model selection we show that the proposed media function fits historical data better than other media functions proposed in earlier studies.

Epidemic patch models applied to pandemic influenza: contact matrix, stochasticity, robustness of predictions.

PubMed

Lunelli, Antonella; Pugliese, Andrea; Rizzo, Caterina

2009-07-01

Due to the recent emergence of H5N1 virus, the modelling of pandemic influenza has become a relevant issue. Here we present an SEIR model formulated to simulate a possible outbreak in Italy, analysing its structure and, more generally, the effect of including specific details into a model. These details regard population heterogeneities, such as age and spatial distribution, as well as stochasticity, that regulates the epidemic dynamics when the number of infectives is low. We discuss and motivate the specific modelling choices made when building the model and investigate how the model details influence the predicted dynamics. Our analysis may help in deciding which elements of complexity are worth including in the design of a deterministic model for pandemic influenza, in a balance between, on the one hand, keeping the model computationally efficient and the number of parameters low and, on the other hand, maintaining the necessary realistic features.

Assortative mating without assortative preference

PubMed Central

Xie, Yu; Cheng, Siwei; Zhou, Xiang

2015-01-01

Assortative mating—marriage of a man and a woman with similar social characteristics—is a commonly observed phenomenon. In the existing literature in both sociology and economics, this phenomenon has mainly been attributed to individuals’ conscious preferences for assortative mating. In this paper, we show that patterns of assortative mating may arise from another structural source even if individuals do not have assortative preferences or possess complementary attributes: dynamic processes of marriages in a closed system. For a given cohort of youth in a finite population, as the percentage of married persons increases, unmarried persons who newly enter marriage are systematically different from those who married earlier, giving rise to the phenomenon of assortative mating. We use microsimulation methods to illustrate this dynamic process, using first the conventional deterministic Gale–Shapley model, then a probabilistic Gale–Shapley model, and then two versions of the encounter mating model. PMID:25918366

Use of recurrence plots in the analysis of pupil diameter dynamics in narcoleptics

NASA Astrophysics Data System (ADS)

Keegan, Andrew P.; Zbilut, J. P.; Merritt, S. L.; Mercer, P. J.

1993-11-01

Recurrence plots were used to evaluate pupil dynamics of subjects with narcolepsy. Preliminary data indicate that this nonlinear method of analyses may be more useful in revealing underlying deterministic differences than traditional methods like FFT and counting statistics.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Health safety nets can break cycles of poverty and disease: a stochastic ecological model

PubMed Central

Pluciński, Mateusz M.; Ngonghala, Calistus N.; Bonds, Matthew H.

2011-01-01

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a ‘safety net’, defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium. PMID:21593026

Bayesian deterministic decision making: a normative account of the operant matching law and heavy-tailed reward history dependency of choices.

PubMed

Saito, Hiroshi; Katahira, Kentaro; Okanoya, Kazuo; Okada, Masato

2014-01-01

The decision making behaviors of humans and animals adapt and then satisfy an "operant matching law" in certain type of tasks. This was first pointed out by Herrnstein in his foraging experiments on pigeons. The matching law has been one landmark for elucidating the underlying processes of decision making and its learning in the brain. An interesting question is whether decisions are made deterministically or probabilistically. Conventional learning models of the matching law are based on the latter idea; they assume that subjects learn choice probabilities of respective alternatives and decide stochastically with the probabilities. However, it is unknown whether the matching law can be accounted for by a deterministic strategy or not. To answer this question, we propose several deterministic Bayesian decision making models that have certain incorrect beliefs about an environment. We claim that a simple model produces behavior satisfying the matching law in static settings of a foraging task but not in dynamic settings. We found that the model that has a belief that the environment is volatile works well in the dynamic foraging task and exhibits undermatching, which is a slight deviation from the matching law observed in many experiments. This model also demonstrates the double-exponential reward history dependency of a choice and a heavier-tailed run-length distribution, as has recently been reported in experiments on monkeys.

Chaos and crises in a model for cooperative hunting: a symbolic dynamics approach.

PubMed

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2009-12-01

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K,C(0)) and (K,sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K(c) decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; MacLaurin, James

2018-06-01

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ɛ-1 . That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-C a /ɛ ) .

Asteroids - the modern challenge of celestial dynamics

NASA Astrophysics Data System (ADS)

Dikova, Smiliana

2002-11-01

Among the most powerful statements in Science are those that mark absolute limits to knowledge. For example, Relativity and Quantum Theory touched the limits of speed and accuracy. Deterministic Chaos - the new scientific paradigma of our days, also falls in this class theories. Chaos means complexity in space and unpredictability in time. It shows the limit of our basic counting system and leads to a limited predictability of the long time dynamical evolution. Perhaps for that reason, in 1986 Sir James Lighthill remarked for all physicists: "We collectively wish to apologize for having misled the general educated public by spreading ideas about the determinism of systems satisfying Newton's laws of motion that, after 1960, were proved incorrect." Our main thesis is that Asteroid Dynamics is the arena where the drama Chaos versus predictability is initiated and developed. The aim of the present research is to show the way in which Deterministic Chaos restricts the long term dynamical predictability of asteroid motions.

Hardware-efficient Bell state preparation using Quantum Zeno Dynamics in superconducting circuits

NASA Astrophysics Data System (ADS)

Flurin, Emmanuel; Blok, Machiel; Hacohen-Gourgy, Shay; Martin, Leigh S.; Livingston, William P.; Dove, Allison; Siddiqi, Irfan

By preforming a continuous joint measurement on a two qubit system, we restrict the qubit evolution to a chosen subspace of the total Hilbert space. This extension of the quantum Zeno effect, called Quantum Zeno Dynamics, has already been explored in various physical systems such as superconducting cavities, single rydberg atoms, atomic ensembles and Bose Einstein condensates. In this experiment, two superconducting qubits are strongly dispersively coupled to a high-Q cavity (χ >> κ) allowing for the doubly excited state | 11 〉 to be selectively monitored. The Quantum Zeno Dynamics in the complementary subspace enables us to coherently prepare a Bell state. As opposed to dissipation engineering schemes, we emphasize that our protocol is deterministic, does not rely direct coupling between qubits and functions only using single qubit controls and cavity readout. Such Quantum Zeno Dynamics can be generalized to larger Hilbert space enabling deterministic generation of many-body entangled states, and thus realizes a decoherence-free subspace allowing alternative noise-protection schemes.

Anomalous finite-size effects in the Battle of the Sexes

NASA Astrophysics Data System (ADS)

Cremer, J.; Reichenbach, T.; Frey, E.

2008-06-01

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.

How to reach linguistic consensus: a proof of convergence for the naming game.

PubMed

De Vylder, Bart; Tuyls, Karl

2006-10-21

In this paper we introduce a mathematical model of naming games. Naming games have been widely used within research on the origins and evolution of language. Despite the many interesting empirical results these studies have produced, most of this research lacks a formal elucidating theory. In this paper we show how a population of agents can reach linguistic consensus, i.e. learn to use one common language to communicate with one another. Our approach differs from existing formal work in two important ways: one, we relax the too strong assumption that an agent samples infinitely often during each time interval. This assumption is usually made to guarantee convergence of an empirical learning process to a deterministic dynamical system. Two, we provide a proof that under these new realistic conditions, our model converges to a common language for the entire population of agents. Finally the model is experimentally validated.

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals.

PubMed

Frasca, Mattia; Sharkey, Kieran J

2016-06-21

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

An Extended Deterministic Dendritic Cell Algorithm for Dynamic Job Shop Scheduling

NASA Astrophysics Data System (ADS)

Qiu, X. N.; Lau, H. Y. K.

The problem of job shop scheduling in a dynamic environment where random perturbation exists in the system is studied. In this paper, an extended deterministic Dendritic Cell Algorithm (dDCA) is proposed to solve such a dynamic Job Shop Scheduling Problem (JSSP) where unexpected events occurred randomly. This algorithm is designed based on dDCA and makes improvements by considering all types of signals and the magnitude of the output values. To evaluate this algorithm, ten benchmark problems are chosen and different kinds of disturbances are injected randomly. The results show that the algorithm performs competitively as it is capable of triggering the rescheduling process optimally with much less run time for deciding the rescheduling action. As such, the proposed algorithm is able to minimize the rescheduling times under the defined objective and to keep the scheduling process stable and efficient.

Mutual Information Rate and Bounds for It

PubMed Central

Baptista, Murilo S.; Rubinger, Rero M.; Viana, Emilson R.; Sartorelli, José C.; Parlitz, Ulrich; Grebogi, Celso

2012-01-01

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators. PMID:23112809

Self-Organized Dynamic Flocking Behavior from a Simple Deterministic Map

NASA Astrophysics Data System (ADS)

Krueger, Wesley

2007-10-01

Coherent motion exhibiting large-scale order, such as flocking, swarming, and schooling behavior in animals, can arise from simple rules applied to an initial random array of self-driven particles. We present a completely deterministic dynamic map that exhibits emergent, collective, complex motion for a group of particles. Each individual particle is driven with a constant speed in two dimensions adopting the average direction of a fixed set of non-spatially related partners. In addition, the particle changes direction by π as it reaches a circular boundary. The dynamical patterns arising from these rules range from simple circular-type convective motion to highly sophisticated, complex, collective behavior which can be easily interpreted as flocking, schooling, or swarming depending on the chosen parameters. We present the results as a series of short movies and we also explore possible order parameters and correlation functions capable of quantifying the resulting coherence.

Density Dependence and Growth Rate: Evolutionary Effects on Resistance Development to Bt (Bacillus thuringiensis).

PubMed

Martinez, Jeannette C; Caprio, Michael A; Friedenberg, Nicholas A

2018-02-09

It has long been recognized that pest population dynamics can affect the durability of a pesticide, but dose remains the primary component of insect resistance management (IRM). For transgenic pesticidal traits such as Bt (Bacillus thuringiensis Berliner (Bacillales: Bacillaceae)), dose (measured as the mortality of susceptibles caused by a toxin) is a relatively fixed characteristic and often falls below the standard definition of high dose. Hence, it is important to understand how pest population dynamics modify durability and what targets they present for IRM. We used a deterministic model of a generic arthropod pest to examine how timing and strength of density dependence interacted with population growth rate and Bt mortality to affect time to resistance. As in previous studies, durability typically reached a minimum at intermediate doses. However, high population growth rates could eliminate benefits of high dose. The timing of density dependence had a more subtle effect. If density dependence operated simultaneously with Bt mortality, durability was insensitive to its strengths. However, if density dependence was driven by postselection densities, decreasing its strength could increase durability. The strength of density dependence could affect durability of both single traits and pyramids, but its influence depended on the timing of density dependence and size of the refuge. Our findings suggest the utility of a broader definition of high dose, one that incorporates population-dynamic context. That maximum growth rates and timing and strength of interactions causing density dependent mortality can all affect durability, also highlights the need for ecologically integrated approaches to IRM research. © The Author(s) 2017. Published by Oxford University Press on behalf of Entomological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology

NASA Astrophysics Data System (ADS)

Dhamala, Mukeshwar; Lai, Ying-Cheng

1999-02-01

Transient chaos is a common phenomenon in nonlinear dynamics of many physical, biological, and engineering systems. In applications it is often desirable to maintain sustained chaos even in parameter regimes of transient chaos. We address how to sustain transient chaos in deterministic flows. We utilize a simple and practical method, based on extracting the fundamental dynamics from time series, to maintain chaos. The method can result in control of trajectories from almost all initial conditions in the original basin of the chaotic attractor from which transient chaos is created. We apply our method to three problems: (1) voltage collapse in electrical power systems, (2) species preservation in ecology, and (3) elimination of undesirable bursting behavior in a chemical reaction system.

Delayed-feedback chimera states: Forced multiclusters and stochastic resonance

NASA Astrophysics Data System (ADS)

Semenov, V.; Zakharova, A.; Maistrenko, Y.; Schöll, E.

2016-07-01

A nonlinear oscillator model with negative time-delayed feedback is studied numerically under external deterministic and stochastic forcing. It is found that in the unforced system complex partial synchronization patterns like chimera states as well as salt-and-pepper-like solitary states arise on the route from regular dynamics to spatio-temporal chaos. The control of the dynamics by external periodic forcing is demonstrated by numerical simulations. It is shown that one-cluster and multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. If a stochastic component is superimposed to the deterministic external forcing, chimera states can be induced in a way similar to stochastic resonance, they appear, therefore, in regimes where they do not exist without noise.

Deterministic chaos in entangled eigenstates

NASA Astrophysics Data System (ADS)

Schlegel, K. G.; Förster, S.

2008-05-01

We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.

Dynamic analysis of a stochastic rumor propagation model

NASA Astrophysics Data System (ADS)

Jia, Fangju; Lv, Guangying

2018-01-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.

Fault Detection for Nonlinear Process With Deterministic Disturbances: A Just-In-Time Learning Based Data Driven Method.

PubMed

Yin, Shen; Gao, Huijun; Qiu, Jianbin; Kaynak, Okyay

2017-11-01

Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.

Parallel and Preemptable Dynamically Dimensioned Search Algorithms for Single and Multi-objective Optimization in Water Resources

NASA Astrophysics Data System (ADS)

Tolson, B.; Matott, L. S.; Gaffoor, T. A.; Asadzadeh, M.; Shafii, M.; Pomorski, P.; Xu, X.; Jahanpour, M.; Razavi, S.; Haghnegahdar, A.; Craig, J. R.

2015-12-01

We introduce asynchronous parallel implementations of the Dynamically Dimensioned Search (DDS) family of algorithms including DDS, discrete DDS, PA-DDS and DDS-AU. These parallel algorithms are unique from most existing parallel optimization algorithms in the water resources field in that parallel DDS is asynchronous and does not require an entire population (set of candidate solutions) to be evaluated before generating and then sending a new candidate solution for evaluation. One key advance in this study is developing the first parallel PA-DDS multi-objective optimization algorithm. The other key advance is enhancing the computational efficiency of solving optimization problems (such as model calibration) by combining a parallel optimization algorithm with the deterministic model pre-emption concept. These two efficiency techniques can only be combined because of the asynchronous nature of parallel DDS. Model pre-emption functions to terminate simulation model runs early, prior to completely simulating the model calibration period for example, when intermediate results indicate the candidate solution is so poor that it will definitely have no influence on the generation of further candidate solutions. The computational savings of deterministic model preemption available in serial implementations of population-based algorithms (e.g., PSO) disappear in synchronous parallel implementations as these algorithms. In addition to the key advances above, we implement the algorithms across a range of computation platforms (Windows and Unix-based operating systems from multi-core desktops to a supercomputer system) and package these for future modellers within a model-independent calibration software package called Ostrich as well as MATLAB versions. Results across multiple platforms and multiple case studies (from 4 to 64 processors) demonstrate the vast improvement over serial DDS-based algorithms and highlight the important role model pre-emption plays in the performance of parallel, pre-emptable DDS algorithms. Case studies include single- and multiple-objective optimization problems in water resources model calibration and in many cases linear or near linear speedups are observed.

A Markov model for the temporal dynamics of balanced random networks of finite size

PubMed Central

Lagzi, Fereshteh; Rotter, Stefan

2014-01-01

The balanced state of recurrent networks of excitatory and inhibitory spiking neurons is characterized by fluctuations of population activity about an attractive fixed point. Numerical simulations show that these dynamics are essentially nonlinear, and the intrinsic noise (self-generated fluctuations) in networks of finite size is state-dependent. Therefore, stochastic differential equations with additive noise of fixed amplitude cannot provide an adequate description of the stochastic dynamics. The noise model should, rather, result from a self-consistent description of the network dynamics. Here, we consider a two-state Markovian neuron model, where spikes correspond to transitions from the active state to the refractory state. Excitatory and inhibitory input to this neuron affects the transition rates between the two states. The corresponding nonlinear dependencies can be identified directly from numerical simulations of networks of leaky integrate-and-fire neurons, discretized at a time resolution in the sub-millisecond range. Deterministic mean-field equations, and a noise component that depends on the dynamic state of the network, are obtained from this model. The resulting stochastic model reflects the behavior observed in numerical simulations quite well, irrespective of the size of the network. In particular, a strong temporal correlation between the two populations, a hallmark of the balanced state in random recurrent networks, are well represented by our model. Numerical simulations of such networks show that a log-normal distribution of short-term spike counts is a property of balanced random networks with fixed in-degree that has not been considered before, and our model shares this statistical property. Furthermore, the reconstruction of the flow from simulated time series suggests that the mean-field dynamics of finite-size networks are essentially of Wilson-Cowan type. We expect that this novel nonlinear stochastic model of the interaction between neuronal populations also opens new doors to analyze the joint dynamics of multiple interacting networks. PMID:25520644

Creating a stage-based deterministic PVA model - the western prairie fringed orchid [Exercise 12

Treesearch

Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke

2003-01-01

Contemporary efforts to conserve populations and species often employ population viability analysis (PVA), a specific application of population modeling that estimates the effects of environmental and demographic processes on population growth rates. These models can also be used to estimate probabilities that a population will fall below a certain level. This...

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

Non-Lipschitzian dynamics for neural net modelling

NASA Technical Reports Server (NTRS)

Zak, Michail

1989-01-01

Failure of the Lipschitz condition in unstable equilibrium points of dynamical systems leads to a multiple-choice response to an initial deterministic input. The evolution of such systems is characterized by a special type of unpredictability measured by unbounded Liapunov exponents. Possible relation of these systems to future neural networks is discussed.

Measures of thermodynamic irreversibility in deterministic and stochastic dynamics

NASA Astrophysics Data System (ADS)

Ford, Ian J.

2015-07-01

It is generally observed that if a dynamical system is sufficiently complex, then as time progresses it will share out energy and other properties amongst its component parts to eliminate any initial imbalances, retaining only fluctuations. This is known as energy dissipation and it is closely associated with the concept of thermodynamic irreversibility, measured by the increase in entropy according to the second law. It is of interest to quantify such behaviour from a dynamical rather than a thermodynamic perspective and to this end stochastic entropy production and the time-integrated dissipation function have been introduced as analogous measures of irreversibility, principally for stochastic and deterministic dynamics, respectively. We seek to compare these measures. First we modify the dissipation function to allow it to measure irreversibility in situations where the initial probability density function (pdf) of the system is asymmetric as well as symmetric in velocity. We propose that it tests for failure of what we call the obversibility of the system, to be contrasted with reversibility, the failure of which is assessed by stochastic entropy production. We note that the essential difference between stochastic entropy production and the time-integrated modified dissipation function lies in the sequence of procedures undertaken in the associated tests of irreversibility. We argue that an assumed symmetry of the initial pdf with respect to velocity inversion (within a framework of deterministic dynamics) can be incompatible with the Past Hypothesis, according to which there should be a statistical distinction between the behaviour of certain properties of an isolated system as it evolves into the far future and the remote past. Imposing symmetry on a velocity distribution is acceptable for many applications of statistical physics, but can introduce difficulties when discussing irreversible behaviour.

Robust planning of dynamic wireless charging infrastructure for battery electric buses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Zhaocai; Song, Ziqi

Battery electric buses with zero tailpipe emissions have great potential in improving environmental sustainability and livability of urban areas. However, the problems of high cost and limited range associated with on-board batteries have substantially limited the popularity of battery electric buses. The technology of dynamic wireless power transfer (DWPT), which provides bus operators with the ability to charge buses while in motion, may be able to effectively alleviate the drawbacks of electric buses. In this paper, we address the problem of simultaneously selecting the optimal location of the DWPT facilities and designing the optimal battery sizes of electric buses formore » a DWPT electric bus system. The problem is first constructed as a deterministic model in which the uncertainty of energy consumption and travel time of electric buses is neglected. The methodology of robust optimization (RO) is then adopted to address the uncertainty of energy consumption and travel time. The affinely adjustable robust counterpart (AARC) of the deterministic model is developed, and its equivalent tractable mathematical programming is derived. Both the deterministic model and the robust model are demonstrated with a real-world bus system. The results of our study demonstrate that the proposed deterministic model can effectively determine the allocation of DWPT facilities and the battery sizes of electric buses for a DWPT electric bus system; and the robust model can further provide optimal designs that are robust against the uncertainty of energy consumption and travel time for electric buses.« less

Robust planning of dynamic wireless charging infrastructure for battery electric buses

DOE PAGES

Liu, Zhaocai; Song, Ziqi

2017-10-01

Battery electric buses with zero tailpipe emissions have great potential in improving environmental sustainability and livability of urban areas. However, the problems of high cost and limited range associated with on-board batteries have substantially limited the popularity of battery electric buses. The technology of dynamic wireless power transfer (DWPT), which provides bus operators with the ability to charge buses while in motion, may be able to effectively alleviate the drawbacks of electric buses. In this paper, we address the problem of simultaneously selecting the optimal location of the DWPT facilities and designing the optimal battery sizes of electric buses formore » a DWPT electric bus system. The problem is first constructed as a deterministic model in which the uncertainty of energy consumption and travel time of electric buses is neglected. The methodology of robust optimization (RO) is then adopted to address the uncertainty of energy consumption and travel time. The affinely adjustable robust counterpart (AARC) of the deterministic model is developed, and its equivalent tractable mathematical programming is derived. Both the deterministic model and the robust model are demonstrated with a real-world bus system. The results of our study demonstrate that the proposed deterministic model can effectively determine the allocation of DWPT facilities and the battery sizes of electric buses for a DWPT electric bus system; and the robust model can further provide optimal designs that are robust against the uncertainty of energy consumption and travel time for electric buses.« less

A parallel implementation of an off-lattice individual-based model of multicellular populations

NASA Astrophysics Data System (ADS)

Harvey, Daniel G.; Fletcher, Alexander G.; Osborne, James M.; Pitt-Francis, Joe

2015-07-01

As computational models of multicellular populations include ever more detailed descriptions of biophysical and biochemical processes, the computational cost of simulating such models limits their ability to generate novel scientific hypotheses and testable predictions. While developments in microchip technology continue to increase the power of individual processors, parallel computing offers an immediate increase in available processing power. To make full use of parallel computing technology, it is necessary to develop specialised algorithms. To this end, we present a parallel algorithm for a class of off-lattice individual-based models of multicellular populations. The algorithm divides the spatial domain between computing processes and comprises communication routines that ensure the model is correctly simulated on multiple processors. The parallel algorithm is shown to accurately reproduce the results of a deterministic simulation performed using a pre-existing serial implementation. We test the scaling of computation time, memory use and load balancing as more processes are used to simulate a cell population of fixed size. We find approximate linear scaling of both speed-up and memory consumption on up to 32 processor cores. Dynamic load balancing is shown to provide speed-up for non-regular spatial distributions of cells in the case of a growing population.

PROJECTED POPULATION-LEVEL EFFECTS OF THIOBENCARB EXPOSURE ON THE MYSID, AMERICAMYSIS BAHIA, AND EXTINCTION PROBABILITY IN A CONCENTRATION-DECAY EXPOSURE SYSTEM

EPA Science Inventory

Population-level effects of the mysid, Americamysis bahia, exposed to varying thiobencarb concentrations were estimated using stage-structured matrix models. A deterministic density-independent matrix model estimated the decrease in population growth rate, l, with increas...

Chaos and unpredictability in evolution of cooperation in continuous time

NASA Astrophysics Data System (ADS)

You, Taekho; Kwon, Minji; Jo, Hang-Hyun; Jung, Woo-Sung; Baek, Seung Ki

2017-12-01

Cooperators benefit others with paying costs. Evolution of cooperation crucially depends on the cost-benefit ratio of cooperation, denoted as c . In this work, we investigate the infinitely repeated prisoner's dilemma for various values of c with four of the representative memory-one strategies, i.e., unconditional cooperation, unconditional defection, tit-for-tat, and win-stay-lose-shift. We consider replicator dynamics which deterministically describes how the fraction of each strategy evolves over time in an infinite-sized well-mixed population in the presence of implementation error and mutation among the four strategies. Our finding is that this three-dimensional continuous-time dynamics exhibits chaos through a bifurcation sequence similar to that of a logistic map as c varies. If mutation occurs with rate μ ≪1 , the position of the bifurcation sequence on the c axis is numerically found to scale as μ0.1, and such sensitivity to μ suggests that mutation may have nonperturbative effects on evolutionary paths. It demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics.

Protein Aggregation/Folding: The Role of Deterministic Singularities of Sequence Hydrophobicity as Determined by Nonlinear Signal Analysis of Acylphosphatase and Aβ(1–40)

PubMed Central

Zbilut, Joseph P.; Colosimo, Alfredo; Conti, Filippo; Colafranceschi, Mauro; Manetti, Cesare; Valerio, MariaCristina; Webber, Charles L.; Giuliani, Alessandro

2003-01-01

The problem of protein folding vs. aggregation was investigated in acylphosphatase and the amyloid protein Aβ(1–40) by means of nonlinear signal analysis of their chain hydrophobicity. Numerical descriptors of recurrence patterns provided the basis for statistical evaluation of folding/aggregation distinctive features. Static and dynamic approaches were used to elucidate conditions coincident with folding vs. aggregation using comparisons with known protein secondary structure classifications, site-directed mutagenesis studies of acylphosphatase, and molecular dynamics simulations of amyloid protein, Aβ(1–40). The results suggest that a feature derived from principal component space characterized by the smoothness of singular, deterministic hydrophobicity patches plays a significant role in the conditions governing protein aggregation. PMID:14645049

Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model.

PubMed

Cairoli, Andrea; Piovani, Duccio; Jensen, Henrik Jeldtoft

2014-12-31

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.

Impact of refining the assessment of dietary exposure to cadmium in the European adult population.

PubMed

Ferrari, Pietro; Arcella, Davide; Heraud, Fanny; Cappé, Stefano; Fabiansson, Stefan

2013-01-01

Exposure assessment constitutes an important step in any risk assessment of potentially harmful substances present in food. The European Food Safety Authority (EFSA) first assessed dietary exposure to cadmium in Europe using a deterministic framework, resulting in mean values of exposure in the range of health-based guidance values. Since then, the characterisation of foods has been refined to better match occurrence and consumption data, and a new strategy to handle left-censoring in occurrence data was devised. A probabilistic assessment was performed and compared with deterministic estimates, using occurrence values at the European level and consumption data from 14 national dietary surveys. Mean estimates in the probabilistic assessment ranged from 1.38 (95% CI = 1.35-1.44) to 2.08 (1.99-2.23) µg kg⁻¹ bodyweight (bw) week⁻¹ across the different surveys, which were less than 10% lower than deterministic (middle bound) mean values that ranged from 1.50 to 2.20 µg kg⁻¹ bw week⁻¹. Probabilistic 95th percentile estimates of dietary exposure ranged from 2.65 (2.57-2.72) to 4.99 (4.62-5.38) µg kg⁻¹ bw week⁻¹, which were, with the exception of one survey, between 3% and 17% higher than middle-bound deterministic estimates. Overall, the proportion of subjects exceeding the tolerable weekly intake of 2.5 µg kg⁻¹ bw ranged from 14.8% (13.6-16.0%) to 31.2% (29.7-32.5%) according to the probabilistic assessment. The results of this work indicate that mean values of dietary exposure to cadmium in the European population were of similar magnitude using determinist or probabilistic assessments. For higher exposure levels, probabilistic estimates were almost consistently larger than deterministic counterparts, thus reflecting the impact of using the full distribution of occurrence values to determine exposure levels. It is considered prudent to use probabilistic methodology should exposure estimates be close to or exceeding health-based guidance values.

Genetic drift and selection in many-allele range expansions.

PubMed

Weinstein, Bryan T; Lavrentovich, Maxim O; Möbius, Wolfram; Murray, Andrew W; Nelson, David R

2017-12-01

We experimentally and numerically investigate the evolutionary dynamics of four competing strains of E. coli with differing expansion velocities in radially expanding colonies. We compare experimental measurements of the average fraction, correlation functions between strains, and the relative rates of genetic domain wall annihilations and coalescences to simulations modeling the population as a one-dimensional ring of annihilating and coalescing random walkers with deterministic biases due to selection. The simulations reveal that the evolutionary dynamics can be collapsed onto master curves governed by three essential parameters: (1) an expansion length beyond which selection dominates over genetic drift; (2) a characteristic angular correlation describing the size of genetic domains; and (3) a dimensionless constant quantifying the interplay between a colony's curvature at the frontier and its selection length scale. We measure these parameters with a new technique that precisely measures small selective differences between spatially competing strains and show that our simulations accurately predict the dynamics without additional fitting. Our results suggest that the random walk model can act as a useful predictive tool for describing the evolutionary dynamics of range expansions composed of an arbitrary number of genotypes with different fitnesses.

Invasive advance of an advantageous mutation: nucleation theory.

PubMed

O'Malley, Lauren; Basham, James; Yasi, Joseph A; Korniss, G; Allstadt, Andrew; Caraco, Thomas

2006-12-01

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions. To understand how individual-level processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. Nucleation theory discriminates between single-cluster and multi-cluster dynamics. A sufficiently low mutation rate, or a sufficiently small environment, generates single-cluster dynamics, an inherently stochastic process; a favorable mutation advances only if the invader cluster reaches a critical radius. For this mode of invasion, we identify the probability distribution of waiting times until the favored allele advances to competitive dominance, and we ask how the critical cluster size varies as propagation or mortality rates vary. Increasing the mutation rate or system size generates multi-cluster invasion, where spatial averaging produces nearly deterministic global dynamics. For this process, an analytical approximation from nucleation theory, called Avrami's Law, describes the time-dependent behavior of the genotype densities with remarkable accuracy.

Computer modeling of dynamic necking in bars

NASA Astrophysics Data System (ADS)

Partom, Yehuda; Lindenfeld, Avishay

2017-06-01

Necking of thin bodies (bars, plates, shells) is one form of strain localization in ductile materials that may lead to fracture. The phenomenon of necking has been studied extensively, initially for quasistatic loading and then also for dynamic loading. Nevertheless, many issues concerning necking are still unclear. Among these are: 1) is necking a random or deterministic process; 2) how does the specimen choose the final neck location; 3) to what extent do perturbations (material or geometrical) influence the neck forming process; and 4) how do various parameters (material, geometrical, loading) influence the neck forming process. Here we address these issues and others using computer simulations with a hydrocode. Among other things we find that: 1) neck formation is a deterministic process, and by changing one of the parameters influencing it monotonously, the final neck location moves monotonously as well; 2) the final neck location is sensitive to the radial velocity of the end boundaries, and as motion of these boundaries is not fully controlled in tests, this may be the reason why neck formation is sometimes regarded as a random process; and 3) neck formation is insensitive to small perturbations, which is probably why it is a deterministic process.

Spatial and temporal dynamics of fucoid populations (Ascophyllum nodosum and Fucus serratus): a comparison between central and range edge populations.

PubMed

Araújo, Rita M; Serrão, Ester A; Sousa-Pinto, Isabel; Åberg, Per

2014-01-01

Persistence of populations at range edges relies on local population dynamics and fitness, in the case of geographically isolated populations of species with low dispersal potential. Focusing on spatial variations in demography helps to predict the long-term capability for persistence of populations across the geographical range of species' distribution. The demography of two ecological and phylogenetically close macroalgal species with different life history characteristics was investigated by using stochastic, stage-based matrix models. Populations of Ascophyllum nodosum and Fucus serratus were sampled for up to 4 years at central locations in France and at their southern range limits in Portugal. The stochastic population growth rate (λ(s)) of A. nodosum was lower and more variable in central than in southern sites whilst for F. serratus this trend was reversed with λ(s) much lower and more variable in southern than in central populations. Individuals were larger in central than in southern populations for both species, which was reflected in the lower transition probabilities of individuals to larger size classes and higher probability of shrinkage in the southern populations. In both central and southern populations elasticity analysis (proportional sensitivity) of population growth rate showed that fertility elements had a small contribution to λ(s) that was more sensitive to changes in matrix transitions corresponding to survival. The highest elasticities were found for loop transitions in A. nodosum and for growth to larger size classes in F. serratus. Sensitivity analysis showed high selective pressure on individual growth for both species at both locations. The results of this study highlight the deterministic role of species-specific life-history traits in population demography across the geographical range of species. Additionally, this study demonstrates that individuals' life-transitions differ in vulnerability to environmental variability and shows the importance of vegetative compared to reproductive stages for the long-term persistence of populations.

