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    We consider structure learning of linear Gaussian structural equation models with weak edges. Since the presence of weak edges can lead to a loss of edge orientations in the true underlying CPDAG, we define a new graphical object that can contain more edge orientations. We show that this object can be recovered from observational data under a type of strong faithfulness assumption. We present a new algorithm for this purpose, called aggregated greedy equivalence search (AGES), that aggregates the solution path of the greedy equivalence search (GES) algorithm for varying values of the penalty parameter. We prove consistency of AGES and demonstrate its performance in a simulation study and on single cell data from Sachs et al. (2005). The algorithm will be made available in the R-package pcalg.
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    We study the linear spatiotemporal stability of an infinite row of equal point-vortices under symmetric confinement between parallel walls. This serves to model the secondary pairing instability in free shear layers, allowing us to study how confinement limits the growth of shear layers through vortex pairings. Using a geometric construction akin to a Legendre transform on the dispersion relation, we compute the growth rate of the instability in different reference frames as a function of frame velocity. This new approach is verified and complemented with numerical computations of the linear impulse response, fully characterizing the absolute/convective nature of the instability. As for the primary instability of parallel tanh profiles, we observe a range of confinement in which absolute instability is promoted. For a given parallel shear layer and channel width, the threshold for absolute/convective instability of the pairing instability depends on the separation distance between consecutive vortices, which is physically determined by the wavelength selected by the previous (primary or pairing) instability. With counterflow and moderate to weak confinement, small wavelength of the vortex row leads to absolute instability. In the present case, however, the result of the secondary pairing instability is to regenerate the flow with an increased wavelength, eventually leading to convective instability. This leads us to propose a wavelength selection criteria, according to which a spatially developing row of vortices in a free shear layer with counterflow can only occur if the distance between vortices is sufficiently large, in comparison to the channel width, so that the pairing instability is convective. The proposed wavelength selection mechanism can serve as a guideline for experimentally obtaining plane shear layers with counterflow, which has remained an experimental challenge.
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    For the solution of the Poisson problem with an $L^\infty$ right hand side \beginequation* \begincases -∆u(x) = f (x) & \mboxin D, u=0 & \mboxon ∂D, \endcases \endequation* we derive an optimal estimate of the form $$ \|u\|_∞≤\|f\|_∞\sigma_D(\|f\|_1/\|f\|_∞), $$ where $\sigma_D$ is a modulus of continuity defined in the interval $[0, |D|]$ and depends only on the domain $D$. In the case when $f\geq 0$ in $D$ the inequality is optimal for any domain and for any values of $\|f\|_1$ and $\|f\|_\infty.$ We also show that $$ \sigma_D(t)≤\sigma_B(t),\text for t∈[0,|D|], $$ where $B$ is a ball and $|B|=|D|$. Using this optimality property of $\sigma,$ we derive Brezis-Galloute-Wainger type inequalities on the $L^\infty$ norm of $u$ in terms of the $L^1$ and $L^\infty$ norms of $f.$ The estimates have explicit coefficients depending on the space dimension $n$ and turn to equality for a specific choice of $u$ when the domain $D$ is a ball. As an application we derive $L^\infty-L^1$ estimates on the $k-$th Laplace eigenfunction of the domain $D.$
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    In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage. We will use the Ellsberg-paradox to illustrate the potential of our approach to deal with well-known paradoxa of decision theory.
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    Among the most interesting predictions in two-dimensional materials with a Dirac cone is the existence of the zeroth Landau level (LL), equally filled by electrons and holes with opposite chirality. The gapless edge states with helical spin structure emerge from Zeeman splitting at the LL filling factor $\nu=0$ gapped quantum Hall state. We present observations of a giant nonlocal four-terminal transport in zero-gap HgTe quantum wells at the $\nu=0$ quantum Hall state. Our experiment clearly demonstrates the existence of the robust helical edge state in a system with single valley Dirac cone materials.
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    We propose a methodology that adapts graph embedding techniques (DeepWalk (Perozzi et al., 2014) and node2vec (Grover and Leskovec, 2016)) as well as cross-lingual vector space mapping approaches (Least Squares and Canonical Correlation Analysis) in order to merge the corpus and ontological sources of lexical knowledge. We also perform comparative analysis of the used algorithms in order to identify the best combination for the proposed system. We then apply this to the task of enhancing the coverage of an existing word embedding's vocabulary with rare and unseen words. We show that our technique can provide considerable extra coverage (over 99%), leading to consistent performance gain (around 10% absolute gain is achieved with w2v-gn-500K cf.\S 3.3) on the Rare Word Similarity dataset.
