Recent Advances in Spatial Interaction Modelling: An Application to the Forecasting of Shopping Travel

1987 ◽  
Vol 19 (2) ◽  
pp. 173-186 ◽  
Author(s):  
C M Guy
Keyword(s):  
Optimal Parameter ◽  
Spatial Interaction ◽  
Specific Model ◽  
Small Sample ◽  
Explanatory Variables ◽  
Interaction Modelling ◽  
Complex Models ◽  
Decay Parameters ◽  
Parameter Values ◽  
Specific Distance

A common problem in the use of singly-constrained spatial interaction shopping models has been that of finding optimal parameter values. This problem has been exacerbated where improvements to the model have involved extra parameters to be estimated. In this paper it is shown that calibration of quite complex models can be achieved through modification of the conventional ‘gravity’ model to a generalised linear model with Poisson error structure and logarithmic link function. Data on observed trips between fifteen residential zones and eighty-three shopping destinations in Cardiff are used to test several models through application of the GLIM computing package. Models involving extra explanatory variables, origin-specific distance-decay parameters, and competing-destinations terms are all shown to offer worthwhile improvements in performance over the conventional singly-constrained model. An individual-specific model is also tested for a small sample of shoppers. Finally, some comments are made concerning the relevance of the Cardiff findings and the wider significance of these methodological advances.

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

scholarly journals Selecting single cell clustering parameter values using subsampling-based robustness metrics

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Ryan B. Patterson-Cross ◽  
Ariel J. Levine ◽  
Vilas Menon
Keyword(s):  
Single Cell ◽  
Optimal Parameter ◽  
Clustering Algorithms ◽  
Cell Types ◽  
Parameter Selection ◽  
Data Set ◽  
Biologically Relevant ◽  
Cell Clustering ◽  
Parameter Values ◽  
Robustness Metrics

Abstract Background Generating and analysing single-cell data has become a widespread approach to examine tissue heterogeneity, and numerous algorithms exist for clustering these datasets to identify putative cell types with shared transcriptomic signatures. However, many of these clustering workflows rely on user-tuned parameter values, tailored to each dataset, to identify a set of biologically relevant clusters. Whereas users often develop their own intuition as to the optimal range of parameters for clustering on each data set, the lack of systematic approaches to identify this range can be daunting to new users of any given workflow. In addition, an optimal parameter set does not guarantee that all clusters are equally well-resolved, given the heterogeneity in transcriptomic signatures in most biological systems. Results Here, we illustrate a subsampling-based approach (chooseR) that simultaneously guides parameter selection and characterizes cluster robustness. Through bootstrapped iterative clustering across a range of parameters, chooseR was used to select parameter values for two distinct clustering workflows (Seurat and scVI). In each case, chooseR identified parameters that produced biologically relevant clusters from both well-characterized (human PBMC) and complex (mouse spinal cord) datasets. Moreover, it provided a simple “robustness score” for each of these clusters, facilitating the assessment of cluster quality. Conclusion chooseR is a simple, conceptually understandable tool that can be used flexibly across clustering algorithms, workflows, and datasets to guide clustering parameter selection and characterize cluster robustness.

A numerical method for determining optimal parameter values in forced periodic operation

1992 ◽  
Vol 47 (3) ◽  
pp. 605-613 ◽  
Author(s):  
Fatih Özgülşen ◽  
Raymond A. Adomaitis ◽  
Ali Çinar
Keyword(s):  
Numerical Method ◽  
Optimal Parameter ◽  
Periodic Operation ◽  
Parameter Values

Understanding the role of different geographical features in the hydrological response of humid mountainous areas through a stepwise clustering scheme

2021 ◽  
Author(s):  
Yaqian Yang ◽  
Jintao Liu
Keyword(s):  
Bulk Density ◽  
Optimal Parameter ◽  
Soil Bulk Density ◽  
Model Parameters ◽  
Hydrological Response ◽  
Runoff Generation ◽  
Explanatory Variables ◽  
Hydrological Responses ◽  
Rainfall Patterns