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State.

PubMed

Lagzi, Fereshteh; Rotter, Stefan

2015-01-01

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the "within" versus "between" connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed "winnerless competition", which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State

PubMed Central

Lagzi, Fereshteh; Rotter, Stefan

2015-01-01

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks. PMID:26407178

Disentangling the stochastic behavior of complex time series

NASA Astrophysics Data System (ADS)

Anvari, Mehrnaz; Tabar, M. Reza Rahimi; Peinke, Joachim; Lehnertz, Klaus

2016-10-01

Complex systems involving a large number of degrees of freedom, generally exhibit non-stationary dynamics, which can result in either continuous or discontinuous sample paths of the corresponding time series. The latter sample paths may be caused by discontinuous events - or jumps - with some distributed amplitudes, and disentangling effects caused by such jumps from effects caused by normal diffusion processes is a main problem for a detailed understanding of stochastic dynamics of complex systems. Here we introduce a non-parametric method to address this general problem. By means of a stochastic dynamical jump-diffusion modelling, we separate deterministic drift terms from different stochastic behaviors, namely diffusive and jumpy ones, and show that all of the unknown functions and coefficients of this modelling can be derived directly from measured time series. We demonstrate appli- cability of our method to empirical observations by a data-driven inference of the deterministic drift term and of the diffusive and jumpy behavior in brain dynamics from ten epilepsy patients. Particularly these different stochastic behaviors provide extra information that can be regarded valuable for diagnostic purposes.

More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators?

PubMed Central

Palmer, T. N.

2014-01-01

This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. In this approach, the conventionally hard boundary between the dynamical core and the sub-grid parametrizations is blurred. This approach is motivated by the relatively shallow power-law spectrum for atmospheric energy on scales of hundreds of kilometres and less. It is first argued that, because of this, the closure schemes for weather and climate simulators should be based on stochastic–dynamic systems rather than deterministic formulae. Second, as high-wavenumber elements of the dynamical core will necessarily inherit this stochasticity during time integration, it is argued that the dynamical core will be significantly over-engineered if all computations, regardless of scale, are performed completely deterministically and if all variables are represented with maximum numerical precision (in practice using double-precision floating-point numbers). As the era of exascale computing is approached, an energy- and computationally efficient approach to cloud-resolved weather and climate simulation is described where determinism and numerical precision are focused on the largest scales only. PMID:24842038

More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators?

PubMed

Palmer, T N

2014-06-28

This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. In this approach, the conventionally hard boundary between the dynamical core and the sub-grid parametrizations is blurred. This approach is motivated by the relatively shallow power-law spectrum for atmospheric energy on scales of hundreds of kilometres and less. It is first argued that, because of this, the closure schemes for weather and climate simulators should be based on stochastic-dynamic systems rather than deterministic formulae. Second, as high-wavenumber elements of the dynamical core will necessarily inherit this stochasticity during time integration, it is argued that the dynamical core will be significantly over-engineered if all computations, regardless of scale, are performed completely deterministically and if all variables are represented with maximum numerical precision (in practice using double-precision floating-point numbers). As the era of exascale computing is approached, an energy- and computationally efficient approach to cloud-resolved weather and climate simulation is described where determinism and numerical precision are focused on the largest scales only.

Noise-induced transitions and shifts in a climate-vegetation feedback model.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-04-01

Motivated by the extremely important role of the Earth's vegetation dynamics in climate changes, we study the stochastic variability of a simple climate-vegetation system. In the case of deterministic dynamics, the system has one stable equilibrium and limit cycle or two stable equilibria corresponding to two opposite (cold and warm) climate-vegetation states. These states are divided by a separatrix going across a point of unstable equilibrium. Some possible stochastic scenarios caused by different externally induced natural and anthropogenic processes inherit properties of deterministic behaviour and drastically change the system dynamics. We demonstrate that the system transitions across its separatrix occur with increasing noise intensity. The climate-vegetation system therewith fluctuates, transits and localizes in the vicinity of its attractor. We show that this phenomenon occurs within some critical range of noise intensities. A noise-induced shift into the range of smaller global average temperatures corresponding to substantial oscillations of the Earth's vegetation cover is revealed. Our analysis demonstrates that the climate-vegetation interactions essentially contribute to climate dynamics and should be taken into account in more precise and complex models of climate variability.

Dispersal and individual quality in a long lived species

USGS Publications Warehouse

Cam, E.; Monnat, J.-Y.; Royle, J. Andrew

2004-01-01

The idea of differences in individual quality has been put forward in numerous long-term studies in long-lived species to explain differences in lifetime production among individuals. Despite the important role of individual heterogeneity in vital rates in demography, population dynamics and life history theory, the idea of 'individual quality' is elusive. It is sometimes assumed to be a static or dynamic individual characteristic. When considered as a dynamic trait, it is sometimes assumed to vary deterministically or stochastically, or to be confounded with the characteristics of the habitat. We addressed heterogeneity in reproductive performance among individuals established in higher-quality habitat in a long-lived seabird species. We used approaches to statistical inference based on individual random effects permitting quantification of heterogeneity in populations and assessment of individual variation from the population mean. We found evidence of heterogeneity in breeding probability, not success probability. We assessed the influence of dispersal on individual reproductive potential. Dispersal is likely to be destabilizing in species with high site and mate fidelity. We detected heterogeneity after dispersal, not before. Individuals may perform well regardless of quality before destabilization, including those that recruited in higher-quality habitat by chance, but only higher-quality individuals may be able to overcome the consequences of dispersal. Importantly, results differed when accounting for individual heterogeneity (an increase in mean breeding probability when individuals dispersed), or not (a decrease in mean breeding probability). In the latter case, the decrease in mean breeding probability may result from a substantial decrease in breeding probability in a few individuals and a slight increase in others. In other words, the pattern observed at the population mean level may not reflect what happens in the majority of individuals.

Quantitative analysis of random ameboid motion

NASA Astrophysics Data System (ADS)

Bödeker, H. U.; Beta, C.; Frank, T. D.; Bodenschatz, E.

2010-04-01

We quantify random migration of the social ameba Dictyostelium discoideum. We demonstrate that the statistics of cell motion can be described by an underlying Langevin-type stochastic differential equation. An analytic expression for the velocity distribution function is derived. The separation into deterministic and stochastic parts of the movement shows that the cells undergo a damped motion with multiplicative noise. Both contributions to the dynamics display a distinct response to external physiological stimuli. The deterministic component depends on the developmental state and ambient levels of signaling substances, while the stochastic part does not.

Diffusion in Deterministic Interacting Lattice Systems

NASA Astrophysics Data System (ADS)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

The threshold of a stochastic delayed SIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2016-11-01

In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

Stochastic assembly in a subtropical forest chronosequence: evidence from contrasting changes of species, phylogenetic and functional dissimilarity over succession.

PubMed

Mi, Xiangcheng; Swenson, Nathan G; Jia, Qi; Rao, Mide; Feng, Gang; Ren, Haibao; Bebber, Daniel P; Ma, Keping

2016-09-07

Deterministic and stochastic processes jointly determine the community dynamics of forest succession. However, it has been widely held in previous studies that deterministic processes dominate forest succession. Furthermore, inference of mechanisms for community assembly may be misleading if based on a single axis of diversity alone. In this study, we evaluated the relative roles of deterministic and stochastic processes along a disturbance gradient by integrating species, functional, and phylogenetic beta diversity in a subtropical forest chronosequence in Southeastern China. We found a general pattern of increasing species turnover, but little-to-no change in phylogenetic and functional turnover over succession at two spatial scales. Meanwhile, the phylogenetic and functional beta diversity were not significantly different from random expectation. This result suggested a dominance of stochastic assembly, contrary to the general expectation that deterministic processes dominate forest succession. On the other hand, we found significant interactions of environment and disturbance and limited evidence for significant deviations of phylogenetic or functional turnover from random expectations for different size classes. This result provided weak evidence of deterministic processes over succession. Stochastic assembly of forest succession suggests that post-disturbance restoration may be largely unpredictable and difficult to control in subtropical forests.

Gene surfing in expanding populations.

PubMed

Hallatschek, Oskar; Nelson, David R

2008-02-01

Large scale genomic surveys are partly motivated by the idea that the neutral genetic variation of a population may be used to reconstruct its migration history. However, our ability to trace back the colonization pathways of a species from their genetic footprints is limited by our understanding of the genetic consequences of a range expansion. Here, we study, by means of simulations and analytical methods, the neutral dynamics of gene frequencies in an asexual population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a "surfing" mechanism [Edmonds, C.A., Lillie, A.S., Cavalli-Sforza, L.L., 2004. Mutations arising in the wave front of an expanding population. Proc. Natl. Acad. Sci. 101, 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our stochastic simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in the presence of cooperation between individuals ("pushed waves") than when individuals proliferate independently ("pulled waves"), and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction-diffusion systems, that yields simple predictions for any deterministic population dynamics. Our analytical theory compares well with the simulation results for pushed waves, but is less accurate in the case of pulled waves when stochastic fluctuations in the tip of the wave are important.

Low-frequency fluctuations in vertical cavity lasers: Experiments versus Lang-Kobayashi dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torcini, Alessandro; Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via Sansone 1, 50019 Sesto Fiorentino; Barland, Stephane

2006-12-15

The limits of applicability of the Lang-Kobayashi (LK) model for a semiconductor laser with optical feedback are analyzed. The model equations, equipped with realistic values of the parameters, are investigated below the solitary laser threshold where low-frequency fluctuations (LFF's) are usually observed. The numerical findings are compared with experimental data obtained for the selected polarization mode from a vertical cavity surface emitting laser (VCSEL) subject to polarization selective external feedback. The comparison reveals the bounds within which the dynamics of the LK model can be considered as realistic. In particular, it clearly demonstrates that the deterministic LK model, for realisticmore » values of the linewidth enhancement factor {alpha}, reproduces the LFF's only as a transient dynamics towards one of the stationary modes with maximal gain. A reasonable reproduction of real data from VCSEL's can be obtained only by considering the noisy LK or alternatively deterministic LK model for extremely high {alpha} values.« less

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing; Walker, Paul D.

2017-02-01

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Comparing reactive and memory-one strategies of direct reciprocity

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Jeong, Hyeong-Chai; Hilbe, Christian; Nowak, Martin A.

2016-05-01

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player’s previous move, and memory-one strategies, which take into account the own and the co-player’s previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.

Scaling theory for the quasideterministic limit of continuous bifurcations.

PubMed

Kessler, David A; Shnerb, Nadav M

2012-05-01

Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when the number of particles N is large. Accordingly, it fails close to the extinction transition, when the amplitude of stochastic fluctuations is comparable with the size of the population. Here we present a general scaling theory of the transition regime for spatially extended systems. We demonstrate this through a detailed study of two fundamental models for out-of-equilibrium phase transitions: the Susceptible-Infected-Susceptible (SIS) that belongs to the directed percolation equivalence class and the Susceptible-Infected-Recovered (SIR) model belonging to the dynamic percolation class. Implementing the Ginzburg criteria we show that the width of the fluctuation-dominated region scales like N^{-κ}, where N is the number of individuals per site and κ=2/(d_{u}-d), d_{u} is the upper critical dimension. Other exponents that control the approach to the deterministic limit are shown to be calculable once κ is known. The theory is extended to include the corrections to the front velocity above the transition. It is supported by the results of extensive numerical simulations for systems of various dimensionalities.

How similar can co-occurring species be in the presence of competition and ecological drift?

PubMed

Capitán, José A; Cuenda, Sara; Alonso, David

2015-09-06

If two species live on a single resource, the one with a slight advantage will out-compete the other: complete competitors cannot coexist. This is known as the competitive exclusion principle. If no extinction occurs, it is because evolutionary adaptation to slightly different niches takes place. Therefore, it is widely accepted that ecological communities are assembled by evolutionary differentiation and progressive adaptation of species to different niches. However, some ecologists have recently challenged this classic paradigm highlighting the importance of chance and stochasticity. Using a synthetic framework for community dynamics, here we show that, while deterministic descriptors predict coexistence, species similarity is limited in a more restrictive way in the presence of stochasticity. We analyse the stochastic extinction phenomenon, showing that extinction occurs as competitive overlap increases above a certain threshold well below its deterministic counterpart. We also prove that the extinction threshold cannot be ascribed only to demographic fluctuations around small population sizes. The more restrictive limit to species similarity is, therefore, a consequence of the complex interplay between competitive interactions and ecological drift. As a practical implication, we show that the existence of a stochastic limit to similarity has important consequences in the recovery of fragmented habitats. © 2015 The Author(s).

How similar can co-occurring species be in the presence of competition and ecological drift?

PubMed Central

Capitán, José A.; Cuenda, Sara; Alonso, David

2015-01-01

If two species live on a single resource, the one with a slight advantage will out-compete the other: complete competitors cannot coexist. This is known as the competitive exclusion principle. If no extinction occurs, it is because evolutionary adaptation to slightly different niches takes place. Therefore, it is widely accepted that ecological communities are assembled by evolutionary differentiation and progressive adaptation of species to different niches. However, some ecologists have recently challenged this classic paradigm highlighting the importance of chance and stochasticity. Using a synthetic framework for community dynamics, here we show that, while deterministic descriptors predict coexistence, species similarity is limited in a more restrictive way in the presence of stochasticity. We analyse the stochastic extinction phenomenon, showing that extinction occurs as competitive overlap increases above a certain threshold well below its deterministic counterpart. We also prove that the extinction threshold cannot be ascribed only to demographic fluctuations around small population sizes. The more restrictive limit to species similarity is, therefore, a consequence of the complex interplay between competitive interactions and ecological drift. As a practical implication, we show that the existence of a stochastic limit to similarity has important consequences in the recovery of fragmented habitats. PMID:26269234

Comparing reactive and memory-one strategies of direct reciprocity

PubMed Central

Baek, Seung Ki; Jeong, Hyeong-Chai; Hilbe, Christian; Nowak, Martin A.

2016-01-01

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player’s previous move, and memory-one strategies, which take into account the own and the co-player’s previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation. PMID:27161141

Bubonic plague: a metapopulation model of a zoonosis.

PubMed Central

Keeling, M J; Gilligan, C A

2000-01-01

Bubonic plague (Yersinia pestis) is generally thought of as a historical disease; however, it is still responsible for around 1000-3000 deaths each year worldwide. This paper expands the analysis of a model for bubonic plague that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the deterministic model, including the force of infection to humans, are shown to be robust to changes in the basic parameters, although variation in the flea searching efficiency, and the movement rates of rats and fleas will be considered throughout the paper. The stochastic behaviour of the corresponding metapopulation model is discussed, with attention focused on the dynamics of rats and the force of infection at the local spatial scale. Short-lived local epidemics in rats govern the invasion of the disease and produce an irregular pattern of human cases similar to those observed. However, the endemic behaviour in a few rat subpopulations allows the disease to persist for many years. This spatial stochastic model is also used to identify the criteria for the spread to human populations in terms of the rat density. Finally, the full stochastic model is reduced to the form of a probabilistic cellular automaton, which allows the analysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidemics and the effects of movement rates, and also to test whether the emergent metapopulation behaviour is a property of the local dynamics rather than the precise details of the model. PMID:11413636

New insights into mechanisms of stem cell daughter fate determination in regenerative tissues.

PubMed

Sada, Aiko; Tumbar, Tudorita

2013-01-01

Stem cells can self-renew and differentiate over extended periods of time. Understanding how stem cells acquire their fates is a central question in stem cell biology. Early work in Drosophila germ line and neuroblast showed that fate choice is achieved by strict asymmetric divisions that can generate each time one stem and one differentiated cell. More recent work suggests that during homeostasis, some stem cells can divide symmetrically to generate two differentiated cells or two identical stem cells to compensate for stem cell loss that occurred by direct differentiation or apoptosis. The interplay of all these factors ensures constant tissue regeneration and the maintenance of stem cell pool size. This interplay can be modeled as a population-deterministic dynamics that, at least in some systems, may be described as stochastic behavior. Here, we overview recent progress made on the characterization of stem cell dynamics in regenerative tissues. Copyright © 2013 Elsevier Inc. All rights reserved.

High Fidelity Preparation of a Single Atom in Its 2D Center of Mass Ground State

NASA Astrophysics Data System (ADS)

Sompet, Pimonpan; Fung, Yin Hsien; Schwartz, Eyal; Hunter, Matthew D. J.; Phrompao, Jindaratsamee; Andersen, Mikkel F.

2017-04-01

Complete control over quantum states of individual atoms is important for the study of the microscopic world. Here, we present a push button method for high fidelity preparation of a single 85Rb atom in the vibrational ground state of tightly focused optical tweezers. The method combines near-deterministic preparation of a single atom with magnetically-insensitive Raman sideband cooling. We achieve 2D cooling in the radial plane with a ground state population of 0.85, which provides a fidelity of 0.7 for the entire procedure (loading and cooling). The Raman beams couple two sublevels (| F = 3 , m = 0 〉 and | F = 2 , m = 0 〉) that are indifferent to magnetic noise to first order. This leads to long atomic coherence times, and allows us to implement the cooling in an environment where magnetic field fluctuations prohibit previously demonstrated variations. Additionally, we implement the trapping and manipulation of two atoms confined in separate dynamically reconfigurable optical tweezers, to study few-body dynamics.

Dynamical Characteristics Common to Neuronal Competition Models

PubMed Central

Shpiro, Asya; Curtu, Rodica; Rinzel, John; Rubin, Nava

2009-01-01

Models implementing neuronal competition by reciprocally inhibitory populations are widely used to characterize bistable phenomena such as binocular rivalry. We find common dynamical behavior in several models of this general type, which differ in their architecture in the form of their gain functions, and in how they implement the slow process that underlies alternating dominance. We focus on examining the effect of the input strength on the rate (and existence) of oscillations. In spite of their differences, all considered models possess similar qualitative features, some of which we report here for the first time. Experimentally, dominance durations have been reported to decrease monotonically with increasing stimulus strength (such as Levelt's “Proposition IV”). The models predict this behavior; however, they also predict that at a lower range of input strength dominance durations increase with increasing stimulus strength. The nonmonotonic dependency of duration on stimulus strength is common to both deterministic and stochastic models. We conclude that additional experimental tests of Levelt's Proposition IV are needed to reconcile models and perception. PMID:17065254

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

PubMed

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Quantifying selection in evolving populations using time-resolved genetic data

NASA Astrophysics Data System (ADS)

Illingworth, Christopher J. R.; Mustonen, Ville

2013-01-01

Methods which uncover the molecular basis of the adaptive evolution of a population address some important biological questions. For example, the problem of identifying genetic variants which underlie drug resistance, a question of importance for the treatment of pathogens, and of cancer, can be understood as a matter of inferring selection. One difficulty in the inference of variants under positive selection is the potential complexity of the underlying evolutionary dynamics, which may involve an interplay between several contributing processes, including mutation, recombination and genetic drift. A source of progress may be found in modern sequencing technologies, which confer an increasing ability to gather information about evolving populations, granting a window into these complex processes. One particularly interesting development is the ability to follow evolution as it happens, by whole-genome sequencing of an evolving population at multiple time points. We here discuss how to use time-resolved sequence data to draw inferences about the evolutionary dynamics of a population under study. We begin by reviewing our earlier analysis of a yeast selection experiment, in which we used a deterministic evolutionary framework to identify alleles under selection for heat tolerance, and to quantify the selection acting upon them. Considering further the use of advanced intercross lines to measure selection, we here extend this framework to cover scenarios of simultaneous recombination and selection, and of two driver alleles with multiple linked neutral, or passenger, alleles, where the driver pair evolves under an epistatic fitness landscape. We conclude by discussing the limitations of the approach presented and outlining future challenges for such methodologies.

Development of a Probabilistic Component Mode Synthesis Method for the Analysis of Non-Deterministic Substructures

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; Ferri, Aldo A.

1995-01-01

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature, researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. This paper presents a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel

2016-10-01

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate howmore » electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.« less

Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces

NASA Astrophysics Data System (ADS)

Molz, F. J.; Murdoch, L. C.; Faybishenko, B.

2013-12-01

Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the complex dynamics. We found that complex dynamics occur even with a constant food supply maintained at the upstream boundary of the biofilm. Results will be presented along with a description of the model, including 3 coupled partial differential equations and examples of the localized and propagating nonlinear dynamics inherent in the system. Contrary to a common opinion that chaos in many mechanical systems is a type of instability, appearing when energy is added, we hypothesize, based on the results of our modeling, that chaos in biofilm dynamics and other microbial ecosystems is driven by a competitive decrease in the food supply (i.e., chemical energy). We also hypothesize that, somewhat paradoxically, this, in turn, may support a long-term system stability that could cause bioclogging in porous media.

Accounting for randomness in measurement and sampling in studying cancer cell population dynamics.

PubMed

Ghavami, Siavash; Wolkenhauer, Olaf; Lahouti, Farshad; Ullah, Mukhtar; Linnebacher, Michael

2014-10-01

Knowing the expected temporal evolution of the proportion of different cell types in sample tissues gives an indication about the progression of the disease and its possible response to drugs. Such systems have been modelled using Markov processes. We here consider an experimentally realistic scenario in which transition probabilities are estimated from noisy cell population size measurements. Using aggregated data of FACS measurements, we develop MMSE and ML estimators and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes. Our numerical results show that the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach for noisy measurements. This provides support for our argument that for the analysis of FACS data one should consider the observed state as a random variable. The second problem we address is about the consequences of estimating the probability of a cell being in a particular state from measurements of small population of cells. We show how the uncertainty arising from small sample sizes can be captured by a distribution for the state probability.

Fishing Quotas, Induced Allee Effect, and Fluctuation-Driven Extinction.

PubMed

Hastings, Harold M; Radin, Michael; Wiandt, Tamas

2017-01-01

We explore the potential of modifications to standard fishery models (for example Gordon-Schafer-Munro) to help understand events such as the collapse of the North Atlantic cod fishery. In particular we find that quota-driven and similar harvesting strategies induce an effective strong Allee effect (collapse if the population falls below a critical level). In the presence of environmental noise, fish population dynamics is similar to a random walk with (non-linear) drift. The expected survival time (first passage time to collapse) is shown to depend sensitively upon the amount of environmental noise and size of the 'safe zone' between the deterministic steady state population and the critical population level at which the system collapses; more precisely it is exponential in the cube of the size of the safe zone divided by the variance of the noise process. Similar scaling can be expected for more survival in more general systems with multiple steady states. Our calculations imply an amplification effect under which small increases in harvest yield large decreases in expected survival time, and one should be cautious in changes in harvesting, especially in fisheries with poor or limited data and fisheries affected by climate change.

Churchill: an ultra-fast, deterministic, highly scalable and balanced parallelization strategy for the discovery of human genetic variation in clinical and population-scale genomics.

PubMed

Kelly, Benjamin J; Fitch, James R; Hu, Yangqiu; Corsmeier, Donald J; Zhong, Huachun; Wetzel, Amy N; Nordquist, Russell D; Newsom, David L; White, Peter

2015-01-20

While advances in genome sequencing technology make population-scale genomics a possibility, current approaches for analysis of these data rely upon parallelization strategies that have limited scalability, complex implementation and lack reproducibility. Churchill, a balanced regional parallelization strategy, overcomes these challenges, fully automating the multiple steps required to go from raw sequencing reads to variant discovery. Through implementation of novel deterministic parallelization techniques, Churchill allows computationally efficient analysis of a high-depth whole genome sample in less than two hours. The method is highly scalable, enabling full analysis of the 1000 Genomes raw sequence dataset in a week using cloud resources. http://churchill.nchri.org/.

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

PubMed

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

Pest persistence and eradication conditions in a deterministic model for sterile insect release.

PubMed

Gordillo, Luis F

2015-01-01

The release of sterile insects is an environment friendly pest control method used in integrated pest management programmes. Difference or differential equations based on Knipling's model often provide satisfactory qualitative descriptions of pest populations subject to sterile release at relatively high densities with large mating encounter rates, but fail otherwise. In this paper, I derive and explore numerically deterministic population models that include sterile release together with scarce mating encounters in the particular case of species with long lifespan and multiple matings. The differential equations account separately the effects of mating failure due to sterile male release and the frequency of mating encounters. When insects spatial spread is incorporated through diffusion terms, computations reveal the possibility of steady pest persistence in finite size patches. In the presence of density dependence regulation, it is observed that sterile release might contribute to induce sudden suppression of the pest population.

A mathematical study of a model for childhood diseases with non-permanent immunity

NASA Astrophysics Data System (ADS)

Moghadas, S. M.; Gumel, A. B.

2003-08-01

Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. Since vaccination is considered to be the most effective strategy against childhood diseases, the development of a framework that would predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial. This paper provides this framework via qualitative and quantitative analysis of a deterministic mathematical model for the transmission dynamics of a childhood disease in the presence of a preventive vaccine that may wane over time. Using global stability analysis of the model, based on constructing a Lyapunov function, it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value. It is also shown that the disease will persist within the population if the coverage level is below this threshold. These results are verified numerically by constructing, and then simulating, a robust semi-explicit second-order finite-difference method.

Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations.

PubMed

Beiran, Manuel; Kruscha, Alexandra; Benda, Jan; Lindner, Benjamin

2018-04-01

We compare the information transmission of a time-dependent signal by two types of uncoupled neuron populations that differ in their sources of variability: i) a homogeneous population whose units receive independent noise and ii) a deterministic heterogeneous population, where each unit exhibits a different baseline firing rate ('disorder'). Our criterion for making both sources of variability quantitatively comparable is that the interspike-interval distributions are identical for both systems. Numerical simulations using leaky integrate-and-fire neurons unveil that a non-zero amount of both noise or disorder maximizes the encoding efficiency of the homogeneous and heterogeneous system, respectively, as a particular case of suprathreshold stochastic resonance. Our findings thus illustrate that heterogeneity can render similarly profitable effects for neuronal populations as dynamic noise. The optimal noise/disorder depends on the system size and the properties of the stimulus such as its intensity or cutoff frequency. We find that weak stimuli are better encoded by a noiseless heterogeneous population, whereas for strong stimuli a homogeneous population outperforms an equivalent heterogeneous system up to a moderate noise level. Furthermore, we derive analytical expressions of the coherence function for the cases of very strong noise and of vanishing intrinsic noise or heterogeneity, which predict the existence of an optimal noise intensity. Our results show that, depending on the type of signal, noise as well as heterogeneity can enhance the encoding performance of neuronal populations.

Study of selected phenotype switching strategies in time varying environment

NASA Astrophysics Data System (ADS)

Horvath, Denis; Brutovsky, Branislav

2016-03-01

Population heterogeneity plays an important role across many research, as well as the real-world, problems. The population heterogeneity relates to the ability of a population to cope with an environment change (or uncertainty) preventing its extinction. However, this ability is not always desirable as can be exemplified by an intratumor heterogeneity which positively correlates with the development of resistance to therapy. Causation of population heterogeneity is therefore in biology and medicine an intensively studied topic. In this paper the evolution of a specific strategy of population diversification, the phenotype switching, is studied at a conceptual level. The presented simulation model studies evolution of a large population of asexual organisms in a time-varying environment represented by a stochastic Markov process. Each organism disposes with a stochastic or nonlinear deterministic switching strategy realized by discrete-time models with evolvable parameters. We demonstrate that under rapidly varying exogenous conditions organisms operate in the vicinity of the bet-hedging strategy, while the deterministic patterns become relevant as the environmental variations are less frequent. Statistical characterization of the steady state regimes of the populations is done using the Hellinger and Kullback-Leibler functional distances and the Hamming distance.

Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.

PubMed

Bressloff, Paul C

2015-01-01

We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous to the modified activity-based equations generated from a neural master equation.

A shifted hyperbolic augmented Lagrangian-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization

NASA Astrophysics Data System (ADS)

Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite M. G. P.

2016-12-01

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. Numerical experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangian compares favorably with other deterministic and stochastic penalty-based methods.

Natural selection of memory-one strategies for the iterated prisoner's dilemma.

PubMed

Kraines, D P; Kraines, V Y

2000-04-21

In the iterated Prisoner's Dilemma, mutually cooperative behavior can become established through Darwinian natural selection. In simulated interactions of stochastic memory-one strategies for the Iterated Prisoner's Dilemma, Nowak and Sigmund discovered that cooperative agents using a Pavlov (Win-Stay Lose-Switch) type strategy eventually dominate a random population. This emergence follows more directly from a deterministic dynamical system based on differential reproductive success or natural selection. When restricted to an environment of memory-one agents interacting in iterated Prisoner's Dilemma games with a 1% noise level, the Pavlov agent is the only cooperative strategy and one of very few others that cannot be invaded by a similar strategy. Pavlov agents are trusting but no suckers. They will exploit weakness but repent if punished for cheating. Copyright 2000 Academic Press.

Realistic Simulation for Body Area and Body-To-Body Networks

PubMed Central

Alam, Muhammad Mahtab; Ben Hamida, Elyes; Ben Arbia, Dhafer; Maman, Mickael; Mani, Francesco; Denis, Benoit; D’Errico, Raffaele

2016-01-01

In this paper, we present an accurate and realistic simulation for body area networks (BAN) and body-to-body networks (BBN) using deterministic and semi-deterministic approaches. First, in the semi-deterministic approach, a real-time measurement campaign is performed, which is further characterized through statistical analysis. It is able to generate link-correlated and time-varying realistic traces (i.e., with consistent mobility patterns) for on-body and body-to-body shadowing and fading, including body orientations and rotations, by means of stochastic channel models. The full deterministic approach is particularly targeted to enhance IEEE 802.15.6 proposed channel models by introducing space and time variations (i.e., dynamic distances) through biomechanical modeling. In addition, it helps to accurately model the radio link by identifying the link types and corresponding path loss factors for line of sight (LOS) and non-line of sight (NLOS). This approach is particularly important for links that vary over time due to mobility. It is also important to add that the communication and protocol stack, including the physical (PHY), medium access control (MAC) and networking models, is developed for BAN and BBN, and the IEEE 802.15.6 compliance standard is provided as a benchmark for future research works of the community. Finally, the two approaches are compared in terms of the successful packet delivery ratio, packet delay and energy efficiency. The results show that the semi-deterministic approach is the best option; however, for the diversity of the mobility patterns and scenarios applicable, biomechanical modeling and the deterministic approach are better choices. PMID:27104537

Realistic Simulation for Body Area and Body-To-Body Networks.

PubMed

Alam, Muhammad Mahtab; Ben Hamida, Elyes; Ben Arbia, Dhafer; Maman, Mickael; Mani, Francesco; Denis, Benoit; D'Errico, Raffaele

2016-04-20

In this paper, we present an accurate and realistic simulation for body area networks (BAN) and body-to-body networks (BBN) using deterministic and semi-deterministic approaches. First, in the semi-deterministic approach, a real-time measurement campaign is performed, which is further characterized through statistical analysis. It is able to generate link-correlated and time-varying realistic traces (i.e., with consistent mobility patterns) for on-body and body-to-body shadowing and fading, including body orientations and rotations, by means of stochastic channel models. The full deterministic approach is particularly targeted to enhance IEEE 802.15.6 proposed channel models by introducing space and time variations (i.e., dynamic distances) through biomechanical modeling. In addition, it helps to accurately model the radio link by identifying the link types and corresponding path loss factors for line of sight (LOS) and non-line of sight (NLOS). This approach is particularly important for links that vary over time due to mobility. It is also important to add that the communication and protocol stack, including the physical (PHY), medium access control (MAC) and networking models, is developed for BAN and BBN, and the IEEE 802.15.6 compliance standard is provided as a benchmark for future research works of the community. Finally, the two approaches are compared in terms of the successful packet delivery ratio, packet delay and energy efficiency. The results show that the semi-deterministic approach is the best option; however, for the diversity of the mobility patterns and scenarios applicable, biomechanical modeling and the deterministic approach are better choices.

