Deterministic Growth Research Articles

Demographic shifts related to mycoheterotrophy and their fitness impacts in two Cephalanthera species

Evolutionary losses of photosynthesis in terrestrial plants all originate in photosynthetic ancestors. The adaptive context under which this transition happens has remained elusive because of the rarity of plants in which both photosynthetic and non-photosynthetic forms exist as a polymorphism. Here, we report on demographic patterns in photosynthetic ("green") and nonphotosynthetic ("albino") individuals within populations of two such species, Cephalanthera damasonium and C. longifolia, which also acquire nutrition from their mycorrhizal hosts (partial mycoheterotrophy). We hypothesized that demographic shifts in albinos relative to greens would include compensatory patterns with respect to fitness, such that maladaptive changes to survival or reproduction would be adaptively countered by changes to other parameters, such as growth probabilities. We tracked individuals in two populations of C. damasonium for 3 yr, and in one population of C. longifolia for 14 yr. We then analyzed vital rates for both phenotypes using general linear mixed models (GLMMs) and multi-state capture mark-recapture models (CMR), and used these models to develop size-classified, function-based population projection matrices. We estimated fitness as the deterministic population growth rate (λ) for each phenotype, and explored the impact of shifts in demographic patterns to albinism via life table response experiments (LTREs). Mortality differed between greens and albinos, but not similarly across species. Albinos generally sprouted less than greens, and flowered more when small but less at other times. Albinos typically had a higher probability of fruiting, although their lower flower numbers yielded lower numbers of fruits overall. Fitness did not differ significantly among phenotypes. Thus, we did not find significant evidence that albinism is adaptive or maladaptive; however, if in fact it is the latter, then we did find evidence of incomplete compensation for declines in survival and reproduction from growth transitions, particularly to small flowering size classes in C. damasonium, and to large vegetative size classes in C. longifolia. These patterns indicate some support for the idea that albinism may lead to the speciation of mycoheterotrophic plants.

Kinetic narrowing of size distribution

We present a model that reveals an interesting possibility for narrowing the size distribution of nanostructures when the deterministic growth rate changes its sign from positive to negative at a certain stationary size. Such a behavior occurs in self-catalyzed one-dimensional III-V nanowires and more generally whenever a negative ``adsorption-desorption'' term in the growth rate is compensated by a positive ``diffusion flux.'' By asymptotically solving the Fokker-Planck equation, we derive an explicit representation for the size distribution that describes either Poissonian broadening or self-regulated narrowing depending on the parameters. We show how the fluctuation-induced spreading of the size distribution can be completely suppressed in systems with size self-stabilization. These results can be used for obtaining size-uniform ensembles of different nanostructures.

Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.