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    Existing marker-less motion capture methods often assume known backgrounds, static cameras, and sequence specific motion priors, which narrows its application scenarios. Here we propose a fully automatic method that given multi-view video, estimates 3D human motion and body shape. We take recent SMPLify \citebogo2016keep as the base method, and extend it in several ways. First we fit the body to 2D features detected in multi-view images. Second, we use a CNN method to segment the person in each image and fit the 3D body model to the contours to further improves accuracy. Third we utilize a generic and robust DCT temporal prior to handle the left and right side swapping issue sometimes introduced by the 2D pose estimator. Validation on standard benchmarks shows our results are comparable to the state of the art and also provide a realistic 3D shape avatar. We also demonstrate accurate results on HumanEva and on challenging dance sequences from YouTube in monocular case.
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    Network coding based peer-to-peer streaming represents an effective solution to aggregate user capacities and to increase system throughput in live multimedia streaming. Nonetheless, such systems are vulnerable to pollution attacks where a handful of malicious peers can disrupt the communication by transmitting just a few bogus packets which are then recombined and relayed by unaware honest nodes, further spreading the pollution over the network. Whereas previous research focused on malicious nodes identification schemes and pollution-resilient coding, in this paper we show pollution countermeasures which make a standard network coding scheme resilient to pollution attacks. Thanks to a simple yet effective analytical model of a reference node collecting packets by malicious and honest neighbors, we demonstrate that i) packets received earlier are less likely to be polluted and ii) short generations increase the likelihood to recover a clean generation. Therefore, we propose a recombination scheme where nodes draw packets to be recombined according to their age in the input queue, paired with a decoding scheme able to detect the reception of polluted packets early in the decoding process and short generations. The effectiveness of our approach is experimentally evaluated in a real system we developed and deployed on hundreds to thousands peers. Experimental evidence shows that, thanks to our simple countermeasures, the effect of a pollution attack is almost canceled and the video quality experienced by the peers is comparable to pre-attack levels.
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    In this paper, we prove that in macroscopic times of order one, the solutions to the truncated BBGKY hierarchy (to second order) converge in the weak coupling limit to the solution of the nonlinear spatially homogeneous Landau equation. The truncated problem describes the formal leading order behavior of the underlying particle dynamics and can be reformulated as a non-Markovian hyperbolic equation, which converges to the Markovian evolution described by the parabolic Landau equation. The analysis in this paper is motivated by Bogolyubov's derivation of the kinetic equation by means of a multiple time scale analysis of the BBGKY hierarchy.
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    We investigate the contact of a rigid cylindrical punch with an adhesive beam mounted on flexible end supports. Adhesion is modeled through an adhesive zone model. The resulting Fredholm integral equation of the first kind is solved by a Galerkin projection method in terms of Chebyshev polynomials. Results are reported for several combinations of adhesive strengths, beam thickness, and support flexibilities characterized through torsional and vertical translational spring stiffnesses. Special attention is paid to the important extreme cases of clamped and simply supported beams. The popular Johnson-Kendall-Roberts (JKR) model for adhesion is obtained as a limit of the adhesive zone model. Finally, we compare our predictions with preliminary experiments and also demonstrate the utility of our approach in modeling complex structural adhesives.
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    Feature selection is playing an increasingly significant role with respect to many computer vision applications spanning from object recognition to visual object tracking. However, most of the recent solutions in feature selection are not robust across different and heterogeneous set of data. In this paper, we address this issue proposing a robust probabilistic latent graph-based feature selection algorithm that performs the ranking step while considering all the possible subsets of features, as paths on a graph, bypassing the combinatorial problem analytically. An appealing characteristic of the approach is that it aims to discover an abstraction behind low-level sensory data, that is, relevancy. Relevancy is modelled as a latent variable in a PLSA-inspired generative process that allows the investigation of the importance of a feature when injected into an arbitrary set of cues. The proposed method has been tested on ten diverse benchmarks, and compared against eleven state of the art feature selection methods. Results show that the proposed approach attains the highest performance levels across many different scenarios and difficulties, thereby confirming its strong robustness while setting a new state of the art in feature selection domain.
