Global dynamics of a chemostat competition model with distributed delay

 We study the global dynamics of n-species competition in a chemostat with distributed delay describing the time-lag involved in the conversion of nutrient to viable biomass. The delay phenomenon is modelled by the gamma distribution. The linear chain trick and a fluctuation lemma are applied to obtain the global limiting behavior of the model. When each population can survive if it is cultured alone, we prove that at most one competitor survives. The winner is the population that has the smallest delayed break-even concentration, provided that the orders of the delay kernels are large and the mean delays modified to include the washout rate (which we call the virtual mean delays) are bounded and close to each other, or the delay kernels modified to include the washout factor (which we call the virtual delay kernels) are close in L ¹-norm. Also, when the virtual mean delays are relatively small, it is shown that the predictions of the distributed delay model are identical with the predictions of the corresponding ODEs model without delay. However, since the delayed break-even concentrations are functions of the parameters appearing in the delay kernels, if the delays are sufficiently large, the prediction of which competitor survives, given by the ODEs model, can differ from that given by the delay model. Received: 9 August 1997 / Revised version: 2 July 1998     

A distributed delay routine-based simulation model of Beauveria bassiana conidial stability in response to environmental stressors

Using published data and equations on therelationship between spore longevity of theentomopathogenic hyphomycetes, Metarhiziumanisopliae var. acridum and Beauveria bassiana (Balsamo) Vuillemin(Deuteromycota: Hyphomycetes) and temperatureand moisture content, a model of sporeviability was constructed based on adistributed-delay routine. The model ismodified via average spore survival time or byincluding an additional attrition (mortality)rate. The model was parameterized usingpublished values from studies on M. a.var. acridum spores, and output comparedfavorably with germination data and with apreviously-developed model. After initializingthe model using parameter estimates of B.bassiana spores from the laboratory andpublished data on changes in (1) spore viabilitywith respect to temperature and moisturecontent, and (2) spore moisture content withrespect to temperature and relative humidity,the model was run using daily min/maxtemperature and relative humidity data andcompared with data from four field experimentsof Mycotech B. bassiana isolate GHAsprayed on canteloupe plants. For two of theexperiments, observed viability trends werecompared to model outputs using weather datafrom both a weather station and fromwithin-canopy temperature and humidity probes. Output using weather station data fitobservations much better than output usingwithin-canopy probe data. For the tworemaining sets of field data, both earlier inthe season, only weather station data wereavailable and the resulting output fitobservations poorly. An attrition rate of 98%was needed to fit output to field data early inthe growing season, and a rate of 74% wasneeded for data collected four weeks later. These attrition rates can be consideredestimates for the proportion of spores dyingfor reasons other than temperature and relativehumidity, and they were attributed largely toUVB radiation due to the more open canopyearlier in the season.     

Stability analysis for HIV infection delay model with protease inhibitor

In this article, we considered a model of HIV-1 infection with a protease inhibitor therapy and three delays. The frequency of the bifurcating periodic solution as well as the threshold value is approximated numerically using realistic parameter. The estimated threshold value is realistic and the frequency of the oscillations is consistent with that of the observed viral blips.     

A model of distributed type associative memory with quantized Hadamard transform

This paper proposes a new correlation matrix network model of associative memory in brain. Each memorized pattern which consists of binary (+1 or-1) elements is preprocessed by a quantized Hadamard transform to increase selectivity. The association ability of a correlation matrix network model depends on the orthogonality between key patterns by which the corresponding memorized patterns are associatively recalled. In a brain model, however, it is rare that the key patterns are mutually orthogonal since they are memorized patterns themselves. The quantized Hadamard transform, presented in this paper, renders the memorized patterns approximately orthogonal. The model is tested by computer simulation.     