Plasma As a Tool for Growth of 1D and 2D Nanomaterials and Their Conversions

The growth of 1D and 2D nanostructures in low pressure oxygen plasma is presented with the special stress on metal-oxide nanowires and their deterministic growth mechanisms. Since the resulting nanostructures not always have required properties for applications their modifications are required. Therefore their conversions into different oxides or sulphites/nitrides are required with either molecules, atoms, electrons or photons. There has been tremendous interest and progress with plasma synthesis of 1D and 2D nanostructures like inorganic nanowires (NWs), nanotubes, nanowalls, nanosheets, etc. in recent years. The advantage of plasma growth is not only abundant quantity, but short time-scales of synthesis and many other advanced properties of materials, e.g. single-crystallinity of materials, superstructure of crystal lattices, pureness, etc. Moreover, such materials show improved performance to others nanomaterials synthesized by other methods when tested in devices. Growing different nanostructures, especially more complex ones like 1D or 2D depends significantly on plasma parameters of interacting plasmas and surface conditions during the growth. The selectivity criteria of plasmas is based mostly on fluxes of charged species and neutral atoms to the surface as well as potential at the surface. All these are further influenced by recombination of plasma species on the surfaces and surface temperatures. Results are seen in creation of nuclei and seeds which lead either to creation of thin layers and nanowalls or nanowire growth. Moreover, in some cases we get also more exotic structures like nanospikes, nanotubes, etc. All this will be demonstrated for the case of different metal oxides (Fe2O3, CuO, etc.) nanostructure growth, especially nanowires where we can create various structures without any deposition from the gas phase but only with reactive gaseous plasma. The metallic substrates are typically exposed to low pressure weakly ionized and highly dissociated oxygen RF plasma at different plasma conditions. The nanowires and nanostructures are grown on the top of thin oxide layer through neutral species and ion recombinations. [1] Results indicate that different densities of the ion current to the side and top area of NW modify the NW growth in height and width. The NW growth is enhanced by presence of ions, and thus implies that it can be controlled by discharge power. [1,2] However there are many drawbacks to resulting nanostructures connected to their properties or even material type. Looking at state of the art of 1D nanostructures like nanowires, much of the progress only resulted in NWs with diameters much greater than their respective quantum confinement scales, i.e. 10–100 nm. Even at this scale, NW-based materials offer enhanced charge transport and smaller diffusion length scales for improved performance with various electrochemical and photo-electrochemical energy conversion and storage applications. However, many times synthesized materials don’t meet specific properties for optimal performance in certain devices, e.g. band gap energies, or they are even hard to obtain. These deficiencies can be eliminated by additional plasma conversion processes, where we can substitute atoms in crystal networks or controllably release them and create defects. Here the NWs or 1D crystalline nanomaterials of metal oxides with diameters less than 100 nm provide a useful platform for creating new materials either as substrates for heteroepitaxy or through the phase transformation with reaction. Specific results with single crystal phase transformation of e.g. hematite (a-Fe2O3) to pyrite (FeS2) NWs will be presented to illustrate the viability of using NWs for creating new materials through plasma particle reformation. [3] Furthermore, the metal oxide NWs can be altered and modified also by other energetic particles like electrons, which cause irradiation damages and release atoms from crystal networks. [4] This process leads to metal oxides with reduced oxide states. All these processes lead to improved properties, tailored band gaps and increased performance of NWs in devices.

Demography and population growth rate of the tree Prosopis flexuosa with contrasting grazing regimes in the Central Monte Desert

One of the most important current challenges for ecologists is to evaluate how human-induced changes in ecosystems would impact viability of populations. Demographic response to anthropogenic impact could help us to understand how to manage those impacts. Using demographic techniques and population projection models, here we assess if demography and population dynamics of the tree Prosopis flexuosa change in cattle grazed areas compared to ungrazed areas in the Central Monte desert, Mendoza, Argentina. To this end, we quantified vital rates and constructed a population projection matrix model to compare the deterministic population growth rate (λ) between grazed and ungrazed areas. We also estimated elasticities of vital rates to evaluate their potential importance for future changes in λ and performed a life table response experiment (LTRE) to identify the life cycle transitions that contribute the most to the observed differences in λ between the two treatments. Although we found differences in demographic processes, such as lower seed production and higher probability of reversion to smaller size classes in young individuals when cattle were present, our results indicate that cattle grazing had no significant effect on λ for this species. According to the elasticity analysis, survival of large trees is the main driver of the population growth rate (λ) of P. flexuosa, and the vital rates related to tree reproduction, such as seed production and germination, have a poor contribution to λ. Therefore, limitations of activities that can affect survival of large trees should be considered as part of the conservation strategy for this species. Our study provides a compilation of demographic information that can be useful to set policies connecting the conservation objectives for this woodlands with that of ranch managers of the area.

Atomic arrangement in immiscible Ag–Cu alloys synthesized far-from-equilibrium

Physical attributes of multicomponent materials of a given chemical composition are determined by atomic arrangement at property-relevant length scales. A potential route to access a vast array of atomic configurations for material property tuning is by synthesis of multicomponent thin films using vapor fluxes with their deposition pattern modulated in the sub-monolayer regime. However, the applicability of this route for creating new functional materials is impeded by the fact that a fundamental understanding of the combined effect of sub-monolayer flux modulation, kinetics and thermodynamics on atomic arrangement is not available in the literature. Here we present a research strategy and verify its viability for addressing the aforementioned gap in knowledge. This strategy encompasses thin film synthesis using a route that generates multi-atomic fluxes with sub-monolayer resolution and precision over a wide range of experimental conditions, deterministic growth simulations and nanoscale microstructural probes. Investigations are focused on structure formation within the archetype immiscible Ag-Cu binary system, revealing that atomic arrangement at different length scales is governed by the arrival pattern of the film forming species, in conjunction with diffusion of near-surface Ag atoms to encapsulate 3D Cu islands growing on 2D Ag layers. The knowledge generated and the methodology presented herein provides the scientific foundation for tailoring atomic arrangement and physical properties in a wide range of miscible and immiscible multinary systems.

