Phenomenological Transparency through Depth of “Inside/Outside” for a Sustainable Architectural Environment

The potential relationship between external and internal spaces in the architectural environment of the post-pandemic era is emerging as an essential issue. Since the early 20th century, the issue of transparency inside and outside architecture has been explored in various fields. This study is motivated by the lack of a leading theory about architectural transparency in the post-pandemic era. First, it revisits the notion of phenomenal transparency in Colin Rowe and Robert Slutzky’s influential text on “literal” and “phenomenal” transparency. Next, it investigates Maurice Merleau-Ponty’s phenomenology for architectural transparency. Last, it scrutinizes practical possibilities using cases from Sejima and Nishizawa and Associates (SAANA). It finds that intertwining the cognition of natural environment and spatial experiential perceptions can create phenomenological architectural experiences. Sustainable architectural transparency may be accomplished when three factors (the visual perception of space, spatial experiential perceptions, and the cognition of natural environment) are incorporated. Further, depth functions as a medium for architectural transparency, intertwining between material and immaterial, literal and phenomenal, and visible and invisible. There is tremendous potential to conduct pilot studies based on this study, to re-evaluate architectural transparency with phenomenological ideas.

Comparison-based centrality measures

Recently, learning only from ordinal information of the type “item x is closer to item y than to item z” has received increasing attention in the machine learning community. Such triplet comparisons are particularly well suited for learning from crowdsourced human intelligence tasks, in which workers make statements about the relative distances in a triplet of items. In this paper, we systematically investigate comparison-based centrality measures on triplets and theoretically analyze their underlying Euclidean notion of centrality. Two such measures already appear in the literature under opposing approaches, and we propose a third measure, which is a natural compromise between these two. We further discuss their relation to statistical depth functions, which comprise desirable properties for centrality measures, and conclude with experiments on real and synthetic datasets for medoid estimation and outlier detection.

Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions

Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based spatial depth versions. The classifiers' performance is considered and compared with some existing classification methods using simulated and real datasets.

Robust multivariate estimation based on statistical depth filters

In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or case-wise contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when the number of considered variables is moderately small. Alqallaf et al. (Ann Stat 37(1):311–331, 2009) show the limits of this approach for a larger number of variables and introduced the independent contamination model (cell-wise contamination) where now the cells are the units to be identified as outliers or not. One approach to deal, at the same time, with both type of contamination is filter out the contaminated cells from the data set and then apply a robust procedure able to handle case-wise outliers and missing values. Here, we develop a general framework to build filters in any dimension based on statistical data depth functions. We show that previous approaches, e.g., Agostinelli et al. (TEST 24(3):441–461, 2015b) and Leung et al. (Comput Stat Data Anal 111:59–76, 2017), are special cases. We illustrate our method by using the half-space depth.

Volumetric soil quality modelling with machine learning in a diverse agricultural landscape in Andalusia, Spain

<p>Soils and soil functions are recognized as a key resource for human well-being throughout time. In an agricultural and forestry perspective, soil functions contribute to food and timber production. Other soil functions are related to freshwater security and energy provisioning. In general, the capacity of a soil to function within specific boundaries is summarised as soil quality. Knowledge about the spatial distribution of soil quality is crucial for sustainable land use and the protection of soils and their functions. This spatial knowledge can be obtained with accurate and efficient machine-learning-based soil mapping approaches, which allow the estimation of the soil quality at distinct locations. However, the vertical distribution of soil properties is usually neglected when assessing soil quality at distinct locations. To overcome such limitations, the depth function of soil properties needs to be incorporated in the modelling. This is not only important to get a better estimation of the overall soil quality throughout the rooting zone, but also to identify factors that limit plant growth, such as strong acidity or alkalinity, and the water holding capacity. Thus, the objective of this study was to model and map the soil quality indicators pH, soil organic carbon, sand, silt and clay content as a volumetric entity. The study area is located in southern Spain in the Province of Seville at the Guadalquivir river. It covers 1,000 km<sup>2</sup> of farmland, citrus and olive plantations, pastures and wood pasture (Dehesa) in the Sierra Morena mountain range, at the Guadalquivir flood plain and tertiary terraces. Soil samples were taken at 130 soil profiles in five depths (or less at shallow soils). The profiles were randomly stratified depending on slope position and land cover. We used a subset of 99 samples from representative soil profiles to assess the overall 513 samples with FT-IR spectroscopy and machine learning methods to model equal-area spline, polynomial and exponential depth functions for each soil quality indicator at each of the 130 profiles. These depth functions were modelled and predicted spatially with a comprehensive set of environmental covariates from remote sensing data, multi-scale terrain analysis and geological maps. By solving the spatially predicted depth functions with a vertical resolution of 5 cm, we obtained a volumetric, i.e. three-dimensional, map of pH, soil organic carbon content and soil texture. Preliminary results are promising for volumetric soil mapping and the estimation of soil quality and limiting factors in three-dimensional space.</p>