Linear and non-linear relationships among the dimensions representing the cognitive structure of emotion

Abstract. The potential of an artificial neural network to perform simple non-linear hydrological transformations is examined. Four neural network models were developed to emulate different facets of a recognised non-linear hydrological transformation equation that possessed a small number of variables and contained no temporal component. The modeling process was based on a set of uniform random distributions. The cloning operation facilitated a direct comparison with the exact equation-based relationship. It also provided broader information about the power of a neural network to emulate existing equations and model non-linear relationships. Several comparisons with least squares multiple linear regression were performed. The first experiment involved a direct emulation of the Xinanjiang Rainfall-Runoff Model. The next two experiments were designed to assess the competencies of two neural solutions that were developed on a reduced number of inputs. This involved the omission and conflation of previous inputs. The final experiment used derived variables to model intrinsic but otherwise concealed internal relationships that are of hydrological interest. Two recent studies have suggested that neural solutions offer no worthwhile improvements in comparison to traditional weighted linear transfer functions for capturing the non-linear nature of hydrological relationships. Yet such fundamental properties are intrinsic aspects of catchment processes that cannot be excluded or ignored. The results from the four experiments that are reported in this paper are used to challenge the interpretations from these two earlier studies and thus further the debate with regards to the appropriateness of neural networks for hydrological modelling.

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Non-linear Relationships Between the Built Environment and Walking Frequency Among Older Adults in Zhongshan, China

Frontiers in Public Health ◽

10.3389/fpubh.2021.686144 ◽

2021 ◽

Vol 9 ◽

Author(s):

Jiani Wu ◽

Chunli Zhao ◽

Chaoyang Li ◽

Tao Wang ◽

Lanjing Wang ◽

...

Keyword(s):

Older Adults ◽

Land Use ◽

Built Environment ◽

Green Space ◽

Additive Model ◽

Walking Behavior ◽

Old Adults ◽

Linear Relationships ◽

Walking Activity ◽

Non Linear

Aim: Promoting walking activity is an effective way to improve the health of older adults. Walking frequency is a critical component of walking behavior and an essential determinant of daily walking levels. To decipher the association between the built environment and walking frequency among older adults, this study's aims are as follows: (1) to empirically test whether non-linear relationships between the two exist, and (2) to identify the thresholds of the built environment characteristics that promote walking.Methods: The walking frequency of old adults was derived from the Zhongshan Household Travel Survey (ZHTS) in 2012. The sample size of old adults aged 60 or over was 4784 from 274 urban and rural neighborhoods. A semi-parametric generalized additive model (GAMM) is used to analyze the non-linear or non-monotonic relationships between the built environment and the walking frequency among older adults.Results: We found that non-linear relationships exist among five out of the six built environment characteristics. Within certain thresholds, the population density, sidewalk density, bus stop density, land use mixture, and the percentage of green space are positively related to older adults' walking trips. Furthermore, the land use mixture and the percentage of green space show an inverse “V”-shaped relationship.Conclusions: Built environment features can either support or hinder the walking frequency among older adults. The findings in the current study contribute to effective land use and transport policies for promoting active travel among older adults.

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Exploring Non-Linear Relationships between Landscape and Aquatic Ecological Condition in Southern Wisconsin

International Journal of Applied Geospatial Research ◽

10.4018/ijagr.2014100101 ◽

2014 ◽

Vol 5 (4) ◽

pp. 1-20 ◽

Cited By ~ 19

Author(s):

Richard R. Shaker ◽

Timothy J. Ehlinger

Keyword(s):

Spatial Data ◽

Geographically Weighted Regression ◽

Ecological Integrity ◽

Linear Analysis ◽

Ecological Condition ◽

Linear Relationships ◽

Non Linear ◽

Complex Landscape ◽

Landscape Impacts

Recent studies have implied the importance of incorporating configuration metrics into landscape-aquatic ecological integrity research; however few have addressed the needs of spatial data while exploring non-linear relationships. This study investigates spatial dependence of a measure of aquatic ecological condition at two basin scales, and the spatial and non-linear role of landscape in explaining that measure across 92 watersheds in Southern Wisconsin. It hypothesizes that: (1) indicators of ecological condition have different spatial needs at subwatershed and watershed scales; (2) land cover composition, urban configuration, and landscape diversity can explain aquatic ecological integrity differently; and (3) global non-linear analysis improve local spatial statistical techniques for explaining and interpreting landscape impacts on aquatic ecological integrity. Results revealed spatial autocorrelation in the measure of aquatic ecological condition at the HUC-12 subwatershed scale, and artificial neural networks (ANN) were an improvement over geographically weighted regression (GWR) for deciphering complex landscape-aquatic condition relationships.

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