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    In a recent work, [Phys. Rev. D. 94, 104010 (2016)], hereafter Paper I, we have numerically studied different prescriptions for the dynamics of a spinning particle in circular motion around a Schwarzschild black hole. In the present work, we continue this line of investigation to the rotating Kerr black hole. We consider the Mathisson-Papapetrou formalism under three different spin-supplementary-conditions (SSC), the Tulczyjew SSC, the Pirani SSC and the Ohashi-Kyrian-Semerak SSC, and analyze the different circular dynamics in terms of the ISCO shifts and the frequency parameter ${x \equiv (M \Omega)^{2/3}}$, where $\Omega$ is the orbital frequency and $M$ is the Kerr black hole mass. Then, we solve numerically the inhomogeneous $(2+1)D$ Teukolsky equation to contrast the asymptotic gravitational wave fluxes for the three cases. Our central observation made in Paper I for the Schwarzschild limit is found to hold true for the Kerr background: the three SSCs reduce to the same circular dynamics and the same radiation fluxes for small frequency parameters but differences arise as $x$ grows close to the ISCO. For a positive Kerr parameter $a=0.9$ the energy fluxes mutually agree with each other within a $0.2\%$ uncertainty up to $x<0.14$, while for $a=-0.9$ this level of agreement is preserved up to $x<0.1$. For large frequencies ($x \gtrsim 0.1$), however, the spin coupling of the Kerr black hole and the spinning body results in significant differences of the circular orbit parameters and the fluxes, especially for the $a=-0.9$ case. Instead, in the study of ISCO the negative Kerr parameter $a=-0.9$ results in less discrepancies in comparison with the positive Kerr parameter $a=0.9$.
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    The cosmic microwave background (CMB) has non-Gaussian features in the temperature fluctuations. An anomalous cold spot surrounded with a hot ring, called the Cold Spot is one of such features. If a large underdence region (supervoid) resides towards the Cold Spot, we would be able to detect a systematic shape distortion in the images of background source galaxies via weak lensing effect. In order to estimate the detectability of such signals, we used the data of $N$-body simulations to simulate full-sky ray-tracing of source galaxies. We searched for a most prominent underdense region using the simulated convergence maps smoothed at a scale of 20 degree and obtained tangential shears around it. The lensing signal expected in a concordant $\Lambda$CDM model can be detected at a signal-to-noise ratio $S/N\sim3$. If a supervoid with a radius of $\sim 200h^{-1}$Mpc and a density contrast $\delta_0 \sim -0.3$ at the centre resides at a redshift $z\sim 0.2$, on-going and near-future weak gravitational lensing surveys would detect a lensing signal with $S/N\sim5$ without resorting to stacking.
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    We consider the asymptotics of large external magnetic field for a 2D Vlasov-Poisson system governing the evolution of a bounded density interacting with a point charge. In a suitable asymptotical regime, we show that the solution converges to a solution of a nonlinear equation with a defect measure. In the case where the charge has mass equal to one, this equation reduces to the Euler equation.
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    We investigate the effect of a global degeneracy in the distribution of entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the non-integer degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spin-chains provides strong analytical evidences corroborating our results.
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    We study non--degenerate CR geometries of hypersurface type that are symmetric in the sense that at each point, there is a CR transformation reverting the CR distribution at that point. We show that they are either flat or homogeneous. We show that non--flat non--degenerate symmetric CR geometries of hypersurface type are covered by CR geometries with a compatible pseudo--Riemannian metric preserved by all symmetries. We construct examples of simply connected flat non--degenerate symmetric CR geometries of hypersurface type that do not carry a compatible pseudo--Riemannian metric that would be preserved by some symmetry at each point.
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    We present a simple method for assessing the quality of generated images in Generative Adversarial Networks (GANs). The method can be applied in any kind of GAN without interfering with the learning procedure or affecting the learning objective. The central idea is to define a likelihood function that correlates with the quality of the generated images. In particular, we derive a Gaussian likelihood function from the distribution of the embeddings (hidden activations) of the real images in the discriminator, and based on this, define two simple measures of how likely it is that the embeddings of generated images are from the distribution of the embeddings of the real images. This yields a simple measure of fitness for generated images, for all varieties of GANs. Empirical results on CIFAR-10 demonstrate a strong correlation between the proposed measures and the perceived quality of the generated images.