On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process

In this paper we study the two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process. The model distinguishes individuals by two different status: the ‘reproductive’ stage and the ‘nonreproductive’ stage. We establish the well-posedness for this model and show that the solution of this model exhibits asynchronous exponential growth by means of semigroups. We also consider a special case in which the individuals in the ‘reproductive’ stage and the ‘nonreproductive’ stage have the same growth rates and give a comparison between this two-phase model with the classical one-phase model.     

Dynamical analysis of a diffusion plant-wrack model with delay

In this paper, in view of the senescence of plant and the decay of wrack, time delays are introduced into the plant-wrack model. The effects of wrack decay and time delay on the dynamical behaviors of the diffusive plant-wrack model are studied analytically and numerically. When the delay is zero, the wrack decay will induce the change of stability of the unique equilibrium point, further lead to the occurrence of the Hopf bifurcation and the Turing instability. When the delay is present, the conditions for the occurrence of the Hopf bifurcation are established. By comparing the results of the model without and with delay, it is found that the increases of delay may induce no stability switches, a single stability switch or multiple stability switches, when the value of wrack decay can stabilize model with zero delay. When the value of wrack decay can destabilize model with zero delay, numerical simulations show that the small delay may cause homogeneous distributions of vegetation, while the larger delay may cause the emergence of periodic oscillation of vegetation. The obtained results provide a basis for understanding the spatiotemporal evolution of such a plant-wrack model with delay.     

Neuronal networks and memory: role of the hippocampus

Learning and memory are related both to cognitive processes and to neurobiological mechanisms. The human pathology focused on the role of the hippocampus and animal experiments have analyzed its implications. The most usually admitted hypothesis is that memories are underlied by distributed specific neural networks defined through the strengthening of certain synapses, under the action of the flow of information during learning. The best candidate for this strengthening of the synapses is a change in synaptic plasticity similar to the artificial phenomenon of long-term potentiation. During memory processes, the hippocampus would play a particular role in information processing (analyzing novelty and significance of the information) and would allow the specification of the neural network, mainly in the cortical territories. We report data in olfactory learning in rats comforting these hypotheses. Considering neurochemistry of memory processes, specific synaptic changes and neuromodulatory processes must be distinguished. We report data about vasopressin illustrating both kinds of mechanisms in the hippocampus.     

An oscillatory neural network model of sparse distributed memory and novelty detection

A model of sparse distributed memory is developed that is based on phase relations between the incoming signals and an oscillatory mechanism for information processing. This includes phase-frequency encoding of input information, natural frequency adaptation among the network oscillators for storage of input signals, and a resonance amplification mechanism that responds to familiar stimuli. Simulations of this model show different types of dynamics in response to new and familiar stimuli. The application of the model to hippocampal working memory is discussed.     

具捕食偏爱的似然竞争模型及模拟分析

在集合种群似然竞争模型的基础上引入了捕食者对猎物偏爱性因素,提出了具捕食偏爱的似然竞争模型.应用动力系统方法研究了系统的平衡态,用计算机模拟研究了偏爱度对平衡态的影响、平衡态在偏爱度与斑块破坏共同作用下的变化、偏爱度对系统演化动态以及空间分布的影响.结果表明:(1)适度地平衡捕食者对各猎物的偏爱度,有利于系统物种共存;(2)斑块破坏对捕食系统的影响程度与捕食者对各猎物的偏爱度密切相关;(3)适当的增加捕食者对优势猎物的偏爱能有效的缩短系统达到稳定共存的驰豫时间;(4)猎物的丰富度与捕食者对该猎物的偏爱度负相关,猎物斑块的破碎化程度与捕食者对该猎物的偏爱度正相关;(5)在遭破坏的斑块上,多食者比单食者更有利于生存.该研究结果对生态保护和生物资源的可持续利用有重要的启发和指导意义.     