Deterministic versus stochastic aspects of superexponential population growth models

Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes, followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.

Epitaxial Growth of Room-Temperature Ferromagnetic MnAs Segments on GaAs Nanowires via Sequential Crystallization.

We investigate the incorporation of manganese into self-catalyzed GaAs nanowires grown in molecular beam epitaxy. Our study reveals that Mn accumulates in the liquid Ga droplet and that no significant incorporation into the nanowire is observed. Using a sequential crystallization of the droplet, we then demonstrate a deterministic and epitaxial growth of MnAs segments at the nanowire tip. This technique may allow the seamless integration of multiple room-temperature ferromagnetic segments into GaAs nanowires with high-crystalline quality.

Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes.

We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.

Financial failure of a startup: a simulation approach

The objective is to develop a simulation model of a startup to assess the ceteris paribus effects of (16) different parameters on the likelihood of financial failure. The deterministic growth path is described by a second-order Pascal distribution. Uncertainty is incorporated assuming a random variable proportional to sales. Three criteria for financial failure are developed to assess the likelihood of different failure types (profitability, solidity, and liquidity failures). Finnish data from 9,066 non-failed and 118 failed startups are used to approximate the value range of the parameters in non-failed and different types of failed startups. For each parameter, effects are analysed for 25 different values based on 1,000 simulation rounds each. The findings strongly emphasise the central role of internal rate of return in the likelihood of each type of failure. They also emphasise importance of early generation of sales for the likelihood of profitability failure and the strong effect of fixed expenses, size of initial investment, and initial equity capital on failure likelihood.

Financial failure of a startup: a simulation approach

The objective is to develop a simulation model of a startup to assess the ceteris paribus effects of (16) different parameters on the likelihood of financial failure. The deterministic growth path is described by a second-order Pascal distribution. Uncertainty is incorporated assuming a random variable proportional to sales. Three criteria for financial failure are developed to assess the likelihood of different failure types (profitability, solidity, and liquidity failures). Finnish data from 9,066 non-failed and 118 failed startups are used to approximate the value range of the parameters in non-failed and different types of failed startups. For each parameter, effects are analysed for 25 different values based on 1,000 simulation rounds each. The findings strongly emphasise the central role of internal rate of return in the likelihood of each type of failure. They also emphasise importance of early generation of sales for the likelihood of profitability failure and the strong effect of fixed expenses, size of initial investment, and initial equity capital on failure likelihood.

Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example

The literature that conducts numerical analysis of equilibrium in models with hyperbolic (quasi-geometric) discounting reports difficulties in achieving convergence. Surprisingly, numerical methods fail to converge even in a simple, deterministic optimal growth problem that has a well-behaved, smooth closed-form solution. We argue that the reason for nonconvergence is that the generalized Euler equation has a continuum of smooth solutions, each of which is characterized by a different integration constant. We propose two types of restrictions that can rule out the multiplicity: boundary conditions and shape restrictions on equilibrium policy functions. With these additional restrictions, the studied numerical methods deliver a unique smooth solution for both the deterministic and stochastic problems in a wide range of the model’s parameters.

Effect of neutron flux on the characteristics of irradiation-induced nanofeatures and hardening in pressure vessel steels

Effects of neutron flux (or dose rate) on the characteristics of irradiation-induced nanofeatures in neutron-irradiated pressure vessel steels were occasionally reported. Such effects let one expect that the mechanical properties mediated by the operation of the nanofeatures as dislocation obstacles would also depend on flux. However, there are controversial views on the presence of flux effects on mechanical properties. The present approach is based on the investigation of pairs of samples from the same batch of material for a number of RPV steels including different levels of Cu as well as base and weld materials. The samples of each pair were irradiated at about the same temperature but different fluxes up to about the same fluence, thus automatically revealing potential flux effects. Small-angle neutron scattering and Vickers hardness testing were applied to characterize the nm-scale solute clusters and the resulting irradiation hardening. A number of analytic models of cluster evolution, namely deterministic growth and coarsening, and hardening as well as combinations thereof were applied to interpret the trends extracted from the experimental results. It is found that there are indeed trends of the cluster size and volume fraction as functions of flux but no resolvable trend for hardening. The absence of a flux effect on hardening can be rationalized in terms of size and number density of solute clusters that enter the hardening expressions. Size and number density depend on flux in opposite directions and, therefore, partly cancel out. Flux effects for the whole set of experimental data including low- and high-Cu base metals and welds can be consistently described by a combination of deterministic growth and dispersed barrier hardening using a unique value of the obstacle strength of solute clusters.

