Vertex Fault Tolerant Additive Spanners

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 $H$ of the network $G$ such that subsequent to the failure of a single vertex, the surviving part of $H$ still contains an \emph{additive} spanner for (the surviving part of) $G$, satisfying $dist(s,t,H\setminus \{v\}) \leq dist(s,t,G\setminus \{v\})+\beta$ for every $s,t,v \in V$. Recently, the problem of constructing fault-tolerant additive spanners resilient to the failure of up to $f$ \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 $2$ and $\widetilde{O}(n^{5/3})$ edges. Our second result is an FT-spanner with additive stretch $6$ and $\widetilde{O}(n^{3/2})$ 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 $S \times V$ for a given subset of sources $S\subseteq V$. The additive stretch bounds of our constructions are 4 and 8 (using a different number of edges)

Hearing through your eyes: neural basis of audiovisual cross-activation, revealed by transcranial alternating current stimulation

Some people experience auditory sensations when seeing visual flashes or movements. This prevalent synaesthesia-like ‘visual-evoked auditory response’ (vEAR) could result either from over-exuberant cross-activation between brain areas, and/or reduced inhibition of normally-occurring cross-activation. We have used transcranial alternating current stimulation (tACS) to test these theories. We applied tACS at 10Hz (alpha-band frequency) or 40Hz (gamma-band), bilaterally either to temporal or occipital sites, while measuring same/different discrimination of paired auditory (A) versus visual (V) 'Morse code' sequences. At debriefing, participants were classified as vEAR or non-vEAR depending on whether they reported 'hearing' the silent flashes. In non-vEAR participants, temporal 10Hz tACS caused impairment of A performance, which correlated with improved V; conversely under occipital tACS, poorer V performance correlated with improved A. This reciprocal pattern suggests that sensory cortices are normally mutually inhibitory, and that alpha-frequency tACS may bias the balance of competition between them. vEAR participants showed no tACS effects, consistent with reduced inhibition, or enhanced cooperation between modalities. In addition, temporal 40Hz tACS impaired V performance, specifically in individuals who showed a performance advantage for V (relative to A). Gamma-frequency tACS may therefore modulate the ability of these individuals to benefit from recoding flashes into the auditory modality, possibly by disrupting cross-activation of auditory areas by visual stimulation. Our results support both theories, suggesting that vEAR may depend on disinhibition of normally-occurring sensory cross-activation, which may be expressed more strongly in some individuals. Furthermore, endogenous alpha and gamma-frequency oscillations may function respectively to inhibit or promote this cross-activation

A two-fluid model describing the finite-collisionality, stationary Alfvén wave in anisotropic plasma

The stationary inertial Alfvén (StIA) wave (Knudsen, 1996) was predicted for cold, collisionless plasma. The model was generalized (Finnegan et al., 2008) to include nonzero values of electron and ion collisional resistivity and thermal pressure. Here, the two-fluid model is further generalized to include anisotropic thermal pressure. A bounded range of values of parallel electron drift velocity is found that excludes periodic stationary Alfvén wave solutions. This exclusion region depends on the value of the local Alfvén speed VA, plasma beta perpendicular to the magnetic field β⊥ and electron temperature anisotropy

Methods for comparative evaluation of propulsion system designs for supersonic aircraft

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

Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces

The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.Comment: LaTeX, 44 pages, to appear in Comm. Math. Phy

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500

Fluctuation theorem for the effusion of an ideal gas

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.Comment: 11 pages, 10 figures, 2 table

Shape oscillations in non-degenerate Bose gases - transition from the collisionless to the hydrodynamic regime

We investigate collective oscillations of non-degenerate clouds of Rb-87 atoms as a function of density in an elongated magnetic trap. For the low-lying M=0 monopole-quadrupole shape oscillation we measure the oscillation frequencies and damping rates. At the highest densities the mean-free-path is smaller than the axial dimension of the sample, which corresponds to collisionally hydrodynamic conditions. This allows us to cover the cross-over from the collisionless to the hydrodynamic regime. The experimental results show good agreement with theory. We also analyze the influence of trap anharmonicities on the oscillations in relation to observed temperature dependencies of the dipole and quadrupole oscillation frequencies. We present convenient expressions to quantify these effects.Comment: 10 pages, 5 figure

Evaluación del comportamiento estructural y de resistencia a la corrosión de armaduras de acero inoxidable austenítico AISI 304 y dúplex AISI 2304 embebidas en morteros de cemento Portland

Se ha evaluado el comportamiento mecánico y estructural de dos aceros inoxidables corrugados, el austenítico EN 1.4301 (AISI 304) y el dúplex EN 1.4362 (AISI 2304), y se han comparado con el tradicional acero al carbono B500SD. El estudio se ha realizado en tres niveles: a nivel de barra, de sección y de pieza. Las diferentes características mecánicas de los aceros inoxidables condicionan el comportamiento a nivel de sección y de pieza estructural. El estudio del comportamiento frente a la corrosión de los dos aceros inoxidables se ha realizado mediante mediciones electroquímicas monitorizando el potencial de corrosión y la resistencia de polarización de armaduras embebidas en probetas de mortero contaminado con diferentes concentraciones de cloruros durante un tiempo de exposición de un año. Ambos aceros inoxidables permanecen en estado pasivo en las probetas para todos los contenidos de cloruros