Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relatio...

We present a novel parameterization-independent exposition of the thirdorder geometric behavior of a surface point. Unlike existing algebraic expositions, our work produces an intuitive explanation of third-order shape, analogous to the principal curvatures and directions that describe secondorder shape. We extract four parameters that provide a quick and concise understanding of the third-orde...

Prior studies have revealed associations of current lead exposure (blood lead) and past lead exposure (bone lead) with risks of hypertension and elevated blood pressure. The authors examined the effects of blood and bone lead on hypertension and elevated blood pressure in the third trimester and postpartum among 1,006 women enrolled in Los Angeles prenatal care clinics between 1995 and 2001. Th...

A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model param...

Any geometric algorithm can be dissected into combinatorial parts and geometric parts. The two parts intertwine in both the description and the implementation of the algorithm. We consider the benefits of relaxing this tight coupling. Coordinate freedom is widely considered the most important principle in designing and implementing geometric systems. By ensuring that client code not manipulate ...

Spatial memories are often organized around reference frames, and environmental shape provides a salient cue to reference frame selection. To date, however, the environmental cues responsible for influencing reference frame selection remain relatively unknown. To connect research on reference frame selection with that on orientation via environmental shape, we explored the extent to which geome...

We compare the standard and geometric approaches to quantum Liouville theory on the pseudosphere by performing perturbative calculations of the one and two point functions up to the third order in the coupling constant. The choice of the Hadamard regularization within the geometric approach leads to a discrepancy with the standard approach. On the other hand, we find complete agreement between ...

Abstract: The divergence function in information geometry, and the discrete Lagrangian in discrete 1 geometric mechanics each induce a differential geometric structure on the product manifold QˆQ. 2 We aim to investigate the relationship between these two objects, and the fundamental role that 3 duality, in the form of Legendre transforms, play in both fields. By establishing an analogy between...

Many classical inequalities are just statements about the convexity or concavity of certain (hidden) underlying functions. This is nicely illustrated by Hardy, Littlewood, and Pólya [5] whose Chapter III deals with “Mean values with an arbitrary function and the theory of convex functions,” and by Steele [12] whose Chapter 6 is called “Convexity—The third pillar.” Yet another illustration is th...

Using superisolated singularities we present examples and counterexamples to some of the most important conjectures regarding invariants of normal surface singularities. More precisely, we show that the " Seiberg-Witten invariant conjecture " (of Nicolaescu and the third author), the " Universal abelian cover conjecture " (of Neumann and Wahl) and the " Geometric genus conjecture " fail (at lea...