On rr-Simple kk-Path

An $r$-simple $k$-path is a {path} in the graph of length $k$ that passes through each vertex at most $r$ times. The $r$-SIMPLE $k$-PATH problem, given a graph $G$ as input, asks whether there exists an $r$-simple $k$-path in $G$. We first show that this problem is NP-Complete. We then show that there is a graph $G$ that contains an $r$-simple $k$-path and no simple path of length greater than $4\log k/\log r$. So this, in a sense, motivates this problem especially when one's goal is to find a short path that visits many vertices in the graph while bounding the number of visits at each vertex. We then give a randomized algorithm that runs in time $$\mathrm{poly}(n)\cdot 2^{O( k\cdot \log r/r)}$$ that solves the $r$-SIMPLE $k$-PATH on a graph with $n$ vertices with one-sided error. We also show that a randomized algorithm with running time $\mathrm{poly}(n)\cdot 2^{(c/2)k/ r}$ with $c<1$ gives a randomized algorithm with running time \poly(n)\cdot 2^{cn} for the Hamiltonian path problem in a directed graph - an outstanding open problem. So in a sense our algorithm is optimal up to an $O(\log r)$ factor

Chapter 14: Vulnerability of seabirds on the Great Barrier Reef to climate change

Seabirds are highly visible, charismatic predators in marine ecosystems that are defined as feeding exclusively at sea, in either nearshore, offshore or pelagic waters. At a conservative estimate there are approximately 0.7 billion individuals of 309 species of seabirds globally. Such high population abundance means that in all ecosystems where seabirds occur the levels of marine resources they consume are significant. Such high consumption rates also mean that seabirds play a number of important functional roles in marine ecosystems, including the transfer of nutrients from offshore and pelagic areas to islands and reefs, seed dispersal and the distribution of organic matter into lower parts of the developing soil profile (eg burrow-nesting species such as shearwaters).This is Chapter 14 of Climate change and the Great Barrier Reef: a vulnerability assessment. The entire book can be found at http://hdl.handle.net/11017/13

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Time-symmetric initial data for binary black holes in numerical relativity

We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily static black holes, in the form of a conformal decomposition of the spatial metric. This solution is isometric to the post-Newtonian metric up to the 2PN order. It represents a non-linear deformation of the solution of Brill and Lindquist, i.e. an asymptotically flat region is connected to two asymptotically flat (in a certain weak sense) sheets, that are the images of the two singularities through appropriate inversion transformations. The total ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are computed by surface integrals performed at infinity. Using second order perturbation theory on the Brill-Lindquist background, we prove that the binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and in agreement with the known post-Newtonian result.Comment: 27 pages, to appear in Phys. Rev.

The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case

Gravitational perturbations about a Kerr black hole in the Newman-Penrose formalism are concisely described by the Teukolsky equation. New numerical methods for studying the evolution of such perturbations require not only the construction of appropriate initial data to describe the collision of two orbiting black holes, but also to know how such new data must be imposed into the Teukolsky equation. In this paper we show how Cauchy data can be incorporated explicitly into the Teukolsky equation for non-rotating black holes. The Teukolsky function $$ and its first time derivative $\partial_t \Psi$ can be written in terms of only the 3-geometry and the extrinsic curvature in a gauge invariant way. Taking a Laplace transform of the Teukolsky equation incorporates initial data as a source term. We show that for astrophysical data the straightforward Green function method leads to divergent integrals that can be regularized like for the case of a source generated by a particle coming from infinity.Comment: 9 pages, REVTEX. Misprints corrected in formulas (2.4)-(2.7). Final version to appear in PR

The influence of whole-body vibration and postural support on activity interference in standing rail passengers

