When growth models are not universal: evidence from marine invertebrates

PubMed Central

Hirst, Andrew G.; Forster, Jack

2013-01-01

The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates. PMID:23945691

The Application of Various Nonlinear Models to Describe Academic Growth Trajectories: An Empirical Analysis Using Four-Wave Longitudinal Achievement Data from a Large Urban School District

ERIC Educational Resources Information Center

Shin, Tacksoo

2012-01-01

This study introduced various nonlinear growth models, including the quadratic conventional polynomial model, the fractional polynomial model, the Sigmoid model, the growth model with negative exponential functions, the multidimensional scaling technique, and the unstructured growth curve model. It investigated which growth models effectively…

Theoretical and Experimental Study of Bacterial Colony Growth in 3D

NASA Astrophysics Data System (ADS)

Shao, Xinxian; Mugler, Andrew; Nemenman, Ilya

2014-03-01

Bacterial cells growing in liquid culture have been well studied and modeled. However, in nature, bacteria often grow as biofilms or colonies in physically structured habitats. A comprehensive model for population growth in such conditions has not yet been developed. Based on the well-established theory for bacterial growth in liquid culture, we develop a model for colony growth in 3D in which a homogeneous colony of cells locally consume a diffusing nutrient. We predict that colony growth is initially exponential, as in liquid culture, but quickly slows to sub-exponential after nutrient is locally depleted. This prediction is consistent with our experiments performed with E. coli in soft agar. Our model provides a baseline to which studies of complex growth process, such as such as spatially and phenotypically heterogeneous colonies, must be compared.

From Experiment to Theory: What Can We Learn from Growth Curves?

PubMed

Kareva, Irina; Karev, Georgy

2018-01-01

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic-exponential, exponential-linear, exponential-linear-saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.

In vivo growth of 60 non-screening detected lung cancers: a computed tomography study.

PubMed

Mets, Onno M; Chung, Kaman; Zanen, Pieter; Scholten, Ernst T; Veldhuis, Wouter B; van Ginneken, Bram; Prokop, Mathias; Schaefer-Prokop, Cornelia M; de Jong, Pim A

2018-04-01

Current pulmonary nodule management guidelines are based on nodule volume doubling time, which assumes exponential growth behaviour. However, this is a theory that has never been validated in vivo in the routine-care target population. This study evaluates growth patterns of untreated solid and subsolid lung cancers of various histologies in a non-screening setting.Growth behaviour of pathology-proven lung cancers from two academic centres that were imaged at least three times before diagnosis (n=60) was analysed using dedicated software. Random-intercept random-slope mixed-models analysis was applied to test which growth pattern most accurately described lung cancer growth. Individual growth curves were plotted per pathology subgroup and nodule type.We confirmed that growth in both subsolid and solid lung cancers is best explained by an exponential model. However, subsolid lesions generally progress slower than solid ones. Baseline lesion volume was not related to growth, indicating that smaller lesions do not grow slower compared to larger ones.By showing that lung cancer conforms to exponential growth we provide the first experimental basis in the routine-care setting for the assumption made in volume doubling time analysis. Copyright ©ERS 2018.

Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth

ERIC Educational Resources Information Center

Castillo-Garsow, Carlos

2010-01-01

Both Thompson and the duo of Confrey and Smith describe how students might be taught to build "ways of thinking" about exponential behavior by coordinating the covariation of two changing quantities, however, these authors build exponential behavior from different meanings of covariation. Confrey and Smith advocate beginning with discrete additive…

Analysis of Dibenzothiophene Desulfurization in a Recombinant Pseudomonas putida Strain▿

PubMed Central

Calzada, Javier; Zamarro, María T.; Alcón, Almudena; Santos, Victoria E.; Díaz, Eduardo; García, José L.; Garcia-Ochoa, Felix

2009-01-01

Biodesulfurization was monitored in a recombinant Pseudomonas putida CECT5279 strain. DszB desulfinase activity reached a sharp maximum at the early exponential phase, but it rapidly decreased at later growth phases. A model two-step resting-cell process combining sequentially P. putida cells from the late and early exponential growth phases was designed to significantly increase biodesulfurization. PMID:19047400

Individual tree-diameter growth model for the Northeastern United States

Treesearch

Richard M. Teck; Donald E. Hilt

1991-01-01

Describes a distance-independent individual-tree diameter growth model for the Northeastern United States. Diameter growth is predicted in two steps using a two parameter, sigmoidal growth function modified by a one parameter exponential decay function with species-specific coefficients. Coefficients are presented for 28 species groups. The model accounts for...

Effects of clustered transmission on epidemic growth Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Merler, Stefano

2016-09-01

Characterizing the early growth profile of an epidemic outbreak is key for predicting the likely trajectory of the number of cases and for designing adequate control measures. Epidemic profiles characterized by exponential growth have been widely observed in the past and a grounding theoretical framework for the analysis of infectious disease dynamics was provided by the pioneering work of Kermack and McKendrick [1]. In particular, exponential growth stems from the assumption that pathogens spread in homogeneous mixing populations; that is, individuals of the population mix uniformly and randomly with each other. However, this assumption was readily recognized as highly questionable [2], and sub-exponential profiles of epidemic growth have been observed in a number of epidemic outbreaks, including HIV/AIDS, foot-and-mouth disease, measles and, more recently, Ebola [3,4].

Flower Power: Sunflowers as a Model for Logistic Growth

ERIC Educational Resources Information Center

Fernandez, Eileen; Geist, Kristi A.

2011-01-01

Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…

Self-charging of identical grains in the absence of an external field.

PubMed

Yoshimatsu, R; Araújo, N A M; Wurm, G; Herrmann, H J; Shinbrot, T

2017-01-06

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Self-charging of identical grains in the absence of an external field

NASA Astrophysics Data System (ADS)

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Something from nothing: self-charging of identical grains

NASA Astrophysics Data System (ADS)

Shinbrot, Troy; Yoshimatsu, Ryuta; Nuno Araujo, Nuno; Wurm, Gerhard; Herrmann, Hans

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. I acknowledge support from NSF/DMR, award 1404792.

Self-charging of identical grains in the absence of an external field

PubMed Central

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. PMID:28059124

2D motility tracking of Pseudomonas putida KT2440 in growth phases using video microscopy

PubMed Central

Davis, Michael L.; Mounteer, Leslie C.; Stevens, Lindsey K.; Miller, Charles D.; Zhou, Anhong

2011-01-01

Pseudomonas putida KT2440 is a gram negative motile soil bacterium important in bioremediation and biotechnology. Thus, it is important to understand its motility characteristics as individuals and in populations. Population characteristics were determined using a modified Gompertz model. Video microscopy and imaging software were utilized to analyze two dimensional (2D) bacteria movement tracks to quantify individual bacteria behavior. It was determined that inoculum density increased the lag time as seeding densities decreased, and that the maximum specific growth rate decreased as seeding densities increased. Average bacterial velocity remained relatively similar throughout exponential growth phase (~20.9 µm/sec), while maximum velocities peak early in exponential growth phase at a velocity of 51.2 µm/sec. Pseudomonas putida KT2440 also favor smaller turn angles indicating they often continue in the same direction after a change in flagella rotation throughout the exponential growth phase. PMID:21334971

Characterizing the reproduction number of epidemics with early subexponential growth dynamics

PubMed Central

Viboud, Cécile; Simonsen, Lone; Moghadas, Seyed M.

2016-01-01

Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible–infectious–removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The generalized-growth concept also provides us a compelling argument for the unexpected extinction of certain emerging disease outbreaks during the early ascending phase. Overall, our approach promotes a more reliable and data-driven characterization of the early epidemic phase, which is important for accurate estimation of the reproduction number and prediction of disease impact. PMID:27707909

Modeling Population Growth and Extinction

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2009-01-01

The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…

An Exponential Growth Learning Trajectory: Students' Emerging Understanding of Exponential Growth through Covariation

ERIC Educational Resources Information Center

Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel

2016-01-01

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…

An exactly solvable, spatial model of mutation accumulation in cancer

NASA Astrophysics Data System (ADS)

Paterson, Chay; Nowak, Martin A.; Waclaw, Bartlomiej

2016-12-01

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

The need for data science in epidemic modelling. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Danon, Leon; Brooks-Pollock, Ellen

2016-09-01

In their review, Chowell et al. consider the ability of mathematical models to predict early epidemic growth [1]. In particular, they question the central prediction of classical differential equation models that the number of cases grows exponentially during the early stages of an epidemic. Using examples including HIV and Ebola, they argue that classical models fail to capture key qualitative features of early growth and describe a selection of models that do capture non-exponential epidemic growth. An implication of this failure is that predictions may be inaccurate and unusable, highlighting the need for care when embarking upon modelling using classical methodology. There remains a lack of understanding of the mechanisms driving many observed epidemic patterns; we argue that data science should form a fundamental component of epidemic modelling, providing a rigorous methodology for data-driven approaches, rather than trying to enforce established frameworks. The need for refinement of classical models provides a strong argument for the use of data science, to identify qualitative characteristics and pinpoint the mechanisms responsible for the observed epidemic patterns.

2D motility tracking of Pseudomonas putida KT2440 in growth phases using video microscopy.

PubMed

Davis, Michael L; Mounteer, Leslie C; Stevens, Lindsey K; Miller, Charles D; Zhou, Anhong

2011-05-01

Pseudomonas putida KT2440 is a gram negative motile soil bacterium important in bioremediation and biotechnology. Thus, it is important to understand its motility characteristics as individuals and in populations. Population characteristics were determined using a modified Gompertz model. Video microscopy and imaging software were utilized to analyze two dimensional (2D) bacteria movement tracks to quantify individual bacteria behavior. It was determined that inoculum density increased the lag time as seeding densities decreased, and that the maximum specific growth rate decreased as seeding densities increased. Average bacterial velocity remained relatively similar throughout the exponential growth phase (~20.9 μm/s), while maximum velocities peak early in the exponential growth phase at a velocity of 51.2 μm/s. P. putida KT2440 also favors smaller turn angles indicating that they often continue in the same direction after a change in flagella rotation throughout the exponential growth phase. Copyright © 2011 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

Kinetic and Stochastic Models of 1D yeast ``prions"

NASA Astrophysics Data System (ADS)

Kunes, Kay

2005-03-01

Mammalian prion proteins (PrP) are of public health interest because of mad cow and chronic wasting diseases. Yeasts have proteins, which can undergo similar reconformation and aggregation processes to PrP; yeast ``prions" are simpler to experimentally study and model. Recent in vitro studies of the SUP35 protein (1), showed long aggregates and pure exponential growth of the misfolded form. To explain this data, we have extended a previous model of aggregation kinetics along with our own stochastic approach (2). Both models assume reconformation only upon aggregation, and include aggregate fissioning and an initial nucleation barrier. We find for sufficiently small nucleation rates or seeding by small dimer concentrations that we can achieve the requisite exponential growth and long aggregates.

Bioconvective patterns, synchrony, and survival. [in light-limited growth model of motile algae culture

NASA Technical Reports Server (NTRS)

Noever, David A.

1990-01-01

With and without bioconvective pattern formation, a theoretical model predicts growth in light-limited cultures of motile algae. At the critical density for pattern formation, the resulting doubly exponential population curves show an inflection. Such growth corresponds quantitatively to experiments in mechanically unstirred cultures. This attaches survival value to synchronized pattern formation.

Modeling Exponential Population Growth

ERIC Educational Resources Information Center

McCormick, Bonnie

2009-01-01

The concept of population growth patterns is a key component of understanding evolution by natural selection and population dynamics in ecosystems. The National Science Education Standards (NSES) include standards related to population growth in sections on biological evolution, interdependence of organisms, and science in personal and social…

Lack of synchronization between iron uptake and cell growth leads to iron overload in Saccharomyces cerevisiae during post-exponential growth modes

PubMed Central

Park, Jinkyu; McCormick, Sean P.; Chakrabarti, Mrinmoy; Lindahl, Paul A.

2014-01-01

Fermenting cells growing exponentially on rich (YPAD) medium transitioned to a slow-growing state as glucose levels declined and their metabolism shifted to respiration. During exponential growth, Fe import and cell growth rates were matched, affording an approximately invariant cellular Fe concentration. During the transitionary period, the high-affinity Fe import rate declined slower than the cell growth rate declined, causing Fe to accumulate, initially as FeIII oxyhydroxide nanoparticles but eventually as mitochondrial and vacuolar Fe. Once in slow-growth mode, Fe import and cell growth rates were again matched, and the cellular Fe concentration was again approximately invariant. Fermenting cells grown on minimal medium (MM) grew more slowly during exponential phase and transitioned to a true stationary state as glucose levels declined. The Fe concentration of MM cells that just entered stationary state was similar to that of YPAD cells, but MM cells continued to accumulate Fe in stationary state. Fe initially accumulated as nanoparticles and high-spin FeII species, but vacuolar FeIII also eventually accumulated. Surprisingly, Fe-packed 5-day-old MM cells suffered no more ROS damage than younger cells, suggesting that Fe concentration alone does not accurately predict the extent of ROS damage. The mode and rate of growth at the time of harvesting dramatically affected cellular Fe content. A mathematical model of Fe metabolism in a growing cell was developed. The model included Fe import via a regulated high-affinity pathway and an unregulated low-affinity pathway. Fe import from the cytosol into vacuoles and mitochondria, and nanoparticle formation were also included. The model captured essential trafficking behavior, demonstrating that cells regulate Fe import in accordance with their overall growth rate and that they misregulate Fe import when nanoparticles accumulate. The lack of regulation of Fe in yeast is perhaps unique compared to the tight regulation of other cellular metabolites. This phenomenon likely derives from the unique chemistry associated with Fe nanoparticle formation. PMID:24344915

Pore‐Scale Hydrodynamics in a Progressively Bioclogged Three‐Dimensional Porous Medium: 3‐D Particle Tracking Experiments and Stochastic Transport Modeling

PubMed Central

Carrel, M.; Dentz, M.; Derlon, N.; Morgenroth, E.

2018-01-01

Abstract Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3‐D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean‐squared displacements, are found to be non‐Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered. PMID:29780184

Pore-Scale Hydrodynamics in a Progressively Bioclogged Three-Dimensional Porous Medium: 3-D Particle Tracking Experiments and Stochastic Transport Modeling

NASA Astrophysics Data System (ADS)

Carrel, M.; Morales, V. L.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2018-03-01

Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3-D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean-squared displacements, are found to be non-Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-01-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-09-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

Optimized O'Neill/Glaser Model for Human Population of Space and its Impact on Survival Probabilities

NASA Technical Reports Server (NTRS)

Curreri, Peter A.

2010-01-01

Two contemporary issues foretell a shift from our historical Earth based industrial economy and habitation to a solar system based society. The first is the limits to Earth's carrying capacity, that is the maximum number of people that the Earth can support before a catastrophic impact to the health of the planet and human species occurs. The simple example of carrying capacity is that of a bacterial colony in a Petri dish with a limited amount of nutrient. The colony experiences exponential population growth until the carrying capacity is reached after which catastrophic depopulation often results. Estimates of the Earth s carrying capacity vary between 14 and 40 billion people. Although at current population growth rates we may have over a century before we reach Earth s carrying limit our influence on climate and resources on the planetary scale is becoming scientifically established. The second issue is the exponential growth of knowledge and technological power. The exponential growth of technology interacts with the exponential growth of population in a manner that is unique to a highly intelligent species. Thus, the predicted consequences (world famines etc.) of the limits to growth have been largely avoided due to technological advances. However, at the mid twentieth century a critical coincidence occurred in these two trends humanity obtained the technological ability to extinguish life on the planetary scale (by nuclear, chemical, biological means) and attained the ability to expand human life beyond Earth. This paper examines an optimized O Neill/Glaser model (O Neill 1975; Curreri 2007; Detweiler and Curreri 2008) for the economic human population of space. Critical to this model is the utilization of extraterrestrial resources, solar power and spaced based labor. A simple statistical analysis is then performed which predicts the robustness of a single planet based technological society versus that of multiple world (independent habitats) society.

Optimized O'Neill/Glaser Model for Human Population of Space and its Impact on Survival Probabilities

NASA Technical Reports Server (NTRS)

Curreri, Peter A.

2010-01-01

Two contemporary issues foretell a shift from our historical Earth based industrial economy and habitation to a solar system based society. The first is the limits to Earth s carrying capacity, that is the maximum number of people that the Earth can support before a catastrophic impact to the health of the planet and human species occurs. The simple example of carrying capacity is that of a bacterial colony in a Petri dish with a limited amount of nutrient. The colony experiences exponential population growth until the carrying capacity is reached after which catastrophic depopulation often results. Estimates of the Earth s carrying capacity vary between 14 and 40 billion people. Although at current population growth rates we may have over a century before we reach Earth s carrying limit our influence on climate and resources on the planetary scale is becoming scientifically established. The second issue is the exponential growth of knowledge and technological power. The exponential growth of technology interacts with the exponential growth of population in a manner that is unique to a highly intelligent species. Thus, the predicted consequences (world famines etc.) of the limits to growth have been largely avoided due to technological advances. However, at the mid twentieth century a critical coincidence occurred in these two trends humanity obtained the technological ability to extinguish life on the planetary scale (by nuclear, chemical, biological means) and attained the ability to expand human life beyond Earth. This paper examines an optimized O Neill/Glaser model (O Neill 1975; Curreri 2007; Detweiler and Curreri 2008) for the economic human population of space. Critical to this model is the utilization of extraterrestrial resources, solar power and spaced based labor. A simple statistical analysis is then performed which predicts the robustness of a single planet based technological society versus that of multiple world (independent habitats) society.

Optimized O'Neill/Glaser Model for Human Population of Space and its Impact on Survival Probabilities

NASA Technical Reports Server (NTRS)

Curreri, Peter A.

2010-01-01

Two contemporary issues foretell a shift from our historical Earth based industrial economy and habitation to a solar system based society. The first is the limits to Earth s carrying capacity, that is the maximum number of people that the Earth can support before a catastrophic impact to the health of the planet and human species occurs. The simple example of carrying capacity is that of a bacterial colony in a Petri dish with a limited amount of nutrient. The colony experiences exponential population growth until the carrying capacity is reached after which catastrophic depopulation often results. Estimates of the Earth s carrying capacity vary between 14 and 40 billion people. Although at current population growth rates we may have over a century before we reach Earth s carrying limit our influence on climate and resources on the planetary scale is becoming scientifically established. The second issue is the exponential growth of knowledge and technological power. The exponential growth of technology interacts with the exponential growth of population in a manner that is unique to a highly intelligent species. Thus, the predicted consequences (world famines etc.) of the limits to growth have been largely avoided due to technological advances. However, at the mid twentieth century a critical coincidence occurred in these two trends humanity obtained the technological ability to extinguish life on the planetary scale (by nuclear, chemical, biological means) and attained the ability to expand human life beyond Earth. This paper examines an optimized O'Neill/Glaser model (O Neill 1975; Curreri 2007; Detweiler and Curreri 2008) for the economic human population of space. Critical to this model is the utilization of extraterrestrial resources, solar power and spaced based labor. A simple statistical analysis is then performed which predicts the robustness of a single planet based technological society versus that of multiple world (independent habitats) society.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Mathematical modeling of ethanol production in solid-state fermentation based on solid medium' dry weight variation.

PubMed

Mazaheri, Davood; Shojaosadati, Seyed Abbas; Zamir, Seyed Morteza; Mousavi, Seyyed Mohammad

2018-04-21

In this work, mathematical modeling of ethanol production in solid-state fermentation (SSF) has been done based on the variation in the dry weight of solid medium. This method was previously used for mathematical modeling of enzyme production; however, the model should be modified to predict the production of a volatile compound like ethanol. The experimental results of bioethanol production from the mixture of carob pods and wheat bran by Zymomonas mobilis in SSF were used for the model validation. Exponential and logistic kinetic models were used for modeling the growth of microorganism. In both cases, the model predictions matched well with the experimental results during the exponential growth phase, indicating the good ability of solid medium weight variation method for modeling a volatile product formation in solid-state fermentation. In addition, using logistic model, better predictions were obtained.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry.

PubMed

García, Míriam R; Vázquez, José A; Teixeira, Isabel G; Alonso, Antonio A

2017-01-01

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

A general theory of early growth?. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

House, Thomas

2016-09-01

Chowell et al. [1] consider the early growth behaviour of various epidemic models that range from phenomenological approaches driven by data to mechanistic descriptions of complex interactions between individuals. This is particularly timely given the recent Ebola epidemic, although non-exponential early growth may be more common (but less immediately evident) than we realise.

Weighted Scaling in Non-growth Random Networks

NASA Astrophysics Data System (ADS)

Chen, Guang; Yang, Xu-Hua; Xu, Xin-Li

2012-09-01

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.

A demographic study of the exponential distribution applied to uneven-aged forests

Treesearch

Jeffrey H. Gove

2016-01-01

A demographic approach based on a size-structured version of the McKendrick-Von Foerster equation is used to demonstrate a theoretical link between the population size distribution and the underlying vital rates (recruitment, mortality and diameter growth) for the population of individuals whose diameter distribution is negative exponential. This model supports the...

Accuracy and equivalence testing of crown ratio models and assessment of their impact on diameter growth and basal area increment predictions of two variants of the Forest Vegetation Simulator

Treesearch

Laura P. Leites; Andrew P. Robinson; Nicholas L. Crookston

2009-01-01

Diameter growth (DG) equations in many existing forest growth and yield models use tree crown ratio (CR) as a predictor variable. Where CR is not measured, it is estimated from other measured variables. We evaluated CR estimation accuracy for the models in two Forest Vegetation Simulator variants: the exponential and the logistic CR models used in the North...

Exponential growth kinetics for Polyporus versicolor and Pleurotus ostreatus in submerged culture

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

Carroad, P.A.; Wilke, C.R.

1977-04-01

Simple mathematical models for a batch culture of pellet-forming fungi in submerged culture were tested on growth data for Polyporus versicolor (ATCC 12679) and Pleurotus ostreatus (ATCC 9415). A kinetic model based on a growth rate proportional to the two-thirds power of the cell mass was shown to be satisfactory. A model based on a growth rate directly proportional to the cell mass fitted the data equally well, however, and may be preferable because of mathematical simplicity.

Microplate-based method for high-throughput screening of microalgae growth potential.

PubMed

Van Wagenen, Jon; Holdt, Susan Løvstad; De Francisci, Davide; Valverde-Pérez, Borja; Plósz, Benedek Gy; Angelidaki, Irini

2014-10-01

Microalgae cultivation conditions in microplates will differ from large-scale photobioreactors in crucial parameters such as light profile, mixing and gas transfer. Hence volumetric productivity (P(v)) measurements made in microplates cannot be directly scaled up. Here we demonstrate that it is possible to use microplates to measure characteristic exponential growth rates and determine the specific growth rate light intensity dependency (μ-I curve), which is useful as the key input for several models that predict P(v). Nannochloropsis salina and Chlorella sorokiniana specific growth rates were measured by repeated batch culture in microplates supplied with continuous light at different intensities. Exponential growth unlimited by gas transfer or self-shading was observable for a period of several days using fluorescence, which is an order of magnitude more sensitive than optical density. The microplate datasets were comparable to similar datasets obtained in photobioreactors and were used an input for the Huesemann model to accurately predict P(v). Copyright © 2014 Elsevier Ltd. All rights reserved.

Dynamic modeling of sludge compaction and consolidation processes in wastewater secondary settling tanks.

PubMed

Abusam, A; Keesman, K J

2009-01-01

The double exponential settling model is the widely accepted model for wastewater secondary settling tanks. However, this model does not estimate accurately solids concentrations in the settler underflow stream, mainly because sludge compression and consolidation processes are not considered. In activated sludge systems, accurate estimation of the solids in the underflow stream will facilitate the calibration process and can lead to correct estimates of particularly kinetic parameters related to biomass growth. Using principles of compaction and consolidation, as in soil mechanics, a dynamic model of the sludge consolidation processes taking place in the secondary settling tanks is developed and incorporated to the commonly used double exponential settling model. The modified double exponential model is calibrated and validated using data obtained from a full-scale wastewater treatment plant. Good agreement between predicted and measured data confirmed the validity of the modified model.

Reduced Heme Levels Underlie the Exponential Growth Defect of the Shewanella oneidensis hfq Mutant

PubMed Central

Mezoian, Taylor; Hunt, Taylor M.; Keane, Meaghan L.; Leonard, Jessica N.; Scola, Shelby E.; Beer, Emma N.; Perdue, Sarah; Pellock, Brett J.

2014-01-01

The RNA chaperone Hfq fulfills important roles in small regulatory RNA (sRNA) function in many bacteria. Loss of Hfq in the dissimilatory metal reducing bacterium Shewanella oneidensis strain MR-1 results in slow exponential phase growth and a reduced terminal cell density at stationary phase. We have found that the exponential phase growth defect of the hfq mutant in LB is the result of reduced heme levels. Both heme levels and exponential phase growth of the hfq mutant can be completely restored by supplementing LB medium with 5-aminolevulinic acid (5-ALA), the first committed intermediate synthesized during heme synthesis. Increasing expression of gtrA, which encodes the enzyme that catalyzes the first step in heme biosynthesis, also restores heme levels and exponential phase growth of the hfq mutant. Taken together, our data indicate that reduced heme levels are responsible for the exponential growth defect of the S. oneidensis hfq mutant in LB medium and suggest that the S. oneidensis hfq mutant is deficient in heme production at the 5-ALA synthesis step. PMID:25356668

Modelling the interactions between Pseudomonas putida and Escherichia coli O157:H7 in fish-burgers: use of the lag-exponential model and of a combined interaction index.

PubMed

Speranza, B; Bevilacqua, A; Mastromatteo, M; Sinigaglia, M; Corbo, M R

2010-08-01

The objective of the current study was to examine the interactions between Pseudomonas putida and Escherichia coli O157:H7 in coculture studies on fish-burgers packed in air and under different modified atmospheres (30 : 40 : 30 O(2) : CO(2) : N(2), 5 : 95 O(2) : CO(2) and 50 : 50 O(2) : CO(2)), throughout the storage at 8 degrees C. The lag-exponential model was applied to describe the microbial growth. To give a quantitative measure of the occurring microbial interactions, two simple parameters were developed: the combined interaction index (CII) and the partial interaction index (PII). Under air, the interaction was significant (P < 0.05) only within the exponential growth phase (CII, 1.72), whereas under the modified atmospheres, the interactions were highly significant (P < 0.001) and occurred both in the exponential and in the stationary phase (CII ranged from 0.33 to 1.18). PII values for E. coli O157:H7 were lower than those calculated for Ps. putida. The interactions occurring into the system affected both E. coli O157:H7 and pseudomonads subpopulations. The packaging atmosphere resulted in a key element. The article provides some useful information on the interactions occurring between E. coli O157:H7 and Ps. putida on fish-burgers. The proposed index describes successfully the competitive growth of both micro-organisms, giving also a quantitative measure of a qualitative phenomenon.

Preferential attachment and growth dynamics in complex systems

NASA Astrophysics Data System (ADS)

Yamasaki, Kazuko; Matia, Kaushik; Buldyrev, Sergey V.; Fu, Dongfeng; Pammolli, Fabio; Riccaboni, Massimo; Stanley, H. Eugene

2006-09-01

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ≈2 observed as a universal feature of many biological, social and economic problems.

Growth and differentiation of human lens epithelial cells in vitro on matrix

NASA Technical Reports Server (NTRS)

Blakely, E. A.; Bjornstad, K. A.; Chang, P. Y.; McNamara, M. P.; Chang, E.; Aragon, G.; Lin, S. P.; Lui, G.; Polansky, J. R.

2000-01-01

PURPOSE: To characterize the growth and maturation of nonimmortalized human lens epithelial (HLE) cells grown in vitro. METHODS: HLE cells, established from 18-week prenatal lenses, were maintained on bovine corneal endothelial (BCE) extracellular matrix (ECM) in medium supplemented with basic fibroblast growth factor (FGF-2). The identity, growth, and differentiation of the cultures were characterized by karyotyping, cell morphology, and growth kinetics studies, reverse transcription-polymerase chain reaction (RT-PCR), immunofluorescence, and Western blot analysis. RESULTS: HLE cells had a male, human diploid (2N = 46) karyotype. The population-doubling time of exponentially growing cells was 24 hours. After 15 days in culture, cell morphology changed, and lentoid formation was evident. Reverse transcription-polymerase chain reaction (RT-PCR) indicated expression of alphaA- and betaB2-crystallin, fibroblast growth factor receptor 1 (FGFR1), and major intrinsic protein (MIP26) in exponential growth. Western analyses of protein extracts show positive expression of three immunologically distinct classes of crystallin proteins (alphaA-, alphaB-, and betaB2-crystallin) with time in culture. By Western blot analysis, expression of p57(KIP2), a known marker of terminally differentiated fiber cells, was detectable in exponential cultures, and levels increased after confluence. MIP26 and gamma-crystallin protein expression was detected in confluent cultures, by using immunofluorescence, but not in exponentially growing cells. CONCLUSIONS: HLE cells can be maintained for up to 4 months on ECM derived from BCE cells in medium containing FGF-2. With time in culture, the cells demonstrate morphologic characteristics of, and express protein markers for, lens fiber cell differentiation. This in vitro model will be useful for investigations of radiation-induced cataractogenesis and other studies of lens toxicity.

Translational resistivity/conductivity of coding sequences during exponential growth of Escherichia coli.

PubMed

Takai, Kazuyuki

2017-01-21

Codon adaptation index (CAI) has been widely used for prediction of expression of recombinant genes in Escherichia coli and other organisms. However, CAI has no mechanistic basis that rationalizes its application to estimation of translational efficiency. Here, I propose a model based on which we could consider how codon usage is related to the level of expression during exponential growth of bacteria. In this model, translation of a gene is considered as an analog of electric current, and an analog of electric resistance corresponding to each gene is considered. "Translational resistance" is dependent on the steady-state concentration and the sequence of the mRNA species, and "translational resistivity" is dependent only on the mRNA sequence. The latter is the sum of two parts: one is the resistivity for the elongation reaction (coding sequence resistivity), and the other comes from all of the other steps of the decoding reaction. This electric circuit model clearly shows that some conditions should be met for codon composition of a coding sequence to correlate well with its expression level. On the other hand, I calculated relative frequency of each of the 61 sense codon triplets translated during exponential growth of E. coli from a proteomic dataset covering over 2600 proteins. A tentative method for estimating relative coding sequence resistivity based on the data is presented. Copyright © 2016. Published by Elsevier Ltd.

A predictability study of Lorenz's 28-variable model as a dynamical system

NASA Technical Reports Server (NTRS)

Krishnamurthy, V.

1993-01-01

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Literature-Based Scientific Learning: A Collaboration Model

ERIC Educational Resources Information Center

Elrod, Susan L.; Somerville, Mary M.

2007-01-01

Amidst exponential growth of knowledge, student insights into the knowledge creation practices of the scientific community can be furthered by science faculty collaborations with university librarians. The Literature-Based Scientific Learning model advances undergraduates' disciplinary mastery and information literacy through experience with…

From the Cover: The growth of business firms: Theoretical framework and empirical evidence

NASA Astrophysics Data System (ADS)

Fu, Dongfeng; Pammolli, Fabio; Buldyrev, S. V.; Riccaboni, Massimo; Matia, Kaushik; Yamasaki, Kazuko; Stanley, H. Eugene

2005-12-01

We introduce a model of proportional growth to explain the distribution Pg(g) of business-firm growth rates. The model predicts that Pg(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the predictions of the model agree with empirical growth distributions and size-variance relationships. proportional growth | preferential attachment | Laplace distribution

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

The growth of business firms: theoretical framework and empirical evidence.

PubMed

Fu, Dongfeng; Pammolli, Fabio; Buldyrev, S V; Riccaboni, Massimo; Matia, Kaushik; Yamasaki, Kazuko; Stanley, H Eugene

2005-12-27

We introduce a model of proportional growth to explain the distribution P(g)(g) of business-firm growth rates. The model predicts that P(g)(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent zeta = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the predictions of the model agree with empirical growth distributions and size-variance relationships.

Fatty acid synthesis in Escherichia coli

PubMed Central

Knivett, V. A.; Cullen, Julia

1967-01-01

1. Fatty acid formation by cells of a strain of Escherichia coli has been studied in the exponential, post-exponential and stationary phases of growth. 2. During the exponential phase of growth, the metabolic quotient (mμmoles of fatty acid synthesized/mg. dry wt. of cells/hr.) for each fatty acid in the extractable lipid was constant. 3. The newly synthesized fatty acid mixtures produced during this phase contained hexadecanoic acid (41%), hexadecenoic acid (31%), octadecenoic acid (21%) and the C17-cyclopropane acid, methylenehexadecanoic acid (4%). 4. As the proportion of newly synthesized material increased, changes in the fatty acid composition of the cells during this period were towards this constant composition. 5. Abrupt changes in fatty acid synthesis occurred when exponential growth ceased. 6. In media in which glycerol, or SO42− or Mg2+, was growth-limiting there was a small accumulation of C17-cyclopropane acid in cells growing in the post-exponential phase of growth. 7. Where either NH4+ or PO43− was growth-limiting and there were adequate supplies of glycerol, Mg2+ and SO42−, there was a marked accumulation of C17-cyclopropane acid and C19-cyclopropane acid appeared. 8. Under appropriate conditions the metabolic quotient for C17-cyclopropane acid increased up to sevenfold at the end of exponential growth. Simultaneously the metabolic quotients of the other acids fell. 9. A mixture of glycerol, Mg2+ and SO42− stimulated cyclopropane acid formation in resting cells. PMID:5340364

Teaching Exponential Growth and Decay: Examples from Medicine

ERIC Educational Resources Information Center

Hobbie, Russell K.

1973-01-01

A treatment of exponential growth and decay is sketched which does not require knowledge of calculus, and hence, it can be applied to many cases in the biological and medical sciences. Some examples are bacterial growth, sterilization, clearance, and drug absorption. (DF)

Coarsening of ion-beam-induced surface ripple in Si: Nonlinear effect vs. geometrical shadowing

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

Datta, Debi Prasad; Chini, Tapas Kumar

The temporal evolution of a periodic ripple pattern on a silicon surface undergoing erosion by 30 keV argon ion bombardment has been studied for two angles of ion incidence of 60 deg. and 70 deg. using ex situ atomic force microscopy (AFM) in ambient condition. The roughness amplitude (w) grows exponentially with sputtering time for both the angle of ion incidence followed by a slow growth process that saturates eventually with almost constant amplitude. Within the exponential growth regime of amplitude, however, ripple wavelength (l) remains constant initially and increases subsequently as a power law fashion l{proportional_to}t{sup n}, where n=0.47{+-}0.02more » for a 60 deg. angle of ion incidence followed by a saturation. Wavelength coarsening was also observed for 70 deg. but ordering in the periodic ripple pattern is destroyed quickly for 70 deg. as compared to 60 deg. . The ripple orientation, average ripple wavelength at the initial stage of ripple evolution, and the exponential growth of ripple amplitude can be described by a linear continuum model. While the wavelength coarsening could possibly be explained in the light of recent hydrodynamic model based continuum theory, the subsequent saturation of wavelength and amplitude was attributed to the effect of geometrical shadowing. This is an experimental result that probably gives a hint about the upper limit of the energy of ion beam rippling for applying the recently developed type of nonlinear continuum model.« less

Rethinking Economics and Education: Exponential Growth and Post-Growth Strategies

ERIC Educational Resources Information Center

Irwin, Ruth

2017-01-01

Education is increasingly vocational and structured to serve the ongoing exponential increase in economic growth. Climate change is an outcome of these same economic values and praxes. Attempts to shift these values and our approach to technology are continually absorbed and overcome by the pressing motif of economic growth. In this article, Ruth…

Effects of reaction-kinetic parameters on modeling reaction pathways in GaN MOVPE growth

NASA Astrophysics Data System (ADS)

Zhang, Hong; Zuo, Ran; Zhang, Guoyi

2017-11-01

In the modeling of the reaction-transport process in GaN MOVPE growth, the selections of kinetic parameters (activation energy Ea and pre-exponential factor A) for gas reactions are quite uncertain, which cause uncertainties in both gas reaction path and growth rate. In this study, numerical modeling of the reaction-transport process for GaN MOVPE growth in a vertical rotating disk reactor is conducted with varying kinetic parameters for main reaction paths. By comparisons of the molar concentrations of major Ga-containing species and the growth rates, the effects of kinetic parameters on gas reaction paths are determined. The results show that, depending on the values of the kinetic parameters, the gas reaction path may be dominated either by adduct/amide formation path, or by TMG pyrolysis path, or by both. Although the reaction path varies with different kinetic parameters, the predicted growth rates change only slightly because the total transport rate of Ga-containing species to the substrate changes slightly with reaction paths. This explains why previous authors using different chemical models predicted growth rates close to the experiment values. By varying the pre-exponential factor for the amide trimerization, it is found that the more trimers are formed, the lower the growth rates are than the experimental value, which indicates that trimers are poor growth precursors, because of thermal diffusion effect caused by high temperature gradient. The effective order for the contribution of major species to growth rate is found as: pyrolysis species > amides > trimers. The study also shows that radical reactions have little effect on gas reaction path because of the generation and depletion of H radicals in the chain reactions when NH2 is considered as the end species.

Value function in economic growth model

NASA Astrophysics Data System (ADS)

Bagno, Alexander; Tarasyev, Alexandr A.; Tarasyev, Alexander M.

2017-11-01

Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton-Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals and an example is given to illustrate construction of the value function in economic growth models.

Research on the exponential growth effect on network topology: Theoretical and empirical analysis

NASA Astrophysics Data System (ADS)

Li, Shouwei; You, Zongjun

Integrated circuit (IC) industry network has been built in Yangtze River Delta with the constant expansion of IC industry. The IC industry network grows exponentially with the establishment of new companies and the establishment of contacts with old firms. Based on preferential attachment and exponential growth, the paper presents the analytical results in which the vertices degree of scale-free network follows power-law distribution p(k)˜k‑γ (γ=2β+1) and parameter β satisfies 0.5≤β≤1. At the same time, we find that the preferential attachment takes place in a dynamic local world and the size of the dynamic local world is in direct proportion to the size of whole networks. The paper also gives the analytical results of no-preferential attachment and exponential growth on random networks. The computer simulated results of the model illustrate these analytical results. Through some investigations on the enterprises, this paper at first presents the distribution of IC industry, composition of industrial chain and service chain firstly. Then, the correlative network and its analysis of industrial chain and service chain are presented. The correlative analysis of the whole IC industry is also presented at the same time. Based on the theory of complex network, the analysis and comparison of industrial chain network and service chain network in Yangtze River Delta are provided in the paper.

Population growth and economic growth.

PubMed

Narayana, D L

1984-01-01

This discussion of the issues relating to the problem posed by population explosion in the developing countries and economic growth in the contemporary world covers the following: predictions of economic and social trends; the Malthusian theory of population; the classical or stationary theory of population; the medical triage model; ecological disaster; the Global 2000 study; the limits to growth; critiques of the Limits to Growth model; nonrenewable resources; food and agriculture; population explosion and stabilization; space and ocean colonization; and the limits perspective. The Limits to Growth model, a general equilibrium anti-growth model, is the gloomiest economic model ever constructed. None of the doomsday models, the Malthusian theory, the classical stationary state, the neo-Malthusian medical triage model, the Global 2000 study, are so far reaching in their consequences. The course of events that followed the publication of the "Limits to Growth" in 1972 in the form of 2 oil shocks, food shock, pollution shock, and price shock seemed to bear out formally the gloomy predictions of the thesis with a remarkable speed. The 12 years of economic experience and the knowledge of resource trends postulate that even if the economic pressures visualized by the model are at work they are neither far reaching nor so drastic. Appropriate action can solve them. There are several limitations to the Limits to Growth model. The central theme of the model, which is overshoot and collapse, is unlikely to be the course of events. The model is too aggregative to be realistic. It exaggerates the ecological disaster arising out of the exponential growth of population and industry. The gross underestimation of renewable resources is a basic flaw of the model. The most critical weakness of the model is its gross underestimation of the historical trend of technological progress and the technological possiblities within industry and agriculture. The model does correctly emphasize the exponential growth of population as the source of several complications for economic growth and human welfare. Stabilization of population by reducing fertility is conducive for improving the quality of population and also advances the longterm management of the population growth and work force utilization. The perspective of longterm economic management involves populatio n planning, control of environmental pollution, conservation of scarce resources, exploration of resources, realization of technological possibilities in agriculture and industry and in farm and factory, and achievement of economic growth and its equitable distribution.

Modeling crust-mantle evolution using radiogenic Sr, Nd, and Pb isotope systematics

NASA Astrophysics Data System (ADS)

Kumari, Seema; Paul, Debajyoti

2015-04-01

The present-day elemental and isotopic composition of Earth's terrestrial reservoirs can be used as geochemical constraints to study evolution of the crust-mantle system. A flexible open system evolutionary model of the Earth, comprising continental crust (CC), upper depleted mantle (UM) -source of mid-ocean ridge basalts (MORB), and lower mantle (LM) reservoir with a D" layer -source of ocean island basalts (OIB), and incorporating key radioactive isotope systematics (Rb-Sr, Sm-Nd, and U-Th-Pb), is solved numerically at 1 Ma time step for 4.55 Ga, the age of the Earth. The best possible solution is the one that produces the present-day concentrations as well as isotopic ratios in terrestrial reservoirs, compiled from published data. Different crustal growth scenarios (exponential, episodic, early and late growth), proposed in earlier studies, and its effect on the evolution of isotope systematics of terrestrial reservoirs is studied. Model simulations strongly favor a layered mantle structure satisfying majority of the isotopic constraints. In the successful model, which is similar to that proposed by Kellogg et al. (1999), the present-day UM comprises of 60% of mantle mass and extends to a depth 1600 km, whereas the LM becomes non-primitive and more enriched than the bulk silicate Earth, mainly due to addition of recycled crustal material. Modeling suggest that isotopic evolution of reservoirs is affected by the mode of crustal growth. Only two scenarios satisfied majority of the Rb-Sr and Sm-Nd isotopic constraints but failed to reproduce the present-day Pb-isotope systematics; exponential growth of crust (mean age, tc=2.3 Ga) and delayed and episodic growth (no growth for initial 900 Ma, tc=2.05 Ga) proposed by Patchett and Arndt (1986). However, assuming a slightly young Earth (4.45 Ga) better satisfies the Pb-isotope systematics. Although, the delayed crustal growth model satisfied Sr-Nd isotopic constraints, presence of early Hadean crust (4.03 and 4.4 Ga detrital zircon in Acasta gneiss and Yilgarn block, respectively), argues against it. One notable feature of successful models is an early depletion of incompatible elements (as well as Th/U ratio in the UM) by the initial 500 Ma, as a result of early formation of continental crust. Our results strongly favor exponential crustal growth and layered mantle structure. Patchett, P.J., Arndt, N.T. (1986), Earth and Planetary Science Letters, 78, 329-338. Kellogg, L.H., Hager, B.H., van der Hilst, R.D (1999), Science, 283, 1881-1884.

Population models of burrowing mayfly recolonization in Western Lake Erie

USGS Publications Warehouse

Madenjian, C.P.; Schloesser, D.W.; Krieger, K.A.

1998-01-01

Burrowing mayflies, Hexagenia spp. (H. limbata and H. rigida), began recolonizing western Lake Erie during the 1990s. Survey data for mayfly nymph densities indicated that the population experienced exponential growth between 1991 and 1997. To predict the time to full recovery of the mayfly population, we fitted logistic models, ranging in carrying capacity from 600 to 2000 nymphs/m2, to these survey data. Based on the fitted logistic curves, we forecast that the mayfly population in western Lake Erie would achieve full recovery between years 1998 and 2000, depending on the carrying capacity of the western basin. Additionally, we estimated the mortality rate of nymphs in western Lake Erie during 1994 and then applied an age-based matrix model to the mayfly population. The results of the matrix population modeling corroborated the exponential growth model application in that both methods yielded an estimate of the population growth rate, r, in excess of 0.8 yr-1. This was the first evidence that mayfly populations are capable of recolonizing large aquatic ecosystems at rates comparable with those observed in much smaller lentic ecosystems. Our model predictions should prove valuable to managers of power plant facilities along the western basin in planning for mayfly emergences and to managers of the yellow perch (Perca flavescens) fishery in western Lake Erie.

Prediction of infarction volume and infarction growth rate in acute ischemic stroke.

PubMed

Kamran, Saadat; Akhtar, Naveed; Alboudi, Ayman; Kamran, Kainat; Ahmad, Arsalan; Inshasi, Jihad; Salam, Abdul; Shuaib, Ashfaq; Qidwai, Uvais

2017-08-08

The prediction of infarction volume after stroke onset depends on the shape of the growth dynamics of the infarction. To understand growth patterns that predict lesion volume changes, we studied currently available models described in literature and compared the models with Adaptive Neuro-Fuzzy Inference System [ANFIS], a method previously unused in the prediction of infarction growth and infarction volume (IV). We included 67 patients with malignant middle cerebral artery [MMCA] stroke who underwent decompressive hemicraniectomy. All patients had at least three cranial CT scans prior to the surgery. The rate of growth and volume of infarction measured on the third CT was predicted with ANFIS without statistically significant difference compared to the ground truth [P = 0.489]. This was not possible with linear, logarithmic or exponential methods. ANFIS was able to predict infarction volume [IV3] over a wide range of volume [163.7-600 cm 3 ] and time [22-110 hours]. The cross correlation [CRR] indicated similarity between the ANFIS-predicted IV3 and original data of 82% for ANFIS, followed by logarithmic 70%, exponential 63% and linear 48% respectively. Our study shows that ANFIS is superior to previously defined methods in the prediction of infarction growth rate (IGR) with reasonable accuracy, over wide time and volume range.

Progress, Exponential Growth and Post-Growth Education

ERIC Educational Resources Information Center

Irwin, Ruth

2017-01-01

Teleological progress is the underlying motif of modern culture, and informs education, innovation, and economic development. Progress includes a gradual increase in consumerism. Since the 1940s, the Keynesian Settlement and its embedded belief in progress is legislated in exponential 2-3% economic growth. Unfortunately, climate change is a direct…

Concepts in solid tumor evolution.

PubMed

Sidow, Arend; Spies, Noah

2015-04-01

Evolutionary mechanisms in cancer progression give tumors their individuality. Cancer evolution is different from organismal evolution, however, and we discuss where concepts from evolutionary genetics are useful or limited in facilitating an understanding of cancer. Based on these concepts we construct and apply the simplest plausible model of tumor growth and progression. Simulations using this simple model illustrate the importance of stochastic events early in tumorigenesis, highlight the dominance of exponential growth over linear growth and differentiation, and explain the clonal substructure of tumors. Copyright © 2015 Elsevier Ltd. All rights reserved.

Parabolic replicator dynamics and the principle of minimum Tsallis information gain

PubMed Central

2013-01-01

Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator systems might reflect the importance of group selection and competition between ensembles of cooperating replicators. Reviewers This article was reviewed by Viswanadham Sridhara (nominated by Claus Wilke), Puushottam Dixit (nominated by Sergei Maslov), and Nick Grishin. For the complete reviews, see the Reviewers’ Reports section. PMID:23937956

Exponentially growing tearing modes in Rijnhuizen Tokamak Project plasmas.

PubMed

Salzedas, F; Schüller, F C; Oomens, A A M

2002-02-18

The local measurement of the island width w, around the resonant surface, allowed a direct test of the extended Rutherford model [P. H. Rutherford, PPPL Report-2277 (1985)], describing the evolution of radiation-induced tearing modes prior to disruptions of tokamak plasmas. It is found that this model accounts very well for the observed exponential growth and supports radiation losses as being the main driving mechanism. The model implies that the effective perpendicular electron heat conductivity in the island is smaller than the global one. Comparison of the local measurements of w with the magnetic perturbed field B showed that w proportional to B1/2 was valid for widths up to 18% of the minor radius.

Individual Differences in a Positional Learning Task across the Adult Lifespan

ERIC Educational Resources Information Center

Rast, Philippe; Zimprich, Daniel

2010-01-01

This study aimed at modeling individual and average non-linear trajectories of positional learning using a structured latent growth curve approach. The model is based on an exponential function which encompasses three parameters: Initial performance, learning rate, and asymptotic performance. These learning parameters were compared in a positional…

Kinetic Model for 1D aggregation of yeast ``prions''

NASA Astrophysics Data System (ADS)

Kunes, Kay; Cox, Daniel; Singh, Rajiv

2004-03-01

Mammalian prion proteins (PrP) are of public health interest because of mad cow and chronic wasting diseases. Yeast have proteins which can undergo similar reconformation and aggregation processes to PrP; yeast forms are simpler to experimentally study and model. Recent in vitro studies of the SUP35 protein(1), showed long aggregates and pure exponential growth of the misfolded form. To explain this data, we have extended a previous model of aggregation kinetics(2). The model assumes reconformation only upon aggregation, and includes aggregate fissioning and an initial nucleation barrier. We find for sufficiently small nucleation rates or seeding by small dimer concentrations that we can achieve the requisite exponential growth and long aggregates. We will compare to a more realistic stochastic kinetics model and present prelimary attempts to describe recent experiments on SUP35 strains. *-Supported by U.S. Army Congressionally Mandated Research Fund. 1) P. Chien and J.S. Weissman, Nature 410, 223 (2001); http://online.kitp.ucsb.edu/online/bionet03/collins/. 2) J. Masel, V.A.> Jansen, M.A. Nowak, Biophys. Chem. 77, 139 (1999).

The acquisition of conditioned responding.

PubMed

Harris, Justin A

2011-04-01

This report analyzes the acquisition of conditioned responses in rats trained in a magazine approach paradigm. Following the suggestion by Gallistel, Fairhurst, and Balsam (2004), Weibull functions were fitted to the trial-by-trial response rates of individual rats. These showed that the emergence of responding was often delayed, after which the response rate would increase relatively gradually across trials. The fit of the Weibull function to the behavioral data of each rat was equaled by that of a cumulative exponential function incorporating a response threshold. Thus, the growth in conditioning strength on each trial can be modeled by the derivative of the exponential--a difference term of the form used in many models of associative learning (e.g., Rescorla & Wagner, 1972). Further analyses, comparing the acquisition of responding with a continuously reinforced stimulus (CRf) and a partially reinforced stimulus (PRf), provided further evidence in support of the difference term. In conclusion, the results are consistent with conventional models that describe learning as the growth of associative strength, incremented on each trial by an error-correction process.

Accumulated distribution of material gain at dislocation crystal growth

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

Rakin, V. I., E-mail: rakin@geo.komisc.ru

2016-05-15

A model for slowing down the tangential growth rate of an elementary step at dislocation crystal growth is proposed based on the exponential law of impurity particle distribution over adsorption energy. It is established that the statistical distribution of material gain on structurally equivalent faces obeys the Erlang law. The Erlang distribution is proposed to be used to calculate the occurrence rates of morphological combinatorial types of polyhedra, presenting real simple crystallographic forms.

Competitive regulation of plant allometry and a generalized model for the plant self-thinning process.

PubMed

Wang, Gang; Yuan, Jianli; Wang, Xizhi; Xiao, Sa; Huang, Wenbing

2004-11-01

Taking into account the individual growth form (allometry) in a plant population and the effects of intraspecific competition on allometry under the population self-thinning condition, and adopting Ogawa's allometric equation 1/y = 1/axb + 1/c as the expression of complex allometry, the generalized model describing the change mode of r (the self-thinning exponential in the self-thinning equation, log M = K + log N, where M is mean plant mass, K is constant, and N is population density) was constructed. Meanwhile, with reference to the changing process of population density to survival curve type B, the exponential, r, was calculated using the software MATHEMATICA 4.0. The results of the numerical simulation show that (1) the value of the self-thinning exponential, r, is mainly determined by allometric parameters; it is most sensitive to change of b of the three allometric parameters, and a and c take second place; (2) the exponential, r, changes continuously from about -3 to the asymptote -1; the slope of -3/2 is a transient value in the population self-thinning process; (3) it is not a 'law' that the slope of the self-thinning trajectory equals or approaches -3/2, and the long-running dispute in ecological research over whether or not the exponential, r, equals -3/2 is meaningless. So future studies on the plant self-thinning process should focus on investigating how plant neighbor competition affects the phenotypic plasticity of plant individuals, what the relationship between the allometry mode and the self-thinning trajectory of plant population is and, in the light of evolution, how plants have adapted to competition pressure by plastic individual growth.