Comparing analysis methods for mutation-accumulation data: a simulation study

We simulated single-generation data for a fitness trait in mutation-accumulation (MA) experiments, and we compared three methods of analysis. Bateman-Mukai (BM) and maximum likelihood (ML) need information on both the MA lines and control lines, while minimum distance (MD) can be applied with or without the control. Both MD and ML assume gamma-distributed mutational effects. ML estimates of the rate of deleterious mutation had larger mean square error (MSE) than MD or BM had due to large outliers. MD estimates obtained by ignoring the mean decline observed from comparison to a control are often better than those obtained using that information. When effects are simulated using the gamma distribution, reducing the precision with which the trait is assayed increases the probability of obtaining no ML or MD estimates but causes no appreciable increase of the MSE. When the residual errors for the means of the simulated lines are sampled from the empirical distribution in a MA experiment, instead of from a normal one, the MSEs of BM, ML, and MD are practically unaffected. When the simulated gamma distribution accounts for a high rate of mild deleterious mutation, BM detects only approximately 30% of the true deleterious mutation rate, while MD or ML detects substantially larger fractions. To test the robustness of the methods, we also added a high rate of common contaminant mutations with constant mild deleterious effect to a low rate of mutations with gamma-distributed deleterious effects and moderate average. In that case, BM detects roughly the same fraction as before, regardless of the precision of the assay, while ML fails to provide estimates. However, MD estimates are obtained by ignoring the control information, detecting approximately 70% of the total mutation rate when the mean of the lines is assayed with good precision, but only 15% for low-precision assays. Contaminant mutations with only tiny deleterious effects could not be detected with acceptable accuracy by any of the above methods.     

入侵杂草化感作用的细胞自动机模拟研究

细胞自动机模型(Cellular Automata Model,简称CA模型)是一种能够表现系统复杂行为的模拟方法,适于研究植物群落时空动态过程.本文利用CA模型,模拟具有化感作用的外来种入侵原有物种所构成植被的过程.模型由产生化感物质的外来种和两个对化感物质敏感性不同的本地种组合成不同类型的群落,利用化感物质作用下受体物种生物活性响应模型及种子扩散负指数分布模型,模拟外来杂草和本地种分布格局的时空动态变化.结果表明,外来种可成功地完全入侵由两个对化感物质敏感的本地种构成的群落空间,但对于由对化感物质敏感的一个本地种及对化感物质具有抗性的另一个本地种构成的群落,外来种只能够与本地种共存.     

A knowledge model for analysis and simulation of regulatory networks

MOTIVATION: In order to aid in hypothesis-driven experimental gene discovery, we are designing a computer application for the automatic retrieval of signal transduction data from electronic versions of scientific publications using natural language processing (NLP) techniques, as well as for visualizing and editing representations of regulatory systems. These systems describe both signal transduction and biochemical pathways within complex multicellular organisms, yeast, and bacteria. This computer application in turn requires the development of a domain-specific ontology, or knowledge model. RESULTS: We introduce an ontological model for the representation of biological knowledge related to regulatory networks in vertebrates. We outline a taxonomy of the concepts, define their 'whole-to-part' relationships, describe the properties of major concepts, and outline a set of the most important axioms. The ontology is partially realized in a computer system designed to aid researchers in biology and medicine in visualizing and editing a representation of a signal transduction system.     

Replication pauses of the wild-type and mutant mitochondrial DNA polymerase gamma: a simulation study

The activity of polymerase γ is complicated, involving both correct and incorrect DNA polymerization events, exonuclease activity, and the disassociation of the polymerase:DNA complex. Pausing of pol-γ might increase the chance of deletion and depletion of mitochondrial DNA. We have developed a stochastic simulation of pol-γ that models its activities on the level of individual nucleotides for the replication of mtDNA. This method gives us insights into the pausing of two pol-γ variants: the A467T substitution that causes PEO and Alpers syndrome, and the exonuclease deficient pol-γ (exo(-)) in premature aging mouse models. To measure the pausing, we analyzed simulation results for the longest time for the polymerase to move forward one nucleotide along the DNA strand. Our model of the exo(-) polymerase had extremely long pauses, with a 30 to 300-fold increase in the time required for the longest single forward step compared to the wild-type, while the naturally occurring A467T variant showed at most a doubling in the length of the pauses compared to the wild-type. We identified the cause of these differences in the polymerase pausing time to be the number of disassociations occurring in each forward step of the polymerase.     