Two Strain Dengue Model with Temporary Cross Immunity and Seasonality

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastien; Stollenwerk, Nico

2010-09-01

Models on dengue fever epidemiology have previously shown critical fluctuations with power law distributions and also deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. In our first model including well known biological features, we found a rich dynamical structure including limit cycles, symmetry breaking bifurcations, torus bifurcations, coexisting attractors including isola solutions and deterministic chaos (as indicated by positive Lyapunov exponents) in a much larger parameter region, which is also biologically more plausible than the previous results of other researches. Based on these findings we will investigate the model structures further including seasonality.

The stochastic energy-Casimir method

NASA Astrophysics Data System (ADS)

Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

2018-04-01

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

Evaluation of the selection methods used in the exIWO algorithm based on the optimization of multidimensional functions

NASA Astrophysics Data System (ADS)

Kostrzewa, Daniel; Josiński, Henryk

2016-06-01

The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version inspired by dynamic growth of weeds colony. The authors of the present paper have modified the exIWO algorithm introducing a set of both deterministic and non-deterministic strategies of individuals' selection. The goal of the project was to evaluate the modified exIWO by testing its usefulness for multidimensional numerical functions optimization. The optimized functions: Griewank, Rastrigin, and Rosenbrock are frequently used as benchmarks because of their characteristics.

Two Strain Dengue Model with Temporary Cross Immunity and Seasonality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguiar, Maira; Ballesteros, Sebastien; Stollenwerk, Nico

Models on dengue fever epidemiology have previously shown critical fluctuations with power law distributions and also deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. In our first model including well known biological features, we found a rich dynamical structure including limit cycles, symmetry breaking bifurcations, torus bifurcations, coexisting attractors including isola solutions and deterministic chaos (as indicated by positive Lyapunov exponents) in a much larger parameter region, which is also biologically more plausible than the previous results of other researches. Based on these findings we will investigate the model structures further including seasonality.

How synapses can enhance sensibility of a neural network

NASA Astrophysics Data System (ADS)

Protachevicz, P. R.; Borges, F. S.; Iarosz, K. C.; Caldas, I. L.; Baptista, M. S.; Viana, R. L.; Lameu, E. L.; Macau, E. E. N.; Batista, A. M.

2018-02-01

In this work, we study the dynamic range in a neural network modelled by cellular automaton. We consider deterministic and non-deterministic rules to simulate electrical and chemical synapses. Chemical synapses have an intrinsic time-delay and are susceptible to parameter variations guided by learning Hebbian rules of behaviour. The learning rules are related to neuroplasticity that describes change to the neural connections in the brain. Our results show that chemical synapses can abruptly enhance sensibility of the neural network, a manifestation that can become even more predominant if learning rules of evolution are applied to the chemical synapses.

Matrix Population Model for Estimating Effects from Time-Varying Aquatic Exposures: Technical Documentation

EPA Science Inventory

The Office of Pesticide Programs models daily aquatic pesticide exposure values for 30 years in its risk assessments. However, only a fraction of that information is typically used in these assessments. The population model employed herein is a deterministic, density-dependent pe...

Chaotic dynamics and control of deterministic ratchets.

PubMed

Family, Fereydoon; Larrondo, H A; Zarlenga, D G; Arizmendi, C M

2005-11-30

Deterministic ratchets, in the inertial and also in the overdamped limit, have a very complex dynamics, including chaotic motion. This deterministically induced chaos mimics, to some extent, the role of noise, changing, on the other hand, some of the basic properties of thermal ratchets; for example, inertial ratchets can exhibit multiple reversals in the current direction. The direction depends on the amount of friction and inertia, which makes it especially interesting for technological applications such as biological particle separation. We overview in this work different strategies to control the current of inertial ratchets. The control parameters analysed are the strength and frequency of the periodic external force, the strength of the quenched noise that models a non-perfectly-periodic potential, and the mass of the particles. Control mechanisms are associated with the fractal nature of the basins of attraction of the mean velocity attractors. The control of the overdamped motion of noninteracting particles in a rocking periodic asymmetric potential is also reviewed. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with noncorrelated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters.

Ultrafast Magnetization Manipulation Using Single Femtosecond Light and Hot-Electron Pulses.

PubMed

Xu, Yong; Deb, Marwan; Malinowski, Grégory; Hehn, Michel; Zhao, Weisheng; Mangin, Stéphane

2017-11-01

Current-induced magnetization manipulation is a key issue for spintronic applications. This manipulation must be fast, deterministic, and nondestructive in order to function in device applications. Therefore, single- electronic-pulse-driven deterministic switching of the magnetization on the picosecond timescale represents a major step toward future developments of ultrafast spintronic systems. Here, the ultrafast magnetization dynamics in engineered Gd x [FeCo] 1- x -based structures are studied to compare the effect of femtosecond laser and hot-electron pulses. It is demonstrated that a single femtosecond hot-electron pulse causes deterministic magnetization reversal in either Gd-rich and FeCo-rich alloys similarly to a femtosecond laser pulse. In addition, it is shown that the limiting factor of such manipulation for perpendicular magnetized films arises from the formation of a multidomain state due to dipolar interactions. By performing time-resolved measurements under various magnetic fields, it is demonstrated that the same magnetization dynamics are observed for both light and hot-electron excitation, and that the full magnetization reversal takes place within 40 ps. The efficiency of the ultrafast current-induced magnetization manipulation is enhanced due to the ballistic transport of hot electrons before reaching the GdFeCo magnetic layer. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Model structure of the stream salmonid simulator (S3)—A dynamic model for simulating growth, movement, and survival of juvenile salmonids

USGS Publications Warehouse

Perry, Russell W.; Plumb, John M.; Jones, Edward C.; Som, Nicholas A.; Hetrick, Nicholas J.; Hardy, Thomas B.

2018-04-06

Fisheries and water managers often use population models to aid in understanding the effect of alternative water management or restoration actions on anadromous fish populations. We developed the Stream Salmonid Simulator (S3) to help resource managers evaluate the effect of management alternatives on juvenile salmonid populations. S3 is a deterministic stage-structured population model that tracks daily growth, movement, and survival of juvenile salmon. A key theme of the model is that river flow affects habitat availability and capacity, which in turn drives density dependent population dynamics. To explicitly link population dynamics to habitat quality and quantity, the river environment is constructed as a one-dimensional series of linked habitat units, each of which has an associated daily time series of discharge, water temperature, and usable habitat area or carrying capacity. The physical characteristics of each habitat unit and the number of fish occupying each unit, in turn, drive survival and growth within each habitat unit and movement of fish among habitat units.The purpose of this report is to outline the underlying general structure of the S3 model that is common among different applications of the model. We have developed applications of the S3 model for juvenile fall Chinook salmon (Oncorhynchus tshawytscha) in the lower Klamath River. Thus, this report is a companion to current application of the S3 model to the Trinity River (in review). The general S3 model structure provides a biological and physical framework for the salmonid freshwater life cycle. This framework captures important demographics of juvenile salmonids aimed at translating management alternatives into simulated population responses. Although the S3 model is built on this common framework, the model has been constructed to allow much flexibility in application of the model to specific river systems. The ability for practitioners to include system-specific information for the physical stream structure, survival, growth, and movement processes ensures that simulations provide results that are relevant to the questions asked about the population under study.

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.

Speculative behavior and asset price dynamics.

PubMed

Westerhoff, Frank

2003-07-01

This paper deals with speculative trading. Guided by empirical observations, a nonlinear deterministic asset pricing model is developed in which traders repeatedly choose between technical and fundamental analysis to determine their orders. The interaction between the trading rules produces complex dynamics. The model endogenously replicates the stylized facts of excess volatility, high trading volumes, shifts in the level of asset prices, and volatility clustering.

Chaos in plasma simulation and experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watts, C.; Newman, D.E.; Sprott, J.C.

1993-09-01

We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFPmore » dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude.

PubMed

Zamora-Chimal, Criseida; Santillán, Moisés; Rodríguez-González, Jesús

2012-10-07

In this paper we introduce a mathematical model for the tryptophan operon regulatory pathway in Bacillus subtilis. This model considers the transcription-attenuation, and the enzyme-inhibition regulatory mechanisms. Special attention is paid to the estimation of all the model parameters from reported experimental data. With the aid of this model we investigate, from a mathematical-modeling point of view, whether the existing multiplicity of regulatory feedback loops is advantageous in some sense, regarding the dynamic response and the biochemical noise in the system. The tryptophan operon dynamic behavior is studied by means of deterministic numeric simulations, while the biochemical noise is analyzed with the aid of stochastic simulations. The model feasibility is tested comparing its stochastic and deterministic results with experimental reports. Our results for the wildtype and for a couple of mutant bacterial strains suggest that the enzyme-inhibition feedback loop, dynamically accelerates the operon response, and plays a major role in the reduction of biochemical noise. Also, the transcription-attenuation feedback loop makes the trp operon sensitive to changes in the endogenous tryptophan level, and increases the amplitude of the biochemical noise. Copyright © 2012 Elsevier Ltd. All rights reserved.

Dynamical behavior of lean swirling premixed flame generated by change in gravitational orientation

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Miyano, Takaya; Shepherd, Ian

2010-11-01

The dynamic behavior of flame front instability in lean swirling premixed flame generated by the effect of gravitational orientation has been experimentally investigated in this work. When the gravitational direction is changed relative to the flame front, i.e., in inverted gravity, an unstably fluctuating flame (unstable flame) is formed in a limited domain of equivalence ratio and swirl number (Gotoda. H et al., Physical Review E, vol. 81, 026211, 2010). The time history of flame front fluctuations show that in the buoyancy-dominated region, chaotic irregular fluctuation with low frequencies is superimposed on the dominant periodic oscillation of the unstable flame. This periodic oscillation is produced by unstable large-scale vortex motion in combustion products generated by a change in the buoyancy/swirl interaction due to the inversion of gravitational orientation. As a result, the dynamic behavior of the unstable flame becomes low-dimensional deterministic chaos. Its dynamics maintains low-dimensional deterministic chaos even in the momentum-dominated region, in which vortex breakdown in the combustion products clearly occurs. These results were clearly demonstrated by the use of nonlinear time series analysis based on chaos theory, which has not been widely applied to the investigation of combustion phenomena.

Effects of deterministic and random refuge in a prey-predator model with parasite infection.

PubMed

Mukhopadhyay, B; Bhattacharyya, R

2012-09-01

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics. Copyright © 2012 Elsevier Inc. All rights reserved.

Hyperchaotic Dynamics for Light Polarization in a Laser Diode

NASA Astrophysics Data System (ADS)

Bonatto, Cristian

2018-04-01

It is shown that a highly randomlike behavior of light polarization states in the output of a free-running laser diode, covering the whole Poincaré sphere, arises as a result from a fully deterministic nonlinear process, which is characterized by a hyperchaotic dynamics of two polarization modes nonlinearly coupled with a semiconductor medium, inside the optical cavity. A number of statistical distributions were found to describe the deterministic data of the low-dimensional nonlinear flow, such as lognormal distribution for the light intensity, Gaussian distributions for the electric field components and electron densities, Rice and Rayleigh distributions, and Weibull and negative exponential distributions, for the modulus and intensity of the orthogonal linear components of the electric field, respectively. The presented results could be relevant for the generation of single units of compact light source devices to be used in low-dimensional optical hyperchaos-based applications.

Stochastic inference with spiking neurons in the high-conductance state

NASA Astrophysics Data System (ADS)

Petrovici, Mihai A.; Bill, Johannes; Bytschok, Ilja; Schemmel, Johannes; Meier, Karlheinz

2016-10-01

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

A Surrogate Technique for Investigating Deterministic Dynamics in Discrete Human Movement.

PubMed

Taylor, Paul G; Small, Michael; Lee, Kwee-Yum; Landeo, Raul; O'Meara, Damien M; Millett, Emma L

2016-10-01

Entropy is an effective tool for investigation of human movement variability. However, before applying entropy, it can be beneficial to employ analyses to confirm that observed data are not solely the result of stochastic processes. This can be achieved by contrasting observed data with that produced using surrogate methods. Unlike continuous movement, no appropriate method has been applied to discrete human movement. This article proposes a novel surrogate method for discrete movement data, outlining the processes for determining its critical values. The proposed technique reliably generated surrogates for discrete joint angle time series, destroying fine-scale dynamics of the observed signal, while maintaining macro structural characteristics. Comparison of entropy estimates indicated observed signals had greater regularity than surrogates and were not only the result of stochastic but also deterministic processes. The proposed surrogate method is both a valid and reliable technique to investigate determinism in other discrete human movement time series.

Dynamic speckle - Interferometry of micro-displacements

NASA Astrophysics Data System (ADS)

Vladimirov, A. P.

2012-06-01

The problem of the dynamics of speckles in the image plane of the object, caused by random movements of scattering centers is solved. We consider three cases: 1) during the observation the points move at random, but constant speeds, and 2) the relative displacement of any pair of points is a continuous random process, and 3) the motion of the centers is the sum of a deterministic movement and random displacement. For the cases 1) and 2) the characteristics of temporal and spectral autocorrelation function of the radiation intensity can be used for determining of individually and the average relative displacement of the centers, their dispersion and the relaxation time. For the case 3) is showed that under certain conditions, the optical signal contains a periodic component, the number of periods is proportional to the derivations of the deterministic displacements. The results of experiments conducted to test and application of theory are given.

Survivability of Deterministic Dynamical Systems

PubMed Central

Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen

2016-01-01

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures. PMID:27405955

Mathematical demography of spotted owls in the Pacific Northwest

Treesearch

B.R. Noon; C.M. Biles

1990-01-01

We examined the mathematical demography of northern spotted owls (Strix occidentalis caurina) using simple deterministic population models. Our goals were to gain insights into the life history strategy, to determine demographic attributes most affecting changes in population size, and to provide guidelines for effective management of spotted owl...

Habitat connectivity and in-stream vegetation control temporal variability of benthic invertebrate communities.

PubMed

Huttunen, K-L; Mykrä, H; Oksanen, J; Astorga, A; Paavola, R; Muotka, T

2017-05-03

One of the key challenges to understanding patterns of β diversity is to disentangle deterministic patterns from stochastic ones. Stochastic processes may mask the influence of deterministic factors on community dynamics, hindering identification of the mechanisms causing variation in community composition. We studied temporal β diversity (among-year dissimilarity) of macroinvertebrate communities in near-pristine boreal streams across 14 years. To assess whether the observed β diversity deviates from that expected by chance, and to identify processes (deterministic vs. stochastic) through which different explanatory factors affect community variability, we used a null model approach. We observed that at the majority of sites temporal β diversity was low indicating high community stability. When stochastic variation was unaccounted for, connectivity was the only variable explaining temporal β diversity, with weakly connected sites exhibiting higher community variability through time. After accounting for stochastic effects, connectivity lost importance, suggesting that it was related to temporal β diversity via random colonization processes. Instead, β diversity was best explained by in-stream vegetation, community variability decreasing with increasing bryophyte cover. These results highlight the potential of stochastic factors to dampen the influence of deterministic processes, affecting our ability to understand and predict changes in biological communities through time.

Relevance of deterministic chaos theory to studies in functioning of dynamical systems

NASA Astrophysics Data System (ADS)

Glagolev, S. N.; Bukhonova, S. M.; Chikina, E. D.

2018-03-01

The paper considers chaotic behavior of dynamical systems typical for social and economic processes. Approaches to analysis and evaluation of system development processes are studies from the point of view of controllability and determinateness. Explanations are given for necessity to apply non-standard mathematical tools to explain states of dynamical social and economic systems on the basis of fractal theory. Features of fractal structures, such as non-regularity, self-similarity, dimensionality and fractionality are considered.

Absorbing phase transitions in deterministic fixed-energy sandpile models

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2018-03-01

We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010), 10.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.

Successional dynamics in Neotropical forests are as uncertain as they are predictable

PubMed Central

Norden, Natalia; Angarita, Héctor A.; Bongers, Frans; Martínez-Ramos, Miguel; Granzow-de la Cerda, Iñigo; van Breugel, Michiel; Lebrija-Trejos, Edwin; Meave, Jorge A.; Vandermeer, John; Williamson, G. Bruce; Finegan, Bryan; Mesquita, Rita; Chazdon, Robin L.

2015-01-01

Although forest succession has traditionally been approached as a deterministic process, successional trajectories of vegetation change vary widely, even among nearby stands with similar environmental conditions and disturbance histories. Here, we provide the first attempt, to our knowledge, to quantify predictability and uncertainty during succession based on the most extensive long-term datasets ever assembled for Neotropical forests. We develop a novel approach that integrates deterministic and stochastic components into different candidate models describing the dynamical interactions among three widely used and interrelated forest attributes—stem density, basal area, and species density. Within each of the seven study sites, successional trajectories were highly idiosyncratic, even when controlling for prior land use, environment, and initial conditions in these attributes. Plot factors were far more important than stand age in explaining successional trajectories. For each site, the best-fit model was able to capture the complete set of time series in certain attributes only when both the deterministic and stochastic components were set to similar magnitudes. Surprisingly, predictability of stem density, basal area, and species density did not show consistent trends across attributes, study sites, or land use history, and was independent of plot size and time series length. The model developed here represents the best approach, to date, for characterizing autogenic successional dynamics and demonstrates the low predictability of successional trajectories. These high levels of uncertainty suggest that the impacts of allogenic factors on rates of change during tropical forest succession are far more pervasive than previously thought, challenging the way ecologists view and investigate forest regeneration. PMID:26080411

Successional dynamics in Neotropical forests are as uncertain as they are predictable.

PubMed

Norden, Natalia; Angarita, Héctor A; Bongers, Frans; Martínez-Ramos, Miguel; Granzow-de la Cerda, Iñigo; van Breugel, Michiel; Lebrija-Trejos, Edwin; Meave, Jorge A; Vandermeer, John; Williamson, G Bruce; Finegan, Bryan; Mesquita, Rita; Chazdon, Robin L

2015-06-30

Although forest succession has traditionally been approached as a deterministic process, successional trajectories of vegetation change vary widely, even among nearby stands with similar environmental conditions and disturbance histories. Here, we provide the first attempt, to our knowledge, to quantify predictability and uncertainty during succession based on the most extensive long-term datasets ever assembled for Neotropical forests. We develop a novel approach that integrates deterministic and stochastic components into different candidate models describing the dynamical interactions among three widely used and interrelated forest attributes--stem density, basal area, and species density. Within each of the seven study sites, successional trajectories were highly idiosyncratic, even when controlling for prior land use, environment, and initial conditions in these attributes. Plot factors were far more important than stand age in explaining successional trajectories. For each site, the best-fit model was able to capture the complete set of time series in certain attributes only when both the deterministic and stochastic components were set to similar magnitudes. Surprisingly, predictability of stem density, basal area, and species density did not show consistent trends across attributes, study sites, or land use history, and was independent of plot size and time series length. The model developed here represents the best approach, to date, for characterizing autogenic successional dynamics and demonstrates the low predictability of successional trajectories. These high levels of uncertainty suggest that the impacts of allogenic factors on rates of change during tropical forest succession are far more pervasive than previously thought, challenging the way ecologists view and investigate forest regeneration.

Absorbing phase transitions in deterministic fixed-energy sandpile models.

PubMed

Park, Su-Chan

2018-03-01

We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.

Deterministic chaos in atmospheric radon dynamics

NASA Astrophysics Data System (ADS)

Cuculeanu, Vasile; Lupu, Alexandru

2001-08-01

The correlation dimension and Lyapunov exponents have been calculated for two time series of atmospheric radon daughter concentrations obtained from four daily measurements during the period 1993-1996. A number of about 6000 activity concentration values of 222Rn and 220Rn daughters have been used. The measuring method is based on aerosol collection on filters. In order to determine the filter activity, a low background gross beta measuring device with Geiger-Müller counter tubes in anticoincidence was used. The small noninteger value of the correlation dimension (≃2.2) and the existence of a positive Lyapunov exponent prove that deterministic chaos is present in the time series of atmospheric 220Rn daughters. This shows that a simple diffusion equation with a parameterized turbulent diffusion coefficient is insufficient for describing the dynamics in the near-ground layer where turbulence is not fully developed and coherent structures dominate. The analysis of 222Rn series confirms that the dynamics of the boundary layer cannot be described by a system of ordinary differential equations with a low number of independent variables.

Estimation of beam material random field properties via sensitivity-based model updating using experimental frequency response functions

NASA Astrophysics Data System (ADS)

Machado, M. R.; Adhikari, S.; Dos Santos, J. M. C.; Arruda, J. R. F.

2018-03-01

Structural parameter estimation is affected not only by measurement noise but also by unknown uncertainties which are present in the system. Deterministic structural model updating methods minimise the difference between experimentally measured data and computational prediction. Sensitivity-based methods are very efficient in solving structural model updating problems. Material and geometrical parameters of the structure such as Poisson's ratio, Young's modulus, mass density, modal damping, etc. are usually considered deterministic and homogeneous. In this paper, the distributed and non-homogeneous characteristics of these parameters are considered in the model updating. The parameters are taken as spatially correlated random fields and are expanded in a spectral Karhunen-Loève (KL) decomposition. Using the KL expansion, the spectral dynamic stiffness matrix of the beam is expanded as a series in terms of discretized parameters, which can be estimated using sensitivity-based model updating techniques. Numerical and experimental tests involving a beam with distributed bending rigidity and mass density are used to verify the proposed method. This extension of standard model updating procedures can enhance the dynamic description of structural dynamic models.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem

PubMed Central

Schilde, M.; Doerner, K.F.; Hartl, R.F.

2014-01-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

NASA Astrophysics Data System (ADS)

Burgos, C.; Cortés, J.-C.; Shaikhet, L.; Villanueva, R.-J.

2018-11-01

First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data.

Enviromental influences on the {sup 137}Cs kinetics of the yellow-bellied turtle (Trachemys Scripta)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peters, E.L.; Brisbin, L.I. Jr.

1996-02-01

Assessments of ecological risk require accurate predictions of contaminant dynamics in natural populations. However, simple deterministic models that assume constant uptake rates and elimination fractions may compromise both their ecological realism and their general application to animals with variable metabolism or diets. In particular, the temperature-dependent model of metabolic rates characteristic of ectotherms may lead to significant differences between observed and predicted contaminant kinetics. We examined the influence of a seasonally variable thermal environment on predicting the uptake and annual cycling of contaminants by ectotherms, using a temperature-dependent model of {sup 137}Cs kinetics in free-living yellow-bellied turtles, Trachemys scripta. Wemore » compared predictions from this model with those of deterministics negative exponential and flexibly shaped Richards sigmoidal models. Concentrations of {sup 137}Cs in a population if this species in Pond B, a radionuclide-contaminated nuclear reactor cooling reservoir, and {sup 137}Cs uptake by the uncontaminated turtles held captive in Pond B for 4 yr confirmed both the pattern of uptake and the equilibrium concentrations predicted by the temperature-dependent model. Almost 90% of the variance on the predicted time-integrated {sup 137}Cs concentration was explainable by linear relationships with model paramaters. The model was also relatively insensitive to uncertainties in the estimates of ambient temperature, suggesting that adequate estimates of temperature-dependent ingestion and elimination may require relatively few measurements of ambient conditions at sites of interest. Analyses of Richards sigmoidal models of {sup 137}Cs uptake indicated significant differences from a negative exponential trajectory in the 1st yr after the turtles` release into Pond B. 76 refs., 7 figs., 5 tabs.« less

Uncertain dynamical systems: A differential game approach

NASA Technical Reports Server (NTRS)

Gutman, S.

1976-01-01

A class of dynamical systems in a conflict situation is formulated and discussed, and the formulation is applied to the study of an important class of systems in the presence of uncertainty. The uncertainty is deterministic and the only assumption is that its value belongs to a known compact set. Asymptotic stability is fully discussed with application to variable structure and model reference control systems.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

A nonlinear dynamical system for combustion instability in a pulse model combustor

NASA Astrophysics Data System (ADS)

Takagi, Kazushi; Gotoda, Hiroshi

2016-11-01

We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.

Characterization of normality of chaotic systems including prediction and detection of anomalies

NASA Astrophysics Data System (ADS)

Engler, Joseph John

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

Seven challenges for metapopulation models of epidemics, including households models.

PubMed

Ball, Frank; Britton, Tom; House, Thomas; Isham, Valerie; Mollison, Denis; Pellis, Lorenzo; Scalia Tomba, Gianpaolo

2015-03-01

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

Origin and Diversification Dynamics of Self-Incompatibility Haplotypes

PubMed Central

Gervais, Camille E.; Castric, Vincent; Ressayre, Adrienne; Billiard, Sylvain

2011-01-01

Self-incompatibility (SI) is a genetic system found in some hermaphrodite plants. Recognition of pollen by pistils expressing cognate specificities at two linked genes leads to rejection of self pollen and pollen from close relatives, i.e., to avoidance of self-fertilization and inbred matings, and thus increased outcrossing. These genes generally have many alleles, yet the conditions allowing the evolution of new alleles remain mysterious. Evolutionary changes are clearly necessary in both genes, since any mutation affecting only one of them would result in a nonfunctional self-compatible haplotype. Here, we study diversification at the S-locus (i.e., a stable increase in the total number of SI haplotypes in the population, through the incorporation of new SI haplotypes), both deterministically (by investigating analytically the fate of mutations in an infinite population) and by simulations of finite populations. We show that the conditions allowing diversification are far less stringent in finite populations with recurrent mutations of the pollen and pistil genes, suggesting that diversification is possible in a panmictic population. We find that new SI haplotypes emerge fastest in populations with few SI haplotypes, and we discuss some implications for empirical data on S-alleles. However, allele numbers in our simulations never reach values as high as observed in plants whose SI systems have been studied, and we suggest extensions of our models that may reconcile the theory and data. PMID:21515570

On problems of analyzing aerodynamic properties of blunted rotary bodies with small random surface distortions under supersonic and hypersonic flows

NASA Astrophysics Data System (ADS)

Degtyar, V. G.; Kalashnikov, S. T.; Mokin, Yu. A.

2017-10-01

The paper considers problems of analyzing aerodynamic properties (ADP) of reenetry vehicles (RV) as blunted rotary bodies with small random surface distortions. The interactions of math simulation of surface distortions, selection of tools for predicting ADPs of shaped bodies, evaluation of different-type ADP variations and their adaptation for dynamic problems are analyzed. The possibilities of deterministic and probabilistic approaches to evaluation of ADP variations are considered. The practical value of the probabilistic approach is demonstrated. The examples of extremal deterministic evaluations of ADP variations for a sphere and a sharp cone are given.

Deterministic quantum controlled-PHASE gates based on non-Markovian environments

NASA Astrophysics Data System (ADS)

Zhang, Rui; Chen, Tian; Wang, Xiang-Bin

2017-12-01

We study the realization of the quantum controlled-PHASE gate in an atom-cavity system beyond the Markovian approximation. The general description of the dynamics for the atom-cavity system without any approximation is presented. When the spectral density of the reservoir has the Lorentz form, by making use of the memory backflow from the reservoir, we can always construct the deterministic quantum controlled-PHASE gate between a photon and an atom, no matter the atom-cavity coupling strength is weak or strong. While, the phase shift in the output pulse hinders the implementation of quantum controlled-PHASE gates in the sub-Ohmic, Ohmic or super-Ohmic reservoirs.

Detecting determinism from point processes.

PubMed

Andrzejak, Ralph G; Mormann, Florian; Kreuz, Thomas

2014-12-01

The detection of a nonrandom structure from experimental data can be crucial for the classification, understanding, and interpretation of the generating process. We here introduce a rank-based nonlinear predictability score to detect determinism from point process data. Thanks to its modular nature, this approach can be adapted to whatever signature in the data one considers indicative of deterministic structure. After validating our approach using point process signals from deterministic and stochastic model dynamics, we show an application to neuronal spike trains recorded in the brain of an epilepsy patient. While we illustrate our approach in the context of temporal point processes, it can be readily applied to spatial point processes as well.

Phase ordering in disordered and inhomogeneous systems

NASA Astrophysics Data System (ADS)

Corberi, Federico; Zannetti, Marco; Lippiello, Eugenio; Burioni, Raffaella; Vezzani, Alessandro

2015-06-01

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth laws of the ordered domain size, namely logarithmic or power law, respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature that governs the presence or the absence of a finite-temperature phase transition.

INTEGRATED PLANNING MODEL - EPA APPLICATIONS

EPA Science Inventory

The Integrated Planning Model (IPM) is a multi-regional, dynamic, deterministic linear programming (LP) model of the electric power sector in the continental lower 48 states and the District of Columbia. It provides forecasts up to year 2050 of least-cost capacity expansion, elec...

Dual Roles for Spike Signaling in Cortical Neural Populations

PubMed Central

Ballard, Dana H.; Jehee, Janneke F. M.

2011-01-01

A prominent feature of signaling in cortical neurons is that of randomness in the action potential. The output of a typical pyramidal cell can be well fit with a Poisson model, and variations in the Poisson rate repeatedly have been shown to be correlated with stimuli. However while the rate provides a very useful characterization of neural spike data, it may not be the most fundamental description of the signaling code. Recent data showing γ frequency range multi-cell action potential correlations, together with spike timing dependent plasticity, are spurring a re-examination of the classical model, since precise timing codes imply that the generation of spikes is essentially deterministic. Could the observed Poisson randomness and timing determinism reflect two separate modes of communication, or do they somehow derive from a single process? We investigate in a timing-based model whether the apparent incompatibility between these probabilistic and deterministic observations may be resolved by examining how spikes could be used in the underlying neural circuits. The crucial component of this model draws on dual roles for spike signaling. In learning receptive fields from ensembles of inputs, spikes need to behave probabilistically, whereas for fast signaling of individual stimuli, the spikes need to behave deterministically. Our simulations show that this combination is possible if deterministic signals using γ latency coding are probabilistically routed through different members of a cortical cell population at different times. This model exhibits standard features characteristic of Poisson models such as orientation tuning and exponential interval histograms. In addition, it makes testable predictions that follow from the γ latency coding. PMID:21687798

Risk assessment for furan contamination through the food chain in Belgian children.

PubMed

Scholl, Georges; Huybrechts, Inge; Humblet, Marie-France; Scippo, Marie-Louise; De Pauw, Edwin; Eppe, Gauthier; Saegerman, Claude

2012-08-01

Young, old, pregnant and immuno-compromised persons are of great concern for risk assessors as they represent the sub-populations most at risk. The present paper focuses on risk assessment linked to furan exposure in children. Only the Belgian population was considered because individual contamination and consumption data that are required for accurate risk assessment were available for Belgian children only. Two risk assessment approaches, the so-called deterministic and probabilistic, were applied and the results were compared for the estimation of daily intake. A significant difference between the average Estimated Daily Intake (EDI) was underlined between the deterministic (419 ng kg⁻¹ body weight (bw) day⁻¹) and the probabilistic (583 ng kg⁻¹ bw day⁻¹) approaches, which results from the mathematical treatment of the null consumption and contamination data. The risk was characterised by two ways: (1) the classical approach by comparison of the EDI to a reference dose (RfD(chronic-oral)) and (2) the most recent approach, namely the Margin of Exposure (MoE) approach. Both reached similar conclusions: the risk level is not of a major concern, but is neither negligible. In the first approach, only 2.7 or 6.6% (respectively in the deterministic and in the probabilistic way) of the studied population presented an EDI above the RfD(chronic-oral). In the second approach, the percentage of children displaying a MoE above 10,000 and below 100 is 3-0% and 20-0.01% in the deterministic and probabilistic modes, respectively. In addition, children were compared to adults and significant differences between the contamination patterns were highlighted. While major contamination was linked to coffee consumption in adults (55%), no item predominantly contributed to the contamination in children. The most important were soups (19%), dairy products (17%), pasta and rice (11%), fruit and potatoes (9% each).

Variation in the local population dynamics of the short-lived Opuntia macrorhiza (Cactaceae).

