Hook of the hamate fractures are uncommon. This fracture is usually seen in sports involving a club or a racquet (i.e., baseball or golf) and is caused by blunt trauma. Stress fractures of the hamate are exceedingly rare. Because of its subcutaneous position and associated soft tissue structures, hook of the hamate fractures can be difficult to diagnosis. When treated early, conservative (non-o...

1. Hook analysis of the washing experiment of Skvortsov et al. To illustrate the benefits of the hook approach we transform the intensity-data of a second washing experiment published recently by Skvortzov et al. [1] into hook-graphs (see Supplementary Figure 1). In this particular experiment the authors labelled only a small number of 18-20 transcripts each of which is interrogated by one 'spi...

Let λ = (λ1, λ2, . . . , λl), λ1 ≥ λ2 ≥ . . . ≥ λl > 0, be a partition of n, λ ⊢ n, and let [λ] = {(i, j) ∈ Z : 1 ≤ i ≤ l, 1 ≤ j ≤ λi} be the corresponding Young diagram. The conjugate partition λ is defined by λj = max{i : λi ≥ j}. We will freely use implications such as i ≤ j ⇒ λi ≥ λj. The hook Hz ⊆ [λ] is the set of squares weakly to the right and below of z = (i, j) ∈ [λ], and the hook len...

The hook-length formula is a well known result expressing the number of standard tableaux of shape λ in terms of the lengths of the hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a q, t-analog of the hook formula given ...

A probabilistic algorithm, called the q-hook walk, is defined. For a given Young diagram, it produces a new one by adding a random box with probabilities, depending on a positive parameter q. The corresponding Markov chain in the space of infinite Young tableaux is closely related to the knot invariant of Jones, constructed via traces of Hecke algebras. For q = 1, the algorithm is essentially t...

A method for preparing bacterial flagellar hook structures is described. The method involves isolating intact flagella from a mutant which makes thermally labile flagellar filaments and heat-treating them to disaggregate the filament preferentially. The resulting hook preparation can be separated and purified by velocity and isopycnic centrifugation. The purified hooks sediment at a relative S ...

This paper summarises key findings from several experiments to determine the most effective branch line weighting options for pelagic longline fisheries. Initial (0-2 m deep) and overall sink rates of a range of line weighting options – each comprising a different combination of weight and leader length (distance between hook and weight) – were compared and several options identified that offer...