Age-dependent predation is not a simple process. II. Wolves,ungulates, and a discrete time model for predation on juveniles with a stabilizing tail

A discrete time model for a predator-prey model, where the predator eats only juvenile prey is developed. The model is developed to capture some of the behavior of wolf-ungulate systems. Age-dependent predation is shown to be a stabilizing influence. The behavior of the model depends critically on the age of senescence of the prey—an extremely small number of old prey individuals represent a very powerful stabilizing factor. The model behaves in a similar fashion to, but is less stable than, an age structured Ricker model.     

用光合-蒸散耦合模型模拟冬小麦CO2通量的日变化

根据SPAC理论建立了一个冬小麦光合和蒸散的耦合模型.冬小麦CO2通量包括冠层光合、呼吸和土壤呼吸.冠层光合采用了Farquhar光合作用生化模型,并通过冠层阻力的参数化将光合作用与蒸腾作用耦合起来.用涡度相关方法观测了CO2通量,对模型进行了验证,结果显示模型可以较好地模拟CO2通量日变化过程.对模型的敏感性分析发现日间CO2通量最敏感的参数是初始量子效率.其次,CO2通量对光响应曲线凸度、CO2补偿点、凋萎点和叶面积指数的变化也有着较强的敏感性;夜间CO2通量敏感的参数是最适温度下Rubisco催化能力和暗呼吸参数.     

用光合-蒸散耦合模型模拟冬小麦CO2通量的日变化

根据 SPAC理论建立了一个冬小麦光合和蒸散的耦合模型。冬小麦 CO2 通量包括冠层光合、呼吸和土壤呼吸。冠层光合采用了 Farquhar光合作用生化模型 ,并通过冠层阻力的参数化将光合作用与蒸腾作用耦合起来。用涡度相关方法观测了 CO2通量 ,对模型进行了验证 ,结果显示模型可以较好地模拟 CO2 通量日变化过程。对模型的敏感性分析发现日间 CO2 通量最敏感的参数是初始量子效率。其次 ,CO2 通量对光响应曲线凸度、CO2 补偿点、凋萎点和叶面积指数的变化也有着较强的敏感性 ;夜间 CO2 通量敏感的参数是最适温度下 Rubisco催化能力和暗呼吸参数     

Modeling of antibiotics production in magneto three-phase airlift fermenter

A mathematical model is developed to describe the performance of a three-phase airlift reactor utilizing a transverse magnetic field. The model is based on the complete mixing model for the bulk of liquid phase and on the Michaelis-Menten kinetics. The model equations are solved by the explicit finite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic field increases the degree of bioconversion. The mathematical model is experimentally verified in a three-phase airlift reactor with P. chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At relatively high magnetic field intensities a certain discrepancy in the model solution was observed when the model over estimates the product concentration.     

A Model of the Peripheral Auditory System Responding to Low-Frequency Tones

A model of the peripheral auditory system responding to low-frequency tone stimulation is given. The model is of the type previously introduced by Weiss (1966). It includes three interconnected parts: a linear model of the ear's mechanical system, a model of the cochlear transducer, and a stochastic model of an auditory nerve fiber. The output of the model accurately mimics many characteristics of the output of some auditory nerve neurons responding to sinusoidal stimuli but is unable to successfully match all reported aspects of data obtained from other of these neurons. Characteristics of the model neurons are discussed.     

A modified mathematical model of the anatomy of the cardiac left ventricle

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.     

Modelling wind driven circulation One Tree Reef,Southern Great Barrier Reef

A vertically integrated numerical model of wind-driven circulation at One Tree Reef is presented. The model is the numerical model SURGE developed originally to study tropical cyclone surge. Current data collected in the reef lagoon and over the reef flats is used to test the model's applicability. The reef topography has been modelled explicitly, rather than using an assumed reef shape, with a grid spacing of 150 m. The model corresponds well to the measured current behaviour. The greatest drawback to use of the model is that, at low tide, currents reverse with depth due to lagoon enclosure and a depth integrated model cannot produce water velocity depth profiles. The model can be used to predict current behaviour in strong wind conditions, such as during a cyclone, and to estimate net flows into and out of the lagoon.     

Orientation hypercolumns of the visual cortex: Ring model

A hypercolumn of the visual cortex is a functional unit formed of neighboring columns whose neurons respond to a stimulus of particular orientation. The function of the hypercolumn is to amplify the orientation tuning of visually evoked responses. According to the conventional simple model of a hypercolumn, neuronal populations with different orientation preferences are distributed on a ring. Every population is described by a firing rate (FR) model. To determine the limitations of the FR-ring model, it was compared with a more detailed ring model, which takes into account the distribution of neurons of each population according to their voltage values. In the case of leaky integrate-and-fire neurons, every neuronal population is described by the Fokker-Planck equation (FPE). The mapping of parameters was obtained. The simulations revealed differences in the behavior of the two models. The FPE-based model reacts faster to a change in stimulus orientation. The FPE ring model gives a steady-state solution in the form of waves of activity traveling on the ring, whereas the FR ring model presents amplitude instability for the same parameter set. The FPE ring model reproduces the characteristic effects of the FR ring model: virtual rotation and symmetry breaking.     

