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NASA recently completed the development and testing of the Efficient Descent Advisor (EDA)-a trajectory-based tool for en route air traffic controllers that computes Optimized Profile Descent (OPD) solutions designed to minimize aircraft fuel consumption and associated carbon dioxide emissions while maximizing airspace throughput. EDA was developed and refined through a series of high fidelity Human-in-the-Loop (HITL) simulations, carried out in a three-year effort with the FAA and Boeing known as 3D-Path Arrival Management (3D-PAM). A final simulation was carried out to assess potential benefits using a prototype that reflected a culmination of previous design decisions. The simulation compared EDA against baseline operations in which controllers were provided with scheduling automation alone, representing metering operations today. For added fidelity, the simulation included models of trajectory prediction uncertainty. Results showed that EDA enabled a 92% improvement in the accuracy by which controllers delivered aircraft to the terminal airspace boundary in conformance with metering schedules. In addition, with EDA, controllers were able to accommodate overtake maneuvers en route without adjustments to the optimal arrival sequence. Furthermore, EDA was shown to reduce fuel consumption in transition airspace by 110 lbs per flight, averaged for all aircraft types and traffic scenarios, with substantially more fuel savings observed for busier traffic conditions and larger aircraft types. Reductions in controller workload were also observed along with a 60% reduction in the number of required maneuver instructions between controllers and pilots. Results from this simulation and previous experiments, together with prototype software and design specifications, were delivered to the FAA for transitioning EDA towards operational deployment.

Using unknotting number, we introduce a link diagram invariant of Hass and Nowik type, which changes at most by 2 under a Reidemeister move. As an application, we show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being unknotted with respect to the number of crossings. Assuming a certain conjecture on unknotting numbers of a certain series of composites of torus knots, we show that the above diagrams need quadratic number of Reidemeister moves for being splitted. Mathematics Subject Classification 2010: 57M25.

A laceration deep enough to reach the bone occurs very rarely in skiing or snowboarding. Two such cases are presented here. In one case, the popliteal fossa of a skier was cut during a collision with a snowboarder. All structures posterior to the knee were severed and the leg became ischaemic. The other case was of a snowboarder who sustained a deep cut to the distal forearm during landing after a jump, resulting in a ''spaghetti wrist''. S nowboarding has become one of the most popular winter sports not only in European countries 1 but also in Japan 2 , especially among young people. Many enjoy snowboarding and skiing on relatively small and crowded public slopes in Japan. As a result, lacerations from the edges of the snowboard can be caused not only to snowboarders themselves during falls but also by snowboarders in collisions. Although several studies on lacerations caused by snowboarding have been published, 3-6 cutting injuries have never received much attention probably because most can successfully be treated by irrigation and simple closure. There have been no reports on deep lacerations caused by snowboard edges.We recently encountered two patients who sustained cuts deep enough to reach the bone from snowboard edges, resulting in life or limb threatening injury. CASE REPORTSCase 1 A 25 year old female skier was hit from behind by a snowboarder while she was standing on a crowded mountain slope. Her left popliteal region was cut by the edge of the snowboard. She was drowsy from haemorrhagic shock when she arrived at the hospital one and a half hours later with a bandage tightly bound around the knee. Systolic/diastolic blood pressure was 73/38 mm Hg, and the pulse was 108 per minute. A tourniquet at the thigh was inflated before the bandage was taken off to avoid massive bleeding from the wound. There was a sharp, transverse, 8 cm long cut in her left popliteal fossa (fig 1), which completely impeded movement of the ankle and toes. The limb distal to the wound was anaesthetic, as well as ischaemic. Plain radiographs revealed air reaching the posterior aspect of the proximal tibia and fibula and a fracture in the neck of the fibula (fig 2). Surgery started about six hours after the injury. The popliteal artery and vein, the tibial and common peroneal nerves, both heads of the gastrocnemius, and the popliteal muscle were found to have been completely severed by the wound, which reached the posterior aspect of the proximal tibia and fibula and had caused a fracture in the neck of the fibula. The popliteal artery and vein were repaired by end to end anastomosis, and the severed muscles were sutured. The two nerves were repaired by epineural suturing under a surgical microscope.Haemoglobin concentration and packed cell volume after the operation were 87 g/l and 25.4% respectively; 1600 ml of blood was transfused during surgery, and an additional 800 ml over the next two days. Magnetic resonance angiography two months later showed patency of the repaired popliteal artery with little stenosis (fig 3). The pat...

Arnold introduced invariants J + , J − and St for generic planar curves. It is known that both J + /2 + St and J − /2 + St are invariants for generic spherical curves. Applying these invariants to underlying curves of knot diagrams, we can obtain lower bounds for the number of Reidemeister moves required for unknotting. J − /2 + St works well to count the minimum number of unmatched RII moves. However, it works only up to a factor of two for RI moves. Let w denote the writhe for a knot diagram. We show that J − /2 + St ± w/2 also gives sharp counts for the number of required RI moves, and demonstrate that it gives a precise estimate for a certain family of diagrams of the unknot with the underlying curve r = 2 + cos(nθ/(n + 1)), (0 ≤ θ ≤ 2(n + 1)π).