Bacteriophages affect evolution of bacterial communities in spatially distributed habitats: a simulation study

Background

Bacteriophages are known to be one of the driving forces of bacterial evolution. Besides promoting horizontal transfer of genes between cells, they may induce directional selection of cells (for instance, according to more or less resistance to phage infection). Switching between lysogenic and lytic pathways results in various types of (co)evolution in host-phage systems. Spatial (more generally, ecological) organization of the living environment is another factor affecting evolution. In this study, we have simulated and analyzed a series of computer models of microbial communities evolving in spatially distributed environments under the pressure of phage infection.

Results

We modeled evolving microbial communities living in spatially distributed flowing environments. Non-specific nutrient supplied in the only spatial direction, resulting in its non-uniform distribution in environment. We varied the time and the location of initial phage infestation of cells as well as switched chemotaxis on and off. Simulations were performed with the Haploid evolutionary constructor software (http://evol-constructor.bionet.nsc.ru/).

Conclusion

Simulations have shown that the spatial location of initial phage invasion may lead to different evolutionary scenarios. Phage infection decreases the speciation rate by more than one order as far as intensified selection blocks the origin of novel viable populations/species, which could carve out potential ecological niches. The dependence of speciation rate on the invasion node location varied on the time of invasion. Speciation rate was found to be lower when the phage invaded fully formed community of sedentary cells (at middle and late times) at the species-rich regions. This is especially noticeable in the case of late-time invasion.

Our simulation study has shown that phage infection affects evolution of microbial community slowing down speciation and stabilizing the system as a whole. This influencing varied in its efficiency depending on spatially-ecological factors as well as community state at the moment of phage invasion.

     

Bacteriophages affect evolution of bacterial communities in spatially distributed habitats: a simulation study

Background

Bacteriophages are known to be one of the driving forces of bacterial evolution. Besides promoting horizontal transfer of genes between cells, they may induce directional selection of cells (for instance, according to more or less resistance to phage infection). Switching between lysogenic and lytic pathways results in various types of (co)evolution in host-phage systems. Spatial (more generally, ecological) organization of the living environment is another factor affecting evolution. In this study, we have simulated and analyzed a series of computer models of microbial communities evolving in spatially distributed environments under the pressure of phage infection.

Results

We modeled evolving microbial communities living in spatially distributed flowing environments. Non-specific nutrient supplied in the only spatial direction, resulting in its non-uniform distribution in environment. We varied the time and the location of initial phage infestation of cells as well as switched chemotaxis on and off. Simulations were performed with the Haploid evolutionary constructor software (http://evol-constructor.bionet.nsc.ru/).

Conclusion

Simulations have shown that the spatial location of initial phage invasion may lead to different evolutionary scenarios. Phage infection decreases the speciation rate by more than one order as far as intensified selection blocks the origin of novel viable populations/species, which could carve out potential ecological niches. The dependence of speciation rate on the invasion node location varied on the time of invasion. Speciation rate was found to be lower when the phage invaded fully formed community of sedentary cells (at middle and late times) at the species-rich regions. This is especially noticeable in the case of late-time invasion.Our simulation study has shown that phage infection affects evolution of microbial community slowing down speciation and stabilizing the system as a whole. This influencing varied in its efficiency depending on spatially-ecological factors as well as community state at the moment of phage invasion.