Modeling the Pre-Industrial Roots of Modern Super-Exponential Population Growth

PubMed Central

Stutz, Aaron Jonas

2014-01-01

To Malthus, rapid human population growth—so evident in 18th Century Europe—was obviously unsustainable. In his Essay on the Principle of Population, Malthus cogently argued that environmental and socioeconomic constraints on population rise were inevitable. Yet, he penned his essay on the eve of the global census size reaching one billion, as nearly two centuries of super-exponential increase were taking off. Introducing a novel extension of J. E. Cohen's hallmark coupled difference equation model of human population dynamics and carrying capacity, this article examines just how elastic population growth limits may be in response to demographic change. The revised model involves a simple formalization of how consumption costs influence carrying capacity elasticity over time. Recognizing that complex social resource-extraction networks support ongoing consumption-based investment in family formation and intergenerational resource transfers, it is important to consider how consumption has impacted the human environment and demography—especially as global population has become very large. Sensitivity analysis of the consumption-cost model's fit to historical population estimates, modern census data, and 21st Century demographic projections supports a critical conclusion. The recent population explosion was systemically determined by long-term, distinctly pre-industrial cultural evolution. It is suggested that modern globalizing transitions in technology, susceptibility to infectious disease, information flows and accumulation, and economic complexity were endogenous products of much earlier biocultural evolution of family formation's embeddedness in larger, hierarchically self-organizing cultural systems, which could potentially support high population elasticity of carrying capacity. Modern super-exponential population growth cannot be considered separately from long-term change in the multi-scalar political economy that connects family formation and intergenerational resource transfers to wider institutions and social networks. PMID:25141019

Modelling the Growth of Swine Flu

ERIC Educational Resources Information Center

Thomson, Ian

2010-01-01

The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…

Sequence-Controlled Polymerization on Facially Amphiphilic Templates at Interfaces

DTIC Science & Technology

2016-06-14

controlled chain growth polymerization. We will synthesize a ?- conjugated “parent” polymer by iterative exponential growth (IEG), attach cyclic olefin...template that is programmed to direct sequence- controlled chain growth polymerization. We will synthesize a ?- conjugated “parent” polymer by iterative...polymerization. We will synthesize a π- conjugated “parent” polymer by organometallic iterative exponential growth (IEG),2 attach cyclic olefin “daughter

Dice and Disease in the Classroom.

ERIC Educational Resources Information Center

Stor, Marilyn; Briggs, William L.

1998-01-01

Presents a mathematics activity to model the exponential growth of the common cold, AIDS, or any other communicable disease. Underscores the effect that a friend's or partner's previous behavior may have on a current relationship and on society at large. (ASK)

Can the Site-Frequency Spectrum Distinguish Exponential Population Growth from Multiple-Merger Coalescents?

PubMed Central

Eldon, Bjarki; Birkner, Matthias; Blath, Jochen; Freund, Fabian

2015-01-01

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a well-known characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular, the weight of the right tail, are, however, affected in specific ways by the two model classes. Using an approximate likelihood method and minimum-distance statistics, our estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiple-merger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough. A normalized version of the SFS (nSFS) is also used as a summary statistic in an approximate Bayesian computation (ABC) approach. The results give further positive evidence as to the general eligibility of the SFS to distinguish between the different histories. PMID:25575536

Morphology-based differences in the thermal response of freshwater phytoplankton.

PubMed

Segura, Angel M; Sarthou, Florencia; Kruk, Carla

2018-05-01

The thermal response of maximum growth rate in morphology-based functional groups (MBFG) of freshwater phytoplankton is analysed. Contrasting an exponential Boltzmann-Arrhenius with a unimodal model, three main features were evaluated: (i) the activation energy of the rise ( E r ), (ii) the presence of a break in the thermal response and (iii) the activation energy of the fall ( E f ). The whole dataset ( N = 563) showed an exponential increase ( E r ∼ 0.5), a break around 24°C and no temperature dependence after the breakpoint ( E f = 0). Contrasting thermal responses among MBFG were found. All groups showed positive activation energy ( E r > 0), four showed no evidence of decline in growth rate (temperature range = 0-35°C) and two presented a breakpoint followed by a sharp decrease in growth rate. Our results evidenced systematic differences between MBFG in the thermal response and a coherent response significantly related to morphological traits other than size (i.e. within MBFG). These results provide relevant information for water quality modelling and climate change predictions. © 2018 The Author(s).

Hypothesized kinetic models for describing the growth of globular and encrusting demosponges.

PubMed

Sipkema, Detmer; Yosef, Nejla A M; Adamczewski, Marcin; Osinga, Ronald; Mendola, Dominick; Tramper, Johannes; Wijffels, René H

2006-01-01

The marine sponges Dysidea avara and Chondrosia reniformis (globular forms) were cultured in the laboratory on a diet of viable Phaeodactylum tricornutum cells and dissolved nutrients (algae and fish powders). Our growth data were combined with literature data for Pseudosuberites andrewsi (a globular sponge) and for the encrusting sponges Oscarella lobularis, Hemimycale columella, and Crambe crambe. The suitability of three growth models-linear, exponential, and radial accretive-for describing the growth of globular and encrusting sponges was assessed. Radial accretive growth was determined to be the best model to describe growth of both encrusting and globular sponges. Average growth rates of 0.051+/-0.016 and 0.019+/-0.003 mm/day (calculated as the increase of the radius of the sponge per day) were obtained experimentally for D. avara and C. reniformis, respectively.

A multilevel approach to examining cephalopod growth using Octopus pallidus as a model.

PubMed

Semmens, Jayson; Doubleday, Zoë; Hoyle, Kate; Pecl, Gretta

2011-08-15

Many aspects of octopus growth dynamics are poorly understood, particularly in relation to sub-adult or adult growth, muscle fibre dynamics and repro-somatic investment. The growth of 5 month old Octopus pallidus cultured in the laboratory was investigated under three temperature regimes over a 12 week period: seasonally increasing temperatures (14-18°C); seasonally decreasing temperatures (18-14°C); and a constant temperature mid-way between seasonal peaks (16°C). Differences in somatic growth at the whole-animal level, muscle tissue structure and rate of gonad development were investigated. Continuous exponential growth was observed, both at a group and at an individual level, and there was no detectable effect of temperature on whole-animal growth rate. Juvenile growth rate (from 1 to 156 days) was also monitored prior to the controlled experiment; exponential growth was observed, but at a significantly faster rate than in the older experimental animals, suggesting that O. pallidus exhibit a double-exponential two-phase growth pattern. There was considerable variability in size-at-age even between individuals growing under identical thermal regimes. Animals exposed to seasonally decreasing temperatures exhibited a higher rate of gonad development compared with animals exposed to increasing temperatures; however, this did not coincide with a detectable decline in somatic growth rate or mantle condition. The ongoing production of new mitochondria-poor and mitochondria-rich muscle fibres (hyperplasia) was observed, indicated by a decreased or stable mean muscle fibre diameter concurrent with an increase in whole-body size. Animals from both seasonal temperature regimes demonstrated higher rates of new mitochondria-rich fibre generation relative to those from the constant temperature regime, but this difference was not reflected in a difference in growth rate at the whole-body level. This is the first study to record ongoing hyperplasia in the muscle tissue of an octopus species, and provides further insight into the complex growth dynamics of octopus.

Interactive effects of temperature, pH, and water activity on the growth kinetics of Shiga toxin-producing Escherichia coli O104:H4 3.

PubMed

Juneja, Vijay K; Mukhopadhyay, Sudarsan; Ukuku, Dike; Hwang, Cheng-An; Wu, Vivian C H; Thippareddi, Harshavardhan

2014-05-01

The risk of non-O157 Shiga toxin-producing Escherichia coli strains has become a growing public health concern. Several studies characterized the behavior of E. coli O157:H7; however, no reports on the influence of multiple factors on E. coli O104:H4 are available. This study examined the effects and interactions of temperature (7 to 46°C), pH (4.5 to 8.5), and water activity (aw ; 0.95 to 0.99) on the growth kinetics of E. coli O104:H4 and developed predictive models to estimate its growth potential in foods. Growth kinetics studies for each of the 23 variable combinations from a central composite design were performed. Growth data were used to obtain the lag phase duration (LPD), exponential growth rate, generation time, and maximum population density (MPD). These growth parameters as a function of temperature, pH, and aw as controlling factors were analyzed to generate second-order response surface models. The results indicate that the observed MPD was dependent on the pH, aw, and temperature of the growth medium. Increasing temperature resulted in a concomitant decrease in LPD. Regression analysis suggests that temperature, pH, and aw significantly affect the LPD, exponential growth rate, generation time, and MPD of E. coli O104:H4. A comparison between the observed values and those of E. coli O157:H7 predictions obtained by using the U. S. Department of Agriculture Pathogen Modeling Program indicated that E. coli O104:H4 grows faster than E. coli O157:H7. The developed models were validated with alfalfa and broccoli sprouts. These models will provide risk assessors and food safety managers a rapid means of estimating the likelihood that the pathogen, if present, would grow in response to the interaction of the three variables assessed.

Why Are There Developmental Stages in Language Learning? A Developmental Robotics Model of Language Development

ERIC Educational Resources Information Center

Morse, Anthony F.; Cangelosi, Angelo

2017-01-01

Most theories of learning would predict a gradual acquisition and refinement of skills as learning progresses, and while some highlight exponential growth, this fails to explain why natural cognitive development typically progresses in stages. Models that do span multiple developmental stages typically have parameters to "switch" between…

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

ERIC Educational Resources Information Center

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

An allometric scaling relation based on logistic growth of cities

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2014-08-01

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential allometry", which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the abovementioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed "logistic allometry". The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

[Dynamics of Cry1ab protein content in the rhizosphere soil and straw debris of transgenic Bt corn].

PubMed

Li, Fan; Wang, Min; Sun, Hong-Wei; Yang, Shu-Ke; Lu, Xing-Bo

2013-07-01

By using ELISA test kits, a field investigation was conducted on the degradation dynamics of CrylAb protein in the rhizosphere soil of Bt corn MON810 at its different growth stages and in the MON810 straws returned into field after harvest. Three models (shift-log model, exponential model, and bi-exponential model) were used to fit the degradation dynamics of the Cry1 Ab protein from the straw debris, and the DT50 and DT90, values were estimated. There existed great differences in the CrylAb protein content in the rhizosphere soil of MON810 at its different growth stages, but overall, the CrylAb protein content was decreased remarkably with the growth of MON810. The degradation of Cry1 Ab protein from the straws covered on soil surface and buried in soil showed the same two-stage pattern, i.e., more rapid at early stage and slow-stable in later period. Within the first week after straw return, the degradation rate of the CrylAb protein from the straws covered on soil surface was significantly higher than that from the straws buried in soil. At 10 d, the degradation rate of the CrylAb protein from the straws covered on soil surface and buried in soil was basically the same, being 88.8% and 88.6%, respectively. After 20 days, the degradation of CrylAb protein entered slow-stable stage. Till at 180 d, a small amount of Cry1Ab protein could still be detected in the straw debris. All of the three models used in this study could fit the decay pattern of the CrylAb protein from the straw debris in field. By comparing the correlation coefficient (r) and the consistency between the measured and calculated DT90, bi-exponential model was considered to be the best.

The Effect of Ion Adsorption on Microbial Dissimilatory Iron-Reduction and the Mobility of Adsorbed As(V)

NASA Astrophysics Data System (ADS)

Meyer, B. A.; Stillings, L. L.

2003-12-01

The effect of varying environmental conditions on the microbial reduction of Fe(III) and the mobility of adsorbed As(V) was investigated by studying the kinetics of reductive dissolution of synthetic, hydrous ferric oxide (HFO) in three batch-reactor experiments. Growth medium, containing HFO as an electron acceptor (EA) and acetate as an electron donor (ED), was dispensed into 500-ml septum sealed serum bottles. Each bottle was inoculated with an enrichment culture (MEC) containing an anaerobic Fe-reducing bacterium obtained from sediments at Milltown Reservoir near Missoula, MT. Each enrichment culture grew for at least 600 hrs and exhibited both exponential and stationary growth. Microbial reduction was monitored by measuring the production of dissolved Fe(II). Total Fe(II) was calculated by applying a Langmuir adsorption model, developed for each growth condition, to the measured dissolved Fe(II). Total Fe(II) production was modeled by: x = Xs(1-e-ket)-[kL(e-ket)]+(kL/ke) where x is the total Fe(II) concentration (mM) at t, ke is the exponential production rate constant (hr-1), Xs is the total Fe(II) concentration (mM) at the time of transition between exponential and stationary growth, t is the time since inoculation minus lag time, and kL is the stationary (linear) production rate constant (mM hr-1). From our experiments we learned that: 1) increasing the concentration of EA from 10-30 mM had no effect on the value of ke, which remained constant at 0.015 hr-1. However, the maximum production rate, Rmax = (ke Xs)+kL, did increase with increasing EA, varying from 0.014-0.031 mM hr-1; 2) increasing the concentration of ED from 10-30 mM had no effect on either ke or Rmax. These values remained constant as ED increased; 3) sorption of As(V) to the EA (in mM ratios of 1:10 and 1:30, As(V):HFO) affected Rmax but not ke. Rmax increased with increasing EA, as observed earlier, but its value was lower than in cultures without arsenic. In the presence of As(V), Rmax was unaffected by increasing ED. Microbial reduction of EA did not result in the release of aqueous As(V) or As(III). In all cases, representative blank and kill controls were run concurrent with growth experiments. No Fe(II) production was observed in the controls. The modeling method showed that increases in Rmax, when observed, were due to an elongated exponential growth phase. We conclude that the availability of surface sites to the culture is the controlling factor in microbial iron reduction. The length of the exponential growth phase depends on the concentration of surface sites available for microbial reduction. Adsorbed Fe(II) or As(V) inhibits reduction by decreasing the concentration of available surface sites. Likewise, increasing the initial concentration of EA increases the concentration of available surface sites thus increasing Rmax.

Understanding Exponential Growth: As Simple as a Drop in a Bucket.

ERIC Educational Resources Information Center

Goldberg, Fred; Shuman, James

1984-01-01

Provides procedures for a simple laboratory activity on exponential growth and its characteristic doubling time. The equipment needed consists of a large plastic bucket, an eyedropper, a stopwatch, an assortment of containers and graduated cylinders, and a supply of water. (JN)

Enhancement of L-phenylalanine production by engineered Escherichia coli using phased exponential L-tyrosine feeding combined with nitrogen source optimization.

PubMed

Yuan, Peipei; Cao, Weijia; Wang, Zhen; Chen, Kequan; Li, Yan; Ouyang, Pingkai

2015-07-01

Nitrogen source optimization combined with phased exponential L-tyrosine feeding was employed to enhance L-phenylalanine production by a tyrosine-auxotroph strain, Escherichia coli YP1617. The absence of (NH4)2SO4, the use of corn steep powder and yeast extract as composite organic nitrogen source were more suitable for cell growth and L-phenylalanine production. Moreover, the optimal initial L-tyrosine level was 0.3 g L(-1) and exponential L-tyrosine feeding slightly improved L-phenylalanine production. Nerveless, L-phenylalanine production was greatly enhanced by a strategy of phased exponential L-tyrosine feeding, where exponential feeding was started at the set specific growth rate of 0.08, 0.05, and 0.02 h(-1) after 12, 32, and 52 h, respectively. Compared with exponential L-tyrosine feeding at the set specific growth rate of 0.08 h(-1), the developed strategy obtained a 15.33% increase in L-phenylalanine production (L-phenylalanine of 56.20 g L(-1)) and a 45.28% decrease in L-tyrosine supplementation. Copyright © 2014 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

Testing mechanistic models of growth in insects.

PubMed

Maino, James L; Kearney, Michael R

2015-11-22

Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes. © 2015 The Author(s).

Socio-Economic Instability and the Scaling of Energy Use with Population Size

PubMed Central

DeLong, John P.; Burger, Oskar

2015-01-01

The size of the human population is relevant to the development of a sustainable world, yet the forces setting growth or declines in the human population are poorly understood. Generally, population growth rates depend on whether new individuals compete for the same energy (leading to Malthusian or density-dependent growth) or help to generate new energy (leading to exponential and super-exponential growth). It has been hypothesized that exponential and super-exponential growth in humans has resulted from carrying capacity, which is in part determined by energy availability, keeping pace with or exceeding the rate of population growth. We evaluated the relationship between energy use and population size for countries with long records of both and the world as a whole to assess whether energy yields are consistent with the idea of an increasing carrying capacity. We find that on average energy use has indeed kept pace with population size over long time periods. We also show, however, that the energy-population scaling exponent plummets during, and its temporal variability increases preceding, periods of social, political, technological, and environmental change. We suggest that efforts to increase the reliability of future energy yields may be essential for stabilizing both population growth and the global socio-economic system. PMID:26091499

Socio-Economic Instability and the Scaling of Energy Use with Population Size.

PubMed

DeLong, John P; Burger, Oskar

2015-01-01

The size of the human population is relevant to the development of a sustainable world, yet the forces setting growth or declines in the human population are poorly understood. Generally, population growth rates depend on whether new individuals compete for the same energy (leading to Malthusian or density-dependent growth) or help to generate new energy (leading to exponential and super-exponential growth). It has been hypothesized that exponential and super-exponential growth in humans has resulted from carrying capacity, which is in part determined by energy availability, keeping pace with or exceeding the rate of population growth. We evaluated the relationship between energy use and population size for countries with long records of both and the world as a whole to assess whether energy yields are consistent with the idea of an increasing carrying capacity. We find that on average energy use has indeed kept pace with population size over long time periods. We also show, however, that the energy-population scaling exponent plummets during, and its temporal variability increases preceding, periods of social, political, technological, and environmental change. We suggest that efforts to increase the reliability of future energy yields may be essential for stabilizing both population growth and the global socio-economic system.

A mathematical model for evolution and SETI.

PubMed

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Modelling Evolution and SETI Mathematically

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2012-05-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factor increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions constrained between the time axis and the exponential growth curve. Finally, since each lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

A Mathematical Model for Evolution and SETI

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Effects of correlations and fees in random multiplicative environments: Implications for portfolio management.

PubMed

Alper, Ofer; Somekh-Baruch, Anelia; Pirvandy, Oz; Schaps, Malka; Yaari, Gur

2017-08-01

Geometric Brownian motion (GBM) is frequently used to model price dynamics of financial assets, and a weighted average of multiple GBMs is commonly used to model a financial portfolio. Diversified portfolios can lead to an increased exponential growth compared to a single asset by effectively reducing the effective noise. The sum of GBM processes is no longer a log-normal process and has a complex statistical properties. The nonergodicity of the weighted average process results in constant degradation of the exponential growth from the ensemble average toward the time average. One way to stay closer to the ensemble average is to maintain a balanced portfolio: keep the relative weights of the different assets constant over time. To keep these proportions constant, whenever assets values change, it is necessary to rebalance their relative weights, exposing this strategy to fees (transaction costs). Two strategies that were suggested in the past for cases that involve fees are rebalance the portfolio periodically and rebalance it in a partial way. In this paper, we study these two strategies in the presence of correlations and fees. We show that using periodic and partial rebalance strategies, it is possible to maintain a steady exponential growth while minimizing the losses due to fees. We also demonstrate how these redistribution strategies perform in a phenomenal way on real-world market data, despite the fact that not all assumptions of the model hold in these real-world systems. Our results have important implications for stochastic dynamics in general and to portfolio management in particular, as we show that there is a superior alternative to the common buy-and-hold strategy, even in the presence of correlations and fees.

Effects of correlations and fees in random multiplicative environments: Implications for portfolio management

NASA Astrophysics Data System (ADS)

Alper, Ofer; Somekh-Baruch, Anelia; Pirvandy, Oz; Schaps, Malka; Yaari, Gur

2017-08-01

Geometric Brownian motion (GBM) is frequently used to model price dynamics of financial assets, and a weighted average of multiple GBMs is commonly used to model a financial portfolio. Diversified portfolios can lead to an increased exponential growth compared to a single asset by effectively reducing the effective noise. The sum of GBM processes is no longer a log-normal process and has a complex statistical properties. The nonergodicity of the weighted average process results in constant degradation of the exponential growth from the ensemble average toward the time average. One way to stay closer to the ensemble average is to maintain a balanced portfolio: keep the relative weights of the different assets constant over time. To keep these proportions constant, whenever assets values change, it is necessary to rebalance their relative weights, exposing this strategy to fees (transaction costs). Two strategies that were suggested in the past for cases that involve fees are rebalance the portfolio periodically and rebalance it in a partial way. In this paper, we study these two strategies in the presence of correlations and fees. We show that using periodic and partial rebalance strategies, it is possible to maintain a steady exponential growth while minimizing the losses due to fees. We also demonstrate how these redistribution strategies perform in a phenomenal way on real-world market data, despite the fact that not all assumptions of the model hold in these real-world systems. Our results have important implications for stochastic dynamics in general and to portfolio management in particular, as we show that there is a superior alternative to the common buy-and-hold strategy, even in the presence of correlations and fees.

Convergence dynamics and pseudo almost periodicity of a class of nonautonomous RFDEs with applications

NASA Astrophysics Data System (ADS)

Fan, Meng; Ye, Dan

2005-09-01

This paper studies the dynamics of a system of retarded functional differential equations (i.e., RF=Es), which generalize the Hopfield neural network models, the bidirectional associative memory neural networks, the hybrid network models of the cellular neural network type, and some population growth model. Sufficient criteria are established for the globally exponential stability and the existence and uniqueness of pseudo almost periodic solution. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle. The paper ends with some applications of the main results to some neural network models and population growth models and numerical simulations.

Photoluminescence study of MBE grown InGaN with intentional indium segregation

NASA Astrophysics Data System (ADS)

Cheung, Maurice C.; Namkoong, Gon; Chen, Fei; Furis, Madalina; Pudavar, Haridas E.; Cartwright, Alexander N.; Doolittle, W. Alan

2005-05-01

Proper control of MBE growth conditions has yielded an In0.13Ga0.87N thin film sample with emission consistent with In-segregation. The photoluminescence (PL) from this epilayer showed multiple emission components. Moreover, temperature and power dependent studies of the PL demonstrated that two of the components were excitonic in nature and consistent with indium phase separation. At 15 K, time resolved PL showed a non-exponential PL decay that was well fitted with the stretched exponential solution expected for disordered systems. Consistent with the assumed carrier hopping mechanism of this model, the effective lifetime, , and the stretched exponential parameter, , decrease with increasing emission energy. Finally, room temperature micro-PL using a confocal microscope showed spatial clustering of low energy emission.

Rapid growth of seed black holes in the early universe by supra-exponential accretion.

PubMed

Alexander, Tal; Natarajan, Priyamvada

2014-09-12

Mass accretion by black holes (BHs) is typically capped at the Eddington rate, when radiation's push balances gravity's pull. However, even exponential growth at the Eddington-limited e-folding time t(E) ~ few × 0.01 billion years is too slow to grow stellar-mass BH seeds into the supermassive luminous quasars that are observed when the universe is 1 billion years old. We propose a dynamical mechanism that can trigger supra-exponential accretion in the early universe, when a BH seed is bound in a star cluster fed by the ubiquitous dense cold gas flows. The high gas opacity traps the accretion radiation, while the low-mass BH's random motions suppress the formation of a slowly draining accretion disk. Supra-exponential growth can thus explain the puzzling emergence of supermassive BHs that power luminous quasars so soon after the Big Bang. Copyright © 2014, American Association for the Advancement of Science.

Particulate and Dissolved Organic Carbon Production by the Heterotrophic Nanoflagellate Pteridomonas danica Patterson and Fenchel.

PubMed

Pelegrí; Christaki; Dolan; Rassoulzadegan

1999-05-01

> Abstract We established a budget of organic carbon utilization of a starved heterotrophic nanoflagellate, Pteridomonas danica, incubated in batch cultures with Escherichia coli as model prey. The cultures were sampled periodically for biomass determinations and total organic carbon dynamics: total organic carbon, total organic carbon <1 µm, and dissolved organic carbon (DOC, <0.2 µm). During the 22 h incubation period, P. danica underwent biovolume variations of 3.2-fold. Gross growth efficiency was 22% and net growth efficiency 40%. P. danica respired 33% and egested 44% of the ingested E. coli carbon during lag and exponential growth phases. The form of the organic carbon egested varied. Of the total ingested carbon, 9% was egested in the form of DOC and occurred mainly during the exponential growth phase; 35% was egested in the form of particulate organic carbon (POC), ranging in size from 0.2 to 1 µm, and took place during the lag phase. P. danica could have reingested as much of 58% of this previously produced POC during the exponential growth phase as food scarcity increased. We concluded that POC egestion by flagellates could represent a significant source of submicrometric particles and colloidal organic matter. In addition, flagellate reingestion of egested POC could play a nonnegligible role in the microbial food web. Finally, the methodology reported in this study has proved to be a useful tool in the study of carbon metabolism in aquatic microorganisms.http://link.springer-ny.com/link/service/journals/00248/bibs/37n4p276.html

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 1; Analysis

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

Extensive slow-crack-growth (SCG) analysis was made using a primary exponential crack-velocity formulation under three widely used load configurations: constant stress rate, constant stress, and cyclic stress. Although the use of the exponential formulation in determining SCG parameters of a material requires somewhat inconvenient numerical procedures, the resulting solutions presented gave almost the same degree of simplicity in both data analysis and experiments as did the power-law formulation. However, the fact that the inert strength of a material should be known in advance to determine the corresponding SCG parameters was a major drawback of the exponential formulation as compared with the power-law formulation.

Small regulatory RNA-induced growth rate heterogeneity of Bacillus subtilis.

PubMed

Mars, Ruben A T; Nicolas, Pierre; Ciccolini, Mariano; Reilman, Ewoud; Reder, Alexander; Schaffer, Marc; Mäder, Ulrike; Völker, Uwe; van Dijl, Jan Maarten; Denham, Emma L

2015-03-01

Isogenic bacterial populations can consist of cells displaying heterogeneous physiological traits. Small regulatory RNAs (sRNAs) could affect this heterogeneity since they act by fine-tuning mRNA or protein levels to coordinate the appropriate cellular behavior. Here we show that the sRNA RnaC/S1022 from the Gram-positive bacterium Bacillus subtilis can suppress exponential growth by modulation of the transcriptional regulator AbrB. Specifically, the post-transcriptional abrB-RnaC/S1022 interaction allows B. subtilis to increase the cell-to-cell variation in AbrB protein levels, despite strong negative autoregulation of the abrB promoter. This behavior is consistent with existing mathematical models of sRNA action, thus suggesting that induction of protein expression noise could be a new general aspect of sRNA regulation. Importantly, we show that the sRNA-induced diversity in AbrB levels generates heterogeneity in growth rates during the exponential growth phase. Based on these findings, we hypothesize that the resulting subpopulations of fast- and slow-growing B. subtilis cells reflect a bet-hedging strategy for enhanced survival of unfavorable conditions.

Optimal savings and the value of population.

PubMed

Arrow, Kenneth J; Bensoussan, Alain; Feng, Qi; Sethi, Suresh P

2007-11-20

We study a model of economic growth in which an exogenously changing population enters in the objective function under total utilitarianism and into the state dynamics as the labor input to the production function. We consider an arbitrary population growth until it reaches a critical level (resp. saturation level) at which point it starts growing exponentially (resp. it stops growing altogether). This requires population as well as capital as state variables. By letting the population variable serve as the surrogate of time, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. The phase diagram consists of a transient curve that reaches the classical curve associated with a positive exponential growth at the time the population reaches the critical level. In the case of an asymptotic population saturation, we expect the transient curve to approach the equilibrium as the population approaches its saturation level. Finally, we characterize the approaches to the classical curve and to the equilibrium.

Optimal savings and the value of population

PubMed Central

Arrow, Kenneth J.; Bensoussan, Alain; Feng, Qi; Sethi, Suresh P.

2007-01-01

We study a model of economic growth in which an exogenously changing population enters in the objective function under total utilitarianism and into the state dynamics as the labor input to the production function. We consider an arbitrary population growth until it reaches a critical level (resp. saturation level) at which point it starts growing exponentially (resp. it stops growing altogether). This requires population as well as capital as state variables. By letting the population variable serve as the surrogate of time, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. The phase diagram consists of a transient curve that reaches the classical curve associated with a positive exponential growth at the time the population reaches the critical level. In the case of an asymptotic population saturation, we expect the transient curve to approach the equilibrium as the population approaches its saturation level. Finally, we characterize the approaches to the classical curve and to the equilibrium. PMID:17984059

Universality of accelerating change

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Shlesinger, Michael F.

2018-03-01

On large time scales the progress of human technology follows an exponential growth trend that is termed accelerating change. The exponential growth trend is commonly considered to be the amalgamated effect of consecutive technology revolutions - where the progress carried in by each technology revolution follows an S-curve, and where the aging of each technology revolution drives humanity to push for the next technology revolution. Thus, as a collective, mankind is the 'intelligent designer' of accelerating change. In this paper we establish that the exponential growth trend - and only this trend - emerges universally, on large time scales, from systems that combine together two elements: randomness and amalgamation. Hence, the universal generation of accelerating change can be attained by systems with no 'intelligent designer'.

Finite-time singularity signature of hyperinflation

NASA Astrophysics Data System (ADS)

Sornette, D.; Takayasu, H.; Zhou, W.-X.

2003-07-01

We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.

Modeling of Phenoxy Acid Herbicide Mineralization and Growth of Microbial Degraders in 15 Soils Monitored by Quantitative Real-Time PCR of the Functional tfdA Gene

PubMed Central

Bælum, Jacob; Prestat, Emmanuel; David, Maude M.; Strobel, Bjarne W.

2012-01-01

Mineralization potentials, rates, and kinetics of the three phenoxy acid (PA) herbicides, 2,4-dichlorophenoxyacetic acid (2,4-D), 4-chloro-2-methylphenoxyacetic acid (MCPA), and 2-(4-chloro-2-methylphenoxy)propanoic acid (MCPP), were investigated and compared in 15 soils collected from five continents. The mineralization patterns were fitted by zero/linear or exponential growth forms of the three-half-order models and by logarithmic (log), first-order, or zero-order kinetic models. Prior and subsequent to the mineralization event, tfdA genes were quantified using real-time PCR to estimate the genetic potential for degrading PA in the soils. In 25 of the 45 mineralization scenarios, ∼60% mineralization was observed within 118 days. Elevated concentrations of tfdA in the range 1 × 105 to 5 × 107 gene copies g−1 of soil were observed in soils where mineralization could be described by using growth-linked kinetic models. A clear trend was observed that the mineralization rates of the three PAs occurred in the order 2,4-D > MCPA > MCPP, and a correlation was observed between rapid mineralization and soils exposed to PA previously. Finally, for 2,4-D mineralization, all seven mineralization patterns which were best fitted by the exponential model yielded a higher tfdA gene potential after mineralization had occurred than the three mineralization patterns best fitted by the Lin model. PMID:22635998

Fine Grained Chaos in AdS2 Gravity

NASA Astrophysics Data System (ADS)

Haehl, Felix M.; Rozali, Moshe

2018-03-01

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^*. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^*(k)˜(k -1 )u^*. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Fine Grained Chaos in AdS_{2} Gravity.

PubMed

Haehl, Felix M; Rozali, Moshe

2018-03-23

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

A Simple Mechanical Experiment on Exponential Growth

ERIC Educational Resources Information Center

McGrew, Ralph

2015-01-01

With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…

Graphene growth process modeling: a physical-statistical approach

NASA Astrophysics Data System (ADS)

Wu, Jian; Huang, Qiang

2014-09-01

As a zero-band semiconductor, graphene is an attractive material for a wide variety of applications such as optoelectronics. Among various techniques developed for graphene synthesis, chemical vapor deposition on copper foils shows high potential for producing few-layer and large-area graphene. Since fabrication of high-quality graphene sheets requires the understanding of growth mechanisms, and methods of characterization and control of grain size of graphene flakes, analytical modeling of graphene growth process is therefore essential for controlled fabrication. The graphene growth process starts with randomly nucleated islands that gradually develop into complex shapes, grow in size, and eventually connect together to cover the copper foil. To model this complex process, we develop a physical-statistical approach under the assumption of self-similarity during graphene growth. The growth kinetics is uncovered by separating island shapes from area growth rate. We propose to characterize the area growth velocity using a confined exponential model, which not only has clear physical explanation, but also fits the real data well. For the shape modeling, we develop a parametric shape model which can be well explained by the angular-dependent growth rate. This work can provide useful information for the control and optimization of graphene growth process on Cu foil.

A field study on the dynamic uptake and transfer of heavy metals in Chinese cabbage and radish in weak alkaline soils.

PubMed

Ai, Shiwei; Guo, Rui; Liu, Bailin; Ren, Liang; Naeem, Sajid; Zhang, Wenya; Zhang, Yingmei

2016-10-01

Vegetables and crops can take up heavy metals when grown on polluted lands. The concentrations and dynamic uptake of heavy metals vary at different growth points for different vegetables. In order to assess the safe consumption of vegetables in weak alkaline farmlands, Chinese cabbage and radish were planted on the farmlands of Baiyin (polluted site) and Liujiaxia (relatively unpolluted site). Firstly, the growth processes of two vegetables were recorded. The growth curves of the two vegetables observed a slow growth at the beginning, an exponential growth period, and a plateau towards the end. Maximum concentrations of copper (Cu), zinc (Zn), lead (Pb), and cadmium (Cd) were presented at the slow growth period and showed a downtrend except the radish shoot. The concentrations of heavy metals (Cu, Zn, and Cd) in vegetables of Baiyin were higher than those of Liujiaxia. In the meanwhile, the uptake contents continued to increase during the growth or halted at maximum at a certain stage. The maximum uptake rates were found on the maturity except for the shoot of radish which took place at the exponential growth stages of root. The sigmoid model could simulate the dynamic processes of growth and heavy metals uptake of Chinese cabbage and radish. Conclusively, heavy metals have higher bioaccumulation tendency for roots in Chinese cabbage and for shoots in radish.

Analysis and IbM simulation of the stages in bacterial lag phase: basis for an updated definition.

PubMed

Prats, Clara; Giró, Antoni; Ferrer, Jordi; López, Daniel; Vives-Rego, Josep

2008-05-07

The lag phase is the initial phase of a culture that precedes exponential growth and occurs when the conditions of the culture medium differ from the pre-inoculation conditions. It is usually defined by means of cell density because the number of individuals remains approximately constant or slowly increases, and it is quantified with the lag parameter lambda. The lag phase has been studied through mathematical modelling and by means of specific experiments. In recent years, Individual-based Modelling (IbM) has provided helpful insights into lag phase studies. In this paper, the definition of lag phase is thoroughly examined. Evolution of the total biomass and the total number of bacteria during lag phase is tackled separately. The lag phase lasts until the culture reaches a maximum growth rate both in biomass and cell density. Once in the exponential phase, both rates are constant over time and equal to each other. Both evolutions are split into an initial phase and a transition phase, according to their growth rates. A population-level mathematical model is presented to describe the transitional phase in cell density. INDividual DIScrete SIMulation (INDISIM) is used to check the outcomes of this analysis. Simulations allow the separate study of the evolution of cell density and total biomass in a batch culture, they provide a depiction of different observed cases in lag evolution at the individual-cell level, and are used to test the population-level model. The results show that the geometrical lag parameter lambda is not appropriate as a universal definition for the lag phase. Moreover, the lag phase cannot be characterized by a single parameter. For the studied cases, the lag phases of both the total biomass and the population are required to fully characterize the evolution of bacterial cultures. The results presented prove once more that the lag phase is a complex process that requires a more complete definition. This will be possible only after the phenomena governing the population dynamics at an individual level of description, and occurring during the lag and exponential growth phases, are well understood.

The Western Africa ebola virus disease epidemic exhibits both global exponential and local polynomial growth rates.

PubMed

Chowell, Gerardo; Viboud, Cécile; Hyman, James M; Simonsen, Lone

2015-01-21

While many infectious disease epidemics are initially characterized by an exponential growth in time, we show that district-level Ebola virus disease (EVD) outbreaks in West Africa follow slower polynomial-based growth kinetics over several generations of the disease. We analyzed epidemic growth patterns at three different spatial scales (regional, national, and subnational) of the Ebola virus disease epidemic in Guinea, Sierra Leone and Liberia by compiling publicly available weekly time series of reported EVD case numbers from the patient database available from the World Health Organization website for the period 05-Jan to 17-Dec 2014. We found significant differences in the growth patterns of EVD cases at the scale of the country, district, and other subnational administrative divisions. The national cumulative curves of EVD cases in Guinea, Sierra Leone, and Liberia show periods of approximate exponential growth. In contrast, local epidemics are asynchronous and exhibit slow growth patterns during 3 or more EVD generations, which can be better approximated by a polynomial than an exponential function. The slower than expected growth pattern of local EVD outbreaks could result from a variety of factors, including behavior changes, success of control interventions, or intrinsic features of the disease such as a high level of clustering. Quantifying the contribution of each of these factors could help refine estimates of final epidemic size and the relative impact of different mitigation efforts in current and future EVD outbreaks.

The Western Africa Ebola Virus Disease Epidemic Exhibits Both Global Exponential and Local Polynomial Growth Rates

PubMed Central

Chowell, Gerardo; Viboud, Cécile; Hyman, James M; Simonsen, Lone

2015-01-01

Background: While many infectious disease epidemics are initially characterized by an exponential growth in time, we show that district-level Ebola virus disease (EVD) outbreaks in West Africa follow slower polynomial-based growth kinetics over several generations of the disease. Methods: We analyzed epidemic growth patterns at three different spatial scales (regional, national, and subnational) of the Ebola virus disease epidemic in Guinea, Sierra Leone and Liberia by compiling publicly available weekly time series of reported EVD case numbers from the patient database available from the World Health Organization website for the period 05-Jan to 17-Dec 2014. Results: We found significant differences in the growth patterns of EVD cases at the scale of the country, district, and other subnational administrative divisions. The national cumulative curves of EVD cases in Guinea, Sierra Leone, and Liberia show periods of approximate exponential growth. In contrast, local epidemics are asynchronous and exhibit slow growth patterns during 3 or more EVD generations, which can be better approximated by a polynomial than an exponential function. Conclusions: The slower than expected growth pattern of local EVD outbreaks could result from a variety of factors, including behavior changes, success of control interventions, or intrinsic features of the disease such as a high level of clustering. Quantifying the contribution of each of these factors could help refine estimates of final epidemic size and the relative impact of different mitigation efforts in current and future EVD outbreaks. PMID:25685633

Biospheric energization and stability

NASA Astrophysics Data System (ADS)

Budding, E.; Ozel, M. E.; Gunduz, G.

2013-09-01

We utilize the physical properties of a hypothetical molecular schema giving rise to an autocatalytic biosphere. A key concept is the driving of terrestrial life as a parametric oscillation: i.e. that the biosphere behaves fundamentally as an oscillatory system into which solar energy is diurnally deposited. The schema, containing 'A, B and C' type components acting together in a 'bottom-up' driving mechanism, underlies all biospheric superstructure. Surviving modes of the oscillation are consistent with Darwinian organization, or hierarchical structures appearing to have top-down propagation through the growth of cellular replication. The model was detailed by Budding et al (2012), where experimental support from the work of Powner et al (2009) is presented, as well as suggestions on supportive fossil evidence. Although the growth in total energization is very slow in this model, it is important to notice its exponential character, suggestive of potential instability. The model is applicable to generally expectable processes on planets, including zonal segregation, complexity growth and Haeckel's biogenic principle within surviving life-forms. Fermi's exobiological paradox can be resolved in terms of the exponential growth and low L solutions of Drake's equation. Feasible values for the particular growth of selected species (the human one in herelevent terrestrial case) allow for L to be less than a few  100 y, recalling Rees' (2004) 'final century' discussion. This arises when the species' disposable energization attains a value comparable to that of the total available daily driving energy. At that point, accidental, or stochastic disturbances of this species' energy ("error") can significantly disrupt the daily driving mechanism.

Comparing Exponential and Exponentiated Models of Drug Demand in Cocaine Users

PubMed Central

Strickland, Justin C.; Lile, Joshua A.; Rush, Craig R.; Stoops, William W.

2016-01-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model, but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use), whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values impact demand parameters and their association with drug-use outcomes when using the exponential model, but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency, in addition to demonstrating construct validity and generalizability. PMID:27929347

Comparing exponential and exponentiated models of drug demand in cocaine users.

PubMed

Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W

2016-12-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

Epidemics, Exponential Functions, and Modeling

ERIC Educational Resources Information Center

Bush, Sarah B.; Gibbons, Katie; Karp, Karen S.; Dillon, Fred

2015-01-01

The phenomenon of outbreaks of dangerous diseases is both intriguing to students and of mathematical significance, which is exactly why the authors engaged eighth graders in an introductory activity on the growth that occurs as an epidemic spreads. Various contexts can set the stage for such an exploration. Reading adolescent literature like…

Technology Acceptance in Social Work Education: Implications for the Field Practicum

ERIC Educational Resources Information Center

Colvin, Alex Don; Bullock, Angela N.

2014-01-01

The exponential growth and sophistication of new information and computer technology (ICT) have greatly influenced human interactions and provided new metaphors for understanding the world. The acceptance and integration of ICT into social work field education are examined here using the technological acceptance model. This article also explores…

Simplifying the complexity of resistance heterogeneity in metastasis

PubMed Central

Lavi, Orit; Greene, James M.; Levy, Doron; Gottesman, Michael M.

2014-01-01

The main goal of treatment regimens for metastasis is to control growth rates, not eradicate all cancer cells. Mathematical models offer methodologies that incorporate high-throughput data with dynamic effects on net growth. The ideal approach would simplify, but not over-simplify, a complex problem into meaningful and manageable estimators that predict a patient’s response to specific treatments. Here, we explore three fundamental approaches with different assumptions concerning resistance mechanisms, in which the cells are categorized into either discrete compartments or described by a continuous range of resistance levels. We argue in favor of modeling resistance as a continuum and demonstrate how integrating cellular growth rates, density-dependent versus exponential growth, and intratumoral heterogeneity improves predictions concerning the resistance heterogeneity of metastases. PMID:24491979

Network patterns in exponentially growing two-dimensional biofilms

NASA Astrophysics Data System (ADS)

Zachreson, Cameron; Yap, Xinhui; Gloag, Erin S.; Shimoni, Raz; Whitchurch, Cynthia B.; Toth, Milos

2017-10-01

Anisotropic collective patterns occur frequently in the morphogenesis of two-dimensional biofilms. These patterns are often attributed to growth regulation mechanisms and differentiation based on gradients of diffusing nutrients and signaling molecules. Here, we employ a model of bacterial growth dynamics to show that even in the absence of growth regulation or differentiation, confinement by an enclosing medium such as agar can itself lead to stable pattern formation over time scales that are employed in experiments. The underlying mechanism relies on path formation through physical deformation of the enclosing environment.

Exponential Growth and the Shifting Global Center of Gravity of Science Production, 1900-2011

ERIC Educational Resources Information Center

Zhang, Liang; Powell, Justin J. W.; Baker, David P.

2015-01-01

Long historical trends in scientific discovery led mid-20th century scientometricians to mark the advent of "big science"--extensive science production--and predicted that over the next few decades, the exponential growth would slow, resulting in lower rates of increase in production at the upper limit of a logistic curve. They were…

For how long can we predict the weather? - Insights into atmospheric predictability from global convection-allowing simulations

NASA Astrophysics Data System (ADS)

Judt, Falko

2017-04-01

A tremendous increase in computing power has facilitated the advent of global convection-resolving numerical weather prediction (NWP) models. Although this technological breakthrough allows for the seamless prediction of weather from local to global scales, the predictability of multiscale weather phenomena in these models is not very well known. To address this issue, we conducted a global high-resolution (4-km) predictability experiment using the Model for Prediction Across Scales (MPAS), a state-of-the-art global NWP model developed at the National Center for Atmospheric Research. The goals of this experiment are to investigate error growth from convective to planetary scales and to quantify the intrinsic, scale-dependent predictability limits of atmospheric motions. The globally uniform resolution of 4 km allows for the explicit treatment of organized deep moist convection, alleviating grave limitations of previous predictability studies that either used high-resolution limited-area models or global simulations with coarser grids and cumulus parameterization. Error growth is analyzed within the context of an "identical twin" experiment setup: the error is defined as the difference between a 20-day long "nature run" and a simulation that was perturbed with small-amplitude noise, but is otherwise identical. It is found that in convectively active regions, errors grow by several orders of magnitude within the first 24 h ("super-exponential growth"). The errors then spread to larger scales and begin a phase of exponential growth after 2-3 days when contaminating the baroclinic zones. After 16 days, the globally averaged error saturates—suggesting that the intrinsic limit of atmospheric predictability (in a general sense) is about two weeks, which is in line with earlier estimates. However, error growth rates differ between the tropics and mid-latitudes as well as between the troposphere and stratosphere, highlighting that atmospheric predictability is a complex problem. The comparatively slower error growth in the tropics and in the stratosphere indicates that certain weather phenomena could potentially have longer predictability than currently thought.

A growth model for directed complex networks with power-law shape in the out-degree distribution

PubMed Central

Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.

2015-01-01

Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141

Measurement of cellular copper levels in Bacillus megaterium during exponential growth and sporulation.

PubMed

Krueger, W B; Kolodziej, B J

1976-01-01

Both atomic absorption spectrophotometry (AAS) and neutron activation analysis have been utilized to determine cellular Cu levels in Bacillus megaterium ATCC 19213. Both methods were selected for their sensitivity to detection of nanogram quantities of Cu. Data from both methods demonstrated identical patterms of Cu uptake during exponenetial growth and sporulation. Late exponential phase cells contained less Cu than postexponential t2 cells while t5 cells contained amounts equivalent to exponential cells. The t11 phase-bright forespore containing cells had a higher Cu content than those of earlier time periods, and the free spores had the highest Cu content. Analysis of the culture medium by AAS corroborated these data by showing concomitant Cu uptake during exponential growth and into t2 postexponential phase of sporulation. From t2 to t4, Cu egressed from the cells followed by a secondary uptake during the maturation of phase-dark forespores into phase-bright forespores (t6--t9).

Fractal dimension and universality in avascular tumor growth

NASA Astrophysics Data System (ADS)

Ribeiro, Fabiano L.; dos Santos, Renato Vieira; Mata, Angélica S.

2017-04-01

For years, the comprehension of the tumor growth process has been intriguing scientists. New research has been constantly required to better understand the complexity of this phenomenon. In this paper, we propose a mathematical model that describes the properties, already known empirically, of avascular tumor growth. We present, from an individual-level (microscopic) framework, an explanation of some phenomenological (macroscopic) aspects of tumors, such as their spatial form and the way they develop. Our approach is based on competitive interaction between the cells. This simple rule makes the model able to reproduce evidence observed in real tumors, such as exponential growth in their early stage followed by power-law growth. The model also reproduces (i) the fractal-space distribution of tumor cells and (ii) the universal growth behavior observed in both animals and tumors. Our analyses suggest that the universal similarity between tumor and animal growth comes from the fact that both can be described by the same dynamic equation—the Bertalanffy-Richards model—even if they do not necessarily share the same biological properties.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

Time Course of Visual Extrapolation Accuracy

DTIC Science & Technology

1995-09-01

The pond and duckweed problem: Three experiments on the misperception of exponential growth . Acta Psychologica 43, 239-251. Wiener, E.L., 1962...random variation in tracker velocity. Both models predicted changes in hit and false alarm rates well, except in a condition where response asymmetries...systematic velocity error in tracking, only random variation in tracker velocity. Both models predicted changes in hit and false alarm rates well

Science and Facebook: The same popularity law!

PubMed

Néda, Zoltán; Varga, Levente; Biró, Tamás S

2017-01-01

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.

Science and Facebook: The same popularity law!

PubMed Central

Varga, Levente; Biró, Tamás S.

2017-01-01

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of “shares” for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4. PMID:28678796

Influences of growth parameters on the reaction pathway during GaN synthesis

NASA Astrophysics Data System (ADS)

Zhang, Zhi; Liu, Zhongyi; Fang, Haisheng

2018-01-01

Gallium nitride (GaN) film growth is a complicated physical and chemical process including fluid flow, heat transfer, species transport and chemical reaction. Study of the reaction mechanism, i.e., the reaction pathway, is important for optimizing the growth process in the actual manufacture. In the paper, the growth pathway of GaN in a closed-coupled showerhead metal-organic chemical vapor deposition (CCS-MOCVD) reactor is investigated in detail using computational fluid dynamics (CFD). Influences of the process parameters, such as the chamber pressure, the inlet temperature, the susceptor temperature and the pre-exponential factor, on the reaction pathway are examined. The results show that increases of the chamber pressure or the inlet temperature, as well as reductions of the susceptor temperature or the pre-exponential factor lead to the adduct route dominating the growth. The deposition rate contributed by the decomposition route, however, can be enhanced dramatically by increasing the inlet temperature, the susceptor temperature and the pre-exponential factor.

Growth models of Rhizophora mangle L. seedlings in tropical southwestern Atlantic

NASA Astrophysics Data System (ADS)

Lima, Karen Otoni de Oliveira; Tognella, Mônica Maria Pereira; Cunha, Simone Rabelo; Andrade, Humber Agrelli de

2018-07-01

The present study selected and compared regression models that best describe the growth curves of Rhizophora mangle seedlings based on the height (cm) and time (days) variables. The Linear, Exponential, Power Law, Monomolecular, Logistic, and Gompertz models were adjusted with non-linear formulations and minimization of the sum of the squares of the residues. The Akaike Information Criterion was used to select the best model for each seedling. After this selection, the determination coefficient, which evaluates how well a model describes height variation as a time function, was inspected. Differing from the classic population ecology studies, the Monomolecular, Three-parameter Logistic, and Gompertz models presented the best performance in describing growth, suggesting they are the most adequate options for long-term studies. The different growth curves reflect the complexity of stem growth at the seedling stage for R. mangle. The analysis of the joint distribution of the parameters initial height, growth rate, and, asymptotic size allowed the study of the species ecological attributes and to observe its intraspecific variability in each model. Our results provide a basis for interpretation of the dynamics of seedlings growth during their establishment in a mature forest, as well as its regeneration processes.

Time-resolved photoluminescence investigation of (Mg, Zn) O alloy growth on a non-polar plane

NASA Astrophysics Data System (ADS)

Mohammed Ali, Mohammed Jassim; Chauveau, J. M.; Bretagnon, T.

2018-04-01

Excitons recombination dynamics in ZnMgO alloy have been studied by time-resolved photoluminescence according to temperature. At low temperature, localisation effects of the exciton are found to play a significant role. The photoluminescence (PL) decays are bi-exponential. The short lifetime has a constant value, whereas the long lifetime shows a dependency with temperature. For temperature higher than 100 K the declines show a mono-exponential decay. The PL declines are dominated by non-radiative process at temperatures above 150 K. The PL lifetime dependancy with temperature is analysed using a model including localisation effects and non-radiative recombinations.

Impact of computational structure-based methods on drug discovery.

PubMed

Reynolds, Charles H

2014-01-01

Structure-based drug design has become an indispensible tool in drug discovery. The emergence of structure-based design is due to gains in structural biology that have provided exponential growth in the number of protein crystal structures, new computational algorithms and approaches for modeling protein-ligand interactions, and the tremendous growth of raw computer power in the last 30 years. Computer modeling and simulation have made major contributions to the discovery of many groundbreaking drugs in recent years. Examples are presented that highlight the evolution of computational structure-based design methodology, and the impact of that methodology on drug discovery.

The use of models to predict potential contamination aboard orbital vehicles

NASA Technical Reports Server (NTRS)

Boraas, Martin E.; Seale, Dianne B.

1989-01-01

A model of fungal growth on air-exposed, nonnutritive solid surfaces, developed for utilization aboard orbital vehicles is presented. A unique feature of this testable model is that the development of a fungal mycelium can facilitate its own growth by condensation of water vapor from its environment directly onto fungal hyphae. The fungal growth rate is limited by the rate of supply of volatile nutrients and fungal biomass is limited by either the supply of nonvolatile nutrients or by metabolic loss processes. The model discussed is structurally simple, but its dynamics can be quite complex. Biofilm accumulation can vary from a simple linear increase to sustained exponential growth, depending on the values of the environmental variable and model parameters. The results of the model are consistent with data from aquatic biofilm studies, insofar as the two types of systems are comparable. It is shown that the model presented is experimentally testable and provides a platform for the interpretation of observational data that may be directly relevant to the question of growth of organisms aboard the proposed Space Station.

Impact of Engaging Teaching Model (ETM) on Students' Attendance

ERIC Educational Resources Information Center

Bukoye, Oyegoke Teslim; Shegunshi, Anjali

2016-01-01

Non-attendance in Higher Education is not a new concept. In recent years with the exponential growth in digital learning, physical attendance has become a more complex issue. Educators are continually advocating an engaging teaching approach for students as a means of enhancing learning. This on-going study focuses on exploring the existing issues…

A Model of Online Education Effecting Holistic Student Formation Appropriate for Global Cross-Cultural Contexts

ERIC Educational Resources Information Center

Hannaford, Ronald Geoffrey

2012-01-01

Factors associated with globalization and unprecedented technological advancement have facilitated the opportunity to take education beyond the boundaries of the physical classroom and geographical borders to serve a global context. While this exponential growth has resulted in more convenient access to learning, increased possibilities for…

Verbal Knowledge, Working Memory, and Processing Speed as Predictors of Verbal Learning in Older Adults

ERIC Educational Resources Information Center

Rast, Philippe

2011-01-01

The present study aimed at modeling individual differences in a verbal learning task by means of a latent structured growth curve approach based on an exponential function that yielded 3 parameters: initial recall, learning rate, and asymptotic performance. Three cognitive variables--speed of information processing, verbal knowledge, working…

A generalized preferential attachment model for business firms growth rates. II. Mathematical treatment

NASA Astrophysics Data System (ADS)

Buldyrev, S. V.; Pammolli, F.; Riccaboni, M.; Yamasaki, K.; Fu, D.-F.; Matia, K.; Stanley, H. E.

2007-05-01

We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent ϕ = 2+b/(1-b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent ζ = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.