PubMed

Haridas, C V; Keeler, Kathleen H; Tenhumberg, Brigitte

2015-03-01

Spatiotemporal variation in demographic rates can have profound effects for population persistence, especially for dispersal-limited species living in fragmented landscapes. Long-term studies of plants in such habitats help with understanding the impacts of fragmentation on population persistence but such studies are rare. In this work, we reanalyzed demographic data from seven years of the short-lived cactus Opuntia macrorhiza var. macrorhiza at five plots in Boulder, Colorado. Previous work combining data from all years and all plots predicted a stable population (deterministic log lamda approximately 0). This approach assumed that all five plots were part of a single population. Since the plots were located in a suburban-agricultural interface separated by highways, grazing lands, and other barriers, and O. macrorhiza is likely dispersal limited, we analyzed the dynamics of each plot separately using stochastic matrix models assuming each plot represented a separate population. We found that the stochastic population growth rate log lamdaS varied widely between populations (log lamdaS = 0.1497, 0.0774, -0.0230, -0.2576, -0.4989). The three populations with the highest growth rates were located close together in space, while the two most isolated populations had the lowest growth rates suggesting that dispersal between populations is critical for the population viability of O. macrorhiza. With one exception, both our prospective (stochastic elasticity) and retrospective (stochastic life table response experiments) analysis suggested that means of stasis and growth, especially of smaller plants, were most important for population growth rate. This is surprising because recruitment is typically the most important vital rate in a short-lived species such as O. macrorhiza. We found that elasticity to the variance was mostly negligible, suggesting that O. macrorhiza populations are buffered against large temporal variation. Finally, single-year elasticities to means of transitions to the smallest stage (mostly due to reproduction) and growth differed considerably from their long-term elasticities. It is important to be aware of this difference when using models to predict the effect of manipulating plant vital rates within the time frame of typical plant demographic studies.

Discrete-time systems with random switches: From systems stability to networks synchronization.

PubMed

Guo, Yao; Lin, Wei; Ho, Daniel W C

2016-03-01

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.

Discrete-time systems with random switches: From systems stability to networks synchronization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Yao; Lin, Wei, E-mail: wlin@fudan.edu.cn; Shanghai Key Laboratory of Contemporary Applied Mathematics, LMNS, and Shanghai Center for Mathematical Sciences, Shanghai 200433

2016-03-15

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developedmore » approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.« less

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

PubMed

Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

2012-01-01

In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

The futility of utility: how market dynamics marginalize Adam Smith

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2000-10-01

Economic theorizing is based on the postulated, nonempiric notion of utility. Economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics I show the following. A utility function generally does not exist mathematically due to nonintegrable dynamics when production/investment are accounted for, resolving Mirowski's thesis. Price as a function of demand does not exist mathematically either. All equilibria are unstable. I then explain how deterministic chaos can be distinguished from random noise at short times. In the generalization to liquid markets and finance theory described by stochastic excess demand dynamics, I also show the following. Market price distributions cannot be rescaled to describe price movements as ‘equilibrium’ fluctuations about a systematic drift in price. Utility maximization does not describe equilibrium. Maximization of the Gibbs entropy of the observed price distribution of an asset would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real, liquid markets (stocks, bonds, foreign exchange). There are three inconsistent definitions of equilibrium used in economics and finance, only one of which is correct. Prices in unregulated free markets are unstable against both noise and rising or falling expectations: Adam Smith's stabilizing invisible hand does not exist, either in mathematical models of liquid market data, or in real market data.

Deterministic Role of Collision Cascade Density in Radiation Defect Dynamics in Si

NASA Astrophysics Data System (ADS)

Wallace, J. B.; Aji, L. B. Bayu; Shao, L.; Kucheyev, S. O.

2018-05-01

The formation of stable radiation damage in solids often proceeds via complex dynamic annealing (DA) processes, involving point defect migration and interaction. The dependence of DA on irradiation conditions remains poorly understood even for Si. Here, we use a pulsed ion beam method to study defect interaction dynamics in Si bombarded in the temperature range from ˜-30 ° C to 210 °C with ions in a wide range of masses, from Ne to Xe, creating collision cascades with different densities. We demonstrate that the complexity of the influence of irradiation conditions on defect dynamics can be reduced to a deterministic effect of a single parameter, the average cascade density, calculated by taking into account the fractal nature of collision cascades. For each ion species, the DA rate exhibits two well-defined Arrhenius regions where different DA mechanisms dominate. These two regions intersect at a critical temperature, which depends linearly on the cascade density. The low-temperature DA regime is characterized by an activation energy of ˜0.1 eV , independent of the cascade density. The high-temperature regime, however, exhibits a change in the dominant DA process for cascade densities above ˜0.04 at.%, evidenced by an increase in the activation energy. These results clearly demonstrate a crucial role of the collision cascade density and can be used to predict radiation defect dynamics in Si.

Deterministic Role of Collision Cascade Density in Radiation Defect Dynamics in Si.

PubMed

Wallace, J B; Aji, L B Bayu; Shao, L; Kucheyev, S O

2018-05-25

The formation of stable radiation damage in solids often proceeds via complex dynamic annealing (DA) processes, involving point defect migration and interaction. The dependence of DA on irradiation conditions remains poorly understood even for Si. Here, we use a pulsed ion beam method to study defect interaction dynamics in Si bombarded in the temperature range from ∼-30 °C to 210 °C with ions in a wide range of masses, from Ne to Xe, creating collision cascades with different densities. We demonstrate that the complexity of the influence of irradiation conditions on defect dynamics can be reduced to a deterministic effect of a single parameter, the average cascade density, calculated by taking into account the fractal nature of collision cascades. For each ion species, the DA rate exhibits two well-defined Arrhenius regions where different DA mechanisms dominate. These two regions intersect at a critical temperature, which depends linearly on the cascade density. The low-temperature DA regime is characterized by an activation energy of ∼0.1  eV, independent of the cascade density. The high-temperature regime, however, exhibits a change in the dominant DA process for cascade densities above ∼0.04 at.%, evidenced by an increase in the activation energy. These results clearly demonstrate a crucial role of the collision cascade density and can be used to predict radiation defect dynamics in Si.

Molecules with an induced dipole moment in a stochastic electric field.

PubMed

Band, Y B; Ben-Shimol, Y

2013-10-01

The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

Nonclassical point of view of the Brownian motion generation via fractional deterministic model

NASA Astrophysics Data System (ADS)

Gilardi-Velázquez, H. E.; Campos-Cantón, E.

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

Distinct Sources of Deterministic and Stochastic Components of Action Timing Decisions in Rodent Frontal Cortex.

PubMed

Murakami, Masayoshi; Shteingart, Hanan; Loewenstein, Yonatan; Mainen, Zachary F

2017-05-17

The selection and timing of actions are subject to determinate influences such as sensory cues and internal state as well as to effectively stochastic variability. Although stochastic choice mechanisms are assumed by many theoretical models, their origin and mechanisms remain poorly understood. Here we investigated this issue by studying how neural circuits in the frontal cortex determine action timing in rats performing a waiting task. Electrophysiological recordings from two regions necessary for this behavior, medial prefrontal cortex (mPFC) and secondary motor cortex (M2), revealed an unexpected functional dissociation. Both areas encoded deterministic biases in action timing, but only M2 neurons reflected stochastic trial-by-trial fluctuations. This differential coding was reflected in distinct timescales of neural dynamics in the two frontal cortical areas. These results suggest a two-stage model in which stochastic components of action timing decisions are injected by circuits downstream of those carrying deterministic bias signals. Copyright © 2017 Elsevier Inc. All rights reserved.

Stability analysis and application of a mathematical cholera model.

PubMed

Liao, Shu; Wang, Jin

2011-07-01

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

PubMed

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Non-Deterministic Modelling of Food-Web Dynamics

PubMed Central

Planque, Benjamin; Lindstrøm, Ulf; Subbey, Sam

2014-01-01

A novel approach to model food-web dynamics, based on a combination of chance (randomness) and necessity (system constraints), was presented by Mullon et al. in 2009. Based on simulations for the Benguela ecosystem, they concluded that observed patterns of ecosystem variability may simply result from basic structural constraints within which the ecosystem functions. To date, and despite the importance of these conclusions, this work has received little attention. The objective of the present paper is to replicate this original model and evaluate the conclusions that were derived from its simulations. For this purpose, we revisit the equations and input parameters that form the structure of the original model and implement a comparable simulation model. We restate the model principles and provide a detailed account of the model structure, equations, and parameters. Our model can reproduce several ecosystem dynamic patterns: pseudo-cycles, variation and volatility, diet, stock-recruitment relationships, and correlations between species biomass series. The original conclusions are supported to a large extent by the current replication of the model. Model parameterisation and computational aspects remain difficult and these need to be investigated further. Hopefully, the present contribution will make this approach available to a larger research community and will promote the use of non-deterministic-network-dynamics models as ‘null models of food-webs’ as originally advocated. PMID:25299245

Chaos and simple determinism in reversed field pinch plasmas: Nonlinear analysis of numerical simulation and experimental data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watts, Christopher A.

In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulatemore » the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

Understanding the transmission dynamics of respiratory syncytial virus using multiple time series and nested models.

PubMed

White, L J; Mandl, J N; Gomes, M G M; Bodley-Tickell, A T; Cane, P A; Perez-Brena, P; Aguilar, J C; Siqueira, M M; Portes, S A; Straliotto, S M; Waris, M; Nokes, D J; Medley, G F

2007-09-01

The nature and role of re-infection and partial immunity are likely to be important determinants of the transmission dynamics of human respiratory syncytial virus (hRSV). We propose a single model structure that captures four possible host responses to infection and subsequent reinfection: partial susceptibility, altered infection duration, reduced infectiousness and temporary immunity (which might be partial). The magnitude of these responses is determined by four homotopy parameters, and by setting some of these parameters to extreme values we generate a set of eight nested, deterministic transmission models. In order to investigate hRSV transmission dynamics, we applied these models to incidence data from eight international locations. Seasonality is included as cyclic variation in transmission. Parameters associated with the natural history of the infection were assumed to be independent of geographic location, while others, such as those associated with seasonality, were assumed location specific. Models incorporating either of the two extreme assumptions for immunity (none or solid and lifelong) were unable to reproduce the observed dynamics. Model fits with either waning or partial immunity to disease or both were visually comparable. The best fitting structure was a lifelong partial immunity to both disease and infection. Observed patterns were reproduced by stochastic simulations using the parameter values estimated from the deterministic models.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

NASA Astrophysics Data System (ADS)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

End-of-life flows of multiple cycle consumer products.

PubMed

Tsiliyannis, C A

2011-11-01

Explicit expressions for the end-of-life flows (EOL) of single and multiple cycle products (MCPs) are presented, including deterministic and stochastic EOL exit. The expressions are given in terms of the physical parameters (maximum lifetime, T, annual cycling frequency, f, number of cycles, N, and early discard or usage loss). EOL flows are also obtained for hi-tech products, which are rapidly renewed and thus may not attain steady state (e.g., electronic products, passenger cars). A ten-step recursive procedure for obtaining the dynamic EOL flow evolution is proposed. Applications of the EOL expressions and the ten-step procedure are given for electric household appliances, industrial machinery, tyres, vehicles and buildings, both for deterministic and stochastic EOL exit, (normal, Weibull and uniform exit distributions). The effect of the physical parameters and the stochastic characteristics on the EOL flow is investigated in the examples: it is shown that the EOL flow profile is determined primarily by the early discard dynamics; it also depends strongly on longevity and cycling frequency: higher lifetime or early discard/loss imply lower dynamic and steady state EOL flows. The stochastic exit shapes the overall EOL dynamic profile: Under symmetric EOL exit distribution, as the variance of the distribution increases (uniform to normal to deterministic) the initial EOL flow rise becomes steeper but the steady state or maximum EOL flow level is lower. The steepest EOL flow profile, featuring the highest steady state or maximum level, as well, corresponds to skew, earlier shifted EOL exit (e.g., Weibull). Since the EOL flow of returned products consists the sink of the reuse/remanufacturing cycle (sink to recycle) the results may be used in closed loop product lifecycle management operations for scheduling and sizing reverse manufacturing and for planning recycle logistics. Decoupling and quantification of both the full age EOL and of the early discard flows is useful, the latter being the target of enacted legislation aiming at increasing reuse. Copyright © 2011 Elsevier Ltd. All rights reserved.

Optimal exploitation strategies for an animal population in a Markovian environment: A theory and an example

USGS Publications Warehouse

Anderson, D.R.

1975-01-01

Optimal exploitation strategies were studied for an animal population in a Markovian (stochastic, serially correlated) environment. This is a general case and encompasses a number of important special cases as simplifications. Extensive empirical data on the Mallard (Anas platyrhynchos) were used as an example of general theory. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. A general mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. The literature and analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, two hypotheses were explored: (1) exploitation mortality represents a largely additive form of mortality, and (2) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under the rather general conditions. Direct feedback control was an integral component in the optimal decision-making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. If we assume that exploitation is largely an additive force of mortality in Mallards, then optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slight concave function of the environmental conditions. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the Mallard breeding population. Dynamic programming is suggested as a very general formulation for realistic solutions to the general optimal exploitation problem. The concepts of state vectors and stage transformations are completely general. Populations can be modeled stochastically and the objective function can include extra-biological factors. The optimal level of exploitation in year t must be based on the observed size of the population and the state of the environment in year t unless the dynamics of the population, the state of the environment, and the result of the exploitation decisions are completely deterministic. Exploitation based on an average harvest, or harvest rate, or designed to maintain a constant breeding population size is inefficient.

Dynamic Stability of Uncertain Laminated Beams Under Subtangential Loads

NASA Technical Reports Server (NTRS)

Goyal, Vijay K.; Kapania, Rakesh K.; Adelman, Howard (Technical Monitor); Horta, Lucas (Technical Monitor)

2002-01-01

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.

Relation Between the Cell Volume and the Cell Cycle Dynamics in Mammalian cell

NASA Astrophysics Data System (ADS)

Magno, A. C. G.; Oliveira, I. L.; Hauck, J. V. S.

2016-08-01

The main goal of this work is to add and analyze an equation that represents the volume in a dynamical model of the mammalian cell cycle proposed by Gérard and Goldbeter (2011) [1]. The cell division occurs when the cyclinB/Cdkl complex is totally degraded (Tyson and Novak, 2011)[2] and it reaches a minimum value. At this point, the cell is divided into two newborn daughter cells and each one will contain the half of the cytoplasmic content of the mother cell. The equations of our base model are only valid if the cell volume, where the reactions occur, is constant. Whether the cell volume is not constant, that is, the rate of change of its volume with respect to time is explicitly taken into account in the mathematical model, then the equations of the original model are no longer valid. Therefore, every equations were modified from the mass conservation principle for considering a volume that changes with time. Through this approach, the cell volume affects all model variables. Two different dynamic simulation methods were accomplished: deterministic and stochastic. In the stochastic simulation, the volume affects every model's parameters which have molar unit, whereas in the deterministic one, it is incorporated into the differential equations. In deterministic simulation, the biochemical species may be in concentration units, while in stochastic simulation such species must be converted to number of molecules which are directly proportional to the cell volume. In an effort to understand the influence of the new equation a stability analysis was performed. This elucidates how the growth factor impacts the stability of the model's limit cycles. In conclusion, a more precise model, in comparison to the base model, was created for the cell cycle as it now takes into consideration the cell volume variation

Detailed numerical investigation of the dissipative stochastic mechanics based neuron model.

PubMed

Güler, Marifi

2008-10-01

Recently, a physical approach for the description of neuronal dynamics under the influence of ion channel noise was proposed in the realm of dissipative stochastic mechanics (Güler, Phys Rev E 76:041918, 2007). Led by the presence of a multiple number of gates in an ion channel, the approach establishes a viewpoint that ion channels are exposed to two kinds of noise: the intrinsic noise, associated with the stochasticity in the movement of gating particles between the inner and the outer faces of the membrane, and the topological noise, associated with the uncertainty in accessing the permissible topological states of open gates. Renormalizations of the membrane capacitance and of a membrane voltage dependent potential function were found to arise from the mutual interaction of the two noisy systems. The formalism therein was scrutinized using a special membrane with some tailored properties giving the Rose-Hindmarsh dynamics in the deterministic limit. In this paper, the resultant computational neuron model of the above approach is investigated in detail numerically for its dynamics using time-independent input currents. The following are the major findings obtained. The intrinsic noise gives rise to two significant coexisting effects: it initiates spiking activity even in some range of input currents for which the corresponding deterministic model is quiet and causes bursting in some other range of input currents for which the deterministic model fires tonically. The renormalization corrections are found to augment the above behavioral transitions from quiescence to spiking and from tonic firing to bursting, and, therefore, the bursting activity is found to take place in a wider range of input currents for larger values of the correction coefficients. Some findings concerning the diffusive behavior in the voltage space are also reported.

Deterministic and stochastic models for middle east respiratory syndrome (MERS)

NASA Astrophysics Data System (ADS)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Calculating complete and exact Pareto front for multiobjective optimization: a new deterministic approach for discrete problems.

PubMed

Hu, Xiao-Bing; Wang, Ming; Di Paolo, Ezequiel

2013-06-01

Searching the Pareto front for multiobjective optimization problems usually involves the use of a population-based search algorithm or of a deterministic method with a set of different single aggregate objective functions. The results are, in fact, only approximations of the real Pareto front. In this paper, we propose a new deterministic approach capable of fully determining the real Pareto front for those discrete problems for which it is possible to construct optimization algorithms to find the k best solutions to each of the single-objective problems. To this end, two theoretical conditions are given to guarantee the finding of the actual Pareto front rather than its approximation. Then, a general methodology for designing a deterministic search procedure is proposed. A case study is conducted, where by following the general methodology, a ripple-spreading algorithm is designed to calculate the complete exact Pareto front for multiobjective route optimization. When compared with traditional Pareto front search methods, the obvious advantage of the proposed approach is its unique capability of finding the complete Pareto front. This is illustrated by the simulation results in terms of both solution quality and computational efficiency.

The Stochastic Modelling of Endemic Diseases

NASA Astrophysics Data System (ADS)

Susvitasari, Kurnia; Siswantining, Titin

2017-01-01

A study about epidemic has been conducted since a long time ago, but genuine progress was hardly forthcoming until the end of the 19th century (Bailey, 1975). Both deterministic and stochastic models were used to describe these. Then, from 1927 to 1939 Kermack and McKendrick introduced a generality of this model, including some variables to consider such as rate of infection and recovery. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, R0. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when R0 ≤ 1, minor epidemic occurs with probability one in both approaches, but when R0 > 1, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when R0 > 1 and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic’s equilibrium.

Exploiting ecology in drug pulse sequences in favour of population reduction.

PubMed

Bauer, Marianne; Graf, Isabella R; Ngampruetikorn, Vudtiwat; Stephens, Greg J; Frey, Erwin

2017-09-01

A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment.

Demographic variation and conservation of the narrow endemic plant Ranunculus weyleri

NASA Astrophysics Data System (ADS)

Cursach, Joana; Besnard, Aurélien; Rita, Juan; Fréville, Hélène

2013-11-01

Ranunculus weyleri is a narrow endemic protected plant from Majorca Island. It is known from only five populations located in two mountain areas 48 km apart. Using demographic data collected from 2007 to 2010, we assessed the demographic status of two populations - font des Coloms (FC) and talaia Moreia (TM) - using Integral Projection Models (IPMs). We showed that none of the two populations were declining under a deterministic model. Population FC was stable (λ = 1.026, CI95% = 0.965-1.093), while population TM showed sign of demographic expansion (λ = 1.113, CI95% = 1.032-1.219). Plant survival, flowering probability and the mean number of seedlings per floral peduncle were lower in TM, whereas growth and the number of floral peduncles per reproductive plant were lower in FC. Elasticity analyses showed that management strategies increasing plant survival and growth would be the most efficient to increase λ for both populations. Herbivory pressure by goats has been shown to be high in TM, resulting in high predation rate on floral peduncles. Controlling goat pressure may thus represent a promising management option, provided that we can demonstrate a negative impact of herbivory by goats on survival and growth which are the most critical parts of the life cycle in this species. Meanwhile, initiating a long-term monitoring is of crucial importance to get more insights into the relationships between environmental variation, plant performance and population dynamics.

Coupled replicator equations for the dynamics of learning in multiagent systems

NASA Astrophysics Data System (ADS)

Sato, Yuzuru; Crutchfield, James P.

2003-01-01

Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game interactions shows that the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos—behaviors that should be expected in heterogeneous multiagent systems described by the general replicator equations we derive.

Coexistence and chaos in complex ecologies [rapid communication

NASA Astrophysics Data System (ADS)

Sprott, J. C.; Vano, J. A.; Wildenberg, J. C.; Anderson, M. B.; Noel, J. K.

2005-02-01

Many complex dynamical systems in ecology, economics, neurology, and elsewhere, in which agents compete for limited resources, exhibit apparently chaotic fluctuations. This Letter proposes a purely deterministic mechanism for evolving robustly but weakly chaotic systems that exhibit adaptation, self-organization, sporadic volatility, and punctuated equilibria.

Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization

NASA Astrophysics Data System (ADS)

Sochi, Taha

2016-09-01

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

Prediction of the Arctic Oscillation in Boreal Winter by Dynamical Seasonal Forecasting Systems

NASA Technical Reports Server (NTRS)

Kang, Daehyun; Lee, Myong-In; Im, Jungho; Kim, Daehyun; Kim, Hye-Mi; Kang, Hyun-Suk; Shubert, Siegfried D.; Arriba, Albertom; MacLachlan, Craig

2013-01-01

This study assesses the prediction skill of the boreal winter Arctic Oscillation (AO) in the state-of-the-art dynamical ensemble prediction systems (EPSs): the UKMO GloSea4, the NCEP CFSv2, and the NASA GEOS-5. Long-term reforecasts made with the EPSs are used to evaluate representations of the AO, and to examine skill scores for the deterministic and probabilistic forecast of the AO index. The reforecasts reproduce the observed changes in the large-scale patterns of the Northern Hemispheric surface temperature, upper-level wind, and precipitation according to the AO phase. Results demonstrate that all EPSs have better prediction skill than the persistence prediction for lead times up to 3-month, suggesting a great potential for skillful prediction of the AO and the associated climate anomalies in seasonal time scale. It is also found that the deterministic and probabilistic forecast skill of the AO in the recent period (1997-2010) is higher than that in the earlier period (1983-1996).

Topological chaos of the spatial prisoner's dilemma game on regular networks.

PubMed

Jin, Weifeng; Chen, Fangyue

2016-02-21

The spatial version of evolutionary prisoner's dilemma on infinitely large regular lattice with purely deterministic strategies and no memories among players is investigated in this paper. Based on the statistical inferences, it is pertinent to confirm that the frequency of cooperation for characterizing its macroscopic behaviors is very sensitive to the initial conditions, which is the most practically significant property of chaos. Its intrinsic complexity is then justified on firm ground from the theory of symbolic dynamics; that is, this game is topologically mixing and possesses positive topological entropy on its subsystems. It is demonstrated therefore that its frequency of cooperation could not be adopted by simply averaging over several steps after the game reaches the equilibrium state. Furthermore, the chaotically changing spatial patterns via empirical observations can be defined and justified in view of symbolic dynamics. It is worth mentioning that the procedure proposed in this work is also applicable to other deterministic spatial evolutionary games therein. Copyright © 2015 Elsevier Ltd. All rights reserved.

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr

2016-10-15

We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product,more » the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.« less

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

The effect of loss of immunity on noise-induced sustained oscillations in epidemics.

PubMed

Chaffee, J; Kuske, R

2011-11-01

The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.

Detection of bifurcations in noisy coupled systems from multiple time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williamson, Mark S., E-mail: m.s.williamson@exeter.ac.uk; Lenton, Timothy M.

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, themore » possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.« less

Detection of bifurcations in noisy coupled systems from multiple time series

NASA Astrophysics Data System (ADS)

Williamson, Mark S.; Lenton, Timothy M.

2015-03-01

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.

Study of a tri-trophic prey-dependent food chain model of interacting populations.

PubMed

Haque, Mainul; Ali, Nijamuddin; Chakravarty, Santabrata

2013-11-01

The current paper accounts for the influence of intra-specific competition among predators in a prey dependent tri-trophic food chain model of interacting populations. We offer a detailed mathematical analysis of the proposed food chain model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. Biologically feasible equilibria of the system are observed and the behaviours of the system around each of them are described. In particular, persistence, stability (local and global) and bifurcation (saddle-node, transcritical, Hopf-Andronov) analysis of this model are obtained. Relevant results from previous well known food chain models are compared with the current findings. Global stability analysis is also carried out by constructing appropriate Lyapunov functions. Numerical simulations show that the present system is capable enough to produce chaotic dynamics when the rate of self-interaction is very low. On the other hand such chaotic behaviour disappears for a certain value of the rate of self interaction. In addition, numerical simulations with experimented parameters values confirm the analytical results and shows that intra-specific competitions bears a potential role in controlling the chaotic dynamics of the system; and thus the role of self interactions in food chain model is illustrated first time. Finally, a discussion of the ecological applications of the analytical and numerical findings concludes the paper. Copyright © 2013 Elsevier Inc. All rights reserved.

Amplification of intrinsic fluctuations by the Lorenz equations

NASA Astrophysics Data System (ADS)

Fox, Ronald F.; Elston, T. C.

1993-07-01

Macroscopic systems (e.g., hydrodynamics, chemical reactions, electrical circuits, etc.) manifest intrinsic fluctuations of molecular and thermal origin. When the macroscopic dynamics is deterministically chaotic, the intrinsic fluctuations may become amplified by several orders of magnitude. Numerical studies of this phenomenon are presented in detail for the Lorenz model. Amplification to macroscopic scales is exhibited, and quantitative methods (binning and a difference-norm) are presented for measuring macroscopically subliminal amplification effects. In order to test the quality of the numerical results, noise induced chaos is studied around a deterministically nonchaotic state, where the scaling law relating the Lyapunov exponent to noise strength obtained for maps is confirmed for the Lorenz model, a system of ordinary differential equations.

Transmission of chronic wasting disease in Wisconsin white-tailed deer: Implications for disease spread and management

USGS Publications Warehouse

Jennelle, Christopher S.; Henaux, Viviane; Wasserberg, Gideon; Thiagarajan, Bala; Rolley, Robert E.; Samuel, Michael D.

2014-01-01

Few studies have evaluated the rate of infection or mode of transmission for wildlife diseases, and the implications of alternative management strategies. We used hunter harvest data from 2002 to 2013 to investigate chronic wasting disease (CWD) infection rate and transmission modes, and address how alternative management approaches affect disease dynamics in a Wisconsin white-tailed deer population. Uncertainty regarding demographic impacts of CWD on cervid populations, human and domestic animal health concerns, and potential economic consequences underscore the need for strategies to control CWD distribution and prevalence. Using maximum-likelihood methods to evaluate alternative multi-state deterministic models of CWD transmission, harvest data strongly supports a frequency-dependent transmission structure with sex-specific infection rates that are two times higher in males than females. As transmissible spongiform encephalopathies are an important and difficult-to-study class of diseases with major economic and ecological implications, our work supports the hypothesis of frequency-dependent transmission in wild deer at a broad spatial scale and indicates that effective harvest management can be implemented to control CWD prevalence. Specifically, we show that harvest focused on the greater-affected sex (males) can result in stable population dynamics and control of CWD within the next 50 years, given the constraints of the model. We also provide a quantitative estimate of geographic disease spread in southern Wisconsin, validating qualitative assessments that CWD spreads relatively slowly. Given increased discovery and distribution of CWD throughout North America, insights from our study are valuable to management agencies and to the general public concerned about the impacts of CWD on white-tailed deer populations.

Transmission of Chronic Wasting Disease in Wisconsin White-Tailed Deer: Implications for Disease Spread and Management

PubMed Central

Jennelle, Christopher S.; Henaux, Viviane; Wasserberg, Gideon; Thiagarajan, Bala; Rolley, Robert E.; Samuel, Michael D.

2014-01-01

Few studies have evaluated the rate of infection or mode of transmission for wildlife diseases, and the implications of alternative management strategies. We used hunter harvest data from 2002 to 2013 to investigate chronic wasting disease (CWD) infection rate and transmission modes, and address how alternative management approaches affect disease dynamics in a Wisconsin white-tailed deer population. Uncertainty regarding demographic impacts of CWD on cervid populations, human and domestic animal health concerns, and potential economic consequences underscore the need for strategies to control CWD distribution and prevalence. Using maximum-likelihood methods to evaluate alternative multi-state deterministic models of CWD transmission, harvest data strongly supports a frequency-dependent transmission structure with sex-specific infection rates that are two times higher in males than females. As transmissible spongiform encephalopathies are an important and difficult-to-study class of diseases with major economic and ecological implications, our work supports the hypothesis of frequency-dependent transmission in wild deer at a broad spatial scale and indicates that effective harvest management can be implemented to control CWD prevalence. Specifically, we show that harvest focused on the greater-affected sex (males) can result in stable population dynamics and control of CWD within the next 50 years, given the constraints of the model. We also provide a quantitative estimate of geographic disease spread in southern Wisconsin, validating qualitative assessments that CWD spreads relatively slowly. Given increased discovery and distribution of CWD throughout North America, insights from our study are valuable to management agencies and to the general public concerned about the impacts of CWD on white-tailed deer populations. PMID:24658535

Invited Review: A review of deterministic effects in cyclic variability of internal combustion engines

DOE PAGES

Finney, Charles E.; Kaul, Brian C.; Daw, C. Stuart; ...

2015-02-18

Here we review developments in the understanding of cycle to cycle variability in internal combustion engines, with a focus on spark-ignited and premixed combustion conditions. Much of the research on cyclic variability has focused on stochastic aspects, that is, features that can be modeled as inherently random with no short term predictability. In some cases, models of this type appear to work very well at describing experimental observations, but the lack of predictability limits control options. Also, even when the statistical properties of the stochastic variations are known, it can be very difficult to discern their underlying physical causes andmore » thus mitigate them. Some recent studies have demonstrated that under some conditions, cyclic combustion variations can have a relatively high degree of low dimensional deterministic structure, which implies some degree of predictability and potential for real time control. These deterministic effects are typically more pronounced near critical stability limits (e.g. near tipping points associated with ignition or flame propagation) such during highly dilute fueling or near the onset of homogeneous charge compression ignition. We review recent progress in experimental and analytical characterization of cyclic variability where low dimensional, deterministic effects have been observed. We describe some theories about the sources of these dynamical features and discuss prospects for interactive control and improved engine designs. In conclusion, taken as a whole, the research summarized here implies that the deterministic component of cyclic variability will become a pivotal issue (and potential opportunity) as engine manufacturers strive to meet aggressive emissions and fuel economy regulations in the coming decades.« less

Deterministic influences exceed dispersal effects on hydrologically-connected microbiomes: Deterministic assembly of hyporheic microbiomes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graham, Emily B.; Crump, Alex R.; Resch, Charles T.

2017-03-28

Subsurface zones of groundwater and surface water mixing (hyporheic zones) are regions of enhanced rates of biogeochemical cycling, yet ecological processes governing hyporheic microbiome composition and function through space and time remain unknown. We sampled attached and planktonic microbiomes in the Columbia River hyporheic zone across seasonal hydrologic change, and employed statistical null models to infer mechanisms generating temporal changes in microbiomes within three hydrologically-connected, physicochemically-distinct geographic zones (inland, nearshore, river). We reveal that microbiomes remain dissimilar through time across all zones and habitat types (attached vs. planktonic) and that deterministic assembly processes regulate microbiome composition in all data subsets.more » The consistent presence of heterotrophic taxa and members of the Planctomycetes-Verrucomicrobia-Chlamydiae (PVC) superphylum nonetheless suggests common selective pressures for physiologies represented in these groups. Further, co-occurrence networks were used to provide insight into taxa most affected by deterministic assembly processes. We identified network clusters to represent groups of organisms that correlated with seasonal and physicochemical change. Extended network analyses identified keystone taxa within each cluster that we propose are central in microbiome composition and function. Finally, the abundance of one network cluster of nearshore organisms exhibited a seasonal shift from heterotrophic to autotrophic metabolisms and correlated with microbial metabolism, possibly indicating an ecological role for these organisms as foundational species in driving biogeochemical reactions within the hyporheic zone. Taken together, our research demonstrates a predominant role for deterministic assembly across highly-connected environments and provides insight into niche dynamics associated with seasonal changes in hyporheic microbiome composition and metabolism.« less

Epidemic characterization and modeling within herd transmission dynamics of an "emerging trans-boundary" camel disease epidemic in Ethiopia.