Probabilistic Analysis of Stress Corrosion Crack Growth and Related Structural Reliability Considerations

The predetection evolution of stress corrosion cracking has been examined as a necessary preliminary to effective detection of such cracks. Anodic dissolution (AD) and hydrogen embrittlement (HE) have been considered to calculate the stress corrosion crack (SCC) growth in AA7050-T6 for a surface-breaking crack with blunt tip in an aqueous environment. Since these processes are not completely deterministic, several advanced statistical methods have been used to introduce probabilistic considerations. Based on the data from designed computer experiments, the computer code developed by the authors (Lee et al., 2015, “A Comprehensive Analysis of the Growth Rate of Stress Corrosion Cracks,” Proc. R. Soc. A, 471(2178), p. 20140703) to conduct deterministic stress corrosion crack growth analysis has been represented by metamodels using Gaussian process regression. Through sensitivity analysis, important variables which need to be calibrated have been identified. The dynamic Bayesian network (DBN) model and Monte Carlo simulation (MCS) have been utilized to quantify uncertainties. Statistical parameters of input variables have been obtained by a machine learning technique. The calibrated model has been validated using Bayesian hypothesis testing. Since the DBN model yields a probability of detection (POD) comparable to the probability based on binary validation data, the probabilistic model with calibrated parameters is expected to well represent the growth of a stress corrosion crack. The results also show that the reliability largely depends on the accuracy of flaw detection methods and on the critical crack length.

Path selection in the growth of rivers

River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

Probability density function solutions to a Bessel type pantograph equation

We extend a cell growth model with a deterministic cell growth rate and asymmetric division to include dispersion. This extension yields a second order functional differential equation, the solution of which is required to be a probability density function for the size of a cell (as measured by DNA content). We study the equation for certain choice of non constant coeffcients that correspond to dispersion, growth and splitting rates. This choice of coeffcients leads to a Bessel type operator, and it is shown that there is a unique probability distribution function that solves the equation. The solution is constructed using the Mellin transform and is given in terms of an infinite series of modified Bessel functions.

A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation.

BackgroundAlthough altered protocols that challenge conventional radiation fractionation have been tested in prospective clinical trials, we still have limited understanding of how to select the most appropriate fractionation schedule for individual patients. Currently, the prescription of definitive radiotherapy is based on the primary site and stage, without regard to patient-specific tumor or host factors that may influence outcome. We hypothesize that the proportion of radiosensitive proliferating cells is dependent on the saturation of the tumor carrying capacity. This may serve as a prognostic factor for personalized radiotherapy (RT) fractionation.MethodsWe introduce a proliferation saturation index (PSI), which is defined as the ratio of tumor volume to the host-influenced tumor carrying capacity. Carrying capacity is as a conceptual measure of the maximum volume that can be supported by the current tumor environment including oxygen and nutrient availability, immune surveillance and acidity. PSI is estimated from two temporally separated routine pre-radiotherapy computed tomography scans and a deterministic logistic tumor growth model. We introduce the patient-specific pre-treatment PSI into a model of tumor growth and radiotherapy response, and fit the model to retrospective data of four non-small cell lung cancer patients treated exclusively with standard fractionation. We then simulate both a clinical trial hyperfractionation protocol and daily fractionations, with equal biologically effective dose, to compare tumor volume reduction as a function of pretreatment PSI.ResultsWith tumor doubling time and radiosensitivity assumed constant across patients, a patient-specific pretreatment PSI is sufficient to fit individual patient response data (R2 = 0.98). PSI varies greatly between patients (coefficient of variation >128 %) and correlates inversely with radiotherapy response. For this study, our simulations suggest that only patients with intermediate PSI (0.45–0.9) are likely to truly benefit from hyperfractionation. For up to 20 % uncertainties in tumor growth rate, radiosensitivity, and noise in radiological data, the absolute estimation error of pretreatment PSI is <10 % for more than 75 % of patients.ConclusionsRoutine radiological images can be used to calculate individual PSI, which may serve as a prognostic factor for radiation response. This provides a new paradigm and rationale to select personalized RT dose-fractionation.