<p>In the mountainous basins with less anthropogenic influence, the hydrological function is mainly affected by climate and landscape, which makes it possible to measure hydrological similarity indirectly by geographical features. Due to the mechanisms of runoff generation can vary geographically, in this study, a simple stepwise clustering scheme was proposed to explore the role of geographical features at different spatial hierarchy in indicating hydrological response. Research methods mainly include (1) Stepwise regression was used to quantitatively show the correlation between 35 geographical features and 35 flow features and identify the important explanatory variables for hydrological response; (2) 64 basins were divided by stepwise clustering scheme, and the overall ability of the scheme to capture hydrological similarity was tested by comparing the optimal parameters; (3) The hydrological similarity of basin groups was measured by the leave-one cross validation of hydrological model parameters. The results showed that: (1) Rainfall features, elevation, slope and soil bulk density are the main explanatory variables. (2) The NSE of basin groups based on stepwise clustering is 0.64, reaches 80% of the optimal parameter sets (NSE=0.80). The NSE of 90% basins is greater than 0.5, 80% is greater than 0.6, and 49% is greater than 0.7. (3) In humid areas, the hydrological responses of the basins with more uniform monthly rainfall and more abundant summer rainfall are more similar, e.g., the NSE of Class 4 is 0.77. Under similar rainfall patterns, the hydrological responses of the basins with higher average altitude, greater slope, more convergent of shape and richer vegetation are more similar, e.g., the NSE of Class 3-2 is 0.72 and that of Class 1-2 is 0.70. In the case of similar rainfall patterns and landforms, the hydrological responses of the basins with smaller soil bulk density are more similar, e.g., the NSE of Class 3-2-2 is 0.80. In conclusion, the stepwise clustering enhances the interpretability of basin classification, and the effect of different geographical features on hydrological response can show the applicability of hydrological simulation in ungauged basins.</p>

scholarly journals Practical Credibility Theory with Emphasis on Optimal Parameter Estimation

1981 ◽  
Vol 12 (2) ◽  
pp. 115-131 ◽  
Author(s):  
F. De Vylder
Keyword(s):  
Optimal Parameter ◽  
Structural Parameters ◽  
Minimum Variance ◽  
Small Sample ◽  
Credibility Theory ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Real Problem ◽  
Estimation Problems ◽  
Optimal Estimators

We develop Hachemeister's regression model in credibility theory (without proofs) and indicate how the involved structural parameters can be estimated from the observable variables (with proofs for the simple results and those not yet published).Large families of unbiased estimators are available. From the practical viewpoint this is rather a handicap because it creates the problem to decide what estimators actually to use. In order to fix optimal estimators, we adopt the small-sample criterion of minimum-variance. But in the research for general solutions three kinds of difficulties arise.(i) The calculations become too lengthy.(ii) The optimal estimators depend on some of the parameters to be estimated. (Then we call them pseudo-estimators).(iii) The optimal estimators depend on new structural parameters defined in terms of fourth-order moments.Only a compromise allows to cope with this reality. Situation (iii) creates new estimation problems. They can only be avoided at the cost of the introduction of special assumptions or approximations. Then problem (i) is more or less automatically solved. By an obvious method of successive approximations pseudo-estimators can serve as true estimators. Thus (ii) is no real problem.

scholarly journals Computational Optimization Study of Transcatheter Aortic Valve Leaflet Design Using Porcine and Bovine Leaflets

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Stefano Travaglino ◽  
Kyle Murdock ◽  
Anh Tran ◽  
Caitlin Martin ◽  
Liang Liang ◽  
...  
Keyword(s):  
Aortic Valve ◽  
Stress Reduction ◽  
Optimal Parameter ◽  
Peak Stress ◽  
Bayesian Optimization ◽  
Fe Model ◽  
Computational Optimization ◽  
Transcatheter Aortic Valve ◽  
Biaxial Tensile Testing ◽  
Parameter Values

Abstract In this study, a Bayesian optimization (BO) based computational framework is developed to investigate the design of transcatheter aortic valve (TAV) leaflets and to optimize leaflet geometry such that its peak stress under the blood pressure of 120 mmHg is reduced. A generic TAV model is parametrized by mathematical equations describing its 2D shape and its 3D stent-leaflet assembly line. Material properties previously obtained for bovine pericardium (BP) and porcine pericardium (PP) via a combination of flexural and biaxial tensile testing were incorporated into the finite element (FE) model of TAV. A BO approach was employed to investigate about 1000 leaflet designs for each material under the nominal circular deployment and physiological loading conditions. The optimal parameter values of the TAV model were obtained, corresponding to leaflet shapes that can reduce the peak stress by 16.7% in BP and 18.0% in PP, compared with that from the initial generic TAV model. Furthermore, it was observed that while peak stresses tend to concentrate near the stent-leaflet attachment edge, optimized geometries benefit from more uniform stress distributions in the leaflet circumferential direction. Our analysis also showed that increasing leaflet contact area redistributes peak stresses to the belly region contributing to peak stress reduction. The results from this study may inspire new TAV designs that can have better durability.

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