Growth of alveoli during postnatal development in humans based on stereological estimation.

PubMed

Herring, Matt J; Putney, Lei F; Wyatt, Gregory; Finkbeiner, Walter E; Hyde, Dallas M

2014-08-15

Alveolarization in humans and nonhuman primates begins during prenatal development. Advances in stereological counting techniques allow accurate assessment of alveolar number; however, these techniques have not been applied to the developing human lung. Based on the recent American Thoracic Society guidelines for stereology, lungs from human autopsies, ages 2 mo to 15 yr, were fractionated and isometric uniform randomly sampled to count the number of alveoli. The number of alveoli was compared with age, weight, and height as well as growth between right and left lungs. The number of alveoli in the human lung increased exponentially during the first 2 yr of life but continued to increase albeit at a reduced rate through adolescence. Alveolar numbers also correlated with the indirect radial alveolar count technique. Growth curves for human alveolarization were compared using historical data of nonhuman primates and rats. The alveolar growth rate in nonhuman primates was nearly identical to the human growth curve. Rats were significantly different, showing a more pronounced exponential growth during the first 20 days of life. This evidence indicates that the human lung may be more plastic than originally thought, with alveolarization occurring well into adolescence. The first 20 days of life in rats implies a growth curve that may relate more to prenatal growth in humans. The data suggest that nonhuman primates are a better laboratory model for studies of human postnatal lung growth than rats. Copyright © 2014 the American Physiological Society.

Internal Membrane Control in Azotobacter vinelandii

PubMed Central

Pate, Jack L.; Shah, Vinod K.; Brill, Winston J.

1973-01-01

Azotobacter vinelandii was grown on N2, NH4+, or NO3−, and an internal membrane network was observed by electron microscopy of thin sections of cells. Cells obtained in early exponential growth contained less internal membrane than did cells from cultures in late exponential growth. It seems likely that O2 has a role in regulating the amount of internal membrane structure. Images PMID:4123239

Stand Competition Determines How Different Tree Species Will Cope with a Warming Climate

PubMed Central

Fernández-de-Uña, Laura; Cañellas, Isabel; Gea-Izquierdo, Guillermo

2015-01-01

Plant-plant interactions influence how forests cope with climate and contribute to modulate species response to future climate scenarios. We analysed the functional relationships between growth, climate and competition for Pinus sylvestris, Quercus pyrenaica and Quercus faginea to investigate how stand competition modifies forest sensitivity to climate and simulated how annual growth rates of these species with different drought tolerance would change throughout the 21st century. Dendroecological data from stands subjected to thinning were modelled using a novel multiplicative nonlinear approach to overcome biases related to the general assumption of a linear relationship between covariates and to better mimic the biological relationships involved. Growth always decreased exponentially with increasing competition, which explained more growth variability than climate in Q. faginea and P. sylvestris. The effect of precipitation was asymptotic in all cases, while the relationship between growth and temperature reached an optimum after which growth declined with warmer temperatures. Our growth projections indicate that the less drought-tolerant P. sylvestris would be more negatively affected by climate change than the studied sub-Mediterranean oaks. Q. faginea and P. sylvestris mean growth would decrease under all the climate change scenarios assessed. However, P. sylvestris growth would decline regardless of the competition level, whereas this decrease would be offset by reduced competition in Q. faginea. Conversely, Q. pyrenaica growth would remain similar to current rates, except for the warmest scenario. Our models shed light on the nature of the species-specific interaction between climate and competition and yield important implications for management. Assuming that individual growth is directly related to tree performance, trees under low competition would better withstand the warmer conditions predicted under climate change scenarios but in a variable manner depending on the species. Thinning following an exponential rule may be desirable to ensure long-term conservation of high-density Mediterranean woodlands, particularly in drought-limited sites. PMID:25826446

The mechanism of double-exponential growth in hyper-inflation

NASA Astrophysics Data System (ADS)

Mizuno, T.; Takayasu, M.; Takayasu, H.

2002-05-01

Analyzing historical data of price indices, we find an extraordinary growth phenomenon in several examples of hyper-inflation in which, price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte Carlo renormalization group method, to the price dynamics. Starting from a microscopic stochastic equation describing dealers’ actions in open markets, we obtain a macroscopic noiseless equation of price consistent with the observation. The effect of auto-catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double-exponential behavior.

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 2; Constant Stress Rate Experiments

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress rate and preload testing at ambient and elevated temperatures. The data fit to the relation of strength versus the log of the stress rate was very reasonable for most of the materials. Also, the preloading technique was determined equally applicable to the case of slow-crack-growth (SCG) parameter n greater than 30 for both the power-law and exponential formulations. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important SCG parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

A new look at atmospheric carbon dioxide

NASA Astrophysics Data System (ADS)

Hofmann, David J.; Butler, James H.; Tans, Pieter P.

Carbon dioxide is increasing in the atmosphere and is of considerable concern in global climate change because of its greenhouse gas warming potential. The rate of increase has accelerated since measurements began at Mauna Loa Observatory in 1958 where carbon dioxide increased from less than 1 part per million per year (ppm yr -1) prior to 1970 to more than 2 ppm yr -1 in recent years. Here we show that the anthropogenic component (atmospheric value reduced by the pre-industrial value of 280 ppm) of atmospheric carbon dioxide has been increasing exponentially with a doubling time of about 30 years since the beginning of the industrial revolution (˜1800). Even during the 1970s, when fossil fuel emissions dropped sharply in response to the "oil crisis" of 1973, the anthropogenic atmospheric carbon dioxide level continued increasing exponentially at Mauna Loa Observatory. Since the growth rate (time derivative) of an exponential has the same characteristic lifetime as the function itself, the carbon dioxide growth rate is also doubling at the same rate. This explains the observation that the linear growth rate of carbon dioxide has more than doubled in the past 40 years. The accelerating growth rate is simply the outcome of exponential growth in carbon dioxide with a nearly constant doubling time of about 30 years (about 2%/yr) and appears to have tracked human population since the pre-industrial era.

Biased phylodynamic inferences from analysing clusters of viral sequences

PubMed Central

Xiang, Fei; Frost, Simon D. W.

2017-01-01

Abstract Phylogenetic methods are being increasingly used to help understand the transmission dynamics of measurably evolving viruses, including HIV. Clusters of highly similar sequences are often observed, which appear to follow a ‘power law’ behaviour, with a small number of very large clusters. These clusters may help to identify subpopulations in an epidemic, and inform where intervention strategies should be implemented. However, clustering of samples does not necessarily imply the presence of a subpopulation with high transmission rates, as groups of closely related viruses can also occur due to non-epidemiological effects such as over-sampling. It is important to ensure that observed phylogenetic clustering reflects true heterogeneity in the transmitting population, and is not being driven by non-epidemiological effects. We qualify the effect of using a falsely identified ‘transmission cluster’ of sequences to estimate phylodynamic parameters including the effective population size and exponential growth rate under several demographic scenarios. Our simulation studies show that taking the maximum size cluster to re-estimate parameters from trees simulated under a randomly mixing, constant population size coalescent process systematically underestimates the overall effective population size. In addition, the transmission cluster wrongly resembles an exponential or logistic growth model 99% of the time. We also illustrate the consequences of false clusters in exponentially growing coalescent and birth-death trees, where again, the growth rate is skewed upwards. This has clear implications for identifying clusters in large viral databases, where a false cluster could result in wasted intervention resources. PMID:28852573

The Exponential Function--Part VIII

ERIC Educational Resources Information Center

Bartlett, Albert A.

1978-01-01

Presents part eight of a continuing series on the exponential function in which, given the current population of the Earth and assuming a constant growth rate of 1.9 percent backward looks at world population are made. (SL)

Scaling behaviour in the growth of companies

NASA Astrophysics Data System (ADS)

Stanley, Michael H. R.; Amaral, Luís A. N.; Buldyrev, Sergey V.; Havlin, Shlomo; Leschhorn, Heiko; Maass, Philipp; Salinger, Michael A.; Stanley, H. Eugene

1996-02-01

A SUCCESSFUL theory of corporate growth should include both the external and internal factors that affect the growth of a company1-18. Whereas traditional models emphasize production-related influences such as investment in physical capital and in research and development18, recent models10-20 recognize the equal importance of organizational infrastructure. Unfortunately, no exhaustive empirical account of the growth of companies exists by which these models can be tested. Here we present a broad, phenomenological picture of the dependence of growth on company size, derived from data for all publicly traded US manufacturing companies between 1975 and 1991. We find that, for firms with similar sales, the distribution of annual (logarithmic) growth rates has an exponential form; the spread in the distribution of rates decreases with increasing sales as a power law over seven orders of magnitude. A model wherein the probability of a company's growth depends on its past as well as present sales accounts for the former observation. As the latter observation applies to companies that manufacture products of all kinds, organizational structures common to all firms might well be stronger determinants of growth than production-related factors, which differ for companies producing different goods.

Population mixture model for nonlinear telomere dynamics

NASA Astrophysics Data System (ADS)

Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl

2008-12-01

Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.

Macromolecular Rate Theory (MMRT) Provides a Thermodynamics Rationale to Underpin the Convergent Temperature Response in Plant Leaf Respiration

NASA Astrophysics Data System (ADS)

Liang, L. L.; Arcus, V. L.; Heskel, M.; O'Sullivan, O. S.; Weerasinghe, L. K.; Creek, D.; Egerton, J. J. G.; Tjoelker, M. G.; Atkin, O. K.; Schipper, L. A.

2017-12-01

Temperature is a crucial factor in determining the rates of ecosystem processes such as leaf respiration (R) - the flux of plant respired carbon dioxide (CO2) from leaves to the atmosphere. Generally, respiration rate increases exponentially with temperature as modelled by the Arrhenius equation, but a recent study (Heskel et al., 2016) showed a universally convergent temperature response of R using an empirical exponential/polynomial model whereby the exponent in the Arrhenius model is replaced by a quadratic function of temperature. The exponential/polynomial model has been used elsewhere to describe shoot respiration and plant respiration. What are the principles that underlie these empirical observations? Here, we demonstrate that macromolecular rate theory (MMRT), based on transition state theory for chemical kinetics, is equivalent to the exponential/polynomial model. We re-analyse the data from Heskel et al. 2016 using MMRT to show this equivalence and thus, provide an explanation based on thermodynamics, for the convergent temperature response of R. Using statistical tools, we also show the equivalent explanatory power of MMRT when compared to the exponential/polynomial model and the superiority of both of these models over the Arrhenius function. Three meaningful parameters emerge from MMRT analysis: the temperature at which the rate of respiration is maximum (the so called optimum temperature, Topt), the temperature at which the respiration rate is most sensitive to changes in temperature (the inflection temperature, Tinf) and the overall curvature of the log(rate) versus temperature plot (the so called change in heat capacity for the system, ). The latter term originates from the change in heat capacity between an enzyme-substrate complex and an enzyme transition state complex in enzyme-catalysed metabolic reactions. From MMRT, we find the average Topt and Tinf of R are 67.0±1.2 °C and 41.4±0.7 °C across global sites. The average curvature (average negative) is -1.2±0.1 kJ.mol-1K-1. MMRT extends the classic transition state theory to enzyme-catalysed reactions and scales up to more complex processes including micro-organism growth rates and ecosystem processes.

Simulating Population Growth.

ERIC Educational Resources Information Center

Byington, Scott

1997-01-01

Presents a strategy to help students grasp the important implications of population growth. Involves an interactive demonstration that allows students to experience exponential and logistic population growth followed by a discussion of the implications of population-growth principles. (JRH)

Cluster-cluster aggregation with particle replication and chemotaxy: a simple model for the growth of animal cells in culture

NASA Astrophysics Data System (ADS)

Alves, S. G.; Martins, M. L.

2010-09-01

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and in vitro drug testing. In the present paper, a cluster-cluster aggregation model with stochastic particle replication and chemotactically driven motility is investigated as a model for the growth of animal cells in culture. The focus is on the scaling laws governing the aggregation kinetics. Our simulations reveal that in the absence of chemotaxy the mean cluster size and the total number of clusters scale in time as stretched exponentials dependent on the particle replication rate. Also, the dynamical cluster size distribution functions are represented by a scaling relation in which the scaling function involves a stretched exponential of the time. The introduction of chemoattraction among the particles leads to distribution functions decaying as power laws with exponents that decrease in time. The fractal dimensions and size distributions of the simulated clusters are qualitatively discussed in terms of those determined experimentally for several normal and tumoral cell lines growing in culture. It is shown that particle replication and chemotaxy account for the simplest cluster size distributions of cellular aggregates observed in culture.

Network structures sustained by internal links and distributed lifetime of old nodes in stationary state of number of nodes

NASA Astrophysics Data System (ADS)

Ikeda, Nobutoshi

2017-12-01

In network models that take into account growth properties, deletion of old nodes has a serious impact on degree distributions, because old nodes tend to become hub nodes. In this study, we aim to provide a simple explanation for why hubs can exist even in conditions where the number of nodes is stationary due to the deletion of old nodes. We show that an exponential increase in the degree of nodes is a natural consequence of the balance between the deletion and addition of nodes as long as a preferential attachment mechanism holds. As a result, the largest degree is determined by the magnitude relationship between the time scale of the exponential growth of degrees and lifetime of old nodes. The degree distribution exhibits a power-law form ˜ k -γ with exponent γ = 1 when the lifetime of nodes is constant. However, various values of γ can be realized by introducing distributed lifetime of nodes.

The release of alginate lyase from growing Pseudomonas syringae pathovar phaseolicola

NASA Technical Reports Server (NTRS)

Ott, C. M.; Day, D. F.; Koenig, D. W.; Pierson, D. L.

2001-01-01

Pseudomonas syringae pathovar phaseolicola, which produces alginate during stationary growth phase, displayed elevated extracellular alginate lyase activity during both mid-exponential and late-stationary growth phases of batch growth. Intracellular activity remained below 22% of the total activity during exponential growth, suggesting that alginate lyase has an extracellular function for this organism. Extracellular enzyme activity in continuous cultures, grown in either nutrient broth or glucose-simple salts medium, peaked at 60% of the washout rate, although nutrient broth-grown cultures displayed more than twice the activity per gram of cell mass. These results imply that growth rate, nutritional composition, or both initiate a release of alginate lyase from viable P. syringae pv. phaseolicola, which could modify its entrapping biofilm.

The Ecology Model of Learning: Evaluating Digital Media Applications (DMAs) Using Established Ecological Subsystems of Learning

ERIC Educational Resources Information Center

Folkestad, James E.; Banning, James

2010-01-01

Digital media applications (DMAs) have emerged in abundance over the last ten years. Enabled by exponential growth in computing power and inexpensive data storage, these applications are easy to use and inexpensive (often free) to own. DMAs not only allow users to produce digital content efficiently they allow users to exploit the connective power…

Revisiting the environmental Kuznets curve hypothesis in a tourism development context.

PubMed

de Vita, Glauco; Katircioglu, Salih; Altinay, Levent; Fethi, Sami; Mercan, Mehmet

2015-11-01

This study investigates empirically an extended version of the Environmental Kuznets Curve model that controls for tourism development. We find that international tourist arrivals into Turkey alongside income, squared income and energy consumption, cointegrate with CO2 emissions. Tourist arrivals, growth, and energy consumption exert a positive and significant impact on CO2 emissions in the long-run. Our results provide empirical support to EKC hypothesis showing that at exponential levels of growth, CO2 emissions decline. The findings suggest that despite the environmental degradation stemming from tourism development, policies aimed at environmental protection should not be pursued at the expense of tourism-led growth.

Bounded energy states in homogeneous turbulent shear flow: An alternative view

NASA Technical Reports Server (NTRS)

Bernard, Peter S.; Speziale, Charles G.

1990-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.

Bacterial Associates Modify Growth Dynamics of the Dinoflagellate Gymnodinium catenatum

PubMed Central

Bolch, Christopher J. S.; Bejoy, Thaila A.; Green, David H.

2017-01-01

Marine phytoplankton cells grow in close association with a complex microbial associate community known to affect the growth, behavior, and physiology of the algal host. The relative scale and importance these effects compared to other major factors governing algal cell growth remain unclear. Using algal-bacteria co-culture models based on the toxic dinoflagellate Gymnodinium catenatum, we tested the hypothesis that associate bacteria exert an independent effect on host algal cell growth. Batch co-cultures of G. catenatum were grown under identical environmental conditions with simplified bacterial communities composed of one-, two-, or three-bacterial associates. Modification of the associate community membership and complexity induced up to four-fold changes in dinoflagellate growth rate, equivalent to the effect of a 5°C change in temperature or an almost six-fold change in light intensity (20–115 moles photons PAR m-2 s-1). Almost three-fold changes in both stationary phase cell concentration and death rate were also observed. Co-culture with Roseobacter sp. DG874 reduced dinoflagellate exponential growth rate and led to a more rapid death rate compared with mixed associate community controls or co-culture with either Marinobacter sp. DG879, Alcanivorax sp. DG881. In contrast, associate bacteria concentration was positively correlated with dinoflagellate cell concentration during the exponential growth phase, indicating growth was limited by supply of dinoflagellate-derived carbon. Bacterial growth increased rapidly at the onset of declining and stationary phases due to either increasing availability of algal-derived carbon induced by nutrient stress and autolysis, or at mid-log phase in Roseobacter co-cultures potentially due to the onset of bacterial-mediated cell lysis. Co-cultures with the three bacterial associates resulted in dinoflagellate and bacterial growth dynamics very similar to more complex mixed bacterial community controls, suggesting that three-way co-cultures are sufficient to model interaction and growth dynamics of more complex communities. This study demonstrates that algal associate bacteria independently modify the growth of the host cell under non-limiting growth conditions and supports the concept that algal–bacterial interactions are an important structuring mechanism in phytoplankton communities. PMID:28469613

Effects of proliferation on the decay of thermotolerance in Chinese hamster cells.

PubMed

Armour, E P; Li, G C; Hahn, G M

1985-09-01

Development and decay of thermotolerance were observed in Chinese hamster HA-1 cells. The thermotolerance kinetics of exponentially growing and fed plateau-phase cells were compared. Following a 10-min heat exposure at 45 degrees C, cells in both growth states had similar rates of development of tolerance to a subsequent 45-min exposure at 45 degrees C. This thermotolerant state started to decay between 12 and 24 hr after the initial heat exposure. The decay appeared to initiate slightly sooner in the exponentially growing cells when compared to the fed plateau-phase cells. During the decay phase, the rate of thermotolerance decay was similar in the two growth conditions. In other experiments, cells were induced to divide at a slower rate by chronic growth (3 months) in a low concentration of fetal calf serum. Under these low serum conditions cells became more sensitive to heat and the rate of decay of thermotolerance remained the same for exponentially growing cells. Plateau-phase cells were also more sensitive, but thermotolerance decayed more rapidly in these cells. Although dramatic cell cycle perturbations were seen in the exponentially growing cells, these changes appeared not to be related to thermotolerance kinetics.

The Exponential Expansion of Simulation in Research

DTIC Science & Technology

2012-12-01

exponential growth of computing power. Although other analytic approaches also benefit from this trend, keyword searches of several scholarly search ... engines reveal that the reliance on simulation is increasing more rapidly. A descriptive analysis paints a compelling picture: simulation is frequently

Scaling behavior in the dynamics of citations to scientific journals

NASA Astrophysics Data System (ADS)

Picoli, S., Jr.; Mendes, R. S.; Malacarne, L. C.; Lenzi, E. K.

2006-08-01

We analyze a database comprising the impact factor (citations per recent items published) of scientific journals for a 13-year period (1992 2004). We find that i) the distribution of impact factors follows asymptotic power law behavior, ii) the distribution of annual logarithmic growth rates has an exponential form, and iii) the width of this distribution decays with the impact factor as a power law with exponent β simeq 0.22. The results ii) and iii) are surprising similar to those observed in the growth dynamics of organizations with complex internal structure suggesting the existence of common mechanisms underlying the dynamics of these systems. We propose a general model for such systems, an extension of the simplest model for firm growth, and compare their predictions with our empirical results.

Explaining mortality rate plateaus

PubMed Central

Weitz, Joshua S.; Fraser, Hunter B.

2001-01-01

We propose a stochastic model of aging to explain deviations from exponential growth in mortality rates commonly observed in empirical studies. Mortality rate plateaus are explained as a generic consequence of considering death in terms of first passage times for processes undergoing a random walk with drift. Simulations of populations with age-dependent distributions of viabilities agree with a wide array of experimental results. The influence of cohort size is well accounted for by the stochastic nature of the model. PMID:11752476

Tribology. Mechanisms of antiwear tribofilm growth revealed in situ by single-asperity sliding contacts.

PubMed

Gosvami, N N; Bares, J A; Mangolini, F; Konicek, A R; Yablon, D G; Carpick, R W

2015-04-03

Zinc dialkyldithiophosphates (ZDDPs) form antiwear tribofilms at sliding interfaces and are widely used as additives in automotive lubricants. The mechanisms governing the tribofilm growth are not well understood, which limits the development of replacements that offer better performance and are less likely to degrade automobile catalytic converters over time. Using atomic force microscopy in ZDDP-containing lubricant base stock at elevated temperatures, we monitored the growth and properties of the tribofilms in situ in well-defined single-asperity sliding nanocontacts. Surface-based nucleation, growth, and thickness saturation of patchy tribofilms were observed. The growth rate increased exponentially with either applied compressive stress or temperature, consistent with a thermally activated, stress-assisted reaction rate model. Although some models rely on the presence of iron to catalyze tribofilm growth, the films grew regardless of the presence of iron on either the tip or substrate, highlighting the critical role of stress and thermal activation. Copyright © 2015, American Association for the Advancement of Science.

Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet

NASA Astrophysics Data System (ADS)

Ahmad, Rida; Mustafa, M.; Hayat, T.; Alsaedi, A.

2016-06-01

Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite-Fe3O4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction.

Representation of Dormant and Active Microbial Dynamics for Ecosystem Modeling

NASA Astrophysics Data System (ADS)

Wang, G.; Mayes, M. A.; Gu, L.; Schadt, C. W.

2013-12-01

Experimental observations and modeling efforts have shown that dormancy is likely a common strategy for microorganisms to contend with environmental stress. We review the state-of-the-art in modeling approaches for microbial dormancy and discuss the rationales of these models. We proved that the physiological state index model is not appropriate for describing transformation between active and dormant states. Based on the generally accepted assumptions summarized from ten existing models, we postulated a new synthetic microbial physiology component within the Microbial-ENzyme-mediated Decomposition (MEND) model. Both the steady state active fraction (rss) and substrate saturation level (Øss) positively depend on two physiological indices: α and β. The index α = mR /(μG+ mR), where μG and mR represent the maximum specific growth and maintenance rates, respectively, for active microbes. β denotes the ratio of dormant to active maintenance rate. The rss equals to Øss only under the condition of β→0, and they are identical to α. When substrate availability is the only limiting factor, the maximum rss is ca. 0.5 with α≤0.5 and β ≤0.01. This threshold value (0.5) of rss (not dynamic r) can explain the low active microbial fractions observed in undisturbed soils. The applications of the improved model to a 14C-labeled glucose induced respiration dataset and a batch experimental dataset show satisfactory model performance. We found that the exponential growth respiration rates can only be used to determine μG and initial active microbial biomass (Ba0), thus we suggest using respiration data representing both exponential growth and non-accelerating phases to robustly determine other important parameters such as initial total live microbial biomass (B0), initial active fraction (r0), μG, α, and the half-saturation constant (Ks). Similar improved representations of microbial physiology should be incorporated into existing ecosystem models in order to account for the significance of dormancy in microbially-mediated processes.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Modeling timelines for translational science in cancer; the impact of technological maturation

PubMed Central

McNamee, Laura M.; Ledley, Fred D.

2017-01-01

This work examines translational science in cancer based on theories of innovation that posit a relationship between the maturation of technologies and their capacity to generate successful products. We examined the growth of technologies associated with 138 anticancer drugs using an analytical model that identifies the point of initiation of exponential growth and the point at which growth slows as the technology becomes established. Approval of targeted and biological products corresponded with technological maturation, with first approval averaging 14 years after the established point and 44 years after initiation of associated technologies. The lag in cancer drug approvals after the increases in cancer funding and dramatic scientific advances of the 1970s thus reflects predictable timelines of technology maturation. Analytical models of technological maturation may be used for technological forecasting to guide more efficient translation of scientific discoveries into cures. PMID:28346525

Pressure resistance of cold-shocked Escherichia coli O157:H7 in ground beef, beef gravy and peptone water.

PubMed

Baccus-Taylor, G S H; Falloon, O C; Henry, N

2015-06-01

(i) To study the effects of cold shock on Escherichia coli O157:H7 cells. (ii) To determine if cold-shocked E. coli O157:H7 cells at stationary and exponential phases are more pressure-resistant than their non-cold-shocked counterparts. (iii) To investigate the baro-protective role of growth media (0·1% peptone water, beef gravy and ground beef). Quantitative estimates of lethality and sublethal injury were made using the differential plating method. There were no significant differences (P > 0·05) in the number of cells killed; cold-shocked or non-cold-shocked. Cells grown in ground beef (stationary and exponential phases) experienced lowest death compared with peptone water and beef gravy. Cold-shock treatment increased the sublethal injury to cells cultured in peptone water (stationary and exponential phases) and ground beef (exponential phase), but decreased the sublethal injury to cells in beef gravy (stationary phase). Cold shock did not confer greater resistance to stationary or exponential phase cells pressurized in peptone water, beef gravy or ground beef. Ground beef had the greatest baro-protective effect. Real food systems should be used in establishing food safety parameters for high-pressure treatments; micro-organisms are less resistant in model food systems, the use of which may underestimate the organisms' resistance. © 2015 The Society for Applied Microbiology.

Evaluation of normalization reference genes for RT-qPCR analysis of spo0A and four sporulation sigma factor genes in Clostridium botulinum Group I strain ATCC 3502.

PubMed

Kirk, David G; Palonen, Eveliina; Korkeala, Hannu; Lindström, Miia

2014-04-01

Heat-resistant spores of Clostridium botulinum can withstand the pasteurization processes in modern food processing. This poses a risk to food safety as spores may germinate into botulinum neurotoxin-producing vegetative cells. Sporulation in Bacillus subtilis, the model organism for sporulation, is regulated by the transcription factor Spo0A and four alternative sigma factors, SigF, SigE, SigG, and SigK. While the corresponding regulators are found in available genomes of C. botulinum, little is known about their expression. To accurately measure the expression of these genes using quantitative reverse-transcriptase PCR (RT-qPCR) during the exponential and stationary growth phases, a suitable normalization reference gene is required. 16S rrn, adK, alaS, era, gluD, gyrA, rpoC, and rpsJ were selected as the candidate reference genes. The most stable candidate reference gene was 16S ribosomal RNA gene (rrn), based on its low coefficient of variation (1.81%) measured during the 18-h study time. Using 16S rrn as the normalization reference gene, the relative expression levels of spo0A, sigF, sigE, sigG, and sigK were measured over 18h. The pattern of expression showed spo0A expression during the logarithmic growth phase, followed by a drop in expression upon entry to the stationary phase. Expression levels of sigF, sigE, and sigG peaked simultaneously at the end of the exponential growth phase. Peak expression of sigK occurred at 18h, however low levels of expression were detected during the exponential phase. These findings suggest these sigma factors play a role in C. botulinum sporulation that is similar, but not equal, to their role in the B. subtilis model. Copyright © 2013 Elsevier Ltd. All rights reserved.

Phosphorus-zinc interactive effects on growth by Selenastrum capricornutum (chlorophyta)

USGS Publications Warehouse

Kuwabara, J.S.

1985-01-01

Culturing experiments in chemically defined growth media were conducted to observe possible Zn and P interactions on Selenastrum capricornutum Printz growth indexes. Elevated Zn concentrations (7.5 ?? 10-8 and 1.5 ?? 10-7 M [Zn2+]) were highly detrimental to algal growth, affecting lag, exponential, and stationary growth phases. P behaved as a yield-limiting nutrient with maximum cell densities increasing linearly with total P. This yield limitation was intensified at elevated Zn concentrations. Although calculated cellular phosphorus concentrations increased markedly with Zn ion activity, elevated Zn concentrations had no apparent effect on rates of phosphorus uptake estimated for Selenastrum during exponential growth. Results indicated that P-Zn interactions were significant in describing Selenastrum cell yield results and are consistent with previous Zn studies on chlorophytes. These P-Zn interactions and the observed inhibitory growth effects of submicromolar Zn concentrations suggest that in nature an apparent P yield-limiting condition may result from elevated Zn concentrations.

Model equations for the Eiffel Tower profile: historical perspective and new results

NASA Astrophysics Data System (ADS)

Weidman, Patrick; Pinelis, Iosif

2004-07-01

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, "in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind". An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).

A mathematical model for generating bipartite graphs and its application to protein networks

NASA Astrophysics Data System (ADS)

Nacher, J. C.; Ochiai, T.; Hayashida, M.; Akutsu, T.

2009-12-01

Complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology. Most of these systems can be organized into networks composed of nodes and interacting edges. Here, we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes. We then use this model to investigate protein-domain networks. A protein can be composed of up to hundreds of domains. Each domain represents a conserved sequence segment with specific functional tasks. We analyze the distribution of domains in Homo sapiens and Arabidopsis thaliana organisms and the statistical analysis shows that while (a) the number of domain types shared by k proteins exhibits a power-law distribution, (b) the number of proteins composed of k types of domains decays as an exponential distribution. The proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of (a) power-law and (b) exponential distributions. Our theoretical and computational results show that this model requires (1) growth process and (2) copy mechanism.

Influence of Natural Organic Matter on Attachment Kinetics of Salmonella Typhimurium

NASA Astrophysics Data System (ADS)

Chowdhury, I.; Zorlu, O.; Hill, J. E.; Walker, S. L.

2011-12-01

Salmonella enterica serovar Typhimurium is one of the most common and virulent bacterial pathogens, usually found in food and water. This waterborne pathogen has been attributed to causing gastroenteritis and typhoid fever, leading to 16 million cases and over half a million deaths worldwide each year. Natural organic matter (NOM) is ubiquitous in environment and previous work has shown NOM to enhance the stability and transport of bacteria cells; hence NOM will certainly interact with Salmonella and affect its transport in environment. The objective of this study was to investigate the influence of NOM (Suwannee River humic acid standard II, SRHA) on the attachment kinetics of a model Salmonella (Salmonella enterica serovar Typhimurium SA5983) to glass. The transport study was conducted in a parallel plate flow chamber using fluorescent microscope to visualize the bacterial cells, which were tagged with green fluorescent protein (GFP). The solution pH was unadjusted, and the flow rate through parallel plate channel was 0.1 mL/min to simulate groundwater conditions. Parameters varied in this study were NOM presence, ion valence (K+, Ca2+) as well as cell growth phase (mid-exponential and late-exponential growth phases). These parameters were chosen because ion valence may alter the NOM conformation and capacity for bridging, as well growth phase impacts the cellular surface chemistry. Extensive characterization of the bacterial cells was conducted including measurements of electrophoretic mobility, hydrophobicity, acidity, surface charge density and extracellular polymeric substance content. Additionally, electrokintic characterization was conducted for the glass. Preliminary results demonstrated the sensitivity of cell attachment to ionic valence and cell growth phase. Also the addition of NOM reduced the attachment of the Salmonella cells significantly under all of these conditions. Without NOM, attachment efficiencies (α) in KCl were similar at both growth phases; however, in the presence of the divalent ion, α decreased as the cells aged. In presence of NOM and KCl, α was significantly lower at late exponential phase than mid exponential phase; whereas, the opposite was observed with divalent ions. These trends indicate the complex role of NOM, which is coupled with ion valence and growth phase, in the transport of Salmonella. Detailed results will be presented along with proposed mechanisms involved in the interactions between Salmonella and NOM. These mechanisms highlight the role this important naturally occurring macromolecule plays in the fate of Salmonella. This understanding will improve our ability to predict the behavior of this pathogen in environmentally relevant conditions.

Scaling Behavior of Firm Growth

NASA Astrophysics Data System (ADS)

Stanley, Michael H. R.; Nunes Amaral, Luis A.; Buldyrev, Sergey V.; Havlin, Shlomo; Leschhorn, Heiko; Maass, Philipp; Salinger, Michael A.; Stanley, H. Eugene

1996-03-01

The theory of the firm is of considerable interest in economics. The standard microeconomic theory of the firm is largely a static model and has thus proved unsatisfactory for addressing inherently dynamic issues such as the growth of economies. In recent years, many have attempted to develop richer models that provide a more accurate representation of firm dynamics due to learning, innovative effort, and the development of organizational infrastructure. The validity of these new, inherently dynamic theories depends on their consistency with the statistical properties of firm growth, e.g. the relationship between growth rates and firm size. Using the Compustat database over the time period 1975-1991, we find: (i) the distribution of annual growth rates for firms with approximately the same sales displays an exponential form with the logarithm of growth rate, and (ii) the fluctuations in the growth rates --- measured by the width of this distribution --- scale as a power law with the firm sales. We place these findings of scaling behavior in the context of conventional economics by considering firm growth dynamics with temporal correlations and also, by considering a hierarchical organization of the departments of a firm.

Measurement of the volume growth rate of single budding yeast with the MOSFET-based microfluidic Coulter counter

PubMed Central

Sun, Jiashu; Stowers, Chris C.; Boczko, Erik M.

2012-01-01

We report on measurements of the volume growth rate of ten individual budding yeast cells using a recently developed MOSFET-based microfluidic Coulter counter. The MOSFET-based microfluidic Coulter counter is very sensitive, provides signals that are immune from the baseline drift, and can work with cell culture media of complex composition. These desirable features allow us to directly measure the volume growth rate of single cells of Saccharomyces cerevisiae LYH3865 strain budding yeast in YNB culture media over a whole cell cycle. Results indicate that all budding yeast follow a sigmoid volume growth profile with reduced growth rates at the initial stage before the bud emerges and the final stage after the daughter gets mature. Analysis of the data indicates that even though all piecewise linear, Gomperitz, and Hill’s function models can fit the global growth profile equally well, the data strongly support local exponential growth phenomenon. Accurate volume growth measurements are important for applications in systems biology where quantitative parameters are required for modeling and simulation. PMID:20717618

Measurement of the volume growth rate of single budding yeast with the MOSFET-based microfluidic Coulter counter.

PubMed

Sun, Jiashu; Stowers, Chris C; Boczko, Erik M; Li, Deyu

2010-11-07

We report on measurements of the volume growth rate of ten individual budding yeast cells using a recently developed MOSFET-based microfluidic Coulter counter. The MOSFET-based microfluidic Coulter counter is very sensitive, provides signals that are immune from the baseline drift, and can work with cell culture media of complex composition. These desirable features allow us to directly measure the volume growth rate of single cells of Saccharomyces cerevisiae LYH3865 strain budding yeast in YNB culture media over a whole cell cycle. Results indicate that all budding yeast follow a sigmoid volume growth profile with reduced growth rates at the initial stage before the bud emerges and the final stage after the daughter gets mature. Analysis of the data indicates that even though all piecewise linear, Gomperitz, and Hill's function models can fit the global growth profile equally well, the data strongly support local exponential growth phenomenon. Accurate volume growth measurements are important for applications in systems biology where quantitative parameters are required for modeling and simulation.

Modeling complexity in engineered infrastructure system: Water distribution network as an example

NASA Astrophysics Data System (ADS)

Zeng, Fang; Li, Xiang; Li, Ke

2017-02-01

The complex topology and adaptive behavior of infrastructure systems are driven by both self-organization of the demand and rigid engineering solutions. Therefore, engineering complex systems requires a method balancing holism and reductionism. To model the growth of water distribution networks, a complex network model was developed following the combination of local optimization rules and engineering considerations. The demand node generation is dynamic and follows the scaling law of urban growth. The proposed model can generate a water distribution network (WDN) similar to reported real-world WDNs on some structural properties. Comparison with different modeling approaches indicates that a realistic demand node distribution and co-evolvement of demand node and network are important for the simulation of real complex networks. The simulation results indicate that the efficiency of water distribution networks is exponentially affected by the urban growth pattern. On the contrary, the improvement of efficiency by engineering optimization is limited and relatively insignificant. The redundancy and robustness, on another aspect, can be significantly improved through engineering methods.

Multi-time series RNA-seq analysis of Enterobacter lignolyticus SCF1 during growth in lignin-amended medium.

PubMed

Orellana, Roberto; Chaput, Gina; Markillie, Lye Meng; Mitchell, Hugh; Gaffrey, Matt; Orr, Galya; DeAngelis, Kristen M

2017-01-01

The production of lignocellulosic-derived biofuels is a highly promising source of alternative energy, but it has been constrained by the lack of a microbial platform capable to efficiently degrade this recalcitrant material and cope with by-products that can be toxic to cells. Species that naturally grow in environments where carbon is mainly available as lignin are promising for finding new ways of removing the lignin that protects cellulose for improved conversion of lignin to fuel precursors. Enterobacter lignolyticus SCF1 is a facultative anaerobic Gammaproteobacteria isolated from tropical rain forest soil collected in El Yunque forest, Puerto Rico under anoxic growth conditions with lignin as sole carbon source. Whole transcriptome analysis of SCF1 during E.lignolyticus SCF1 lignin degradation was conducted on cells grown in the presence (0.1%, w/w) and the absence of lignin, where samples were taken at three different times during growth, beginning of exponential phase, mid-exponential phase and beginning of stationary phase. Lignin-amended cultures achieved twice the cell biomass as unamended cultures over three days, and in this time degraded 60% of lignin. Transcripts in early exponential phase reflected this accelerated growth. A complement of laccases, aryl-alcohol dehydrogenases, and peroxidases were most up-regulated in lignin amended conditions in mid-exponential and early stationary phases compared to unamended growth. The association of hydrogen production by way of the formate hydrogenlyase complex with lignin degradation suggests a possible value added to lignin degradation in the future.

Multi-time series RNA-seq analysis of Enterobacter lignolyticus SCF1 during growth in lignin-amended medium

PubMed Central

Chaput, Gina; Markillie, Lye Meng; Mitchell, Hugh; Gaffrey, Matt; Orr, Galya; DeAngelis, Kristen M.

2017-01-01

The production of lignocellulosic-derived biofuels is a highly promising source of alternative energy, but it has been constrained by the lack of a microbial platform capable to efficiently degrade this recalcitrant material and cope with by-products that can be toxic to cells. Species that naturally grow in environments where carbon is mainly available as lignin are promising for finding new ways of removing the lignin that protects cellulose for improved conversion of lignin to fuel precursors. Enterobacter lignolyticus SCF1 is a facultative anaerobic Gammaproteobacteria isolated from tropical rain forest soil collected in El Yunque forest, Puerto Rico under anoxic growth conditions with lignin as sole carbon source. Whole transcriptome analysis of SCF1 during E.lignolyticus SCF1 lignin degradation was conducted on cells grown in the presence (0.1%, w/w) and the absence of lignin, where samples were taken at three different times during growth, beginning of exponential phase, mid-exponential phase and beginning of stationary phase. Lignin-amended cultures achieved twice the cell biomass as unamended cultures over three days, and in this time degraded 60% of lignin. Transcripts in early exponential phase reflected this accelerated growth. A complement of laccases, aryl-alcohol dehydrogenases, and peroxidases were most up-regulated in lignin amended conditions in mid-exponential and early stationary phases compared to unamended growth. The association of hydrogen production by way of the formate hydrogenlyase complex with lignin degradation suggests a possible value added to lignin degradation in the future. PMID:29049419

Transformations of the distribution of nuclei formed in a nucleation pulse: Interface-limited growth.

PubMed

Shneidman, Vitaly A

2009-10-28

A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r( *) (-) and is allowed to nucleate during a finite time interval t(n), after which the supersaturation is abruptly reduced to a fixed value with a larger critical radius r( *) (+). The size-distribution of nucleated particles f(r,t) further evolves due to their deterministic growth and decay for r larger or smaller than r( *) (+), respectively. A general analytic expressions for f(r,t) is obtained, and it is shown that after a large growth time t this distribution approaches an asymptotic shape determined by two dimensionless parameters, lambda related to t(n), and Lambda=r( *) (+)/r( *) (-). This shape is strongly asymmetric with an exponential and double-exponential cutoffs at small and large sizes, respectively, and with a broad near-flat top in case of a long pulse. Conversely, for a short pulse the distribution acquires a distinct maximum at r=r(max)(t) and approaches a universal shape exp[zeta-e(zeta)], with zeta proportional to r-r(max), independent of the pulse duration. General asymptotic predictions are examined in terms of Zeldovich-Frenkel nucleation model where the entire transient behavior can be described in terms of the Lambert W function. Modifications for the Turnbull-Fisher model are also considered, and analytics is compared with exact numerics. Results are expected to have direct implementations in analysis of two-step annealing crystallization experiments, although other applications might be anticipated due to universality of the nucleation pulse technique.

Size-dependent standard deviation for growth rates: Empirical results and theoretical modeling

NASA Astrophysics Data System (ADS)

Podobnik, Boris; Horvatic, Davor; Pammolli, Fabio; Wang, Fengzhong; Stanley, H. Eugene; Grosse, I.

2008-05-01

We study annual logarithmic growth rates R of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of R can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation σ(R) on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates R of wages of 161 different occupations, we find a power-law dependence of the standard deviation σ(R) on the average value of the wages with a scaling exponent β≈0.14 close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation σ(R) of the annual logarithmic growth rate R increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of σ(R) on the average payroll with a scaling exponent β≈-0.08 . Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.

Size-dependent standard deviation for growth rates: empirical results and theoretical modeling.

PubMed

Podobnik, Boris; Horvatic, Davor; Pammolli, Fabio; Wang, Fengzhong; Stanley, H Eugene; Grosse, I

2008-05-01

We study annual logarithmic growth rates R of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of R can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation sigma(R) on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates R of wages of 161 different occupations, we find a power-law dependence of the standard deviation sigma(R) on the average value of the wages with a scaling exponent beta approximately 0.14 close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation sigma(R) of the annual logarithmic growth rate R increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of sigma(R) on the average payroll with a scaling exponent beta approximately -0.08 . Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 3; Constant Stress and Cyclic Stress Experiments

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on advanced structural ceramics tested under constant stress and cyclic stress loading at ambient and elevated temperatures. The data fit to the relation between the time to failure and applied stress (or maximum applied stress in cyclic loading) was very reasonable for most of the materials studied. It was also found that life prediction for cyclic stress loading from data of constant stress loading in the exponential formulation was in good agreement with the experimental data, resulting in a similar degree of accuracy as compared with the power-law formulation. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important slow-crack-growth (SCG) parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy.

PubMed

He, Yixuan; Kodali, Anita; Wallace, Dorothy I

2018-06-14

Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of patients still remains less than half. Recent studies have indicated that bevacizumab, an anti-VEGF drug used in treatment of several other cancer types, may be effective for treating neuroblastoma as well. However, its effect on neuroblastoma has not been well characterized. While traditional experiments are costly and time-consuming, mathematical models are capable of simulating complex systems quickly and inexpensively. In this study, we present a model of vascular tumor growth of neuroblastoma IMR-32 that is complex enough to replicate experimental data across a range of tumor cell properties measured in a suite of in vitro and in vivo experiments. The model provides quantitative insight into tumor vasculature, predicting a linear relationship between vasculature and tumor volume. The tumor growth model was coupled with known pharmacokinetics and pharmacodynamics of the VEGF blocker bevacizumab to study its effect on neuroblastoma growth dynamics. The results of our model suggest that total administered bevacizumab concentration per week, as opposed to dosage regimen, is the major determining factor in tumor suppression. Our model also establishes an exponentially decreasing relationship between administered bevacizumab concentration and tumor growth rate.

Computational Combustion

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

Westbrook, C K; Mizobuchi, Y; Poinsot, T J

2004-08-26

Progress in the field of computational combustion over the past 50 years is reviewed. Particular attention is given to those classes of models that are common to most system modeling efforts, including fluid dynamics, chemical kinetics, liquid sprays, and turbulent flame models. The developments in combustion modeling are placed into the time-dependent context of the accompanying exponential growth in computer capabilities and Moore's Law. Superimposed on this steady growth, the occasional sudden advances in modeling capabilities are identified and their impacts are discussed. Integration of submodels into system models for spark ignition, diesel and homogeneous charge, compression ignition engines, surfacemore » and catalytic combustion, pulse combustion, and detonations are described. Finally, the current state of combustion modeling is illustrated by descriptions of a very large jet lifted 3D turbulent hydrogen flame with direct numerical simulation and 3D large eddy simulations of practical gas burner combustion devices.« less

Quantitative Study on Corrosion of Steel Strands Based on Self-Magnetic Flux Leakage.

PubMed

Xia, Runchuan; Zhou, Jianting; Zhang, Hong; Liao, Leng; Zhao, Ruiqiang; Zhang, Zeyu

2018-05-02

This paper proposed a new computing method to quantitatively and non-destructively determine the corrosion of steel strands by analyzing the self-magnetic flux leakage (SMFL) signals from them. The magnetic dipole model and three growth models (Logistic model, Exponential model, and Linear model) were proposed to theoretically analyze the characteristic value of SMFL. Then, the experimental study on the corrosion detection by the magnetic sensor was carried out. The setup of the magnetic scanning device and signal collection method were also introduced. The results show that the Logistic Growth model is verified as the optimal model for calculating the magnetic field with good fitting effects. Combined with the experimental data analysis, the amplitudes of the calculated values ( B xL ( x,z ) curves) agree with the measured values in general. This method provides significant application prospects for the evaluation of the corrosion and the residual bearing capacity of steel strand.

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557

Inhomogeneous growth of fluctuations of concentration of inertial particles in channel turbulence

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Schmidt, Lukas; Ditlevsen, Peter; van Reeuwijk, Maarten; Holzner, Markus

2018-06-01

We study the growth of concentration fluctuations of weakly inertial particles in the turbulent channel flow starting with a smooth initial distribution. The steady-state concentration is singular and multifractal so the growth describes the increasingly rugged structure of the distribution. We demonstrate that inhomogeneity influences the growth of concentration fluctuations profoundly. For homogeneous turbulence the growth is exponential and is fully determined by Kolmogorov scale eddies.We derive lognormality of the statistics in this case. The growth exponents of the moments are proportional to the sum of Lyapunov exponents, which is quadratic in the small inertia of the particles. In contrast, for inhomogeneous turbulence the growth is linear in inertia. It involves correlations of inertial range and viscous scale eddies that turn the growth into a stretched exponential law with exponent three halves. We demonstrate using direct numerical simulations that the resulting growth rate can differ by orders of magnitude over channel height. This strong variation might have relevance in the planetary boundary layer.

Induction of a global stress response during the first step of Escherichia coli plate growth.

PubMed

Cuny, Caroline; Lesbats, Maïalène; Dukan, Sam

2007-02-01

We have investigated the first events that occur when exponentially grown cells are transferred from a liquid medium (Luria-Bertani [LB]) to a solid medium (LB agar [LBA]). We observed an initial lag phase of 180 min for the wild type MG1655 without any apparent growth. This lack of growth was independent of the bacterial physiological state (either the stationary or the exponential phase), the solid medium composition, or the number of cells on the plate, but it was dependent on the bacterial genotype. Using lacZ-reporter fusions and two-dimensional electrophoresis analysis, we observed that when cells from exponential-phase cultures were plated on LBA, several global regulons, like heat shock regulons (RpoH, RpoE, CpxAR) and oxidative-stress regulons (SoxRS, OxyR, Fur), were immediately induced. Our results indicate that in order to grow on plates, bacteria must not only adapt to new conditions but also perceive a real stress.

Divalent cation mobility throughout exponential growth and sporulation of Bacillus megaterium.

PubMed

Krueger, W B; Kolodziej, B J

1978-01-01

Each of the five elements considered was taken up by Bacillus megaterium during exponential growth. Initial Mg and Mn uptake was rapid and ended by mid-log. For Ca, Fe, and Zn, uptake continued throughout exponential growth. Elements were released from the cells immediately following initial uptake. For Mn, egression continued to t2, with release of 36% of total accumulated. Secondary uptake followed immediately and continued through stage V. Magnesium egression continued to t1 with release of 33% accumulated. Secondary uptake began by t5 (stage IV) and continued slowly through sporulation. Calcium egression ceased by t4 with release of 25% total accumulated. Secondary uptake began by t6 (stage V) and continued until depleted. Zinc egression stopped by t5 with release of 34% accumulated with some secondary uptake by stage V. Iron egression terminated at t4 with release of 59% of total accumulated. This was followed by secondary uptake after t12 (stage VI).

The Exponential Expansion of Simulation: How Simulation has Grown as a Research Tool

DTIC Science & Technology

2012-09-01

exponential growth of computing power. Although other analytic approaches also benefit from this trend, keyword searches of several scholarly search ... engines reveal that the reliance on simulation is increasing more rapidly. A descriptive analysis paints a compelling picture: simulation is frequently

Power Law Versus Exponential Form of Slow Crack Growth of Advanced Structural Ceramics: Dynamic Fatigue

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Gyekenyesi, John P.

2002-01-01

The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.

The Interrelationship between Promoter Strength, Gene Expression, and Growth Rate

PubMed Central

Klesmith, Justin R.; Detwiler, Emily E.; Tomek, Kyle J.; Whitehead, Timothy A.

2014-01-01

In exponentially growing bacteria, expression of heterologous protein impedes cellular growth rates. Quantitative understanding of the relationship between expression and growth rate will advance our ability to forward engineer bacteria, important for metabolic engineering and synthetic biology applications. Recently, a work described a scaling model based on optimal allocation of ribosomes for protein translation. This model quantitatively predicts a linear relationship between microbial growth rate and heterologous protein expression with no free parameters. With the aim of validating this model, we have rigorously quantified the fitness cost of gene expression by using a library of synthetic constitutive promoters to drive expression of two separate proteins (eGFP and amiE) in E. coli in different strains and growth media. In all cases, we demonstrate that the fitness cost is consistent with the previous findings. We expand upon the previous theory by introducing a simple promoter activity model to quantitatively predict how basal promoter strength relates to growth rate and protein expression. We then estimate the amount of protein expression needed to support high flux through a heterologous metabolic pathway and predict the sizable fitness cost associated with enzyme production. This work has broad implications across applied biological sciences because it allows for prediction of the interplay between promoter strength, protein expression, and the resulting cost to microbial growth rates. PMID:25286161

The Exponential Function, XI: The New Flat Earth Society.

ERIC Educational Resources Information Center

Bartlett, Albert A.

1996-01-01

Discusses issues related to perpetual population growth. Argues that if we believe that there are no limits to growth, we will have to abandon the concept of a spherical Earth which puts limits to growth. (JRH)

Combining Orthogonal Chain-End Deprotections and Thiol-Maleimide Michael Coupling: Engineering Discrete Oligomers by an Iterative Growth Strategy.

PubMed

Huang, Zhihao; Zhao, Junfei; Wang, Zimu; Meng, Fanying; Ding, Kunshan; Pan, Xiangqiang; Zhou, Nianchen; Li, Xiaopeng; Zhang, Zhengbiao; Zhu, Xiulin

2017-10-23

Orthogonal maleimide and thiol deprotections were combined with thiol-maleimide coupling to synthesize discrete oligomers/macromolecules on a gram scale with molecular weights up to 27.4 kDa (128mer, 7.9 g) using an iterative exponential growth strategy with a degree of polymerization (DP) of 2 n -1. Using the same chemistry, a "readable" sequence-defined oligomer and a discrete cyclic topology were also created. Furthermore, uniform dendrons were fabricated using sequential growth (DP=2 n -1) or double exponential dendrimer growth approaches (DP=22n -1) with significantly accelerated growth rates. A versatile, efficient, and metal-free method for construction of discrete oligomers with tailored structures and a high growth rate would greatly facilitate research into the structure-property relationships of sophisticated polymeric materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

The use of real-time PCR to study Penicillium chrysogenum growth kinetics on solid food at different water activities.

PubMed

Arquiza, J M R Apollo; Hunter, Jean

2014-09-18

Fungal growth on solid foods can make them unfit for human consumption, but certain specialty foods require fungi to produce their characteristic properties. In either case, a reliable way of measuring biomass is needed to study how various factors (e.g. water activity) affect fungal growth rates on these substrates. Biochemical markers such as chitin, glucosamine or ergosterol have been used to estimate fungal growth, but they cannot distinguish between individual species in mixed culture. In this study, a real-time polymerase chain reaction (rt-PCR) protocol specific for a target fungal species was used to quantify its DNA while growing on solid food. The measured amount of DNA was then related to the biomass present using an experimentally determined DNA-to-biomass ratio. The highly sensitive rt-PCR biomass assay was found to have a wide range, able to quantify the target DNA within a six orders-of-magnitude difference. The method was used to monitor germination and growth of Penicillium chrysogenum spores on a model porous food (cooked wheat flour) at 25°C and different water activities of 0.973, 0.936, and 0.843. No growth was observed at 0.843, but lag, exponential and stationary phases were identified in the growth curves for the higher water activities. The calculated specific growth rates (μ) during the exponential phase were almost identical, at 0.075/h and 0.076/h for aw=0.973 and 0.936, respectively. The specificity of the method was demonstrated by measuring the biomass of P. chrysogenum while growing together with Aspergillus niger on solid media at aw=0.973. Copyright © 2014 Elsevier B.V. All rights reserved.

