Reliability Analysis of the Groundwater Conceptual Model

The hydrologic model is the foundation of water resource management and planning. Conceptual model is the essential component of groundwater model. Due to limited understanding of natural hydrogeological conditions, the conceptual model is always constructed incompletely. Therefore, the uncertainty in the model's output is evitable when natural groundwater field is simulated by a single groundwater model. A synthetic groundwater model is built and regarded as the true model, and three alternative conceptual models are constructed by considering incomplete hydrogeological conditions. The outputs (groundwater budget terms from boundary conditions) of these groundwater models are analyzed statistically. The results show that when the conceptual model is closer to the true hydrogeological conditions, the distributions of outputs of the groundwater model are more concentrated on the true outputs. Therefore, the more reliable the structure of the conceptual model is, the more reliable the output of the groundwater model is. Moreover, the uncertainty caused by the conceptual model cannot be compensated by parameter uncertainty.     

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.     

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Model of the spreading dynamics of a hospital infection

The article deals with the epidemiological model and the corresponding mathematical model of the spread of hospital infection. The mathematical apparatus of Markov's heterogeneous chain is used. The model may be used for the analysis and planning of antiepidemic measures, as well as for the evaluation of their effectiveness. The conditions for the possibility of the application of the newly developed mathematical model have been formulated. The method for calculating the parameters of the model on the basis of data on morbidity in different forms of hospital infection is presented. An example of using the above model for the analysis of the data of observation is considered in detail.     

A Mixed Model of Mutation for Electrophoretic Identity of Proteins within and between Populations

A model which is a mixture of the model of infinite alleles and the Ohta-Kimura model of stepwise mutation has been proposed for the study of eletcrophoretic variants in natural populations. Mutations which alter the mobility of a protein are divided into two classes: stepwise mutations and nonstepwise mutations. It is assumed that stepwise mutations follow the Ohta-Kimura model while nonstepwise mutations follow the infinite allele model. It is then shown that even if the proportion of nonstepwise mutations is only 5%, with the other 95% stepwise mutations, the effective number of alleles given by the present model is considerably larger than that given by the Ohta-Kimura model of stepwise mutation. The result has also been applied to study Nei's genetic distance.     

The Effect of Branch Length Variation on the Selection of Models of Molecular Evolution

Models of sequence evolution play an important role in molecular evolutionary studies. The use of inappropriate models of evolution may bias the results of the analysis and lead to erroneous conclusions. Several procedures for selecting the best-fit model of evolution for the data at hand have been proposed, like the likelihood ratio test (LRT) and the Akaike (AIC) and Bayesian (BIC) information criteria. The relative performance of these model-selecting algorithms has not yet been studied under a range of different model trees. In this study, the influence of branch length variation upon model selection is characterized. This is done by simulating sequence alignments under a known model of nucleotide substitution, and recording how often this true model is recovered by different model-fitting strategies. Results of this study agree with previous simulations and suggest that model selection is reasonably accurate. However, different model selection methods showed distinct levels of accuracy. Some LRT approaches showed better performance than the AIC or BIC information criteria. Within the LRTs, model selection is affected by the complexity of the initial model selected for the comparisons, and only slightly by the order in which different parameters are added to the model. A specific hierarchy of LRTs, which starts from a simple model of evolution, performed overall better than other possible LRT hierarchies, or than the AIC or BIC. Received: 2 October 2000 / Accepted: 4 January 2001     

从临床到基础：硝酸甘油实验性偏头痛大鼠模型信度和效度评价

具有良好信度和效度的动物模型是从实验室到临床转译研究成功的保证,为进一步应用硝酸甘油（glycerol trinitrate,GTN）偏头痛大鼠模型,对其信度和效度进行评价。效度包括表面效度、建构效度、标准关联效度。衡量表面效度的标准是症状同源性。GTN偏头痛大鼠模型行为学表现与人类偏头痛有一定的相似性。建构效度主要指动物模型对理论假说的解释度,GTN模型复制了偏头痛的神经源性炎症及痛觉增敏,具有较好的建构效度。标准关联效度即预测效度主要表现为药理学反应及其在临床的干预实验。GTN模型对典型抗偏头痛药物麦角胺的反应较敏感,但是该模型的预测力效度仍未有效建立。GTN偏头痛大鼠在不同的地区、不同的实验室均已成功复制,表明其有较好的信度。     

Mathematical model of children mortality

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.     

中国北方城市常见绿化植物夏季气孔导度影响因素及模型比较

利用Jarvis和Ball两种常规气孔导度模拟模型和人工神经网络模型(ANN)对中国北方城市常见的6种绿化植物的夏季气孔导度变化动态进行了模拟。结果表明:贴梗海棠(Chaenomeles speciosa)和龙爪槐(Sophora japonica)的最优模拟模型为Ball模型,木兰(Magnolia liliflora)最优模拟模型为Jarvis模型,而日本樱花(Prunus yedoensis)、金钟花(Forsythia viridissima)、紫荆(Cercis chinensis)的最优模拟模型为ANN模型。这表明ANN模型可以有效的改善气孔导度环境响应行为的数值模拟。环境因子的多元逐步回归结果和人工神经网络模型敏感性分析表明PAR是夏季气孔导度环境因子中最敏感的要素,而Ta则是其中最不敏感的要素。     

Application of CT images in the diagnosis of lung cancer based on finite mixed model