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    A theoretical investigation has been made to study the cylindrical and spherical electron-acoustic shock waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system containing two distinct groups of electrons (one inertial non-relativistic cold electrons and other inertialess ultra-relativistic hot electrons) and positively charged static ions. By employing well known reductive perturbation method the modified Burgers (mB) equation has been derived. It is seen that only rarefactive shock waves can propagate in such a quantum plasma system. The effects of degenerate plasma pressure and number density of hot and cold electron fluids, nonplanar geometry, and positively charged static ions are responsible to modify the fundamental properties of EASWs. It is also observed that the properties of planar mB shocks are quite different from those of nonplanar mB shocks. The findings of the present investigation should be useful in understanding the nonlinear phenomena associated with nonplanar EAWs in both space and laboratory plasmas.
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    The object of this paper is to study $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds. We investigate $\eta$-Ricci solitons in the case when its potential vector field is exactly the characteristic vector field $\xi$ of the $(\varepsilon)$-almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and $(\varepsilon)$-para Sasakian manifolds admitting $\eta$-Ricci solitons. Finally we obtain some results for $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2)-tensor fields.
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    Results of a comprehensive shell model (SM) analyses, within the full $f_{5/2}pg_{9/2}$ model space, of the recently available experimental data [P. Ruotsalainen et al., Phy. Rec. C \bf 88, 024320 (2013)] with four $T=0$ bands and one $T=1$ band in the odd-odd $N=Z$ nucleus $^{66}$As are presented. The calculations are performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. For the lowest two $T=0$ bands and the $T=1$ band, the results are in reasonable agreement with experimental data and deformed shell model is used to identify their intrinsic structure. For the $T=1$ band, structural change at $8^+$ is predicted. For the third $9^+$ band with $T=0$, the shell model $B(E2)$ values and quadrupole moments (in addition to energies) are consistent with the interpretation in terms of aligned isoscalar $np$ pair in $g_{9/2}$ orbit coupled to the $^{64}$Ge ground band. Similarly, the $9^+$ level of band 4 and a close lying $5^+$ level are found to be isomeric states in the analysis. Finally, energies of the band 5 members calculated using shell model with both positive and negative parity show that the observed levels are most likely negative parity levels. The SM results with jj44b are also compared with the results obtained using JUN45 interaction.
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    Cogadh Gaedhel re Gallaibh ("The War of the Gaedhil with the Gaill") is a medieval Irish text, telling how an army under the leadership of Brian Boru challenged Viking invaders and their allies in Ireland, culminating with the Battle of Clontarf in 1014. Brian's victory is widely remembered for breaking Viking power in Ireland, although much modern scholarship disputes traditional perceptions. Instead of an international conflict between Irish and Viking, interpretations based on revisionist scholarship consider it a domestic feud or civil war. Counter-revisionists challenge this view and a lively debate continues. Here we introduce quantitative measures to the discussions. We present statistical analyses of network data embedded in the text to position its sets of interactions on a spectrum from the domestic to the international. This delivers a picture that lies between antipodal traditional and revisionist extremes, hostilities recorded in the text are mostly between Irish and Viking - but internal conflict forms a significant proportion of the negative interactions too. Additionally, we quantitatively compare the network properties of Cogadh Gaedhel re Gallaibh to those of other epic-type narratives and find that, in many ways, they resemble those of the Iliad.
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    The Future Circular Collider (FCC), currently in the design phase, will address many outstanding questions in particle physics. The technology to succeed in this 100 km circumference collider goes beyond present limits. Ultra-high vacuum conditions in the beam pipe is one essential requirement to provide a smooth operation. Different physics phenomena as photon-, ion- and electron- induced desorption and thermal outgassing of the chamber walls challenge this requirement. This paper presents an analytical model and a computer code PyVASCO that supports the design of a stable vacuum system by providing an overview of all the gas dynamics happening inside the beam pipes. A mass balance equation system describes the density distribution of the four dominating gas species $\text{H}_2, \text{CH}_4$, $\text{CO}$ and $\text{CO}_2$. An appropriate solving algorithm is discussed in detail and a validation of the model including a comparison of the output to the readings of LHC gauges is presented. This enables the evaluation of different designs for the FCC.
