The Lorenz curve for assessing economic inequality depicts the relation between two cumulative distribution functions (CDFs), one for the distribution of incomes or wealth and the other for their first-moment distribution. By contrast, the receiver operating characteristic (ROC) curve for evaluating diagnostic systems depicts the relation between the complements of two CDFs, one for the distrib...

Given two distinct points S and E on a simply-connected domain (without holes) enclosed by a closed parametric curve, this paper provides an algorithm to find the shortest interior path (SIP) between the two points in the domain. SIP consists of portions of curves along with straight line segments that are tangential to the curve. The algorithm initially computes point-curve tangents and bitang...

High-resolution spectra, including hyperfine structure, have been observed for numerous vibrational-rotational levels (v ,N) of the 4 S Rydberg state of the NaK molecule. The data have been used to construct a Rydberg–Klein–Rees potential curve, and this molecular potential has been further refined using the inverse perturbation approximation method. Bound-free emission from the 4 S electronic ...

Abstract We study the Glauber dynamics of a two dimensional Blume-Capel model (or dilute Ising model) with Kac potential parametrized by (β, θ) the “inverse temperature” and the “chemical potential”. We prove that the locally averaged spin field rescales to the solution of the dynamical Φ4 equation near a curve in the (β, θ) plane and to the solution of the dynamical Φ6 equation near one point ...

Several applications of nonlinear principal component analysis (NPCA) have appeared recently in process monitoring and fault diagnosis. In this paper a new approach is proposed for fault detection based on principal curves and genetic algorithms. The principal curve is a generation of linear principal component (PCA) introduced by Hastie as a parametric curve passes satisfactorily through the m...

Humans achieve greater jump height during a counter-movement jump (CMJ) than in a squat jump (SJ). However, the crucial difference is the mean mechanical power output during the propulsion phase, which could be determined by intrinsic neuro-muscular mechanisms for power production. We measured M. vastus lateralis (VL) fascicle length changes and activation patterns and assessed the force-length...

We study the Yang-Lee zeros of a random matrix partition function with the global symmetries of the QCD partition function. We consider both zeros in the complex chemical potential plane and in the complex mass plane. In both cases we find that the zeros are located on a curve. In the thermodynamic limit, the zeros appear to merge to form a cut. The shape of this limiting curve can be obtained ...