ObjectiveInvestigating the application of CT images when diagnosing lung cancer based on finite mixture model is the objective. Method: 120 clean healthy rats were taken as the research objects to establish lung cancer rat model and carry out lung CT image examination. After the successful CT image data preprocessing, the image is segmented by different methods, which include lung nodule segmentation on the basis of Adaptive Particle Swarm Optimization – Gaussian mixture model (APSO-GMM), lung nodule segmentation on the basis of Adaptive Particle Swarm Optimization – gamma mixture model (APSO-GaMM), lung nodule segmentation based on statistical information and self-selected mixed distribution model, and lung nodule segmentation based on neighborhood information and self-selected mixed distribution model. The segmentation effect is evaluated. Results: Compared with the results of lung nodule segmentation based on statistical information and self-selected mixed distribution model, the Dice coefficient of lung nodule segmentation based on neighborhood information and self-selected mixed distribution model is higher, the relative final measurement accuracy is smaller, the segmentation is more accurate, but the running time is longer. Compared with APSO-GMM and APSO-GaMM, the dice value of self-selected mixed distribution model segmentation method is larger, and the final measurement accuracy is smaller. Conclusion: Among the five methods, the dice value of the self-selected mixed distribution model based on neighborhood information is the largest, and the relative accuracy of the final measurement is the smallest, indicating that the segmentation effect of the self-selected mixed distribution model based on neighborhood information is the best.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

The Effect of Carrier Distribution on Performance of ENZ-Based Electro-Absorption Modulator

Recently, epsilon-near-zero (ENZ) has been emerging as an important field of research which is the study of light-matter interactions in the presence of materials with zero permittivity. Since in many scientific works the uniform model of carrier distribution of Indium tin oxide (ITO) has been utilized, we want to investigate ENZ effect in ITO material and the effect of accurate carrier distribution on the performance of a modulator. For this reason, an electro-absorption (EA) modulators with a new configuration based on silicon slot modulator with indium thin oxide material is proposed. To study the effect of ENZ effect in ITO, the semiconductor model (realistic model) is utilized to model the carrier distribution in the ITO material. In this model, there is not any assumption. As a result, by applying the gate voltage, the insertion loss is increased 1.61 dB/μm in comparison with unbiased conditions. Also, the uniform model is used. Compared with the realistic model, the extinction ratio and figure-of-merit significantly enhance based on the uniform model, but the trends of results like insertion loss are so far from the realistic model. It can be found that the realistic model is reliable and the results are closer to reality.

     

The use of the inverted linear model of enzyme decay to plan a strategy for enzymatic batch reactions and to assess the industrial applicability of immobilized enzyme preparations

This article is concerned with the development of a model to plan a strategy for an enzymatic batch process where enzyme is subjected to deactivation described by the inverted linear decay model. The particular system studied is the enzymatic hydrolysis of penicillin to 6-amino penicillanic acid (6 APA), but the model can be utilized with other batch systems as long as the decay of the immobilized enzyme (IME) preparation is described by the inverted linear decay model. The model developed is eminently practical and simple and several example of its application are shown. Experimental data obtained in a small pilot plant batch recirculated reactor on the average are well fitted by this model. For IME systems whose decay is best described by the first-order decay model, it is not possible to use the same approach.     

Analysis of the Lynch-Granger model for olfactory cortex

The behavior of the Lynch-Granger model for layer-II piriform cortex is reviewed, and a simple neural model with similar properties is introduced. This model allows us to understand the observed functionality of the Lynch-Granger model intuitively, and suggests which of the many biological facts introduced into the original model are relevant to this particular behavior.     

Prediction of the power of detection of marker-quantitative trait locus linkages using analysis of variance

Analysis of variance can be used to detect the linkage of segregating quantitative trait loci (QTLs) to molecular markers in outbred populations. Using independent full-sib families and assuming linkage equilibrium, equations to predict the power of detection of a QTL are described. These equations are based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed. A simple prediction of power from the mean squares is used that assumes a random model so that in the mixed-model situation this is an approximation. Simulation is used to illustrate the failure of the random model to predict mean squares and, hence, the power. The mixed model is shown to provide accurate prediction of the mean squares and, using the approximation, of power.     

Experimental evaluation of a model for cometabolism: Prediction of simultaneous degradation of trichloroethylene and methane by a methanotrophic mixed culture

A model for cometabolism is verified experimentally for a defined methanotrophic mixed culture. The model includes the effects of cell growth, endogenous cell decay, product toxicity, and competitive inhibition with the assumption that cometabolic transformation rates are enhanced by reducing power obtained from oxidation of growth substrates. A theoretical transformation yield is used to quantify the enhancement resulting from growth substrate oxidation. A systematic method for evaluating model parameters independently is described. The applicability of the model is evaluated by comparing experimental data for methanotrophic cometabolism of TCE with model predictions from independently measured model parameters. Propagation of errors is used to quantify errors in parameter estimates and in the final prediction. The model successfully predicts TCE transformation and methane utilization for a wide range of concentrations of TCE (0.5 to 9 mg/L) and methane (0.05 to 6 mg/L). (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 492-501, 1997.     

A Stochastic Model of the Repetitive Activity of Neurons

A recurrent model of the repetitive firing of neurons responding to stimuli of long duration is given. The model assumes a deterministic threshold potential and a membrane potential which is composed of both deterministic and random components. The model accurately reproduces interval statistics obtained from different neurons discharging repetitively over a wide range of discharge rates. It is shown that the model has three important parameters; the time course of threshold recovery following a discharge, the variance of the random component, and the level of excitatory drive. The model is extended, by the use of hyperpolarizing afterpotentials, to include negative correlation between successive interspike intervals.     

Asymptotic analysis of a chemotactic model of bacteria colonies

An estimate of the distance between spots generated by a bacterial colony model is obtained. The model describes the morphogenesis of a spot pattern in colonies of chemotactic strains of Escherichia coli. Asymptotic methods for other cell-chemotaxis models, which have been successfully used by previous researchers, can be applied also to this model. However the calculations and the result is more complicated for this model. The result is verified by comparing it with the results by numerical computations of solutions of the model.