Scheduling precedence graphs of bounded height

The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384–393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22–35; D. Dolev and M. K. Warmuth, “Scheduling Flat Graphs,” IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.     

Oxoneptunium(v) as part of the framework of a polyoxometalate

(NH4)14Na4[(Np3W4O15)(H2O)3(BiW9O33)3].62H2O (1) and (NH4)14.5Na3.5[(Np3W4O15)(H2O)3(SbW9O33)3].40.5H2O (2) each contain three neptunyl(v) moieties encapsulated within heteropolyoxotungstate frameworks in which axial {NpO2}+ oxygens form one face of a WO6 octahedron.     

Functional exploration of the human spinal cord during voluntary movement and somatosensory stimulation

Demonstrations of the possibility of obtaining functional information from the spinal cord in humans using functional magnetic resonance imaging (fMRI) have been growing in number and sophistication, but the technique and the results that it provides are still perceived by the scientific community with a greater degree of scepticism than fMRI investigations of brain function. Here we review the literature on spinal fMRI in humans during voluntary movements and somatosensory stimulation. Particular attention is given to study design, acquisition and statistical analysis of the images, and to the agreement between the obtained results and existing knowledge regarding spinal cord anatomy and physiology.     

Multi-shot turbo spin-echo for 3D vascular space occupancy imaging

Vascular space occupancy (VASO) is a magnetic resonance imaging technique sensitive to cerebral blood volume, and is a potential alternative to the blood oxygenation level dependent (BOLD) sensitive technique as a basis for functional mapping of the neurovascular response to a task. Many implementations of VASO have made use of echo-planar imaging strategies that allow rapid acquisition, but risk introducing potentially confounding BOLD effects. Recently, multi-slice and 3D VASO techniques have been implemented to increase the imaging volume beyond the single slice of early reports. These techniques usually rely, however, on advanced scanner software or hardware not yet available in many centers. In the present study, we have implemented a short-echo time, multi-shot 3D Turbo Spin-Echo (TSE) VASO sequence that provided 8-slice coverage on a routine clinical scanner. The proposed VASO sequence was tested in assessing the response of the human motor cortex during a block design finger tapping task in 10 healthy subjects. Significant VASO responses, inversely correlated with the task, were found at both individual and group level. The location and extent of VASO responses were in close correspondence to those observed using a conventional BOLD acquisition in the same subjects. Although the spatial coverage and temporal resolution achieved were limited, robust and consistent VASO responses were observed. The use of a susceptibility insensitive volumetric TSE VASO sequence may have advantages in locations where conventional BOLD and echo-planar based VASO imaging is compromised.     

Avoided-crossing-based liquid-crystal photonic-bandgap notch filter

We demonstrate a highly tunable deep notch filter realized in a liquid-crystal photonic-bandgap (LCPBG) fiber. The filter is realized without inducing a long-period grating in the fiber but simply by filling a solid-core photonic-crystal fiber with a liquid crystal and exploiting avoided crossings within the bandgap of the LCPBG fiber. The filter is demonstrated experimentally and investigated using numerical simulations. A high degree of tuning of the spectral position of the deep notch is also demonstrated.