PubMed

Megersa, Bekele; Biffa, Demelash; Abunna, Fufa; Regassa, Alemayehu; Bohlin, Jon; Skjerve, Eystein

2012-10-01

A highly acute and contagious camel disease, an epidemic wave of unknown etiology, referred to here as camel sudden death syndrome, has plagued camel population in countries in the Horn of Africa. To better understand its epidemic patterns and transmission dynamics, we used epidemiologic parameters and differential equation deterministic modeling (SEIR/D-model) to predict the outcome likelihood following an exposure of susceptible camel population. Our results showed 45.7, 17.6, and 38.6 % overall morbidity, mortality, and case fatality rates of the epidemic, respectively. Pregnant camels had the highest mortality and case fatality rates, followed by breeding males, and lactating females, implying serious socioeconomic consequences. Disease dynamics appeared to be linked to livestock trade route and animal movements. The epidemic exhibited a strong basic reproductive number (R (0)) with an average of 16 camels infected by one infectious case during the entire infectious period. The epidemic curve suggested that the critical moment of the disease development is approximately between 30 and 40 days, where both infected/exposed and infectious camels are at their highest numbers. The lag between infected/infectious curves indicates a time-shift of approximately 3-5 days from when a camel is infected and until it becomes infectious. According to this predictive model, of all animals exposed to the infection, 66.8 % (n = 868) and 33.2 % (n = 431) had recovered and died, respectively, at the end of epidemic period. Hence, if early measures are not taken, such an epidemic could cause a much more devastative effect, within short period of time than the anticipated proportion.

About the discrete-continuous nature of a hematopoiesis model for Chronic Myeloid Leukemia.

PubMed

Gaudiano, Marcos E; Lenaerts, Tom; Pacheco, Jorge M

2016-12-01

Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can - on average - easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system. Copyright © 2016 Elsevier Inc. All rights reserved.

Geometric Universality in Brain Allosteric Protein Dynamics: Complex Hydrophobic Transformation Predicts Mutual Recognition by Polypeptides and Proteins,

DTIC Science & Technology

1986-10-01

organic acids using the Hammett equation , has been called the hydrophobic effect.’ Water adjusts its geometry to maximize the number of intact hydrogen...understanding both structural stability with respect to the underlying equations (not initial values) and phase transitions in these dynamical hierarchies...for quantitative characterization. Although the complicated behavior is gen- erated by deterministic equations , its description in entropies leads to

PROCEEDINGS OF THE SYMPOSIUM ON SYSTEM THEORY, NEW YORK, N. Y. APRIL 20, 21, 22 1965. VOLUME XV.

DTIC Science & Technology

The papers presented at the symposium may be grouped as follows: (1) What is system theory ; (2) Representations of systems; (3) System dynamics; (4...Non-deterministic systems; (5) Optimal systems; and (6) Applications of system theory .

Intrinsically-generated fluctuating activity in excitatory-inhibitory networks.

PubMed

Mastrogiuseppe, Francesca; Ostojic, Srdjan

2017-04-01

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsically generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynamical regimes of randomly-connected rate networks with segregated excitatory and inhibitory populations, and firing rates constrained to be positive. These works derived general dynamical mean field (DMF) equations describing the fluctuating dynamics, but solved these equations only in the case of purely inhibitory networks. Using a simplified excitatory-inhibitory architecture in which DMF equations are more easily tractable, here we show that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks. In presence of excitation, intrinsically generated fluctuations induce a strong increase in mean firing rates, a phenomenon that is much weaker in purely inhibitory networks. Excitation moreover induces two different fluctuating regimes: for moderate overall coupling, recurrent inhibition is sufficient to stabilize fluctuations; for strong coupling, firing rates are stabilized solely by the upper bound imposed on activity, even if inhibition is stronger than excitation. These results extend to more general network architectures, and to rate networks receiving noisy inputs mimicking spiking activity. Finally, we show that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons.

Linking river management to species conservation using dynamic landscape scale models

USGS Publications Warehouse

Freeman, Mary C.; Buell, Gary R.; Hay, Lauren E.; Hughes, W. Brian; Jacobson, Robert B.; Jones, John W.; Jones, S.A.; LaFontaine, Jacob H.; Odom, Kenneth R.; Peterson, James T.; Riley, Jeffrey W.; Schindler, J. Stephen; Shea, C.; Weaver, J.D.

2013-01-01

Efforts to conserve stream and river biota could benefit from tools that allow managers to evaluate landscape-scale changes in species distributions in response to water management decisions. We present a framework and methods for integrating hydrology, geographic context and metapopulation processes to simulate effects of changes in streamflow on fish occupancy dynamics across a landscape of interconnected stream segments. We illustrate this approach using a 482 km2 catchment in the southeastern US supporting 50 or more stream fish species. A spatially distributed, deterministic and physically based hydrologic model is used to simulate daily streamflow for sub-basins composing the catchment. We use geographic data to characterize stream segments with respect to channel size, confinement, position and connectedness within the stream network. Simulated streamflow dynamics are then applied to model fish metapopulation dynamics in stream segments, using hypothesized effects of streamflow magnitude and variability on population processes, conditioned by channel characteristics. The resulting time series simulate spatially explicit, annual changes in species occurrences or assemblage metrics (e.g. species richness) across the catchment as outcomes of management scenarios. Sensitivity analyses using alternative, plausible links between streamflow components and metapopulation processes, or allowing for alternative modes of fish dispersal, demonstrate large effects of ecological uncertainty on model outcomes and highlight needed research and monitoring. Nonetheless, with uncertainties explicitly acknowledged, dynamic, landscape-scale simulations may prove useful for quantitatively comparing river management alternatives with respect to species conservation.

Intrinsically-generated fluctuating activity in excitatory-inhibitory networks

PubMed Central

Mastrogiuseppe, Francesca; Ostojic, Srdjan

2017-01-01

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsically generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynamical regimes of randomly-connected rate networks with segregated excitatory and inhibitory populations, and firing rates constrained to be positive. These works derived general dynamical mean field (DMF) equations describing the fluctuating dynamics, but solved these equations only in the case of purely inhibitory networks. Using a simplified excitatory-inhibitory architecture in which DMF equations are more easily tractable, here we show that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks. In presence of excitation, intrinsically generated fluctuations induce a strong increase in mean firing rates, a phenomenon that is much weaker in purely inhibitory networks. Excitation moreover induces two different fluctuating regimes: for moderate overall coupling, recurrent inhibition is sufficient to stabilize fluctuations; for strong coupling, firing rates are stabilized solely by the upper bound imposed on activity, even if inhibition is stronger than excitation. These results extend to more general network architectures, and to rate networks receiving noisy inputs mimicking spiking activity. Finally, we show that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons. PMID:28437436

Extinction risk of Ipomopsis sancti-spiritus in Holy Ghost Canyon with and without management intervention

Treesearch

Joyce Maschinski

2001-01-01

Small populations are threatened with deterministic and stochastic events that can drive the number of individuals below a critical threshold for survival. Long-term studies allow us to increase our understanding of processes required for their conservation. In the past 7 years, the population of the federally endangered Holy Ghost ipomopsis (Ipomopsis sancti-spiritus...

Rabies epidemic model with uncertainty in parameters: crisp and fuzzy approaches

NASA Astrophysics Data System (ADS)

Ndii, M. Z.; Amarti, Z.; Wiraningsih, E. D.; Supriatna, A. K.

2018-03-01

A deterministic mathematical model is formulated to investigate the transmission dynamics of rabies. In particular, we investigate the effects of vaccination, carrying capacity and the transmission rate on the rabies epidemics and allow for uncertainty in the parameters. We perform crisp and fuzzy approaches. We find that, in the case of crisp parameters, rabies epidemics may be interrupted when the carrying capacity and the transmission rate are not high. Our findings suggest that limiting the growth of dog population and reducing the potential contact between susceptible and infectious dogs may aid in interrupting rabies epidemics. We extend the work by considering a fuzzy carrying capacity and allow for low, medium, and high level of carrying capacity. The result confirms the results obtained by using crisp carrying capacity, that is, when the carrying capacity is not too high, the vaccination could confine the disease effectively.

The importance of environmental variability and management control error to optimal harvest policies

USGS Publications Warehouse

Hunter, C.M.; Runge, M.C.

2004-01-01

State-dependent strategies (SDSs) are the most general form of harvest policy because they allow the harvest rate to depend, without constraint, on the state of the system. State-dependent strategies that provide an optimal harvest rate for any system state can be calculated, and stochasticity can be appropriately accommodated in this optimization. Stochasticity poses 2 challenges to harvest policies: (1) the population will never be at the equilibrium state; and (2) stochasticity induces uncertainty about future states. We investigated the effects of 2 types of stochasticity, environmental variability and management control error, on SDS harvest policies for a white-tailed deer (Odocoileus virginianus) model, and contrasted these with a harvest policy based on maximum sustainable yield (MSY). Increasing stochasticity resulted in more conservative SDSs; that is, higher population densities were required to support the same harvest rate, but these effects were generally small. As stochastic effects increased, SDSs performed much better than MSY. Both deterministic and stochastic SDSs maintained maximum mean annual harvest yield (AHY) and optimal equilibrium population size (Neq) in a stochastic environment, whereas an MSY policy could not. We suggest 3 rules of thumb for harvest management of long-lived vertebrates in stochastic systems: (1) an SDS is advantageous over an MSY policy, (2) using an SDS rather than an MSY is more important than whether a deterministic or stochastic SDS is used, and (3) for SDSs, rankings of the variability in management outcomes (e.g., harvest yield) resulting from parameter stochasticity can be predicted by rankings of the deterministic elasticities.

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks.

PubMed

Ben Abdallah, Emna; Folschette, Maxime; Roux, Olivier; Magnin, Morgan

2017-01-01

This paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors. We present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature. The originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

Ecological Succession Pattern of Fungal Community in Soil along a Retreating Glacier

PubMed Central

Tian, Jianqing; Qiao, Yuchen; Wu, Bing; Chen, Huai; Li, Wei; Jiang, Na; Zhang, Xiaoling; Liu, Xingzhong

2017-01-01

Accelerated by global climate changing, retreating glaciers leave behind soil chronosequences of primary succession. Current knowledge of primary succession is mainly from studies of vegetation dynamics, whereas information about belowground microbes remains unclear. Here, we combined shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. We investigated fungal succession and community assembly via high-throughput sequencing along a well-established glacier forefront chronosequence that spans 2–188 years of deglaciation. Shannon diversity and evenness peaked at a distance of 370 m and declined afterwards. The response of fungal diversity to distance varied in different phyla. Basidiomycota Shannon diversity significantly decreased with distance, while the pattern of Rozellomycota Shannon diversity was unimodal. Abundance of most frequencies OTU2 (Cryptococcus terricola) increased with successional distance, whereas that of OTU65 (Tolypocladium tundrense) decreased. Based on null deviation analyses, composition of the fungal community was initially governed by deterministic processes strongly but later less deterministic processes. Our results revealed that distance, altitude, soil microbial biomass carbon, soil microbial biomass nitrogen and NH4+–N significantly correlated with fungal community composition along the chronosequence. These results suggest that the drivers of fungal community are dynamics in a glacier chronosequence, that may relate to fungal ecophysiological traits and adaptation in an evolving ecosystem. The information will provide understanding the mechanistic underpinnings of microbial community assembly during ecosystem succession under different scales and scenario. PMID:28649234

Ecological Succession Pattern of Fungal Community in Soil along a Retreating Glacier.

PubMed

Tian, Jianqing; Qiao, Yuchen; Wu, Bing; Chen, Huai; Li, Wei; Jiang, Na; Zhang, Xiaoling; Liu, Xingzhong

2017-01-01

Accelerated by global climate changing, retreating glaciers leave behind soil chronosequences of primary succession. Current knowledge of primary succession is mainly from studies of vegetation dynamics, whereas information about belowground microbes remains unclear. Here, we combined shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. We investigated fungal succession and community assembly via high-throughput sequencing along a well-established glacier forefront chronosequence that spans 2-188 years of deglaciation. Shannon diversity and evenness peaked at a distance of 370 m and declined afterwards. The response of fungal diversity to distance varied in different phyla. Basidiomycota Shannon diversity significantly decreased with distance, while the pattern of Rozellomycota Shannon diversity was unimodal. Abundance of most frequencies OTU2 ( Cryptococcus terricola ) increased with successional distance, whereas that of OTU65 ( Tolypocladium tundrense ) decreased. Based on null deviation analyses, composition of the fungal community was initially governed by deterministic processes strongly but later less deterministic processes. Our results revealed that distance, altitude, soil microbial biomass carbon, soil microbial biomass nitrogen and [Formula: see text]-N significantly correlated with fungal community composition along the chronosequence. These results suggest that the drivers of fungal community are dynamics in a glacier chronosequence, that may relate to fungal ecophysiological traits and adaptation in an evolving ecosystem. The information will provide understanding the mechanistic underpinnings of microbial community assembly during ecosystem succession under different scales and scenario.

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

Nonlinear unitary quantum collapse model with self-generated noise

NASA Astrophysics Data System (ADS)

Geszti, Tamás

2018-04-01

Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.

Genetic architecture and the evolution of sex.

PubMed

Lohaus, Rolf; Burch, Christina L; Azevedo, Ricardo B R

2010-01-01

Theoretical investigations of the advantages of sex have tended to treat the genetic architecture of organisms as static and have not considered that genetic architecture might coevolve with reproductive mode. As a result, some potential advantages of sex may have been missed. Using a gene network model, we recently showed that recombination imposes selection for robustness to mutation and that negative epistasis can evolve as a by-product of this selection. These results motivated a detailed exploration of the mutational deterministic hypothesis, a hypothesis in which the advantage of sex depends critically on epistasis. We found that sexual populations do evolve higher mean fitness and lower genetic load than asexual populations at equilibrium, and, under moderate stabilizing selection and large population size, these equilibrium sexual populations resist invasion by asexuals. However, we found no evidence that these long- and short-term advantages to sex were explained by the negative epistasis that evolved in our experiments. The long-term advantage of sex was that sexual populations evolved a lower deleterious mutation rate, but this property was not sufficient to account for the ability of sexual populations to resist invasion by asexuals. The ability to resist asexual invasion was acquired simultaneously with an increase in recombinational robustness that minimized the cost of sex. These observations provide the first direct evidence that sexual reproduction does indeed select for conditions that favor its own maintenance. Furthermore, our results highlight the importance of considering a dynamic view of the genetic architecture to understand the evolution of sex and recombination.

Active adaptive management for reintroduction of an animal population

USGS Publications Warehouse

Runge, Michael C.

2013-01-01

Captive animals are frequently reintroduced to the wild in the face of uncertainty, but that uncertainty can often be reduced over the course of the reintroduction effort, providing the opportunity for adaptive management. One common uncertainty in reintroductions is the short-term survival rate of released adults (a release cost), an important factor because it can affect whether releasing adults or juveniles is better. Information about this rate can improve the success of the reintroduction program, but does the expected gain offset the costs of obtaining the information? I explored this question for reintroduction of the griffon vulture (Gyps fulvus) by framing the management question as a belief Markov decision process, characterizing uncertainty about release cost with 2 information state variables, and finding the solution using stochastic dynamic programming. For a reintroduction program of fixed length (e.g., 5 years of releases), the optimal policy in the final release year resembles the deterministic solution: release either all adults or all juveniles depending on whether the point estimate for the survival rate in question is above or below a specific threshold. But the optimal policy in the earlier release years 1) includes release of a mixture of juveniles and adults under some circumstances, and 2) recommends release of adults even when the point estimate of survival is much less than the deterministic threshold. These results show that in an iterated decision setting, the optimal decision in early years can be quite different from that in later years because of the value of learning. 

δ-exceedance records and random adaptive walks

NASA Astrophysics Data System (ADS)

Park, Su-Chan; Krug, Joachim

2016-08-01

We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition {Y}k\\gt {Y}k-1-{δ }k-1 with a deterministic sequence {δ }k\\gt 0 called the handicap. For constant {δ }k\\equiv δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al 2015 Phys. Rev. E 91 042707). Here we explore the behavior for general probability distributions and decreasing and increasing sequences {δ }k, focusing in particular on the case when {δ }k matches the typical spacing between subsequent records in the underlying simple record process without handicap. We find that a continuous phase transition occurs only in the exponential case, but a novel kind of first order transition emerges when {δ }k is increasing. The problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes, where {δ }k corresponds to the change of the deterministic fitness component after k mutational steps. The results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum.

Stochastic and deterministic model of microbial heat inactivation.

PubMed

Corradini, Maria G; Normand, Mark D; Peleg, Micha

2010-03-01

Microbial inactivation is described by a model based on the changing survival probabilities of individual cells or spores. It is presented in a stochastic and discrete form for small groups, and as a continuous deterministic model for larger populations. If the underlying mortality probability function remains constant throughout the treatment, the model generates first-order ("log-linear") inactivation kinetics. Otherwise, it produces survival patterns that include Weibullian ("power-law") with upward or downward concavity, tailing with a residual survival level, complete elimination, flat "shoulder" with linear or curvilinear continuation, and sigmoid curves. In both forms, the same algorithm or model equation applies to isothermal and dynamic heat treatments alike. Constructing the model does not require assuming a kinetic order or knowledge of the inactivation mechanism. The general features of its underlying mortality probability function can be deduced from the experimental survival curve's shape. Once identified, the function's coefficients, the survival parameters, can be estimated directly from the experimental survival ratios by regression. The model is testable in principle but matching the estimated mortality or inactivation probabilities with those of the actual cells or spores can be a technical challenge. The model is not intended to replace current models to calculate sterility. Its main value, apart from connecting the various inactivation patterns to underlying probabilities at the cellular level, might be in simulating the irregular survival patterns of small groups of cells and spores. In principle, it can also be used for nonthermal methods of microbial inactivation and their combination with heat.

Accumulation of neutral mutations in growing cell colonies with competition.

PubMed

Sorace, Ron; Komarova, Natalia L

2012-12-07

Neutral mutations play an important role in many biological processes including cancer initiation and progression, the generation of drug resistance in bacterial and viral diseases as well as cancers, and the development of organs in multicellular organisms. In this paper we study how neutral mutants are accumulated in nonlinearly growing colonies of cells subject to growth constraints such as crowding or lack of resources. We investigate different types of growth control which range from "division-controlled" to "death-controlled" growth (and various mixtures of both). In division-controlled growth, the burden of handling overcrowding lies with the process of cell-divisions, the divisions slow down as the carrying capacity is approached. In death-controlled growth, it is death rate that increases to slow down expansion. We show that division-controlled growth minimizes the number of accumulated mutations, and death-controlled growth corresponds to the maximum number of mutants. We check that these results hold in both deterministic and stochastic settings. We further develop a general (deterministic) theory of neutral mutations and achieve an analytical understanding of the mutant accumulation in colonies of a given size in the absence of back-mutations. The long-term dynamics of mutants in the presence of back-mutations is also addressed. In particular, with equal forward- and back-mutation rates, if division-controlled and a death-controlled types are competing for space and nutrients, cells obeying division-controlled growth will dominate the population. Copyright © 2012 Elsevier Ltd. All rights reserved.

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Teaching Deterministic Chaos through Music.

ERIC Educational Resources Information Center

Chacon, R.; And Others

1992-01-01

Presents music education as a setting for teaching nonlinear dynamics and chaotic behavior connected with fixed-point and limit-cycle attractors. The aim is not music composition but a first approach to an interdisciplinary tool suitable for a single-session class, at either the secondary or undergraduate level, for the introduction of these…

Chaos without nonlinear dynamics.

PubMed

Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

2006-07-14

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.

Deterministic representation of chaos with application to turbulence

NASA Technical Reports Server (NTRS)

Zak, M.

1987-01-01

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

A theory for El Nino and the Southern Oscillation

NASA Technical Reports Server (NTRS)

Cane, M. A.; Zebiak, S. E.

1985-01-01

A coupled atmosphere-ocean model is presented for El Nino and the Southern Oscillation that reproduces its major features, including its recurrence at irregular intervals. The interannual El Nino-Southern Oscillation cycle is maintained by deterministic interactions in the tropical Pacific region. Ocean dynamics alter sea-surface temperature, changing the atmospheric heating; the resulting changes in surface wind alter the ocean dynamics. Annually varying mean conditions largely determine the spatial pattern and temporal evolution of El Nino events.

Dynamical Localization for Unitary Anderson Models

NASA Astrophysics Data System (ADS)

Hamza, Eman; Joye, Alain; Stolz, Günter

2009-11-01

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.

Modeling metapopulation dynamics for single species of seabirds

USGS Publications Warehouse

Buckley, P.A.; Downer, R.; McCullough, D.R.; Barrett, R.H.

1992-01-01

Seabirds share many characteristics setting them apart from other birds. Importantly, they breed more or less obligatorily in local clusters of colonies that can move regularly from site to site, and they routinely exchange breeders. The properties of such metapopulations have only recently begun to be examined, often with models that are occupancy-based (using only colony presence or absence data) and deterministic (using single, empirically determined values for each of several population biology parameters). Some recent models are now frequency-based (using actual population sizes at each site), as well as stochastic (randomly varying critical parameters between biologically realistic limits), yielding better estimates of the behavior of future populations. Using two such models designed to quantify relative risks of population changes under different future scenarios (RAMAS/stage and RAMAS/space), we have examined probable future populations dynamics for three hypothetical seabirds -- an albatross, a cormorant, and a tern. With real parameters and ranges of values we alternatively modelled each species with and without density dependence, as well as with their numbers in a single, large colony, or in many smaller ones, distributed evenly or lognormally. We produced a series of species-typical lines for different population risks over the 50 years we simulated. We call these curves Instantaneous Threat Assessments (ITAs), and their shapes mirror the varying life history characteristics of our three species. We also demonstrated (by a process known as sensitivity analysis) that the most important parameters determining future population fates of all three species were correlation of mean growth rate among colonies; dispersal rate of present and future breeders; subadult survivorship; and the number of subpopulations (=colonies) - in roughly that descending order of importance. In addition, density dependence was found to markedly alter ITA line shape and position, dramatically in the tern. Finally, we show that for each of our three seabirds, a substantial reduction in the risk of the entire population's going to extinction was provided by a metapopulation (i.e. colonial) breeding structure -- thus comfortably confirming what avian ecologists have long known but about which population modellers are somtimes still unsure.

Superfluid in a shaken optical lattice: quantum critical dynamics and topological defect engineering

NASA Astrophysics Data System (ADS)

Gaj, Anita; Feng, Lei; Clark, Logan W.; Chin, Cheng

2017-04-01

We present our recent studies of non-equilibrium dynamics in Bose-Einstein condensates using the shaken optical lattice. By increasing the shaking amplitude we observe a quantum phase transition from an ordinary superfluid to an effectively ferromagnetic superfluid composed of discrete domains with different quasi-momentum. We investigate the critical dynamics during which the domain structure and domain walls emerge. We demonstrate the use of a digital micromirror device to deterministically create desired domain structure. Using this technique we develop a clearer picture of the quantum critical dynamics at early times and its impact on the domain structure long after the transition.

Impacts of Considering Climate Variability on Investment Decisions in Ethiopia

NASA Astrophysics Data System (ADS)

Strzepek, K.; Block, P.; Rosegrant, M.; Diao, X.

2005-12-01

In Ethiopia, climate extremes, inducing droughts or floods, are not unusual. Monitoring the effects of these extremes, and climate variability in general, is critical for economic prediction and assessment of the country's future welfare. The focus of this study involves adding climate variability to a deterministic, mean climate-driven agro-economic model, in an attempt to understand its effects and degree of influence on general economic prediction indicators for Ethiopia. Four simulations are examined, including a baseline simulation and three investment strategies: simulations of irrigation investment, roads investment, and a combination investment of both irrigation and roads. The deterministic model is transformed into a stochastic model by dynamically adding year-to-year climate variability through climate-yield factors. Nine sets of actual, historic, variable climate data are individually assembled and implemented into the 12-year stochastic model simulation, producing an ensemble of economic prediction indicators. This ensemble allows for a probabilistic approach to planning and policy making, allowing decision makers to consider risk. The economic indicators from the deterministic and stochastic approaches, including rates of return to investments, are significantly different. The predictions of the deterministic model appreciably overestimate the future welfare of Ethiopia; the predictions of the stochastic model, utilizing actual climate data, tend to give a better semblance of what may be expected. Inclusion of climate variability is vital for proper analysis of the predictor values from this agro-economic model.

JCCRER Project 2.3 -- Deterministic effects of occupational exposure to radiation. Phase 1: Feasibility study; Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Okladnikova, N.; Pesternikova, V.; Sumina, M.

1998-12-01

Phase 1 of Project 2.3, a short-term collaborative Feasibility Study, was funded for 12 months starting on 1 February 1996. The overall aim of the study was to determine the practical feasibility of using the dosimetric and clinical data on the MAYAK worker population to study the deterministic effects of exposure to external gamma radiation and to internal alpha radiation from inhaled plutonium. Phase 1 efforts were limited to the period of greatest worker exposure (1948--1954) and focused on collaboratively: assessing the comprehensiveness, availability, quality, and suitability of the Russian clinical and dosimetric data for the study of deterministic effects;more » creating an electronic data base containing complete clinical and dosimetric data on a small, representative sample of MAYAK workers; developing computer software for the testing of a currently used health risk model of hematopoietic effects; and familiarizing the US team with the Russian diagnostic criteria and techniques used in the identification of Chronic Radiation Sickness.« less

Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems

NASA Astrophysics Data System (ADS)

Deco, Gustavo; Martí, Daniel

2007-03-01

The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability.

Developing Stochastic Models as Inputs for High-Frequency Ground Motion Simulations

NASA Astrophysics Data System (ADS)

Savran, William Harvey

High-frequency ( 10 Hz) deterministic ground motion simulations are challenged by our understanding of the small-scale structure of the earth's crust and the rupture process during an earthquake. We will likely never obtain deterministic models that can accurately describe these processes down to the meter scale length required for broadband wave propagation. Instead, we can attempt to explain the behavior, in a statistical sense, by including stochastic models defined by correlations observed in the natural earth and through physics based simulations of the earthquake rupture process. Toward this goal, we develop stochastic models to address both of the primary considerations for deterministic ground motion simulations: namely, the description of the material properties in the crust, and broadband earthquake source descriptions. Using borehole sonic log data recorded in Los Angeles basin, we estimate the spatial correlation structure of the small-scale fluctuations in P-wave velocities by determining the best-fitting parameters of a von Karman correlation function. We find that Hurst exponents, nu, between 0.0-0.2, vertical correlation lengths, az, of 15-150m, an standard deviation, sigma of about 5% characterize the variability in the borehole data. Usin these parameters, we generated a stochastic model of velocity and density perturbations and combined with leading seismic velocity models to perform a validation exercise for the 2008, Chino Hills, CA using heterogeneous media. We find that models of velocity and density perturbations can have significant effects on the wavefield at frequencies as low as 0.3 Hz, with ensemble median values of various ground motion metrics varying up to +/-50%, at certain stations, compared to those computed solely from the CVM. Finally, we develop a kinematic rupture generator based on dynamic rupture simulations on geometrically complex faults. We analyze 100 dynamic rupture simulations on strike-slip faults ranging from Mw 6.4-7.2. We find that our dynamic simulations follow empirical scaling relationships for inter-plate strike-slip events, and provide source spectra comparable with an o -2 model. Our rupture generator reproduces GMPE medians and intra-event standard deviations spectral accelerations for an ensemble of 10 Hz fully-deterministic ground motion simulations, as compared to NGA West2 GMPE relationships up to 0.2 seconds.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

NASA Astrophysics Data System (ADS)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Deterministic Migration-Based Separation of White Blood Cells.

PubMed

Kim, Byeongyeon; Choi, Young Joon; Seo, Hyekyung; Shin, Eui-Cheol; Choi, Sungyoung

2016-10-01

Functional and phenotypic analyses of peripheral white blood cells provide useful clinical information. However, separation of white blood cells from peripheral blood requires a time-consuming, inconvenient process and thus analyses of separated white blood cells are limited in clinical settings. To overcome this limitation, a microfluidic separation platform is developed to enable deterministic migration of white blood cells, directing the cells into designated positions according to a ridge pattern. The platform uses slant ridge structures on the channel top to induce the deterministic migration, which allows efficient and high-throughput separation of white blood cells from unprocessed whole blood. The extent of the deterministic migration under various rheological conditions is explored, enabling highly efficient migration of white blood cells in whole blood and achieving high-throughput separation of the cells (processing 1 mL of whole blood less than 7 min). In the separated cell population, the composition of lymphocyte subpopulations is well preserved, and T cells secrete cytokines without any functional impairment. On the basis of the results, this microfluidic platform is a promising tool for the rapid enrichment of white blood cells, and it is useful for functional and phenotypic analyses of peripheral white blood cells. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

3D Dynamic Rupture Simulations along the Wasatch Fault, Utah, Incorporating Rough-fault Topography

NASA Astrophysics Data System (ADS)

Withers, Kyle; Moschetti, Morgan

2017-04-01

Studies have found that the Wasatch Fault has experienced successive large magnitude (>Mw 7.2) earthquakes, with an average recurrence interval near 350 years. To date, no large magnitude event has been recorded along the fault, with the last rupture along the Salt Lake City segment occurring 1300 years ago. Because of this, as well as the lack of strong ground motion records in basins and from normal-faulting earthquakes worldwide, seismic hazard in the region is not well constrained. Previous numerical simulations have modeled deterministic ground motion in the heavily populated regions of Utah, near Salt Lake City, but were primarily restricted to low frequencies ( 1 Hz). Our goal is to better assess broadband ground motions from the Wasatch Fault Zone. Here, we extend deterministic ground motion prediction to higher frequencies ( 5 Hz) in this region by using physics-based spontaneous dynamic rupture simulations along a normal fault with characteristics derived from geologic observations. We use a summation by parts finite difference code (Waveqlab3D) with rough-fault topography following a self-similar fractal distribution (over length scales from 100 m to the size of the fault) and include off-fault plasticity to simulate ruptures > Mw 6.5. Geometric complexity along fault planes has previously been shown to generate broadband sources with spectral energy matching that of observations. We investigate the impact of varying the hypocenter location, as well as the influence that multiple realizations of rough-fault topography have on the rupture process and resulting ground motion. We utilize Waveqlab3's computational efficiency to model wave-propagation to a significant distance from the fault with media heterogeneity at both long and short spatial wavelengths. These simulations generate a synthetic dataset of ground motions to compare with GMPEs, in terms of both the median and inter and intraevent variability.

Dynamic Routing of Aircraft in the Presence of Adverse Weather Using a POMDP Framework

NASA Technical Reports Server (NTRS)

Balaban, Edward; Roychoudhury, Indranil; Spirkovska, Lilly; Sankararaman, Shankar; Kulkarni, Chetan; Arnon, Tomer

2017-01-01

Each year weather-related airline delays result in hundreds of millions of dollars in additional fuel burn, maintenance, and lost revenue, not to mention passenger inconvenience. The current approaches for aircraft route planning in the presence of adverse weather still mainly rely on deterministic methods. In contrast, this work aims to deal with the problem using a Partially Observable Markov Decision Processes (POMDPs) framework, which allows for reasoning over uncertainty (including uncertainty in weather evolution over time) and results in solutions that are more robust to disruptions. The POMDP-based decision support system is demonstrated on several scenarios involving convective weather cells and is benchmarked against a deterministic planning system with functionality similar to those currently in use or under development.

Broken flow symmetry explains the dynamics of small particles in deterministic lateral displacement arrays.

