Search Results (3)

The Gini coefficient, while widely used to quantify inequality in biological size distributions, lacks the capacity to resolve directional asymmetry inherent in Lorenz curves, a critical limitation for understanding skewed resource allocation strategies. To address this, we extend our prior geometric framework of the rotated and right-shifted Lorenz curve (RRLC) by introducing two original asymmetry metrics: the positional shift ratio (P_L, defined as $x_c/\sqrt{2}$, where $x_c$ is the x-coordinate of the RRLC’s maximum value point) and the area ratio (P_A, defined as A_L/(A_L + A_R), where A_L and A_R denote the areas under the left and right segments of the RRLC). These indices uniquely dissect contributions of dominant versus small individuals to overall inequality, with P_L reflecting the peak position of the RRLC and P_A quantifying the area dominance of its left segment. Theoretically, P_L directly links to the classical Lorenz asymmetry coefficient S (defined as $S=x_c^{\prime }+y_c^{\prime }$, where $\left(x_c^{\prime },y_c^{\prime }\right)$ is the tangent point on the original Lorenz curve with a 45° slope) through S = 2 − 2P_L, bridging geometric transformation and parametric asymmetry analysis. Applied to 480 Shibataea chinensis Nakai shoots, our analysis revealed that over 99% exhibited pronounced left-skewed distributions, where abundant large leaves drove the majority of leaf area inequality, challenging assumptions of symmetry in plant canopy resource allocation. The framework’s robustness was further validated by the strong correlation between P_A and P_L. By transforming abstract Lorenz curves into interpretable bell-shaped performance curves, this work provides a novel toolkit for analyzing asymmetric size distributions in ecology. The proposed metrics can be applied to refine light-use models, monitor phenotypic plasticity under environmental stress, and scale trait variations across biological hierarchies, thereby advancing both theoretical and applied research in plant ecology. Full article

Ethylene-Vinyl Acetate (EVA) copolymer was synthesized from ethylene and vinyl acetate at high temperatures and ultra-high pressures. In this condition, any reactor disturbances, such as process or mechanical faults, may trigger the run-away decomposition reaction. This paper proposes a procedure for constructing a conditional health status prediction structure that uses a virtual health index (HI) to monitor the reactor bearing’s remaining useful life (RUL). The piecewise linear remaining useful life (PL-RUL) model was constructed by machine learning regression methods trained on the vibration and distributed control system (DCS) datasets. This process consists of using Welch’s power spectrum density transformation and machine learning regression methods to fit the PL-RUL model, following a health status construction process. In this research, we search for and determine the optimum value for the remaining useful life period (T_RUL), a key parameter for the PL-RUL model for the system, as 70 days. This paper uses four-fold cross-validation to evaluate seven different regression algorithms and concludes that the Extremely randomized trees (ERTs) is the best machine learning model for predicting PL-RUL, with an average relative absolute error (RAE) of 0.307 and a Linearity of 15.064. The Gini importance of the ensemble trees is used to identify the critical frequency bands and prepare them for additional dimensionality reduction. Compared to two frequency band selection techniques, the RAE and Linearity prediction results can be further improved to 0.22 and 8.38. Full article

This paper presents and compares several text classification models that can be used to extract the outcome of a judgment from justice decisions, i.e., legal documents summarizing the different rulings made by a judge. Such models can be used to gather important statistics about cases, e.g., success rate based on specific characteristics of cases’ parties or jurisdiction, and are therefore important for the development of Judicial prediction not to mention the study of Law enforcement in general. We propose in particular the generalized Gini-PLS which better considers the information in the distribution tails while attenuating, as in the simple Gini-PLS, the influence exerted by outliers. Modeling the studied task as a supervised binary classification, we also introduce the LOGIT-Gini-PLS suited to the explanation of a binary target variable. In addition, various technical aspects regarding the evaluated text classification approaches which consists of combinations of representations of judgments and classification algorithms are studied using an annotated corpora of French justice decisions. Full article