The study of animal foraging behaviour is of practical ecological importance 1 , and exemplifies the wider scientific problem of optimizing search strategies 2 .Lévy flights are random walks whose step lengths come from probability distributions with heavy power-law tails 3, 4 , such that clusters of short steps are connected by rare long steps. flight durations (time intervals between landing on the ocean) were then calculated as consecutive hours for which a bird remained dry, to a resolution of 1 h. It was assumed that birds landed on the water solely to feed, and that flight durations were thus indicative of distances between prey.Time series for 19 separate foraging trips 7 were pooled to give a total of 363 3 flights. The resulting log-log histogram of flight durations gave a straight line with a slope of approximately 2, and is reproduced in Supplementary Fig. 1 from the original raw data. The crux of the conclusion that the albatrosses were performing Lévy flights was that the slope of 2 implied the probability density function (pdf) of flight durations t (in hours), was 7, 10for t ≥ 1 h (leaving out the normalization constant). This is consistent with the Lévy flight definition that the tail of the pdf is of the power-law form t −µ , where 1 < µ ≤ 3 (though technically this is a Lévy walk 4,7,22 We first analyze a newer, larger, and higher resolution data set of albatross flight durations to test for Lévy flights. In 2004, 20 wandering albatrosses on BirdIsland were each fitted with a salt-water logger and a GPS device. The GPS data were too infrequent (at most one location h −1 ) to give distances between landings, but were needed to estimate each bird's departure time from Bird Island, in order to calculate the duration of the initial flight before first landing on the water (we calculated return flights similarly). The resulting data set of flight records was 4 pooled, as in ref. 7, yielding a total of 1416 flights to a resolution of 10 s (Fig. 1).The flights ≥ 1 h are clearly inconsistent with coming from the power law t −2 ascertained 7 for the 1992 data. Furthermore, data from a power law of any exponent (not just 2) would yield a straight line 23 , and this is clearly not the case.In fact, the flight durations t (in h) are consistent with coming from the shifted gamma distribution given by the pdfwhere y = t − 1/120 accounts for the assumed 30 s period before the bird searches for new food sources (see Methods), s = 0.31 is the shape parameter, r = 0.41 h −1 is the rate parameter, and Γ(·) is the gamma function. Equation (2) is valid for flights >30 s; for shorter flights we have f (t) = 0. The exponential term of (2) dominates for large t, implying Poisson behaviour, such that for long enough flights the birds essentially encounter prey randomly with a constant low probability.A Brownian random walker's displacement increases as t H where H = 1/2.If H > 1/2, we have "superdiffusion" as originally inferred in Fig. 2a The gamma distribution (2) has µ = 1 − s = 0.69. This is such a slow powerlaw ...

Colistin is an antibiotic of last resort, but has poor efficacy and resistance is a growing problem. Whilst it is well established that colistin disrupts the bacterial outer membrane by selectively targeting lipopolysaccharide (LPS), it was unclear how this led to bacterial killing. We discovered that MCR-1 mediated colistin resistance in Escherichia coli is due to modified LPS at the cytoplasmic rather than outer membrane. In doing so, we also demonstrated that colistin exerts bactericidal activity by targeting LPS in the cytoplasmic membrane. We then exploited this information to devise a new therapeutic approach. Using the LPS transport inhibitor murepavadin, we were able to cause LPS accumulation in the cytoplasmic membrane of Pseudomonas aeruginosa, which resulted in increased susceptibility to colistin in vitro and improved treatment efficacy in vivo. These findings reveal new insight into the mechanism by which colistin kills bacteria, providing the foundations for novel approaches to enhance therapeutic outcomes.

The aim of this study was to describe the anatomical locations of the femoral attachments of the anteromedial (AM) and posterolateral (PL) bundles of the anterior cruciate ligament (ACL). Twenty-two human cadaver knees with intact ACLs were used. The femoral attachments of the two bundles were identified, marked and photographed. They were measured and described in terms of the o'clock positions parallel to the femoral long axis and parallel to the roof of the intercondylar notch. The centres of the bundles were also measured in a high-low and a superficial-deep manner referencing from the centre of the posterior femoral condyle, and with respect to their positions within a measurement grid defined in this study. The bulk of the AM bundle was attached between the 9.30 and 11.30 o'clock positions and the PL bundle between the 8.30 and 10 o'clock positions. The AM and PL bundles were consistently found in specific zones of the measurement grid. Using the posterior condyle reference method, the centre of the AM bundle was at 68 ± 7% (range 57-78) in a shallow-deep direction and 55 ± 5% (44-62) in a high-low direction. The PL bundle was found at 56 ± 8% (40-73) in a shallow-deep direction, and 62 ± 7.0% (40-70) in a high-low direction. The attachment was oriented at 37° to the femoral long axis. The results from this study could be used to guide ACL reconstruction techniques.

This paper describes the anatomy of the posterior cruciate ligament (PCL) and the meniscofemoral ligaments (MFLs). The fibres of the PCL may be split into two functional bundles; the anterolateral bundle (ALB) and the posteromedial bundle (PMB), relating to their femoral attachments. The tibial attachment is relatively compact, with the ALB anterior to the PLB. These bundles are not isometric: the ALB is tightest in the mid-arc of knee flexion, the PMB is tight at both extension and deep flexion. At least one MFL is present in 93% of knees. On the femur, the anterior MFL attaches distal to the PCL, close to the articular cartilage; the posterior MFL attaches proximal to the PCL. They both attach distally to the posterior horn of the lateral meniscus. Their slanting orientation allows the MFLs to resist tibial posterior drawer.