8,330 research outputs found

    Vertex Fault Tolerant Additive Spanners

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    A {\em fault-tolerant} structure for a network is required to continue functioning following the failure of some of the network's edges or vertices. In this paper, we address the problem of designing a {\em fault-tolerant} additive spanner, namely, a subgraph HH of the network GG such that subsequent to the failure of a single vertex, the surviving part of HH still contains an \emph{additive} spanner for (the surviving part of) GG, satisfying dist(s,t,H{v})dist(s,t,G{v})+βdist(s,t,H\setminus \{v\}) \leq dist(s,t,G\setminus \{v\})+\beta for every s,t,vVs,t,v \in V. Recently, the problem of constructing fault-tolerant additive spanners resilient to the failure of up to ff \emph{edges} has been considered by Braunschvig et. al. The problem of handling \emph{vertex} failures was left open therein. In this paper we develop new techniques for constructing additive FT-spanners overcoming the failure of a single vertex in the graph. Our first result is an FT-spanner with additive stretch 22 and O~(n5/3)\widetilde{O}(n^{5/3}) edges. Our second result is an FT-spanner with additive stretch 66 and O~(n3/2)\widetilde{O}(n^{3/2}) edges. The construction algorithm consists of two main components: (a) constructing an FT-clustering graph and (b) applying a modified path-buying procedure suitably adopted to failure prone settings. Finally, we also describe two constructions for {\em fault-tolerant multi-source additive spanners}, aiming to guarantee a bounded additive stretch following a vertex failure, for every pair of vertices in S×VS \times V for a given subset of sources SVS\subseteq V. The additive stretch bounds of our constructions are 4 and 8 (using a different number of edges)

    Methods for comparative evaluation of propulsion system designs for supersonic aircraft

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    The propulsion system comparative evaluation study was conducted to define a rapid, approximate method for evaluating the effects of propulsion system changes for an advanced supersonic cruise airplane, and to verify the approximate method by comparing its mission performance results with those from a more detailed analysis. A table look up computer program was developed to determine nacelle drag increments for a range of parametric nacelle shapes and sizes. Aircraft sensitivities to propulsion parameters were defined. Nacelle shapes, installed weights, and installed performance was determined for four study engines selected from the NASA supersonic cruise aircraft research (SCAR) engine studies program. Both rapid evaluation method (using sensitivities) and traditional preliminary design methods were then used to assess the four engines. The method was found to compare well with the more detailed analyses

    Breakdown of disordered media by surface loads

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    We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus, G, as a function of the order parameter, \phi, describing the state of damage, and also the ``spalled'' material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behaviour in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behaviour of G with \phi is explored analytically and numerically, close to \phi=0 and \phi=1 and in the vicinity of \phi_c, when the shear load is close but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.Comment: 15 pages, 7 figure

    Does the Superior Colliculus Control Perceptual Sensitivity or Choice Bias during Attention? Evidence from a Multialternative Decision Framework

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    Distinct networks in the forebrain and the midbrain coordinate to control spatial attention. The critical involvement of the superior colliculus (SC)—the central structure in the midbrain network—in visuospatial attention has been shown by four seminal, published studies in monkeys (Macaca mulatta) performing multialternative tasks. However, due to the lack of a mechanistic framework for interpreting behavioral data in such tasks, the nature of the SC's contribution to attention remains unclear. Here we present and validate a novel decision framework for analyzing behavioral data in multialternative attention tasks. We apply this framework to re-examine the behavioral evidence from these published studies. Our model is a multidimensional extension to signal detection theory that distinguishes between two major classes of attentional mechanisms: those that alter the quality of sensory information or “sensitivity,” and those that alter the selective gating of sensory information or “choice bias.” Model-based simulations and model-based analyses of data from these published studies revealed a converging pattern of results that indicated that choice-bias changes, rather than sensitivity changes, were the primary outcome of SC manipulation. Our results suggest that the SC contributes to attentional performance predominantly by generating a spatial choice bias for stimuli at a selected location, and that this bias operates downstream of forebrain mechanisms that enhance sensitivity. The findings lead to a testable mechanistic framework of how the midbrain and forebrain networks interact to control spatial attention

    Miniature photonic-crystal hydrophone optimized for ocean acoustics

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    This work reports on an optical hydrophone that is insensitive to hydrostatic pressure, yet capable of measuring acoustic pressures as low as the background noise in the ocean in a frequency range of 1 Hz to 100 kHz. The miniature hydrophone consists of a Fabry-Perot interferometer made of a photonic-crystal reflector interrogated with a single-mode fiber, and is compatible with existing fiber-optic technologies. Three sensors with different acoustic power ranges placed within a sub-wavelength sized hydrophone head allow a high dynamic range in the excess of 160 dB with a low harmonic distortion of better than -30 dB. A method for suppressing cross coupling between sensors in the same hydrophone head is also proposed. A prototype was fabricated, assembled, and tested. The sensitivity was measured from 100 Hz to 100 kHz, demonstrating a minimum detectable pressure down to 12 {\mu}Pa (1-Hz noise bandwidth), a flatband wider than 10 kHz, and very low distortion
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