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    We explore the possible mass radius relation of compact stars for the equation of states with a first order phase transition. The low density matter is described by a nuclear matter equation of state resulting from fits to nuclear properties. A constant speed of sound parametrization is used to describe the high density matter phase with the speed of sound $c_s^2=1$. A classification scheme of four distinct categories including twin star solutions, i. e. solutions with the same mass but differing radii, is found which are compatible with the $M \ge 2M_\odot$ pulsar mass constraint. We show the dependence of the mass and radius differences on the transition parameters and delineate that higher twin star masses are more likely to be accompanied by large radius differences. These massive twin stars are generated by high values of the discontinuity in the energy density and the lowest possible values of the transition pressure that still result in masses of $M \geq 2M_\odot$ at the maximum of the hadronic branch.
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    The rise of atomically thin materials has the potential to enable a paradigm shift in modern technologies by introducing multi-functional materials in the semiconductor industry. To date the growth of high quality atomically thin semiconductors (e.g. WS2) is one of the most pressing challenges to unleash the potential of these materials and the growth of mono- or bi-layers with high crystal quality is yet to see its full realization. Here, we show that the novel use of molecular precursors in the controlled synthesis of mono- and bi-layer WS2 leads to superior material quality compared to the widely used topotactic transformation of WO3-based precursors. Record high room temperature charge carrier mobility up to 52 cm2/Vs and ultra-sharp photoluminescence linewidth of just 36 meV over submillimeter areas demonstrate that the quality of this material supersedes also that of naturally occurring materials. By exploiting surface diffusion kinetics of W and S species adsorbed onto a substrate, a deterministic layer thickness control has also been achieved promoting the design of scalable synthesis routes.
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    We investigate the ionising effect of low energy cosmic rays (CRs) from a young star on its protoplanetary disk (PPD). We consider specifically the effect of $\sim3\,$GeV protons injected at the inner edge of the PPD. An increase in the ionisation fraction as a result of these CRs could allow the magnetorotational instability to operate in otherwise magnetically dead regions of the disk. For the typical values assumed we find an ionisation rate of $\zeta_\mathrm{CR} \sim 10^{-17}\mathrm{s^{-1}}$ at $1\,$au. The transport equation is solved by treating the propagation of the CRs as diffusive. We find for increasing diffusion coefficients the CRs penetrate further in the PPD, while varying the mass density profile of the disk is found to have little effect. We investigate the effect of an energy spectrum of CRs. The influence of a disk wind is examined by including an advective term. For advective wind speeds between $1-100\mathrm{km\,s^{-1}}$ diffusion dominates at all radii considered here (out to 10$\,$au) for reasonable diffusion coefficients. Overall, we find that low energy CRs can significantly ionise the midplane of PPDs out to $\sim\,1\,$au. By increasing the luminosity or energy of the CRs, within plausible limits, their radial influence could increase to $\sim2\,$au at the midplane but it remains challenging to significantly ionise the midplane further out.
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    We present 2271 radial velocity measurements taken on 118 single-line binary stars, taken over eight years with the CORALIE spectrograph. The binaries consist of F/G/K primaries and M-dwarf secondaries. They were initially discovered photometrically by the WASP planet survey, as their shallow eclipses mimic a hot-Jupiter transit. The observations we present permit a precise characterisation of the binary orbital elements and mass function. With modelling of the primary star this mass function is converted to a mass of the secondary star. In the future, this spectroscopic work will be combined with precise photometric eclipses to draw an empirical mass/radius relation for the bottom of the mass sequence. This has applications in both stellar astrophysics and the growing number of exoplanet surveys around M-dwarfs. In particular, we have discovered 34 systems with a secondary mass below $0.2 M_\odot$, and so we will ultimately double the known number of very low-mass stars with well characterised mass and radii. We are able to detect eccentricities as small as 0.001 and orbital periods to sub-second precision. Our sample can revisit some earlier work on the tidal evolution of close binaries, extending it to low mass ratios. We find some binaries that are eccentric at orbital periods < 3 days, while our longest circular orbit has a period of 10.4 days. By collating the EBLM binaries with published WASP planets and brown dwarfs, we derive a mass spectrum with twice the resolution of previous work. We compare the WASP/EBLM sample of tightly-bound orbits with work in the literature on more distant companions up to 10 AU. We note that the brown dwarf desert appears wider, as it carves into the planetary domain for our short-period orbits. This would mean that a significantly reduced abundance of planets begins at $\sim 3M_{\rm Jup}$, well before the Deuterium-burning limit. [abridged]
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    We introduce an exact mapping between the Dirac equation in (1+1)D curved spacetime (DCS) and a multi-photon quantum Rabi model (mQRM). A background of a (1+1)D black hole (BH) requires a QRM with one and two-photon terms, that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1+1)D BH, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the mQRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wavefunction.