A thorough investigation of the progressive reset dynamics in HfO{sub 2}-based resistive switching structures

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

Lorenzi, P., E-mail: lorenzi@die.uniroma1.it; Rao, R.; Irrera, F.

2015-09-14

According to previous reports, filamentary electron transport in resistive switching HfO{sub 2}-based metal-insulator-metal structures can be modeled using a diode-like conduction mechanism with a series resistance. Taking the appropriate limits, the model allows simulating the high (HRS) and low (LRS) resistance states of the devices in terms of exponential and linear current-voltage relationships, respectively. In this letter, we show that this simple equivalent circuit approach can be extended to represent the progressive reset transition between the LRS and HRS if a generalized logistic growth model for the pre-exponential diode current factor is considered. In this regard, it is demonstrated heremore » that a Verhulst logistic model does not provide accurate results. The reset dynamics is interpreted as the sequential deactivation of multiple conduction channels spanning the dielectric film. Fitting results for the current-voltage characteristics indicate that the voltage sweep rate only affects the deactivation rate of the filaments without altering the main features of the switching dynamics.« less

Growth of Juniperus and Potentilla using Liquid Exponential and Controlled-release Fertilizers

Treesearch

R. Kasten Dumroese

2003-01-01

Juniperus scopularum Sarg. (Rocky Mountain juniper) and Potentilla fruticosa L. 'Gold Drop (gold drop potentilla) plants grown in containers had similar or better morphology, higher nitrogen concentrations and contents, and higher N-use efficiency when grown with liquid fertilizer applied at an exponentially increasing rate as...

Saccharomyces cerevisiae biofilm tolerance towards systemic antifungals depends on growth phase.

PubMed

Bojsen, Rasmus; Regenberg, Birgitte; Folkesson, Anders

2014-12-04

Biofilm-forming Candida species cause infections that can be difficult to eradicate, possibly because of antifungal drug tolerance mechanisms specific to biofilms. In spite of decades of research, the connection between biofilm and drug tolerance is not fully understood. We used Saccharomyces cerevisiae as a model for drug susceptibility of yeast biofilms. Confocal laser scanning microscopy showed that S. cerevisiae and C. glabrata form similarly structured biofilms and that the viable cell numbers were significantly reduced by treatment of mature biofilms with amphotericin B but not voriconazole, flucytosine, or caspofungin. We showed that metabolic activity in yeast biofilm cells decreased with time, as visualized by FUN-1 staining, and mature, 48-hour biofilms contained cells with slow metabolism and limited growth. Time-kill studies showed that in exponentially growing planktonic cells, voriconazole had limited antifungal activity, flucytosine was fungistatic, caspofungin and amphotericin B were fungicidal. In growth-arrested cells, only amphotericin B had antifungal activity. Confocal microscopy and colony count viability assays revealed that the response of growing biofilms to antifungal drugs was similar to the response of exponentially growing planktonic cells. The response in mature biofilm was similar to that of non-growing planktonic cells. These results confirmed the importance of growth phase on drug efficacy. We showed that in vitro susceptibility to antifungal drugs was independent of biofilm or planktonic growth mode. Instead, drug tolerance was a consequence of growth arrest achievable by both planktonic and biofilm populations. Our results suggest that efficient strategies for treatment of yeast biofilm might be developed by targeting of non-dividing cells.

Correlation between genome reduction and bacterial growth.

PubMed

Kurokawa, Masaomi; Seno, Shigeto; Matsuda, Hideo; Ying, Bei-Wen

2016-12-01

Genome reduction by removing dispensable genomic sequences in bacteria is commonly used in both fundamental and applied studies to determine the minimal genetic requirements for a living system or to develop highly efficient bioreactors. Nevertheless, whether and how the accumulative loss of dispensable genomic sequences disturbs bacterial growth remains unclear. To investigate the relationship between genome reduction and growth, a series of Escherichia coli strains carrying genomes reduced in a stepwise manner were used. Intensive growth analyses revealed that the accumulation of multiple genomic deletions caused decreases in the exponential growth rate and the saturated cell density in a deletion-length-dependent manner as well as gradual changes in the patterns of growth dynamics, regardless of the growth media. Accordingly, a perspective growth model linking genome evolution to genome engineering was proposed. This study provides the first demonstration of a quantitative connection between genomic sequence and bacterial growth, indicating that growth rate is potentially associated with dispensable genomic sequences. © The Author 2016. Published by Oxford University Press on behalf of Kazusa DNA Research Institute.

Ergodicity Breaking in Geometric Brownian Motion

NASA Astrophysics Data System (ADS)

Peters, O.; Klein, W.

2013-03-01

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.

Exponential energy growth due to slow parameter oscillations in quantum mechanical systems.

PubMed

Turaev, Dmitry

2016-05-01

It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.

Fresh and Dry Mass Estimates of Hermetia illucens (Linnaeus, 1758) (Diptera: Stratiomyidae) Larvae Associated with Swine Decomposition in Urban Area of Central Amazonia.

PubMed

Barros, L M; Martins, R T; Ferreira-Keppler, R L; Gutjahr, A L N

2017-08-04

Information on biomass is substantial for calculating growth rates and may be employed in the medicolegal and economic importance of Hermetia illucens (Linnaeus, 1758). Although biomass is essential to understanding many ecological processes, it is not easily measured. Biomass may be determined by directly weighing or indirectly through regression models of fresh/dry mass versus body dimensions. In this study, we evaluated the association between morphometry and fresh/dry mass of immature H. illucens using linear, exponential, and power regression models. We measured width and length of the cephalic capsule, overall body length, and width of the largest abdominal segment of 280 larvae. Overall body length and width of the largest abdominal segment were the best predictors for biomass. Exponential models best fitted body dimensions and biomass (both fresh and dry), followed by power and linear models. In all models, fresh and dry biomass were strongly correlated (>75%). Values estimated by the models did not differ from observed ones, and prediction power varied from 27 to 79%. Accordingly, the correspondence between biomass and body dimensions should facilitate and motivate the development of applied studies involving H. illucens in the Amazon region.

A Regression Framework for Effect Size Assessments in Longitudinal Modeling of Group Differences

PubMed Central

Feingold, Alan

2013-01-01

The use of growth modeling analysis (GMA)--particularly multilevel analysis and latent growth modeling--to test the significance of intervention effects has increased exponentially in prevention science, clinical psychology, and psychiatry over the past 15 years. Model-based effect sizes for differences in means between two independent groups in GMA can be expressed in the same metric (Cohen’s d) commonly used in classical analysis and meta-analysis. This article first reviews conceptual issues regarding calculation of d for findings from GMA and then introduces an integrative framework for effect size assessments that subsumes GMA. The new approach uses the structure of the linear regression model, from which effect sizes for findings from diverse cross-sectional and longitudinal analyses can be calculated with familiar statistics, such as the regression coefficient, the standard deviation of the dependent measure, and study duration. PMID:23956615

Liver fibrosis: stretched exponential model outperforms mono-exponential and bi-exponential models of diffusion-weighted MRI.

PubMed

Seo, Nieun; Chung, Yong Eun; Park, Yung Nyun; Kim, Eunju; Hwang, Jinwoo; Kim, Myeong-Jin

2018-07-01

To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF). Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC # , α # ). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV). Diagnostic accuracy for HF staging was highest for DDC # (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p < 0.001), D t (0.575 ± 0.05, p < 0.001) and f (0.669 ± 0.04, p = 0.035). The parameters from stretched exponential DWI and D p showed higher areas under the ROC curve (AUCs) for determining significant fibrosis (≥F2) and cirrhosis (F = 4) than other parameters. However, D p showed significantly higher measurement variability (CoV, 74.6%) than DDC # (16.1%, p < 0.001) and α # (15.1%, p < 0.001). Stretched exponential DWI is a promising method for HF staging with good diagnostic performance and fewer b-value acquisitions, allowing shorter acquisition time. • Stretched exponential DWI provides a precise and accurate model for HF staging. • Stretched exponential DWI parameters are more reliable than D p from bi-exponential DWI model • Acquisition of six b values is sufficient to obtain accurate DDC and α.

Slow crack growth in glass in combined mode I and mode II loading

NASA Technical Reports Server (NTRS)

Shetty, D. K.; Rosenfield, A. R.

1991-01-01

Slow crack growth in soda-lime glass under combined mode I and mode II loading was investigated in precracked disk specimens in which pure mode I, pure mode II, and various combinations of mode I and mode II were achieved by loading in diametral compression at selected angles with respect to symmetric radial cracks. It is shown that slow crack growth under these conditions can be described by a simple exponential relationship with elastic strain energy release rate as the effective crack-driving force parameter. It is possible to interpret this equation in terms of theoretical models that treat subcritical crack growth as a thermally activated bond-rupture process with an activation energy dependent on the environment, and the elastic energy release rate as the crack-driving force parameter.

A global perspective of the limits of prediction skill based on the ECMWF ensemble

NASA Astrophysics Data System (ADS)

Zagar, Nedjeljka

2016-04-01

In this talk presents a new model of the global forecast error growth applied to the forecast errors simulated by the ensemble prediction system (ENS) of the ECMWF. The proxy for forecast errors is the total spread of the ECMWF operational ensemble forecasts obtained by the decomposition of the wind and geopotential fields in the normal-mode functions. In this way, the ensemble spread can be quantified separately for the balanced and inertio-gravity (IG) modes for every forecast range. Ensemble reliability is defined for the balanced and IG modes comparing the ensemble spread with the control analysis in each scale. The results show that initial uncertainties in the ECMWF ENS are largest in the tropical large-scale modes and their spatial distribution is similar to the distribution of the short-range forecast errors. Initially the ensemble spread grows most in the smallest scales and in the synoptic range of the IG modes but the overall growth is dominated by the increase of spread in balanced modes in synoptic and planetary scales in the midlatitudes. During the forecasts, the distribution of spread in the balanced and IG modes grows towards the climatological spread distribution characteristic of the analyses. The ENS system is found to be somewhat under-dispersive which is associated with the lack of tropical variability, primarily the Kelvin waves. The new model of the forecast error growth has three fitting parameters to parameterize the initial fast growth and a more slow exponential error growth later on. The asymptotic values of forecast errors are independent of the exponential growth rate. It is found that the asymptotic values of the errors due to unbalanced dynamics are around 10 days while the balanced and total errors saturate in 3 to 4 weeks. Reference: Žagar, N., R. Buizza, and J. Tribbia, 2015: A three-dimensional multivariate modal analysis of atmospheric predictability with application to the ECMWF ensemble. J. Atmos. Sci., 72, 4423-4444.

Magnetic helicity generation in the frame of Kazantsev model

NASA Astrophysics Data System (ADS)

Yushkov, Egor V.; Lukin, Alexander S.

2017-11-01

Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry.

Implications of Biospheric Energization

NASA Astrophysics Data System (ADS)

Budding, Edd; Demircan, Osman; Gündüz, Güngör; Emin Özel, Mehmet

2016-07-01

Our physical model relating to the origin and development of lifelike processes from very simple beginnings is reviewed. This molecular ('ABC') process is compared with the chemoton model, noting the role of the autocatalytic tuning to the time-dependent source of energy. This substantiates a Darwinian character to evolution. The system evolves from very simple beginnings to a progressively more highly tuned, energized and complex responding biosphere, that grows exponentially; albeit with a very low net growth factor. Rates of growth and complexity in the evolution raise disturbing issues of inherent stability. Autocatalytic processes can include a fractal character to their development allowing recapitulative effects to be observed. This property, in allowing similarities of pattern to be recognized, can be useful in interpreting complex (lifelike) systems.

Preneoplastic lesion growth driven by the death of adjacent normal stem cells

PubMed Central

Chao, Dennis L.; Eck, J. Thomas; Brash, Douglas E.; Maley, Carlo C.; Luebeck, E. Georg

2008-01-01

Clonal expansion of premalignant lesions is an important step in the progression to cancer. This process is commonly considered to be a consequence of sustaining a proliferative mutation. Here, we investigate whether the growth trajectory of clones can be better described by a model in which clone growth does not depend on a proliferative advantage. We developed a simple computer model of clonal expansion in an epithelium in which mutant clones can only colonize space left unoccupied by the death of adjacent normal stem cells. In this model, competition for space occurs along the frontier between mutant and normal territories, and both the shapes and the growth rates of lesions are governed by the differences between mutant and normal cells' replication or apoptosis rates. The behavior of this model of clonal expansion along a mutant clone's frontier, when apoptosis of both normal and mutant cells is included, matches the growth of UVB-induced p53-mutant clones in mouse dorsal epidermis better than a standard exponential growth model that does not include tissue architecture. The model predicts precancer cell mutation and death rates that agree with biological observations. These results support the hypothesis that clonal expansion of premalignant lesions can be driven by agents, such as ionizing or nonionizing radiation, that cause cell killing but do not directly stimulate cell replication. PMID:18815380

Effect of benzalkonium chloride on viability and energy metabolism in exponential- and stationary-growth-phase cells of Listeria monocytogenes.

PubMed

Luppens, S B; Abee, T; Oosterom, J

2001-04-01

The difference in killing exponential- and stationary-phase cells of Listeria monocytogenes by benzalkonium chloride (BAC) was investigated by plate counting and linked to relevant bioenergetic parameters. At a low concentration of BAC (8 mg liter(-1)), a similar reduction in viable cell numbers was observed for stationary-phase cells and exponential-phase cells (an approximately 0.22-log unit reduction), although their membrane potential and pH gradient were dissipated. However, at higher concentrations of BAC, exponential-phase cells were more susceptible than stationary-phase cells. At 25 mg liter(-1), the difference in survival on plates was more than 3 log units. For both types of cells, killing, i.e., more than 1-log unit reduction in survival on plates, coincided with complete inhibition of acidification and respiration and total depletion of ATP pools. Killing efficiency was not influenced by the presence of glucose, brain heart infusion medium, or oxygen. Our results suggest that growth phase is one of the major factors that determine the susceptibility of L. monocytogenes to BAC.

Thermal acclimation affects growth and lipophilic toxin production in a strain of cosmopolitan harmful alga Dinophysis acuminata.

PubMed

Basti, Leila; Suzuki, Toshiyuki; Uchida, Hajime; Kamiyama, Takashi; Nagai, Satoshi

2018-03-01

Species of the harmful algal bloom (HAB) genera Dinophysis are causative of one of the most widespread and expanding HAB events associated with the human intoxication, diarrheic shellfish poisoning (DSP). The effects of warming temperature on the physiology and toxinology of these mixotrophic species remain intractable due to their low biomass in nature and difficulties in establishing and maintaining them in culture. Hence, the present study investigated the influence of warming temperature, encompassing present and predicted climate scenarios, on growth and toxin production in a strain of the most cosmopolitan DSP-causative species, Dinophysis acuminata. The strain was isolated from western Japan, acclimated, and cultured over extended time spans. The specific growth and toxin production rates were highest at 20-26 °C and 17-29 °C, respectively, and had significant linear relationships during exponential phase. The cellular toxin production of okadaic acid and pectenotoxin-2 were highest during early exponential growth phase at temperatures ≤17 °C but highest during late stationary phase at temperatures ≥20 °C. The cellular toxin production of Dinophysistoxin-1, however, increased from early exponential to late stationary growth phase independently from temperature. The net toxin productions were not affected by acclimation temperature but significantly affected by growth and were highest during early exponential growth phase. Warming water temperatures increase growth and promote toxin production of D. acuminata, potentially increasing incidence of diarrheic shellfish poisoning events and closures of shellfish production. It is likely that D. acuminata is more toxic at low cell densities during bloom initiation in winter, and at high cell densities during bloom termination in spring-autumn. The results of the present research are also of importance for the mass production of D. acuminata for subsequent studies of the toxicological and pharmacological bioactivities of DSTs and PTX2, and the fate of these toxins in the natural environment and the vectoring shellfish molluscs. Copyright © 2018. Published by Elsevier B.V.

Control of Growth Rate by Initial Substrate Concentration at Values Below Maximum Rate

PubMed Central

Gaudy, Anthony F.; Obayashi, Alan; Gaudy, Elizabeth T.

1971-01-01

The hyperbolic relationship between specific growth rate, μ, and substrate concentration, proposed by Monod and used since as the basis for the theory of steady-state growth in continuous-flow systems, was tested experimentally in batch cultures. Use of a Flavobacterium sp. exhibiting a high saturation constant for growth in glucose minimal medium allowed direct measurement of growth rate and substrate concentration throughout the growth cycle in medium containing a rate-limiting initial concentration of glucose. Specific growth rates were also measured for a wide range of initial glucose concentrations. A plot of specific growth rate versus initial substrate concentration was found to fit the hyperbolic equation. However, the instantaneous relationship between specific growth rate and substrate concentration during growth, which is stated by the equation, was not observed. Well defined exponential growth phases were developed at initial substrate concentrations below that required for support of the maximum exponential growth rate and a constant doubling time was maintained until 50% of the substrate had been used. It is suggested that the external substrate concentration initially present “sets” the specific growth rate by establishing a steady-state internal concentration of substrate, possibly through control of the number of permeation sites. PMID:5137579

Multi-time series RNA-seq analysis of Enterobacter lignolyticus SCF1 during growth in lignin-amended medium

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

Orellana, Roberto; Chaput, Gina; Markillie, Lye Meng

The production of lignocellulosic-derived biofuels is a highly promising source of alternative energy, but it has been constrained by the lack of a microbial platform capable to efficiently degrade this recalcitrant material and cope with by-products that can be toxic to cells. Species that naturally grow in environments where carbon is mainly available as lignin are promising for finding new ways of removing the lignin that protects cellulose for improved conversion of lignin to fuel precursors. Enterobacter lignolyticus SCF1 is a facultative anaerobic Gammaproteobacteria isolated from tropical rain forest soil collected in El Yunque forest, Puerto Rico under anoxic growthmore » conditions with lignin as sole carbon source. Whole transcriptome analysis of SCF1 during E.lignolyticus SCF1 lignin degradation was conducted on cells grown in the presence (0.1%, w/w) and the absence of lignin, where samples were taken at three different times during growth, beginning of exponential phase, mid-exponential phase and beginning of stationary phase. Lignin-amended cultures achieved twice the cell biomass as unamended cultures over three days, and in this time degraded 60% of lignin. Transcripts in early exponential phase reflected this accelerated growth. A complement of laccases, aryl-alcohol dehydrogenases, and peroxidases were most up-regulated in lignin amended conditions in mid-exponential and early stationary phases compared to unamended growth. The association of hydrogen production by way of the formate hydrogenlyase complex with lignin degradation suggests a possible value added to lignin degradation in the future.« less

Proteomic analysis of growth phase-dependent expression of Legionella pneumophila proteins which involves regulation of bacterial virulence traits.

PubMed

Hayashi, Tsuyoshi; Nakamichi, Masahiro; Naitou, Hirotaka; Ohashi, Norio; Imai, Yasuyuki; Miyake, Masaki

2010-07-22

Legionella pneumophila, which is a causative pathogen of Legionnaires' disease, expresses its virulent traits in response to growth conditions. In particular, it is known to become virulent at a post-exponential phase in vitro culture. In this study, we performed a proteomic analysis of differences in expression between the exponential phase and post-exponential phase to identify candidates associated with L. pneumophila virulence using 2-Dimentional Fluorescence Difference Gel Electrophoresis (2D-DIGE) combined with Matrix-Assisted Laser Desorption/Ionization-Mass Spectrometry (MALDI-TOF-MS). Of 68 identified proteins that significantly differed in expression between the two growth phases, 64 were up-regulated at a post-exponential phase. The up-regulated proteins included enzymes related to glycolysis, ketone body biogenesis and poly-3-hydroxybutyrate (PHB) biogenesis, suggesting that L. pneumophila may utilize sugars and lipids as energy sources, when amino acids become scarce. Proteins related to motility (flagella components and twitching motility-associated proteins) were also up-regulated, predicting that they enhance infectivity of the bacteria in host cells under certain conditions. Furthermore, 9 up-regulated proteins of unknown function were found. Two of them were identified as novel bacterial factors associated with hemolysis of sheep red blood cells (SRBCs). Another 2 were found to be translocated into macrophages via the Icm/Dot type IV secretion apparatus as effector candidates in a reporter assay with Bordetella pertussis adenylate cyclase. The study will be helpful for virulent analysis of L. pneumophila from the viewpoint of physiological or metabolic modulation dependent on growth phase.

Multi-time series RNA-seq analysis of Enterobacter lignolyticus SCF1 during growth in lignin-amended medium

DOE PAGES

Orellana, Roberto; Chaput, Gina; Markillie, Lye Meng; ...

2017-10-19

The production of lignocellulosic-derived biofuels is a highly promising source of alternative energy, but it has been constrained by the lack of a microbial platform capable to efficiently degrade this recalcitrant material and cope with by-products that can be toxic to cells. Species that naturally grow in environments where carbon is mainly available as lignin are promising for finding new ways of removing the lignin that protects cellulose for improved conversion of lignin to fuel precursors. Enterobacter lignolyticus SCF1 is a facultative anaerobic Gammaproteobacteria isolated from tropical rain forest soil collected in El Yunque forest, Puerto Rico under anoxic growthmore » conditions with lignin as sole carbon source. Whole transcriptome analysis of SCF1 during E.lignolyticus SCF1 lignin degradation was conducted on cells grown in the presence (0.1%, w/w) and the absence of lignin, where samples were taken at three different times during growth, beginning of exponential phase, mid-exponential phase and beginning of stationary phase. Lignin-amended cultures achieved twice the cell biomass as unamended cultures over three days, and in this time degraded 60% of lignin. Transcripts in early exponential phase reflected this accelerated growth. A complement of laccases, aryl-alcohol dehydrogenases, and peroxidases were most up-regulated in lignin amended conditions in mid-exponential and early stationary phases compared to unamended growth. The association of hydrogen production by way of the formate hydrogenlyase complex with lignin degradation suggests a possible value added to lignin degradation in the future.« less

An Attempt to Standardize the Calculation of Growth Velocity of Preterm Infants-Evaluation of Practical Bedside Methods.

PubMed

Fenton, Tanis R; Anderson, Diane; Groh-Wargo, Sharon; Hoyos, Angela; Ehrenkranz, Richard A; Senterre, Thibault

2018-05-01

To examine how well growth velocity recommendations for preterm infants fit with current growth references: Fenton 2013, Olsen 2010, INTERGROWTH 2015, and the World Health Organization Growth Standard 2006. The Average (2-point), Exponential (2-point), Early (1-point) method weight-gains were calculated for 1,4,8,12, and 16-week time-periods. Growth references' weekly velocities (g/kg/d, gram/day and cm/week) were illustrated graphically with frequently-quoted 15 g/kg/d, 10-30 grams/day and 1 cm/week rates superimposed. The 15 g/kg/d and 1 cm/week growth velocity rates were calculated from 24-50 weeks, superimposed on the Fenton and Olsen preterm growth charts. The Average and Exponential g/kg/d estimates showed close agreement for all ages (range 5.0-18.9 g/kg/d), while the Early method yielded values as high as 41 g/kg/d. All 3 preterm growth references were similar to 15 g/kg/d rate at 34 weeks, but rates were higher prior and lower at older ages. For gram/day, the growth references changed from 10 to 30 grams/day for 24-33 weeks. Head growth rates generally fit the 1 cm/week velocity for 23-30 weeks, and length growth rates fit for 37-40 weeks. The calculated g/kg/d curves deviated from the growth charts, first downward, then steeply crossed the median curves near term. Human growth is not constant through gestation and early infancy. The frequently-quoted 15 g/kg/d, 10-30 gram/day and 1 cm/week only fit current growth references for limited time periods. Rates of 15-20 g/kg/d (calculated using average or exponential methods) are a reasonable goal for infants 23-36 weeks, but not beyond. Copyright © 2017 Elsevier Inc. All rights reserved.

A Reduced Model for the Magnetorotational Instability

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-11-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

Genome-scale model guided design of Propionibacterium for enhanced propionic acid production.

PubMed

Navone, Laura; McCubbin, Tim; Gonzalez-Garcia, Ricardo A; Nielsen, Lars K; Marcellin, Esteban

2018-06-01

Production of propionic acid by fermentation of propionibacteria has gained increasing attention in the past few years. However, biomanufacturing of propionic acid cannot compete with the current oxo-petrochemical synthesis process due to its well-established infrastructure, low oil prices and the high downstream purification costs of microbial production. Strain improvement to increase propionic acid yield is the best alternative to reduce downstream purification costs. The recent generation of genome-scale models for a number of Propionibacterium species facilitates the rational design of metabolic engineering strategies and provides a new opportunity to explore the metabolic potential of the Wood-Werkman cycle. Previous strategies for strain improvement have individually targeted acid tolerance, rate of propionate production or minimisation of by-products. Here we used the P. freudenreichii subsp . shermanii and the pan- Propionibacterium genome-scale metabolic models (GEMs) to simultaneously target these combined issues. This was achieved by focussing on strategies which yield higher energies and directly suppress acetate formation. Using P. freudenreichii subsp . shermanii , two strategies were assessed. The first tested the ability to manipulate the redox balance to favour propionate production by over-expressing the first two enzymes of the pentose-phosphate pathway (PPP), Zwf (glucose-6-phosphate 1-dehydrogenase) and Pgl (6-phosphogluconolactonase). Results showed a 4-fold increase in propionate to acetate ratio during the exponential growth phase. Secondly, the ability to enhance the energy yield from propionate production by over-expressing an ATP-dependent phosphoenolpyruvate carboxykinase (PEPCK) and sodium-pumping methylmalonyl-CoA decarboxylase (MMD) was tested, which extended the exponential growth phase. Together, these strategies demonstrate that in silico design strategies are predictive and can be used to reduce by-product formation in Propionibacterium . We also describe the benefit of carbon dioxide to propionibacteria growth, substrate conversion and propionate yield.

Self-replication: Nanostructure evolution

NASA Astrophysics Data System (ADS)

Simmel, Friedrich C.

2017-10-01

DNA origami nanostructures were utilized to replicate a seed pattern that resulted in the growth of populations of nanostructures. Exponential growth could be controlled by environmental conditions depending on the preferential requirements of each population.

Simulation and modeling of whistler mode wave growth through cyclotron resonance with energetic electrons in the magnetosphere

NASA Astrophysics Data System (ADS)

Carlson, Curtis Ray

New models and simulations of wave growth experienced by electromagnetic waves propagating through the magnetosphere in the whistler mode are presented. The main emphasis is to simulate single frequency wave pulses, in the 2 to 6 kHz range, that have been injected into the magnetosphere, near L approximately 4. Simulations using a new transient model reproduce exponential wave growth and saturation coincident with a linearly increasing frequency versus time (up to 60 Hz/s). Unique methods for calculating the phased bunched currents, stimulated radiation, and radiation propagation are based upon test particle trajectories calculated by integrating nonlinear equations of motion generalized to allow the evolution of the frequency and wave number at each point in space. Results show the importance of the transient aspects in the wave growth process. The wave growth established as the wave propagates toward the equator is given a spatially advancing wave phase structure by the geomagnetic inhomogeneity. Through the feedback of this radiation upon other electrons, the conditions are set up which result in the linearly increasing output frequency with time. The transient simulations also show that features like growth rate and total growth are simply related to the various parameters, such as applied wave intensity, energetic electron flux, and energetic electron distribution.

U-shaped, double-tapered, fiber-optic sensor for effective biofilm growth monitoring.

PubMed

Zhong, Nianbing; Zhao, Mingfu; Li, Yishan

2016-02-01

To monitor biofilm growth on polydimethylsiloxane in a photobioreactor effectively, the biofilm cells and liquids were separated and measured using a sensor with two U-shaped, double-tapered, fiber-optic probes (Sen. and Ref. probes). The probes' Au-coated hemispherical tips enabled double-pass evanescent field absorption. The Sen. probe sensed the cells and liquids inside the biofilm. The polyimide-silica hybrid-film-coated Ref. probe separated the liquids from the biofilm cells and analyzed the liquid concentration. The biofilm structure and active biomass were also examined to confirm the effectiveness of the measurement using a simulation model. The sensor was found to effectively respond to the biofilm growth in the adsorption through exponential phases at thicknesses of 0-536 μm.

Thermal and solutal conditions at the tips of a directional dendritic growth front

NASA Technical Reports Server (NTRS)

Mccay, T. D.; Mccay, Mary H.; Hopkins, John A.

1991-01-01

The line-of-sight averaged, time-dependent dendrite tip concentrations for the diffusion dominated vertical directional solidification of a metal model (ammonium chloride and water) were obtained by extrapolating exponentially fit diffusion layer profiles measured using a laser interferometer. The tip concentrations were shown to increase linearly with time throughout the diffusion dominated growth process for an initially stagnant dendritic array. The process was terminated for the cases chosen by convective breakdown suffered when the conditionally stable diffusion layer exceeded the critical Rayleigh criteria. The transient tip concentrations were determined to significantly exceed the values predicted for steady state, thus producing much larger constitutional undercoolings. This has ramifications for growth speeds, arm spacings and the dendritic structure itself.

Mutant number distribution in an exponentially growing population

NASA Astrophysics Data System (ADS)

Keller, Peter; Antal, Tibor

2015-01-01

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.

Low intensity infrared laser induces filamentation in Escherichia coli cells

NASA Astrophysics Data System (ADS)

Fonseca, A. S.; Presta, G. A.; Geller, M.; Paoli, F.

2011-10-01

Low intensity continuous wave and pulsed emission modes laser is used in treating many diseases and the resulting biostimulative effect on tissues has been described, yet the photobiological basis is not well understood. The aim of this wok was to evaluate, using bacterial filamentation assay, effects of laser on Escherichia coli cultures in exponential and stationary growth phase. E. coli cultures, proficient and deficient on DNA repair, in exponential and stationary growth phase, were exposed to low intensity infrared laser, aliquots were spread onto microscopic slides, stained by Gram method, visualized by optical microscopy, photographed and percentage of bacterial filamentation were determined. Low intensity infrared laser with therapeutic fluencies and different emission modes can induce bacterial filamentation in cultures of E. coli wild type, fpg/ mutM, endonuclease III and exonuclease III mutants in exponential and stationary growth phase. This study showed induction of bacterial, filamentation in E. coli cultures expose to low intensity infrared laser and attention to laser therapy protocols, which should take into account fluencies, wavelengths, tissue conditions, and genetic characteristics of cells before beginning treatment.

Statistical steady states in turbulent droplet condensation

NASA Astrophysics Data System (ADS)

Bec, Jeremie; Krstulovic, Giorgio; Siewert, Christoph

2017-11-01

We investigate the general problem of turbulent condensation. Using direct numerical simulations we show that the fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. This leads to propose a Lagrangian stochastic model consisting of a set of integro-differential equations for the joint evolution of the squared radius and the supersaturation along droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution.

Avoiding Steric Congestion in Dendrimer Growth through Proportionate Branching. A Twist on da Vinci's Rule of Tree Branching

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

Yue, Xuyi; Taraban, Marc B.; Hyland, Laura L.

2012-10-05

In making defect-free macromolecules, the challenge occurs during chemical synthesis. This challenge is especially pronounced in dendrimer synthesis where exponential growth quickly leads to steric congestion. To overcome this difficulty, proportionate branching in dendrimer growth is proposed. In proportionate branching, both the number and the length of branches increase exponentially but in opposite directions to mimic tree growth. The effectiveness of this strategy is demonstrated through the synthesis of a fluorocarbon dendron containing 243 chemically identical fluorine atoms with a MW of 9082 Da. Monodispersity is confirmed by nuclear magnetic resonance spectroscopy, mass spectrometry, and small-angle X-ray scattering. Moreover, growingmore » different parts proportionately, as nature does, could be a general strategy to achieve defect-free synthesis of macromolecules.« less

On the Prony series representation of stretched exponential relaxation

NASA Astrophysics Data System (ADS)

Mauro, John C.; Mauro, Yihong Z.

2018-09-01

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

Limits to Growth--A Role Playing Activity.

ERIC Educational Resources Information Center

Intercom, 1985

1985-01-01

In this lesson, junior high students consider two instances of exponential population growth--one at the local community level and one at the world level--as a way of illuminating some of the problems posed by growth and the limits that may curtail it. (RM)

Resource acquisition, distribution and end-use efficiencies and the growth of industrial society

NASA Astrophysics Data System (ADS)

Jarvis, A.; Jarvis, S.; Hewitt, N.

2015-01-01

A key feature of the growth of industrial society is the acquisition of increasing quantities of resources from the environment and their distribution for end use. With respect to energy, growth has been near exponential for the last 160 years. We attempt to show that the global distribution of resources that underpins this growth may be facilitated by the continual development and expansion of near optimal directed networks. If so, the distribution efficiencies of these networks must decline as they expand due to path lengths becoming longer and more tortuous. To maintain long-term exponential growth the physical limits placed on the distribution networks appear to be counteracted by innovations deployed elsewhere in the system: namely at the points of acquisition and end use. We postulate that the maintenance of growth at the specific rate of ~2.4% yr-1 stems from an implicit desire to optimise patterns of energy use over human working lifetimes.

A mutant (‘lab strain’) of the hyperthermophilic archaeon Pyrococcus furiosus, lacking flagella, has unusual growth physiology

DOE PAGES

Lewis, Derrick L.; Notey, Jaspreet S.; Chandrayan, Sanjeev K.; ...

2014-12-04

In this paper, a mutant (‘lab strain’) of the hyperthermophilic archaeon Pyrococcus furiosus DSM3638 exhibited an extended exponential phase and atypical cell aggregation behavior. Genomic DNA from the mutant culture was sequenced and compared to wild-type (WT) DSM3638, revealing 145 genes with one or more insertions, deletions, or substitutions (12 silent, 33 amino acid substitutions, and 100 frame shifts). Approximately, half of the mutated genes were transposases or hypothetical proteins. The WT transcriptome revealed numerous changes in amino acid and pyrimidine biosynthesis pathways coincidental with growth phase transitions, unlike the mutant whose transcriptome reflected the observed prolonged exponential phase. Targetedmore » gene deletions, based on frame-shifted ORFs in the mutant genome, in a genetically tractable strain of P. furiosus (COM1) could not generate the extended exponential phase behavior observed for the mutant. For example, a putative radical SAM family protein (PF2064) was the most highly up-regulated ORF (>25-fold) in the WT between exponential and stationary phase, although this ORF was unresponsive in the mutant; deletion of this gene in P. furiosus COM1 resulted in no apparent phenotype. On the other hand, frame-shifting mutations in the mutant genome negatively impacted transcription of a flagellar biosynthesis operon (PF0329-PF0338).Consequently, cells in the mutant culture lacked flagella and, unlike the WT, showed minimal evidence of exopolysaccharide-based cell aggregation in post-exponential phase. Finally, electron microscopy of PF0331-PF0337 deletions in P. furiosus COM1 showed that absence of flagella impacted normal cell aggregation behavior and, furthermore, indicated that flagella play a key role, beyond motility, in the growth physiology of P. furiosus.« less

A mutant (‘lab strain’) of the hyperthermophilic archaeon Pyrococcus furiosus, lacking flagella, has unusual growth physiology

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

Lewis, Derrick L.; Notey, Jaspreet S.; Chandrayan, Sanjeev K.

In this paper, a mutant (‘lab strain’) of the hyperthermophilic archaeon Pyrococcus furiosus DSM3638 exhibited an extended exponential phase and atypical cell aggregation behavior. Genomic DNA from the mutant culture was sequenced and compared to wild-type (WT) DSM3638, revealing 145 genes with one or more insertions, deletions, or substitutions (12 silent, 33 amino acid substitutions, and 100 frame shifts). Approximately, half of the mutated genes were transposases or hypothetical proteins. The WT transcriptome revealed numerous changes in amino acid and pyrimidine biosynthesis pathways coincidental with growth phase transitions, unlike the mutant whose transcriptome reflected the observed prolonged exponential phase. Targetedmore » gene deletions, based on frame-shifted ORFs in the mutant genome, in a genetically tractable strain of P. furiosus (COM1) could not generate the extended exponential phase behavior observed for the mutant. For example, a putative radical SAM family protein (PF2064) was the most highly up-regulated ORF (>25-fold) in the WT between exponential and stationary phase, although this ORF was unresponsive in the mutant; deletion of this gene in P. furiosus COM1 resulted in no apparent phenotype. On the other hand, frame-shifting mutations in the mutant genome negatively impacted transcription of a flagellar biosynthesis operon (PF0329-PF0338).Consequently, cells in the mutant culture lacked flagella and, unlike the WT, showed minimal evidence of exopolysaccharide-based cell aggregation in post-exponential phase. Finally, electron microscopy of PF0331-PF0337 deletions in P. furiosus COM1 showed that absence of flagella impacted normal cell aggregation behavior and, furthermore, indicated that flagella play a key role, beyond motility, in the growth physiology of P. furiosus.« less

Modulation of lens cell adhesion molecules by particle beams

NASA Technical Reports Server (NTRS)

McNamara, M. P.; Bjornstad, K. A.; Chang, P. Y.; Chou, W.; Lockett, S. J.; Blakely, E. A.

2001-01-01

Cell adhesion molecules (CAMs) are proteins which anchor cells to each other and to the extracellular matrix (ECM), but whose functions also include signal transduction, differentiation, and apoptosis. We are testing a hypothesis that particle radiations modulate CAM expression and this contributes to radiation-induced lens opacification. We observed dose-dependent changes in the expression of beta 1-integrin and ICAM-1 in exponentially-growing and confluent cells of a differentiating human lens epithelial cell model after exposure to particle beams. Human lens epithelial (HLE) cells, less than 10 passages after their initial culture from fetal tissue, were grown on bovine corneal endothelial cell-derived ECM in medium containing 15% fetal bovine serum and supplemented with 5 ng/ml basic fibroblast growth factor (FGF-2). Multiple cell populations at three different stages of differentiation were prepared for experiment: cells in exponential growth, and cells at 5 and 10 days post-confluence. The differentiation status of cells was characterized morphologically by digital image analysis, and biochemically by Western blotting using lens epithelial and fiber cell-specific markers. Cultures were irradiated with single doses (4, 8 or 12 Gy) of 55 MeV protons and, along with unirradiated control samples, were fixed using -20 degrees C methanol at 6 hours after exposure. Replicate experiments and similar experiments with helium ions are in progress. The intracellular localization of beta 1-integrin and ICAM-1 was detected by immunofluorescence using monoclonal antibodies specific for each CAM. Cells known to express each CAM were also processed as positive controls. Both exponentially-growing and confluent, differentiating cells demonstrated a dramatic proton-dose-dependent modulation (upregulation for exponential cells, downregulation for confluent cells) and a change in the intracellular distribution of the beta 1-integrin, compared to unirradiated controls. In contrast, there was a dose-dependent increase in ICAM-1 immunofluorescence in confluent, but not exponentially-growing cells. These results suggest that proton irradiation downregulates beta 1-integrin and upregulates ICAM-1, potentially contributing to cell death or to aberrant differentiation via modulation of anchorage and/or signal transduction functions. Quantification of the expression levels of the CAMs by Western analysis is in progress.

Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.

PubMed

Yan, Wanfeng; van Tuyll van Serooskerken, Edgar

2015-01-01

Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator.

Estimation of Staphylococcus aureus growth parameters from turbidity data: characterization of strain variation and comparison of methods.

PubMed

Lindqvist, R

2006-07-01

Turbidity methods offer possibilities for generating data required for addressing microorganism variability in risk modeling given that the results of these methods correspond to those of viable count methods. The objectives of this study were to identify the best approach for determining growth parameters based on turbidity data and use of a Bioscreen instrument and to characterize variability in growth parameters of 34 Staphylococcus aureus strains of different biotypes isolated from broiler carcasses. Growth parameters were estimated by fitting primary growth models to turbidity growth curves or to detection times of serially diluted cultures either directly or by using an analysis of variance (ANOVA) approach. The maximum specific growth rates in chicken broth at 17 degrees C estimated by time to detection methods were in good agreement with viable count estimates, whereas growth models (exponential and Richards) underestimated growth rates. Time to detection methods were selected for strain characterization. The variation of growth parameters among strains was best described by either the logistic or lognormal distribution, but definitive conclusions require a larger data set. The distribution of the physiological state parameter ranged from 0.01 to 0.92 and was not significantly different from a normal distribution. Strain variability was important, and the coefficient of variation of growth parameters was up to six times larger among strains than within strains. It is suggested to apply a time to detection (ANOVA) approach using turbidity measurements for convenient and accurate estimation of growth parameters. The results emphasize the need to consider implications of strain variability for predictive modeling and risk assessment.

Modeling the growth processes of polyelectrolyte multilayers using a quartz crystal resonator.

PubMed

Salomäki, Mikko; Kankare, Jouko

2007-07-26

The layer-by-layer buildup of chitosan/hyaluronan (CH/HA) and poly(l-lysine)/hyaluronan (PLL/HA) multilayers was followed on a quartz crystal resonator (QCR) in different ionic strengths and at different temperatures. These polyelectrolytes were chosen to demonstrate the method whereby useful information is retrieved from acoustically thick polymer layers during their buildup. Surface acoustic impedance recorded in these measurements gives a single or double spiral when plotted in the complex plane. The shape of this spiral depends on the viscoelasticity of the layer material and regularity of the growth process. The polymer layer is assumed to consist of one or two zones. A mathematical model was devised to represent the separation of the layer to two zones with different viscoelastic properties. Viscoelastic quantities of the layer material and the mode and parameters of the growth process were acquired by fitting a spiral to the experimental data. In all the cases the growth process was mainly exponential as a function of deposition cycles, the growth exponent being between 0.250 and 0.275.

Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078

Turbulent particle transport in streams: can exponential settling be reconciled with fluid mechanics?

PubMed

McNair, James N; Newbold, J Denis

2012-05-07

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances. Copyright © 2012 Elsevier Ltd. All rights reserved.

Seeing How Money Grows.

ERIC Educational Resources Information Center

Metz, James

2001-01-01

Describes an activity designed to help students connect the ideas of linear growth and exponential growth through graphs of the future value of accounts that earn simple interest and accounts that earn compound interest. Includes worksheets and solutions. (KHR)

Modelling the work to be done by Escherichia coli to adapt to sudden temperature upshifts.

PubMed

Swinnen, I A M; Bernaerts, K; Van Impe, J F

2006-05-01

This paper studies and models the effect of the amplitude of a sudden temperature upshift DeltaT on the adaptation period of Escherichia coli, in terms of the work to be done by the cells during the subsequent lag phase (i.e., the product of growth rate mumax and lag phase duration lambda). Experimental data are obtained from bioreactor experiments with E. coli K12 MG1655. At a predetermined time instant during the exponential growth phase, a sudden temperature upshift is applied (no other environmental changes take place). The length of the (possibly) induced lag phase and the specific growth rate after the shift are quantified with the growth model of Baranyi and Roberts (Int J Food Microbiol 23, 1994, 277). Different models to describe the evolution of the product lambda x mumax as a function of the amplitude of the temperature shift are statistically compared. The evolution of lambda x mumax is influenced by the amplitude of the temperature shift DeltaT and by the normal physiological temperature range. As some cut-off is observed, the linear model with translation is preferred to describe this evolution. This work contributes to the characterization of microbial lag phenomena, in this case for E. coli K12 MG1655, in view of accurate predictive model building.

Assessment of Enterotoxin Production and Cross-Contamination of Staphylococcus aureus between Food Processing Materials and Ready-To-Eat Cooked Fish Paste.

PubMed

Tango, Charles Nkufi; Hong, Sung-Sam; Wang, Jun; Oh, Deog-Hwan

2015-12-01

This study evaluated Staphylococcus aureus growth and subsequent staphylococcal enterotoxin A production in tryptone soy broth and on ready-to-eat cooked fish paste at 12 to 37 °C, as well as cross-contamination between stainless steel, polyethylene, and latex glove at room temperature. A model was developed using Barany and Roberts's growth model, which satisfactorily described the suitable growth of S. aureus with R(2)-adj from 0.94 to 0.99. Except at 12 °C, S. aureus cells in TSB presented a lag time lower (14.64 to 1.65 h), grew faster (0.08 to 0.31 log CFU/h) and produced SEA at lower cell density levels (5.65 to 6.44 log CFU/mL) compare to those inoculated on cooked fish paste with data of 16.920 to 1.985 h, 0.02 to 0.23 log CFU/h, and 6.19 to 7.11 log CFU/g, respectively. Staphylococcal enterotoxin type A (SEA) visual immunoassay test showed that primary SEA detection varied considerably among different storage temperature degrees and media. For example, it occurred only during exponential phase at 30 and 37 °C in TSB, but in cooked fish paste it took place at late exponential phase of S. aureus growth at 20 and 25 °C. The SEA detection test was negative on presence of S. aureus on cooked fish paste stored at 12 and 15 °C, although cell density reached level of 6.12 log CFU/g at 15 °C. Cross-contamination expressed as transfer rate of S. aureus from polyethylene surface to cooked fish paste surface was slower than that observed with steel surface to cooked fish paste under same conditions. These results provide helpful information for controlling S. aureus growth, SEA production and cross-contamination during processing of cooked fish paste. © 2015 Institute of Food Technologists®

Global climate changes as forecast by Goddard Institute for Space Studies three-dimensional model

NASA Technical Reports Server (NTRS)

Hansen, J.; Fung, I.; Lacis, A.; Rind, D.; Lebedeff, S.; Ruedy, R.; Russell, G.

1988-01-01

The global climate effects of time-dependent atmospheric trace gas and aerosol variations are simulated by NASA-Goddard's three-dimensional climate model II, which possesses 8 x 10-deg horizontal resolution, for the cases of a 100-year control run and three different atmospheric composition scenarios in which trace gas growth is respectively a continuation of current exponential trends, a reduced linear growth, and a rapid curtailment of emissions due to which net climate forcing no longer increases after the year 2000. The experiments begin in 1958, run to the present, and encompass measured or estimated changes in CO2, CH4, N2O, chlorofluorocarbons, and stratospheric aerosols. It is shown that the greenhouse warming effect may be clearly identifiable in the 1990s.

A model for mHealth skills training for clinicians: meeting the future now

PubMed Central

Malvey, Donna M.; Neigel, Alexis R.

2017-01-01

We describe the current state of mHealth skills acquisition, education, and training available to clinical professionals in educational programs. We discuss how telemedicine experienced exponential growth due in large part to the ubiquity of the mobile phone. An outcome of this unprecedented growth has been the emergence of the need for technology skills training programs for clinicians that address extant curricula gaps. We propose a model to guide the development of future training programs that incorporate effective training strategies across five domains: (I) digital communication skills; (II) technology literacy and usage skills; (III) deploying telehealth products and services; (VI) regulatory and compliance issues; and (V) telehealth business case. These domains are discussed within the context of interprofessional teams and broader organizational factors. PMID:28736733

A model for mHealth skills training for clinicians: meeting the future now.

PubMed

Slovensky, Donna J; Malvey, Donna M; Neigel, Alexis R

2017-01-01

We describe the current state of mHealth skills acquisition, education, and training available to clinical professionals in educational programs. We discuss how telemedicine experienced exponential growth due in large part to the ubiquity of the mobile phone. An outcome of this unprecedented growth has been the emergence of the need for technology skills training programs for clinicians that address extant curricula gaps. We propose a model to guide the development of future training programs that incorporate effective training strategies across five domains: (I) digital communication skills; (II) technology literacy and usage skills; (III) deploying telehealth products and services; (VI) regulatory and compliance issues; and (V) telehealth business case. These domains are discussed within the context of interprofessional teams and broader organizational factors.

Psychophysics of time perception and intertemporal choice models

NASA Astrophysics Data System (ADS)

Takahashi, Taiki; Oono, Hidemi; Radford, Mark H. B.

2008-03-01

Intertemporal choice and psychophysics of time perception have been attracting attention in econophysics and neuroeconomics. Several models have been proposed for intertemporal choice: exponential discounting, general hyperbolic discounting (exponential discounting with logarithmic time perception of the Weber-Fechner law, a q-exponential discount model based on Tsallis's statistics), simple hyperbolic discounting, and Stevens' power law-exponential discounting (exponential discounting with Stevens' power time perception). In order to examine the fitness of the models for behavioral data, we estimated the parameters and AICc (Akaike Information Criterion with small sample correction) of the intertemporal choice models by assessing the points of subjective equality (indifference points) at seven delays. Our results have shown that the orders of the goodness-of-fit for both group and individual data were [Weber-Fechner discounting (general hyperbola) > Stevens' power law discounting > Simple hyperbolic discounting > Exponential discounting], indicating that human time perception in intertemporal choice may follow the Weber-Fechner law. Indications of the results for neuropsychopharmacological treatments of addiction and biophysical processing underlying temporal discounting and time perception are discussed.

Modeling the growth of individuals in plant populations: local density variation in a strand population of Xanthium strumarium (Asteraceae).

PubMed

Weiner, J; Kinsman, S; Williams, S

1998-11-01

We studied the growth of individual Xanthium strumarium plants growing at four naturally occurring local densities on a beach in Maine: (1) isolated plants, (2) pairs of plants ≤1 cm apart, (3) four plants within 4 cm of each other, and (4) discrete dense clumps of 10-39 plants. A combination of nondestructive measurements every 2 wk and parallel calibration harvests provided very good estimates of the growth in aboveground biomass of over 400 individual plants over 8 wk and afforded the opportunity to fit explicit growth models to 293 of them. There was large individual variation in growth and resultant size within the population and within all densities. Local crowding played a role in determining plant size within the population: there were significant differences in final size between all densities except pairs and quadruples, which were almost identical. Overall, plants growing at higher densities were more variable in growth and final size than plants growing at lower densities, but this was due to increased variation among groups (greater variation in local density and/or greater environmental heterogeneity), not to increased variation within groups. Thus, there was no evidence of size asymmetric competition in this population. The growth of most plants was close to exponential over the study period, but half the plants were slightly better fit by a sigmoidal (logistic) model. The proportion of plants better fit by the logistic model increased with density and with initial plant size. The use of explicit growth models over several growth intervals to describe stand development can provide more biological content and more statistical power than "growth-size" methods that analyze growth intervals separately.

Determining the Kinetic Parameters Characteristic of Microalgal Growth.

ERIC Educational Resources Information Center

Martinez Sancho, Maria Eugenie; And Others

1991-01-01

An activity in which students obtain a growth curve for algae, identify the exponential and linear growth phases, and calculate the parameters which characterize both phases is described. The procedure, a list of required materials, experimental conditions, analytical technique, and a discussion of the interpretations of individual results are…

Evolution and mass extinctions as lognormal stochastic processes

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics). (5) But the most striking new result is that the well-known `Molecular Clock of Evolution', namely the `constant rate of Evolution at the molecular level' as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life. (6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms. (7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time. In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based upon b-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are the particular case of exponential growth.

Both nursery and field performance determine suitable nitrogen supply of nursery-grown, exponentially fertilized Chinese pine

Treesearch

Jiaxi Wang; Guolei Li; Jeremiah R. Pinto; Jiajia Liu; Wenhui Shi; Yong Liu

2015-01-01

Optimum fertilization levels are often determined solely from nursery growth responses. However, it is the performance of the seedling on the outplanting site that is the most important. For Pinus species seedlings, little information is known about the field performance of plants cultured with different nutrient rates, especially with exponential fertilization. In...

Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies

PubMed Central

Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.

2016-01-01

We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373

Shotgun proteomic monitoring of Clostridium acetobutylicum during stationary phase of butanol fermentation using xylose and comparison with the exponential phase

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

Sivagnanam, Kumaran; Raghavan, Vijaya G. S.; Shah, Manesh B

2012-01-01

Economically viable production of solvents through acetone butanol ethanol (ABE) fermentation requires a detailed understanding of Clostridium acetobutylicum. This study focuses on the proteomic profiling of C. acetobutylicum ATCC 824 from the stationary phase of ABE fermentation using xylose and compares with the exponential growth by shotgun proteomics approach. Comparative proteomic analysis revealed 22.9% of the C. acetobutylicum genome and 18.6% was found to be common in both exponential and stationary phases. The proteomic profile of C. acetobutylicum changed during the ABE fermentation such that 17 proteins were significantly differentially expressed between the two phases. Specifically, the expression of fivemore » proteins namely, CAC2873, CAP0164, CAP0165, CAC3298, and CAC1742 involved in the solvent production pathway were found to be significantly lower in the stationary phase compared to the exponential growth. Similarly, the expression of fucose isomerase (CAC2610), xylulose kinase (CAC2612), and a putative uncharacterized protein (CAC2611) involved in the xylose utilization pathway were also significantly lower in the stationary phase. These findings provide an insight into the metabolic behavior of C. acetobutylicum between different phases of ABE fermentation using xylose.« less

A Modified Tri-Exponential Model for Multi-b-value Diffusion-Weighted Imaging: A Method to Detect the Strictly Diffusion-Limited Compartment in Brain

PubMed Central

Zeng, Qiang; Shi, Feina; Zhang, Jianmin; Ling, Chenhan; Dong, Fei; Jiang, Biao

2018-01-01

Purpose: To present a new modified tri-exponential model for diffusion-weighted imaging (DWI) to detect the strictly diffusion-limited compartment, and to compare it with the conventional bi- and tri-exponential models. Methods: Multi-b-value diffusion-weighted imaging (DWI) with 17 b-values up to 8,000 s/mm2 were performed on six volunteers. The corrected Akaike information criterions (AICc) and squared predicted errors (SPE) were calculated to compare these three models. Results: The mean f0 values were ranging 11.9–18.7% in white matter ROIs and 1.2–2.7% in gray matter ROIs. In all white matter ROIs: the AICcs of the modified tri-exponential model were the lowest (p < 0.05 for five ROIs), indicating the new model has the best fit among these models; the SPEs of the bi-exponential model were the highest (p < 0.05), suggesting the bi-exponential model is unable to predict the signal intensity at ultra-high b-value. The mean ADCvery−slow values were extremely low in white matter (1–7 × 10−6 mm2/s), but not in gray matter (251–445 × 10−6 mm2/s), indicating that the conventional tri-exponential model fails to represent a special compartment. Conclusions: The strictly diffusion-limited compartment may be an important component in white matter. The new model fits better than the other two models, and may provide additional information. PMID:29535599

Spatiotemporal Distribution of β-Amyloid in Alzheimer Disease Is the Result of Heterogeneous Regional Carrying Capacities.

