Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Differential Adaptive Stress Testing of Airborne Collision Avoidance Systems

The next-generation Airborne Collision Avoidance System (ACAS X) is currently being developed and tested to replace the Traffic Alert and Collision Avoidance System (TCAS) as the next international standard for collision avoidance. To validate the safety of the system, stress testing in simulation is one of several approaches for analyzing near mid-air collisions (NMACs). Understanding how NMACs can occur is important for characterizing risk and informingdevelopment of the system. Recently, adaptive stress testing (AST) has been proposed as a way to find the most likely path to a failure event. The simulation-based approach accelerates search by formulating stress testing as a sequential decision process then optimizing it using reinforcement learning. The approach has been successfully applied to stress test a prototype of ACAS Xin various simulated aircraft encounters. In some applications, we are not as interestedin the system's absolute performance as its performance relative to another system. Such situations arise, for example, during regression testing or when deciding whether a new system should replace an existing system. In our collision avoidance application, we are interested in finding cases where ACAS X fails but TCAS succeeds in resolving a conflict. Existing approaches do not provide an efficient means to perform this type of analysis. This paper extends the AST approach to differential analysis by searching two simulators simultaneously and maximizing the difference between their outcomes. We call this approach differential adaptive stress testing (DAST). We apply DAST to compare a prototype of ACAS X against TCAS and show examples of encounters found by the algorithm

Prospects for observing and localizing gravitational-wave transients with advanced LIGO and advanced virgo

We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg^2 to 20 deg^2 will require at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone

Role of high tibial osteotomy in chronic injuries of posterior cruciate ligament and posterolateral corner

High tibial osteotomy (HTO) is a surgical procedure used to change the mechanical weight-bearing axis and alter the loads carried through the knee. Conventional indications for HTO are medial compartment osteoarthritis and varus malalignment of the knee causing pain and dysfunction. Traditionally, knee instability associated with varus thrust has been considered a contraindication. However, today the indications include patients with chronic ligament deficiencies and malalignment, because an HTO procedure can change not only the coronal but also the sagittal plane of the knee. The sagittal plane has generally been ignored in HTO literature, but its modification has a significant impact on biomechanics and joint stability. Indeed, decreased posterior tibial slope causes posterior tibia translation and helps the anterior cruciate ligament (ACL)-deficient knee. Vice versa, increased tibial slope causes anterior tibia translation and helps the posterior cruciate ligament (PCL)-deficient knee. A review of literature shows that soft tissue procedures alone are often unsatisfactory for chronic posterior instability if alignment is not corrected. Since limb alignment is the most important factor to consider in lower limb reconstructive surgery, diagnosis and treatment of limb malalignment should not be ignored in management of chronic ligamentous instabilities. This paper reviews the effects of chronic posterior instability and tibial slope alteration on knee and soft tissues, in addition to planning and surgical technique for chronic posterior and posterolateral instability with HTO

Integrated monitoring of mola mola behaviour in space and time

Over the last decade, ocean sunfish movements have been monitored worldwide using various satellite tracking methods. This study reports the near-real time monitoring of finescale (< 10 m) behaviour of sunfish. The study was conducted in southern Portugal in May 2014 and involved satellite tags and underwater and surface robotic vehicles to measure both the movements and the contextual environment of the fish. A total of four individuals were tracked using custom-made GPS satellite tags providing geolocation estimates of fine-scale resolution. These accurate positions further informed sunfish areas of restricted search (ARS), which were directly correlated to steep thermal frontal zones. Simultaneously, and for two different occasions, an Autonomous Underwater Vehicle (AUV) videorecorded the path of the tracked fish and detected buoyant particles in the water column. Importantly, the densities of these particles were also directly correlated to steep thermal gradients. Thus, both sunfish foraging behaviour (ARS) and possibly prey densities, were found to be influenced by analogous environmental conditions. In addition, the dynamic structure of the water transited by the tracked individuals was described by a Lagrangian modelling approach. The model informed the distribution of zooplankton in the region, both horizontally and in the water column, and the resultant simulated densities positively correlated with sunfish ARS behaviour estimator (r(s) = 0.184, p < 0.001). The model also revealed that tracked fish opportunistically displace with respect to subsurface current flow. Thus, we show how physical forcing and current structure provide a rationale for a predator's finescale behaviour observed over a two weeks in May 2014

Resilience of benthic deep-sea fauna to mining activities

With increasing demand for mineral resources, extraction of polymetallic sulphides at hydrothermal vents, cobalt-rich ferromanganese crusts at seamounts, and polymetallic nodules on abyssal plains may be imminent. Here, we shortly introduce ecosystem characteristics of mining areas, report on recent mining developments, and identify potential stress and disturbances created by mining. We analyze species' potential resistance to future mining and perform meta-analyses on population density and diversity recovery after disturbances most similar to mining: volcanic eruptions at vents, fisheries on seamounts, and experiments that mimic nodule mining on abyssal plains. We report wide variation in recovery rates among taxa, size, and mobility of fauna. While densities and diversities of some taxa can recover to or even exceed pre-disturbance levels, community composition remains affected after decades. The loss of hard substrata or alteration of substrata composition may cause substantial community shifts that persist over geological timescales at mined sites. (C) 2017 Elsevier Ltd. All rights reserved.European Union Seventh Framework Programme (FP7) under the MIDAS project; FCT [IF/00029/2014/CP1230/CT0002, SFRH/ BPD/110278/2015]; Spanish RTD project NUREIEV [CTM2013-44598-R]; Ministry of Economy and Competitiveness [SGR 1068]; Generalitat de Catalunya autonomous government; European Union Horizon research and innovation programme [689518]; Fundacao para a Ciencia e a Tecnologia [UID/MAR/04292/2013]; German Ministry of Research (BMBF) [03F0707A-G]; Program Investigador FCT [IF/01194/2013/CP1199/CT0002]info:eu-repo/semantics/publishedVersio