16,391 research outputs found
On Effective Constraints for the Riemann-Lanczos System of Equations
There have been conflicting points of view concerning the Riemann--Lanczos
problem in 3 and 4 dimensions. Using direct differentiation on the defining
partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar
(in dimensions n > 2) have argued that there are effective constraints so that
not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of
integrability of ideals of differential forms Bampi and Caviglia have argued
that there are no such constraints in dimensions n < 5, and that, in these
dimensions, all Riemann tensors can have Lanczos potentials. In this paper we
give a simple direct derivation of a constraint equation, confirm explicitly
that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue
that the Bampi and Caviglia conclusion must therefore be flawed. In support of
this, we refer to the recent work of Dolan and Gerber on the three dimensional
problem; by a method closely related to that of Bampi and Caviglia, they have
found an 'internal identity' which we demonstrate is precisely the three
dimensional version of the effective constraint originally found by Massa and
Pagani, and Edgar.Comment: 9pages, Te
Correlation of satellite lightning observations with ground-based lightning experiments in Florida, Texas and Oklahoma
Satellite observations of lightning were correlated with ground-based measurements of lightning from data bases obtained at three separate sites. The percentage of ground-based observations of lightning that would be seen by an orbiting satellite was determined
A local potential for the Weyl tensor in all dimensions
In all dimensions and arbitrary signature, we demonstrate the existence of a
new local potential -- a double (2,3)-form -- for the Weyl curvature tensor,
and more generally for all tensors with the symmetry properties of the Weyl
curvature tensor. The classical four-dimensional Lanczos potential for a Weyl
tensor -- a double (2,1)-form -- is proven to be a particular case of the new
potential: its double dual.Comment: 7 pages; Late
Comparison of Randomized Multifocal Mapping and Temporal Phase Mapping of Visual Cortex for Clinical Use
fMRI is becoming an important clinical tool for planning and guidance of surgery to treat brain tumors, arteriovenous malformations, and epileptic foci. For visual cortex mapping, the most popular paradigm by far is temporal phase mapping, although random multifocal stimulation paradigms have drawn increased attention due to their ability to identify complex response fields and their random properties. In this study we directly compared temporal phase and multifocal vision mapping paradigms with respect to clinically relevant factors including: time efficiency, mapping completeness, and the effects of noise. Randomized, multifocal mapping accurately decomposed the response of single voxels to multiple stimulus locations and made correct retinotopic assignments as noise levels increased despite decreasing sensitivity. Also, multifocal mapping became less efficient as the number of stimulus segments (locations) increased from 13 to 25 to 49 and when duty cycle was increased from 25% to 50%. Phase mapping, on the other hand, activated more extrastriate visual areas, was more time efficient in achieving statistically significant responses, and had better sensitivity as noise increased, though with an increase in systematic retinotopic mis-assignments. Overall, temporal phase mapping is likely to be a better choice for routine clinical applications though random multifocal mapping may offer some unique advantages for selected applications
Interpreting a conformally flat pure radiation space-time
A physical interpretation is presented of the general class of conformally
flat pure radiation metrics that has recently been identified by Edgar and
Ludwig. It is shown that, at least in the weak field limit, successive wave
surfaces can be represented as null (half) hyperplanes rolled around a
two-dimensional null cone. In the impulsive limit, the solution reduces to a
pp-wave whose direction of propagation depends on retarded time. In the general
case, there is a coordinate singularity which corresponds to an envelope of the
wave surfaces. The global structure is discussed and a possible vacuum
extension through the envelope is proposed.Comment: 9 pages, Plain TeX, 2 figures. To appear in Class. Quantum Grav.
Reference adde
Nuclear processes associated with plant immunity and pathogen susceptibility
Plants are sessile organisms that have evolved exquisite and sophisticated mechanisms to adapt to their biotic and abiotic environment. Plants deploy receptors and vast signalling networks to detect, transmit and respond to a given biotic threat by inducing properly dosed defence responses. Genetic analyses and, more recently, next-generation -omics approaches have allowed unprecedented insights into the mechanisms that drive immunity. Similarly, functional genomics and the emergence of pathogen genomes have allowed reciprocal studies on the mechanisms governing pathogen virulence and host susceptibility, collectively allowing more comprehensive views on the processes that govern disease and resistance. Among others, the identification of secreted pathogen molecules (effectors) that modify immunity-associated processes has changed the plant–microbe interactions conceptual landscape. Effectors are now considered both important factors facilitating disease and novel probes, suited to study immunity in plants. In this review, we will describe the various mechanisms and processes that take place in the nucleus and help regulate immune responses in plants. Based on the premise that any process required for immunity could be targeted by pathogen effectors, we highlight and describe a number of functional assays that should help determine effector functions and their impact on immune-related processes. The identification of new effector functions that modify nuclear processes will help dissect nuclear signalling further and assist us in our bid to bolster immunity in crop plants
- …