PubMed

Whittington, Alex; Sharp, David J; Gunn, Roger N

2018-05-01

β-amyloid (Aβ) accumulation in the brain is 1 of 2 pathologic hallmarks of Alzheimer disease (AD), and the spatial distribution of Aβ has been studied extensively ex vivo. Methods: We applied mathematical modeling to Aβ in vivo PET imaging data to investigate competing theories of Aβ spread in AD. Results: Our results provided evidence that Aβ accumulation starts in all brain regions simultaneously and that its spatiotemporal distribution is due to heterogeneous regional carrying capacities (regional maximum possible concentration of Aβ) for the aggregated protein rather than to longer-term spreading from seed regions. Conclusion: The in vivo spatiotemporal distribution of Aβ in AD can be mathematically modeled using a logistic growth model in which the Aβ carrying capacity is heterogeneous across the brain but the exponential growth rate and time of half maximal Aβ concentration are constant. © 2018 by the Society of Nuclear Medicine and Molecular Imaging.

Blackmail propagation on small-world networks

NASA Astrophysics Data System (ADS)

Shao, Zhi-Gang; Jian-Ping Sang; Zou, Xian-Wu; Tan, Zhi-Jie; Jin, Zhun-Zhi

2005-06-01

The dynamics of the blackmail propagation model based on small-world networks is investigated. It is found that for a given transmitting probability λ the dynamical behavior of blackmail propagation transits from linear growth type to logistical growth one with the network randomness p increases. The transition takes place at the critical network randomness pc=1/N, where N is the total number of nodes in the network. For a given network randomness p the dynamical behavior of blackmail propagation transits from exponential decrease type to logistical growth one with the transmitting probability λ increases. The transition occurs at the critical transmitting probability λc=1/, where is the average number of the nearest neighbors. The present work will be useful for understanding computer virus epidemics and other spreading phenomena on communication and social networks.

U-shaped, double-tapered, fiber-optic sensor for effective biofilm growth monitoring

PubMed Central

Zhong, Nianbing; Zhao, Mingfu; Li, Yishan

2016-01-01

To monitor biofilm growth on polydimethylsiloxane in a photobioreactor effectively, the biofilm cells and liquids were separated and measured using a sensor with two U-shaped, double-tapered, fiber-optic probes (Sen. and Ref. probes). The probes’ Au-coated hemispherical tips enabled double-pass evanescent field absorption. The Sen. probe sensed the cells and liquids inside the biofilm. The polyimide–silica hybrid-film-coated Ref. probe separated the liquids from the biofilm cells and analyzed the liquid concentration. The biofilm structure and active biomass were also examined to confirm the effectiveness of the measurement using a simulation model. The sensor was found to effectively respond to the biofilm growth in the adsorption through exponential phases at thicknesses of 0–536 μm. PMID:26977344

Complex Physiology and Compound Stress Responses during Fermentation of Alkali-Pretreated Corn Stover Hydrolysate by an Escherichia coli Ethanologen

PubMed Central

Schwalbach, Michael S.; Tremaine, Mary; Marner, Wesley D.; Zhang, Yaoping; Bothfeld, William; Higbee, Alan; Grass, Jeffrey A.; Cotten, Cameron; Reed, Jennifer L.; da Costa Sousa, Leonardo; Jin, Mingjie; Balan, Venkatesh; Ellinger, James; Dale, Bruce; Kiley, Patricia J.

2012-01-01

The physiology of ethanologenic Escherichia coli grown anaerobically in alkali-pretreated plant hydrolysates is complex and not well studied. To gain insight into how E. coli responds to such hydrolysates, we studied an E. coli K-12 ethanologen fermenting a hydrolysate prepared from corn stover pretreated by ammonia fiber expansion. Despite the high sugar content (∼6% glucose, 3% xylose) and relatively low toxicity of this hydrolysate, E. coli ceased growth long before glucose was depleted. Nevertheless, the cells remained metabolically active and continued conversion of glucose to ethanol until all glucose was consumed. Gene expression profiling revealed complex and changing patterns of metabolic physiology and cellular stress responses during an exponential growth phase, a transition phase, and the glycolytically active stationary phase. During the exponential and transition phases, high cell maintenance and stress response costs were mitigated, in part, by free amino acids available in the hydrolysate. However, after the majority of amino acids were depleted, the cells entered stationary phase, and ATP derived from glucose fermentation was consumed entirely by the demands of cell maintenance in the hydrolysate. Comparative gene expression profiling and metabolic modeling of the ethanologen suggested that the high energetic cost of mitigating osmotic, lignotoxin, and ethanol stress collectively limits growth, sugar utilization rates, and ethanol yields in alkali-pretreated lignocellulosic hydrolysates. PMID:22389370

Compound haplotypes at Xp11.23 and human population growth in Eurasia.

PubMed

Alonso, S; Armour, J A L

2004-09-01

To investigate patterns of diversity and the evolutionary history of Eurasians, we have sequenced a 2.8 kb region at Xp11.23 in a sample of African and Eurasian chromosomes. This region is in a long intron of CLCN5 and is immediately flanked by a highly variable minisatellite, DXS255, and a human-specific Ta0 LINE. Compared to Africans, Eurasians showed a marked reduction in sequence diversity. The main Euro-Asiatic haplotype seems to be the ancestral haplotype for the whole sample. Coalescent simulations, including recombination and exponential growth, indicate a median length of strong linkage disequilibrium, up to approximately 9 kb for this area. The Ka/Ks ratio between the coding sequence of human CLCN5 and its mouse orthologue is much less than 1. This implies that the region sequenced is unlikely to be under the strong influence of positive selective processes on CLCN5, mutations in which have been associated with disorders such as Dent's disease. In contrast, a scenario based on a population bottleneck and exponential growth seems a more likely explanation for the reduced diversity observed in Eurasians. Coalescent analysis and linked minisatellite diversity (which reaches a gene diversity value greater than 98% in Eurasians) suggest an estimated age of origin of the Euro-Asiatic diversity compatible with a recent out-of-Africa model for colonization of Eurasia by modern Homo sapiens.

Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.

Development of confidence limits by pivotal functions for estimating software reliability

NASA Technical Reports Server (NTRS)

Dotson, Kelly J.

1987-01-01

The utility of pivotal functions is established for assessing software reliability. Based on the Moranda geometric de-eutrophication model of reliability growth, confidence limits for attained reliability and prediction limits for the time to the next failure are derived using a pivotal function approach. Asymptotic approximations to the confidence and prediction limits are considered and are shown to be inadequate in cases where only a few bugs are found in the software. Departures from the assumed exponentially distributed interfailure times in the model are also investigated. The effect of these departures is discussed relative to restricting the use of the Moranda model.

A rational approach to improving productivity in recombinant Pichia pastoris fermentation.

PubMed

d'Anjou, M C; Daugulis, A J

2001-01-05

A Mut(S) Pichia pastoris strain that had been genetically modified to produce and secrete sea raven antifreeze protein was used as a model system to demonstrate the implementation of a rational, model-based approach to improve process productivity. A set of glycerol/methanol mixed-feed continuous stirred-tank reactor (CSTR) experiments was performed at the 5-L scale to characterize the relationship between the specific growth rate and the cell yield on methanol, the specific methanol consumption rate, the specific recombinant protein formation rate, and the productivity based on secreted protein levels. The range of dilution rates studied was 0. 01 to 0.10 h(-1), and the residual methanol concentration was kept constant at approximately 2 g/L (below the inhibitory level). With the assumption that the cell yield on glycerol was constant, the cell yield on methanol increased from approximately 0.5 to 1.5 over the range studied. A maximum specific methanol consumption rate of 20 mg/g. h was achieved at a dilution rate of 0.06 h(-1). The specific product formation rate and the volumetric productivity based on product continued to increase over the range of dilution rates studied, and the maximum values were 0.06 mg/g. h and 1.7 mg/L. h, respectively. Therefore, no evidence of repression by glycerol was observed over this range, and operating at the highest dilution rate studied maximized productivity. Fed-batch mass balance equations, based on Monod-type kinetics and parameters derived from data collected during the CSTR work, were then used to predict cell growth and recombinant protein production and to develop an exponential feeding strategy using two carbon sources. Two exponential fed-batch fermentations were conducted according to the predicted feeding strategy at specific growth rates of 0.03 h(-1) and 0.07 h(-1) to verify the accuracy of the model. Cell growth was accurately predicted in both fed-batch runs; however, the model underestimated recombinant product concentration. The overall volumetric productivity of both runs was approximately 2.2 mg/L. h, representing a tenfold increase in the productivity compared with a heuristic feeding strategy. Copyright 2001 John Wiley & Sons, Inc.

Investigation of hyperelastic models for nonlinear elastic behavior of demineralized and deproteinized bovine cortical femur bone.

PubMed

Hosseinzadeh, M; Ghoreishi, M; Narooei, K

2016-06-01

In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney-Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential-exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential-exponential and general exponential-power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress-stretch curves were shown a good agreement with the experimental data. Copyright © 2016 Elsevier Ltd. All rights reserved.

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

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

Kawasaki, Masahiro; Yamada, Masaki; ICRR, University of Tokyo, Kashiwa, 277-8582

2014-02-03

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

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

Kawasaki, Masahiro; Yamada, Masaki, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: yamadam@icrr.u-tokyo.ac.jp

2014-02-01

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

PubMed

Ross, E W; Taub, I A; Doona, C J; Feeherry, F E; Kustin, K

2005-03-15

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

Suppression of Metastasis by Primary Tumor and Acceleration of Metastasis Following Primary Tumor Resection: A Natural Law?

PubMed

Hanin, Leonid; Rose, Jason

2018-03-01

We study metastatic cancer progression through an extremely general individual-patient mathematical model that is rooted in the contemporary understanding of the underlying biomedical processes yet is essentially free of specific biological assumptions of mechanistic nature. The model accounts for primary tumor growth and resection, shedding of metastases off the primary tumor and their selection, dormancy and growth in a given secondary site. However, functional parameters descriptive of these processes are assumed to be essentially arbitrary. In spite of such generality, the model allows for computing the distribution of site-specific sizes of detectable metastases in closed form. Under the assumption of exponential growth of metastases before and after primary tumor resection, we showed that, regardless of other model parameters and for every set of site-specific volumes of detected metastases, the model-based likelihood-maximizing scenario is always the same: complete suppression of metastatic growth before primary tumor resection followed by an abrupt growth acceleration after surgery. This scenario is commonly observed in clinical practice and is supported by a wealth of experimental and clinical studies conducted over the last 110 years. Furthermore, several biological mechanisms have been identified that could bring about suppression of metastasis by the primary tumor and accelerated vascularization and growth of metastases after primary tumor resection. To the best of our knowledge, the methodology for uncovering general biomedical principles developed in this work is new.

Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana I.; Bhowmich, Aklant K.; Dell, Zachary R.; Pandian, Arun; Stanic, Milos; Stellingwerf, Robert F.; Swisher, Nora C.

2017-10-01

We focus on classical problem of dependence on the initial conditions of the initial growth-rate of strong shocks driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics (SPH) simulations to describe the simulations data with statistical confidence in a broad parameter regime. For given values of the shock strength, fluids' density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio, and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data. National Science Foundation, USA.

Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana I.; Bhowmich, Aklant K.; Dell, Zachary R.; Pandian, Arun; Stanic, Milos; Stellingwerf, Robert F.; Swisher, Nora C.

2017-11-01

We focus on classical problem of dependence on the initial conditions of the initial growth-rate of strong shocks driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics (SPH) simulations to describe the simulations data with statistical confidence in a broad parameter regime. For given values of the shock strength, fluids' density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio, and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data. National Science Foundation, USA.

Dynamic Predictive Model for Growth of Bacillus cereus from Spores in Cooked Beans.

PubMed

Juneja, Vijay K; Mishra, Abhinav; Pradhan, Abani K

2018-02-01

Kinetic growth data for Bacillus cereus grown from spores were collected in cooked beans under several isothermal conditions (10 to 49°C). Samples were inoculated with approximately 2 log CFU/g heat-shocked (80°C for 10 min) spores and stored at isothermal temperatures. B. cereus populations were determined at appropriate intervals by plating on mannitol-egg yolk-polymyxin agar and incubating at 30°C for 24 h. Data were fitted into Baranyi, Huang, modified Gompertz, and three-phase linear primary growth models. All four models were fitted to the experimental growth data collected at 13 to 46°C. Performances of these models were evaluated based on accuracy and bias factors, the coefficient of determination ( R 2 ), and the root mean square error. Based on these criteria, the Baranyi model best described the growth data, followed by the Huang, modified Gompertz, and three-phase linear models. The maximum growth rates of each primary model were fitted as a function of temperature using the modified Ratkowsky model. The high R 2 values (0.95 to 0.98) indicate that the modified Ratkowsky model can be used to describe the effect of temperature on the growth rates for all four primary models. The acceptable prediction zone (APZ) approach also was used for validation of the model with observed data collected during single and two-step dynamic cooling temperature protocols. When the predictions using the Baranyi model were compared with the observed data using the APZ analysis, all 24 observations for the exponential single rate cooling were within the APZ, which was set between -0.5 and 1 log CFU/g; 26 of 28 predictions for the two-step cooling profiles also were within the APZ limits. The developed dynamic model can be used to predict potential B. cereus growth from spores in beans under various temperature conditions or during extended chilling of cooked beans.

Prediction of fire growth on furniture using CFD

NASA Astrophysics Data System (ADS)

Pehrson, Richard David

A fire growth calculation method has been developed that couples a computational fluid dynamics (CFD) model with bench scale cone calorimeter test data for predicting the rate of flame spread on compartment contents such as furniture. The commercial CFD code TASCflow has been applied to solve time averaged conservation equations using an algebraic multigrid solver with mass weighted skewed upstream differencing for advection. Closure models include k-e for turbulence, eddy breakup for combustion following a single step irreversible reaction with Arrhenius rate constant, finite difference radiation transfer, and conjugate heat transfer. Radiation properties are determined from concentrations of soot, CO2 and H2O using the narrow band model of Grosshandler and exponential wide band curve fit model of Modak. The growth in pyrolyzing area is predicted by treating flame spread as a series of piloted ignitions based on coupled gas-fluid boundary conditions. The mass loss rate from a given surface element follows the bench scale test data for input to the combustion prediction. The fire growth model has been tested against foam-fabric mattresses and chairs burned in the furniture calorimeter. In general, agreement between model and experiment for peak heat release rate (HRR), time to peak HRR, and total energy lost is within +/-20%. Used as a proxy for the flame spread velocity, the slope of the HRR curve predicted by model agreed with experiment within +/-20% for all but one case.

An Analysis of Wave Interactions in Swept-Wing Flows

NASA Technical Reports Server (NTRS)

Reed, H. L.

1984-01-01

Crossflow instabilities dominate disturbance growth in the leading-edge region of swept wings. Streamwise vortices in a boundary layer strongly influence the behavior of other disturbances. Amplification of crossflow vortices near the leading edge produces a residual spanwise nonuniformity in the mid-chord regions where Tollmien-Schlichting (T-S) waves are strongly amplified. Should the T-S wave undergo double-exponential growth because of this effect, the usual transition prediction methods would fail. The crossflow/Tollmien-Schlichting wave interaction was modeled as a secondary instability. The effects of suction are included, and different stability criteria are examined. The results are applied to laminar flow control wings characteristic of energy-efficient aircraft designs.

Quantification and isotopic analysis of intracellular sulfur metabolites in the dissimilatory sulfate reduction pathway

NASA Astrophysics Data System (ADS)

Sim, Min Sub; Paris, Guillaume; Adkins, Jess F.; Orphan, Victoria J.; Sessions, Alex L.

2017-06-01

Microbial sulfate reduction exhibits a normal isotope effect, leaving unreacted sulfate enriched in 34S and producing sulfide that is depleted in 34S. However, the magnitude of sulfur isotope fractionation is quite variable. The resulting changes in sulfur isotope abundance have been used to trace microbial sulfate reduction in modern and ancient ecosystems, but the intracellular mechanism(s) underlying the wide range of fractionations remains unclear. Here we report the concentrations and isotopic ratios of sulfur metabolites in the dissimilatory sulfate reduction pathway of Desulfovibrio alaskensis. Intracellular sulfate and APS levels change depending on the growth phase, peaking at the end of exponential phase, while sulfite accumulates in the cell during stationary phase. During exponential growth, intracellular sulfate and APS are strongly enriched in 34S. The fractionation between internal and external sulfate is up to 49‰, while at the same time that between external sulfate and sulfide is just a few permil. We interpret this pattern to indicate that enzymatic fractionations remain large but the net fractionation between sulfate and sulfide is muted by the closed-system limitation of intracellular sulfate. This 'reservoir effect' diminishes upon cessation of exponential phase growth, allowing the expression of larger net sulfur isotope fractionations. Thus, the relative rates of sulfate exchange across the membrane versus intracellular sulfate reduction should govern the overall (net) fractionation that is expressed. A strong reservoir effect due to vigorous sulfate reduction might be responsible for the well-established inverse correlation between sulfur isotope fractionation and the cell-specific rate of sulfate reduction, while at the same time intraspecies differences in sulfate uptake and/or exchange rates could account for the significant scatter in this relationship. Our approach, together with ongoing investigations of the kinetic isotope fractionation by key enzymes in the sulfate reduction pathway, should provide an empirical basis for a quantitative model relating the magnitude of microbial isotope fractionation to their environmental and physiological controls.

Open system models of isotopic evolution in Earth's silicate reservoirs: Implications for crustal growth and mantle heterogeneity

NASA Astrophysics Data System (ADS)

Kumari, Seema; Paul, Debajyoti; Stracke, Andreas

2016-12-01

An open system evolutionary model of the Earth, comprising continental crust (CC), upper and lower mantle (UM, LM), and an additional isolated reservoir (IR) has been developed to study the isotopic evolution of the silicate Earth. The model is solved numerically at 1 Myr time steps over 4.55 Gyr of Earth history to reproduce both the present-day concentrations and isotope ratios of key radioactive decay systems (Rb-Sr, Sm-Nd, and U-Th-Pb) in these terrestrial reservoirs. Various crustal growth scenarios - continuous versus episodic and early versus late crustal growth - and their effect on the evolution of Sr-Nd-Pb isotope systematics in the silicate reservoirs have been evaluated. Modeling results where the present-day UM is ∼60% of the total mantle mass and a lower mantle that is non-primitive reproduce the estimated geochemical composition and isotope ratios in Earth's silicate reservoirs. The isotopic evolution of the silicate Earth is strongly affected by the mode of crustal growth; only an exponential crustal growth pattern with crustal growth since the early Archean satisfactorily explains the chemical and isotopic evolution of the crust-mantle system and accounts for the so-called Pb paradoxes. Assuming that the OIB source is located in the deeper mantle, our model could, however, not reproduce its target ɛNd of +4.6 for the UM, which has been estimated from the average isotope ratios of 32 individual ocean island localities. Hence, either mantle plumes sample the LM in a non-representative way, or the simplified model set-up does not capture the full complexity of Earth's lower mantle (Nd isotope) evolution. Compared to the results obtained for a 4.55 Ga Earth, a model assuming a protracted U-Pb evolution of silicate Earth by ca. 100 Myr reproduces a slightly better fit for the Pb isotope ratios in Earth's silicate reservoirs. One notable feature of successful models is the early depletion of incompatible elements (as well as rapid decrease in Th/U) in the UM within the initial 500 Myr, as a result of early formation of CC, which supports other evidence in favor of the presence of Hadean continental crust. Therefore, a chondritic Th/U ratio (4 ± 0.2) in the UM until 2 Gyr appears rather unlikely. We find that the κ conundrum - the observation that measured Th/U ratios and those deduced from 208Pb-206Pb isotope systematics differ - is a natural outcome of an open system evolution in which preferential recycling of U for the past 2 Gyr has played a dominant role. Overall, our simulations strongly favor exponential crustal growth, starting in the early Hadean, the transient preservation of compositionally distinct mantle reservoirs over billion year time periods, and a generally less incompatible element depleted, but non-primitive composition of the lower mantle.

Propagation of ion acoustic wave energy in the plume of a high-current LaB6 hollow cathode

NASA Astrophysics Data System (ADS)

Jorns, Benjamin A.; Dodson, Christoper; Goebel, Dan M.; Wirz, Richard

2017-08-01

A frequency-averaged quasilinear model is derived and experimentally validated for the evolution of ion acoustic turbulence (IAT) along the centerline of a 100-A class, LaB6 hollow cathode. Probe-based diagnostics and a laser induced fluorescence system are employed to measure the properties of both the turbulence and the background plasma parameters as they vary spatially in the cathode plume. It is shown that for the three discharge currents investigated, 100 A, 130 A, and 160 A, the spatial growth of the total energy density of the IAT in the near field of the cathode plume is exponential and agrees quantitatively with the predicted growth rates from the quasilinear formulation. However, in the downstream region of the cathode plume, the growth of IAT energy saturates at a level that is commensurate with the Sagdeev limit. The experimental validation of the quasilinear model for IAT growth and its limitations are discussed in the context of numerical efforts to describe self-consistently the plasma processes in the hollow cathode plume.

Effect of Policy Analysis on Indonesia’s Maritime Cluster Development Using System Dynamics Modeling

NASA Astrophysics Data System (ADS)

Nursyamsi, A.; Moeis, A. O.; Komarudin

2018-03-01

As an archipelago with two third of its territory consist of water, Indonesia should address more attention to its maritime industry development. One of the catalyst to fasten the maritime industry growth is by developing a maritime cluster. The purpose of this research is to gain understanding of the effect if Indonesia implement maritime cluster policy to the growth of maritime economic and its role to enhance the maritime cluster performance, hence enhancing Indonesia’s maritime industry as well. The result of the constructed system dynamic model simulation shows that with the effect of maritime cluster, the growth of employment rate and maritime economic is much bigger that the business as usual case exponentially. The result implies that the government should act fast to form a legitimate cluster maritime organizer institution so that there will be a synergize, sustainable, and positive maritime cluster environment that will benefit the performance of Indonesia’s maritime industry.

Tipping Points, Great and Small

NASA Astrophysics Data System (ADS)

Morrison, Foster

2010-12-01

The Forum by Jordan et al. [2010] addressed environmental problems of various scales in great detail, but getting the critical message through to the formulators of public policies requires going back to basics, namely, that exponential growth (of a population, an economy, or most anything else) is not sustainable. When have you heard any politician or economist from anywhere across the ideological spectrum say anything other than that more growth is essential? There is no need for computer models to demonstrate “limits to growth,” as was done in the 1960s. Of course, as one seeks more details, the complexity of modeling will rapidly outstrip the capabilities of both observation and computing. This is common with nonlinear systems, even simple ones. Thus, identifying all possible “tipping points,” as suggested by Jordan et al. [2010], and then stopping just short of them, is impractical if not impossible. The main thing needed to avoid environmental disasters is a bit of common sense.

A comparative assessment of preclinical chemotherapeutic response of tumors using quantitative non-Gaussian diffusion MRI

PubMed Central

Xu, Junzhong; Li, Ke; Smith, R. Adam; Waterton, John C.; Zhao, Ping; Ding, Zhaohua; Does, Mark D.; Manning, H. Charles; Gore, John C.

2016-01-01

Background Diffusion-weighted MRI (DWI) signal attenuation is often not mono-exponential (i.e. non-Gaussian diffusion) with stronger diffusion weighting. Several non-Gaussian diffusion models have been developed and may provide new information or higher sensitivity compared with the conventional apparent diffusion coefficient (ADC) method. However the relative merits of these models to detect tumor therapeutic response is not fully clear. Methods Conventional ADC, and three widely-used non-Gaussian models, (bi-exponential, stretched exponential, and statistical model), were implemented and compared for assessing SW620 human colon cancer xenografts responding to barasertib, an agent known to induce apoptosis via polyploidy. Bayesian Information Criterion (BIC) was used for model selection among all three non-Gaussian models. Results All of tumor volume, histology, conventional ADC, and three non-Gaussian DWI models could show significant differences between control and treatment groups after four days of treatment. However, only the non-Gaussian models detected significant changes after two days of treatment. For any treatment or control group, over 65.7% of tumor voxels indicate the bi-exponential model is strongly or very strongly preferred. Conclusion Non-Gaussian DWI model-derived biomarkers are capable of detecting tumor earlier chemotherapeutic response of tumors compared with conventional ADC and tumor volume. The bi-exponential model provides better fitting compared with statistical and stretched exponential models for the tumor and treatment models used in the current work. PMID:27919785

Time-resolved, nonequilibrium carrier dynamics in Si-on-glass thin films for photovoltaic cells

DOE PAGES

Serafini, John; Akbas, Yunus; Crandall, Lucas; ...

2016-03-02

Here, a femtosecond pump–probe spectroscopy method was used to characterize the growth process and transport properties of amorphous silicon-on-glass, thin films, intended as absorbers for photovoltaic cells. We collected normalized transmissivity change (ΔT/T) waveforms and interpreted them using a comprehensive three-rate equation electron trapping and recombination model. Optically excited ~300–500 nm thick Si films exhibited a bi-exponential carrier relaxation with the characteristic times varying from picoseconds to nanoseconds depending on the film growth process. From our comprehensive trapping model, we could determine that for doped and intrinsic films with very low hydrogen dilution the dominant relaxation mode was carrier trapping;more » while for intrinsic films with large hydrogen content and some texture, it was the standard electron–phonon cooling. In both cases, the initial nonequilibrium relaxation was followed by Shockley–Read–Hall recombination. An excellent fit between the model and the ΔT/T experimental transients was obtained and a correlation between the Si film growth process, its hydrogen content, and the associated trap concentration was demonstrated.« less

Role of community tolerance level (CTL) in predicting the prevalence of the annoyance of road and rail noise.

PubMed

Schomer, Paul; Mestre, Vincent; Fidell, Sanford; Berry, Bernard; Gjestland, Truls; Vallet, Michel; Reid, Timothy

2012-04-01

Fidell et al. [(2011), J. Acoust. Soc. Am. 130(2), 791-806] have shown (1) that the rate of growth of annoyance with noise exposure reported in attitudinal surveys of the annoyance of aircraft noise closely resembles the exponential rate of change of loudness with sound level, and (2) that the proportion of a community highly annoyed and the variability in annoyance prevalence rates in communities are well accounted for by a simple model with a single free parameter: a community tolerance level (abbreviated CTL, and represented symbolically in mathematical expressions as L(ct)), expressed in units of DNL. The current study applies the same modeling approach to predicting the prevalence of annoyance of road traffic and rail noise. The prevalence of noise-induced annoyance of all forms of transportation noise is well accounted for by a simple, loudness-like exponential function with community-specific offsets. The model fits all of the road traffic findings well, but the prevalence of annoyance due to rail noise is more accurately predicted separately for interviewing sites with and without high levels of vibration and/or rattle.

Proceedings of the Third International Workshop on Multistrategy Learning, May 23-25 Harpers Ferry, WV.

DTIC Science & Technology

1996-09-16

approaches are: • Adaptive filtering • Single exponential smoothing (Brown, 1963) * The Box-Jenkins methodology ( ARIMA modeling ) - Linear exponential... ARIMA • Linear exponential smoothing: Holt’s two parameter modeling (Box and Jenkins, 1976). However, there are two approach (Holt et al., 1960) very...crucial disadvantages: The most important point in - Winters’ three parameter method (Winters, 1960) ARIMA modeling is model identification. As shown in

A class of vertex-edge-growth small-world network models having scale-free, self-similar and hierarchical characters

NASA Astrophysics Data System (ADS)

Ma, Fei; Su, Jing; Hao, Yongxing; Yao, Bing; Yan, Guanghui

2018-02-01

The problem of uncovering the internal operating function of network models is intriguing, demanded and attractive in researches of complex networks. Notice that, in the past two decades, a great number of artificial models are built to try to answer the above mentioned task. Based on the different growth ways, these previous models can be divided into two categories, one type, possessing the preferential attachment, follows a power-law P(k) ∼k-γ, 2 < γ < 3. The other has exponential-scaling feature, P(k) ∼α-k. However, there are no models containing above two kinds of growth ways to be presented, even the study of interconnection between these two growth manners in the same model is lacking. Hence, in this paper, we construct a class of planar and self-similar graphs motivated from a new attachment way, vertex-edge-growth network-operation, more precisely, the couple of both them. We report that this model is sparse, small world and hierarchical. And then, not only is scale-free feature in our model, but also lies the degree parameter γ(≈ 3 . 242) out the typical range. Note that, we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power-law parameter γ, and the preferential attachment plays a dominate role on the development of networks over time. At the end of this paper, we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements.

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

NASA Astrophysics Data System (ADS)

Wienkers, A. F.; Ogilvie, G. I.

2018-07-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalizes the often-used Cartesian shearing box model. The numerical method is an overall second-order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localize the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of 'bursty' dynamics such as the superhump phenomenon.

Exponential model for option prices: Application to the Brazilian market

NASA Astrophysics Data System (ADS)

Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.

2016-03-01

In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.

Possible stretched exponential parametrization for humidity absorption in polymers.

PubMed

Hacinliyan, A; Skarlatos, Y; Sahin, G; Atak, K; Aybar, O O

2009-04-01

Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.

The social architecture of capitalism

NASA Astrophysics Data System (ADS)

Wright, Ian

2005-02-01

A dynamic model of the social relations between workers and capitalists is introduced. The model self-organises into a dynamic equilibrium with statistical properties that are in close qualitative and in many cases quantitative agreement with a broad range of known empirical distributions of developed capitalism, including the power-law firm size distribution, the Laplace firm and GDP growth distribution, the lognormal firm demises distribution, the exponential recession duration distribution, the lognormal-Pareto income distribution, and the gamma-like firm rate-of-profit distribution. Normally these distributions are studied in isolation, but this model unifies and connects them within a single causal framework. The model also generates business cycle phenomena, including fluctuating wage and profit shares in national income about values consistent with empirical studies. The generation of an approximately lognormal-Pareto income distribution and an exponential-Pareto wealth distribution demonstrates that the power-law regime of the income distribution can be explained by an additive process on a power-law network that models the social relation between employers and employees organised in firms, rather than a multiplicative process that models returns to investment in financial markets. A testable consequence of the model is the conjecture that the rate-of-profit distribution is consistent with a parameter-mix of a ratio of normal variates with means and variances that depend on a firm size parameter that is distributed according to a power-law.

Equilibrium and Balanced Growth of a Vegetative Crop

PubMed Central

SEGINER, IDO

2004-01-01

• Model A previously developed dynamic model, NICOLET, designed to predict growth and nitrate content of a lettuce crop, is subjected to (virtual) constant environmental conditions. For every combination of shoot and root environment, the cell sap, here assumed to reside in the ‘vacuole’ compartment, equilibrates at a certain nitrate concentration level. This, in turn, defines the composition of the crop in terms of carbon and nitrogen content in each of the three compartments of the model. Growth under constant environmental conditions is defined as ‘equilibrium’ growth (EG). If, in addition, the source strengths of carbon and nitrogen balance each other, as well as the sink strength of the growing crop, the growth is said to be ‘balanced’ (BG). • Results It is shown that the range of BG approximately coincides with the range of ‘mild’ nitrogen stress, where reduction in nitrogen availability results in a mild reduction of relative growth rate (RGR). Beyond a certain low nitrate concentration in the cell sap, the N‐stress becomes ‘severe’ and the loss of growth increases considerably. • Conclusions The model is able to mimic the five central observations of many constant‐environment growth‐chamber experiments, namely (1) the initial exponential growth and later decline of the RGR, (2) the constant chemical composition, (3) the equality of the RGR and the relative nutrient supply rate (RNR), (4) the proportionality between the N : C ratio and the RNR, and (5) the proportionality between the water content and the reduced N content. Guidelines for the optimal combination of the shoot and root environments are suggested. PMID:14681082

[Peculiarities of growth of the monocellular green algae culture after the influence of electromagnetic field in deuterated water-containing media].

PubMed

Semenov, K T; Aslanian, R R

2013-01-01

Exposing the inoculum of monocellular green algae Dunalialla tertiolecta and Tetraselmis viridis to 50 Hz electromagnetic field for several hours resulted in a reduced growth rate in both cultures. It was ascertained that heavy water inhibited growth of algae Dunaliella tertiolecta. The light water activated growth of the culture in the exponential phase only.

Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Modelling the effect of temperature, water activity and pH on the growth of Serpula lacrymans.

PubMed

Maurice, S; Coroller, L; Debaets, S; Vasseur, V; Le Floch, G; Barbier, G

2011-12-01

To predict the risk factors for building infestation by Serpula lacrymans, which is one of the most destructive fungi causing timber decay in buildings. The growth rate was assessed on malt extract agar media at temperatures between 1.5 and 45°C, at water activity (a(w)) over the range of 0.800-0.993 and at pH ranges from 1.5 to 11.0. The radial growth rate (μ) and the lag phase (λ) were estimated from the radial growth kinetics via the plots radius vs time. These parameters were then modelled as a function of the environmental factors tested. Models derived from the cardinal model (CM) were used to fit the experimental data and allowed an estimation of the optimal and limit values for fungal growth. Optimal growth rate occurred at 20°C, at high a(w) level (0.993) and at a pH range between 4.0 and 6.0. The strain effect on the temperature parameters was further evaluated using 14 strains of S. lacrymans. The robustness of the temperature model was validated on data sets measured in two different wood-based media (Quercus robur L. and Picea abies). The two-step procedure of exponential model with latency followed by the CM with inflection gives reliable predictions for the growth conditions of a filamentous fungus in our study. The procedure was validated for the study of abiotic factors on the growth rate of S. lacrymans. This work describes the usefulness of evaluating the effect of physico-chemical factors on fungal growth in predictive building mycology. Consequently, the developed mathematical models for predicting fungal growth on a macroscopic scale can be used as a tool for risk assessment of timber decay in buildings. © 2011 The Authors. Journal of Applied Microbiology © 2011 The Society for Applied Microbiology.

Production and Reutilization of Fluorescent Dissolved Organic Matter by a Marine Bacterial Strain, Alteromonas macleodii

PubMed Central

Goto, Shuji; Tada, Yuya; Suzuki, Koji; Yamashita, Youhei

2017-01-01

The recalcitrant fraction of marine dissolved organic matter (DOM) plays an important role in carbon storage on the earth’s surface. Bacterial production of recalcitrant DOM (RDOM) has been proposed as a carbon sequestration process. It is still unclear whether bacterial physiology can affect RDOM production. In this study, we conducted a batch culture using the marine bacterial isolate Alteromonas macleodii, a ubiquitous gammaproteobacterium, to evaluate the linkage between bacterial growth and DOM production. Glucose (1 mmol C L-1) was used as the sole carbon source, and the bacterial number, the DOM concentration in terms of carbon, and the excitation–emission matrices (EEMs) of DOM were monitored during the 168-h incubation. The incubation period was partitioned into the exponential growth (0–24 h) and stationary phases (24–168 h) based on the growth curve. Although the DOM concentration decreased during the exponential growth phase due to glucose consumption, it remained stable during the stationary phase, corresponding to approximately 4% of the initial glucose in terms of carbon. Distinct fluorophores were not evident in the EEMs at the beginning of the incubation, but DOM produced by the strain exhibited five fluorescent peaks during exponential growth. Two fluorescent peaks were similar to protein-like fluorophores, while the others could be categorized as humic-like fluorophores. All fluorophores increased during the exponential growth phase. The tryptophan-like fluorophore decreased during the stationary phase, suggesting that the strain reused the large exopolymer. The tyrosine-like fluorophore seemed to be stable during the stationary phase, implying that the production of tyrosine-containing small peptides through the degradation of exopolymers was correlated with the reutilization of the tyrosine-like fluorophore. Two humic-like fluorophores that showed emission maxima at the longer wavelength (525 nm) increased during the stationary phase, while the other humic-like fluorophore, which had a shorter emission wavelength (400 nm) and was categorized as recalcitrant, was stable. These humic-like fluorophore behaviors during incubation indicated that the composition of bacterial humic-like fluorophores, which were unavailable to the strain, differed between growth phases. Our results suggest that bacterial physiology can affect RDOM production and accumulation in the ocean interior. PMID:28400762

Production of a Biosurfactant from Torulopsis bombicola

PubMed Central

Cooper, D. G.; Paddock, D. A.

1984-01-01

Two types of carbon sources—carbohydrate and vegetable oil—are necessary to obtain large yields of biosurfactant from Torulopsis bombicola ATCC 22214. Most of the surfactant is produced in the late exponential phase of growth. It is possible to grow the yeast on a single carbon source and then add the other type of substrate, after the exponential growth phase, and cause a burst of surfactant production. This product is a mixture of glycolipids. The maximum yield is 70 g liter−1, or 35% of the weight of the substrate used. An economic comparison demonstrated that this biosurfactant could be produced significantly more cheaply than any of the previously reported microbial surfactants. PMID:16346455

Ponderomotive electron acceleration in a silicon-based nanoplasmonic waveguide.

PubMed

Sederberg, S; Elezzabi, A Y

2014-10-17

Ponderomotive electron acceleration is demonstrated in a semiconductor-loaded nanoplasmonic waveguide. Photogenerated free carriers are accelerated by the tightly confined nanoplasmonic fields and reach energies exceeding the threshold for impact ionization. Broadband (375 nm ≤ λ ≤ 650  nm) white light emission is observed from the nanoplasmonic waveguides. Exponential growth of visible light emission confirms the exponential growth of the electron population, demonstrating the presence of an optical-field-driven electron avalanche. Electron sweeping dynamics are visualized using pump-probe measurements, and a sweeping time of 1.98 ± 0.40 ps is measured. These findings offer a means to harness the potential of the emerging field of ultrafast nonlinear nanoplasmonics.

Ultrascale Visualization of Climate Data

NASA Technical Reports Server (NTRS)

Williams, Dean N.; Bremer, Timo; Doutriaux, Charles; Patchett, John; Williams, Sean; Shipman, Galen; Miller, Ross; Pugmire, David R.; Smith, Brian; Steed, Chad;

Changes of ploidy during the Azotobacter vinelandii growth cycle.

PubMed Central

Maldonado, R; Jiménez, J; Casadesús, J

1994-01-01

The size of the Azotobacter vinelandii chromosome is approximately 4,700 kb, as calculated by pulsed-field electrophoretic separation of fragments digested with the rarely cutting endonucleases SpeI and SwaI. Surveys of DNA content per cell by flow cytometry indicated the existence of ploidy changes during the A. vinelandii growth cycle in rich medium. Early-exponential-phase cells have a ploidy level similar to that of Escherichia coli or Salmonella typhimurium (probably ca. four chromosomes per cell), but a continuous increase of DNA content per cell is observed during growth. Late-exponential-phase cells may contain > 40 chromosomes per cell, while cells in the early stationary stage may contain > 80 chromosomes per cell. In late-stationary-phase cultures, the DNA content per cell is even higher, probably over 100 chromosome equivalents per cell. A dramatic change is observed in old stationary-phase cultures, when the population of highly polyploid bacteria segregates cells with low ploidy. The DNA content of the latter cells resembles that of cysts, suggesting that the process may reflect the onset of cyst differentiation. Cells with low ploidy are also formed when old stationary-phase cultures are diluted into fresh medium. Addition of rifampin to exponential-phase cultures causes a rapid increase in DNA content, indicating that A. vinelandii initiates multiple rounds of chromosome replication per cell division. Growth in minimal medium does not result in the spectacular changes of ploidy observed during rapid growth; this observation suggests that the polyploidy of A. vinelandii may not exist outside the laboratory. Images PMID:8021173

Development and growth of fruit bodies and crops of the button mushroom, Agaricus bisporus.

PubMed

Straatsma, Gerben; Sonnenberg, Anton S M; van Griensven, Leo J L D

2013-10-01

We studied the appearance of fruit body primordia, the growth of individual fruit bodies and the development of the consecutive flushes of the crop. Relative growth, measured as cap expansion, was not constant. It started extremely rapidly, and slowed down to an exponential rate with diameter doubling of 1.7 d until fruit bodies showed maturation by veil breaking. Initially many outgrowing primordia were arrested, indicating nutritional competition. After reaching 10 mm diameter, no growth arrest occurred; all growing individuals, whether relatively large or small, showed an exponential increase of both cap diameter and biomass, until veil breaking. Biomass doubled in 0.8 d. Exponential growth indicates the absence of competition. Apparently there exist differential nutritional requirements for early growth and for later, continuing growth. Flushing was studied applying different picking sizes. An ordinary flushing pattern occurred at an immature picking size of 8 mm diameter (picking mushrooms once a day with a diameter above 8 mm). The smallest picking size yielded the highest number of mushrooms picked, confirming the competition and arrested growth of outgrowing primordia: competition seems less if outgrowing primordia are removed early. The flush duration (i.e. between the first and last picking moments) was not affected by picking size. At small picking size, the subsequent flushes were not fully separated in time but overlapped. Within 2 d after picking the first individuals of the first flush, primordia for the second flush started outgrowth. Our work supports the view that the acquisition of nutrients by the mycelium is demand rather than supply driven. For formation and early outgrowth of primordia, indications were found for an alternation of local and global control, at least in the casing layer. All these data combined, we postulate that flushing is the consequence of the depletion of some unknown specific nutrition required by outgrowing primordia. Copyright © 2013 The British Mycological Society. Published by Elsevier Ltd. All rights reserved.

Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Champredon, David; Earn, David J. D.

2016-09-01

Mechanistic mathematical modelling of the population dynamics of infectious diseases has advanced tremendously over the last few decades [1-6]. Transmission models have been applied to countless diseases of public health importance, including seasonal and pandemic influenza [7], childhood diseases such as measles [8,9] and whooping cough [10], vector transmitted diseases such as malaria [11] and dengue [12], and waterborne diseases such as cholera [13-15]. Much attention in recent years has been directed to emergent diseases such as SARS [16], new subtypes of influenza [17,18], Ebola [19,20], and Zika [21], for which an understanding of early outbreak dynamics is critical.

Use of chemostat cultures mimicking different phases of wine fermentations as a tool for quantitative physiological analysis

PubMed Central

2014-01-01

Background Saccharomyces cerevisiae is the most relevant yeast species conducting the alcoholic fermentation that takes place during winemaking. Although the physiology of this model organism has been extensively studied, systematic quantitative physiology studies of this yeast under winemaking conditions are still scarce, thus limiting the understanding of fermentative metabolism of wine yeast strains and the systematic description, modelling and prediction of fermentation processes. In this study, we implemented and validated the use of chemostat cultures as a tool to simulate different stages of a standard wine fermentation, thereby allowing to implement metabolic flux analyses describing the sequence of metabolic states of S. cerevisae along the wine fermentation. Results Chemostat cultures mimicking the different stages of standard wine fermentations of S. cerevisiae EC1118 were performed using a synthetic must and strict anaerobic conditions. The simulated stages corresponded to the onset of the exponential growth phase, late exponential growth phase and cells just entering stationary phase, at dilution rates of 0.27, 0.04, 0.007 h−1, respectively. Notably, measured substrate uptake and product formation rates at each steady state condition were generally within the range of corresponding conversion rates estimated during the different batch fermentation stages. Moreover, chemostat data were further used for metabolic flux analysis, where biomass composition data for each condition was considered in the stoichiometric model. Metabolic flux distributions were coherent with previous analyses based on batch cultivations data and the pseudo-steady state assumption. Conclusions Steady state conditions obtained in chemostat cultures reflect the environmental conditions and physiological states of S. cerevisiae corresponding to the different growth stages of a typical batch wine fermentation, thereby showing the potential of this experimental approach to systematically study the effect of environmental relevant factors such as temperature, sugar concentration, C/N ratio or (micro) oxygenation on the fermentative metabolism of wine yeast strains. PMID:24928139

Plant growth and respiration re-visited: maintenance respiration defined – it is an emergent property of, not a separate process within, the system – and why the respiration : photosynthesis ratio is conservative

PubMed Central

Thornley, John H. M.

2011-01-01

Background and Aims Plant growth and respiration still has unresolved issues, examined here using a model. The aims of this work are to compare the model's predictions with McCree's observation-based respiration equation which led to the ‘growth respiration/maintenance respiration paradigm’ (GMRP) – this is required to give the model credibility; to clarify the nature of maintenance respiration (MR) using a model which does not represent MR explicitly; and to examine algebraic and numerical predictions for the respiration:photosynthesis ratio. Methods A two-state variable growth model is constructed, with structure and substrate, applicable on plant to ecosystem scales. Four processes are represented: photosynthesis, growth with growth respiration (GR), senescence giving a flux towards litter, and a recycling of some of this flux. There are four significant parameters: growth efficiency, rate constants for substrate utilization and structure senescence, and fraction of structure returned to the substrate pool. Key Results The model can simulate McCree's data on respiration, providing an alternative interpretation to the GMRP. The model's parameters are related to parameters used in this paradigm. MR is defined and calculated in terms of the model's parameters in two ways: first during exponential growth at zero growth rate; and secondly at equilibrium. The approaches concur. The equilibrium respiration:photosynthesis ratio has the value of 0·4, depending only on growth efficiency and recycling fraction. Conclusions McCree's equation is an approximation that the model can describe; it is mistaken to interpret his second coefficient as a maintenance requirement. An MR rate is defined and extracted algebraically from the model. MR as a specific process is not required and may be replaced with an approach from which an MR rate emerges. The model suggests that the respiration:photosynthesis ratio is conservative because it depends on two parameters only whose values are likely to be similar across ecosystems. PMID:21948663

Parameter estimation and order selection for an empirical model of VO2 on-kinetics.

PubMed

Alata, O; Bernard, O

2007-04-27

In humans, VO2 on-kinetics are noisy numerical signals that reflect the pulmonary oxygen exchange kinetics at the onset of exercise. They are empirically modelled as a sum of an offset and delayed exponentials. The number of delayed exponentials; i.e. the order of the model, is commonly supposed to be 1 for low-intensity exercises and 2 for high-intensity exercises. As no ground truth has ever been provided to validate these postulates, physiologists still need statistical methods to verify their hypothesis about the number of exponentials of the VO2 on-kinetics especially in the case of high-intensity exercises. Our objectives are first to develop accurate methods for estimating the parameters of the model at a fixed order, and then, to propose statistical tests for selecting the appropriate order. In this paper, we provide, on simulated Data, performances of Simulated Annealing for estimating model parameters and performances of Information Criteria for selecting the order. These simulated Data are generated with both single-exponential and double-exponential models, and noised by white and Gaussian noise. The performances are given at various Signal to Noise Ratio (SNR). Considering parameter estimation, results show that the confidences of estimated parameters are improved by increasing the SNR of the response to be fitted. Considering model selection, results show that Information Criteria are adapted statistical criteria to select the number of exponentials.

Regulatory design governing progression of population growth phases in bacteria.

PubMed

Martínez-Antonio, Agustino; Lomnitz, Jason G; Sandoval, Santiago; Aldana, Maximino; Savageau, Michael A

2012-01-01

It has long been noted that batch cultures inoculated with resting bacteria exhibit a progression of growth phases traditionally labeled lag, exponential, pre-stationary and stationary. However, a detailed molecular description of the mechanisms controlling the transitions between these phases is lacking. A core circuit, formed by a subset of regulatory interactions involving five global transcription factors (FIS, HNS, IHF, RpoS and GadX), has been identified by correlating information from the well- established transcriptional regulatory network of Escherichia coli and genome-wide expression data from cultures in these different growth phases. We propose a functional role for this circuit in controlling progression through these phases. Two alternative hypotheses for controlling the transition between the growth phases are first, a continuous graded adjustment to changing environmental conditions, and second, a discontinuous hysteretic switch at critical thresholds between growth phases. We formulate a simple mathematical model of the core circuit, consisting of differential equations based on the power-law formalism, and show by mathematical and computer-assisted analysis that there are critical conditions among the parameters of the model that can lead to hysteretic switch behavior, which--if validated experimentally--would suggest that the transitions between different growth phases might be analogous to cellular differentiation. Based on these provocative results, we propose experiments to test the alternative hypotheses.

Identification of growth phases and influencing factors in cultivations with AGE1.HN cells using set-based methods.

PubMed

Borchers, Steffen; Freund, Susann; Rath, Alexander; Streif, Stefan; Reichl, Udo; Findeisen, Rolf

2013-01-01

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.

Identification of Growth Phases and Influencing Factors in Cultivations with AGE1.HN Cells Using Set-Based Methods

PubMed Central

Borchers, Steffen; Freund, Susann; Rath, Alexander; Streif, Stefan; Reichl, Udo; Findeisen, Rolf

2013-01-01

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty. PMID:23936299

A modelling approach to vaccination and contraception programmes for rabies control in fox populations.

PubMed Central

Suppo, C; Naulin, J M; Langlais, M; Artois, M

2000-01-01

In a previous study, three of the authors designed a one-dimensional model to simulate the propagation of rabies within a growing fox population; the influence of various parameters on the epidemic model was studied, including oral-vaccination programmes. In this work, a two-dimensional model of a fox population having either an exponential or a logistic growth pattern was considered. Using numerical simulations, the efficiencies of two prophylactic methods (fox contraception and vaccination against rabies) were assessed, used either separately or jointly. It was concluded that far lower rates of administration are necessary to eradicate rabies, and that the undesirable side-effects of each programme disappear, when both are used together. PMID:11007334

Source term evaluation for combustion modeling

NASA Technical Reports Server (NTRS)

Sussman, Myles A.

1993-01-01

A modification is developed for application to the source terms used in combustion modeling. The modification accounts for the error of the finite difference scheme in regions where chain-branching chemical reactions produce exponential growth of species densities. The modification is first applied to a one-dimensional scalar model problem. It is then generalized to multiple chemical species, and used in quasi-one-dimensional computations of shock-induced combustion in a channel. Grid refinement studies demonstrate the improved accuracy of the method using this modification. The algorithm is applied in two spatial dimensions and used in simulations of steady and unsteady shock-induced combustion. Comparisons with ballistic range experiments give confidence in the numerical technique and the 9-species hydrogen-air chemistry model.

A gamma variate model that includes stretched exponential is a better fit for gastric emptying data from mice

PubMed Central

Bajzer, Željko; Gibbons, Simon J.; Coleman, Heidi D.; Linden, David R.

2015-01-01

Noninvasive breath tests for gastric emptying are important techniques for understanding the changes in gastric motility that occur in disease or in response to drugs. Mice are often used as an animal model; however, the gamma variate model currently used for data analysis does not always fit the data appropriately. The aim of this study was to determine appropriate mathematical models to better fit mouse gastric emptying data including when two peaks are present in the gastric emptying curve. We fitted 175 gastric emptying data sets with two standard models (gamma variate and power exponential), with a gamma variate model that includes stretched exponential and with a proposed two-component model. The appropriateness of the fit was assessed by the Akaike Information Criterion. We found that extension of the gamma variate model to include a stretched exponential improves the fit, which allows for a better estimation of T1/2 and Tlag. When two distinct peaks in gastric emptying are present, a two-component model is required for the most appropriate fit. We conclude that use of a stretched exponential gamma variate model and when appropriate a two-component model will result in a better estimate of physiologically relevant parameters when analyzing mouse gastric emptying data. PMID:26045615

Constraining f(T) teleparallel gravity by big bang nucleosynthesis: f(T) cosmology and BBN.

PubMed

Capozziello, S; Lambiase, G; Saridakis, E N

2017-01-01

We use Big Bang Nucleosynthesis (BBN) observational data on the primordial abundance of light elements to constrain f ( T ) gravity. The three most studied viable f ( T ) models, namely the power law, the exponential and the square-root exponential are considered, and the BBN bounds are adopted in order to extract constraints on their free parameters. For the power-law model, we find that the constraints are in agreement with those obtained using late-time cosmological data. For the exponential and the square-root exponential models, we show that for reliable regions of parameters space they always satisfy the BBN bounds. We conclude that viable f ( T ) models can successfully satisfy the BBN constraints.

Nonlinear Dynamics and the Growth of Literature.

ERIC Educational Resources Information Center

Tabah, Albert N.

1992-01-01

Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…

Bounded energy states in homogeneous turbulent shear flow - An alternative view

NASA Technical Reports Server (NTRS)

Bernard, P. S.; Speziale, C. G.

1992-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k-epsilon model modified to account for net vortex stretching.

Resource acquisition, distribution and end-use efficiencies and the growth of industrial society

NASA Astrophysics Data System (ADS)

Jarvis, A. J.; Jarvis, S. J.; Hewitt, C. N.