PubMed

Kim, Sung-Cheol; Wunsch, Benjamin H; Hu, Huan; Smith, Joshua T; Austin, Robert H; Stolovitzky, Gustavo

2017-06-27

Deterministic lateral displacement (DLD) is a technique for size fractionation of particles in continuous flow that has shown great potential for biological applications. Several theoretical models have been proposed, but experimental evidence has demonstrated that a rich class of intermediate migration behavior exists, which is not predicted. We present a unified theoretical framework to infer the path of particles in the whole array on the basis of trajectories in a unit cell. This framework explains many of the unexpected particle trajectories reported and can be used to design arrays for even nanoscale particle fractionation. We performed experiments that verify these predictions and used our model to develop a condenser array that achieves full particle separation with a single fluidic input.

Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

PubMed

Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A

2011-04-07

The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

PubMed

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

Psychological effect on single-species population models in a polluted environment.

PubMed

Wei, Fengying; Chen, Lihong

2017-08-01

We formulate and investigate the psychological effect of single-species population models in a polluted environment in this paper. For the deterministic single-species population model, the conditions that guarantee the local extinction and persistence in the mean are derived firstly. We then show that, around the pollution-free equilibrium, the stochastic single-species population is weakly persistent in the mean, and is stochastically permanent under some conditions. As a consequence, some numerical simulations demonstrate the efficiency of the main results. Copyright © 2017 Elsevier Inc. All rights reserved.

GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Duboscq, Romain

2015-08-01

GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross-Pitaevskii equations that arise in the physics of Bose-Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross-Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.

Salmon Life Cycle Models Illuminate Population Consequences of Disparate Survival and Behavior Between Hatchery- and Wild-Origin Fish

NASA Astrophysics Data System (ADS)

Beakes, M.; Satterthwaite, W.; Petrik, C.; Hendrix, N.; Danner, E.; Lindley, S. T.

2016-02-01

In past decades there has been a heavy reliance on the production of hatchery-reared fish to supplement declining population numbers of Pacific salmon. In some cases, the benefits of hatchery supplementation have been negligible despite concerted long-term stocking efforts. The management and conservation of depressed salmon populations, via hatchery practices or otherwise, can be improved by expanding our understanding of the dissimilarities between hatchery and wild salmon and how each interacts with the environment. In this study we use a stage-structured salmon life-cycle model to explore the population consequences of disparate survival and behavior between hatchery and wild-origin fall-run Chinook Salmon (Oncorhynchus tshawytscha) in the California Central Valley. We couple empirically-based statistical functions with deterministic theoretical models to identify how environmental conditions (e.g., water temperature, flow) and habitat drive the survival and abundance of both hatchery and wild salmon as they integrate across riverscapes and cross marine and freshwater ecosystem boundaries during their life cycle. Results from this study suggest that hatchery practices can lead to dissimilar interactions between hatchery and wild salmon and the environmental conditions they experience. As such, the population dynamics of fall-run Chinook Salmon in the California Central Valley are partly dependent on the composition of individuals that make up their populations. In total, this study improves out ability to conserve imperiled salmonids by identifying mechanistic linkages between the natal origin of salmon, survival and behavior, and the environment at spatiotemporal scales relevant to salmon populations and fisheries management.

Coherent Two-Mode Dynamics of a Nanowire Force Sensor

NASA Astrophysics Data System (ADS)

Braakman, Floris R.; Rossi, Nicola; Tütüncüoglu, Gözde; Morral, Anna Fontcuberta i.; Poggio, Martino

2018-05-01

Classically coherent dynamics analogous to those of quantum two-level systems are studied in the setting of force sensing. We demonstrate quantitative control over the coupling between two orthogonal mechanical modes of a nanowire cantilever through measurement of avoided crossings as we deterministically position the nanowire inside an electric field. Furthermore, we demonstrate Rabi oscillations between the two mechanical modes in the strong-coupling regime. These results give prospects of implementing coherent two-mode control techniques for force-sensing signal enhancement.

Effects of noise on a computational model for disease states of mood disorders

NASA Astrophysics Data System (ADS)

Tobias Huber, Martin; Krieg, Jürgen-Christian; Braun, Hans Albert; Moss, Frank

2000-03-01

Nonlinear dynamics are currently proposed to explain the progressive course of recurrent mood disorders starting with isolated episodes and ending with accelerated irregular (``chaotic") mood fluctuations. Such a low-dimensional disease model is attractive because of its principal accordance with biological disease models, i.e. the kindling and biological rhythms model. However, most natural systems are nonlinear and noisy and several studies in the neuro- and physical sciences have demonstrated interesting cooperative behaviors arising from interacting random and deterministic dynamics. Here, we consider the effects of noise on a recent neurodynamical model for the timecourse of affective disorders (Huber et al.: Biological Psychiatry 1999;46:256-262). We describe noise effects on temporal patterns and mean episode frequencies of various in computo disease states. Our simulations demonstrate that noise can cause unstructured randomness or can maximize periodic order. The frequency of episode occurence can increase with noise but it can also remain unaffected or even can decrease. We show further that noise can make visible bifurcations before they would normally occur under deterministic conditions and we quantify this behavior with a recently developed statistical method. All these effects depend critically on both, the dynamic state and the noise intensity. Implications for neurobiology and course of mood disorders are discussed.

Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators

NASA Astrophysics Data System (ADS)

Guo, H.; Karpov, M.; Lucas, E.; Kordts, A.; Pfeiffer, M. H. P.; Brasch, V.; Lihachev, G.; Lobanov, V. E.; Gorodetsky, M. L.; Kippenberg, T. J.

2017-01-01

Temporal dissipative Kerr solitons in optical microresonators enable the generation of ultrashort pulses and low-noise frequency combs at microwave repetition rates. They have been demonstrated in a growing number of microresonator platforms, enabling chip-scale frequency combs, optical synthesis of low-noise microwaves and multichannel coherent communications. In all these applications, accessing and maintaining a single-soliton state is a key requirement--one that remains an outstanding challenge. Here, we study the dynamics of multiple-soliton states and report the discovery of a simple mechanism that deterministically switches the soliton state by reducing the number of solitons one by one. We demonstrate this control in Si3N4 and MgF2 resonators and, moreover, we observe a secondary peak to emerge in the response of the system to a pump modulation, an effect uniquely associated with the soliton regime. Exploiting this feature, we map the multi-stability diagram of a microresonator experimentally. Our measurements show the physical mechanism of the soliton switching and provide insight into soliton dynamics in microresonators. The technique provides a method to sequentially reduce, monitor and stabilize an arbitrary state with solitons, in particular allowing for feedback stabilization of single-soliton states, which is necessary for practical applications.

Within-Host Dynamics of the Emergence of Tomato Yellow Leaf Curl Virus Recombinants

PubMed Central

Urbino, Cica; Gutiérrez, Serafin; Antolik, Anna; Bouazza, Nabila; Doumayrou, Juliette; Granier, Martine; Martin, Darren P.; Peterschmitt, Michel

2013-01-01

Tomato yellow leaf curl virus (TYLCV) is a highly damaging begomovirus native to the Middle East. TYLCV has recently spread worldwide, recombining with other begomoviruses. Recent analysis of mixed infections between TYLCV and Tomato leaf curl Comoros begomovirus (ToLCKMV) has shown that, although natural selection preserves certain co-evolved intra-genomic interactions, numerous and diverse recombinants are produced at 120 days post-inoculation (dpi), and recombinant populations from different tomato plants are very divergent. Here, we investigate the population dynamics that lead to such patterns in tomato plants co-infected with TYLCV and ToLCKMV either by agro-inoculation or using the natural whitefly vector Bemisia tabaci. We monitored the frequency of parental and recombinant genotypes independently in 35 plants between 18 and 330 dpi and identified 177 recombinants isolated at different times. Recombinants were detected from 18 dpi and their frequency increased over time to reach about 50% at 150 dpi regardless of the inoculation method. The distribution of breakpoints detected on 96 fully sequenced recombinants was consistent with a continuous generation of new recombinants as well as random and deterministic effects in their maintenance. A severe population bottleneck of around 10 genomes was estimated during early systemic infection–a phenomenon that could account partially for the heterogeneity in recombinant patterns observed among plants. The detection of the same recombinant genome in six of the thirteen plants analysed beyond 30 dpi supported the influence of selection on observed recombination patterns. Moreover, a highly virulent recombinant genotype dominating virus populations within one plant has, apparently, the potential to be maintained in the natural population according to its infectivity, within-host accumulation, and transmission efficiency - all of which were similar or intermediate to those of the parent genotypes. Our results anticipate the outcomes of natural encounters between TYLCV and ToLCKMV. PMID:23472190

Discrete stochastic simulation methods for chemically reacting systems.

PubMed

Cao, Yang; Samuels, David C

2009-01-01

Discrete stochastic chemical kinetics describe the time evolution of a chemically reacting system by taking into account the fact that, in reality, chemical species are present with integer populations and exhibit some degree of randomness in their dynamical behavior. In recent years, with the development of new techniques to study biochemistry dynamics in a single cell, there are increasing studies using this approach to chemical kinetics in cellular systems, where the small copy number of some reactant species in the cell may lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. This chapter reviews the fundamental theory related to stochastic chemical kinetics and several simulation methods based on that theory. We focus on nonstiff biochemical systems and the two most important discrete stochastic simulation methods: Gillespie's stochastic simulation algorithm (SSA) and the tau-leaping method. Different implementation strategies of these two methods are discussed. Then we recommend a relatively simple and efficient strategy that combines the strengths of the two methods: the hybrid SSA/tau-leaping method. The implementation details of the hybrid strategy are given here and a related software package is introduced. Finally, the hybrid method is applied to simple biochemical systems as a demonstration of its application.

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers.

PubMed

Bhowmick, Amiya Ranjan; Bandyopadhyay, Subhadip; Rana, Sourav; Bhattacharya, Sabyasachi

2016-01-01

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. Copyright © 2015 Elsevier Inc. All rights reserved.

Random attractor of non-autonomous stochastic Boussinesq lattice system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Min, E-mail: zhaomin1223@126.com; Zhou, Shengfan, E-mail: zhoushengfan@yahoo.com

2015-09-15

In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Generation of Werner states via collective decay of coherently driven atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agarwal, Girish S.; Kapale, Kishore T.

2006-02-15

We show deterministic generation of Werner states as a steady state of the collective decay dynamics of a pair of neutral atoms coupled to a leaky cavity and strong coherent drive. We also show how the scheme can be extended to generate a 2N-particle analogue of the bipartite Werner states.

The Signal Importance of Noise

ERIC Educational Resources Information Center

Macy, Michael; Tsvetkova, Milena

2015-01-01

Noise is widely regarded as a residual category--the unexplained variance in a linear model or the random disturbance of a predictable pattern. Accordingly, formal models often impose the simplifying assumption that the world is noise-free and social dynamics are deterministic. Where noise is assigned causal importance, it is often assumed to be a…

Persistence and memory timescales in root-zone soil moisture dynamics

Treesearch

Khaled Ghannam; Taro Nakai; Athanasios Paschalis; Andrew C. Oishi; Ayumi Kotani; Yasunori Igarashi; Tomo' omi Kumagai; Gabriel G. Katul

2016-01-01

The memory timescale that characterizes root-zone soil moisture remains the dominant measure in seasonal forecasts of land-climate interactions. This memory is a quasi-deterministic timescale associated with the losses (e.g., evapotranspiration) from the soil column and is often interpreted as persistence in soil moisture states. Persistence, however,...

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics

NASA Astrophysics Data System (ADS)

Naruemon, Rueangkham; Charin, Modchang

2016-04-01

Most biochemical processes in cells are usually modeled by reaction-diffusion (RD) equations. In these RD models, the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the mean-square displacement (MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous sub-diffusion in the RD system at some or all times. The time-dependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations. Project supported by the Thailand Research Fund and Mahidol University (Grant No. TRG5880157), the Thailand Center of Excellence in Physics (ThEP), CHE, Thailand, and the Development Promotion of Science and Technology.

Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations.

PubMed

Hong, Hyunsuk; O'Keeffe, Kevin P; Strogatz, Steven H

2016-10-01

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction p of oscillators are positively coupled, attracting all others, while the remaining fraction 1-p are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a critical width γ c in the frequency distribution below which the system spontaneously synchronizes. Moreover, this γ c is independent of p. Hence, our model and the traditional Kuramoto model (recovered when p = 1) have the same critical width γ c . We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of p < 1.

The role of predictive uncertainty in the operational management of reservoirs

NASA Astrophysics Data System (ADS)

Todini, E.

2014-09-01

The present work deals with the operational management of multi-purpose reservoirs, whose optimisation-based rules are derived, in the planning phase, via deterministic (linear and nonlinear programming, dynamic programming, etc.) or via stochastic (generally stochastic dynamic programming) approaches. In operation, the resulting deterministic or stochastic optimised operating rules are then triggered based on inflow predictions. In order to fully benefit from predictions, one must avoid using them as direct inputs to the reservoirs, but rather assess the "predictive knowledge" in terms of a predictive probability density to be operationally used in the decision making process for the estimation of expected benefits and/or expected losses. Using a theoretical and extremely simplified case, it will be shown why directly using model forecasts instead of the full predictive density leads to less robust reservoir management decisions. Moreover, the effectiveness and the tangible benefits for using the entire predictive probability density instead of the model predicted values will be demonstrated on the basis of the Lake Como management system, operational since 1997, as well as on the basis of a case study on the lake of Aswan.

Emergence of chaos in a spatially confined reactive system

NASA Astrophysics Data System (ADS)

Voorsluijs, Valérie; De Decker, Yannick

2016-11-01

In spatially restricted media, interactions between particles and local fluctuations of density can lead to important deviations of the dynamics from the unconfined, deterministic picture. In this context, we investigated how molecular crowding can affect the emergence of chaos in small reactive systems. We developed to this end an amended version of the Willamowski-Rössler model, where we account for the impenetrability of the reactive species. We analyzed the deterministic kinetics of this model and studied it with spatially-extended stochastic simulations in which the mobility of particles is included explicitly. We show that homogeneous fluctuations can lead to a destruction of chaos through a fluctuation-induced collision between chaotic trajectories and absorbing states. However, an interplay between the size of the system and the mobility of particles can counterbalance this effect so that chaos can indeed be found when particles diffuse slowly. This unexpected effect can be traced back to the emergence of spatial correlations which strongly affect the dynamics. The mobility of particles effectively acts as a new bifurcation parameter, enabling the system to switch from stationary states to absorbing states, oscillations or chaos.

Front propagation and effect of memory in stochastic desertification models with an absorbing state

NASA Astrophysics Data System (ADS)

Herman, Dor; Shnerb, Nadav M.

2017-08-01

Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and irreversible (catastrophic shift). However, recent studies show that the inherent stochasticity of the birth-death process, when superimposed on the presence of an absorbing state, may lead to a continuous (second order) transition even if the deterministic dynamics supports a catastrophic transition. Following these works we present here a numerical study of a one-dimensional stochastic desertification model, where the deterministic predictions are confronted with the observed dynamics. Our results suggest that a stochastic spatial system allows for a propagating front only when its active phase invades the inactive (desert) one. In the extinction phase one observes transient front propagation followed by a global collapse. In the presence of a seed bank the vegetation state is shown to be more robust against demographic stochasticity, but the transition in that case still belongs to the directed percolation equivalence class.

Evolution with Stochastic Fitness and Stochastic Migration

PubMed Central

Rice, Sean H.; Papadopoulos, Anthony

2009-01-01

Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory. PMID:19816580

Dynamically consistent parameterization of mesoscale eddies. Part III: Deterministic approach

NASA Astrophysics Data System (ADS)

Berloff, Pavel

2018-07-01

This work continues development of dynamically consistent parameterizations for representing mesoscale eddy effects in non-eddy-resolving and eddy-permitting ocean circulation models and focuses on the classical double-gyre problem, in which the main dynamic eddy effects maintain eastward jet extension of the western boundary currents and its adjacent recirculation zones via eddy backscatter mechanism. Despite its fundamental importance, this mechanism remains poorly understood, and in this paper we, first, study it and, then, propose and test its novel parameterization. We start by decomposing the reference eddy-resolving flow solution into the large-scale and eddy components defined by spatial filtering, rather than by the Reynolds decomposition. Next, we find that the eastward jet and its recirculations are robustly present not only in the large-scale flow itself, but also in the rectified time-mean eddies, and in the transient rectified eddy component, which consists of highly anisotropic ribbons of the opposite-sign potential vorticity anomalies straddling the instantaneous eastward jet core and being responsible for its continuous amplification. The transient rectified component is separated from the flow by a novel remapping method. We hypothesize that the above three components of the eastward jet are ultimately driven by the small-scale transient eddy forcing via the eddy backscatter mechanism, rather than by the mean eddy forcing and large-scale nonlinearities. We verify this hypothesis by progressively turning down the backscatter and observing the induced flow anomalies. The backscatter analysis leads us to formulating the key eddy parameterization hypothesis: in an eddy-permitting model at least partially resolved eddy backscatter can be significantly amplified to improve the flow solution. Such amplification is a simple and novel eddy parameterization framework implemented here in terms of local, deterministic flow roughening controlled by single parameter. We test the parameterization skills in an hierarchy of non-eddy-resolving and eddy-permitting modifications of the original model and demonstrate, that indeed it can be highly efficient for restoring the eastward jet extension and its adjacent recirculation zones. The new deterministic parameterization framework not only combines remarkable simplicity with good performance but also is dynamically transparent, therefore, it provides a powerful alternative to the common eddy diffusion and emerging stochastic parameterizations.

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation

PubMed Central

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation. PMID:26761487

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation.

PubMed

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother's old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother's old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington's genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.

Effect of Streamflow Forecast Uncertainty on Real-Time Reservoir Operation

NASA Astrophysics Data System (ADS)

Zhao, T.; Cai, X.; Yang, D.

2010-12-01

Various hydrological forecast products have been applied to real-time reservoir operation, including deterministic streamflow forecast (DSF), DSF-based probabilistic streamflow forecast (DPSF), and ensemble streamflow forecast (ESF), which represent forecast uncertainty in the form of deterministic forecast error, deterministic forecast error-based uncertainty distribution, and ensemble forecast errors, respectively. Compared to previous studies that treat these forecast products as ad hoc inputs for reservoir operation models, this paper attempts to model the uncertainties involved in the various forecast products and explores their effect on real-time reservoir operation decisions. In hydrology, there are various indices reflecting the magnitude of streamflow forecast uncertainty; meanwhile, few models illustrate the forecast uncertainty evolution process. This research introduces Martingale Model of Forecast Evolution (MMFE) from supply chain management and justifies its assumptions for quantifying the evolution of uncertainty in streamflow forecast as time progresses. Based on MMFE, this research simulates the evolution of forecast uncertainty in DSF, DPSF, and ESF, and applies the reservoir operation models (dynamic programming, DP; stochastic dynamic programming, SDP; and standard operation policy, SOP) to assess the effect of different forms of forecast uncertainty on real-time reservoir operation. Through a hypothetical single-objective real-time reservoir operation model, the results illustrate that forecast uncertainty exerts significant effects. Reservoir operation efficiency, as measured by a utility function, decreases as the forecast uncertainty increases. Meanwhile, these effects also depend on the type of forecast product being used. In general, the utility of reservoir operation with ESF is nearly as high as the utility obtained with a perfect forecast; the utilities of DSF and DPSF are similar to each other but not as efficient as ESF. Moreover, streamflow variability and reservoir capacity can change the magnitude of the effects of forecast uncertainty, but not the relative merit of DSF, DPSF, and ESF. Schematic diagram of the increase in forecast uncertainty with forecast lead-time and the dynamic updating property of real-time streamflow forecast

Probabilistic population projections with migration uncertainty

PubMed Central

Azose, Jonathan J.; Ševčíková, Hana; Raftery, Adrian E.

2016-01-01

We produce probabilistic projections of population for all countries based on probabilistic projections of fertility, mortality, and migration. We compare our projections to those from the United Nations’ Probabilistic Population Projections, which uses similar methods for fertility and mortality but deterministic migration projections. We find that uncertainty in migration projection is a substantial contributor to uncertainty in population projections for many countries. Prediction intervals for the populations of Northern America and Europe are over 70% wider, whereas prediction intervals for the populations of Africa, Asia, and the world as a whole are nearly unchanged. Out-of-sample validation shows that the model is reasonably well calibrated. PMID:27217571

Invasion fitness for gene-culture co-evolution in family-structured populations and an application to cumulative culture under vertical transmission.

PubMed

Mullon, Charles; Lehmann, Laurent

2017-08-01

Human evolution depends on the co-evolution between genetically determined behaviors and socially transmitted information. Although vertical transmission of cultural information from parent to offspring is common in hominins, its effects on cumulative cultural evolution are not fully understood. Here, we investigate gene-culture co-evolution in a family-structured population by studying the invasion fitness of a mutant allele that influences a deterministic level of cultural information (e.g., amount of knowledge or skill) to which diploid carriers of the mutant are exposed in subsequent generations. We show that the selection gradient on such a mutant, and the concomitant level of cultural information it generates, can be evaluated analytically under the assumption that the cultural dynamic has a single attractor point, thereby making gene-culture co-evolution in family-structured populations with multigenerational effects mathematically tractable. We apply our result to study how genetically determined phenotypes of individual and social learning co-evolve with the level of adaptive information they generate under vertical transmission. We find that vertical transmission increases adaptive information due to kin selection effects, but when information is transmitted as efficiently between family members as between unrelated individuals, this increase is moderate in diploids. By contrast, we show that the way resource allocation into learning trades off with allocation into reproduction (the "learning-reproduction trade-off") significantly influences levels of adaptive information. We also show that vertical transmission prevents evolutionary branching and may therefore play a qualitative role in gene-culture co-evolutionary dynamics. More generally, our analysis of selection suggests that vertical transmission can significantly increase levels of adaptive information under the biologically plausible condition that information transmission between relatives is more efficient than between unrelated individuals. Copyright © 2017 Elsevier Inc. All rights reserved.

Persistent oscillations and backward bifurcation in a malaria model with varying human and mosquito populations: implications for control.

PubMed

Ngonghala, Calistus N; Teboh-Ewungkem, Miranda I; Ngwa, Gideon A

2015-06-01

We derive and study a deterministic compartmental model for malaria transmission with varying human and mosquito populations. Our model considers disease-related deaths, asymptomatic immune humans who are also infectious, as well as mosquito demography, reproduction and feeding habits. Analysis of the model reveals the existence of a backward bifurcation and persistent limit cycles whose period and size is determined by two threshold parameters: the vectorial basic reproduction number Rm, and the disease basic reproduction number R0, whose size can be reduced by reducing Rm. We conclude that malaria dynamics are indeed oscillatory when the methodology of explicitly incorporating the mosquito's demography, feeding and reproductive patterns is considered in modeling the mosquito population dynamics. A sensitivity analysis reveals important control parameters that can affect the magnitudes of Rm and R0, threshold quantities to be taken into consideration when designing control strategies. Both Rm and the intrinsic period of oscillation are shown to be highly sensitive to the mosquito's birth constant λm and the mosquito's feeding success probability pw. Control of λm can be achieved by spraying, eliminating breeding sites or moving them away from human habitats, while pw can be controlled via the use of mosquito repellant and insecticide-treated bed-nets. The disease threshold parameter R0 is shown to be highly sensitive to pw, and the intrinsic period of oscillation is also sensitive to the rate at which reproducing mosquitoes return to breeding sites. A global sensitivity and uncertainty analysis reveals that the ability of the mosquito to reproduce and uncertainties in the estimations of the rates at which exposed humans become infectious and infectious humans recover from malaria are critical in generating uncertainties in the disease classes.

Modeling heterogeneous responsiveness of intrinsic apoptosis pathway

PubMed Central

2013-01-01

Background Apoptosis is a cell suicide mechanism that enables multicellular organisms to maintain homeostasis and to eliminate individual cells that threaten the organism’s survival. Dependent on the type of stimulus, apoptosis can be propagated by extrinsic pathway or intrinsic pathway. The comprehensive understanding of the molecular mechanism of apoptotic signaling allows for development of mathematical models, aiming to elucidate dynamical and systems properties of apoptotic signaling networks. There have been extensive efforts in modeling deterministic apoptosis network accounting for average behavior of a population of cells. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level. Results To address the inevitable randomness in the intrinsic apoptosis mechanism, we develop a theoretical and computational modeling framework of intrinsic apoptosis pathway at single-cell level, accounting for both deterministic and stochastic behavior. Our deterministic model, adapted from the well-accepted Fussenegger model, shows that an additional positive feedback between the executioner caspase and the initiator caspase plays a fundamental role in yielding the desired property of bistability. We then examine the impact of intrinsic fluctuations of biochemical reactions, viewed as intrinsic noise, and natural variation of protein concentrations, viewed as extrinsic noise, on behavior of the intrinsic apoptosis network. Histograms of the steady-state output at varying input levels show that the intrinsic noise could elicit a wider region of bistability over that of the deterministic model. However, the system stochasticity due to intrinsic fluctuations, such as the noise of steady-state response and the randomness of response delay, shows that the intrinsic noise in general is insufficient to produce significant cell-to-cell variations at physiologically relevant level of molecular numbers. Furthermore, the extrinsic noise represented by random variations of two key apoptotic proteins, namely Cytochrome C and inhibitor of apoptosis proteins (IAP), is modeled separately or in combination with intrinsic noise. The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Finally, simulations illustrate that the mean abundance of fluctuating IAP protein is positively correlated with the degree of cellular stochasticity of the intrinsic apoptosis pathway. Conclusions Our theoretical and computational study shows that the pronounced non-genetic heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations. In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness. PMID:23875784

Reliability-based structural optimization: A proposed analytical-experimental study

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson; Nikolaidis, Efstratios

1993-01-01

An analytical and experimental study for assessing the potential of reliability-based structural optimization is proposed and described. In the study, competing designs obtained by deterministic and reliability-based optimization are compared. The experimental portion of the study is practical because the structure selected is a modular, actively and passively controlled truss that consists of many identical members, and because the competing designs are compared in terms of their dynamic performance and are not destroyed if failure occurs. The analytical portion of this study is illustrated on a 10-bar truss example. In the illustrative example, it is shown that reliability-based optimization can yield a design that is superior to an alternative design obtained by deterministic optimization. These analytical results provide motivation for the proposed study, which is underway.

Additivity Principle in High-Dimensional Deterministic Systems

NASA Astrophysics Data System (ADS)

Saito, Keiji; Dhar, Abhishek

2011-12-01

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.180601], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

Broken flow symmetry explains the dynamics of small particles in deterministic lateral displacement arrays

PubMed Central

Kim, Sung-Cheol; Wunsch, Benjamin H.; Hu, Huan; Smith, Joshua T.; Stolovitzky, Gustavo

2017-01-01

Deterministic lateral displacement (DLD) is a technique for size fractionation of particles in continuous flow that has shown great potential for biological applications. Several theoretical models have been proposed, but experimental evidence has demonstrated that a rich class of intermediate migration behavior exists, which is not predicted. We present a unified theoretical framework to infer the path of particles in the whole array on the basis of trajectories in a unit cell. This framework explains many of the unexpected particle trajectories reported and can be used to design arrays for even nanoscale particle fractionation. We performed experiments that verify these predictions and used our model to develop a condenser array that achieves full particle separation with a single fluidic input. PMID:28607075

Development of a stock-recruitment model and assessment of biological reference points for the Lake Erie walleye fishery

USGS Publications Warehouse

Zhao, Yingming; Kocovsky, Patrick M.; Madenjian, Charles P.

2013-01-01

We developed an updated stock–recruitment relationship for Lake Erie Walleye Sander vitreus using the Akaike information criterion model selection approach. Our best stock–recruitment relationship was a Ricker spawner–recruit function to which spring warming rate was added as an environmental variable, and this regression model explained 39% of the variability in Walleye recruitment over the 1978 through 2006 year-classes. Thus, most of the variability in Lake Erie Walleye recruitment appeared to be attributable to factors other than spawning stock size and spring warming rate. The abundance of age-0 Gizzard Shad Dorosoma cepedianum, which was an important term in previous models, may still be an important factor for Walleye recruitment, but poorer ability to monitor Gizzard Shad since the late 1990s could have led to that term failing to appear in our best model. Secondly, we used numerical simulation to demonstrate how to use the stock recruitment relationship to characterize the population dynamics (such as stable age structure, carrying capacity, and maximum sustainable yield) and some biological reference points (such as fishing rates at different important biomass or harvest levels) for an age-structured population in a deterministic way.

Noise in ecosystems: a short review.

PubMed

Spagnolo, B; Valenti, D; Fiasconaro, A

2004-06-01

Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we briefly review the noise-induced effects in three different ecosystems: (i) two competing species; (ii) three interacting species, one predator and two preys, and (iii) N-interacting species. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is random in cases (i) and (iii), and a periodical function, which accounts for the environmental temperature, in case (ii). We find noise-induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise-delayed extinction, and noise-induced pattern formation with nonmonotonic behaviors of patterns areas and of the density correlation as a function of the multiplicative noise intensity. The asymptotic behavior of the time average of the i(th) population when the ecosystem is composed of a great number of interacting species is obtained and the effect of the noise on the asymptotic probability distributions of the populations is discussed.

Preface to special issue in honor of Carlos Castillo-Chavez.

PubMed

Levin, Simon A

2013-01-01

A little more than a quarter-century ago, I received an inquiry from a young Assistant Professor of Applied Mathematics at the University of Tulsa, the honoree of this volume, Carlos Castillo-Chavez. Though he was well situated in a faculty job, he was not satisfied: He was interested in mathematical biology, having written an excellent thesis in population biology with Fred Brauer at Wisconsin entitled Linear and Nonlinear Deterministic Character-Dependent Models with Time Delay in Population Dynamics. But that success had only whetted his appetite to become more deeply embedded in biology, and he was prepared to give up his faculty job to start a postdoctoral fellowship in ecology. It is always difficult to read in such letters what potential exists in the author; but there was something about what Carlos wrote, the obvious sacrifice he was prepared to make, and my regard for Fred Brauer that convinced me that I must meet this fellow. We did meet, for lunch in an LA restaurant, and the qualities that have led to his remarkable career were immediately obvious. I resolved on the spot to make sure he joined our group. Carlos arrived at Cornell shortly thereafter, and did not leave for nearly twenty years.

Changes in seasonal climate outpace compensatory density-dependence in eastern brook trout

USGS Publications Warehouse

Bassar, Ronald D.; Letcher, Benjamin H.; Nislow, Keith H.; Whiteley, Andrew R.

2016-01-01

Understanding how multiple extrinsic (density-independent) factors and intrinsic (density-dependent) mechanisms influence population dynamics has become increasingly urgent in the face of rapidly changing climates. It is particularly unclear how multiple extrinsic factors with contrasting effects among seasons are related to declines in population numbers and changes in mean body size and whether there is a strong role for density-dependence. The primary goal of this study was to identify the roles of seasonal variation in climate driven environmental direct effects (mean stream flow and temperature) versus density-dependence on population size and mean body size in eastern brook trout (Salvelinus fontinalis). We use data from a 10-year capture-mark-recapture study of eastern brook trout in four streams in Western Massachusetts, USA to parameterize a discrete-time population projection model. The model integrates matrix modeling techniques used to characterize discrete population structures (age, habitat type and season) with integral projection models (IPMs) that characterize demographic rates as continuous functions of organismal traits (in this case body size). Using both stochastic and deterministic analyses we show that decreases in population size are due to changes in stream flow and temperature and that these changes are larger than what can be compensated for through density-dependent responses. We also show that the declines are due mostly to increasing mean stream temperatures decreasing the survival of the youngest age class. In contrast, increases in mean body size over the same period are the result of indirect changes in density with a lesser direct role of climate-driven environmental change.

Chaos and the evolution of cooperation.

