Is there a best model structure? II. Comparing the model structures of different fate models

Activated sludge models are widely used for planning and optimisation of wastewater treatment plants and on line applications are under development to support the operation of complex treatment plants. A proper model is crucial for all of these applications. The task of parameter calibration is focused in several papers and applications. An essential precondition for this task is an appropriately defined model structure, which is often given much less attention. Different model structures for a large scale treatment plant with circulation flow are discussed in this paper. A more systematic method to derive a suitable model structure is applied to this case. Results of a numerical hydraulic model are used for this purpose. The importance of these efforts are proven by a high sensitivity of the simulation results with respect to the selection of the model structure and the hydraulic conditions. Finally it is shown, that model calibration was possible only by adjusting to the hydraulic behaviour and without any changes of biological parameters.

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New model structures and projective (injective) cotorsion pairs

Journal of Algebra and Its Applications ◽

10.1142/s0219498823500366 ◽

2021 ◽

Author(s):

Aimin Xu

Keyword(s):

Positive Integer ◽

Triangulated Categories ◽

Model Structure ◽

Cotorsion Pair ◽

Flat Dimension ◽

Gorenstein Projective Module ◽

Chain Complexes ◽

Cotorsion Pairs ◽

Gorenstein Injective ◽

Model Structures

Let [Formula: see text] be either the category of [Formula: see text]-modules or the category of chain complexes of [Formula: see text]-modules and [Formula: see text] a cofibrantly generated hereditary abelian model structure on [Formula: see text]. First, we get a new cofibrantly generated model structure on [Formula: see text] related to [Formula: see text] for any positive integer [Formula: see text], and hence, one can get new algebraic triangulated categories. Second, it is shown that any [Formula: see text]-strongly Gorenstein projective module gives rise to a projective cotorsion pair cogenerated by a set. Finally, let [Formula: see text] be an [Formula: see text]-module with finite flat dimension and [Formula: see text] a positive integer, if [Formula: see text] is an exact sequence of [Formula: see text]-modules with every [Formula: see text] Gorenstein injective, then [Formula: see text] is injective.

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Cotorsion pairs and model structures on Ch(R)

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091510000489 ◽

2011 ◽

Vol 54 (3) ◽

pp. 783-797 ◽

Cited By ~ 26

Author(s):

Gang Yang ◽

Zhongkui Liu

Keyword(s):

Model Structure ◽

Cotorsion Pair ◽

Projective Model ◽

Cotorsion Pairs ◽

Category Of Modules ◽

The Given ◽

Model Structures

AbstractWe show that if the given cotorsion pair $(\mathcal{A},\mathcal{B})$ in the category of modules is complete and hereditary, then both of the induced cotorsion pairs in the category of complexes are complete. We also give a cofibrantly generated model structure that can be regarded as a generalization of the projective model structure.

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The influence of conceptual model structure on model performance: a comparative study for 237 French catchments

Hydrology and Earth System Sciences ◽

10.5194/hess-17-4227-2013 ◽

2013 ◽

Vol 17 (10) ◽

pp. 4227-4239 ◽

Cited By ~ 51

Author(s):

W. R. van Esse ◽

C. Perrin ◽

M. J. Booij ◽

D. C. M. Augustijn ◽

F. Fenicia ◽

...

Keyword(s):

Conceptual Model ◽

Performance Metrics ◽

Low Flow ◽

Multiple Time ◽

Large Set ◽

Model Structure ◽

Flow Measurements ◽

Flexible Approach ◽

Fixed Model ◽

Model Structures

Abstract. Models with a fixed structure are widely used in hydrological studies and operational applications. For various reasons, these models do not always perform well. As an alternative, flexible modelling approaches allow the identification and refinement of the model structure as part of the modelling process. In this study, twelve different conceptual model structures from the SUPERFLEX framework are compared with the fixed model structure GR4H, using a large set of 237 French catchments and discharge-based performance metrics. The results show that, in general, the flexible approach performs better than the fixed approach. However, the flexible approach has a higher chance of inconsistent results when calibrated on two different periods. When analysing the subset of 116 catchments where the two approaches produce consistent performance over multiple time periods, their average performance relative to each other is almost equivalent. From the point of view of developing a well-performing fixed model structure, the findings favour models with parallel reservoirs and a power function to describe the reservoir outflow. In general, conceptual hydrological models perform better on larger and/or wetter catchments than on smaller and/or drier catchments. The model structures performed poorly when there were large climatic differences between the calibration and validation periods, in catchments with flashy flows, and in catchments with unexplained variations in low flow measurements.

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Hybrid Model Structure for Diabetic Retinopathy Classification

Journal of Healthcare Engineering ◽

10.1155/2020/8840174 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Hao Liu ◽

Keqiang Yue ◽

Siyi Cheng ◽

Chengming Pan ◽

Jie Sun ◽

...

