Curvature conditions for the occurrence of a class of spacetime singularities

It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition.Comment: RevTeX, 6 pages, no figures. To be published in J. Math. Phy

Generalized Strong Curvature Singularities and Cosmic Censorship

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.Comment: LaTeX, 11 pages, no figures, to appear in Mod. Phys. Lett.

Feature Selection with the Boruta Package

This article describes a R package Boruta, implementing a novel feature selection algorithm for finding \emph{all relevant variables}. The algorithm is designed as a wrapper around a Random Forest classification algorithm. It iteratively removes the features which are proved by a statistical test to be less relevant than random probes. The Boruta package provides a convenient interface to the algorithm. The short description of the algorithm and examples of its application are presented.

Effective Normal Stress Alteration due to Pore Pressure Changes Induced by Dynamic Slip Propagation on a Plane Between Dissimilar Materials

Recent, detailed examinations of fault zones show that walls of faults are often bordered by materials that are different from each other and from the more uniform material farther away. In addition, they show that the ultracataclastic core of mature fault zones, where slip is concentrated, is less permeable to flow across it than the adjoining material of the damage zone. Inhomogeneous slip at the interface between materials with different poroelastic properties and permeabilities causes a change in pore pressure there. Because slip causes compression on one side of the fault wall and extension on the other, the pore pressure on the fault increases substantially when the compressed side is significantly more permeable and decreases when, instead, the extended side is more permeable. This change in pore pressure alters the effective normal stress on the slip plane in a way that is analogous to the normal stress alteration in sliding between elastically dissimilar solids. The magnitude of the effect due to induced pore pressure can be comparable to or larger than that induced by sliding between elastic solids with a dissimilarity of properties consistent with seismic observations. The induced pore pressure effect is increased by increasing contrast in permeability, but the normal stress alteration due to elastic contrast increases rapidly as the rupture velocity approaches the generalized Rayleigh velocity. Because the alteration in effective normal stress due to either effect can be positive or negative, depending on the contrast in properties, the two effects can augment or offset each other.Earth and Planetary SciencesEngineering and Applied Science

Feature Selection with the Boruta Package

This article describes a R package Boruta, implementing a novel feature selection algorithm for finding emph{all relevant variables}. The algorithm is designed as a wrapper around a Random Forest classification algorithm. It iteratively removes the features which are proved by a statistical test to be less relevant than random probes. The Boruta package provides a convenient interface to the algorithm. The short description of the algorithm and examples of its application are presented