PubMed

Nowak, M; Sigmund, K

1993-06-01

The "iterated prisoner's dilemma" is the most widely used model for the evolution of cooperation in biological societies. Here we show that a heterogeneous population consisting of simple strategies, whose behavior is totally specified by the outcome of the previous round, can lead to persistent periodic or highly irregular (chaotic) oscillations in the frequencies of the strategies and the overall level of cooperation. The levels of cooperation jump up and down in an apparently unpredictable fashion. Small recurrent and simultaneous invasion attempts (caused by mutation) can change the evolutionary dynamics from converging to an evolutionarily stable strategy to periodic oscillations and chaos. Evolution can be twisted away from defection, toward cooperation. Adding "generous tit-for-tat" greatly increases the overall level of cooperation and can lead to long periods of steady cooperation. Since May's paper [May, R. M. (1976) Nature (London) 261, 459-467], "simple mathematical models with very complicated dynamics" have been found in many biological applications, but here we provide an example of a biologically relevant evolutionary game whose dynamics display deterministic chaos. The simulations bear some resemblance to the irregular cycles displayed by the frequencies of host genotypes and specialized parasites in evolutionary "arms races" [Hamilton, W. D., Axelrod, R. & Tanese, R. (1990) Proc. Natl. Acad. Sci. USA 87, 3566-3573; Seger, J. (1988) Philos. Trans. R. Soc. London B 319, 541-555].

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Front propagation and clustering in the stochastic nonlocal Fisher equation

NASA Astrophysics Data System (ADS)

Ganan, Yehuda A.; Kessler, David A.

2018-04-01

In this work, we study the problem of front propagation and pattern formation in the stochastic nonlocal Fisher equation. We find a crossover between two regimes: a steadily propagating regime for not too large interaction range and a stochastic punctuated spreading regime for larger ranges. We show that the former regime is well described by the heuristic approximation of the system by a deterministic system where the linear growth term is cut off below some critical density. This deterministic system is seen not only to give the right front velocity, but also predicts the onset of clustering for interaction kernels which give rise to stable uniform states, such as the Gaussian kernel, for sufficiently large cutoff. Above the critical cutoff, distinct clusters emerge behind the front. These same features are present in the stochastic model for sufficiently small carrying capacity. In the latter, punctuated spreading, regime, the population is concentrated on clusters, as in the infinite range case, which divide and separate as a result of the stochastic noise. Due to the finite interaction range, if a fragment at the edge of the population separates sufficiently far, it stabilizes as a new cluster, and the processes begins anew. The deterministic cutoff model does not have this spreading for large interaction ranges, attesting to its purely stochastic origins. We show that this mode of spreading has an exponentially small mean spreading velocity, decaying with the range of the interaction kernel.

Front propagation and clustering in the stochastic nonlocal Fisher equation.

PubMed

Ganan, Yehuda A; Kessler, David A

2018-04-01

In this work, we study the problem of front propagation and pattern formation in the stochastic nonlocal Fisher equation. We find a crossover between two regimes: a steadily propagating regime for not too large interaction range and a stochastic punctuated spreading regime for larger ranges. We show that the former regime is well described by the heuristic approximation of the system by a deterministic system where the linear growth term is cut off below some critical density. This deterministic system is seen not only to give the right front velocity, but also predicts the onset of clustering for interaction kernels which give rise to stable uniform states, such as the Gaussian kernel, for sufficiently large cutoff. Above the critical cutoff, distinct clusters emerge behind the front. These same features are present in the stochastic model for sufficiently small carrying capacity. In the latter, punctuated spreading, regime, the population is concentrated on clusters, as in the infinite range case, which divide and separate as a result of the stochastic noise. Due to the finite interaction range, if a fragment at the edge of the population separates sufficiently far, it stabilizes as a new cluster, and the processes begins anew. The deterministic cutoff model does not have this spreading for large interaction ranges, attesting to its purely stochastic origins. We show that this mode of spreading has an exponentially small mean spreading velocity, decaying with the range of the interaction kernel.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Improving Project Management with Simulation and Completion Distribution Functions

NASA Technical Reports Server (NTRS)

Cates, Grant R.

2004-01-01

Despite the critical importance of project completion timeliness, management practices in place today remain inadequate for addressing the persistent problem of project completion tardiness. A major culprit in late projects is uncertainty, which most, if not all, projects are inherently subject to. This uncertainty resides in the estimates for activity durations, the occurrence of unplanned and unforeseen events, and the availability of critical resources. In response to this problem, this research developed a comprehensive simulation based methodology for conducting quantitative project completion time risk analysis. It is called the Project Assessment by Simulation Technique (PAST). This new tool enables project stakeholders to visualize uncertainty or risk, i.e. the likelihood of their project completing late and the magnitude of the lateness, by providing them with a completion time distribution function of their projects. Discrete event simulation is used within PAST to determine the completion distribution function for the project of interest. The simulation is populated with both deterministic and stochastic elements. The deterministic inputs include planned project activities, precedence requirements, and resource requirements. The stochastic inputs include activity duration growth distributions, probabilities for events that can impact the project, and other dynamic constraints that may be placed upon project activities and milestones. These stochastic inputs are based upon past data from similar projects. The time for an entity to complete the simulation network, subject to both the deterministic and stochastic factors, represents the time to complete the project. Repeating the simulation hundreds or thousands of times allows one to create the project completion distribution function. The Project Assessment by Simulation Technique was demonstrated to be effective for the on-going NASA project to assemble the International Space Station. Approximately $500 million per month is being spent on this project, which is scheduled to complete by 2010. NASA project stakeholders participated in determining and managing completion distribution functions produced from PAST. The first result was that project stakeholders improved project completion risk awareness. Secondly, using PAST, mitigation options were analyzed to improve project completion performance and reduce total project cost.

Random yet deterministic: convergent immunoglobulin responses to influenza.

PubMed

Martins, Andrew J; Tsang, John S

2014-09-01

B cell clonal expansion is a hallmark of host-defense and vaccination responses. Given the vast immunoglobulin repertoire, individuals may expand B cells carrying largely distinct immunoglobulin genes following antigenic challenge. Using immunoglobulin-repertoire sequencing to dynamically track responses to influenza vaccination, Jackson et al. find evidence of convergent immunoglobulin responses across individuals. Published by Elsevier Ltd.

Neural nets with terminal chaos for simulation of non-deterministic patterns

NASA Technical Reports Server (NTRS)

Zak, Michail

1993-01-01

Models for simulating some aspects of neural intelligence are presented and discussed. Special attention is given to terminal neurodynamics as a particular architecture of terminal dynamics suitable for modeling information flows. Applications of terminal chaos to information fusion as well as to planning and modeling coordination among neurons in biological systems are disussed.

An Adjoint State Method for Three-Dimensional Transmission Traveltime Tomography Using First-Arrivals

DTIC Science & Technology

2006-01-30

detail next. 3.2 Fast Sweeping Method for Equation (1) The fast sweeping method was originated in Boue and Dupis [5], its first PDE formulation was in...Geophysics, 50:903–923, 1985. [5] M. Boue and P. Dupuis. Markov chain approximations for deterministic control prob- lems with affine dynamics and

Using State-Space Model with Regime Switching to Represent the Dynamics of Facial Electromyography (EMG) Data

ERIC Educational Resources Information Center

Yang, Manshu; Chow, Sy-Miin

2010-01-01

Facial electromyography (EMG) is a useful physiological measure for detecting subtle affective changes in real time. A time series of EMG data contains bursts of electrical activity that increase in magnitude when the pertinent facial muscles are activated. Whereas previous methods for detecting EMG activation are often based on deterministic or…

The Deterministic Information Bottleneck

NASA Astrophysics Data System (ADS)

Strouse, D. J.; Schwab, David

2015-03-01

A fundamental and ubiquitous task that all organisms face is prediction of the future based on past sensory experience. Since an individual's memory resources are limited and costly, however, there is a tradeoff between memory cost and predictive payoff. The information bottleneck (IB) method (Tishby, Pereira, & Bialek 2000) formulates this tradeoff as a mathematical optimization problem using an information theoretic cost function. IB encourages storing as few bits of past sensory input as possible while selectively preserving the bits that are most predictive of the future. Here we introduce an alternative formulation of the IB method, which we call the deterministic information bottleneck (DIB). First, we argue for an alternative cost function, which better represents the biologically-motivated goal of minimizing required memory resources. Then, we show that this seemingly minor change has the dramatic effect of converting the optimal memory encoder from stochastic to deterministic. Next, we propose an iterative algorithm for solving the DIB problem. Additionally, we compare the IB and DIB methods on a variety of synthetic datasets, and examine the performance of retinal ganglion cell populations relative to the optimal encoding strategy for each problem.

Effects of Noise on Ecological Invasion Processes: Bacteriophage-mediated Competition in Bacteria

NASA Astrophysics Data System (ADS)

Joo, Jaewook; Eric, Harvill; Albert, Reka

2007-03-01

Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in nature. Using an experimental system of bacteriophage-mediated competition in bacterial populations and a deterministic model, we have shown in [Joo et al 2005] that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of the initial phage concentration and other phage and host parameters such as the infection-causing contact rate, the spontaneous and infection-induced lysis rates, and the phage burst size. Here we investigate the effects of stochastic fluctuations on bacterial invasion facilitated by bacteriophage, and examine the validity of the deterministic approach. We use both numerical and analytical methods of stochastic processes to identify the source of noise and assess its magnitude. We show that the conclusions obtained from the deterministic model are robust against stochastic fluctuations, yet deviations become prominently large when the phage are more pathological to the invading bacterial strain.

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

PubMed

Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O

2006-03-01

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

Exact and approximate stochastic simulation of intracellular calcium dynamics.

PubMed

Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von

2011-01-01

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

Local-scale Partitioning of Functional and Phylogenetic Beta Diversity in a Tropical Tree Assemblage.

PubMed

Yang, Jie; Swenson, Nathan G; Zhang, Guocheng; Ci, Xiuqin; Cao, Min; Sha, Liqing; Li, Jie; Ferry Slik, J W; Lin, Luxiang

2015-08-03

The relative degree to which stochastic and deterministic processes underpin community assembly is a central problem in ecology. Quantifying local-scale phylogenetic and functional beta diversity may shed new light on this problem. We used species distribution, soil, trait and phylogenetic data to quantify whether environmental distance, geographic distance or their combination are the strongest predictors of phylogenetic and functional beta diversity on local scales in a 20-ha tropical seasonal rainforest dynamics plot in southwest China. The patterns of phylogenetic and functional beta diversity were generally consistent. The phylogenetic and functional dissimilarity between subplots (10 × 10 m, 20 × 20 m, 50 × 50 m and 100 × 100 m) was often higher than that expected by chance. The turnover of lineages and species function within habitats was generally slower than that across habitats. Partitioning the variation in phylogenetic and functional beta diversity showed that environmental distance was generally a better predictor of beta diversity than geographic distance thereby lending relatively more support for deterministic environmental filtering over stochastic processes. Overall, our results highlight that deterministic processes play a stronger role than stochastic processes in structuring community composition in this diverse assemblage of tropical trees.

Deterministic direct reprogramming of somatic cells to pluripotency.

PubMed

Rais, Yoach; Zviran, Asaf; Geula, Shay; Gafni, Ohad; Chomsky, Elad; Viukov, Sergey; Mansour, Abed AlFatah; Caspi, Inbal; Krupalnik, Vladislav; Zerbib, Mirie; Maza, Itay; Mor, Nofar; Baran, Dror; Weinberger, Leehee; Jaitin, Diego A; Lara-Astiaso, David; Blecher-Gonen, Ronnie; Shipony, Zohar; Mukamel, Zohar; Hagai, Tzachi; Gilad, Shlomit; Amann-Zalcenstein, Daniela; Tanay, Amos; Amit, Ido; Novershtern, Noa; Hanna, Jacob H

2013-10-03

Somatic cells can be inefficiently and stochastically reprogrammed into induced pluripotent stem (iPS) cells by exogenous expression of Oct4 (also called Pou5f1), Sox2, Klf4 and Myc (hereafter referred to as OSKM). The nature of the predominant rate-limiting barrier(s) preventing the majority of cells to successfully and synchronously reprogram remains to be defined. Here we show that depleting Mbd3, a core member of the Mbd3/NuRD (nucleosome remodelling and deacetylation) repressor complex, together with OSKM transduction and reprogramming in naive pluripotency promoting conditions, result in deterministic and synchronized iPS cell reprogramming (near 100% efficiency within seven days from mouse and human cells). Our findings uncover a dichotomous molecular function for the reprogramming factors, serving to reactivate endogenous pluripotency networks while simultaneously directly recruiting the Mbd3/NuRD repressor complex that potently restrains the reactivation of OSKM downstream target genes. Subsequently, the latter interactions, which are largely depleted during early pre-implantation development in vivo, lead to a stochastic and protracted reprogramming trajectory towards pluripotency in vitro. The deterministic reprogramming approach devised here offers a novel platform for the dissection of molecular dynamics leading to establishing pluripotency at unprecedented flexibility and resolution.

Time Correlations in Mode Hopping of Coupled Oscillators

NASA Astrophysics Data System (ADS)

Heltberg, Mathias L.; Krishna, Sandeep; Jensen, Mogens H.

2017-05-01

We study the dynamics in a system of coupled oscillators when Arnold Tongues overlap. By varying the initial conditions, the deterministic system can be attracted to different limit cycles. Adding noise, the mode hopping between different states become a dominating part of the dynamics. We simplify the system through a Poincare section, and derive a 1D model to describe the dynamics. We explain that for some parameter values of the external oscillator, the time distribution of occupancy in a state is exponential and thus memoryless. In the general case, on the other hand, it is a sum of exponential distributions characteristic of a system with time correlations.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

Monitoring the Heavens, Today, and Tomorrow

NASA Technical Reports Server (NTRS)

Johnson, Nicholas L.

2006-01-01

The current Earth satellite population in LEO for all sizes is relatively well-established by a combination of deterministic and statistical means. At higher altitudes, the population of satellites with diameters of less than 1 m is not well defined. Although a few new sensors might become operational in the near- to mid-term, no major improvement in environment characterization is anticipated during this period. With the increasing deployment of micro- and pico-satellites and with the continued growth of the small debris population, a need exists for better space surveillance to support spacecraft design and operations.

First-passage problems: A probabilistic dynamic analysis for degraded structures

NASA Technical Reports Server (NTRS)

Shiao, Michael C.; Chamis, Christos C.

1990-01-01

Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.

Chaotic itinerancy in the oscillator neural network without Lyapunov functions.

PubMed

Uchiyama, Satoki; Fujisaka, Hirokazu

2004-09-01

Chaotic itinerancy (CI), which is defined as an incessant spontaneous switching phenomenon among attractor ruins in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case of an oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S. Uchiyama and H. Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neurodynamics. It is found that CI in neural nets can be understood as the intermittent dynamics of weakly destabilized chaotic retrieval solutions. Copyright 2004 American Institute of Physics

Incorporating GIS and remote sensing for census population disaggregation

NASA Astrophysics Data System (ADS)

Wu, Shuo-Sheng'derek'

Census data are the primary source of demographic data for a variety of researches and applications. For confidentiality issues and administrative purposes, census data are usually released to the public by aggregated areal units. In the United States, the smallest census unit is census blocks. Due to data aggregation, users of census data may have problems in visualizing population distribution within census blocks and estimating population counts for areas not coinciding with census block boundaries. The main purpose of this study is to develop methodology for estimating sub-block areal populations and assessing the estimation errors. The City of Austin, Texas was used as a case study area. Based on tax parcel boundaries and parcel attributes derived from ancillary GIS and remote sensing data, detailed urban land use classes were first classified using a per-field approach. After that, statistical models by land use classes were built to infer population density from other predictor variables, including four census demographic statistics (the Hispanic percentage, the married percentage, the unemployment rate, and per capita income) and three physical variables derived from remote sensing images and building footprints vector data (a landscape heterogeneity statistics, a building pattern statistics, and a building volume statistics). In addition to statistical models, deterministic models were proposed to directly infer populations from building volumes and three housing statistics, including the average space per housing unit, the housing unit occupancy rate, and the average household size. After population models were derived or proposed, how well the models predict populations for another set of sample blocks was assessed. The results show that deterministic models were more accurate than statistical models. Further, by simulating the base unit for modeling from aggregating blocks, I assessed how well the deterministic models estimate sub-unit-level populations. I also assessed the aggregation effects and the resealing effects on sub-unit estimates. Lastly, from another set of mixed-land-use sample blocks, a mixed-land-use model was derived and compared with a residential-land-use model. The results of per-field land use classification are satisfactory with a Kappa accuracy statistics of 0.747. Model Assessments by land use show that population estimates for multi-family land use areas have higher errors than those for single-family land use areas, and population estimates for mixed land use areas have higher errors than those for residential land use areas. The assessments of sub-unit estimates using a simulation approach indicate that smaller areas show higher estimation errors, estimation errors do not relate to the base unit size, and resealing improves all levels of sub-unit estimates.

Developing and Implementing the Data Mining Algorithms in RAVEN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sen, Ramazan Sonat; Maljovec, Daniel Patrick; Alfonsi, Andrea

The RAVEN code is becoming a comprehensive tool to perform probabilistic risk assessment, uncertainty quantification, and verification and validation. The RAVEN code is being developed to support many programs and to provide a set of methodologies and algorithms for advanced analysis. Scientific computer codes can generate enormous amounts of data. To post-process and analyze such data might, in some cases, take longer than the initial software runtime. Data mining algorithms/methods help in recognizing and understanding patterns in the data, and thus discover knowledge in databases. The methodologies used in the dynamic probabilistic risk assessment or in uncertainty and error quantificationmore » analysis couple system/physics codes with simulation controller codes, such as RAVEN. RAVEN introduces both deterministic and stochastic elements into the simulation while the system/physics code model the dynamics deterministically. A typical analysis is performed by sampling values of a set of parameter values. A major challenge in using dynamic probabilistic risk assessment or uncertainty and error quantification analysis for a complex system is to analyze the large number of scenarios generated. Data mining techniques are typically used to better organize and understand data, i.e. recognizing patterns in the data. This report focuses on development and implementation of Application Programming Interfaces (APIs) for different data mining algorithms, and the application of these algorithms to different databases.« less

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Diffusive and subdiffusive dynamics of indoor microclimate: a time series modeling.

PubMed

Maciejewska, Monika; Szczurek, Andrzej; Sikora, Grzegorz; Wyłomańska, Agnieszka

2012-09-01

The indoor microclimate is an issue in modern society, where people spend about 90% of their time indoors. Temperature and relative humidity are commonly used for its evaluation. In this context, the two parameters are usually considered as behaving in the same manner, just inversely correlated. This opinion comes from observation of the deterministic components of temperature and humidity time series. We focus on the dynamics and the dependency structure of the time series of these parameters, without deterministic components. Here we apply the mean square displacement, the autoregressive integrated moving average (ARIMA), and the methodology for studying anomalous diffusion. The analyzed data originated from five monitoring locations inside a modern office building, covering a period of nearly one week. It was found that the temperature data exhibited a transition between diffusive and subdiffusive behavior, when the building occupancy pattern changed from the weekday to the weekend pattern. At the same time the relative humidity consistently showed diffusive character. Also the structures of the dependencies of the temperature and humidity data sets were different, as shown by the different structures of the ARIMA models which were found appropriate. In the space domain, the dynamics and dependency structure of the particular parameter were preserved. This work proposes an approach to describe the very complex conditions of indoor air and it contributes to the improvement of the representative character of microclimate monitoring.

Constructing networks from a dynamical system perspective for multivariate nonlinear time series.

PubMed

Nakamura, Tomomichi; Tanizawa, Toshihiro; Small, Michael

2016-03-01

We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series.

Comparison of Dynamical Behaviors Between Monofunctional and Bifunctional Two-Component Signaling Modules

NASA Astrophysics Data System (ADS)

Yang, Xiyan; Wu, Yahao; Yuan, Zhanjiang

2015-06-01

Two-component signaling modules exist extensively in bacteria and microbes. These modules can be, based on their distinct network structures, divided into two types: the monofunctional system (denoted by MFS) where the sensor kinase (SK) modulates only phosphorylation of the response regulator (RR), and the bifunctional system (denoted by BFS) where the SK catalyzes both phosphorylation and dephosphorylation of the RR. Here, we analyze dynamical behaviors of these two systems based on stability theory, focusing on differences between them. The analysis of the deterministic behavior indicates that there is no difference between the two modules, that is, each system has the unique stable steady state. However, there are significant differences in stochastic behavior between them. Specifically, if the mean phosphorylated SK level is kept the same for the two modules, then the variance and the Fano factor for the phosphorylated RR in the BFS are always no less than those in the MFS, indicating that bifunctionality always enhances fluctuations. The correlation between the phosphorylated SK and the phosphorylated RR in the BFS is always positive mainly due to competition between system components, but this correlation in the MFS may be positive, almost zero, or negative, depending on the ratio between two rate constants. Our overall analysis indicates that differences between dynamical behaviors of monofunctional and bifunctional signaling modules are mainly in the stochastic rather than deterministic aspect.

Population dynamics of the Concho water snake in rivers and reservoirs

USGS Publications Warehouse

Whiting, M.J.; Dixon, J.R.; Greene, B.D.; Mueller, J.M.; Thornton, O.W.; Hatfield, J.S.; Nichols, J.D.; Hines, J.E.

2008-01-01

The Concho Water Snake (Nerodia harteri paucimaculata) is confined to the Concho–Colorado River valley of central Texas, thereby occupying one of the smallest geographic ranges of any North American snake. In 1986, N. h. paucimaculata was designated as a federally threatened species, in large part because of reservoir projects that were perceived to adversely affect the amount of habitat available to the snake. During a ten-year period (1987–1996), we conducted capture–recapture field studies to assess dynamics of five subpopulations of snakes in both natural (river) and man-made (reservoir) habitats. Because of differential sampling of subpopulations, we present separate results for all five subpopulations combined (including large reservoirs) and three of the five subpopulations (excluding large reservoirs). We used multistate capture–recapture models to deal with stochastic transitions between pre-reproductive and reproductive size classes and to allow for the possibility of different survival and capture probabilities for the two classes. We also estimated both the finite rate of increase (λ) for a deterministic, stage-based, female-only matrix model using the average litter size, and the average rate of adult population change, λ ˆ, which describes changes in numbers of adult snakes, using a direct capture–recapture approach to estimation. Average annual adult survival was about 0.23 and similar for males and females. Average annual survival for subadults was about 0.14. The parameter estimates from the stage-based projection matrix analysis all yielded asymptotic values of λ < 1, suggesting populations that are not viable. However, the direct estimates of average adult λ for the three subpopulations excluding major reservoirs were λ ˆ  =  1.26, SE ˆ(λ ˆ)  =  0.18 and λ ˆ  =  0.99, SE ˆ(λ ˆ)  =  0.79, based on two different models. Thus, the direct estimation approach did not provide strong evidence of population declines of the riverine subpopulations, but the estimates are characterized by substantial uncertainty.

Spatiotemporal pattern formation in a prey-predator model under environmental driving forces

NASA Astrophysics Data System (ADS)

Sirohi, Anuj Kumar; Banerjee, Malay; Chakraborti, Anirban

2015-09-01

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.

The Bilinear Product Model of Hysteresis Phenomena

NASA Astrophysics Data System (ADS)

Kádár, György

1989-01-01

In ferromagnetic materials non-reversible magnetization processes are represented by rather complex hysteresis curves. The phenomenological description of such curves needs the use of multi-valued, yet unambiguous, deterministic functions. The history dependent calculation of consecutive Everett-integrals of the two-variable Preisach-function can account for the main features of hysteresis curves in uniaxial magnetic materials. The traditional Preisach model has recently been modified on the basis of population dynamics considerations, removing the non-real congruency property of the model. The Preisach-function was proposed to be a product of two factors of distinct physical significance: a magnetization dependent function taking into account the overall magnetization state of the body and a bilinear form of a single variable, magnetic field dependent, switching probability function. The most important statement of the bilinear product model is, that the switching process of individual particles is to be separated from the book-keeping procedure of their states. This empirical model of hysteresis can easily be extended to other irreversible physical processes, such as first order phase transitions.

Anderson transition in a three-dimensional kicked rotor

NASA Astrophysics Data System (ADS)

Wang, Jiao; García-García, Antonio M.

2009-03-01

We investigate Anderson localization in a three-dimensional (3D) kicked rotor. By a finite-size scaling analysis we identify a mobility edge for a certain value of the kicking strength k=kc . For k>kc dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3D Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region k≈kc we carry out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations, the number variance is linear, level repulsion is still observed, and quantum diffusion is anomalous with ⟨p2⟩∝t2/3 . We note that in the 3D kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3D kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion. However we have found that certain choices of irrational periods enhance Anderson localization effects.

The noisy edge of traveling waves

PubMed Central

Hallatschek, Oskar

2011-01-01

Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling waves remain elusive because they are often dominated by rare fluctuations in the wave tip, which have defied any rigorous analysis so far. Here, we show that by adjusting nonlinear model details, noisy traveling waves can be solved exactly. The moment equations of these tuned models are closed and have a simple analytical structure resembling the deterministic approximation supplemented by a nonlocal cutoff term. The peculiar form of the cutoff shapes the noisy edge of traveling waves and is critical for the correct prediction of the wave speed and its fluctuations. Our approach is illustrated and benchmarked using the example of fitness waves arising in simple models of microbial evolution, which are highly sensitive to number fluctuations. We demonstrate explicitly how these models can be tuned to account for finite population sizes and determine how quickly populations adapt as a function of population size and mutation rates. More generally, our method is shown to apply to a broad class of models, in which number fluctuations are generated by branching processes. Because of this versatility, the method of model tuning may serve as a promising route toward unraveling universal properties of complex discrete particle systems. PMID:21187435

Evolution of phenotypic clusters through competition and local adaptation along an environmental gradient.

PubMed

Leimar, Olof; Doebeli, Michael; Dieckmann, Ulf

2008-04-01

We have analyzed the evolution of a quantitative trait in populations that are spatially extended along an environmental gradient, with gene flow between nearby locations. In the absence of competition, there is stabilizing selection toward a locally best-adapted trait that changes gradually along the gradient. According to traditional ideas, gradual spatial variation in environmental conditions is expected to lead to gradual variation in the evolved trait. A contrasting possibility is that the trait distribution instead breaks up into discrete clusters. Doebeli and Dieckmann (2003) argued that competition acting locally in trait space and geographical space can promote such clustering. We have investigated this possibility using deterministic population dynamics for asexual populations, analyzing our model numerically and through an analytical approximation. We examined how the evolution of clusters is affected by the shape of competition kernels, by the presence of Allee effects, and by the strength of gene flow along the gradient. For certain parameter ranges clustering was a robust outcome, and for other ranges there was no clustering. Our analysis shows that the shape of competition kernels is important for clustering: the sign structure of the Fourier transform of a competition kernel determines whether the kernel promotes clustering. Also, we found that Allee effects promote clustering, whereas gene flow can have a counteracting influence. In line with earlier findings, we could demonstrate that phenotypic clustering was favored by gradients of intermediate slope.

Is the Grass Always Greener? Comparing the Environmental Impact of Conventional, Natural and Grass-Fed Beef Production Systems.

PubMed

Capper, Judith L

2012-04-10

This study compared the environmental impact of conventional, natural and grass-fed beef production systems. A deterministic model based on the metabolism and nutrient requirements of the beef population was used to quantify resource inputs and waste outputs per 1.0 × 10⁸ kg of hot carcass weight beef in conventional (CON), natural (NAT) and grass-fed (GFD) production systems. Production systems were modeled using characteristic management practices, population dynamics and production data from U.S. beef production systems. Increased productivity (slaughter weight and growth rate) in the CON system reduced the cattle population size required to produce 1.0 × 10⁸ kg of beef compared to the NAT or GFD system. The CON system required 56.3% of the animals, 24.8% of the water, 55.3% of the land and 71.4% of the fossil fuel energy required to produce 1.0 × 10⁸ kg of beef compared to the GFD system. The carbon footprint per 1.0 × 10⁸ kg of beef was lowest in the CON system (15,989 × 10³ t), intermediate in the NAT system (18,772 × 10³ t) and highest in the GFD system (26,785 × 10³ t). The challenge to the U.S beef industry is to communicate differences in system environmental impacts to facilitate informed dietary choice.

Soil erosion assessment - Mind the gap

NASA Astrophysics Data System (ADS)

Kim, Jongho; Ivanov, Valeriy Y.; Fatichi, Simone

2016-12-01

Accurate assessment of erosion rates remains an elusive problem because soil loss is strongly nonunique with respect to the main drivers. In addressing the mechanistic causes of erosion responses, we discriminate between macroscale effects of external factors - long studied and referred to as "geomorphic external variability", and microscale effects, introduced as "geomorphic internal variability." The latter source of erosion variations represents the knowledge gap, an overlooked but vital element of geomorphic response, significantly impacting the low predictability skill of deterministic models at field-catchment scales. This is corroborated with experiments using a comprehensive physical model that dynamically updates the soil mass and particle composition. As complete knowledge of microscale conditions for arbitrary location and time is infeasible, we propose that new predictive frameworks of soil erosion should embed stochastic components in deterministic assessments of external and internal types of geomorphic variability.

From qualitative data to quantitative models: analysis of the phage shock protein stress response in Escherichia coli

PubMed Central

2011-01-01

Background Bacteria have evolved a rich set of mechanisms for sensing and adapting to adverse conditions in their environment. These are crucial for their survival, which requires them to react to extracellular stresses such as heat shock, ethanol treatment or phage infection. Here we focus on studying the phage shock protein (Psp) stress response in Escherichia coli induced by a phage infection or other damage to the bacterial membrane. This system has not yet been theoretically modelled or analysed in silico. Results We develop a model of the Psp response system, and illustrate how such models can be constructed and analyzed in light of available sparse and qualitative information in order to generate novel biological hypotheses about their dynamical behaviour. We analyze this model using tools from Petri-net theory and study its dynamical range that is consistent with currently available knowledge by conditioning model parameters on the available data in an approximate Bayesian computation (ABC) framework. Within this ABC approach we analyze stochastic and deterministic dynamics. This analysis allows us to identify different types of behaviour and these mechanistic insights can in turn be used to design new, more detailed and time-resolved experiments. Conclusions We have developed the first mechanistic model of the Psp response in E. coli. This model allows us to predict the possible qualitative stochastic and deterministic dynamic behaviours of key molecular players in the stress response. Our inferential approach can be applied to stress response and signalling systems more generally: in the ABC framework we can condition mathematical models on qualitative data in order to delimit e.g. parameter ranges or the qualitative system dynamics in light of available end-point or qualitative information. PMID:21569396

Impact of Simian Immunodeficiency Virus Infection on Chimpanzee Population Dynamics

PubMed Central

Rudicell, Rebecca S.; Holland Jones, James; Wroblewski, Emily E.; Learn, Gerald H.; Li, Yingying; Robertson, Joel D.; Greengrass, Elizabeth; Grossmann, Falk; Kamenya, Shadrack; Pintea, Lilian; Mjungu, Deus C.; Lonsdorf, Elizabeth V.; Mosser, Anna; Lehman, Clarence; Collins, D. Anthony; Keele, Brandon F.; Goodall, Jane; Hahn, Beatrice H.; Pusey, Anne E.; Wilson, Michael L.

