Thomas Decomposition of Algebraic and Differential Systems

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple

Study of secondary-flow patterns in an annular cascade of turbine nozzle blades with vortex design

In order to increase understanding of the origin of losses in a turbine, the secondary-flow components in the boundary layers and the blade wakes of an annular cascade of turbine nozzle blades (vortex design) was investigated. A detailed study was made of the total-pressure contours and, particularly, of the inner-wall loss cores downstream of the blades. The inner-wall loss core associated with a blade of the turbine-nozzle cascade is largely the accumulation of low-momentum fluids originating elsewhere in the cascade. This accumulation is effected by a secondary-flow mechanism which acts to transport the low-momentum fluids across the channels on the walls and radially in the blade wakes and boundary layers. The patterns of secondary flow were determined by use of hydrogen sulfide traces, paint, flow fences, and total pressure surveys. At one flow condition investigated, the radial transport of low-momentum fluid in the blade wake and on the suction surface near the trailing edge accounted for 65 percent of the loss core; 30 percent resulted from flow in the thickened boundary layer on the suction surface and 35 percent from flow in the blade wake

Comparison of secondary flows and boundary-layer accumulations in several turbine nozzles

An investigation was made of losses and secondary flows in three different turbine nozzle configurations in annular cascade. Appreciable outer shroud loss cores (passage vortices) were found to exist at the discharge of blades which had thickened suction surface boundary layers near the outer shroud. Blade designs having thinner boundary layers did not show such outer shroud loss cores, but indicated greater inward radial flow of low momentum air, in the wake loss is to this extent an indication of the presence or absence of radial flow. The blade wake was a combination of profile loss and low momentum air from the outer shroud, and the magnitude of the wake loss is to this extent an indication of the presence or absence of radial flow. At a high Mach number, shock-boundary-layer thickening on the blade suction surfaces provided an additional radial flow path for low momentum air, which resulted in large inner shroud loss regions accompanied by large deviations from design values of discharge angle. (author

An Exact No Free Lunch Theorem for Community Detection

A precondition for a No Free Lunch theorem is evaluation with a loss function which does not assume a priori superiority of some outputs over others. A previous result for community detection by Peel et al. (2017) relies on a mismatch between the loss function and the problem domain. The loss function computes an expectation over only a subset of the universe of possible outputs; thus, it is only asymptotically appropriate with respect to the problem size. By using the correct random model for the problem domain, we provide a stronger, exact No Free Lunch theorem for community detection. The claim generalizes to other set-partitioning tasks including core/periphery separation, $k$-clustering, and graph partitioning. Finally, we review the literature of proposed evaluation functions and identify functions which (perhaps with slight modifications) are compatible with an exact No Free Lunch theorem

Arabidopsis TAO1 is a TIR-NB-LRR protein that contributes to disease resistance induced by the Pseudomonas syringae effector AvrB

The type III effector protein encoded by avirulence gene B (AvrB) is delivered into plant cells by pathogenic strains of Pseudomonas syringae. There, it localizes to the plasma membrane and triggers immunity mediated by the Arabidopsis coiled-coil (CC)-nucleotide binding (NB)-leucine-rich repeat (LRR) disease resistance protein RPM1. The sequence unrelated type III effector avirulence protein encoded by avirulence gene Rpm1 (AvrRpm1) also activates RPM1. AvrB contributes to virulence after delivery from P. syringae in leaves of susceptible soybean plants, and AvrRpm1 does the same in Arabidopsis rpm1 plants. Conditional overexpression of AvrB in rpm1 plants results in leaf chlorosis. In a genetic screen for mutants that lack AvrB-dependent chlorosis in an rpm1 background, we isolated TAO1 (target of AvrB operation), which encodes a Toll-IL-1 receptor (TIR)-NB-LRR disease resistance protein. In rpm1 plants, TAO1 function results in the expression of the pathogenesis-related protein 1 (PR-1) gene, suggestive of a defense response. In RPM1 plants, TAO1 contributes to disease resistance in response to Pto (P. syringae pathovars tomato) DC3000(avrB), but not against Pto DC3000(avrRpm1). The tao1–5 mutant allele, a stop mutation in the LRR domain of TAO1, posttranscriptionally suppresses RPM1 accumulation. These data provide evidence of genetically separable disease resistance responses to AvrB and AvrRpm1 in Arabidopsis. AvrB activates both RPM1, a CC-NB-LRR protein, and TAO1, a TIR-NB-LRR protein. These NB-LRR proteins then act additively to generate a full disease resistance response to P. syringae expressing this type III effector