2015-10-01

A key feature of the growth of industrial society is the acquisition of increasing quantities of resources from the environment and their distribution for end-use. With respect to energy, the growth of industrial society appears to have been near-exponential for the last 160 years. We provide evidence that indicates that the global distribution of resources that underpins this growth may be facilitated by the continual development and expansion of near-optimal directed networks (roads, railways, flight paths, pipelines, cables etc.). However, despite this continual striving for optimisation, the distribution efficiencies of these networks must decline over time as they expand due to path lengths becoming longer and more tortuous. Therefore, to maintain long-term exponential growth the physical limits placed on the distribution networks appear to be counteracted by innovations deployed elsewhere in the system, namely at the points of acquisition and end-use of resources. We postulate that the maintenance of the growth of industrial society, as measured by global energy use, at the observed rate of ~ 2.4 % yr-1 stems from an implicit desire to optimise patterns of energy use over human working lifetimes.

[Effect of the development phase and growth rate of a Shigella sonnei population on the reproduction of homologous bacteriophage].

PubMed

Voroshilova, N N; Kazakova, T B

1983-04-01

This study showed that the minimum latent period (20 minutes) of the intracellular multiplication of dysentery bacteriophage S-9 in the population of S. sonnei substrate strain under the conditions of static heterogeneous surface batch cultivation was observed at the end of the lag phase and at the growth acceleration phase, in the first and second thirds of the exponential curve, while the maximum latent period (35-40 minutes) was observed at the stationary phase. The maximum yield of phage S-9 from one infected bacterial cell (628.3 +/- 116.8) was registered during the first third of the phase of the exponential growth of the bacterial population and the minimum yield (18.66 +/- 6.6), at the beginning of the lag phase. The significant direct correlation between the specific growth rate of the bacterial population and the yield of the phage from one infected bacterial cell at the end of the lag phase, at the growth acceleration and deceleration phases, as well as the significant inverse correlation between the yield of the phage and the time of the generation of the bacterial population at the growth acceleration phase were established.

Ecological requirements for pallid sturgeon reproduction and recruitment in the Missouri River—A synthesis of science, 2005 to 2012

USGS Publications Warehouse

Delonay, Aaron J.; Chojnacki, Kimberly A.; Jacobson, Robert B.; Albers, Janice L.; Braaten, Patrick J.; Bulliner, Edward A.; Elliott, Caroline M.; Erwin, Susannah O.; Fuller, David B; Haas, Justin D.; Ladd, Hallie L.A.; Mestl, Gerald E.; Papoulias, Diana M.; Wildhaber, Mark L.

2016-01-20

Scientific understanding of the ecological requirements of pallid sturgeon has increased almost exponentially in the last two decades, and efforts are now turning from understanding fundamental biology of the species to quantifying how population dynamics relate to potential management actions. Progress in developing the science needed to inform management actions on the Missouri River may benefit from continuation of monitoring of reproductive cycles, reproductive movements, growth, and survival of telemetry tagged adults, increased emphasis on focused, complementary field and laboratory studies of factors influencing early life history, implementation of studies to resolve the role of food limitations in growth, survival, and reproductive condition, and implementation of studies designed specifically to parameterize models linking management to populations.

Multiple relaxations of the cluster surface diffusion in a homoepitaxial SrTiO3 layer

NASA Astrophysics Data System (ADS)

Woo, Chang-Su; Chu, Kanghyun; Song, Jong-Hyun; Yang, Chan-Ho

2018-03-01

We examine the surface diffusion process of adatomic clusters on a (001)-oriented SrTiO3 single crystal using reflection high energy electron diffraction (RHEED). We find that the recovery curve of the RHEED intensity acquired after a homoepitaxial half-layer growth can be accurately fit into a double exponential function, indicating the existence of two dominant relaxation mechanisms. The characteristic relaxation times at selected growth temperatures are investigated to determine the diffusion activation barriers of 0.67 eV and 0.91 eV, respectively. The Monte Carlo simulation of the cluster hopping model suggests that the decrease in the number of dimeric and trimeric clusters during surface diffusion is the origin of the observed relaxation phenomena.

Early stages of Ostwald ripening

NASA Astrophysics Data System (ADS)

Shneidman, Vitaly A.

2013-07-01

The Becker-Döring (BD) nucleation equation is known to predict a narrow double-exponential front (DEF) in the distribution of growing particles over sizes, which is due to early transient effects. When mass conservation is included, nucleation is eventually exhausted while independent growth is replaced by ripening. Despite the enormous difference in the associated time scales, and the resulting demand on numerics, within the generalized BD model the early DEF is shown to be crucial for the selection of the unique self-similar Lifshitz-Slyozov-Wagner asymptotic regime. Being preserved till the latest stages of growth, the DEF provides a universal part of the initial conditions for the ripening problem, regardless of the mass exchange mechanism between the nucleus and the matrix.

Most-Critical Transient Disturbances in an Incompressible Flat-Plate Boundary Layer

NASA Astrophysics Data System (ADS)

Monschke, Jason; White, Edward

2015-11-01

Transient growth is a linear disturbance growth mechanism that plays a key role in roughness-induced boundary-layer transition. It occurs when superposed stable, non-orthogonal continuous spectrum modes experience algebraic disturbance growth followed by exponential decay. Algebraic disturbance growth can modify the basic state making it susceptible to secondary instabilities rapidly leading to transition. Optimal disturbance theory was developed to model the most-dangerous disturbances. However, evidence suggests roughness-induced transient growth is sub-optimal yet leads to transition earlier than optimal theory suggests. This research computes initial disturbances most unstable to secondary instabilities to further develop the applicability of transient growth theory to surface roughness. The main approach is using nonlinear adjoint optimization with solutions of the parabolized Navier-Stokes and BiGlobal stability equations. Two objective functions were considered: disturbance kinetic energy growth and sinuous instability growth rate. The first objective function was used as validation of the optimization method. Counter-rotating streamwise vortices located low in the boundary layer maximize the sinuous instability growth rate. The authors would like to acknowledge NASA and the AFOSR for funding this work through AFOSR Grant FA9550-09-1-0341.

The matrix exponential in transient structural analysis

NASA Technical Reports Server (NTRS)

Minnetyan, Levon

1987-01-01

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Modeling of magnitude distributions by the generalized truncated exponential distribution

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-01-01

The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cutoff exponential distribution (CED). The TED is frequently used in seismic hazard analysis although it has a weak point: when two TEDs with equal parameters except the upper bound magnitude are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. We overcome it by the generalization of the abovementioned exponential distributions: the generalized truncated exponential distribution (GTED). Therein, identical exponential distributions are mixed by the probability distribution of the correct cutoff points. This distribution model is flexible in the vicinity of the upper bound magnitude and is equal to the exponential distribution for smaller magnitudes. Additionally, the exponential distributions TED and CED are special cases of the GTED. We discuss the possible ways of estimating its parameters and introduce the normalized spacing for this purpose. Furthermore, we present methods for geographic aggregation and differentiation of the GTED and demonstrate the potential and universality of our simple approach by applying it to empirical data. The considerable improvement by the GTED in contrast to the TED is indicated by a large difference between the corresponding values of the Akaike information criterion.

A Coarse-Grained Biophysical Model of E. coli and Its Application to Perturbation of the rRNA Operon Copy Number

PubMed Central

Tadmor, Arbel D.; Tlusty, Tsvi

2008-01-01

We propose a biophysical model of Escherichia coli that predicts growth rate and an effective cellular composition from an effective, coarse-grained representation of its genome. We assume that E. coli is in a state of balanced exponential steady-state growth, growing in a temporally and spatially constant environment, rich in resources. We apply this model to a series of past measurements, where the growth rate and rRNA-to-protein ratio have been measured for seven E. coli strains with an rRNA operon copy number ranging from one to seven (the wild-type copy number). These experiments show that growth rate markedly decreases for strains with fewer than six copies. Using the model, we were able to reproduce these measurements. We show that the model that best fits these data suggests that the volume fraction of macromolecules inside E. coli is not fixed when the rRNA operon copy number is varied. Moreover, the model predicts that increasing the copy number beyond seven results in a cytoplasm densely packed with ribosomes and proteins. Assuming that under such overcrowded conditions prolonged diffusion times tend to weaken binding affinities, the model predicts that growth rate will not increase substantially beyond the wild-type growth rate, as indicated by other experiments. Our model therefore suggests that changing the rRNA operon copy number of wild-type E. coli cells growing in a constant rich environment does not substantially increase their growth rate. Other observations regarding strains with an altered rRNA operon copy number, such as nucleoid compaction and the rRNA operon feedback response, appear to be qualitatively consistent with this model. In addition, we discuss possible design principles suggested by the model and propose further experiments to test its validity. PMID:18437222

Competitive fitness during feast and famine: how SOS DNA polymerases influence physiology and evolution in Escherichia coli.

PubMed

Corzett, Christopher H; Goodman, Myron F; Finkel, Steven E

2013-06-01

Escherichia coli DNA polymerases (Pol) II, IV, and V serve dual roles by facilitating efficient translesion DNA synthesis while simultaneously introducing genetic variation that can promote adaptive evolution. Here we show that these alternative polymerases are induced as cells transition from exponential to long-term stationary-phase growth in the absence of induction of the SOS regulon by external agents that damage DNA. By monitoring the relative fitness of isogenic mutant strains expressing only one alternative polymerase over time, spanning hours to weeks, we establish distinct growth phase-dependent hierarchies of polymerase mutant strain competitiveness. Pol II confers a significant physiological advantage by facilitating efficient replication and creating genetic diversity during periods of rapid growth. Pol IV and Pol V make the largest contributions to evolutionary fitness during long-term stationary phase. Consistent with their roles providing both a physiological and an adaptive advantage during stationary phase, the expression patterns of all three SOS polymerases change during the transition from log phase to long-term stationary phase. Compared to the alternative polymerases, Pol III transcription dominates during mid-exponential phase; however, its abundance decreases to <20% during long-term stationary phase. Pol IV transcription dominates as cells transition out of exponential phase into stationary phase and a burst of Pol V transcription is observed as cells transition from death phase to long-term stationary phase. These changes in alternative DNA polymerase transcription occur in the absence of SOS induction by exogenous agents and indicate that cell populations require appropriate expression of all three alternative DNA polymerases during exponential, stationary, and long-term stationary phases to attain optimal fitness and undergo adaptive evolution.

Forgotten Fundamentals of the Energy Crisis

ERIC Educational Resources Information Center

Bartlett, Albert A.

1978-01-01

Explains using exponential mathematics, the effect of growth on rate of consuming energy resources. Concludes that we are running out of energy resources at a greater rate than many people think. Lists few options left such as conservation by stopping growth of consumption, recycling, and research to develop alternate sources. (GA)

Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 2: Structure Design for State Estimation with Secondary Measurements

PubMed Central

2017-01-01

This work investigates the design of alternative monitoring tools based on state estimators for industrial crystallization systems with nucleation, growth, and agglomeration kinetics. The estimation problem is regarded as a structure design problem where the estimation model and the set of innovated states have to be chosen; the estimator is driven by the available measurements of secondary variables. On the basis of Robust Exponential estimability arguments, it is found that the concentration is distinguishable with temperature and solid fraction measurements while the crystal size distribution (CSD) is not. Accordingly, a state estimator structure is selected such that (i) the concentration (and other distinguishable states) are innovated by means of the secondary measurements processed with the geometric estimator (GE), and (ii) the CSD is estimated by means of a rigorous model in open loop mode. The proposed estimator has been tested through simulations showing good performance in the case of mismatch in the initial conditions, parametric plant-model mismatch, and noisy measurements. PMID:28890604

Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 2: Structure Design for State Estimation with Secondary Measurements.

PubMed

Porru, Marcella; Özkan, Leyla

2017-08-30

This work investigates the design of alternative monitoring tools based on state estimators for industrial crystallization systems with nucleation, growth, and agglomeration kinetics. The estimation problem is regarded as a structure design problem where the estimation model and the set of innovated states have to be chosen; the estimator is driven by the available measurements of secondary variables. On the basis of Robust Exponential estimability arguments, it is found that the concentration is distinguishable with temperature and solid fraction measurements while the crystal size distribution (CSD) is not. Accordingly, a state estimator structure is selected such that (i) the concentration (and other distinguishable states) are innovated by means of the secondary measurements processed with the geometric estimator (GE), and (ii) the CSD is estimated by means of a rigorous model in open loop mode. The proposed estimator has been tested through simulations showing good performance in the case of mismatch in the initial conditions, parametric plant-model mismatch, and noisy measurements.

Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.

PubMed

Luque-Fernandez, Miguel Angel; Belot, Aurélien; Quaresma, Manuela; Maringe, Camille; Coleman, Michel P; Rachet, Bernard

2016-10-01

In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

Thin film modeling of crystal dissolution and growth in confinement.

PubMed

Gagliardi, Luca; Pierre-Louis, Olivier

2018-01-01

We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication approximation. The model also accounts for the disjoining pressure and surface tension. Within this framework, we obtain evolution equations which govern the nonequilibrium dynamics of the crystal interface. Based on this model, we explore the problem of dissolution under an external load, known as pressure solution. We find that in steady state, diverging (power-law) crystal-surface repulsions lead to flat contacts with a monotonic increase of the dissolution rate as a function of the load. Forces induced by viscous dissipation then surpass those due to disjoining pressure at large enough loads. In contrast, finite repulsions (exponential) lead to sharp pointy contacts with a dissolution rate independent of the load and the liquid viscosity. Ultimately, in steady state, the crystal never touches the substrate when pressed against it. This result is independent from the nature of the crystal-surface interaction due to the combined effects of viscosity and surface tension.

Thin film modeling of crystal dissolution and growth in confinement

NASA Astrophysics Data System (ADS)

Gagliardi, Luca; Pierre-Louis, Olivier

2018-01-01

We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication approximation. The model also accounts for the disjoining pressure and surface tension. Within this framework, we obtain evolution equations which govern the nonequilibrium dynamics of the crystal interface. Based on this model, we explore the problem of dissolution under an external load, known as pressure solution. We find that in steady state, diverging (power-law) crystal-surface repulsions lead to flat contacts with a monotonic increase of the dissolution rate as a function of the load. Forces induced by viscous dissipation then surpass those due to disjoining pressure at large enough loads. In contrast, finite repulsions (exponential) lead to sharp pointy contacts with a dissolution rate independent of the load and the liquid viscosity. Ultimately, in steady state, the crystal never touches the substrate when pressed against it. This result is independent from the nature of the crystal-surface interaction due to the combined effects of viscosity and surface tension.

A dynamic growth model of macroalgae: Application in an estuary recovering from treated wastewater and earthquake-driven eutrophication

NASA Astrophysics Data System (ADS)

Ren, Jeffrey S.; Barr, Neill G.; Scheuer, Kristin; Schiel, David R.; Zeldis, John

2014-07-01

A dynamic growth model of macroalgae was developed to predict growth of the green macroalga Ulva sp. in response to changes in environmental variables. The model is based on common physiological behaviour of macroalgae and hence has general applicability to macroalgae. Three state variables (nitrogen, carbon and phosphorus) were used to describe physiological processes and functional differences between nutrient and carbon uptakes. Carbon uptake is modelled as a function of temperature, light, algal internal state and water current, while nutrient uptake depends on internal state, temperature and environmental nutrient level. Growth can only occur when nutrients in the environment and in the internal storage pools (N-quota and P-quota) reach threshold levels. Physiological rates follow the Arrhenius relationship and increase exponentially with increasing temperature within the temperature tolerance range of a species. When parameterised and applied to Ulva sp. in the eutrophic Avon-Heathcote Estuary, New Zealand, the model generally reproduced field observations of Ulva sp. growth and abundance. Growth followed a clear seasonal cycle with biomass increasing from early-middle summer, reaching peak values in early autumn and then decreasing. Conversely, N-quotient levels were maximal during the winter months, declining during summer peak growth. These seasonal patterns were collectively driven by temperature, light intensity and nutrients. The model captured the N-quota and growth responses of Ulva sp. to the N-reduction arising from diversion of treated wastewater from the Avon-Heathcote Estuary to an offshore outfall in 2010, and of raw sewage N-discharges resulting from wastewater infrastructure damage caused by the Canterbury earthquakes in 2011. Sensitivity analyses revealed that temperature-related parameters and maximum uptake rate of C were among the most sensitive parameters in predicting biomass. In addition, the earthquake-derived changes in reduction of immersion time and decrease in the start biomass prior to summer blooms were shown to drive considerable declines in summer growth and biomass of Ulva sp.

Quantitative imaging reveals heterogeneous growth dynamics and treatment-dependent residual tumor distributions in a three-dimensional ovarian cancer model

NASA Astrophysics Data System (ADS)

Celli, Jonathan P.; Rizvi, Imran; Evans, Conor L.; Abu-Yousif, Adnan O.; Hasan, Tayyaba

2010-09-01

Three-dimensional tumor models have emerged as valuable in vitro research tools, though the power of such systems as quantitative reporters of tumor growth and treatment response has not been adequately explored. We introduce an approach combining a 3-D model of disseminated ovarian cancer with high-throughput processing of image data for quantification of growth characteristics and cytotoxic response. We developed custom MATLAB routines to analyze longitudinally acquired dark-field microscopy images containing thousands of 3-D nodules. These data reveal a reproducible bimodal log-normal size distribution. Growth behavior is driven by migration and assembly, causing an exponential decay in spatial density concomitant with increasing mean size. At day 10, cultures are treated with either carboplatin or photodynamic therapy (PDT). We quantify size-dependent cytotoxic response for each treatment on a nodule by nodule basis using automated segmentation combined with ratiometric batch-processing of calcein and ethidium bromide fluorescence intensity data (indicating live and dead cells, respectively). Both treatments reduce viability, though carboplatin leaves micronodules largely structurally intact with a size distribution similar to untreated cultures. In contrast, PDT treatment disrupts micronodular structure, causing punctate regions of toxicity, shifting the distribution toward smaller sizes, and potentially increasing vulnerability to subsequent chemotherapeutic treatment.

Thermal growth potential of Atlantic cod by the end of the 21st century.

PubMed

Butzin, Martin; Pörtner, Hans-Otto

2016-12-01

Ocean warming may lead to smaller body sizes of marine ectotherms, because metabolic rates increase exponentially with temperature while the capacity of the cardiorespiratory system to match enhanced oxygen demands is limited. Here, we explore the impact of rising sea water temperatures on Atlantic cod (Gadus morhua), an economically important fish species. We focus on changes in the temperature-dependent growth potential by a transfer function model combining growth observations with climate model ensemble temperatures. Growth potential is expressed in terms of asymptotic body weight and depends on water temperature. We consider changes between the periods 1985-2004 and 2081-2100, assuming that future sea water temperatures will evolve according to climate projections for IPCC AR5 scenario RCP8.5. Our model projects a response of Atlantic cod to future warming, differentiated according to ocean regions, leading to increases of asymptotic weight in the Barents Sea, while weights are projected to decline at the southern margin of the biogeographic range. Southern spawning areas will disappear due to thermal limitation of spawning stages. These projections match the currently observed biogeographic shifts and the temperature- and oxygen-dependent decline in routine aerobic scope at southern distribution limits. © 2016 John Wiley & Sons Ltd.

FOG: Fighting the Achilles' Heel of Gossip Protocols with Fountain Codes

NASA Astrophysics Data System (ADS)

Champel, Mary-Luc; Kermarrec, Anne-Marie; Le Scouarnec, Nicolas

Gossip protocols are well known to provide reliable and robust dissemination protocols in highly dynamic systems. Yet, they suffer from high redundancy in the last phase of the dissemination. In this paper, we combine fountain codes (rateless erasure-correcting codes) together with gossip protocols for a robust and fast content dissemination in large-scale dynamic systems. The use of fountain enables to eliminate the unnecessary redundancy of gossip protocols. We propose the design of FOG, which fully exploits the first exponential growth phase (where the data is disseminated exponentially fast) of gossip protocols while avoiding the need for the shrinking phase by using fountain codes. FOG voluntarily increases the number of disseminations but limits those disseminations to the exponential growth phase. In addition, FOG creates a split-graph overlay that splits the peers between encoders and forwarders. Forwarder peers become encoders as soon as they have received the whole content. In order to benefit even further and quicker from encoders, FOG biases the dissemination towards the most advanced peers to make them complete earlier.

Marketing percolation

NASA Astrophysics Data System (ADS)

Goldenberg, J.; Libai, B.; Solomon, S.; Jan, N.; Stauffer, D.

2000-09-01

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass, Manage. Sci. 15 (1969) 215). This mean-field approach is contrasted with the discrete percolation on a lattice, with simulations of "social percolation" (Solomon et al., Physica A 277 (2000) 239) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.

Scaling and intermittency in incoherent α-shear dynamo

NASA Astrophysics Data System (ADS)

Mitra, Dhrubaditya; Brandenburg, Axel

2012-03-01

We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian.

Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

NASA Astrophysics Data System (ADS)

Honda, Ryojiro; Wakita, Jun-ichi; Katori, Makoto

2015-11-01

Under hard-agar and nutrient-rich conditions, a cell of Bacillus subtilis grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential folding processes, and multifold structures extend over an agar plate. We report that the growth process from the exponential phase to the stationary phase is well described by the time evolution of fractal dimensions of the filament configuration. We propose a method of characterizing filament configurations using a set of lengths of multifold parts of a filament. Systems of differential equations are introduced to describe the folding processes that create multifold structures in the early stage of the growth process. We show that the fitting of experimental data to the solutions of equations is excellent, and the parameters involved in our model systems are determined.

Effect of deposition rate and NNN interactions on adatoms mobility in epitaxial growth

NASA Astrophysics Data System (ADS)

Hamouda, Ajmi B. H.; Mahjoub, B.; Blel, S.

2017-07-01

This paper provides a detailed analysis of the surface diffusion problem during epitaxial step-flow growth using a simple theoretical model for the diffusion equation of adatoms concentration. Within this framework, an analytical expression for the adatom mobility as a function of the deposition rate and the Next-Nearest-Neighbor (NNN) interactions is derived and compared with the effective mobility computed from kinetic Monte Carlo (kMC) simulations. As far as the 'small' step velocity or relatively weak deposition rate commonly used for copper growth is concerned, an excellent quantitative agreement with the theoretical prediction is found. The effective adatoms mobility is shown to exhibit an exponential decrease with NNN interactions strength and increases in roughly linear behavior versus deposition rate F. The effective step stiffness and the adatoms mobility are also shown to be closely related to the concentration of kinks.

Decay and growth laws in homogeneous shear turbulence

NASA Astrophysics Data System (ADS)

Briard, Antoine; Gomez, Thomas; Mons, Vincent; Sagaut, Pierre

2016-07-01

Homogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow part of the pressure-strain tensor is derived for the return to isotropy process when mean velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter.

Simulating the effects of climatic variation on stem carbon accumulation of a ponderosa pine stand: comparison with annual growth increment data.

PubMed

Hunt, E R; Martin, F C; Running, S W

1991-01-01

Simulation models of ecosystem processes may be necessary to separate the long-term effects of climate change on forest productivity from the effects of year-to-year variations in climate. The objective of this study was to compare simulated annual stem growth with measured annual stem growth from 1930 to 1982 for a uniform stand of ponderosa pine (Pinus ponderosa Dougl.) in Montana, USA. The model, FOREST-BGC, was used to simulate growth assuming leaf area index (LAI) was either constant or increasing. The measured stem annual growth increased exponentially over time; the differences between the simulated and measured stem carbon accumulations were not large. Growth trends were removed from both the measured and simulated annual increments of stem carbon to enhance the year-to-year variations in growth resulting from climate. The detrended increments from the increasing LAI simulation fit the detrended increments of the stand data over time with an R(2) of 0.47; the R(2) increased to 0.65 when the previous year's simulated detrended increment was included with the current year's simulated increment to account for autocorrelation. Stepwise multiple linear regression of the detrended increments of the stand data versus monthly meteorological variables had an R(2) of 0.37, and the R(2) increased to 0.47 when the previous year's meteorological data were included to account for autocorrelation. Thus, FOREST-BGC was more sensitive to the effects of year-to-year climate variation on annual stem growth than were multiple linear regression models.

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-05-01

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Determination of co-metabolism for 1,1,1-trichloro-2,2-bis(4-chlorophenyl) ethane (DDT) degradation with enzymes from Trametes versicolor U97.

PubMed

Sari, Ajeng Arum; Tachibana, Sanro; Itoh, Kazutaka

2012-08-01

Trametes versicolor U97 isolated from nature degraded 73% of the 1,1,1-trichloro-2,2-bis(4-chlorophenyl) ethane (DDT) in a malt extract liquid medium after a 40-d incubation period. This paper presents a kinetic study of microbial growth using the Monod equation. T. versicolor U97 degraded DDT during an exponential growth phase, using glucose as a carbon source for growth. The growth of T. versicolor U97 was not affected by DDT. DDT was degraded by T. versicolor U97 only when the secondary metabolism coincided with the production of several enzymes. Furthermore, modeling of several inhibitors using the partial least squares function in Minitab 15, revealed lignin peroxidase (98.7 U/l) plays a role in the degradation of DDT. T. versicolor U97 produced several metabolites included a single-ring aromatic compound, 4-chlorobenzoic acid. Copyright © 2012 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

Estimating chlorophyll content of spartina alterniflora at leaf level using hyper-spectral data

NASA Astrophysics Data System (ADS)

Wang, Jiapeng; Shi, Runhe; Liu, Pudong; Zhang, Chao; Chen, Maosi

2017-09-01

Spartina alterniflora, one of most successful invasive species in the world, was firstly introduced to China in 1979 to accelerate sedimentation and land formation via so-called "ecological engineering", and it is now widely distributed in coastal saltmarshes in China. A key question is how to retrieve chlorophyll content to reflect growth status, which has important implication of potential invasiveness. In this work, an estimation model of chlorophyll content of S. alterniflora was developed based on hyper-spectral data in the Dongtan Wetland, Yangtze Estuary, China. The spectral reflectance of S. alterniflora leaves and their corresponding chlorophyll contents were measured, and then the correlation analysis and regression (i.e., linear, logarithmic, quadratic, power and exponential regression) method were established. The spectral reflectance was transformed and the feature parameters (i.e., "san bian", "lv feng" and "hong gu") were extracted to retrieve the chlorophyll content of S. alterniflora . The results showed that these parameters had a large correlation coefficient with chlorophyll content. On the basis of the correlation coefficient, mathematical models were established, and the models of power and exponential based on SDb had the least RMSE and larger R2 , which had a good performance regarding the inversion of chlorophyll content of S. alterniflora.

Extension of Liouville Formalism to Postinstability Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

NASA Astrophysics Data System (ADS)

Maslov, Sergei; Sneppen, Kim

2017-01-01

Determinants of species diversity in microbial ecosystems remain poorly understood. Bacteriophages are believed to increase the diversity by the virtue of Kill-the-Winner infection bias preventing the fastest growing organism from taking over the community. Phage-bacterial ecosystems are traditionally described in terms of the static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced by losses due to phage predation. Here we consider a more dynamic scenario in which phage infections give rise to abrupt and severe collapses of bacterial populations whenever they become sufficiently large. As a consequence, each bacterial population in our model follows cyclic dynamics of exponential growth interrupted by sudden declines. The total population of all species fluctuates around the carrying capacity of the environment, making these cycles cryptic. While a subset of the slowest growing species in our model is always driven towards extinction, in general the overall ecosystem diversity remains high. The number of surviving species is inversely proportional to the variation in their growth rates but increases with the frequency and severity of phage-induced collapses. Thus counter-intuitively we predict that microbial communities exposed to more violent perturbations should have higher diversity.

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

PubMed Central

Maslov, Sergei; Sneppen, Kim

2017-01-01

Determinants of species diversity in microbial ecosystems remain poorly understood. Bacteriophages are believed to increase the diversity by the virtue of Kill-the-Winner infection bias preventing the fastest growing organism from taking over the community. Phage-bacterial ecosystems are traditionally described in terms of the static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced by losses due to phage predation. Here we consider a more dynamic scenario in which phage infections give rise to abrupt and severe collapses of bacterial populations whenever they become sufficiently large. As a consequence, each bacterial population in our model follows cyclic dynamics of exponential growth interrupted by sudden declines. The total population of all species fluctuates around the carrying capacity of the environment, making these cycles cryptic. While a subset of the slowest growing species in our model is always driven towards extinction, in general the overall ecosystem diversity remains high. The number of surviving species is inversely proportional to the variation in their growth rates but increases with the frequency and severity of phage-induced collapses. Thus counter-intuitively we predict that microbial communities exposed to more violent perturbations should have higher diversity. PMID:28051127

Mapping the Spread of Methamphetamine Abuse in California From 1995 to 2008

PubMed Central

Ponicki, William R.; Remer, Lillian G.; Waller, Lance A.; Zhu, Li; Gorman, Dennis M.

2013-01-01

Objectives. From 1983 to 2008, the incidence of methamphetamine abuse and dependence (MA) presenting at hospitals in California increased 13-fold. We assessed whether this growth could be characterized as a drug epidemic. Methods. We geocoded MA discharges to residential zip codes from 1995 through 2008. We related discharges to population and environmental characteristics using Bayesian Poisson conditional autoregressive models, correcting for small area effects and spatial misalignment and enabling an assessment of contagion between areas. Results. MA incidence increased exponentially in 3 phases interrupted by implementation of laws limiting access to methamphetamine precursors. MA growth from 1999 through 2008 was 17% per year. MA was greatest in areas with larger White or Hispanic low-income populations, small household sizes, and good connections to highway systems. Spatial misalignment was a source of bias in estimated effects. Spatial autocorrelation was substantial, accounting for approximately 80% of error variance in the model. Conclusions. From 1995 through 2008, MA exhibited signs of growth and spatial spread characteristic of drug epidemics, spreading most rapidly through low-income White and Hispanic populations living outside dense urban areas. PMID:23078474

Cyberinfrastructure for the NSF Ocean Observatories Initiative

NASA Astrophysics Data System (ADS)

Orcutt, J. A.; Vernon, F. L.; Arrott, M.; Chave, A.; Krueger, I.; Schofield, O.; Glenn, S.; Peach, C.; Nayak, A.

2007-12-01

The Internet today is vastly different than the Internet that we knew even five years ago and the changes that will be evident five years from now, when the NSF Ocean Observatories Initiative (OOI) prototype has been installed, are nearly unpredictable. Much of this progress is based on the exponential growth in capabilities of consumer electronics and information technology; the reality of this exponential behavior is rarely appreciated. For example, the number of transistors on a square cm of silicon will continue to double every 18 months, the density of disk storage will double every year, and network bandwidth will double every eight months. Today's desktop 2TB RAID will be 64TB and the 10Gbps Regional Scale Network fiber optical connection will be running at 1.8Tbps. The same exponential behavior characterizes the future of genome sequencing. The first two sequences of composites of individuals' genes cost tens of millions of dollars in 2001. Dr. Craig Venter just published a more accurate complete human genome (his own) at a cost on the order of 100,000. The J. Craig Venter Institute has provided support for the X Prize for Genomics offering 10M to the first successful sequencing of a human genome for $1,000. It's anticipated that the prize will be won within five years. Major advances in technology that are broadly viewed as disruptive or revolutionary rather than evolutionary will often depend upon the exploitation of exponential expansions in capability. Applications of these ideas to the OOI will be discussed. Specifically, the agile ability to scale cyberinfrastructure commensurate with the exponential growth of sensors, networks and computational capability and demand will be described.

Control of three-dimensional waves on thin liquid films

NASA Astrophysics Data System (ADS)

Tomlin, Ruben; Gomes, Susana; Pavliotis, Greg; Papageorgiou, Demetrios

2017-11-01

We consider a weakly nonlinear model for interfacial waves on three-dimensional thin films on inclined flat planes - the Kuramoto-Sivashinsky equation. The flow is driven by gravity, and is allowed to be overlying or hanging on the flat substrate. Blowing and suction controls are applied at the substrate surface. We explore the instability of the transverse modes for hanging arrangements, which are unbounded and grow exponentially. The structure of the equations allows us to construct optimal transverse controls analytically to prevent this transverse growth. We also may consider the influence of transverse modes on overlying film flows, these modes are damped out if uncontrolled. We also consider the more physical concept of point actuated controls which are modelled using Dirac delta functions. We first study the case of proportional control, where the actuation at a point depends on the local interface height alone. Here, we study the influence of control strength and number/location of actuators on the possible stabilization of the zero solution. We also consider the full feedback problem, which assumes that we can observe the full interface and allow communication between actuators. Using these controls we can obtain exponential stability where proportional controls fail, and stabilize non-trivial solutions.

Interaction of estradiol and high density lipoproteins on proliferation of the human breast cancer cell line MCF-7 adapted to grow in serum free conditions

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

Jozan, S.; Faye, J.C.; Tournier, J.F.

1985-11-27

The responsiveness of the human mammary carcinoma cell line MCF-7 to estradiol and tamoxifen treatment has been studied in different culture conditions. Cells from exponentially growing cultures were compared with cells in their initial cycles after replating from confluent cultures (''confluent-log'' cells). It has been observed that estradiol stimulation of tritiated thymidine incorporation decreases with cell density and that ''confluent-log'' cells are estrogen unresponsive for a period of four cell cycles in serum-free medium conditions. On the other hand, growth of cells replated from exponentially growing, as well as from confluent cultures, can be inhibited by tamoxifen or a combinedmore » treatment with tamoxifen and the progestin levonorgestrel. This growth inhibitory effect can be rescued by estradiol when cells are replated from exponentially growing cultures. The growth inhibitory effect cannot be rescued by estradiol alone (10(-10) to 10(-8) M) when cells are replated from confluent cultures. In this condition, the addition of steroid depleted serum is necessary to reverse the state of estradiol unresponsiveness. Serum can be replaced by high density lipoproteins but not by low density lipoproteins or lipoprotein deficient serum. The present data show that estradiol and HDL interact in the control of MCF-7 cell proliferation.« less

A signature of 12 microRNAs is robustly associated with growth rate in a variety of CHO cell lines.

PubMed

Klanert, Gerald; Jadhav, Vaibhav; Shanmukam, Vinoth; Diendorfer, Andreas; Karbiener, Michael; Scheideler, Marcel; Bort, Juan Hernández; Grillari, Johannes; Hackl, Matthias; Borth, Nicole

2016-10-10

As Chinese Hamster Ovary (CHO) cells are the cell line of choice for the production of human-like recombinant proteins, there is interest in genetic optimization of host cell lines to overcome certain limitations in their growth rate and protein secretion. At the same time, a detailed understanding of these processes could be used to advantage by identification of marker transcripts that characterize states of performance. In this context, microRNAs (miRNAs) that exhibit a robust correlation to the growth rate of CHO cells were determined by analyzing miRNA expression profiles in a comprehensive collection of 46 samples including CHO-K1, CHO-S and CHO-DUKXB11, which were adapted to various culture conditions, and analyzed in different growth stages using microarrays. By applying Spearman or Pearson correlation coefficient criteria of>|0.6|, miRNAs with high correlation to the overall growth, or growth rates observed in exponential, serum-free, and serum-free exponential phase were identified. An overlap of twelve miRNAs common for all sample sets was revealed, with nine positively and three negatively correlating miRNAs. The here identified panel of miRNAs can help to understand growth regulation in CHO cells and contains putative engineering targets as well as biomarkers for cell lines with advantageous growth characteristics. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Estimating time since infection in early homogeneous HIV-1 samples using a poisson model

PubMed Central

2010-01-01

Background The occurrence of a genetic bottleneck in HIV sexual or mother-to-infant transmission has been well documented. This results in a majority of new infections being homogeneous, i.e., initiated by a single genetic strain. Early after infection, prior to the onset of the host immune response, the viral population grows exponentially. In this simple setting, an approach for estimating evolutionary and demographic parameters based on comparison of diversity measures is a feasible alternative to the existing Bayesian methods (e.g., BEAST), which are instead based on the simulation of genealogies. Results We have devised a web tool that analyzes genetic diversity in acutely infected HIV-1 patients by comparing it to a model of neutral growth. More specifically, we consider a homogeneous infection (i.e., initiated by a unique genetic strain) prior to the onset of host-induced selection, where we can assume a random accumulation of mutations. Previously, we have shown that such a model successfully describes about 80% of sexual HIV-1 transmissions provided the samples are drawn early enough in the infection. Violation of the model is an indicator of either heterogeneous infections or the initiation of selection. Conclusions When the underlying assumptions of our model (homogeneous infection prior to selection and fast exponential growth) are met, we are under a very particular scenario for which we can use a forward approach (instead of backwards in time as provided by coalescent methods). This allows for more computationally efficient methods to derive the time since the most recent common ancestor. Furthermore, the tool performs statistical tests on the Hamming distance frequency distribution, and outputs summary statistics (mean of the best fitting Poisson distribution, goodness of fit p-value, etc). The tool runs within minutes and can readily accommodate the tens of thousands of sequences generated through new ultradeep pyrosequencing technologies. The tool is available on the LANL website. PMID:20973976

Two-stage unified stretched-exponential model for time-dependence of threshold voltage shift under positive-bias-stresses in amorphous indium-gallium-zinc oxide thin-film transistors

NASA Astrophysics Data System (ADS)

Jeong, Chan-Yong; Kim, Hee-Joong; Hong, Sae-Young; Song, Sang-Hun; Kwon, Hyuck-In

2017-08-01

In this study, we show that the two-stage unified stretched-exponential model can more exactly describe the time-dependence of threshold voltage shift (ΔV TH) under long-term positive-bias-stresses compared to the traditional stretched-exponential model in amorphous indium-gallium-zinc oxide (a-IGZO) thin-film transistors (TFTs). ΔV TH is mainly dominated by electron trapping at short stress times, and the contribution of trap state generation becomes significant with an increase in the stress time. The two-stage unified stretched-exponential model can provide useful information not only for evaluating the long-term electrical stability and lifetime of the a-IGZO TFT but also for understanding the stress-induced degradation mechanism in a-IGZO TFTs.

Asian Pentecostalism: A Religion Whose Only Limit Is the Sky

ERIC Educational Resources Information Center

Ma, Wonsuk

2004-01-01

The study surveys the current growth of Pentecostal Christianity, as defined broadly, in Asia, particularly in comparison with Latin America and Africa, predicting that the future growth is expected to be exponential. In a brief historical survey, the continent is divided into four categories depending on the beginning and development of…

Health Information Needs of d/Deaf Adolescent Females: A Call to Action

ERIC Educational Resources Information Center

Smith, Chad E.; Massey-Stokes, Marilyn; Lieberth, Ann

2012-01-01

Adolescent health and health literacy are critical health topics recognized in Healthy People 2020. Evidence indicates that adolescents who are d/Deaf have unique health-related needs, yet health communication efforts have not reached them. Despite the Internet's exponential growth and the growth of online health information-seeking behavior among…

Skills for the Future.

ERIC Educational Resources Information Center

Smith, Gary R.

This publication contains two miniunits to help students in grades 7-12 build skills for the future. The exercises can also be adapted for use in grades 4-6. Each of the miniunits contains several exercises to build specific skills. Miniunit One, "The Arithmetic of Growth," deals with two concepts--exponential growth and doubling time. These two…

Systematic modelling and design evaluation of unperturbed tumour dynamics in xenografts.

PubMed

Parra Guillen, Zinnia P Patricia; Mangas Sanjuan, Victor; Garcia-Cremades, Maria; Troconiz, Inaki F; Mo, Gary; Pitou, Celine; Iversen, Philip W; Wallin, Johan E

2018-04-24

Xenograft mice are largely used to evaluate the efficacy of oncological drugs during preclinical phases of drug discovery and development. Mathematical models provide a useful tool to quantitatively characterise tumour growth dynamics and also optimise upcoming experiments. To the best of our knowledge, this is the first report where unperturbed growth of a large set of tumour cell lines (n=28) has been systematically analysed using the model proposed by Simeoni in the context of non-linear mixed effect (NLME). Exponential growth was identified as the governing mechanism in the majority of the cell lines, with constant rate values ranging from 0.0204 to 0.203 day -1 No common patterns could be observed across tumour types, highlighting the importance of combining information from different cell lines when evaluating drug activity. Overall, typical model parameters were precisely estimated using designs where tumour size measurements were taken every two days. Moreover, reducing the number of measurement to twice per week, or even once per week for cell lines with low growth rates, showed little impact on parameter precision. However, in order to accurately characterise parameter variability (i.e. relative standard errors below 50%), a sample size of at least 50 mice is needed. This work illustrates the feasibility to systematically apply NLME models to characterise tumour growth in drug discovery and development, and constitutes a valuable source of data to optimise experimental designs by providing an a priori sampling window and minimising the number of samples required. The American Society for Pharmacology and Experimental Therapeutics.

The penny pusher: a cellular model of lens growth.

PubMed

Shi, Yanrong; De Maria, Alicia; Lubura, Snježana; Šikić, Hrvoje; Bassnett, Steven

2014-12-16

The mechanisms that regulate the number of cells in the lens and, therefore, its size and shape are unknown. We examined the dynamic relationship between proliferative behavior in the epithelial layer and macroscopic lens growth. The distribution of S-phase cells across the epithelium was visualized by confocal microscopy and cell populations were determined from orthographic projections of the lens surface. The number of S-phase cells in the mouse lens epithelium fell exponentially, to an asymptotic value of approximately 200 cells by 6 months. Mitosis became increasingly restricted to a 300-μm-wide swath of equatorial epithelium, the germinative zone (GZ), within which two peaks in labeling index were detected. Postnatally, the cell population increased to approximately 50,000 cells at 4 weeks of age. Thereafter, the number of cells declined, despite continued growth in lens dimensions. This apparently paradoxical observation was explained by a time-dependent increase in the surface area of cells at all locations. The cell biological measurements were incorporated into a physical model, the Penny Pusher. In this simple model, cells were considered to be of a single type, the proliferative behavior of which depended solely on latitude. Simulations using the Penny Pusher predicted the emergence of cell clones and were in good agreement with data obtained from earlier lineage-tracing studies. The Penny Pusher, a simple stochastic model, offers a useful conceptual framework for the investigation of lens growth mechanisms and provides a plausible alternative to growth models that postulate the existence of lens stem cells. Copyright 2015 The Association for Research in Vision and Ophthalmology, Inc.

Optimal Disturbances in Boundary Layers Subject to Streamwise Pressure Gradient

NASA Technical Reports Server (NTRS)

Tumin, Anatoli; Ashpis, David E.

2003-01-01

Laminar-turbulent transition in shear flows is still an enigma in the area of fluid mechanics. The conventional explanation of the phenomenon is based on the instability of the shear flow with respect to infinitesimal disturbances. The conventional hydrodynamic stability theory deals with the analysis of normal modes that might be unstable. The latter circumstance is accompanied by an exponential growth of the disturbances that might lead to laminar-turbulent transition. Nevertheless, in many cases, the transition scenario bypasses the exponential growth stage associated with the normal modes. This type of transition is called bypass transition. An understanding of the phenomenon has eluded us to this day. One possibility is that bypass transition is associated with so-called algebraic (non-modal) growth of disturbances in shear flows. In the present work, an analysis of the optimal disturbances/streamwise vortices associated with the transient growth mechanism is performed for boundary layers in the presence of a streamwise pressure gradient. The theory will provide the optimal spacing of the control elements in the spanwise direction and their placement in the streamwise direction.

Constant growth rate can be supported by decreasing energy flux and increasing aerobic glycolysis.

PubMed

Slavov, Nikolai; Budnik, Bogdan A; Schwab, David; Airoldi, Edoardo M; van Oudenaarden, Alexander

2014-05-08

Fermenting glucose in the presence of enough oxygen to support respiration, known as aerobic glycolysis, is believed to maximize growth rate. We observed increasing aerobic glycolysis during exponential growth, suggesting additional physiological roles for aerobic glycolysis. We investigated such roles in yeast batch cultures by quantifying O2 consumption, CO2 production, amino acids, mRNAs, proteins, posttranslational modifications, and stress sensitivity in the course of nine doublings at constant rate. During this course, the cells support a constant biomass-production rate with decreasing rates of respiration and ATP production but also decrease their stress resistance. As the respiration rate decreases, so do the levels of enzymes catalyzing rate-determining reactions of the tricarboxylic-acid cycle (providing NADH for respiration) and of mitochondrial folate-mediated NADPH production (required for oxidative defense). The findings demonstrate that exponential growth can represent not a single metabolic/physiological state but a continuum of changing states and that aerobic glycolysis can reduce the energy demands associated with respiratory metabolism and stress survival. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Multi-time series RNA-seq analysis of Enterobacter lignolyticus SCF1 during growth in lignin-amended medium

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

Orellana, Roberto; Chaput, Gina; Markillie, Lye Meng

The production of lignocellulosic-derived biofuels is a highly promising source of alternative energy, but it has been constrained by the lack of a microbial platform capable to efficiently degrade this recalcitrant material and cope with by-products that can be toxic to cells. Species that naturally grow in environments where carbon is mainly available as lignin are promising for finding new ways of removing the lignin that protects cellulose for improved conversion of lignin to fuel precursors. Enterobacter lignolyticus SCF1 is a facultative anaerobic Gammaproteobacteria isolated from tropical rain forest soil collected in El Yunque forest, Puerto Rico under anoxic growthmore » conditions with lignin as sole carbon source. Whole transcriptome analysis of SCF1 during E.lignolyticus SCF1 lignin degradation was conducted on cells grown in the presence (0.1%, w/w) and the absence of lignin, where samples were taken at three different times during growth, beginning of exponential phase, midexponential phase and beginning of stationary phase. Lignin-amended cultures achieved twice the cell biomass as unamended cultures over three days, and in this time degraded 60% of lignin. Transcripts in early exponential phase reflected this accelerated growth. A complement of laccases, aryl-alcohol dehydrogenases, and peroxidases were most up-regulated in lignin amended conditions in mid-exponential and early stationary phases compared to unamended growth. The association of hydrogen production by way of the formate hydrogenlyase complex with lignin degradation suggests a possible value added to lignin degradation in the future.« less

A New Insight into the Earthquake Recurrence Studies from the Three-parameter Generalized Exponential Distributions

NASA Astrophysics Data System (ADS)

Pasari, S.; Kundu, D.; Dikshit, O.

2012-12-01

Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.

Value of the distant future: Model-independent results

NASA Astrophysics Data System (ADS)

Katz, Yuri A.

2017-01-01

This paper shows that the model-independent account of correlations in an interest rate process or a log-consumption growth process leads to declining long-term tails of discount curves. Under the assumption of an exponentially decaying memory in fluctuations of risk-free real interest rates, I derive the analytical expression for an apt value of the long run discount factor and provide a detailed comparison of the obtained result with the outcome of the benchmark risk-free interest rate models. Utilizing the standard consumption-based model with an isoelastic power utility of the representative economic agent, I derive the non-Markovian generalization of the Ramsey discounting formula. Obtained analytical results allowing simple calibration, may augment the rigorous cost-benefit and regulatory impact analysis of long-term environmental and infrastructure projects.

Dynamics of one model of the fast kinematic dynamo

NASA Astrophysics Data System (ADS)

Medvedev, Timur; Medvedev, Vladislav; Zhuzhoma, Evgeny

2018-03-01

We suggest a new model of the fast nondissipative kinematic dynamo which describes the phenomenon of exponential growth of the magnetic field caused by the motion of the conducting medium. This phenomenon is known to occur in the evolution of magnetic fields of astrophysical bodies. In the 1970s A.D. Sakharov and Ya.B. Zeldovich proposed a “rope” scheme of this process which in terms of the modern theory of dynamical systems can be described as Smale solenoid. The main disadvantage of this scheme is that it is non-conservative. Our model is a modification of the Sakharov-Zeldovich’s model. We apply methods of the theory of dynamical systems to prove that it is free of this fault in the neighborhood of the nonwandering set.

Understanding tree growth responses after partial cuttings: A new approach

PubMed Central

Rossi, Sergio; Lussier, Jean-Martin; Walsh, Denis; Morin, Hubert

2017-01-01

Forest ecosystem management heads towards the use of partial cuttings. However, the wide variation in growth response of residual trees remains unexplained, preventing a suitable prediction of forest productivity. The aim of the study was to assess individual growth and identify the driving factors involved in the responses of residual trees. Six study blocks in even-aged black spruce [Picea mariana (Mill.) B.S.P.] stands of the eastern Canadian boreal forest were submitted to experimental shelterwood and seed-tree treatments. Individual-tree models were applied to 1039 trees to analyze their patterns of radial growth during the 10 years after partial cutting by using the nonlinear Schnute function on tree-ring series. The trees exhibited different growth patterns. A sigmoid growth was detected in 32% of trees, mainly in control plots of older stands. Forty-seven percent of trees located in the interior of residual strips showed an S-shape, which was influenced by stand mortality, harvested intensity and dominant height. Individuals showing an exponential pattern produced the greatest radial growth after cutting and were edge trees of younger stands with higher dominant height. A steady growth decline was observed in 4% of trees, represented by the individuals suppressed and insensitive to the treatment. The analyses demonstrated that individual nonlinear models are able to assess the variability in growth within the stand and the factors involved in the occurrence of the different growth patterns, thus improving understanding of the tree responses to partial cutting. This new approach can sustain forest management strategies by defining the best conditions to optimize the growth yield of residual trees. PMID:28222200

Understanding tree growth responses after partial cuttings: A new approach.

PubMed

Montoro Girona, Miguel; Rossi, Sergio; Lussier, Jean-Martin; Walsh, Denis; Morin, Hubert

2017-01-01

Forest ecosystem management heads towards the use of partial cuttings. However, the wide variation in growth response of residual trees remains unexplained, preventing a suitable prediction of forest productivity. The aim of the study was to assess individual growth and identify the driving factors involved in the responses of residual trees. Six study blocks in even-aged black spruce [Picea mariana (Mill.) B.S.P.] stands of the eastern Canadian boreal forest were submitted to experimental shelterwood and seed-tree treatments. Individual-tree models were applied to 1039 trees to analyze their patterns of radial growth during the 10 years after partial cutting by using the nonlinear Schnute function on tree-ring series. The trees exhibited different growth patterns. A sigmoid growth was detected in 32% of trees, mainly in control plots of older stands. Forty-seven percent of trees located in the interior of residual strips showed an S-shape, which was influenced by stand mortality, harvested intensity and dominant height. Individuals showing an exponential pattern produced the greatest radial growth after cutting and were edge trees of younger stands with higher dominant height. A steady growth decline was observed in 4% of trees, represented by the individuals suppressed and insensitive to the treatment. The analyses demonstrated that individual nonlinear models are able to assess the variability in growth within the stand and the factors involved in the occurrence of the different growth patterns, thus improving understanding of the tree responses to partial cutting. This new approach can sustain forest management strategies by defining the best conditions to optimize the growth yield of residual trees.

Nucleation and growth kinetics during metal-induced layer exchange crystallization of Ge thin films at low temperatures

NASA Astrophysics Data System (ADS)

Hu, Shu; McIntyre, Paul C.

2012-02-01

The kinetics of Al-catalyzed layer exchange crystallization of amorphous germanium (Ge) thin films at low temperatures is reported. Observation of Ge mass transport from an underlying amorphous Ge layer to the Al film surface through an interposed sub-nanometer GeOx interfacial layer allows independent measurement of the areal density and average area of crystalline Ge islands formed on the film surface. We show that bias-voltage stressing of the interfacial layer can be used to control the areal density of nucleated Ge islands. Based on experimental observations, the Johnson-Mehl-Avrami-Kolmogorov phase transformation theory is used to model nanoscale nucleation and growth of Ge islands in two dimensions. Ge island nucleation kinetics follows an exponentially decaying nucleation rate with time. Ge island growth kinetics switches from linear growth at a constant growth velocity to diffusion-limited growth as the growth front advances. The transition point between these two regimes depends on the Ge nucleation site density and the annealing temperature. Knowledge of the kinetics of low-temperature crystallization is important in achieving textured polycrystalline Ge thin films with large grains for applications in large-area electronics and solar energy conversion.

Simulated remodeling of loaded collagen networks via strain-dependent enzymatic degradation and constant-rate fiber growth

PubMed Central

Hadi, M.F.; Sander, E.A.; Ruberti, J.W.; Barocas, V. H.

2011-01-01

Recent work has demonstrated that enzymatic degradation of collagen fibers exhibits strain-dependent kinetics. Conceptualizing how the strain dependence affects remodeling of collagenous tissues is vital to our understanding of collagen management in native and bioengineered tissues. As a first step towards this goal, the current study puts forward a multiscale model for enzymatic degradation and remodeling of collagen networks for two sample geometries we routinely use in experiments as model tissues. The multiscale model, driven by microstructural data from an enzymatic decay experiment, includes an exponential strain-dependent kinetic relation for degradation and constant growth. For a dogbone sample under uniaxial load, the model predicted that the distribution of fiber diameters would spread over the course of degradation because of variation in individual fiber load. In a cross-shaped sample, the central region, which experiences smaller, more isotropic loads, showed more decay and less spread in fiber diameter compared to the arms. There was also a slight shift in average orientation in different regions of the cruciform. PMID:22180691

Drug Resistance and the Kinetics of Metastatic Cancer

NASA Astrophysics Data System (ADS)

Blagoev, Krastan B.