2010-01-01

Like human immunodeficiency virus type 1 (HIV-1), simian immunodeficiency virus of chimpanzees (SIVcpz) can cause CD4+ T cell loss and premature death. Here, we used molecular surveillance tools and mathematical modeling to estimate the impact of SIVcpz infection on chimpanzee population dynamics. Habituated (Mitumba and Kasekela) and non-habituated (Kalande) chimpanzees were studied in Gombe National Park, Tanzania. Ape population sizes were determined from demographic records (Mitumba and Kasekela) or individual sightings and genotyping (Kalande), while SIVcpz prevalence rates were monitored using non-invasive methods. Between 2002–2009, the Mitumba and Kasekela communities experienced mean annual growth rates of 1.9% and 2.4%, respectively, while Kalande chimpanzees suffered a significant decline, with a mean growth rate of −6.5% to −7.4%, depending on population estimates. A rapid decline in Kalande was first noted in the 1990s and originally attributed to poaching and reduced food sources. However, between 2002–2009, we found a mean SIVcpz prevalence in Kalande of 46.1%, which was almost four times higher than the prevalence in Mitumba (12.7%) and Kasekela (12.1%). To explore whether SIVcpz contributed to the Kalande decline, we used empirically determined SIVcpz transmission probabilities as well as chimpanzee mortality, mating and migration data to model the effect of viral pathogenicity on chimpanzee population growth. Deterministic calculations indicated that a prevalence of greater than 3.4% would result in negative growth and eventual population extinction, even using conservative mortality estimates. However, stochastic models revealed that in representative populations, SIVcpz, and not its host species, frequently went extinct. High SIVcpz transmission probability and excess mortality reduced population persistence, while intercommunity migration often rescued infected communities, even when immigrating females had a chance of being SIVcpz infected. Together, these results suggest that the decline of the Kalande community was caused, at least in part, by high levels of SIVcpz infection. However, population extinction is not an inevitable consequence of SIVcpz infection, but depends on additional variables, such as migration, that promote survival. These findings are consistent with the uneven distribution of SIVcpz throughout central Africa and explain how chimpanzees in Gombe and elsewhere can be at equipoise with this pathogen. PMID:20886099

Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

NASA Astrophysics Data System (ADS)

Vijaykumar, Adithya; Ouldridge, Thomas E.; ten Wolde, Pieter Rein; Bolhuis, Peter G.

2017-03-01

The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic molecular dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, J. Chem. Phys. 143, 214102 (2015)]. Here we extend this multiscale MD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We present the novel algorithm focusing on Brownian dynamics only, although the methodology is generic. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm, we discuss its performance. The rotational Brownian dynamics MD-GFRD multiscale method will open up the possibility for large scale simulations of protein signalling networks.

Deterministic Chaos: Proposal of an Informal Educational Activity Aimed at High School Students

ERIC Educational Resources Information Center

Greco, Valeria; Spagnolo, Salvatore

2016-01-01

Chaos theory is not present in the Italian school curricula and textbooks in spite of being present in many topics of classical physics and in everyday life. Chaotic dynamics, in fact, are involved in phenomena easily accessible to everyone or in events experienced by most people in their lives (the dripping of a faucet which keeps people awoken…

Effects of structural error on the estimates of parameters of dynamical systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1986-01-01

In this paper, the notion of 'near-equivalence in probability' is introduced for identifying a system in the presence of several error sources. Following some basic definitions, necessary and sufficient conditions for the identifiability of parameters are given. The effects of structural error on the parameter estimates for both the deterministic and stochastic cases are considered.

Dynamic Routing and Coordination in Multi-Agent Networks

DTIC Science & Technology

2016-06-10

SECURITY CLASSIFICATION OF: Supported by this project, we designed innovative routing, planning and coordination strategies for robotic networks and...tasks partitioned among robots , in what order are they to be performed, and along which deterministic routes or according to which stochastic rules do...individual robots move. The fundamental novelties and our recent breakthroughs supported by this project are manifold: (1) the application 1

Multi-Strain Deterministic Chaos in Dengue Epidemiology, A Challenge for Computational Mathematics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Kooi, Bob W.; Stollenwerk, Nico

2009-09-01

Recently, we have analysed epidemiological models of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra has to be applied in comparison to get further insight into such dynamical structures. Especially, Lyapunov spectra, which quantify the predictability horizon in the epidemiological system, are computationally very demanding. We show ways to speed up computations of such Lyapunov spectra by a factor of more than ten by parallelizing previously used sequential C programs. Such fast computations of Lyapunov spectra will be especially of use in future investigations of seasonally forced versions of the present models, as they are needed for data analysis.

Separation of red blood cells in deep deterministic lateral displacement devices

NASA Astrophysics Data System (ADS)

Kabacaoglu, Gokberk; Biros, George

2017-11-01

Microfluidic cell separation techniques are of great interest since they help rapid medical diagnoses and tests. Deterministic lateral displacement (DLD) is one of them. A DLD device consists of arrays of pillars. Main flow and alignment of the pillars define two different directions. Size-based separation of rigid spherical particles is possible as they follow one of these directions depending on their sizes. However, the separation of non-spherical deformable particles such as red blood cells (RBCs) is more complicated than that due to their intricate dynamics. We study the separation of RBCs in DLD using an in-house integral equation solver. We systematically investigate the effects of the interior fluid viscosity and the membrane elasticity of an RBC on its behavior. These mechanical properties of a cell determine its deformability, which can be altered by several diseases. We particularly consider deep devices in which an RBC can show rich dynamics such as tank-treading and tumbling. It turns out that strong hydrodynamic lift force moves the tank-treading cells along the pillars and downward force leads the tumbling ones to move with the flow. Thereby, deformability-based separation of RBCs is possible.

Experimental study and simulation of space charge stimulated discharge

NASA Astrophysics Data System (ADS)

Noskov, M. D.; Malinovski, A. S.; Cooke, C. M.; Wright, K. A.; Schwab, A. J.

2002-11-01

The electrical discharge of volume distributed space charge in poly(methylmethacrylate) (PMMA) has been investigated both experimentally and by computer simulation. The experimental space charge was implanted in dielectric samples by exposure to a monoenergetic electron beam of 3 MeV. Electrical breakdown through the implanted space charge region within the sample was initiated by a local electric field enhancement applied to the sample surface. A stochastic-deterministic dynamic model for electrical discharge was developed and used in a computer simulation of these breakdowns. The model employs stochastic rules to describe the physical growth of the discharge channels, and deterministic laws to describe the electric field, the charge, and energy dynamics within the discharge channels and the dielectric. Simulated spatial-temporal and current characteristics of the expanding discharge structure during physical growth are quantitatively compared with the experimental data to confirm the discharge model. It was found that a single fixed set of physically based dielectric parameter values was adequate to simulate the complete family of experimental space charge discharges in PMMA. It is proposed that such a set of parameters also provides a useful means to quantify the breakdown properties of other dielectrics.

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

PubMed

Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2017-01-01

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

The giant acoustic atom - a single quantum system with a deterministic time delay

NASA Astrophysics Data System (ADS)

Guo, Lingzhen; Grimsmo, Arne; Frisk Kockum, Anton; Pletyukhov, Mikhail; Johansson, Göran

2017-04-01

We investigate the quantum dynamics of a single transmon qubit coupled to surface acoustic waves (SAWs) via two distant connection points. Since the acoustic speed is five orders of magnitude slower than the speed of light, the travelling time between the two connection points needs to be taken into account. Therefore, we treat the transmon qubit as a giant atom with a deterministic time delay. We find that the spontaneous emission of the system, formed by the giant atom and the SAWs between its connection points, initially follows a polynomial decay law instead of an exponential one, as would be the case for a small atom. We obtain exact analytical results for the scattering properties of the giant atom up to two-phonon processes by using a diagrammatic approach. The time delay gives rise to novel features in the reflection, transmission, power spectra, and second-order correlation functions of the system. Furthermore, we find the short-time dynamics of the giant atom for arbitrary drive strength by a numerically exact method for open quantum systems with a finite-time-delay feedback loop. L. G. acknowledges financial support from Carl-Zeiss Stiftung (0563-2.8/508/2).

Exploration of cellular reaction systems.

PubMed

Kirkilionis, Markus

2010-01-01

We discuss and review different ways to map cellular components and their temporal interaction with other such components to different non-spatially explicit mathematical models. The essential choices made in the literature are between discrete and continuous state spaces, between rule and event-based state updates and between deterministic and stochastic series of such updates. The temporal modelling of cellular regulatory networks (dynamic network theory) is compared with static network approaches in two first introductory sections on general network modelling. We concentrate next on deterministic rate-based dynamic regulatory networks and their derivation. In the derivation, we include methods from multiscale analysis and also look at structured large particles, here called macromolecular machines. It is clear that mass-action systems and their derivatives, i.e. networks based on enzyme kinetics, play the most dominant role in the literature. The tools to analyse cellular reaction networks are without doubt most complete for mass-action systems. We devote a long section at the end of the review to make a comprehensive review of related tools and mathematical methods. The emphasis is to show how cellular reaction networks can be analysed with the help of different associated graphs and the dissection into modules, i.e. sub-networks.

Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier.

PubMed

Sharma, Vijay

2009-09-10

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

PubMed Central

Sharma, Vijay

2009-01-01

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts. PMID:19812706

Deterministic ripple-spreading model for complex networks.

PubMed

Hu, Xiao-Bing; Wang, Ming; Leeson, Mark S; Hines, Evor L; Di Paolo, Ezequiel

2011-04-01

This paper proposes a deterministic complex network model, which is inspired by the natural ripple-spreading phenomenon. The motivations and main advantages of the model are the following: (i) The establishment of many real-world networks is a dynamic process, where it is often observed that the influence of a few local events spreads out through nodes, and then largely determines the final network topology. Obviously, this dynamic process involves many spatial and temporal factors. By simulating the natural ripple-spreading process, this paper reports a very natural way to set up a spatial and temporal model for such complex networks. (ii) Existing relevant network models are all stochastic models, i.e., with a given input, they cannot output a unique topology. Differently, the proposed ripple-spreading model can uniquely determine the final network topology, and at the same time, the stochastic feature of complex networks is captured by randomly initializing ripple-spreading related parameters. (iii) The proposed model can use an easily manageable number of ripple-spreading related parameters to precisely describe a network topology, which is more memory efficient when compared with traditional adjacency matrix or similar memory-expensive data structures. (iv) The ripple-spreading model has a very good potential for both extensions and applications.

Negative mobility of a Brownian particle: Strong damping regime

NASA Astrophysics Data System (ADS)

Słapik, A.; Łuczka, J.; Spiechowicz, J.

2018-02-01

We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.

Effects of delay and noise in a negative feedback regulatory motif

NASA Astrophysics Data System (ADS)

Palassini, Matteo; Dies, Marta

2009-03-01

The small copy number of the molecules involved in gene regulation can induce nontrivial stochastic phenomena such as noise-induced oscillations. An often neglected aspect of regulation dynamics are the delays involved in transcription and translation. Delays introduce analytical and computational complications because the dynamics is non-Markovian. We study the interplay of noise and delays in a negative feedback model of the p53 core regulatory network. Recent experiments have found pronounced oscillations in the concentrations of proteins p53 and Mdm2 in individual cells subjected to DNA damage. Similar oscillations occur in the Hes-1 and NK-kB systems, and in circadian rhythms. Several mechanisms have been proposed to explain this oscillatory behaviour, such as deterministic limit cycles, with and without delay, or noise-induced excursions in excitable models. We consider a generic delayed Master Equation incorporating the activation of Mdm2 by p53 and the Mdm2-promoted degradation of p53. In the deterministic limit and for large delays, the model shows a Hopf bifurcation. Via exact stochastic simulations, we find strong noise-induced oscillations well outside the limit-cycle region. We propose that this may be a generic mechanism for oscillations in gene regulatory systems.

Integrating Kinetic Model of E. coli with Genome Scale Metabolic Fluxes Overcomes Its Open System Problem and Reveals Bistability in Central Metabolism

PubMed Central

Mannan, Ahmad A.; Toya, Yoshihiro; Shimizu, Kazuyuki; McFadden, Johnjoe; Kierzek, Andrzej M.; Rocco, Andrea

2015-01-01

An understanding of the dynamics of the metabolic profile of a bacterial cell is sought from a dynamical systems analysis of kinetic models. This modelling formalism relies on a deterministic mathematical description of enzyme kinetics and their metabolite regulation. However, it is severely impeded by the lack of available kinetic information, limiting the size of the system that can be modelled. Furthermore, the subsystem of the metabolic network whose dynamics can be modelled is faced with three problems: how to parameterize the model with mostly incomplete steady state data, how to close what is now an inherently open system, and how to account for the impact on growth. In this study we address these challenges of kinetic modelling by capitalizing on multi-‘omics’ steady state data and a genome-scale metabolic network model. We use these to generate parameters that integrate knowledge embedded in the genome-scale metabolic network model, into the most comprehensive kinetic model of the central carbon metabolism of E. coli realized to date. As an application, we performed a dynamical systems analysis of the resulting enriched model. This revealed bistability of the central carbon metabolism and thus its potential to express two distinct metabolic states. Furthermore, since our model-informing technique ensures both stable states are constrained by the same thermodynamically feasible steady state growth rate, the ensuing bistability represents a temporal coexistence of the two states, and by extension, reveals the emergence of a phenotypically heterogeneous population. PMID:26469081

Respiratory virus transmission dynamics determine timing of asthma exacerbation peaks: Evidence from a population-level model.

PubMed

Eggo, Rosalind M; Scott, James G; Galvani, Alison P; Meyers, Lauren Ancel

2016-02-23

Asthma exacerbations exhibit a consistent annual pattern, closely mirroring the school calendar. Although respiratory viruses--the "common cold" viruses--are implicated as a principal cause, there is little evidence to link viral prevalence to seasonal differences in risk. We jointly fit a common cold transmission model and a model of biological and environmental exacerbation triggers to estimate effects on hospitalization risk. Asthma hospitalization rate, influenza prevalence, and air quality measures are available, but common cold circulation is not; therefore, we generate estimates of viral prevalence using a transmission model. Our deterministic multivirus transmission model includes transmission rates that vary when school is closed. We jointly fit the two models to 7 y of daily asthma hospitalizations in adults and children (66,000 events) in eight metropolitan areas. For children, we find that daily viral prevalence is the strongest predictor of asthma hospitalizations, with transmission reduced by 45% (95% credible interval =41-49%) during school closures. We detect a transient period of nonspecific immunity between infections lasting 19 (17-21) d. For adults, hospitalizations are more variable, with influenza driving wintertime peaks. Neither particulate matter nor ozone was an important predictor, perhaps because of the large geographic area of the populations. The school calendar clearly and predictably drives seasonal variation in common cold prevalence, which results in the "back-to-school" asthma exacerbation pattern seen in children and indirectly contributes to exacerbation risk in adults. This study provides a framework for anticipating the seasonal dynamics of common colds and the associated risks for asthmatics.

Respiratory virus transmission dynamics determine timing of asthma exacerbation peaks: Evidence from a population-level model

PubMed Central

Scott, James G.; Galvani, Alison P.; Meyers, Lauren Ancel

2016-01-01

Asthma exacerbations exhibit a consistent annual pattern, closely mirroring the school calendar. Although respiratory viruses—the “common cold” viruses—are implicated as a principal cause, there is little evidence to link viral prevalence to seasonal differences in risk. We jointly fit a common cold transmission model and a model of biological and environmental exacerbation triggers to estimate effects on hospitalization risk. Asthma hospitalization rate, influenza prevalence, and air quality measures are available, but common cold circulation is not; therefore, we generate estimates of viral prevalence using a transmission model. Our deterministic multivirus transmission model includes transmission rates that vary when school is closed. We jointly fit the two models to 7 y of daily asthma hospitalizations in adults and children (66,000 events) in eight metropolitan areas. For children, we find that daily viral prevalence is the strongest predictor of asthma hospitalizations, with transmission reduced by 45% (95% credible interval =41–49%) during school closures. We detect a transient period of nonspecific immunity between infections lasting 19 (17–21) d. For adults, hospitalizations are more variable, with influenza driving wintertime peaks. Neither particulate matter nor ozone was an important predictor, perhaps because of the large geographic area of the populations. The school calendar clearly and predictably drives seasonal variation in common cold prevalence, which results in the “back-to-school” asthma exacerbation pattern seen in children and indirectly contributes to exacerbation risk in adults. This study provides a framework for anticipating the seasonal dynamics of common colds and the associated risks for asthmatics. PMID:26858436

Stochastic and deterministic processes regulate spatio-temporal variation in seed bank diversity

Treesearch

Alejandro A. Royo; Todd E. Ristau

2013-01-01

Seed banks often serve as reservoirs of taxonomic and genetic diversity that buffer plant populations and influence post-disturbance vegetation trajectories; yet evaluating their importance requires understanding how their composition varies within and across spatial and temporal scales (α- and β-diversity). Shifts in seed bank diversity are strongly...

Current issues and actions in radiation protection of patients.

PubMed

Holmberg, Ola; Malone, Jim; Rehani, Madan; McLean, Donald; Czarwinski, Renate

2010-10-01

Medical application of ionizing radiation is a massive and increasing activity globally. While the use of ionizing radiation in medicine brings tremendous benefits to the global population, the associated risks due to stochastic and deterministic effects make it necessary to protect patients from potential harm. Current issues in radiation protection of patients include not only the rapidly increasing collective dose to the global population from medical exposure, but also that a substantial percentage of diagnostic imaging examinations are unnecessary, and the cumulative dose to individuals from medical exposure is growing. In addition to this, continued reports on deterministic injuries from safety related events in the medical use of ionizing radiation are raising awareness on the necessity for accident prevention measures. The International Atomic Energy Agency is engaged in several activities to reverse the negative trends of these current issues, including improvement of the justification process, the tracking of radiation history of individual patients, shared learning of safety significant events, and the use of comprehensive quality audits in the clinical environment. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Adaptation to Temporally Fluctuating Environments by the Evolution of Maternal Effects.

PubMed

Dey, Snigdhadip; Proulx, Stephen R; Teotónio, Henrique

2016-02-01

All organisms live in temporally fluctuating environments. Theory predicts that the evolution of deterministic maternal effects (i.e., anticipatory maternal effects or transgenerational phenotypic plasticity) underlies adaptation to environments that fluctuate in a predictably alternating fashion over maternal-offspring generations. In contrast, randomizing maternal effects (i.e., diversifying and conservative bet-hedging), are expected to evolve in response to unpredictably fluctuating environments. Although maternal effects are common, evidence for their adaptive significance is equivocal since they can easily evolve as a correlated response to maternal selection and may or may not increase the future fitness of offspring. Using the hermaphroditic nematode Caenorhabditis elegans, we here show that the experimental evolution of maternal glycogen provisioning underlies adaptation to a fluctuating normoxia-anoxia hatching environment by increasing embryo survival under anoxia. In strictly alternating environments, we found that hermaphrodites evolved the ability to increase embryo glycogen provisioning when they experienced normoxia and to decrease embryo glycogen provisioning when they experienced anoxia. At odds with existing theory, however, populations facing irregularly fluctuating normoxia-anoxia hatching environments failed to evolve randomizing maternal effects. Instead, adaptation in these populations may have occurred through the evolution of fitness effects that percolate over multiple generations, as they maintained considerably high expected growth rates during experimental evolution despite evolving reduced fecundity and reduced embryo survival under one or two generations of anoxia. We develop theoretical models that explain why adaptation to a wide range of patterns of environmental fluctuations hinges on the existence of deterministic maternal effects, and that such deterministic maternal effects are more likely to contribute to adaptation than randomizing maternal effects.

Adaptation to Temporally Fluctuating Environments by the Evolution of Maternal Effects

PubMed Central

Dey, Snigdhadip; Proulx, Stephen R.; Teotónio, Henrique

2016-01-01

All organisms live in temporally fluctuating environments. Theory predicts that the evolution of deterministic maternal effects (i.e., anticipatory maternal effects or transgenerational phenotypic plasticity) underlies adaptation to environments that fluctuate in a predictably alternating fashion over maternal-offspring generations. In contrast, randomizing maternal effects (i.e., diversifying and conservative bet-hedging), are expected to evolve in response to unpredictably fluctuating environments. Although maternal effects are common, evidence for their adaptive significance is equivocal since they can easily evolve as a correlated response to maternal selection and may or may not increase the future fitness of offspring. Using the hermaphroditic nematode Caenorhabditis elegans, we here show that the experimental evolution of maternal glycogen provisioning underlies adaptation to a fluctuating normoxia–anoxia hatching environment by increasing embryo survival under anoxia. In strictly alternating environments, we found that hermaphrodites evolved the ability to increase embryo glycogen provisioning when they experienced normoxia and to decrease embryo glycogen provisioning when they experienced anoxia. At odds with existing theory, however, populations facing irregularly fluctuating normoxia–anoxia hatching environments failed to evolve randomizing maternal effects. Instead, adaptation in these populations may have occurred through the evolution of fitness effects that percolate over multiple generations, as they maintained considerably high expected growth rates during experimental evolution despite evolving reduced fecundity and reduced embryo survival under one or two generations of anoxia. We develop theoretical models that explain why adaptation to a wide range of patterns of environmental fluctuations hinges on the existence of deterministic maternal effects, and that such deterministic maternal effects are more likely to contribute to adaptation than randomizing maternal effects. PMID:26910440

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations.

PubMed

Ngwa, Gideon A; Teboh-Ewungkem, Miranda I

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed.

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations

PubMed Central

Ngwa, Gideon A.

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed. PMID:27579053

Evaluation of a Stochastic Inactivation Model for Heat-Activated Spores of Bacillus spp. ▿

PubMed Central

Corradini, Maria G.; Normand, Mark D.; Eisenberg, Murray; Peleg, Micha

2010-01-01

Heat activates the dormant spores of certain Bacillus spp., which is reflected in the “activation shoulder” in their survival curves. At the same time, heat also inactivates the already active and just activated spores, as well as those still dormant. A stochastic model based on progressively changing probabilities of activation and inactivation can describe this phenomenon. The model is presented in a fully probabilistic discrete form for individual and small groups of spores and as a semicontinuous deterministic model for large spore populations. The same underlying algorithm applies to both isothermal and dynamic heat treatments. Its construction does not require the assumption of the activation and inactivation kinetics or knowledge of their biophysical and biochemical mechanisms. A simplified version of the semicontinuous model was used to simulate survival curves with the activation shoulder that are reminiscent of experimental curves reported in the literature. The model is not intended to replace current models to predict dynamic inactivation but only to offer a conceptual alternative to their interpretation. Nevertheless, by linking the survival curve's shape to probabilities of events at the individual spore level, the model explains, and can be used to simulate, the irregular activation and survival patterns of individual and small groups of spores, which might be involved in food poisoning and spoilage. PMID:20453137

Ikeda-like chaos on a dynamically filtered supercontinuum light source

NASA Astrophysics Data System (ADS)

Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent

2016-08-01

We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

Influence of changes in initial conditions for the simulation of dynamic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotyrba, Martin

2015-03-10

Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, sociology, physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a paradigm popularly referred to as the butterfly effect. Small differences in initial conditions field widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In this paperinfluence of changes in initial conditions will bemore » presented for the simulation of Lorenz system.« less

Dynamic principle for ensemble control tools.

PubMed

Samoletov, A; Vasiev, B

2017-11-28

Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure. The principle covers both stochastic and deterministic thermostat schemes. Our method has a clear advantage over a range of proposed and widely used thermostat schemes that are based on formal mathematical reasoning. Following the derivation of the proposed principle, we show its generality and illustrate its applications including design of temperature control tools that differ from the Nosé-Hoover-Langevin scheme.

"The Theory was Beautiful Indeed": Rise, Fall and Circulation of Maximizing Methods in Population Genetics (1930-1980).

PubMed

Grodwohl, Jean-Baptiste

2017-08-01

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: "our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection" (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this "obsession", by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura's and Richard Lewontin's works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.

Go big or go home: impact of screening coverage on syphilis infection dynamics.

PubMed

Tuite, Ashleigh; Fisman, David

2016-02-01

Syphilis outbreaks in urban men who have sex with men (MSM) are an ongoing public health challenge in many high-income countries, despite intensification of efforts to screen and treat at-risk individuals. We sought to understand how population-level coverage of asymptomatic screening impacts the ability to control syphilis transmission. We developed a risk-structured deterministic compartmental mathematical model of syphilis transmission in a population of sexually active MSM. We assumed a baseline level of treatment of syphilis cases due to seeking medical care in all scenarios. We evaluated the impact of sustained annual population-wide screening coverage ranging from 0% to 90% on syphilis incidence over the short term (20 years) and at endemic equilibrium. The relationship between screening coverage and equilibrium syphilis incidence displayed an inverted U-shape relationship, with peak equilibrium incidence occurring with 20-30% annual screening coverage. Annual screening of 62% of the population was required for local elimination (incidence <1 case per 100 000 population). Results were qualitatively similar in the face of differing programmatic, behavioural and natural history assumptions, although the screening thresholds for local elimination differed. With 6-monthly or 3-monthly screening, the population coverage required to achieve local elimination was reduced to 39% or 23%, respectively. Although screening has the potential to control syphilis outbreaks, suboptimal coverage may paradoxically lead to a higher equilibrium infection incidence than that observed in the absence of intervention. Suboptimal screening programme design should be considered as a possible contributor to unsuccessful syphilis control programmes in the context of the current epidemic. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences

NASA Astrophysics Data System (ADS)

Chisholm, Rebecca H.; Lorenzi, Tommaso; Desvillettes, Laurent; Hughes, Barry D.

2016-08-01

Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible and illustrate that while epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of "epigenetic load" and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a "proof of concept" of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.

Namib Desert edaphic bacterial, fungal and archaeal communities assemble through deterministic processes but are influenced by different abiotic parameters.

PubMed

Johnson, Riegardt M; Ramond, Jean-Baptiste; Gunnigle, Eoin; Seely, Mary; Cowan, Don A

2017-03-01

The central Namib Desert is hyperarid, where limited plant growth ensures that biogeochemical processes are largely driven by microbial populations. Recent research has shown that niche partitioning is critically involved in the assembly of Namib Desert edaphic communities. However, these studies have mainly focussed on the Domain Bacteria. Using microbial community fingerprinting, we compared the assembly of the bacterial, fungal and archaeal populations of microbial communities across nine soil niches from four Namib Desert soil habitats (riverbed, dune, gravel plain and salt pan). Permutational multivariate analysis of variance indicated that the nine soil niches presented significantly different physicochemistries (R 2  = 0.8306, P ≤ 0.0001) and that bacterial, fungal and archaeal populations were soil niche specific (R 2  ≥ 0.64, P ≤ 0.001). However, the abiotic drivers of community structure were Domain-specific (P < 0.05), with P, clay and sand fraction, and NH 4 influencing bacterial, fungal and archaeal communities, respectively. Soil physicochemistry and soil niche explained over 50% of the variation in community structure, and communities displayed strong non-random patterns of co-occurrence. Taken together, these results demonstrate that in central Namib Desert soil microbial communities, assembly is principally driven by deterministic processes.

Cost-effectiveness of Population Screening for BRCA Mutations in Ashkenazi Jewish Women Compared With Family History–Based Testing

PubMed Central

Manchanda, Ranjit; Legood, Rosa; Burnell, Matthew; McGuire, Alistair; Raikou, Maria; Loggenberg, Kelly; Wardle, Jane; Sanderson, Saskia; Gessler, Sue; Side, Lucy; Balogun, Nyala; Desai, Rakshit; Kumar, Ajith; Dorkins, Huw; Wallis, Yvonne; Chapman, Cyril; Taylor, Rohan; Jacobs, Chris; Tomlinson, Ian; Beller, Uziel; Menon, Usha

2015-01-01

Background: Population-based testing for BRCA1/2 mutations detects the high proportion of carriers not identified by cancer family history (FH)–based testing. We compared the cost-effectiveness of population-based BRCA testing with the standard FH-based approach in Ashkenazi Jewish (AJ) women. Methods: A decision-analytic model was developed to compare lifetime costs and effects amongst AJ women in the UK of BRCA founder-mutation testing amongst: 1) all women in the population age 30 years or older and 2) just those with a strong FH (≥10% mutation risk). The model assumes that BRCA carriers are offered risk-reducing salpingo-oophorectomy and annual MRI/mammography screening or risk-reducing mastectomy. Model probabilities utilize the Genetic Cancer Prediction through Population Screening trial/published literature to estimate total costs, effects in terms of quality-adjusted life-years (QALYs), cancer incidence, incremental cost-effectiveness ratio (ICER), and population impact. Costs are reported at 2010 prices. Costs/outcomes were discounted at 3.5%. We used deterministic/probabilistic sensitivity analysis (PSA) to evaluate model uncertainty. Results: Compared with FH-based testing, population-screening saved 0.090 more life-years and 0.101 more QALYs resulting in 33 days’ gain in life expectancy. Population screening was found to be cost saving with a baseline-discounted ICER of -£2079/QALY. Population-based screening lowered ovarian and breast cancer incidence by 0.34% and 0.62%. Assuming 71% testing uptake, this leads to 276 fewer ovarian and 508 fewer breast cancer cases. Overall, reduction in treatment costs led to a discounted cost savings of £3.7 million. Deterministic sensitivity analysis and 94% of simulations on PSA (threshold £20000) indicated that population screening is cost-effective, compared with current NHS policy. Conclusion: Population-based screening for BRCA mutations is highly cost-effective compared with an FH-based approach in AJ women age 30 years and older. PMID:25435542

A stochastic chemostat model with an inhibitor and noise independent of population sizes

NASA Astrophysics Data System (ADS)

Sun, Shulin; Zhang, Xiaolu

2018-02-01

In this paper, a stochastic chemostat model with an inhibitor is considered, here the inhibitor is input from an external source and two organisms in chemostat compete for a nutrient. Firstly, we show that the system has a unique global positive solution. Secondly, by constructing some suitable Lyapunov functions, we investigate that the average in time of the second moment of the solutions of the stochastic model is bounded for a relatively small noise. That is, the asymptotic behaviors of the stochastic system around the equilibrium points of the deterministic system are studied. However, the sufficient large noise can make the microorganisms become extinct with probability one, although the solutions to the original deterministic model may be persistent. Finally, the obtained analytical results are illustrated by computer simulations.

Dog and cat management through sterilization: Implications for population dynamics and veterinary public policies.

PubMed

Dias, Ricardo Augusto; Baquero, Oswaldo Santos; Guilloux, Aline Gil Alves; Moretti, Caio Figueiredo; de Lucca, Tosca; Rodrigues, Ricardo Conde Alves; Castagna, Cláudio Luiz; Presotto, Douglas; Kronitzky, Yury Cezar; Grisi-Filho, José Henrique Hildebrand; Ferreira, Fernando; Amaku, Marcos

2015-11-01

The present study aimed to compare different sterilization scenarios allowing the adoption of the most adequate strategy to control owned dog and cat population sizes as the official veterinary public policy for animal control in an urban area of Campinas municipality, Brazil. To achieve this goal, the vital parameters of the owned pet population were measured in a neighborhood of Campinas called Jardim Vila Olimpia through questionnaires used in two census studies performed in February 2012 and June 2013. Different hypothetical sterilization scenarios were compared with the scenario of a single sterilization campaign performed in the study area between the census studies. Using a deterministic mathematical model, population dynamics were simulated for these different scenarios. We have observed that for both owned dogs and cats, the impact on the population size achieved by a single sterilization campaign would be diluted over the years, equating to the impact achieved by the usual sterilization rate practiced before the sterilization campaign yearly. Moreover, using local and global sensitivity analyses, we assessed the relative influence on animal population evolution of each vital parameter used in the mathematical models. The more influential parameters for both species were the carrying capacity of the environment and sterilization rates of males and females (for both species). We observed that even with sterilizing 100% of the intact animals annually, it would not be possible to obtain proportions greater than 86% and 88% of sterilized dogs and cats, respectively, after 20 years due to the high introduction of new intact animals. There is no public dog and cat sterilization service in place in the city, and sporadic and local sterilization campaigns are performed with a prior communication to the owners to bring their animals to be sterilized in a selected veterinary facility. If a sterilization campaign was performed annually in the study area, it would have the most favorable cost effectiveness ratio after 20 years compared to the scenarios of 50% and 100% sterilization of intact animals annually. These results allowed the veterinary public policy stakeholders to make decisions based on scientific evidence to implement adequate control of dog and cat populations in urban areas, aiming to reduce zoonosis transmission to humans and other problems associated with uncontrolled animal populations. Copyright © 2015 Elsevier B.V. All rights reserved.

Self-organization of complex networks as a dynamical system

NASA Astrophysics Data System (ADS)

Aoki, Takaaki; Yawata, Koichiro; Aoyagi, Toshio

2015-01-01

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

Self-organization of complex networks as a dynamical system.

PubMed

Aoki, Takaaki; Yawata, Koichiro; Aoyagi, Toshio

2015-01-01

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.