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    For an integer $ k\geq 2 $, let $ \{F^{(k)}_{n} \}_{n\geq 0}$ be the $ k$--generalized Fibonacci sequence which starts with $ 0, \ldots, 0, 1 $ ($ k $ terms) and each term afterwards is the sum of the $ k $ preceding terms. In this paper, we find all integers $c$ having at least two representations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$.
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    In monocular vision systems, lack of knowledge about metric distances caused by the inherent scale ambiguity can be a strong limitation for some applications. We offer a method for fusing inertial measurements with monocular odometry or tracking to estimate metric distances in inertial-monocular systems and to increase the rate of pose estimates. As we performed the fusion in a loosely-coupled manner, each input block can be easily replaced with one's preference, which makes our method quite flexible. We experimented our method using the ORB-SLAM algorithm for the monocular tracking input and Euler forward integration to process the inertial measurements. We chose sets of data recorded on UAVs to design a suitable system for flying robots.
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    In this paper, we study the static Born-Infeld equation $$ -\mathrmdiv\left(\frac∇u\sqrt1-|∇u|^2\right)=\sum_k=1^n a_k\delta_x_k\quad\mboxin \mathbb R^N,\qquad \lim_|x|\to∞u(x)=0, $$ where $N\ge3$, $a_k\in\mathbb R$ for all $k=1,\dots,n$, $x_k\in\mathbb R^N$ are the positions of the point charges, possibly non symmetrically distributed, and $\delta_{x_k}$ is the Dirac delta distribution centered at $x_k$. For this problem, we give explicit quantitative sufficient conditions on $a_k$ and $x_k$ to guarantee that the minimizer of the energy functional associated to the problem solves the associated Euler-Lagrange equation. Furthermore, we provide a more rigorous proof of some previous results on the nature of the singularities of the minimizer at the points $x_k$'s depending on the sign of charges $a_k$'s. For every $m\in\mathbb N$, we also consider the approximated problem $$ -\sum_h=1^m\alpha_h\Delta_2hu=\sum_k=1^n a_k\delta_x_k\quad\mboxin \mathbb R^N, \qquad\lim_|x|\to∞u(x)=0 $$ where the differential operator is replaced by its Taylor expansion of order $2m$, see (2.1). It is known that each of these problems has a unique solution. We study the regularity of the approximating solution, the nature of its singularities, and the asymptotic behavior of the solution and of its gradient near the singularities.
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    Generation of small droplets (aerosols) by waves breaking in surf zone exerts influence over a broad range of geophysical and climatological changes in proximity of coastal lines. Droplets may be formed by bubble bursting with jet and film fragmentation, wind tearing from wave crests etc., while theoretical understanding of such processes is still incomplete. Here we disclose a new multiscale mechanism in which small-scale perturbations (ripples) on water surface are controlled by the large-scale wave dynamics in a way analogous to the adiabatic transport in quantum mechanics. Unlike classical hydrodynamic instabilities, this results in a super-exponential steepness amplification for small-scale ripples. We propose that this explosive increase of ripple steepness explains the breakdown of a smooth water surface into a spray with small droplets, commonly observed in ocean waves prior to overturning even in the absence of wind. The developed quantitative theory is shown to be in excellent agreement with numerical simulations.
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    We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model consists of a Peierls-Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The $\Gamma$-limit of this energy was deduced by Garroni and Müller (2005 and 2006). Our main result shows that the gradient flows of these $\Gamma$-convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-monotone loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen-Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the $\Gamma$-limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation.