Modeling Exposure Intensity and Susceptibility-Latency Effect from Retrospective Cohort Data - Application to Lung Cancer Mortality in Blackfoot Disease Endemic Area in Taiwan

It is challenge in epidemiology to characterize the temperol aspect of exposure-disease association. The authors propose a stochastic model to deal with exposures that are time-dependent and exhibit susceptibility and latency effects. The model is applied to a retrospective cohort data on lung cancer mortality in the blackfoot disease endemic area in Taiwan. The authors compare the proposed model with the multistage model, the back-calculation model, the catalytic model, and the age-period-cohort models.     

A theory of drug tolerance and dependence I: a conceptual analysis

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behavior to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.     

Component inertia modeling of segmental wobbling and rigid masses

A modification to an existing mathematical model is described, which permits the determination of subject-specific inertia parameters for wobbling and rigid masses of female body segments. The model comprises segment-specific soft tissue, bone, and lung components. A total of 59 geometric solids (40 soft tissue, 17 bone, 2 lung) were used to represent the body components. Ninety-five anthropometric measurements were collected from 7 female participants and were used to develop and evaluate the model. The success of the model is evaluated using predicted mass and mass distribution. The overall absolute accuracy in predicted whole body mass was better than 3.0%, with a maximum error of 4.9%. The appropriateness of the cadaver-based density values used in the model is addressed and the accuracy of the component inertia model in relation to uniform density models is discussed. The model offers a novel approach for determining component inertia parameters, which have been used successfully in a wobbling mass model to produce realistic kinetic analyses of drop-landings.     

A discrete-time model with vaccination for a measles epidemic.

A discrete-time, age-independent SIR-type epidemic model is formulated and analyzed. The effects of vaccination are also included in the model. Three mathematically important properties are verified for the model: solutions are nonnegative, the population size is time-invariant, and the epidemic concludes with all individuals either remaining susceptible or becoming immune (a property typical of SIR models). The model is applied to a measles epidemic on a university campus. The simulated results are in good agreement with the actual data if it is assumed that the population mixes nonhomogeneously. The results of the simulations indicate that a rate of immunity greater than 98% may be required to prevent an epidemic in a university population. The model has applications to other contagious diseases of SIR type. Furthermore, the simulated results of the model can easily be compared to data, and the effects of a vaccination program can be examined.     

A Population-Based Morphologically Structured Model for Hyphal Growth and Product Formation in Streptomycin Fermentation

Summary A population model discriminating the hyphae according to the hyphal length and a morphologically structured model considering the specific function of different morphological forms of a hypha are combined together to describe mycelial growth, substrate consumption and secondary metabolite formation in streptomycin fermentation. In the population model, the growth modes of hyphae with different age or length are considered, while in the morphologically structured model, the morphological forms of hyphae and their functions in growth and metabolism are described. The population model and the morphologically structured model are interrelated by a branching function and a differentiation function. In the model, the growth rate of immature apical compartment is distinguished from those of matured ones, branching is proposed to occur only in the subapical region, and the hyphal compartment is assumed to synthesize secondary metabolites. The model is successfully applied to simulate the batch fermentation process of streptomycin production. The growth characteristics of filamentous microorganisms are also discussed using the model predictions.     

From isotropic to anisotropic side chain representations: comparison of three models for residue contact estimation

The criterion to determine residue contact is a fundamental problem in deriving knowledge-based mean-force potential energy calculations for protein structures. A frequently used criterion is to require the side chain center-to-center distance or the -to- atom distance to be within a pre-determined cutoff distance. However, the spatially anisotropic nature of the side chain determines that it is challenging to identify the contact pairs. This study compares three side chain contact models: the Atom Distance criteria (ADC) model, the Isotropic Sphere Side chain (ISS) model and the Anisotropic Ellipsoid Side chain (AES) model using 424 high resolution protein structures in the Protein Data Bank. The results indicate that the ADC model is the most accurate and ISS is the worst. The AES model eliminates about 95% of the incorrectly counted contact-pairs in the ISS model. Algorithm analysis shows that AES model is the most computational intensive while ADC model has moderate computational cost. We derived a dataset of the mis-estimated contact pairs by AES model. The most misjudged pairs are Arg-Glu, Arg-Asp and Arg-Tyr. Such a dataset can be useful for developing the improved AES model by incorporating the pair-specific information for the cutoff distance.     

An Input‐Output Model of Extended Producer Responsibility

Under an extended producer responsibility (EPR) system, when a producer delivers a product to the market it must also pay a takeback fee, which is used to cover the costs of end‐of‐life disposal. EPR systems are currently used in Europe and beyond to manage a variety of products, including packaging and used tires. In this article we develop an input‐output (IO) model that is able to assess the impacts of an EPR system, and is based on the waste IO (WIO) model. The WIO model is itself a hybrid‐unit model extension of the Leontief model that is able to capture the substitution effect between recycled/recovered material/energy from waste treatment and their non‐waste cognates. The resulting EPRIO model, besides the conventional direct and indirect effects of the Leontief model and the substitution effects of the WIO model, is able to capture the opportunity costs of financing the EPR system, and additionally requires the specification of an alternative waste management policy, with its own opportunity costs. The impact of an EPR policy is thus the difference between the impacts of the reference EPR and the alternative waste treament policies. The resulting model is illustrated with a simple example of a used tire management EPR system.