     

CEDAR: communication efficient distributed analysis for regressions

Electronic health records (EHRs) offer great promises for advancing precision medicine and, at the same time, present significant analytical challenges. Particularly, it is often the case that patient-level data in EHRs cannot be shared across institutions (data sources) due to government regulations and/or institutional policies. As a result, there are growing interests about distributed learning over multiple EHRs databases without sharing patient-level data. To tackle such challenges, we propose a novel communication efficient method that aggregates the optimal estimates of external sites, by turning the problem into a missing data problem. In addition, we propose incorporating posterior samples of remote sites, which can provide partial information on the missing quantities and improve efficiency of parameter estimates while having the differential privacy property and thus reducing the risk of information leaking. The proposed approach, without sharing the raw patient level data, allows for proper statistical inference. We provide theoretical investigation for the asymptotic properties of the proposed method for statistical inference as well as differential privacy, and evaluate its performance in simulations and real data analyses in comparison with several recently developed methods.     

An HBV model with diffusion and time delay

In this paper, a hepatitis B virus (HBV) model with spatial diffusion and saturation response of the infection rate is investigated, in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an infected steady state and an uninfected steady state is discussed. By comparison arguments, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. If the basic reproductive number is greater than unity, by successively modifying the coupled lower-upper solution pairs, sufficient conditions are obtained for the global stability of the infected steady state. Numerical simulations are carried out to illustrate the main results.     

How spatial resource distribution and memory impact foraging success: A hybrid model and mechanistic index

Understanding how animals forage has always been a fundamental issue in Ethology and has become critical more recently in Environmental Conservation. Since the formalization of optimal foraging theory, theoretical models intended to depict the behavior of a generic forager have served as the main tools to analyze and ultimately comprehend the mechanisms of foraging. Due to complexity and technical constraints, these models have traditionally focused on single aspects of foraging, leaving out other concurrent processes that may also interplay. The recent inclusion of several facets inside united models has given rise to interesting results on the importance of interacting factors such as memory and resource heterogeneity.In this paper, we present a hybrid model integrating metabolism, foraging decisions, memory, as well as spatially explicit movement and resource distribution. We use it to examine the effects of spatial resource distribution – an aspect often neglected in favor of probabilistic resource heterogeneity – on the viability of a generic random-walking forager, and rely on the model to devise an ecological metric that can explain and render the relative profitability of given spatial distributions. Furthermore, we assess the significance of memory properties relatively to the profitability of resource distributions. Most notably, we reveal contrasted effects of memory depending on the aspect of resource varied in space (i.e. prey abundance, or prey body mass).On the whole, a general comparison of our findings with results obtained with spatially implicit models leads us to stress the complex interaction between memory and spatial resource distribution as well as the criticality of spatial representation in the modeling of foraging. Accordingly, we conclude with a discussion on the ecological implications of these results, as well as the advantages of hybrid modeling for the accurate simulation of foraging.     

Statistical analysis of the gamma evaluation acceptance criteria: A simulation study of 2D dose distributions under error free conditions

PurposeTo investigate the statistical distribution of the gamma value under error-free conditions, in order to study the relation between the gamma evaluation failure rate and statistically significant deviations in the general situation.MethodsThe 2D absorbed dose distribution for 30 clinical head-and-neck IMRT fields were calculated in a QC phantom. For the same fields, dose measurements were simulated by assuming that the calculated value represented the expectation value, and by adding a random spatial uncertainty of 1–9 mm (1SD) and a random dose uncertainty of 1%–3% (1SD). The simulated measurements were then compared to the calculated dose using the gamma evaluation, and the distribution of the failure rate (i.e. the probability of gamma values above unity) was analysed.ResultsFor a wide range of the random measurement uncertainty, a distinct peak in the failure rate distribution was observed. The presence of higher failure rates was associated with large values of the second order derivative of the dose distribution. For spatial uncertainties larger than or equal to the resolution of the dose matrix, and for reasonable dose uncertainties, the median value of the failure rate distribution was fairly constant.ConclusionsSimulations showed, in the general case, that the probability of having a gamma value above unity under error-free conditions was not spatially uniform. We believe that this shortcoming may be partly responsible for the limited ability of the gamma evaluation method to detect errors in clinically relevant situations.