Keyword(s):

Diabetic Retinopathy ◽

Hybrid Model ◽

Network Models ◽

Classification Performance ◽

Cross Entropy ◽

Model Structure ◽

Training Process ◽

Neural Network Models ◽

Entropy Loss ◽

Model Structures

Diabetic retinopathy (DR) is one of the most common complications of diabetes and the main cause of blindness. The progression of the disease can be prevented by early diagnosis of DR. Due to differences in the distribution of medical conditions and low labor efficiency, the best time for diagnosis and treatment was missed, which results in impaired vision. Using neural network models to classify and diagnose DR can improve efficiency and reduce costs. In this work, an improved loss function and three hybrid model structures Hybrid-a, Hybrid-f, and Hybrid-c were proposed to improve the performance of DR classification models. EfficientNetB4, EfficientNetB5, NASNetLarge, Xception, and InceptionResNetV2 CNNs were chosen as the basic models. These basic models were trained using enhance cross-entropy loss and cross-entropy loss, respectively. The output of the basic models was used to train the hybrid model structures. Experiments showed that enhance cross-entropy loss can effectively accelerate the training process of the basic models and improve the performance of the models under various evaluation metrics. The proposed hybrid model structures can also improve DR classification performance. Compared with the best-performing results in the basic models, the accuracy of DR classification was improved from 85.44% to 86.34%, the sensitivity was improved from 98.48% to 98.77%, the specificity was improved from 71.82% to 74.76%, the precision was improved from 90.27% to 91.37%, and the F1 score was improved from 93.62% to 93.9% by using hybrid model structures.

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Impact of the models structure uncertainty in flood simulations: Simbach case study

10.5194/egusphere-egu2020-15216 ◽

2020 ◽

Author(s):

Qing Lin ◽

Jorge Leandro ◽

Markus Disse ◽

Daniel Sturm

Keyword(s):

Flash Flood ◽

Drainage System ◽

Model Structure ◽

Flood Simulation ◽

Hydraulic Models ◽

Uncertainty Factor ◽

Model Component ◽

Model Structure Uncertainty ◽

Flood Simulations ◽

Model Structures

The quantification of model structure uncertainty on hydraulic models is very important for flash flood simulations. The choice of an appropriate model structure complexity and assessment of the impacts due to infrastructure failure can have a huge impact on the simulation results. To assess the risk of flash floods, coupled hydraulic models, including 1D-sewer drainage and 2D-surface run-off models are required for urban areas because they include the bidirectional water exchange, which occurs between sewer and overland flow in a city [1]. By including various model components, we create different model structures. For example, modelling the inflow to the city with the 2D surface-runoff or with the delineated 1D model; including the sewer system or use a surrogate as an alternative; modifying the connectivity of manholes and pumps; or representing the drainage system failures during flood events. As the coupling pattern becomes complex, quantifying the model structure uncertainty is essential for the model structure evaluation. If one model component leads to higher model uncertainty, it is reasonable to conclude that the new component has a large impact in our model and therefore needs to be accounted for; if one component has a less impact in the overall uncertainty, then the model structure can be simplified, by removing that model component. In this study, we set up seven different model structures [2] for the German city of Simbach. By comparison with two inflow calculation types (1D-delineated inflow or 2D-catchment), the existence of drainage system and infrastructure failures, the Model Uncertainty Factor (MUF) is calculated to quantify the model structure uncertainties and further trade-off values with Parameter Uncertainty Factor (PUF) [3]. Finally, we can obtain a more efficient hydraulic model with the essential model structure for urban flash flood simulation. &#160; <ol>1. Leandro, J., Chen, A. S., Djordjevic, S., and Dragan, S. (2009). "A comparison of 1D/1D and 1D/2D coupled hydraulic models for urban flood simulation." Journal of Hydraulic Engineering-ASCE, 6(1):495-504.</ol> <ol>2. Leandro, J., Schumann, A., and Pfister, A. (2016). A step towards considering the spatial heterogeneity of urban, key features in urban hydrology flood modelling. J. Hydrol., Elsevier, 535 (4), 356-365.</ol> <ol>3. Van Zelm, R., Huijbregts, M.A.J. (2013). Quantifying the trade-off between parameter and model structure uncertainty in life cycle impact assessment, Environ. Sci. Technol., 47(16), pp. 9274-9280.</ol> &#160;

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Incremental model breakdown to assess the multi-hypotheses problem

10.5194/hess-2017-691 ◽

2017 ◽

Author(s):

Florian U. Jehn ◽

Lutz Breuer ◽

Tobias Houska ◽

Konrad Bestian ◽

Philipp Kraft

Keyword(s):

Model Performance ◽

Complex Model ◽

Model Parameters ◽

Model Structure ◽

Objective Functions ◽

Final Model ◽

Incremental Model ◽

Model Efficiency ◽

Improved Model ◽

Model Structures

Abstract. The ambiguous representation of hydrological processes have led to the formulation of the multiple hypotheses approach in hydrological modelling, which requires new ways of model construction. However, most recent studies focus only on the comparison of predefined model structures or building a model step-by-step. This study tackles the problem the other way around: We start with one complex model structure, which includes all processes deemed to be important for the catchment. Next, we create 13 additional simplified models, where some of the processes from the starting structure are disabled. The performance of those models is evaluated using three objective functions (logarithmic Nash-Sutcliffe, percentage bias and the ratio between root mean square error to the standard deviation of the measured data). Through this incremental breakdown, we identify the most important processes and detect the restraining ones. This procedure allows constructing a more streamlined, subsequent 15th model with improved model performance, less uncertainty and higher model efficiency. We benchmark the original Model 1 with the final Model 15 and find that the incremental model breakdown leads to a structure with good model performance, fewer but more relevant processes and less model parameters.