General formulation of Luria-Delbrück distribution of the number of mutants.

The Luria-Delbrück experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the past 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far from the experimental condition. We derive here the properties of this distribution for arbitrary growth function for both the deterministic and stochastic growth of the mutants. The derivation we propose uses the number of wild-type bacteria as the independent variable instead of time. The derivation is surprisingly simple and versatile, allowing many generalizations to be taken easily into account.

Reproduction, abundance, and population growth for a fisher (Pekania pennanti) population in the Sierra National Forest, California

In the west coast region of the United States, fishers (Pekania pennanti) exist in 2 remnant populations—1 in northern California and 1 in the southern Sierra Nevada, California—and 3 reintroduced populations (western Washington, southern Oregon, and northeastern California). The West Coast Distinct Population Segment of fishers encompassing all of these populations was proposed for listing as threatened by the U.S. Fish and Wildlife Service in October 2014. There are likely fewer than 500 total fishers in the southern Sierra Nevada population isolate, but empirical data on demographic rates, population size, and population growth are almost entirely lacking. Our goal was to estimate demographic parameters and current abundance of a fisher population at the north margin of the southern Sierra Nevada region. Radiocollared fishers were monitored from 2007 to 2013 to estimate survival and demographic rates, and camera traps were used to estimate population size based on detections of individual animals in a capture– mark–resight (CMR) framework. A Leslie matrix model was used to estimate a deterministic population growth rate (λ). Fisher abundance ranged from 48 animals in 2010 to 62 animals in 2012, whereas mean population density varied from 0.075 to 0.096 fishers/km 2 . Reproductive status was determined for 89 of 93 total denning opportunities; denning and weaning rates were estimated at 84% and 70%, and litter size was 1.6 kits. We documented 8 den failures, mostly associated with predator attacks. Demographic rates in the study population were comparable to reports from elsewhere in California or Oregon, but the CMR-based population density was the lowest reported in the United States. The estimated λ for the population was 0.966 (range 0.786–1.155), which was in agreement with no indication of a positive or negative trend in population density. An encouraging result from sensitivity analyses was that minor improvements in fisher survival and fecundity, facilitated by proposed mitigation or management to reduce exposure to several agents of mortality, could improve λ to 1.06–1.09 over the longer term. We believe that the combination of a population growth rate slightly below 1.0, small population size and low density, multiple challenges to survival and reproduction, and damage to habitat from wildfires warrants concern for the viability of the fisher population in our study area, which may extend to the overall southern Sierra Nevada population if λ trends below 1.0 in other parts of the region. There is a need for continued monitoring and potential mitigation for threats to survival to assure continued presence of fishers in the southern Sierra Nevada, California.

Stochastic modelling of Listeria monocytogenes single cell growth in cottage cheese with mesophilic lactic acid bacteria from aroma producing cultures

A stochastic model was developed for simultaneous growth of low numbers of Listeria monocytogenes and populations of lactic acid bacteria from the aroma producing cultures applied in cottage cheese. During more than two years, different batches of cottage cheese with aroma culture were analysed for pH, lactic acid concentration and initial concentration of lactic acid bacteria. These data and bootstrap sampling were used to represent product variability in the stochastic model. Lag time data were estimated from observed growth data (lactic acid bacteria) and from literature on L. monocytogenes single cells. These lag time data were expressed as relative lag times and included in growth models. A stochastic model was developed from an existing deterministic growth model including the effect of five environmental factors and inter-bacterial interaction [Østergaard, N.B, Eklöw, A and Dalgaard, P. 2014. Modelling the effect of lactic acid bacteria from starter- and aroma culture on growth of Listeria monocytogenes in cottage cheese. International Journal of Food Microbiology. 188, 15-25]. Growth of L. monocytogenes single cells, using lag time distributions corresponding to three different stress levels, was simulated. The simulated growth was subsequently compared to growth of low concentrations (0.4-1.0CFU/g) of L. monocytogenes in cottage cheese, exposed to similar stresses, and in general a good agreement was observed. In addition, growth simulations were performed using population relative lag time distributions for L. monocytogenes as reported in literature. Comparably good predictions were obtained as for the simulations performed using lag time data for individual cells of L. monocytogenes. Therefore, when lag time data for individual cells are not available, it was suggested that relative lag time distributions for L. monocytogenes can be used as a qualified default assumption when simulating growth of low concentrations of L. monocytogenes.