2012-02-01

Most metastatic cancers after initial response to current drug therapies develop resistance to the treatment. We present cancer data and a theory that explains the observed kinetics of tumor growth in cancer patients and using a stochastic model based on this theory we relate the kinetics of tumor growth to Kaplan-Meyer survival curves. The theory points to the tumor growth rate as the most important parameter determining the outcome of a drug treatment. The overall tumor growth or decay rate is a reflection of the balance between cell division, senescence and apoptosis and we propose that the deviation of the decay rate from exponential is a measure of the emergence of drug resistance. In clinical trials the progression free survival, the overall survival, and the shape of the Kaplan-Meyer plots are determined by the tumor growth rate probability distribution among the patients in the trial. How drug treatments modify this distribution will also be described. At the end of the talk we will discuss the connection between the theory described here and the age related cancer mortality rates in the United States.

Towards enhancing and delaying disturbances in free shear flows

NASA Technical Reports Server (NTRS)

Criminale, W. O.; Jackson, T. L.; Lasseigne, D. G.

1994-01-01

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Growth phase-dependent induction of stationary-phase promoters of Escherichia coli in different gram-negative bacteria.

PubMed Central

Miksch, G; Dobrowolski, P

1995-01-01

RSF1010-derived plasmids carrying a fusion of a promoterless lacZ gene with the sigma s-dependent growth phase-regulated promoters of Escherichia coli, bolAp1 and fic, were constructed. The plasmids were mobilized into the gram-negative bacterial species Acetobacter methanolicus, Xanthomonas campestris, Pseudomonas putida, and Rhizobium meliloti. The beta-galactosidase activities of bacterial cultures were determined during exponential and stationary growth phases. Transcriptional activation of the fic promoter in the different bacteria was growth phase dependent as in E. coli and was initiated generally during the transition to stationary phase. The induction of the bolA promoter was also growth phase dependent in the bacteria tested. While the expression in E. coli and R. meliloti was initiated during the transition from exponential to stationary phase, the induction in A. methanolicus, P. putida, and X. campestris started some hours after stationary growth phase was reached. In all the species tested, DNA fragments hybridizing with the rpoS gene of E. coli were detected. The results show that in different gram-negative bacteria, stationary-phase-specific sigma factors which are structurally and functionally homologous to sigma s and are able to recognize the promoter sequences of both bolA and fic exist. PMID:7665531

Statistical mechanics and scaling of fault populations with increasing strain in the Corinth Rift

NASA Astrophysics Data System (ADS)

Michas, Georgios; Vallianatos, Filippos; Sammonds, Peter

2015-12-01

Scaling properties of fracture/fault systems are studied in order to characterize the mechanical properties of rocks and to provide insight into the mechanisms that govern fault growth. A comprehensive image of the fault network in the Corinth Rift, Greece, obtained through numerous field studies and marine geophysical surveys, allows for the first time such a study over the entire area of the Rift. We compile a detailed fault map of the area and analyze the scaling properties of fault trace-lengths by using a statistical mechanics model, derived in the framework of generalized statistical mechanics and associated maximum entropy principle. By using this framework, a range of asymptotic power-law to exponential-like distributions are derived that can well describe the observed scaling patterns of fault trace-lengths in the Rift. Systematic variations and in particular a transition from asymptotic power-law to exponential-like scaling are observed to be a function of increasing strain in distinct strain regimes in the Rift, providing quantitative evidence for such crustal processes in a single tectonic setting. These results indicate the organization of the fault system as a function of brittle strain in the Earth's crust and suggest there are different mechanisms for fault growth in the distinct parts of the Rift. In addition, other factors such as fault interactions and the thickness of the brittle layer affect how the fault system evolves in time. The results suggest that regional strain, fault interactions and the boundary condition of the brittle layer may control fault growth and the fault network evolution in the Corinth Rift.

Xylem traits, leaf longevity and growth phenology predict growth and mortality response to defoliation in northern temperate forests.

PubMed

Foster, Jane R

2017-09-01

Defoliation outbreaks are biological disturbances that alter tree growth and mortality in temperate forests. Trees respond to defoliation in many ways; some recover rapidly, while others decline gradually or die. Functional traits such as xylem anatomy, growth phenology or non-structural carbohydrate (NSC) storage could explain these responses, but idiosyncratic measures used by defoliation studies have frustrated efforts to generalize among species. Here, I test for functional differences with published growth and mortality data from 37 studies, including 24 tree species and 11 defoliators from North America and Eurasia. I synthesized data into standardized variables suitable for numerical models and used linear mixed-effects models to test the hypotheses that responses to defoliation vary among species and functional groups. Standardized data show that defoliation responses vary in shape and degree. Growth decreased linearly or curvilinearly, least in ring-porous Quercus and deciduous conifers (by 10-40% per 100% defoliation), whereas growth of diffuse-porous hardwoods and evergreen conifers declined by 40-100%. Mortality increased exponentially with defoliation, most rapidly for evergreen conifers, then diffuse-porous, then ring-porous species and deciduous conifers (Larix). Goodness-of-fit for functional-group models was strong (R2c = 0.61-0.88), if lower than species-specific mixed-models (R2c = 0.77-0.93), providing useful alternatives when species data are lacking. These responses are consistent with functional differences in leaf longevity, wood growth phenology and NSC storage. When defoliator activity lags behind wood-growth, either because xylem-growth precedes budburst (Quercus) or defoliator activity peaks later (sawflies on Larix), impacts on annual wood-growth will always be lower. Wood-growth phenology of diffuse-porous species and evergreen conifers coincides with defoliation and responds more drastically, and lower axial NSC storage makes them more vulnerable to mortality as stress accumulates. These functional differences in response apply in general to disturbances that cause spring defoliation and provide a framework that should be incorporated into forest growth and vegetation models. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

State of charge modeling of lithium-ion batteries using dual exponential functions

NASA Astrophysics Data System (ADS)

Kuo, Ting-Jung; Lee, Kung-Yen; Huang, Chien-Kang; Chen, Jau-Horng; Chiu, Wei-Li; Huang, Chih-Fang; Wu, Shuen-De

2016-05-01

A mathematical model is developed by fitting the discharging curve of LiFePO4 batteries and used to investigate the relationship between the state of charge and the closed-circuit voltage. The proposed mathematical model consists of dual exponential terms and a constant term which can fit the characteristics of dual equivalent RC circuits closely, representing a LiFePO4 battery. One exponential term presents the stable discharging behavior and the other one presents the unstable discharging behavior and the constant term presents the cut-off voltage.

Metabolic Profiling and Flux Analysis of MEL-2 Human Embryonic Stem Cells during Exponential Growth at Physiological and Atmospheric Oxygen Concentrations

PubMed Central

Titmarsh, Drew; Krömer, Jens O.; Kao, Li-Pin; Nielsen, Lars; Wolvetang, Ernst; Cooper-White, Justin

2014-01-01

As human embryonic stem cells (hESCs) steadily progress towards regenerative medicine applications there is an increasing emphasis on the development of bioreactor platforms that enable expansion of these cells to clinically relevant numbers. Surprisingly little is known about the metabolic requirements of hESCs, precluding the rational design and optimisation of such platforms. In this study, we undertook an in-depth characterisation of MEL-2 hESC metabolic behaviour during the exponential growth phase, combining metabolic profiling and flux analysis tools at physiological (hypoxic) and atmospheric (normoxic) oxygen concentrations. To overcome variability in growth profiles and the problem of closing mass balances in a complex environment, we developed protocols to accurately measure uptake and production rates of metabolites, cell density, growth rate and biomass composition, and designed a metabolic flux analysis model for estimating internal rates. hESCs are commonly considered to be highly glycolytic with inactive or immature mitochondria, however, whilst the results of this study confirmed that glycolysis is indeed highly active, we show that at least in MEL-2 hESC, it is supported by the use of oxidative phosphorylation within the mitochondria utilising carbon sources, such as glutamine to maximise ATP production. Under both conditions, glycolysis was disconnected from the mitochondria with all of the glucose being converted to lactate. No difference in the growth rates of cells cultured under physiological or atmospheric oxygen concentrations was observed nor did this cause differences in fluxes through the majority of the internal metabolic pathways associated with biogenesis. These results suggest that hESCs display the conventional Warburg effect, with high aerobic activity despite high lactate production, challenging the idea of an anaerobic metabolism with low mitochondrial activity. The results of this study provide new insight that can be used in rational bioreactor design and in the development of novel culture media for hESC maintenance and expansion. PMID:25412279

Tumour model with intrusive morphology, progressive phenotypical heterogeneity and memory

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Alqahtani, Rubayyi T.

2018-03-01

The model of a tumour, taking into account invasive morphology, progressive phenotypical heterogeneity and also memory, is developed and analyzed in this paper. Three models are investigated: first we consider the model describing the proliferation concentrates in proximity of tumour boundaries, in which the oxygen levels are pronounced. Then we consider the model where the oxygen around the tumour is considered to be unchanged by the vascular system. Finally, we investigate the model of growth of tumours using the concept of non-local operators with the Mittag-Leffler kernel. We provide the numerical solution using the extended 3/8 Simpson method for the new trends of fractional integration for the proliferation concentrates in the proximity of the tumour model. Then we provide the exact solutions of the Gompertz model with three different fractional differentiations involving power law, exponential decay law and the Mittag-Leffler law.

T7 phage factor required for managing RpoS in Escherichia coli.

PubMed

Tabib-Salazar, Aline; Liu, Bing; Barker, Declan; Burchell, Lynn; Qimron, Udi; Matthews, Steve J; Wigneshweraraj, Sivaramesh

2018-06-05

T7 development in Escherichia coli requires the inhibition of the housekeeping form of the bacterial RNA polymerase (RNAP), Eσ 70 , by two T7 proteins: Gp2 and Gp5.7. Although the biological role of Gp2 is well understood, that of Gp5.7 remains to be fully deciphered. Here, we present results from functional and structural analyses to reveal that Gp5.7 primarily serves to inhibit Eσ S , the predominant form of the RNAP in the stationary phase of growth, which accumulates in exponentially growing E. coli as a consequence of the buildup of guanosine pentaphosphate [(p)ppGpp] during T7 development. We further demonstrate a requirement of Gp5.7 for T7 development in E. coli cells in the stationary phase of growth. Our finding represents a paradigm for how some lytic phages have evolved distinct mechanisms to inhibit the bacterial transcription machinery to facilitate phage development in bacteria in the exponential and stationary phases of growth.

Sampling through time and phylodynamic inference with coalescent and birth–death models

PubMed Central

Volz, Erik M.; Frost, Simon D. W.

2014-01-01

Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the birth–death-sampling model (BDM), in the context of estimating population size and birth rates in a population growing exponentially according to the birth–death branching process. For sequences sampled at a single time, we found the coalescent and the BDM gave virtually indistinguishable results in terms of the growth rates and fraction of the population sampled, even when sampling from a small population. For sequences sampled at multiple time points, we find that the birth–death model estimators are subject to large bias if the sampling process is misspecified. Since BDMs incorporate a model of the sampling process, we show how much of the statistical power of BDMs arises from the sequence of sample times and not from the genealogical tree. This motivates the development of a new coalescent estimator, which is augmented with a model of the known sampling process and is potentially more precise than the coalescent that does not use sample time information. PMID:25401173

Piecewise exponential models to assess the influence of job-specific experience on the hazard of acute injury for hourly factory workers

PubMed Central

2013-01-01

Background An inverse relationship between experience and risk of injury has been observed in many occupations. Due to statistical challenges, however, it has been difficult to characterize the role of experience on the hazard of injury. In particular, because the time observed up to injury is equivalent to the amount of experience accumulated, the baseline hazard of injury becomes the main parameter of interest, excluding Cox proportional hazards models as applicable methods for consideration. Methods Using a data set of 81,301 hourly production workers of a global aluminum company at 207 US facilities, we compared competing parametric models for the baseline hazard to assess whether experience affected the hazard of injury at hire and after later job changes. Specific models considered included the exponential, Weibull, and two (a hypothesis-driven and a data-driven) two-piece exponential models to formally test the null hypothesis that experience does not impact the hazard of injury. Results We highlighted the advantages of our comparative approach and the interpretability of our selected model: a two-piece exponential model that allowed the baseline hazard of injury to change with experience. Our findings suggested a 30% increase in the hazard in the first year after job initiation and/or change. Conclusions Piecewise exponential models may be particularly useful in modeling risk of injury as a function of experience and have the additional benefit of interpretability over other similarly flexible models. PMID:23841648

Density-Dependent Growth in Invasive Lionfish (Pterois volitans)

PubMed Central

Benkwitt, Cassandra E.

2013-01-01

Direct demographic density dependence is necessary for population regulation and is a central concept in ecology, yet has not been studied in many invasive species, including any invasive marine fish. The red lionfish (Pterois volitans) is an invasive predatory marine fish that is undergoing exponential population growth throughout the tropical western Atlantic. Invasive lionfish threaten coral-reef ecosystems, but there is currently no evidence of any natural population control. Therefore, a manipulative field experiment was conducted to test for density dependence in lionfish. Juvenile lionfish densities were adjusted on small reefs and several demographic rates (growth, recruitment, immigration, and loss) were measured throughout an 8-week period. Invasive lionfish exhibited direct density dependence in individual growth rates, as lionfish grew slower at higher densities throughout the study. Individual growth in length declined linearly with increasing lionfish density, while growth in mass declined exponentially with increasing density. There was no evidence, however, for density dependence in recruitment, immigration, or loss (mortality plus emigration) of invasive lionfish. The observed density-dependent growth rates may have implications for which native species are susceptible to lionfish predation, as the size and type of prey that lionfish consume is directly related to their body size. The absence of density-dependent loss, however, contrasts with many native coral-reef fish species and suggests that for the foreseeable future manual removals may be the only effective local control of this invasion. PMID:23825604

Density-dependent growth in invasive Lionfish (Pterois volitans).

PubMed

Benkwitt, Cassandra E

2013-01-01

Direct demographic density dependence is necessary for population regulation and is a central concept in ecology, yet has not been studied in many invasive species, including any invasive marine fish. The red lionfish (Pterois volitans) is an invasive predatory marine fish that is undergoing exponential population growth throughout the tropical western Atlantic. Invasive lionfish threaten coral-reef ecosystems, but there is currently no evidence of any natural population control. Therefore, a manipulative field experiment was conducted to test for density dependence in lionfish. Juvenile lionfish densities were adjusted on small reefs and several demographic rates (growth, recruitment, immigration, and loss) were measured throughout an 8-week period. Invasive lionfish exhibited direct density dependence in individual growth rates, as lionfish grew slower at higher densities throughout the study. Individual growth in length declined linearly with increasing lionfish density, while growth in mass declined exponentially with increasing density. There was no evidence, however, for density dependence in recruitment, immigration, or loss (mortality plus emigration) of invasive lionfish. The observed density-dependent growth rates may have implications for which native species are susceptible to lionfish predation, as the size and type of prey that lionfish consume is directly related to their body size. The absence of density-dependent loss, however, contrasts with many native coral-reef fish species and suggests that for the foreseeable future manual removals may be the only effective local control of this invasion.

Historical Patterns of Change: The Lessons of the 1980s.

ERIC Educational Resources Information Center

Geiger, Roger L.

This paper seeks to assess the current state of academic research in light of long-term trends in the development of science. It presents three perspectives on the growth of scientific research: (1) Derek de Solla Price's (1963) hypothesis that science has exhibited exponential growth, roughly doubling every 15 years since the 17th century; (2)…

GROWTH AND CHANGES IN BIOCHEMICAL COMPOSITION DURING LARVAL DEVELOPMENT OF THE STONE CRAB, MENIPPE ADINA WILLIAMS AND FELDER, 1986

EPA Science Inventory

Larval development in Menippe adina was associated with changes in weight and biochemical composition. Larvae of the stone crab, M. adina, were mass-reared under laboratory conditions (28|C; 20o/ooS) from hatching to the megalopal stage. Growth in M. adina is exponential througho...

Conceptions and Misconceptions about "Western Buddhism": Issues and Approaches for the Classroom

ERIC Educational Resources Information Center

Berkwitz, Stephen C.

2004-01-01

This article responds to the exponential growth in academic textbooks on Western or American Buddhism by arguing that popular trade books written by Buddhist teachers in the West make more effective tools for teaching and learning about the growth of Buddhism in western societies. The use of such texts in the classroom provides students with…

Strand displacement amplification as an in vitro model for rolling-circle replication: deletion formation and evolution during serial transfer.

PubMed Central

Walter, N G; Strunk, G

1994-01-01

Strand displacement amplification is an isothermal DNA amplification reaction based on a restriction endonuclease nicking its recognition site and a polymerase extending the nick at its 3' end, displacing the downstream strand. The reaction resembles rolling-circle replication of single-stranded phages and small plasmids. The displaced sense strand serves as target for an antisense reaction and vice versa, resulting in exponential growth and the autocatalytic nature of this in vitro reaction as long as the template is the limiting agent. We describe the optimization of strand displacement amplification for in vitro evolution experiments under serial transfer conditions. The reaction was followed and controlled by use of the fluorescent dye thiazole orange binding to the amplified DNA. We were able to maintain exponential growth conditions with a doubling time of 3.0 min throughout 100 transfers or approximately 350 molecular generations by using an automatic handling device. Homology of in vitro amplification with rolling-circle replication was mirrored by the occurring evolutionary processes. Deletion events most likely caused by a slipped mispairing mechanism as postulated for in vivo replication took place. Under our conditions, the mutation rate was high and a molecular quasi-species formed with a mutant lacking internal hairpin formation ability and thus outgrowing all other species under dGTP/dCTP deficiency. Images PMID:8058737

A Simulation of the ECSS Help Desk with the Erlang a Model

DTIC Science & Technology

2011-03-01

a popular distribution is the exponential distribution as shown in Figure 3. Figure 3: Exponential Distribution ( Bourke , 2001) Exponential...System Sciences, Vol 8, 235B. Bourke , P. (2001, January). Miscellaneous Functions. Retrieved January 22, 2011, from http://local.wasp.uwa.edu.au

Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

How polyamine synthesis inhibitors and cinnamic acid affect tropane alkaloid production.

PubMed

Marconi, Patricia L; Alvarez, María A; Pitta-Alvarez, Sandra I

2007-01-01

Hairy roots of Brugmansia candida produce the tropane alkaloids scopolamine and hyoscyamine. In an attempt to divert the carbon flux from competing pathways and thus enhance productivity, the polyamine biosynthesis inhibitors cyclohexylamine (CHA) and methylglyoxal-bis-guanylhydrazone (MGBG) and the phenylalanine-ammonia-lyase inhibitor cinnamic acid were used. CHA decreased the specific productivity of both alkaloids but increased significantly the release of scopolamine (approx 500%) when it was added in the mid-exponential phase. However, when CHA was added for only 48 h during the exponential phase, the specific productivity of both alkaloids increased (approx 200%), favoring scopolamine. Treatment with MGBG was detrimental to growth but promoted release into the medium of both alkaloids. However, when it was added for 48 h during the exponential phase, MGBG increased the specific productivity (approx 200%) and release (250- 1800%) of both alkaloids. Cinnamic acid alone also favored release but not specific productivity. When a combination of CHA or MGBG with cinnamic acid was used, the results obtained were approximately the same as with each polyamine biosynthesis inhibitor alone, although to a lesser extent. Regarding root morphology, CHA inhibited growth of primary roots and ramification. However, it had a positive effect on elongation of lateral roots.

Bacillus subtilis Swarmer Cells Lead the Swarm, Multiply, and Generate a Trail of Quiescent Descendants.

PubMed

Hamouche, Lina; Laalami, Soumaya; Daerr, Adrian; Song, Solène; Holland, I Barry; Séror, Simone J; Hamze, Kassem; Putzer, Harald

2017-02-07

Bacteria adopt social behavior to expand into new territory, led by specialized swarmers, before forming a biofilm. Such mass migration of Bacillus subtilis on a synthetic medium produces hyperbranching dendrites that transiently (equivalent to 4 to 5 generations of growth) maintain a cellular monolayer over long distances, greatly facilitating single-cell gene expression analysis. Paradoxically, while cells in the dendrites (nonswarmers) might be expected to grow exponentially, the rate of swarm expansion is constant, suggesting that some cells are not multiplying. Little attention has been paid to which cells in a swarm are actually multiplying and contributing to the overall biomass. Here, we show in situ that DNA replication, protein translation and peptidoglycan synthesis are primarily restricted to the swarmer cells at dendrite tips. Thus, these specialized cells not only lead the population forward but are apparently the source of all cells in the stems of early dendrites. We developed a simple mathematical model that supports this conclusion. Swarming motility enables rapid coordinated surface translocation of a microbial community, preceding the formation of a biofilm. This movement occurs in thin films and involves specialized swarmer cells localized to a narrow zone at the extreme swarm edge. In the B. subtilis system, using a synthetic medium, the swarm front remains as a cellular monolayer for up to 1.5 cm. Swarmers display high-velocity whirls and vortexing and are often assumed to drive community expansion at the expense of cell growth. Surprisingly, little attention has been paid to which cells in a swarm are actually growing and contributing to the overall biomass. Here, we show that swarmers not only lead the population forward but continue to multiply as a source of all cells in the community. We present a model that explains how exponential growth of only a few cells is compatible with the linear expansion rate of the swarm. Copyright © 2017 Hamouche et al.

Universality Classes of Interaction Structures for NK Fitness Landscapes

NASA Astrophysics Data System (ADS)

Hwang, Sungmin; Schmiegelt, Benjamin; Ferretti, Luca; Krug, Joachim

2018-07-01

Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of k ≤ L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

Universality Classes of Interaction Structures for NK Fitness Landscapes

NASA Astrophysics Data System (ADS)

Hwang, Sungmin; Schmiegelt, Benjamin; Ferretti, Luca; Krug, Joachim

2018-02-01

Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of k ≤ L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

The exponential distribution is the most widely used reliability analysis. This distribution is very suitable for representing the lengths of life of many cases and is available in a simple statistical form. The characteristic of this distribution is a constant hazard rate. The exponential distribution is the lower rank of the Weibull distributions. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability analysis using Bayesian analysis approach and presenting their analytic methods. The cases are limited to the models with independent causes of failure. A non-informative prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations.

PubMed

Lee, UnJin; Skinner, John J; Reinitz, John; Rosner, Marsha Rich; Kim, Eun-Jin

2015-01-01

There has been increasing awareness in the wider biological community of the role of clonal phenotypic heterogeneity in playing key roles in phenomena such as cellular bet-hedging and decision making, as in the case of the phage-λ lysis/lysogeny and B. Subtilis competence/vegetative pathways. Here, we report on the effect of stochasticity in growth rate, cellular memory/intermittency, and its relation to phenotypic heterogeneity. We first present a linear stochastic differential model with finite auto-correlation time, where a randomly fluctuating growth rate with a negative average is shown to result in exponential growth for sufficiently large fluctuations in growth rate. We then present a non-linear stochastic self-regulation model where the loss of coherent self-regulation and an increase in noise can induce a shift from bounded to unbounded growth. An important consequence of these models is that while the average change in phenotype may not differ for various parameter sets, the variance of the resulting distributions may considerably change. This demonstrates the necessity of understanding the influence of variance and heterogeneity within seemingly identical clonal populations, while providing a mechanism for varying functional consequences of such heterogeneity. Our results highlight the importance of a paradigm shift from a deterministic to a probabilistic view of clonality in understanding selection as an optimization problem on noise-driven processes, resulting in a wide range of biological implications, from robustness to environmental stress to the development of drug resistance.

The RNAi machinery controls distinct responses to environmental signals in the basal fungus Mucor circinelloides.

PubMed

Nicolás, Francisco E; Vila, Ana; Moxon, Simon; Cascales, María D; Torres-Martínez, Santiago; Ruiz-Vázquez, Rosa M; Garre, Victoriano

2015-03-25

RNA interference (RNAi) is a conserved mechanism of genome defence that can also have a role in the regulation of endogenous functions through endogenous small RNAs (esRNAs). In fungi, knowledge of the functions regulated by esRNAs has been hampered by lack of clear phenotypes in most mutants affected in the RNAi machinery. Mutants of Mucor circinelloides affected in RNAi genes show defects in physiological and developmental processes, thus making Mucor an outstanding fungal model for studying endogenous functions regulated by RNAi. Some classes of Mucor esRNAs map to exons (ex-siRNAs) and regulate expression of the genes from which they derive. To have a broad picture of genes regulated by the silencing machinery during vegetative growth, we have sequenced and compared the mRNA profiles of mutants in the main RNAi genes by using RNA-seq. In addition, we have achieved a more complete phenotypic characterization of silencing mutants. Deletion of any main RNAi gene provoked a deep impact in mRNA accumulation at exponential and stationary growth. Genes showing increased mRNA levels, as expected for direct ex-siRNAs targets, but also genes with decreased expression were detected, suggesting that, most probably, the initial ex-siRNA targets regulate the expression of other genes, which can be up- or down-regulated. Expression of 50% of the genes was dependent on more than one RNAi gene in agreement with the existence of several classes of ex-siRNAs produced by different combinations of RNAi proteins. These combinations of proteins have also been involved in the regulation of different cellular processes. Besides genes regulated by the canonical RNAi pathway, this analysis identified processes, such as growth at low pH and sexual interaction that are regulated by a dicer-independent non-canonical RNAi pathway. This work shows that the RNAi pathways play a relevant role in the regulation of a significant number of endogenous genes in M. circinelloides during exponential and stationary growth phases and opens up an important avenue for in-depth study of genes involved in the regulation of physiological and developmental processes in this fungal model.

A New Strategy in Observer Modeling for Greenhouse Cucumber Seedling Growth

PubMed Central

Qiu, Quan; Zheng, Chenfei; Wang, Wenping; Qiao, Xiaojun; Bai, He; Yu, Jingquan; Shi, Kai

2017-01-01

State observer is an essential component in computerized control loops for greenhouse-crop systems. However, the current accomplishments of observer modeling for greenhouse-crop systems mainly focus on mass/energy balance, ignoring physiological responses of crops. As a result, state observers for crop physiological responses are rarely developed, and control operations are typically made based on experience rather than actual crop requirements. In addition, existing observer models require a large number of parameters, leading to heavy computational load and poor application feasibility. To address these problems, we present a new state observer modeling strategy that takes both environmental information and crop physiological responses into consideration during the observer modeling process. Using greenhouse cucumber seedlings as an instance, we sample 10 physiological parameters of cucumber seedlings at different time point during the exponential growth stage, and employ them to build growth state observers together with 8 environmental parameters. Support vector machine (SVM) acts as the mathematical tool for observer modeling. Canonical correlation analysis (CCA) is used to select the dominant environmental and physiological parameters in the modeling process. With the dominant parameters, simplified observer models are built and tested. We conduct contrast experiments with different input parameter combinations on simplified and un-simplified observers. Experimental results indicate that physiological information can improve the prediction accuracies of the growth state observers. Furthermore, the simplified observer models can give equivalent or even better performance than the un-simplified ones, which verifies the feasibility of CCA. The current study can enable state observers to reflect crop requirements and make them feasible for applications with simplified shapes, which is significant for developing intelligent greenhouse control systems for modern greenhouse production. PMID:28848565

A New Strategy in Observer Modeling for Greenhouse Cucumber Seedling Growth.

PubMed

Qiu, Quan; Zheng, Chenfei; Wang, Wenping; Qiao, Xiaojun; Bai, He; Yu, Jingquan; Shi, Kai

2017-01-01

State observer is an essential component in computerized control loops for greenhouse-crop systems. However, the current accomplishments of observer modeling for greenhouse-crop systems mainly focus on mass/energy balance, ignoring physiological responses of crops. As a result, state observers for crop physiological responses are rarely developed, and control operations are typically made based on experience rather than actual crop requirements. In addition, existing observer models require a large number of parameters, leading to heavy computational load and poor application feasibility. To address these problems, we present a new state observer modeling strategy that takes both environmental information and crop physiological responses into consideration during the observer modeling process. Using greenhouse cucumber seedlings as an instance, we sample 10 physiological parameters of cucumber seedlings at different time point during the exponential growth stage, and employ them to build growth state observers together with 8 environmental parameters. Support vector machine (SVM) acts as the mathematical tool for observer modeling. Canonical correlation analysis (CCA) is used to select the dominant environmental and physiological parameters in the modeling process. With the dominant parameters, simplified observer models are built and tested. We conduct contrast experiments with different input parameter combinations on simplified and un-simplified observers. Experimental results indicate that physiological information can improve the prediction accuracies of the growth state observers. Furthermore, the simplified observer models can give equivalent or even better performance than the un-simplified ones, which verifies the feasibility of CCA. The current study can enable state observers to reflect crop requirements and make them feasible for applications with simplified shapes, which is significant for developing intelligent greenhouse control systems for modern greenhouse production.

Ablation of steel by microsecond pulse trains

NASA Astrophysics Data System (ADS)

Windeler, Matthew Karl Ross

Laser micromachining is an important material processing technique used in industry and medicine to produce parts with high precision. Control of the material removal process is imperative to obtain the desired part with minimal thermal damage to the surrounding material. Longer pulsed lasers, with pulse durations of milli- and microseconds, are used primarily for laser through-cutting and welding. In this work, a two-pulse sequence using microsecond pulse durations is demonstrated to achieve consistent material removal during percussion drilling when the delay between the pulses is properly defined. The light-matter interaction moves from a regime of surface morphology changes to melt and vapour ejection. Inline coherent imaging (ICI), a broadband, spatially-coherent imaging technique, is used to monitor the ablation process. The pulse parameter space is explored and the key regimes are determined. Material removal is observed when the pulse delay is on the order of the pulse duration. ICI is also used to directly observe the ablation process. Melt dynamics are characterized by monitoring surface changes during and after laser processing at several positions in and around the interaction region. Ablation is enhanced when the melt has time to flow back into the hole before the interaction with the second pulse begins. A phenomenological model is developed to understand the relationship between material removal and pulse delay. Based on melt refilling the interaction region, described by logistic growth, and heat loss, described by exponential decay, the model is fit to several datasets. The fit parameters reflect the pulse energies and durations used in the ablation experiments. For pulse durations of 50 us with pulse energies of 7.32 mJ +/- 0.09 mJ, the logisitic growth component of the model reaches half maximum after 8.3 mus +/- 1.1 us and the exponential decays with a rate of 64 mus +/- 15 us. The phenomenological model offers an interpretation of the material removal process.

Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly

NASA Astrophysics Data System (ADS)

Eugène, Sarah; Xue, Wei-Feng; Robert, Philippe; Doumic, Marie

2016-05-01

Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic differential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model offers a new perspective and paves the way for a new and efficient approach on extracting vital information regarding the key initial events of amyloid formation.

Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2006-01-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Adaptive Optimal Stochastic State Feedback Control of Resistive Wall Modes in Tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2007-06-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least square method with exponential forgetting factor and covariance resetting is used to identify the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Poverty trap formed by the ecology of infectious diseases

PubMed Central

Bonds, Matthew H.; Keenan, Donald C.; Rohani, Pejman; Sachs, Jeffrey D.

2010-01-01

While most of the world has enjoyed exponential economic growth, more than one-sixth of the world is today roughly as poor as their ancestors were many generations ago. Widely accepted general explanations for the persistence of such poverty have been elusive and are needed by the international development community. Building on a well-established model of human infectious diseases, we show how formally integrating simple economic and disease ecology models can naturally give rise to poverty traps, where initial economic and epidemiological conditions determine the long-term trajectory of the health and economic development of a society. This poverty trap may therefore be broken by improving health conditions of the population. More generally, we demonstrate that simple human ecological models can help explain broad patterns of modern economic organization. PMID:20007179

Very slow growth of Escherichia coli.

PubMed Central

Chesbro, W; Evans, T; Eifert, R

1979-01-01

A recycling fermentor (a chemostat with 100% biomass feedback) was used to study glucose-limited behavior of Escherichia coli B. The expectation from mass transfer analysis that growth would asymptotically approach a limit mass determined by the glucose provision rate (GPR) and the culture's maintenance requirement was not met. Instead, growth proceeded at progressively lower rates through three distinct phases. After the fermentor was seeded, but before glucose became limiting, growth followed the usual, exponential path (phase 1). About 12 h postseeding, residual glucose in the fermentor fell below 1 microgram . ml-1 and the growth rate (dx/dt) became constant and a linear function of GPR (phase 2). The specific growth rate, mu, therefore fell continuously throughout the phase. Biomass yield and glucose assimilation (13%) were near the level for exponential growth, however, and independent of GPR over a broad range. At a critical specific growth rate (0.04 h-1 for this strain), phase 2 ended abruptly and phase 3 commenced. In phase 3, the growth rate was again constant, although lower than in phase 2, so that mu continued to fall, but growth rates and yields were praboloid functions of GPR. They were never zero, however, at any positive value of GPR. By inference, the fraction of metabolic energy used for maintenance functions is constant for a given GPR, although different for phases 2 and 3, and independent of biomass. In both phases 2 and 3, orcinol, diphenylamine, and Lowry reactive materials were secreted at near-constant rates such that over 50% as much biosynthetic mass was secreted as was retained by the cells. Images PMID:378981

An optimized small animal tumour model for experimentation with low energy protons.

PubMed

Beyreuther, Elke; Brüchner, Kerstin; Krause, Mechthild; Schmidt, Margret; Szabo, Rita; Pawelke, Jörg

2017-01-01

The long-term aim of developing laser based particle acceleration towards clinical application requires not only substantial technological progress, but also the radiobiological characterization of the resulting ultra-short and ultra-intensive particle beam pulses. After comprehensive cell studies a mouse ear tumour model was established allowing for the penetration of low energy protons (~20 MeV) currently available at laser driven accelerators. The model was successfully applied for a first tumour growth delay study with laser driven electrons, whereby the need of improvements crop out. To optimise the mouse ear tumour model with respect to a stable, high take rate and a lower number of secondary tumours, Matrigel was introduced for tumour cell injection. Different concentrations of two human tumour cell lines (FaDu, LN229) and Matrigel were evaluated for stable tumour growth and fulfilling the allocation criteria for irradiation experiments. The originally applied cell injection with PBS was performed for comparison and to assess the long-term stability of the model. Finally, the optimum suspension of cells and Matrigel was applied to determine applicable dose ranges for tumour growth delay studies by 200 kV X-ray irradiation. Both human tumour models showed a high take rate and exponential tumour growth starting at a volume of ~10 mm3. As disclosed by immunofluorescence analysis these small tumours already interact with the surrounding tissue and activate endothelial cells to form vessels. The formation of delimited, solid tumours at irradiation size was shown by standard H&E staining and a realistic dose range for inducing tumour growth delay without permanent tumour control was obtained for both tumour entities. The already established mouse ear tumour model was successfully upgraded now providing stable tumour growth with high take rate for two tumour entities (HNSCC, glioblastoma) that are of interest for future irradiation experiments at experimental accelerators.

Growth of bacteria in 3-d colonies

PubMed Central

Mugler, Andrew; Kim, Justin

2017-01-01

The dynamics of growth of bacterial populations has been extensively studied for planktonic cells in well-agitated liquid culture, in which all cells have equal access to nutrients. In the real world, bacteria are more likely to live in physically structured habitats as colonies, within which individual cells vary in their access to nutrients. The dynamics of bacterial growth in such conditions is poorly understood, and, unlike that for liquid culture, there is not a standard broadly used mathematical model for bacterial populations growing in colonies in three dimensions (3-d). By extending the classic Monod model of resource-limited population growth to allow for spatial heterogeneity in the bacterial access to nutrients, we develop a 3-d model of colonies, in which bacteria consume diffusing nutrients in their vicinity. By following the changes in density of E. coli in liquid and embedded in glucose-limited soft agar, we evaluate the fit of this model to experimental data. The model accounts for the experimentally observed presence of a sub-exponential, diffusion-limited growth regime in colonies, which is absent in liquid cultures. The model predicts and our experiments confirm that, as a consequence of inter-colony competition for the diffusing nutrients and of cell death, there is a non-monotonic relationship between total number of colonies within the habitat and the total number of individual cells in all of these colonies. This combined theoretical-experimental study reveals that, within 3-d colonies, E. coli cells are loosely packed, and colonies produce about 2.5 times as many cells as the liquid culture from the same amount of nutrients. We verify that this is because cells in liquid culture are larger than in colonies. Our model provides a baseline description of bacterial growth in 3-d, deviations from which can be used to identify phenotypic heterogeneities and inter-cellular interactions that further contribute to the structure of bacterial communities. PMID:28749935

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Paradoxical Long-Timespan Opening of the Hole in Self-Supported Water Films of Nanometer Thickness.

PubMed

Barkay, Z; Bormashenko, E

2017-05-16

The opening of holes in self-supported thin (nanoscaled) water films has been investigated in situ with the environmental scanning electron microscope. The opening of a hole occurs within a two-stage process. In the first stage, the rim surrounding a hole is formed, resembling the process that is observed under the puncturing of soap bubbles. In the second stage, the exponential growth of the hole is observed, with a characteristic time of a dozen seconds. We explain the exponential kinetics of hole growth by the balance between inertia (gravity) and viscous dissipation. The kinetics of opening a microscaled hole is governed by the processes taking place in the nanothick bulk of the self-supported liquid film. Nanoparticles provide markers for the visualization of the processes occurring in self-supported thin nanoscale liquid films.

Mathematical Modeling of Extinction of Inhomogeneous Populations

PubMed Central

Karev, G.P.; Kareva, I.

2016-01-01

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

Using Exponential Smoothing to Specify Intervention Models for Interrupted Time Series.

ERIC Educational Resources Information Center

Mandell, Marvin B.; Bretschneider, Stuart I.

1984-01-01

The authors demonstrate how exponential smoothing can play a role in the identification of the intervention component of an interrupted time-series design model that is analogous to the role that the sample autocorrelation and partial autocorrelation functions serve in the identification of the noise portion of such a model. (Author/BW)

Forecast of the number of patients with end-stage renal disease in the United States to the year 2010.

PubMed

Xue, J L; Ma, J Z; Louis, T A; Collins, A J

2001-12-01

As the United States end-stage renal disease (ESRD) program enters the new millennium, the continued growth of the ESRD population poses a challenge for policy makers, health care providers, and financial planners. To assist in future planning for the ESRD program, the growth of patient numbers and Medicare costs was forecasted to the year 2010 by modeling of historical data from 1982 through 1997. A stepwise autoregressive method and exponential smoothing models were used. The forecasting models for ESRD patient numbers demonstrated mean errors of -0.03 to 1.03%, relative to the observed values. The model for Medicare payments demonstrated -0.12% mean error. The R(2) values for the forecasting models ranged from 99.09 to 99.98%. On the basis of trends in patient numbers, this forecast projects average annual growth of the ESRD populations of approximately 4.1% for new patients, 6.4% for long-term ESRD patients, 7.1% for dialysis patients, 6.1% for patients with functioning transplants, and 8.2% for patients on waiting lists for transplants, as well as 7.7% for Medicare expenditures. The numbers of patients with ESRD in 2010 are forecasted to be 129,200 +/- 7742 (95% confidence limits) new patients, 651,330 +/- 15,874 long-term ESRD patients, 520,240 +/- 25,609 dialysis patients, 178,806 +/- 4349 patients with functioning transplants, and 95,550 +/- 5478 patients on waiting lists. The forecasted Medicare expenditures are projected to increase to $28.3 +/- 1.7 billion by 2010. These projections are subject to many factors that may alter the actual growth, compared with the historical patterns. They do, however, provide a basis for discussing the future growth of the ESRD program and how the ESRD community can meet the challenges ahead.

Relaxation processes in a low-order three-dimensional magnetohydrodynamics model

NASA Technical Reports Server (NTRS)

Stribling, Troy; Matthaeus, William H.

1991-01-01

The time asymptotic behavior of a Galerkin model of 3D magnetohydrodynamics (MHD) has been interpreted using the selective decay and dynamic alignment relaxation theories. A large number of simulations has been performed that scan a parameter space defined by the rugged ideal invariants, including energy, cross helicity, and magnetic helicity. It is concluded that time asymptotic state can be interpreted as a relaxation to minimum energy. A simple decay model, based on absolute equilibrium theory, is found to predict a mapping of initial onto time asymptotic states, and to accurately describe the long time behavior of the runs when magnetic helicity is present. Attention is also given to two processes, operating on time scales shorter than selective decay and dynamic alignment, in which the ratio of kinetic to magnetic energy relaxes to values 0(1). The faster of the two processes takes states initially dominant in magnetic energy to a state of near-equipartition between kinetic and magnetic energy through power law growth of kinetic energy. The other process takes states initially dominant in kinetic energy to the near-equipartitioned state through exponential growth of magnetic energy.

Quantitative proteomic analysis reveals a simple strategy of global resource allocation in bacteria

PubMed Central

Hui, Sheng; Silverman, Josh M; Chen, Stephen S; Erickson, David W; Basan, Markus; Wang, Jilong; Hwa, Terence; Williamson, James R

2015-01-01

A central aim of cell biology was to understand the strategy of gene expression in response to the environment. Here, we study gene expression response to metabolic challenges in exponentially growing Escherichia coli using mass spectrometry. Despite enormous complexity in the details of the underlying regulatory network, we find that the proteome partitions into several coarse-grained sectors, with each sector's total mass abundance exhibiting positive or negative linear relations with the growth rate. The growth rate-dependent components of the proteome fractions comprise about half of the proteome by mass, and their mutual dependencies can be characterized by a simple flux model involving only two effective parameters. The success and apparent generality of this model arises from tight coordination between proteome partition and metabolism, suggesting a principle for resource allocation in proteome economy of the cell. This strategy of global gene regulation should serve as a basis for future studies on gene expression and constructing synthetic biological circuits. Coarse graining may be an effective approach to derive predictive phenomenological models for other ‘omics’ studies. PMID:25678603

Fearless versus fearful speculative financial bubbles

NASA Astrophysics Data System (ADS)

Andersen, J. V.; Sornette, D.

2004-06-01

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies nine time series that have been previously considered as bubbles ending in crashes. The model predicts the existence of two anomalous behaviors occurring simultaneously: (i) super-exponential price growth and (ii) volatility growth, that we refer to as the “fearful singular bubble” regime. Out of the nine time series, we find that five pass our tests and can be characterized as “fearful singular bubbles”. The four other cases are the information technology Nasdaq bubble and three bubbles of the Hang Seng index ending in crashes in 1987, 1994 and 1997. According to our analysis, these four bubbles have developed with essentially no significant increase of their volatility. This paper thus proposes that speculative bubbles ending in crashes form two groups hitherto unrecognized, namely those accompanied by increasing volatility (reflecting increasing risk perception) and those without change of volatility (reflecting an absence of risk perception).

EFFECT OF TEMPERATURE ON THE COMPOSITION OF FATTY ACIDS IN ESCHERICHIA COLI

PubMed Central

Marr, Allen G.; Ingraham, John L.

1962-01-01

Marr, Allen G. (University of California, Davis) and John L. Ingraham. Effect of temperature on composition of fatty acids in Escherichia coli. J. Bacteriol. 84:1260–1267. 1962.—Variations in the temperature of growth and in the composition of the medium alter the proportions of individual fatty acids in the lipids of Escherichia coli. As the temperature of growth is lowered, the proportion of unsaturated fatty acids (hexadecenoic and octadecenoic acids) increases. The increase in content of unsaturated acids with a decrease in temperature of growth occurs in both minimal and complex media. Cells harvested in the stationary phase contained large amounts of cyclopropane fatty acids (methylenehexadecanoic and methylene octadecanoic acids) in comparison with cells harvested during exponential growth. Cells grown in a chemostat, limited by the concentration of ammonium salts, show a much higher content of saturated fatty acids (principally palmitic acid) than do cells harvested from an exponentially-growing batch culture in the same medium. Cells grown in a chemostat, limited by the concentration of glucose, show a slightly higher content of unsaturated fatty acids than cells from the corresponding batch culture. The results do not indicate a direct relation between fatty acid composition and minimal growth temperature. PMID:16561982

Saturation of the magnetorotational instability at large Elsasser number

NASA Astrophysics Data System (ADS)

Jamroz, B.; Julien, K.; Knobloch, E.

2008-09-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still but not negligible. The regime explored retains the condition that (viscous and ohmic) dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

An exponential growth of computational phantom research in radiation protection, imaging, and radiotherapy: A review of the fifty-year history

PubMed Central

Xu, X. George

2014-01-01

Radiation dose calculation using models of the human anatomy has been a subject of great interest to radiation protection, medical imaging, and radiotherapy. However, early pioneers of this field did not foresee the exponential growth of research activity as observed today. This review article walks the reader through the history of the research and development in this field of study which started some 50 years ago. This review identifies a clear progression of computational phantom complexity which can be denoted by three distinct generations. The first generation of stylized phantoms, representing a grouping of less than dozen models, was initially developed in the 1960s at Oak Ridge National Laboratory to calculate internal doses from nuclear medicine procedures. Despite their anatomical simplicity, these computational phantoms were the best tools available at the time for internal/external dosimetry, image evaluation, and treatment dose evaluations. A second generation of a large number of voxelized phantoms arose rapidly in the late 1980s as a result of the increased availability of tomographic medical imaging and computers. Surprisingly, the last decade saw the emergence of the third generation of phantoms which are based on advanced geometries called boundary representation (BREP) in the form of Non-Uniform Rational B-Splines (NURBS) or polygonal meshes. This new class of phantoms now consists of over 287 models including those used for non-ionizing radiation applications. This review article aims to provide the reader with a general understanding of how the field of computational phantoms came about and the technical challenges it faced at different times. This goal is achieved by defining basic geometry modeling techniques and by analyzing selected phantoms in terms of geometrical features and dosimetric problems to be solved. The rich historical information is summarized in four tables that are aided by highlights in the text on how some of the most well-known phantoms were developed and used in practice. Some of the information covered in this review has not been previously reported, for example, the CAM and CAF phantoms developed in 1970s for space radiation applications. The author also clarifies confusion about “population-average” prospective dosimetry needed for radiological protection under the current ICRP radiation protection system and “individualized” retrospective dosimetry often performed for medical physics studies. To illustrate the impact of computational phantoms, a section of this article is devoted to examples from the author’s own research group. Finally the author explains an unexpected finding during the course of preparing for this article that the phantoms from the past 50 years followed a pattern of exponential growth. The review ends on a brief discussion of future research needs (A supplementary file “3DPhantoms.pdf” to Figure 15 is available for download that will allow a reader to interactively visualize the phantoms in 3D). PMID:25144730

An exponential growth of computational phantom research in radiation protection, imaging, and radiotherapy: a review of the fifty-year history.

PubMed

Xu, X George

2014-09-21

Radiation dose calculation using models of the human anatomy has been a subject of great interest to radiation protection, medical imaging, and radiotherapy. However, early pioneers of this field did not foresee the exponential growth of research activity as observed today. This review article walks the reader through the history of the research and development in this field of study which started some 50 years ago. This review identifies a clear progression of computational phantom complexity which can be denoted by three distinct generations. The first generation of stylized phantoms, representing a grouping of less than dozen models, was initially developed in the 1960s at Oak Ridge National Laboratory to calculate internal doses from nuclear medicine procedures. Despite their anatomical simplicity, these computational phantoms were the best tools available at the time for internal/external dosimetry, image evaluation, and treatment dose evaluations. A second generation of a large number of voxelized phantoms arose rapidly in the late 1980s as a result of the increased availability of tomographic medical imaging and computers. Surprisingly, the last decade saw the emergence of the third generation of phantoms which are based on advanced geometries called boundary representation (BREP) in the form of Non-Uniform Rational B-Splines (NURBS) or polygonal meshes. This new class of phantoms now consists of over 287 models including those used for non-ionizing radiation applications. This review article aims to provide the reader with a general understanding of how the field of computational phantoms came about and the technical challenges it faced at different times. This goal is achieved by defining basic geometry modeling techniques and by analyzing selected phantoms in terms of geometrical features and dosimetric problems to be solved. The rich historical information is summarized in four tables that are aided by highlights in the text on how some of the most well-known phantoms were developed and used in practice. Some of the information covered in this review has not been previously reported, for example, the CAM and CAF phantoms developed in 1970s for space radiation applications. The author also clarifies confusion about 'population-average' prospective dosimetry needed for radiological protection under the current ICRP radiation protection system and 'individualized' retrospective dosimetry often performed for medical physics studies. To illustrate the impact of computational phantoms, a section of this article is devoted to examples from the author's own research group. Finally the author explains an unexpected finding during the course of preparing for this article that the phantoms from the past 50 years followed a pattern of exponential growth. The review ends on a brief discussion of future research needs (a supplementary file '3DPhantoms.pdf' to figure 15 is available for download that will allow a reader to interactively visualize the phantoms in 3D).

Capitalizing on the Dynamic Features of Excel to Consider Growth Rates and Limits

ERIC Educational Resources Information Center

Taylor, Daniel; Moore-Russo, Deborah

2012-01-01

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

Biological growth functions describe published site index curves for Lake States timber species.

Treesearch

Allen L. Lundgren; William A. Dolid

1970-01-01

Two biological growth functions, an exponential-monomolecular function and a simple monomolecular function, have been fit to published site index curves for 11 Lake States tree species: red, jack, and white pine, balsam fir, white and black spruce, tamarack, white-cedar, aspen, red oak, and paper birch. Both functions closely fit all published curves except those for...

Online Privacy, Security and Ethical Dilemma: A Recent Study.

ERIC Educational Resources Information Center

Karmakar, Nitya L.

The Internet remains as a wonder for the 21st century and its growth is phenomenon. According to a recent survey, the online population is now about 500 million globally and if this trend continues, it should reach 700 million by the end of 2002. This exponential growth of the Internet has given rise to several security, privacy and ethical…

Comparing growth of ponderosa pine in two growing media

Treesearch

R. Kasten Dumroese

2009-01-01

I compared growth of container ponderosa pine (Pinus ponderosa) seedlings grown in a 1:1 (v:v) Sphagnum peat moss:coarse vermiculite medium (P:V) and a 7:3 (v:v) Sphagnum peat moss:Douglas-fir sawdust medium (P:S) at three different irrigation regimes. By using exponential fertilization techniques, I was able to supply seedlings with similar amounts...

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

Effect of growth phase on the fatty acid compositions of four species of marine diatoms

NASA Astrophysics Data System (ADS)

Liang, Ying; Mai, Kangsen

2005-04-01

The fatty acid compositions of four species of marine diatoms ( Chaetoceros gracilis MACC/B13, Cylindrotheca fusiformis MACC/B211, Phaeodactylum tricornutum MACC/B221 and Nitzschia closterium MACC/B222), cultivated at 22°C±1°C with the salinity of 28 in f/2 medium and harvested in the exponential growth phase, the early stationary phase and the late stationary phase, were determined. The results showed that growth phase has significant effect on most fatty acid contents in the four species of marine diatoms. The proportions of 16:0 and 16:1n-7 fatty acids increased while those of 16:3n-4 and eicosapentaenoic acid (EPA) decreased with increasing culture age in all species studied. The subtotal of saturated fatty acids (SFA) increased with the increasing culture age in all species with the exception of B13. The subtotal of monounsaturated fatty acids (MUFA) increased while that of polyunsaturated fatty acids (PUFA) decreased with culture age in the four species of marine diatoms. MUFA reached their lowest value in the exponential growth phase, whereas PUFA reached their highest value in the same phase.

Inhibitors of protein phosphorylation including the retinoblastoma protein induce germination of Candida albicans.

PubMed

Cho, T; Hamatake, H; Hagihara, Y; Kaminishi, H

2000-02-01

It has been previously shown that the induction of germination in Candida albicans occurs following its cessation of growth as a yeast. Similarly, mammalian cells undergo a differentiation process that is preceded by a growth cessation associated with a hypophosphorylation of proteins of the retinoblastoma gene family. It is postulated that a similar type of mechanism may be operative in C. albicans and protein phosphorylation inhibitors: forskolin (stimulates cyclic adenosine monophosphate production), okadaic acid (phosphatase inhibitor) and D-erythro-sphingosine (retinoblastoma protein phosphorylation inhibitor) have been used to further strengthen this hypothesis. Okadaic acid (1-1000 nM) and D-erythro-sphingosine (100 microM) significantly inhibited the growth of yeast cells of C. albicans. D-Erythro-sphingosine at 1000 microM was candidicidal. Forskolin did not significantly affect growth. Exponentially grown C. albicans pretreated with forskolin (10 microM), okadaic acid (1000 nM) or D-erythro-sphingosine (100 microM) readily germinated. In comparison, when these inhibitors were incorporated in the same medium, germination of exponentially grown cells did not occur. These results suggest that protein dephosphorylation may be necessary at an early stage of the yeast-hyphae transition in C. albicans.

Use of a digital camera to monitor the growth and nitrogen status of cotton.