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The impact of hydrological model structure on the simulation of extreme runoff events

Natural Hazards and Earth System Science ◽

10.5194/nhess-21-961-2021 ◽

2021 ◽

Vol 21 (3) ◽

pp. 961-976

Author(s):

Gijs van Kempen ◽

Karin van der Wiel ◽

Lieke Anna Melsen

Keyword(s):

Hydrological Model ◽

Low Flow ◽

Temperate Climate ◽

Hydrological Process ◽

Model Structure ◽

Hydrological Models ◽

Climate Zones ◽

The Impact ◽

Model Structures ◽

Runoff Events

Abstract. Hydrological extremes affect societies and ecosystems around the world in many ways, stressing the need to make reliable predictions using hydrological models. However, several different hydrological models can be selected to simulate extreme events. A difference in hydrological model structure results in a spread in the simulation of extreme runoff events. We investigated the impact of different model structures on the magnitude and timing of simulated extreme high- and low-flow events by combining two state-of-the-art approaches: a modular modelling framework (FUSE) and large ensemble meteorological simulations. This combination of methods created the opportunity to isolate the impact of specific hydrological process formulations at long return periods without relying on statistical models. We showed that the impact of hydrological model structure was larger for the simulation of low-flow compared to high-flow events and varied between the four evaluated climate zones. In cold and temperate climate zones, the magnitude and timing of extreme runoff events were significantly affected by different parameter sets and hydrological process formulations, such as evaporation. In the arid and tropical climate zones, the impact of hydrological model structures on extreme runoff events was smaller. This novel combination of approaches provided insights into the importance of specific hydrological process formulations in different climate zones, which can support adequate model selection for the simulation of extreme runoff events.

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Model Structures for the 𝔸1-homotopy Category

The Norm Residue Theorem in Motivic Cohomology ◽

10.23943/princeton/9780691191041.003.0012 ◽

2019 ◽

pp. 175-212

Author(s):

Christian Haesemeyer ◽

Charles A. Weibel

Keyword(s):

Full Subcategory ◽

Homotopy Category ◽

Symmetric Power ◽

Model Structure ◽

Model Categories ◽

Simplicial Presheaves ◽

Basic Ideas ◽

Quillen Model ◽

Model Structures ◽

Bousfield Localization

This chapter provides the 𝔸1-local projective model structure on the categories of simplicial presheaves and simplicial presheaves with transfers. These model categories, written as Δ‎opPshv(Sm)𝔸1 and Δ‎op PST(Sm)𝔸1, are first defined. Their respective homotopy categories are Ho(Sm) and the full subcategory DM eff nis ≤0 of DM eff nis. Afterward, this chapter introduces the notions of radditive presheaves and ̅Δ‎-closed classes, and develops their basic properties. The theory of ̅Δ‎-closed classes is needed because the extension of symmetric power functors to simplicial radditive presheaves is not a left adjoint. This chapter uses many of the basic ideas of Quillen model categories, which is a category equipped with three classes of morphisms satisfying five axioms. In addition, much of the material in this chapter is based upon the technique of Bousfield localization.

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Am 1 Semiempirical Mo Calculations of Torsional Barriers and Structural Reorganization in Radical Ions of Pbo and Pbzt Model Structures

MRS Proceedings ◽

10.1557/proc-291-591 ◽

1992 ◽

Vol 291 ◽

Cited By ~ 1

Author(s):

John W. Connolly ◽

Douglas S. Dudis

Keyword(s):

Molecular Orbital ◽

Electronic Charge ◽

Model Structure ◽

Electrical Conductor ◽

Frontier Orbitals ◽

Structural Reorganization ◽

Anion Formation ◽

Highest Occupied Molecular Orbital ◽

Semiempirical Mo Calculations ◽

Model Structures

ABSTRACTAM 1 semiempirical calculations on model structures of neutral, anionic and cationic poly(p-phenylenebenzobisthiazole), PBZT, offer an explanation why the PBZT anion has been shown to be an electrical conductor while the PBZT cation is not. To wit, the highest occupied molecular orbital (HOMO) in the PBZT model structure is centered primarily on the sulfur atoms, resulting in concentration of the positive charge on the sulfur atom when the cation is formed. The lowest occupied molecular orbital (LUMO) is far more delocalized and consequently anion formation produces a species which has electronic charge delocalized over the entire model structure. Similar calculations on model structures of neutral, anionic and cationic poly(p-phenyienebenzobisoxazole), PBO, indicate that both frontier orbitals, i. e., the HOMO and the LUMO are delocalized.

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