We prove that every flat tensor-idempotent in the module category Mod- of a tensor-triangulated category comes from a unique smashing ideal in . We deduce that the lattice of smashing ideals forms a frame.

The diagnosis of smear-positive pulmonary tuberculosis in a medical officer working in a metropolitan Australian neonatal intensive care unit led to a contact investigation involving 125 neonates, 165 relatives, and 122 healthcare workers with varying degrees of exposure. There was no evidence of nosocomial tuberculosis transmission from the index case.

3D-MHD numerical simulations of bipolar, hypersonic, weakly magnetized jets and synthetic synchrotron observations are presented to study the structure and evolution of magnetic fields in FR II radio sources. The magnetic field setup in the jet is initially random. The power of the jets as well as the observational viewing angle are investigated. We find that synthetic polarization maps agree with observations and show that magnetic fields inside the sources are shaped by the jets' backflow. Polarimetry statistics correlates with time, the viewing angle and the jet-to-ambient density contrast. The magnetic structure inside thin elongated sources is more uniform than for ones with fatter cocoons. Jets increase the magnetic energy in cocoons, in proportion to the jet velocity. Both, filaments in synthetic emission maps and 3D magnetic power spectra suggest that turbulence develops in evolved sources.

Some weaknesses of current decision support technologies are discussed. Numerical methods have strong theoretical foundations but are representationally weak, and only deal with a small part of the decision process. Knowledge-based systems offer greater flexibility, but have not been accompanied by a clear decision theory. Theoretical development of symbolic decision procedures is advocated, an approach to the design of decision support systems based on first-order logic is presented, and work on this approach is reviewed. A central proposal is an extended form of inference called argumentation; reasoning qualitatively for and against decision options from generalized domain theories. Argumentation captures a natural and familiar form of reasoning, and contributes to the robustness, flexibility and intelligibility of problem solving, while having a clear theoretical basis. Argumentation was developed initially for medical applications though it may have much wider applicability.

This article surveys existing practical implementations of both defeasible and argumentation-based reasoning engines and associated literature. We aim to summarize the current state of the art in the research area, show that there are many similiarities and connections between the various implementations and also highlight the differences regarding evaluation goals and strategies. An important goal of this paper is to argue for the need for well-designed empirical evaluations, as well as formal complexity analysis, in order to justify the practical applicability of a reasoning engine. There are indeed many challenges to be faced in developing implementations of argumentation. Not least of these is the inherent computational complexity of the formal models. We cover some of the ways these challenges have been addressed, and provide pointers for future directions in realizing the goal of practical argumentation.