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.     

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     

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.     

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。     

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.

     

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 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.     

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.     

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.     

Assessing the Performance of Neural Encoding Models in the Presence of Noise

An analytical method is introduced for evaluating the performance of neural encoding models. The method addresses a critical question that arises during the course of the development and validation of encoding models: is a given model near optimal in terms of its accuracy in predicting the stimulus-elicited responses of a neural system, or can the predictive accuracy be improved significantly by further model development? The evaluation method is based on a derivation of the minimum mean-square error between actual responses and modeled responses. It is formulated as a comparison between the mean-square error of the candidate model and the theoretical minimum mean-square error attainable through an optimal model for the system. However, no a priori information about the nature of the optimal model is required. The theoretically minimum error is determined solely from the coherence function between pairs of system responses to repeated presentations of the same dynamic stimulus. Thus, the performance of the candidate model is judged against the performance of an optimal model rather than against that of an arbitrarily assumed model. Using this method, we evaluated a linear model for neural encoding by mechanosensory cells in the cricket cercal system. At low stimulus intensities, the best-fit linear model of encoding by single cells was found to be nearly optimal, even though the coherence between stimulus-response pairs (a commonly used measure of system linearity) was low. In this low-stimulus-intensity regime, the mean square error of the linear model was on the order of the power of the cell responses. In contrast, at higher stimulus intensities the linear model was not an accurate representation of neural encoding, even though the stimulus-response coherence was substantially higher than in the low-intensity regime.     

痛风性关节炎动物模型的改良

目的通过改良痛风性关节炎动物模型,制备出更符合人类痛风性关节炎机制的动物模型。方法通过Coderre法与次黄嘌呤相结合（模型B）、Coderre法与氧嗪酸相结合（模型A）的方法建立痛风性关节炎动物模型,采用全自动生化分析仪测定血尿酸水平,观察关节滑膜组织形态学改变及大鼠不同时相步态变化,并将两种方法加以比较。结果模型B组大鼠血尿酸水平显著降低,关节滑膜组织形态学及不同时相大鼠步态改变明显,与模型A组比较有统计学意义。结论Coderre法与次黄嘌呤相结合方法建立大鼠痛风性关节炎动物模型更符合人类痛风性关节炎机制的动物模型。     

Object-oriented graphical modeling of FMSs

Presented in the article is a method for constructing a graphical model of an FMS by using a new modeling tool called JR-net (Job Resource relation-net). JR-net is an object-oriented graphical tool for modeling automated manufacturing systems (AMSs), such as FMSs, FASs, and AS/RSs. As with the object-oriented modeling paradigm of Rumbaugh et al. (1991), the JR-net modeling framework supports the three stages of models: static layout model (object model); job flow model (functional model); and supervisory control model (dynamic model). In this article, the existing JR-net structure (Park 1992, Han et al., 1995) is extended further to make it a graphical tool for FMS modeling. Using the extended JR-net, a step-by-step procedure for constructing a graphical model of FMSs is presented. Also addressed are issues of classifying FMSs in terms of their generic functions and of utilizing the JR-net model of FMSs.     

Topographic components analysis of evoked potentials: estimation of model parameters and evaluation of parameter uniqueness

The purpose of this paper is to evaluate the practicability of the ‘topographic components model’ proposed by Möcks¹ for the spatio-temporal characterization of multi-channel evoked potentials (EP), and to present a complete and detailed algorithm for this method of analysis. Details of the algorithm are discussed along with various computational issues, especially with regard to contrasts with traditional principal components analysis. The algorithm is applied to multi-channel pattern-shift visual EP data obtained from normal subjects, and the model is demonstrated to provide data reduction of 71% with a relative mean-squared error (MSE) of 2%. Obvious features of the data are seen to be reflected in the estimated model parameters, lending support to the appropriateness of the model. The results also demonstrate that although the model parameters are uniquely identifiable in theory¹, care must be taken when fitting the model to insure that the MSE is not so insensitive to perturbations in the model parameters that they are rendered ‘non-unique’ for all practical purposes. The proper selection of model order is shown to play a critical role in avoiding this problem. Finally, a theoretical analysis is presented which evaluates the relationship between parameter ‘uniqueness’, model order, and the non-orthogonality of the model components.     

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.     

The principle of optimality as the foundation of biotechnological modeling

There are many points of contact between optimization problems and modeling. On the one hand the model adjustment process itself as a process of estimation is closely connected with optimization, in that it is to produce what is in one sense the best possible model. The basic structure of the optimization problem as problem in decision making with the necessary input of an objective function is thus evident. On the other hand a model is never an end in itself but on the basis of its simulation capacity a means to an end, for example in biotechnological optimization. From this point of view the model is a product of scientific work and thus an economic value. Equally, through its intended purpose the model exhibits a utility value. A complete evaluation of the model as a condition of rational modeling must take into account both these aspects. That is possible in principle by adding the modeling expenditure to expenditure for the realization of biotechnological processes, expressing the economic consequences of model quality as an objective function, and minimizing the specific total expenditure for the product to be produced. Biotechnological practice requires that the “optimum” model is approached by means of iterative processes. Some practical examples will make the process clear, taking into account qualitative (semantic) and quantitative (accuracy) aspects of the utility value.