PubMed

Jia, Biao; He, Haibing; Ma, Fuyu; Diao, Ming; Jiang, Guiying; Zheng, Zhong; Cui, Jin; Fan, Hua

2014-01-01

The main objective of this study was to develop a nondestructive method for monitoring cotton growth and N status using a digital camera. Digital images were taken of the cotton canopies between emergence and full bloom. The green and red values were extracted from the digital images and then used to calculate canopy cover. The values of canopy cover were closely correlated with the normalized difference vegetation index and the ratio vegetation index and were measured using a GreenSeeker handheld sensor. Models were calibrated to describe the relationship between canopy cover and three growth properties of the cotton crop (i.e., aboveground total N content, LAI, and aboveground biomass). There were close, exponential relationships between canopy cover and three growth properties. And the relationships for estimating cotton aboveground total N content were most precise, the coefficients of determination (R(2)) value was 0.978, and the root mean square error (RMSE) value was 1.479 g m(-2). Moreover, the models were validated in three fields of high-yield cotton. The result indicated that the best relationship between canopy cover and aboveground total N content had an R(2) value of 0.926 and an RMSE value of 1.631 g m(-2). In conclusion, as a near-ground remote assessment tool, digital cameras have good potential for monitoring cotton growth and N status.

State of the World 1984

NASA Astrophysics Data System (ADS)

Singer, S. Fred

Long before Ronald Reagan asked voters whether they were better off today than they were 4 years ago, many thoughtful people were asking whether the world as a whole was becoming a better place to live. The Malthusian point of view, restated by the Club of Rome's Limits to Growth, made an enormous impact on the world when it appeared in 1972. Its simplistic message, disguised in computer models, was that exponential growth cannot be maintained forever. Specifically, it predicted imminent exhaustion of food and natural resources and death from evergrowing pollution. Its successor volume, Global 2000, published with the encouragement of the Carter White House in 1980, was more restrained but also predicted general doom. It was responded to by The Resourceful Earth (sponsored by the Heritage Foundation), which views the future as rosy and contradicts Global 2000 on almost every point.

Complex Autocatalysis in Simple Chemistries.

PubMed

Virgo, Nathaniel; Ikegami, Takashi; McGregor, Simon

2016-01-01

Life on Earth must originally have arisen from abiotic chemistry. Since the details of this chemistry are unknown, we wish to understand, in general, which types of chemistry can lead to complex, lifelike behavior. Here we show that even very simple chemistries in the thermodynamically reversible regime can self-organize to form complex autocatalytic cycles, with the catalytic effects emerging from the network structure. We demonstrate this with a very simple but thermodynamically reasonable artificial chemistry model. By suppressing the direct reaction from reactants to products, we obtain the simplest kind of autocatalytic cycle, resulting in exponential growth. When these simple first-order cycles are prevented from forming, the system achieves superexponential growth through more complex, higher-order autocatalytic cycles. This leads to nonlinear phenomena such as oscillations and bistability, the latter of which is of particular interest regarding the origins of life.

The impacts of precipitation amount simulation on hydrological modeling in Nordic watersheds

NASA Astrophysics Data System (ADS)

Li, Zhi; Brissette, Fancois; Chen, Jie

2013-04-01

Stochastic modeling of daily precipitation is very important for hydrological modeling, especially when no observed data are available. Precipitation is usually modeled by two component model: occurrence generation and amount simulation. For occurrence simulation, the most common method is the first-order two-state Markov chain due to its simplification and good performance. However, various probability distributions have been reported to simulate precipitation amount, and spatiotemporal differences exist in the applicability of different distribution models. Therefore, assessing the applicability of different distribution models is necessary in order to provide more accurate precipitation information. Six precipitation probability distributions (exponential, Gamma, Weibull, skewed normal, mixed exponential, and hybrid exponential/Pareto distributions) are directly and indirectly evaluated on their ability to reproduce the original observed time series of precipitation amount. Data from 24 weather stations and two watersheds (Chute-du-Diable and Yamaska watersheds) in the province of Quebec (Canada) are used for this assessment. Various indices or statistics, such as the mean, variance, frequency distribution and extreme values are used to quantify the performance in simulating the precipitation and discharge. Performance in reproducing key statistics of the precipitation time series is well correlated to the number of parameters of the distribution function, and the three-parameter precipitation models outperform the other models, with the mixed exponential distribution being the best at simulating daily precipitation. The advantage of using more complex precipitation distributions is not as clear-cut when the simulated time series are used to drive a hydrological model. While the advantage of using functions with more parameters is not nearly as obvious, the mixed exponential distribution appears nonetheless as the best candidate for hydrological modeling. The implications of choosing a distribution function with respect to hydrological modeling and climate change impact studies are also discussed.

Modulation of Medium pH by Caulobacter crescentus Facilitates Recovery from Uranium-Induced Growth Arrest

PubMed Central

Park, Dan M.

2014-01-01

The oxidized form of uranium [U(VI)] predominates in oxic environments and poses a major threat to ecosystems. Due to its ability to mineralize U(VI), the oligotroph Caulobacter crescentus is an attractive candidate for U(VI) bioremediation. However, the physiological basis for U(VI) tolerance is unclear. Here we demonstrated that U(VI) caused a temporary growth arrest in C. crescentus and three other bacterial species, although the duration of growth arrest was significantly shorter for C. crescentus. During the majority of the growth arrest period, cell morphology was unaltered and DNA replication initiation was inhibited. However, during the transition from growth arrest to exponential phase, cells with shorter stalks were observed, suggesting a decoupling between stalk development and the cell cycle. Upon recovery from growth arrest, C. crescentus proliferated with a growth rate comparable to that of a control without U(VI), although a fraction of these cells appeared filamentous with multiple replication start sites. Normal cell morphology was restored by the end of exponential phase. Cells did not accumulate U(VI) resistance mutations during the prolonged growth arrest, but rather, a reduction in U(VI) toxicity occurred concomitantly with an increase in medium pH. Together, these data suggest that C. crescentus recovers from U(VI)-induced growth arrest by reducing U(VI) toxicity through pH modulation. Our finding represents a unique U(VI) detoxification strategy and provides insight into how microbes cope with U(VI) under nongrowing conditions, a metabolic state that is prevalent in natural environments. PMID:25002429

Comparing TCV experimental VDE responses with DINA code simulations

NASA Astrophysics Data System (ADS)

Favez, J.-Y.; Khayrutdinov, R. R.; Lister, J. B.; Lukash, V. E.

2002-02-01

The DINA free-boundary equilibrium simulation code has been implemented for TCV, including the full TCV feedback and diagnostic systems. First results showed good agreement with control coil perturbations and correctly reproduced certain non-linear features in the experimental measurements. The latest DINA code simulations, presented in this paper, exploit discharges with different cross-sectional shapes and different vertical instability growth rates which were subjected to controlled vertical displacement events (VDEs), extending previous work with the DINA code on the DIII-D tokamak. The height of the TCV vessel allows observation of the non-linear evolution of the VDE growth rate as regions of different vertical field decay index are crossed. The vertical movement of the plasma is found to be well modelled. For most experiments, DINA reproduces the S-shape of the vertical displacement in TCV with excellent precision. This behaviour cannot be modelled using linear time-independent models because of the predominant exponential shape due to the unstable pole of any linear time-independent model. The other most common equilibrium parameters like the plasma current Ip, the elongation κ, the triangularity δ, the safety factor q, the ratio between the averaged plasma kinetic pressure and the pressure of the poloidal magnetic field at the edge of the plasma βp, and the internal self inductance li also show acceptable agreement. The evolution of the growth rate γ is estimated and compared with the evolution of the closed-loop growth rate calculated with the RZIP linear model, confirming the origin of the observed behaviour.

Exponential Acceleration of VT Seismicity in the Years Prior to Major Eruptions of Basaltic Volcanoes

NASA Astrophysics Data System (ADS)

Lengline, O.; Marsan, D.; Got, J.; Pinel, V.

2007-12-01

The evolution of the seismicity at three basaltic volcanoes (Kilauea, Mauna-Loa and Piton de la Fournaise) is analysed during phases of magma accumulation. We show that the VT seismicity during these time-periods is characterized by an exponential increase at long-time scale (years). Such an exponential acceleration can be explained by a model of seismicity forced by the replenishment of a magmatic reservoir. The increase in stress in the edifice caused by this replenishment is modeled. This stress history leads to a cumulative number of damage, ie VT earthquakes, following the same exponential increase as found for seismicity. A long-term seismicity precursor is thus detected at basaltic volcanoes. Although this precursory signal is not able to predict the onset times of futures eruptions (as no diverging point is present in the model), it may help mitigating volcanic hazards.

Repopulation Kinetics and the Linear-Quadratic Model

NASA Astrophysics Data System (ADS)

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

Multiserver Queueing Model subject to Single Exponential Vacation

NASA Astrophysics Data System (ADS)

Vijayashree, K. V.; Janani, B.

2018-04-01

A multi-server queueing model subject to single exponential vacation is considered. The arrivals are allowed to join the queue according to a Poisson distribution and services takes place according to an exponential distribution. Whenever the system becomes empty, all the servers goes for a vacation and returns back after a fixed interval of time. The servers then starts providing service if there are waiting customers otherwise they will wait to complete the busy period. The vacation times are also assumed to be exponentially distributed. In this paper, the stationary and transient probabilities for the number of customers during ideal and functional state of the server are obtained explicitly. Also, numerical illustrations are added to visualize the effect of various parameters.

Changes in speed distribution: Applying aggregated safety effect models to individual vehicle speeds.

PubMed

Vadeby, Anna; Forsman, Åsa

2017-06-01

This study investigated the effect of applying two aggregated models (the Power model and the Exponential model) to individual vehicle speeds instead of mean speeds. This is of particular interest when the measure introduced affects different parts of the speed distribution differently. The aim was to examine how the estimated overall risk was affected when assuming the models are valid on an individual vehicle level. Speed data from two applications of speed measurements were used in the study: an evaluation of movable speed cameras and a national evaluation of new speed limits in Sweden. The results showed that when applied on individual vehicle speed level compared with aggregated level, there was essentially no difference between these for the Power model in the case of injury accidents. However, for fatalities the difference was greater, especially for roads with new cameras where those driving fastest reduced their speed the most. For the case with new speed limits, the individual approach estimated a somewhat smaller effect, reflecting that changes in the 15th percentile (P15) were somewhat larger than changes in P85 in this case. For the Exponential model there was also a clear, although small, difference between applying the model to mean speed changes and individual vehicle speed changes when speed cameras were used. This applied both for injury accidents and fatalities. There were also larger effects for the Exponential model than for the Power model, especially for injury accidents. In conclusion, applying the Power or Exponential model to individual vehicle speeds is an alternative that provides reasonable results in relation to the original Power and Exponential models, but more research is needed to clarify the shape of the individual risk curve. It is not surprising that the impact on severe traffic crashes was larger in situations where those driving fastest reduced their speed the most. Further investigations on use of the Power and/or the Exponential model at individual vehicle level would require more data on the individual level from a range of international studies. Copyright © 2017 Elsevier Ltd. All rights reserved.

Kinetic behaviours of aggregate growth driven by time-dependent migration, birth and death

NASA Astrophysics Data System (ADS)

Zhu, Sheng-Qing; Yang, Shun-You; Ke, Jianhong; Lin, Zhenquan

2008-12-01

We propose a dynamic growth model to mimic some social phenomena, such as the evolution of cities' population, in which monomer migrations occur between any two aggregates and monomer birth/death can simultaneously occur in each aggregate. Considering the fact that the rate kernels of migration, birth and death processes may change with time, we assume that the migration rate kernel is ijf(t), and the self-birth and death rate kernels are ig1(t) and ig2(t), respectively. Based on the mean-field rate equation, we obtain the exact solution of this model and then discuss semi-quantitatively the scaling behaviour of the aggregate size distribution at large times. The results show that in the long-time limit, (i) if ∫t0g1(t') dt'/∫t0g2(t') dt' >= 1 or exp{∫t0[g2(t') - g1(t')] dt'}/∫t0f(t') dt' → 0, the aggregate size distribution ak(t) can obey a generalized scaling form; (ii) if ∫t0g1(t') dt'/∫t0g2(t') dt' → 0 and exp ∫t0[g2(t') - g1(t') dt'/∫t0f(t') dt' → ∞, ak(t) can take a scale-free form and decay exponentially in size k; (iii) ak(t) will satisfy a modified scaling law in the remaining cases. Moreover, the total mass of aggregates depends strongly on the net birth rate g1(t) - g2(t) and evolves exponentially as exp{∫t0[g1(t') - g2(t')] dt'}, which is in qualitative agreement with the evolution of the total population of a country in real world.

Effect of Inhibition of Deoxyribonucleic Acid and Protein Synthesis on the Direction of Cell Wall Growth in Streptococcus faecalis

PubMed Central

Higgins, M. L.; Daneo-Moore, L.; Boothby, D.; Shockman, G. D.

1974-01-01

Selective inhibition of protein synthesis in Streptococcus faecalis (ATCC 9790) was accompanied by a rapid and severe inhibition of cell division and a reduction of enlargement of cellular surface area. Continued synthesis of cell wall polymers resulted in rapid thickening of the wall to an extent not seen in exponential-phase populations. Thus, the normal direction of wall growth was changed from a preferential feeding out of new wall surface to that of thickening existing cell surfaces. However, the overall manner in which the wall thickened, from nascent septa toward polar regions, was the same in both exponential-phase and inhibited populations. In contrast, selective inhibition of deoxyribonucleic acid (DNA) synthesis using mitomycin C was accompanied by an increase in cellular surface area and by division of about 80% of the cells in random populations. Little or no wall thickening was observed until the synthesis of macromolecules other than DNA was impaired and further cell division ceased. Concomitant inhibition of both DNA and protein synthesis inhibited cell division but permitted an increase in average cell volume. In such doubly inhibited cells, walls thickened less than in cells inhibited for protein synthesis only. On the basis of the results obtained, a model for cell surface enlargement and cell division is presented. The model proposes that: (i) each wall enlargement site is influenced by an individual chromosome replication cycle; (ii) during chromosome replication peripheral surface enlargement would be favored over thickening (or septation); (iii) a signal associated with chromosome termination would favor thickening (and septation) at the expense of surface enlargement; and (iv) a factor or signal related to protein synthesis would be required for one or more of the near terminal stages of cell division or cell separation, or both. Images PMID:4133352

Standardized Percentile Curves of Body Mass Index of Northeast Iranian Children Aged 25 to 60 Months

PubMed Central

Emdadi, Maryam; Safarian, Mohammad; Doosti, Hassan

2011-01-01

Objective Growth charts are widely used to assess children's growth status and can provide a trajectory of growth during early important months of life. Racial differences necessitate using local growth charts. This study aimed to provide standardized growth curves of body mass index (BMI) for children living in northeast Iran. Methods A total of 23730 apparently healthy boys and girls aged 25 to 60 months recruited for 20 days from those attending community clinics for routine health checks. Anthropometric measurements were done by trained health staff using WHO methodology. The LMSP method with maximum penalized likelihood, the Generalized Additive Models, the Box-Cox power exponential distribution distribution, Akaike Information Criteria and Generalized Akaike Criteria with penalty equal to 3 [GAIC(3)], and Worm plot and Q-tests as goodness of fit tests were used to construct the centile reference charts. Findings The BMI centile curves for boys and girls aged 25 to 60 months were drawn utilizing a population of children living in northeast Iran. Conclusion The results of the current study demonstrate the possibility of preparation of local growth charts and their importance in evaluating children's growth. Also their differences, relative to those prepared by global references, reflect the necessity of preparing local charts in future studies using longitudinal data. PMID:23056770

Effects of exogenous inosine monophosphate on growth performance, flavor compounds, enzyme activity, and gene expression of muscle tissues in chicken.

PubMed

Yan, Junshu; Liu, Peifeng; Xu, Liangmei; Huan, Hailin; Zhou, Weiren; Xu, Xiaoming; Shi, Zhendan

2018-04-01

The goal of this experiment was to examine effects of diets supplemented with exogenous inosine monophosphate (IMP) on the growth performance, flavor compounds, enzyme activity and gene expression of chicken. A total of 1,500 healthy, 1-day-old male 3-yellow chickens were used for a 52-d experimental period. Individuals were randomly divided into 5 groups (group I, II, III, IV, V) with 6 replicates per group, and fed a basal diet supplemented with 0.0, 0.05, 0.1, 0.2, and 0.3% IMP, respectively. There was no significant response to the increasing dietary IMP level in average daily feed intake (ADFI), average daily gain (ADG), and feed:gain ratio (F/G) (P ≥ 0.05). IMP content of the breast and thigh muscle showed an exponential and linear response to the increasing dietary IMP level (P < 0.05), the highest IMP content was obtained when the diet with 0.3% and 0.2% exogenous IMP was fed. There were significant effects of IMP level in diet on free amino acids (FAA) (exponential, linear and quadratic effect, P < 0.05) and delicious amino acids (DAA) (quadratic effect, P < 0.01) content in breast muscle. FAA and DAA content in thigh muscle showed an exponential and linear response (P < 0.05), and quadratic response (P < 0.01) to the increasing dietary IMP level, the highest FAA and DAA content was obtained when the diet with 0.2% exogenous IMP was fed. Dietary IMP supplementation had a quadratic effect on 5΄-NT and the alkaline phosphatase (ALP) enzyme activity in the breast muscle (P < 0.05), and the adenosine triphosphate (ATP) enzyme activity in the thigh muscles increased exponentially and linearly with increasing IMP level in diet (exponential effect, P = 0.061; linear effect, P = 0.059). Cyclohydrolase (ATIC) gene expression in thigh muscle had a quadratic response to the increasing dietary IMP level (P < 0.05), 0.2% exogenous IMP group had the highest (AMPD1) gene expression of the breast muscle and ATIC gene expression of the thigh muscle. These results indicate that dietary IMP did not affect the growth performance of chicken, the diet with 0.2 to 0.3% exogenous IMP is optimal to improve the meat flavor quality in chicken.

Identification of Metabolic Pathways Expressed by Pichia anomala Kh6 in the Presence of the Pathogen Botrytis cinerea on Apple: New Possible Targets for Biocontrol Improvement

PubMed Central

Kwasiborski, Anthony; Bajji, Mohammed; Renaut, Jenny; Delaplace, Pierre; Jijakli, M. Haissam

2014-01-01

Yeast Pichia anomala strain Kh6 Kurtzman (Saccharomycetales: Endomycetaceae) exhibits biological control properties that provide an alternative to the chemical fungicides currently used by fruit or vegetable producers against main post-harvest pathogens, such as Botrytis cinerea (Helotiales: Sclerotiniaceae). Using an in situ model that takes into account interactions between organisms and a proteomic approach, we aimed to identify P. anomala metabolic pathways influenced by the presence of B. cinerea. A total of 105 and 60 P. anomala proteins were differentially represented in the exponential and stationary growth phases, respectively. In the exponential phase and in the presence of B. cinerea, the pentose phosphate pathway seems to be enhanced and would provide P. anomala with the needed nucleic acids and energy for the wound colonisation. In the stationary phase, P. anomala would use alcoholic fermentation both in the absence and presence of the pathogen. These results would suggest that the competitive colonisation of apple wounds could be implicated in the mode of action of P. anomala against B. cinerea. PMID:24614090

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

NASA Astrophysics Data System (ADS)

Wettlaufer, John; Toppaladoddi, Srikanth

We study the seasonal changes in the thickness distribution of Arctic sea ice, g (h) , under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g (h) , in which the thermodynamic growth growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to an observationally consistent thermodynamic model. We find that due to the combined effects of thermodynamics and mechanics, g (h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2. Because g (h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, ΔF0 , increases. The mean ice thickness decays exponentially with ΔF0 , but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone. NASA Grant NNH13ZDA001N-CRYO and Swedish Research Council Grant No. 638-2013-9243.

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

Scaling relationships of channel networks at large scales: Examples from two large-magnitude watersheds in Brittany, France

NASA Astrophysics Data System (ADS)

Crave, A.; Davy, P.

1997-01-01

We present a statistical analysis on two watersheds in French Brittany whose drainage areas are about 10,000 and 2000 km2. The channel system was analysed from the digitised blue lines of the 1:100,000 map and from a 250-m DEM. Link lengths follow an exponential distribution, consistent with the Markovian model of channel branching proposed by Smart (1968). The departure from the exponential distribution for small lengths, that has been extensively discussed before, results from a statistical effect due to the finite number of channels and junctions. The Strahler topology applied on channels defines a self-similar organisation whose similarity dimension is about 1.7, that is clearly smaller than the value of 2 expected for a random organisation. The similarity dimension is consistent with an independent measurement of the Horton ratios of stream numbers and lengths. The variables defined by an upstream integral (drainage area, mainstream length, upstream length) follow power-law distributions limited at large scales by a finite size effect, due to the finite area of the watersheds. A special emphasis is given to the exponent of the drainage area, aA, that has been previously discussed in the context of different aggregation models relevant to channel network growth. We show that aA is consistent with 4/3, a value that was obtained and analytically demonstrated from directed random walk aggregating models, inspired by the model of Scheidegger (1967). The drainage density and mainstream length present no simple scaling with area, except at large areas where they tend to trivial values: constant density and square root of drainage area, respectively. These asymptotic limits necessarily imply that the space dimension of channel networks is 2, equal to the embedding space. The limits are reached for drainage areas larger than 100 km2. For smaller areas, the asymptotic limit represents either a lower bound (drainage density) or an upper bound (mainstream length) of the distributions. Because the fluctuations of the drainage density slowly converge to a finite limit, the system could be adequately described as a fat fractal, where the average drainage density is the sum of a constant plus a fluctuation decreasing as a power law with integrating area. A fat fractal hypothesis could explain why the similarity dimension is not equal to the fractal capacity dimension, as it is for thin fractals. The physical consequences are not yet really understood, but we draw an analogy with a directed aggregating system where the growth process involves both stochastic and deterministic growth. These models are known to be fat fractals, and the deterministic growth, which constitutes a fundamental ingredient of these models, could be attributed in river systems to the role of terrestrial gravity.

Automatic selection of arterial input function using tri-exponential models

NASA Astrophysics Data System (ADS)

Yao, Jianhua; Chen, Jeremy; Castro, Marcelo; Thomasson, David

2009-02-01

Dynamic Contrast Enhanced MRI (DCE-MRI) is one method for drug and tumor assessment. Selecting a consistent arterial input function (AIF) is necessary to calculate tissue and tumor pharmacokinetic parameters in DCE-MRI. This paper presents an automatic and robust method to select the AIF. The first stage is artery detection and segmentation, where knowledge about artery structure and dynamic signal intensity temporal properties of DCE-MRI is employed. The second stage is AIF model fitting and selection. A tri-exponential model is fitted for every candidate AIF using the Levenberg-Marquardt method, and the best fitted AIF is selected. Our method has been applied in DCE-MRIs of four different body parts: breast, brain, liver and prostate. The success rates in artery segmentation for 19 cases are 89.6%+/-15.9%. The pharmacokinetic parameters computed from the automatically selected AIFs are highly correlated with those from manually determined AIFs (R2=0.946, P(T<=t)=0.09). Our imaging-based tri-exponential AIF model demonstrated significant improvement over a previously proposed bi-exponential model.

Comparison of kinetic model for biogas production from corn cob

NASA Astrophysics Data System (ADS)

Shitophyta, L. M.; Maryudi

2018-04-01

Energy demand increases every day, while the energy source especially fossil energy depletes increasingly. One of the solutions to overcome the energy depletion is to provide renewable energies such as biogas. Biogas can be generated by corn cob and food waste. In this study, biogas production was carried out by solid-state anaerobic digestion. The steps of biogas production were the preparation of feedstock, the solid-state anaerobic digestion, and the measurement of biogas volume. This study was conducted on TS content of 20%, 22%, and 24%. The aim of this research was to compare kinetic models of biogas production from corn cob and food waste as a co-digestion using the linear, exponential equation, and first-kinetic models. The result showed that the exponential equation had a better correlation than the linear equation on the ascending graph of biogas production. On the contrary, the linear equation had a better correlation than the exponential equation on the descending graph of biogas production. The correlation values on the first-kinetic model had the smallest value compared to the linear and exponential models.

Modeling of single event transients with dual double-exponential current sources: Implications for logic cell characterization

DOE PAGES

Black, Dolores Archuleta; Robinson, William H.; Wilcox, Ian Zachary; ...

2015-08-07

Single event effects (SEE) are a reliability concern for modern microelectronics. Bit corruptions can be caused by single event upsets (SEUs) in the storage cells or by sampling single event transients (SETs) from a logic path. Likewise, an accurate prediction of soft error susceptibility from SETs requires good models to convert collected charge into compact descriptions of the current injection process. This paper describes a simple, yet effective, method to model the current waveform resulting from a charge collection event for SET circuit simulations. The model uses two double-exponential current sources in parallel, and the results illustrate why a conventionalmore » model based on one double-exponential source can be incomplete. Furthermore, a small set of logic cells with varying input conditions, drive strength, and output loading are simulated to extract the parameters for the dual double-exponential current sources. As a result, the parameters are based upon both the node capacitance and the restoring current (i.e., drive strength) of the logic cell.« less

A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential

NASA Astrophysics Data System (ADS)

Ma, Xiao; Zheng, Wei-Fan; Jiang, Bao-Shan; Zhang, Ji-Ye

2016-10-01

With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver’s random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11572264, 11172247, 11402214, and 61373009).

[Application of exponential smoothing method in prediction and warning of epidemic mumps].

PubMed

Shi, Yun-ping; Ma, Jia-qi

2010-06-01

To analyze the daily data of epidemic Mumps in a province from 2004 to 2008 and set up exponential smoothing model for the prediction. To predict and warn the epidemic mumps in 2008 through calculating 7-day moving summation and removing the effect of weekends to the data of daily reported mumps cases during 2005-2008 and exponential summation to the data from 2005 to 2007. The performance of Holt-Winters exponential smoothing is good. The result of warning sensitivity was 76.92%, specificity was 83.33%, and timely rate was 80%. It is practicable to use exponential smoothing method to warn against epidemic Mumps.

An IDEA for Short Term Outbreak Projection: Nearcasting Using the Basic Reproduction Number

PubMed Central

Fisman, David N.; Hauck, Tanya S.; Tuite, Ashleigh R.; Greer, Amy L.

2013-01-01

Background Communicable disease outbreaks of novel or existing pathogens threaten human health around the globe. It would be desirable to rapidly characterize such outbreaks and develop accurate projections of their duration and cumulative size even when limited preliminary data are available. Here we develop a mathematical model to aid public health authorities in tracking the expansion and contraction of outbreaks with explicit representation of factors (other than population immunity) that may slow epidemic growth. Methodology The Incidence Decay and Exponential Adjustment (IDEA) model is a parsimonious function that uses the basic reproduction number R0, along with a discounting factor to project the growth of outbreaks using only basic epidemiological information (e.g., daily incidence counts). Principal Findings Compared to simulated data, IDEA provides highly accurate estimates of total size and duration for a given outbreak when R0 is low or moderate, and also identifies turning points or new waves. When tested with an outbreak of pandemic influenza A (H1N1), the model generates estimated incidence at the i+1th serial interval using data from the ith serial interval within an average of 20% of actual incidence. Conclusions and Significance This model for communicable disease outbreaks provides rapid assessments of outbreak growth and public health interventions. Further evaluation in the context of real-world outbreaks will establish the utility of IDEA as a tool for front-line epidemiologists. PMID:24391797

An IDEA for short term outbreak projection: nearcasting using the basic reproduction number.

PubMed

Fisman, David N; Hauck, Tanya S; Tuite, Ashleigh R; Greer, Amy L

2013-01-01

Communicable disease outbreaks of novel or existing pathogens threaten human health around the globe. It would be desirable to rapidly characterize such outbreaks and develop accurate projections of their duration and cumulative size even when limited preliminary data are available. Here we develop a mathematical model to aid public health authorities in tracking the expansion and contraction of outbreaks with explicit representation of factors (other than population immunity) that may slow epidemic growth. The Incidence Decay and Exponential Adjustment (IDEA) model is a parsimonious function that uses the basic reproduction number R0, along with a discounting factor to project the growth of outbreaks using only basic epidemiological information (e.g., daily incidence counts). Compared to simulated data, IDEA provides highly accurate estimates of total size and duration for a given outbreak when R0 is low or moderate, and also identifies turning points or new waves. When tested with an outbreak of pandemic influenza A (H1N1), the model generates estimated incidence at the i+1(th) serial interval using data from the i(th) serial interval within an average of 20% of actual incidence. This model for communicable disease outbreaks provides rapid assessments of outbreak growth and public health interventions. Further evaluation in the context of real-world outbreaks will establish the utility of IDEA as a tool for front-line epidemiologists.

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement

PubMed Central

Gustman, Alan L.; Steinmeier, Thomas L.

2012-01-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used. PMID:22711946

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.

PubMed

Gustman, Alan L; Steinmeier, Thomas L

2012-06-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.

The Arrhenius equation revisited.

PubMed

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

2012-01-01

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.

Formation and characterization of metallic iron grains in coal-based reduction of oolitic iron ore

NASA Astrophysics Data System (ADS)

Sun, Yong-sheng; Han, Yue-xin; Li, Yan-feng; Li, Yan-jun

2017-02-01

To reveal the formation and characteristics of metallic iron grains in coal-based reduction, oolitic iron ore was isothermally reduced in various reduction times at various reduction temperatures. The microstructure and size of the metallic iron phase were investigated by scanning electron microscopy, energy-dispersive X-ray spectroscopy, and a Bgrimm process mineralogy analyzer. In the results, the reduced Fe separates from the ore and forms metallic iron protuberances, and then the subsequent reduced Fe diffuses to the protuberances and grows into metallic iron grains. Most of the metallic iron grains exist in the quasi-spherical shape and inlaid in the slag matrix. The cumulative frequency of metallic iron grain size is markedly influenced by both reduction time and temperature. With increasing reduction temperature and time, the grain size of metallic iron obviously increases. According to the classical grain growth equation, the growth kinetic parameters, i.e., time exponent, growth activation energy, and pre-exponential constant, are estimated to be 1.3759 ± 0.0374, 103.18 kJ·mol-1, and 922.05, respectively. Using these calculated parameters, a growth model is established to describe the growth behavior of metallic iron grains.

On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein-Gauss-Bonnet model with a Λ-term

NASA Astrophysics Data System (ADS)

Ernazarov, K. K.

2017-12-01

We consider a (m + 2)-dimensional Einstein-Gauss-Bonnet (EGB) model with the cosmological Λ-term. We restrict the metrics to be diagonal ones and find for certain Λ = Λ(m) class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions m > 2 and 1. Any solution from this class describes an accelerated expansion of m-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Composition and occurrence of lipid droplets in the cyanobacterium Nostoc punctiforme.

PubMed

Peramuna, Anantha; Summers, Michael L

2014-12-01

Inclusions of neutral lipids termed lipid droplets (LDs) located throughout the cell were identified in the cyanobacterium Nostoc punctiforme by staining with lipophylic fluorescent dyes. LDs increased in number upon entry into stationary phase and addition of exogenous fructose indicating a role for carbon storage, whereas high-light stress did not increase LD numbers. LD accumulation increased when nitrate was used as the nitrogen source during exponential growth as compared to added ammonia or nitrogen-fixing conditions. Analysis of isolated LDs revealed enrichment of triacylglycerol (TAG), α-tocopherol, and C17 alkanes. LD TAG from exponential phase growth contained mainly saturated C16 and C18 fatty acids, whereas stationary phase LD TAG had additional unsaturated fatty acids characteristic of whole cells. This is the first characterization of cyanobacterial LD composition and conditions leading to their production. Based upon their abnormally large size and atypical location, these structures represent a novel sub-organelle in cyanobacteria.

Light-induced biophotonic emission from plant tissues.

PubMed

Bajpai, R P; Bajpai, P K

1992-07-01

The emission of biophotons in the visible range, following a delay time of 2-200 seconds after exposure to light, has been measured in germinating seeds, roots, flowers, leaves, and cells. It was found that the biophotonic signals are reproducible and light-induced. The observed signals from germinating seeds of Phaseolus aures and decaying leaves of Eucalyptus are presented to show that the signals have characteristic kinetics and intensity. The kinetics of the signal was found to be independent of the stage of growth or decay, though its intensity varied with biological factors. The kinetics in the first minute is characterized by a single exponential decay term while that in the region t less than or equal to 200 s is characterized by two exponentials. The variation in the intensity of the signal with mass, state of hydration, and growth, and the effect of inhibitors in various systems (e.g. leaves, lichen, Chlorella) are reported.

Exponential growth and Gaussian—like fluctuations of solutions of stochastic differential equations with maximum functionals

NASA Astrophysics Data System (ADS)

Appleby, J. A. D.; Wu, H.

2008-11-01

In this paper we consider functional differential equations subjected to either instantaneous state-dependent noise, or to a white noise perturbation. The drift of the equations depend linearly on the current value and on the maximum of the solution. The functional term always provides positive feedback, while the instantaneous term can be mean-reverting or can exhibit positive feedback. We show in the white noise case that if the instantaneous term is mean reverting and dominates the history term, then solutions are recurrent, and upper bounds on the a.s. growth rate of the partial maxima of the solution can be found. When the instantaneous term is weaker, or is of positive feedback type, we determine necessary and sufficient conditions on the diffusion coefficient which ensure the exact exponential growth of solutions. An application of these results to an inefficient financial market populated by reference traders and speculators is given, in which the difference between the current instantaneous returns and maximum of the returns over the last few time units is used to determine trading strategies.

Dichromatic and monochromatic laser radiation effects on survival and morphology of Pantoea agglomerans

NASA Astrophysics Data System (ADS)

Thomé, A. M. C.; Souza, B. P.; Mendes, J. P. M.; Soares, L. C.; Trajano, E. T. L.; Fonseca, A. S.

2017-05-01

Despite the beneficial effects of low-level lasers on wound healing, their application for treatment of infected injuries is controversial because low-level lasers could stimulate bacterial growth exacerbating the infectious process. Thus, the aim of this work was to evaluate in vitro effects of low-level lasers on survival, morphology and cell aggregation of Pantoea agglomerans. P. agglomerans samples were isolated from human pressure injuries and cultures were exposed to low-level monochromatic and simultaneous dichromatic laser radiation to study the survival, cell aggregation, filamentation and morphology of bacterial cells in exponential and stationary growth phases. Fluence, wavelength and emission mode were those used in therapeutic protocols for wound healing. Data show no changes in morphology and cell aggregation, but dichromatic laser radiation decreased bacterial survival in exponential growth phase and monochromatic red and infrared lasers increased bacterial survival at the same fluence. Simultaneous dichromatic laser radiation induces biological effects that differ from those induced by monochromatic laser radiation and simultaneous dichromatic laser could be the option for treatment of infected pressure injuries by Pantoea agglomerans.

Exponential quantum spreading in a class of kicked rotor systems near high-order resonances

NASA Astrophysics Data System (ADS)

Wang, Hailong; Wang, Jiao; Guarneri, Italo; Casati, Giulio; Gong, Jiangbin

2013-11-01

Long-lasting exponential quantum spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.234104 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting exponential quantum spreading under much more general conditions. In particular, we adopt the so-called “spinor” representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat band (or an effectively flat band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies toward a better understanding of high-order resonance behavior in δ-kicked quantum systems.

The significance of intergranular diffusion to the mechanisms and kinetics of porphyroblast crystallization

NASA Astrophysics Data System (ADS)

Carlson, William D.

1989-09-01

The spatial disposition, compositional zoning profiles, and size distributions of garnet crystals in 11 specimens of pelitic schist from the Picuris Range of New Mexico (USA) demonstrate that the kinetics of intergranular diffusion controlled the nucleation and growth mechanisms of porphyroblasts in these rocks. An ordered disposition of garnet centers and a significant correlation between crystal radius and near-neighbor distances manifest suppressed nucleation of new crystals in diffusionally depleted zones surrounding pre-existing crystals. Compositional zoning profiles require diffusionally controlled growth, the rate of which increases exponentially as temperature increases with time; an acceleration factor for growth rate can be estimated from a comparison of compositional profiles for crystals of different sizes in each specimen. Crystal size distributions are interpreted as the result of nucleation rates that accelerate exponentially with increasing temperature early in the crystallization process, but decline in the later stages because of suppression effects in the vicinity of earlier-formed nuclei. Simulations of porphyroblast crystallization, based upon thermally accelerated diffusionally influenced nucleation kinetics and diffusionally controlled growth kinetics, quantitatively replicate textural relations in the rocks. The simulations employ only two variable parameters, which are evaluated by fitting of crystal size distributions. Both have physical significance. The first is an acceleration factor for nucleation, with a magnitude reflecting the prograde increase during the nucleation interval of the chemical affinity for the reaction in undepleted regions of the rock. The second is a measure of the relative sizes of the porphyroblast and the diffusionally depleted zone surrounding it. Crystal size distributions for the Picuris Range garnets correspond very closely to those in the literature from a variety of other localities for garnet and other minerals. The same kinetic model accounts quantitatively for crystal size distributions of porphyroblastic garnet, phlogopite, sphene, and pyroxene in rocks from both regional and contact metamorphic occurrences. These commonalities indicate that intergranular diffusion may be the dominant kinetic factor in the crystallization of porphyroblasts in a wide variety of metamorphic environments.

Quantitative Interaction Effects of Carbon Dioxide, Sodium Chloride, and Sodium Nitrite on Neurotoxin Gene Expression in Nonproteolytic Clostridium botulinum Type B

PubMed Central

Lövenklev, Maria; Artin, Ingrid; Hagberg, Oskar; Borch, Elisabeth; Holst, Elisabet; Rådström, Peter

2004-01-01

The effects of carbon dioxide, sodium chloride, and sodium nitrite on type B botulinum neurotoxin (BoNT/B) gene (cntB) expression in nonproteolytic Clostridium botulinum were investigated in a tryptone-peptone-yeast extract (TPY) medium. Various concentrations of these selected food preservatives were studied by using a complete factorial design in order to quantitatively study interaction effects, as well as main effects, on the following responses: lag phase duration (LPD), growth rate, relative cntB expression, and extracellular BoNT/B production. Multiple linear regression was used to set up six statistical models to quantify and predict these responses. All combinations of NaCl and NaNO2 in the growth medium resulted in a prolonged lag phase duration and in a reduction in the specific growth rate. In contrast, the relative BoNT/B gene expression was unchanged, as determined by the cntB-specific quantitative reverse transcription-PCR method. This was confirmed when we measured the extracellular BoNT/B concentration by an enzyme-linked immunosorbent assay. CO2 was found to have a major effect on gene expression when the cntB mRNA levels were monitored in the mid-exponential, late exponential, and late stationary growth phases. The expression of cntB relative to the expression of the 16S rRNA gene was stimulated by an elevated CO2 concentration; the cntB mRNA level was fivefold greater in a 70% CO2 atmosphere than in a 10% CO2 atmosphere. These findings were also confirmed when we analyzed the extracellular BoNT/B concentration; we found that the concentrations were 27 ng · ml−1 · unit of optical density−1 in the 10% CO2 atmosphere and 126 ng · ml−1 · unit of optical density−1 in the 70% CO2 atmosphere. PMID:15128553

Structure of the nucleoid in cells of Streptococcus faecalis.

PubMed Central

Daneo-Moore, L; Dicker, D; Higgins, M L

1980-01-01

The structure of the nucleoid of Streptococcus faecalis (ATCC 9790) was examined and compared in the unfixed and fixed states by immersive refractometry and electron microscopy. It appears from these studies that the nucleoid structure is much more centralized in unfixed chloramphenicol-treated (stationary-phase) cells than it is in cells in the exponential phase of growth. The more dispersed configuration of the exponential-phase nucleoid could be preserved by fixation in glutaraldehyde, but not in Formalin or in osmium tetroxide. One important factor in explaining these differences in preservation is that glutaraldehyde (but not Formalin or osmium tetroxide) can rapidly cross-link the amino groups of macromolecules in cells. It was also observed that osmium tetroxide resulted in a preferential breakdown of nascent ribonucleic acid. These results are interpreted as indicating that glutaraldehyde is able to stabilize the exponential-phase nucleoid before it assumes the more central appearance seen in osmium tetroxide- and Formalin-fixed cells. These results are discussed in terms of the proposed organization of the exponential-phase nucleoid in unfixed cells. Images PMID:6767695

An empirical model for transient crater growth in granular targets based on direct observations

NASA Astrophysics Data System (ADS)

Yamamoto, Satoru; Barnouin-Jha, Olivier S.; Toriumi, Takashi; Sugita, Seiji; Matsui, Takafumi

2009-09-01

The present paper describes observations of crater growth up to the time of transient crater formation and presents a new empirical model for transient crater growth as a function of time. Polycarbonate projectiles were impacted vertically into soda-lime glass sphere targets using a single-stage light-gas gun. Using a new technique with a laser sheet illuminating the target [Barnouin-Jha, O.S., Yamamoto, S., Toriumi, T., Sugita, S., Matsui, T., 2007. Non-intrusive measurements of the crater growth. Icarus, 188, 506-521], we measured the temporal change in diameter of crater cavities (diameter growth). The rate of increase in diameter at early times follows a power law relation, but the data at later times (before the end of transient crater formation) deviates from the power law relation. In addition, the power law exponent at early times and the degree of deviation from a power law at later times depend on the target. In order to interpret these features, we proposed to modify Maxwell's Z-model under the assumption that the strength of the excavation flow field decreases exponentially with time. We also derived a diameter growth model as: d(t)∝[1-exp(-βt)]γ, where d(t) is the apparent diameter of the crater cavity at time t after impact, and β and γ are constants. We demonstrated that the diameter growth model could represent well the experimental data for various targets with different target material properties, such as porosity or angle of repose. We also investigated the diameter growth for a dry sand target, which has been used to formulate previous scaling relations. The obtained results showed that the dry sand target has larger degree of deviation from a power law, indicating that the target material properties of the dry sand target have a significant effect on diameter growth, especially at later times. This may suggest that the previously reported scaling relations should be reexamined in order to account for the late-stage behavior with the effect of target material properties.

A decades-long fast-rise-exponential-decay flare in low-luminosity AGN NGC 7213

NASA Astrophysics Data System (ADS)

Yan, Zhen; Xie, Fu-Guo

2018-03-01

We analysed the four-decades-long X-ray light curve of the low-luminosity active galactic nucleus (LLAGN) NGC 7213 and discovered a fast-rise-exponential-decay (FRED) pattern, i.e. the X-ray luminosity increased by a factor of ≈4 within 200 d, and then decreased exponentially with an e-folding time ≈8116 d (≈22.2 yr). For the theoretical understanding of the observations, we examined three variability models proposed in the literature: the thermal-viscous disc instability model, the radiation pressure instability model, and the TDE model. We find that a delayed tidal disruption of a main-sequence star is most favourable; either the thermal-viscous disc instability model or radiation pressure instability model fails to explain some key properties observed, thus we argue them unlikely.

Loss of EGF binding and cation transport response during differentiation of mouse neuroblastoma cells.

PubMed

Mummery, C L; van der Saag, P T; de Laat, S W

1983-01-01

Mouse neuroblastoma cells (clone N1E-115) differentiate in culture upon withdrawal of serum growth factors and acquire the characteristics of neurons. We have shown tht exponentially growing N1E-115 cells possess functional epidermal growth factor (EGF) receptors but that the capacity for binding EGF and for stimulation of DNA synthesis is lost as the cells differentiate. Furthermore, in exponentially growing cells, EGF induces a rapid increase in amiloride-sensitive Na+ influx, followed by stimulation of the (Na+-K+)ATPase, indicating that activation of the Na+/H+ exchange mechanism in N1E-115 cells [1] may be induced by EGF. The ionic response is also lost during differentiation, but we have shown that the stimulation of both Na+ and K+ influx is directly proportional to the number of occupied receptors in all cells whether exponentially growing or differentiating, thus only indirectly dependent on the external EGF concentration. The linearity of the relationships indicates that there is no rate-limiting step between EGF binding and the ionic response. Our data would suggest that as neuroblastoma cells differentiate and acquire neuronal properties, their ability to respond to mitogens, both biologically and in the activation of cation transport processes, progressively decreases owing to the loss of the appropriate receptors.

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model.

PubMed

Bennett, Kevin M; Schmainda, Kathleen M; Bennett, Raoqiong Tong; Rowe, Daniel B; Lu, Hanbing; Hyde, James S

2003-10-01

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Copyright 2003 Wiley-Liss, Inc.

Predicting Subnational Ebola Virus Disease Epidemic Dynamics from Sociodemographic Indicators

PubMed Central

Valeri, Linda; Patterson-Lomba, Oscar; Gurmu, Yared; Ablorh, Akweley; Bobb, Jennifer; Townes, F. William; Harling, Guy

2016-01-01

Background The recent Ebola virus disease (EVD) outbreak in West Africa has spread wider than any previous human EVD epidemic. While individual-level risk factors that contribute to the spread of EVD have been studied, the population-level attributes of subnational regions associated with outbreak severity have not yet been considered. Methods To investigate the area-level predictors of EVD dynamics, we integrated time series data on cumulative reported cases of EVD from the World Health Organization and covariate data from the Demographic and Health Surveys. We first estimated the early growth rates of epidemics in each second-level administrative district (ADM2) in Guinea, Sierra Leone and Liberia using exponential, logistic and polynomial growth models. We then evaluated how these growth rates, as well as epidemic size within ADM2s, were ecologically associated with several demographic and socio-economic characteristics of the ADM2, using bivariate correlations and multivariable regression models. Results The polynomial growth model appeared to best fit the ADM2 epidemic curves, displaying the lowest residual standard error. Each outcome was associated with various regional characteristics in bivariate models, however in stepwise multivariable models only mean education levels were consistently associated with a worse local epidemic. Discussion By combining two common methods—estimation of epidemic parameters using mathematical models, and estimation of associations using ecological regression models—we identified some factors predicting rapid and severe EVD epidemics in West African subnational regions. While care should be taken interpreting such results as anything more than correlational, we suggest that our approach of using data sources that were publicly available in advance of the epidemic or in real-time provides an analytic framework that may assist countries in understanding the dynamics of future outbreaks as they occur. PMID:27732614

The generalized truncated exponential distribution as a model for earthquake magnitudes

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-04-01

The random distribution of small, medium and large earthquake magnitudes follows an exponential distribution (ED) according to the Gutenberg-Richter relation. But a magnitude distribution is truncated in the range of very large magnitudes because the earthquake energy is finite and the upper tail of the exponential distribution does not fit well observations. Hence the truncated exponential distribution (TED) is frequently applied for the modelling of the magnitude distributions in the seismic hazard and risk analysis. The TED has a weak point: when two TEDs with equal parameters, except the upper bound magnitude, are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters, except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. It also applies to alternative distribution models. The presented generalized truncated exponential distribution (GTED) overcomes this weakness. The ED and the TED are special cases of the GTED. Different issues of the statistical inference are also discussed and an example of empirical data is presented in the current contribution.

Developing spatially explicit footprints of plausible land-use scenarios in the Santa Cruz Watershed, Arizona and Sonora

USGS Publications Warehouse

Norman, Laura M.; Feller, Mark; Villarreal, Miguel L.

2012-01-01

The SLEUTH urban growth model is applied to a binational dryland watershed to envision and evaluate plausible future scenarios of land use change into the year 2050. Our objective was to create a suite of geospatial footprints portraying potential land use change that can be used to aid binational decision-makers in assessing the impacts relative to sustainability of natural resources and potential socio-ecological consequences of proposed land-use management. Three alternatives are designed to simulate different conditions: (i) a Current Trends Scenario of unmanaged exponential growth, (ii) a Conservation Scenario with managed growth to protect the environment, and (iii) a Megalopolis Scenario in which growth is accentuated around a defined international trade corridor. The model was calibrated with historical data extracted from a time series of satellite images. Model materials, methodology, and results are presented. Our Current Trends Scenario predicts the footprint of urban growth to approximately triple from 2009 to 2050, which is corroborated by local population estimates. The Conservation Scenario results in protecting 46% more of the Evergreen class (more than 150,000 acres) than the Current Trends Scenario and approximately 95,000 acres of Barren Land, Crops, Deciduous Forest (Mesquite Bosque), Grassland/Herbaceous, Urban/Recreational Grasses, and Wetlands classes combined. The Megalopolis Scenario results also depict the preservation of some of these land-use classes compared to the Current Trends Scenario, most notably in the environmentally important headwaters region. Connectivity and areal extent of land cover types that provide wildlife habitat were preserved under the alternative scenarios when compared to Current Trends.

Efficacy of SCH27899 in an Animal Model of Legionnaires' Disease Using Immunocompromised A/J Mice

PubMed Central

Brieland, Joan K.; Loebenberg, David; Menzel, Fred; Hare, Roberta S.

2000-01-01

The efficacy of SCH27899, a new everninomicin antibiotic, against replicative Legionella pneumophila lung infections in an immunocompromised host was evaluated using a murine model of Legionnaires' disease. A/J mice were immunocompromised with cortisone acetate and inoculated intratracheally with L. pneumophila serogroup 1 (105 CFU per mouse). At 24 h postinoculation, mice were administered either SCH27899 (6 to 60 mg/kg [MPK] intravenously) or a placebo once daily for 5 days, and mortality and intrapulmonary growth of L. pneumophila were assessed. In the absence of SCH27899, there was 100% mortality in L. pneumophila-infected mice, with exponential intrapulmonary growth of the bacteria. In contrast, administration of SCH27899 at a dose of ≥30 MPK resulted in ≥90% survival of infected mice, which was associated with inhibition of intrapulmonary growth of L. pneumophila. In subsequent studies, the efficacy of SCH27899 was compared to ofloxacin (OFX) and azithromycin (AZI). Administration of SCH27899, OFX, or AZI at a dose of ≥30 MPK once daily for 5 days resulted in ≥85% survival of infected mice and inhibition of intrapulmonary growth of the bacteria. However, L. pneumophila CFU were recovered in lung homogenates following cessation of therapy with all three antibiotics. These studies demonstrate that SCH27899 effectively prevents fatal replicative L. pneumophila lung infection in immunocompromised A/J mice by inhibition of intrapulmonary growth of the bacteria. However, in this murine model of pulmonary legionellosis, SCH27899, like OFX and AZI, was bacteriostatic. PMID:10770771

Interrogating the Escherichia coli cell cycle by cell dimension perturbations

PubMed Central

Zheng, Hai; Ho, Po-Yi; Jiang, Meiling; Tang, Bin; Liu, Weirong; Li, Dengjin; Yu, Xuefeng; Kleckner, Nancy E.; Amir, Ariel; Liu, Chenli

2016-01-01

Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter’s growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ. We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed “adder-per-origin” model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation. PMID:27956612

Interrogating the Escherichia coli cell cycle by cell dimension perturbations.

PubMed

Zheng, Hai; Ho, Po-Yi; Jiang, Meiling; Tang, Bin; Liu, Weirong; Li, Dengjin; Yu, Xuefeng; Kleckner, Nancy E; Amir, Ariel; Liu, Chenli

2016-12-27

Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter's growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed "adder-per-origin" model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation.

Exploring Explanations of Subglacial Bedform Sizes Using Statistical Models.

PubMed

Hillier, John K; Kougioumtzoglou, Ioannis A; Stokes, Chris R; Smith, Michael J; Clark, Chris D; Spagnolo, Matteo S

2016-01-01

Sediments beneath modern ice sheets exert a key control on their flow, but are largely inaccessible except through geophysics or boreholes. In contrast, palaeo-ice sheet beds are accessible, and typically characterised by numerous bedforms. However, the interaction between bedforms and ice flow is poorly constrained and it is not clear how bedform sizes might reflect ice flow conditions. To better understand this link we present a first exploration of a variety of statistical models to explain the size distribution of some common subglacial bedforms (i.e., drumlins, ribbed moraine, MSGL). By considering a range of models, constructed to reflect key aspects of the physical processes, it is possible to infer that the size distributions are most effectively explained when the dynamics of ice-water-sediment interaction associated with bedform growth is fundamentally random. A 'stochastic instability' (SI) model, which integrates random bedform growth and shrinking through time with exponential growth, is preferred and is consistent with other observations of palaeo-bedforms and geophysical surveys of active ice sheets. Furthermore, we give a proof-of-concept demonstration that our statistical approach can bridge the gap between geomorphological observations and physical models, directly linking measurable size-frequency parameters to properties of ice sheet flow (e.g., ice velocity). Moreover, statistically developing existing models as proposed allows quantitative predictions to be made about sizes, making the models testable; a first illustration of this is given for a hypothesised repeat geophysical survey of bedforms under active ice. Thus, we further demonstrate the potential of size-frequency distributions of subglacial bedforms to assist the elucidation of subglacial processes and better constrain ice sheet models.

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

CMB constraints on β-exponential inflationary models

NASA Astrophysics Data System (ADS)

Santos, M. A.; Benetti, M.; Alcaniz, J. S.; Brito, F. A.; Silva, R.

2018-03-01

We analyze a class of generalized inflationary models proposed in ref. [1], known as β-exponential inflation. We show that this kind of potential can arise in the context of brane cosmology, where the field describing the size of the extra-dimension is interpreted as the inflaton. We discuss the observational viability of this class of model in light of the latest Cosmic Microwave Background (CMB) data from the Planck Collaboration through a Bayesian analysis, and impose tight constraints on the model parameters. We find that the CMB data alone prefer weakly the minimal standard model (ΛCDM) over the β-exponential inflation. However, when current local measurements of the Hubble parameter, H0, are considered, the β-inflation model is moderately preferred over the ΛCDM cosmology, making the study of this class of inflationary models interesting in the context of the current H0 tension.

Firing patterns in the adaptive exponential integrate-and-fire model.

PubMed

Naud, Richard; Marcille, Nicolas; Clopath, Claudia; Gerstner, Wulfram

2008-11-01

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.