Travel time has generally been regarded as an unproductive period, representing a means-to-an-end in order to engage in activities at specific destinations. Rapid developments in mobile technology have provided people with innovative ways to multi-task and engage in meaningful activities while travelling. Rail transportation specifically, offers passengers advantages over other means of transportation as there is no need to focus on driving tasks. Due to the increase in passenger numbers and limited seating availability in train carriages, over one third of rail passengers are required to stand while travelling (DfT, 2013). The vibration to which rail passengers are exposed has been shown to interfere with the performance of activities and for standing passengers, it is often necessary to use postural supports such as holding on to grab rails or leaning on walls in order to maintain stability. The overall aim of the research is to evaluate the influence of whole-body vibration (WBV) exposure and standing posture on the performance of manual control tasks and the associated subjective workloads experienced by rail passengers. The use of supports, such as a backrest in seated postures, has been found to influence the response of the human body to WBV exposure, yet no reported studies have investigated the effects of postural supports on the response of the body in standing postures. Understanding how the body is affected in these conditions would increase the current state of knowledge on the biomechanical responses of the human body to vibration exposure and provide improved representation of standing postures within vibration standards (for example, ISO2631-4 (2001)) and guidelines for device interface design. A field study, using direct observation, was conducted to assess the behaviour of standing rail passengers and determine the characteristics of typical vibration exposures. This information provided the basis for the design of four subsequent laboratory studies. The main investigations of the laboratory studies were the influence of WBV exposure on objective performance measures, such as task completion time and error rate, and subjective workloads (for example, NASA TLX) for a range of manual control tasks. One of these laboratory studies evaluated the influence of various postural supports (for example, backrests) on the biomechanical responses of standing individuals. Measurements obtained during the field investigation indicated that the vibration exposures did not exceed the EU Physical Agents Exposure Action Value (EAV) and therefore posed little risk of injury. Vibration magnitudes in the horizontal directions (x- and y-axes) were higher than in the vertical direction (z-axis) and it was necessary for standing passengers to alter behaviours and use supports in order to maintain stability while travelling. The results of the laboratory studies indicated that in conditions where decrements in task performance occurred, the extent to which performance was degraded increased progressively with increases in vibration magnitude. There were conditions (for example, in the continuous control task and the Overhead Handle supported posture in the serial control task) where vibration exposure showed no significant influence on performance measures. This suggested that individuals were able to adapt and compensate for the added stress of vibration exposure in order to maintain performance levels however, this occurred at the expense of mental workload. The workload experienced by the participants increased with corresponding increases in magnitude. Vibration frequency-dependent effects in performance and workload were found to match the biomechanical responses (apparent mass and transmissibility) of the human body and resemble the frequency weightings described in the standards (ISO2631-1 (1997)). During the serial control task, the postures which demonstrated the greatest decrements to performance (for example, Lean Shoulder and Lean Back ) corresponded to the same postures that showed the greatest influence on the biomechanical responses of the body. It was concluded therefore, that measurements of the biomechanical responses to WBV could be used to offer predictions for the likelihood of activity interference. Consideration should however, be given to the applicability of this research before these results can be generalised to wider contexts. Further validation is recommended for future work to include different conditions in order to substantiate the findings of this research

Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure

Refraction Wiggles for Measuring Fluid Depth and Velocity from Video

We present principled algorithms for measuring the velocity and 3D location of refractive fluids, such as hot air or gas, from natural videos with textured backgrounds. Our main observation is that intensity variations related to movements of refractive fluid elements, as observed by one or more video cameras, are consistent over small space-time volumes. We call these intensity variations “refraction wiggles”, and use them as features for tracking and stereo fusion to recover the fluid motion and depth from video sequences. We give algorithms for 1) measuring the (2D, projected) motion of refractive fluids in monocular videos, and 2) recovering the 3D position of points on the fluid from stereo cameras. Unlike pixel intensities, wiggles can be extremely subtle and cannot be known with the same level of confidence for all pixels, depending on factors such as background texture and physical properties of the fluid. We thus carefully model uncertainty in our algorithms for robust estimation of fluid motion and depth. We show results on controlled sequences, synthetic simulations, and natural videos. Different from previous approaches for measuring refractive flow, our methods operate directly on videos captured with ordinary cameras, do not require auxiliary sensors, light sources or designed backgrounds, and can correctly detect the motion and location of refractive fluids even when they are invisible to the naked eye.Shell ResearchMotion Sensing Wi-Fi Sensor Networks Co. (Grant 6925133)National Science Foundation (U.S.). Graduate Research Fellowship (Grant 1122374)Microsoft Research (PhD Fellowship

A multi-factorial model for performance under vibration

Whole-body vibration affects drivers and passengers in vehicles. These people could be performing a variety of tasks that could be directly related to the control of the vehicle, or could be something unrelated to the vehicle. There is potential for the exposure to WBV whilst performing a task to adversely affect task performance. This paper uses two case studies to illustrate a model of performance and workload whilst exposed to vibration. It is shown that performance whilst completing a discrete task (Purdue pegboard) is easily affected by vibration, but a continuous task (steering wheel) is unaffected. However, in both cases, the self-reported workload increases with vibration. A model is presented that shows that where there is adaptive capacity of the operator, they are able to compensate for the vibration with greater control but at the cost of workload. However, beyond a coping threshold the performance will degrade

Effects of horizontal whole-body vibration and standing posture on activity interference

Standing people are exposed to whole-body vibration in many environments. This paper investigates the effects of horizontal whole-body vibration and standing posture on task performance. Sixteen participants were exposed to random vibration (up to 4Hz), whilst performing a timed pegboard task in two standing postures. Objective and subjective indicators of performance were used. Time taken to complete the task increased progressively with increases in vibration magnitude; the fore-and-aft posture generally showed greater performance decrements and postural interruptions (>1.0ms-2 r.m.s.) than the lateral. For both postures, performance was better during y-axis vibration than during x-axis vibration. Subjective ratings showed similar trends to time data. Impairments due to dual axis exposure were well predicted using r.s.s. summation calculations based on single axis components. These results indicate that best performance for those standing in moving environments will be achieved if individuals adopt a lateral posture with the most severe vibration in the y-axis