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    We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces. Finally, the asymptotic optimality of these inequalities is illustrated in various examples of non necessarily quasi-greedy bases.
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    We study the faint radio population using wide-field very long baseline interferometry (VLBI) observations of 2865 known radio sources in the Cosmic Evolution Survey (COSMOS) field. The main objective of the project was to determine where active galactic nuclei (AGN) are present. The combination of number of sources, sensitivity, angular resolution and area covered by this project are unprecedented. We have detected 468 radio sources, expected to be AGNs, with the Very Long Baseline Array (VLBA) at 1.4 GHz. This is, to date, the largest sample assembled of VLBI detected sources in the sub-mJy regime. The input sample was taken from previous observations with the Very Large Array (VLA). We present the catalogue with additional multiwavelength information. We find a detection fraction of 20%, considering only those sources from the input catalogue which were in principle detectable with the VLBA (2361). As a function of redshift, we see no evolution of the detection fraction over the redshift range 0.5<z<3. In addition, we find that faint radio sources typically have a greater fraction of their radio luminosity in a compact core: ~70% of the sub-mJy sources detected with the VLBA have more than half of their total radio luminosity in a VLBI-scale component, whereas this is true for only ~30% of the sources that are brighter than 10 mJy. This suggests that fainter radio sources differ intrinsically from brighter ones. Across our entire sample, we find the predominant morphological classification of the host galaxies of the VLBA detected sources to be early type (57%), although this varies with redshift and at z>1.5 we find that spiral galaxies become the most prevalent (48%). We demonstrate that wide-field VLBI observations, together with new calibration methods such as multi-source self-calibration and mosaicing, result in information which is difficult or impossible to obtain otherwise.
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    We study the properties of the dissipative accretion flow around rotating black holes in presence of mass loss. We obtain the complete set of global inflow-outflow solutions in the steady state by solving the underlying conservation equations self-consistently. We observe that global inflow-outflow solutions are not the isolated solution, instead such solutions are possible for wide range of inflow parameters. Accordingly, we identify the boundary of the parameter space for outflows, spanned by the angular momentum ($\lambda_{\rm in}$) and the energy (${\cal E}_{\rm in}$) at the inner sonic point ($x_{\rm in}$), as function of the dissipation parameters and find that parameter space gradually shrinks with the increase of dissipation rates. Further, we examine the properties of the outflow rate $R_{\dot m}$ (defined as the ratio of outflow to inflow mass flux) and ascertain that dissipative processes play the decisive role in determining the outflow rates. We calculate the limits on the maximum outflow rate ($R_{\dot{m}}^{\rm max}$) in terms of viscosity parameter ($\alpha$) as well as black hole spin ($a_k$) and obtain the limiting range as $3\% \le R_{\dot{m}}^{\rm max} \le 19\%$. Moreover, we calculate the viable range of $\alpha$ that admits the coupled inflow-outflow solutions and find that $\alpha \lesssim 0.25$ for $R_{\dot m} \ne 0$. Finally, we discuss the observational implication of our formalism to infer the spin of the black holes. Towards this, considering the highest observed QPO frequency of black hole source GRO J1655-40 ($\sim 450$ Hz), we constrain the spin value of the source as $a_k \ge 0.57$.
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    Using a projection-based decoupling of the Fokker-Planck equation, control strategies that allow to speed up the convergence to the stationary distribution are investigated. By means of an operator theoretic framework for a bilinear control system, two different feedback control laws are proposed. Projected Riccati and Lyapunov equations are derived and properties of the associated solutions are given. The well-posedness of the closed loop systems is shown and local and global stabilization results, respectively, are obtained. An essential tool in the construction of the controls is the choice of appropriate control shape functions. Results for a two dimensional double well potential illustrate the theoretical findings in a numerical setup.
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Recent comments

Alvaro M. Alhambra Jul 24 2017 16:10 UTC

This paper has just been updated and we thought it would be a good
idea to advertise it here. It was originally submitted a year ago, and
it has now been essentially rewritten, with two new authors added.

We have fixed some of the original results and now we:
-Show how some fundamental theorem

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gae Jul 21 2017 17:58 UTC

Dear Marco, indeed the description in those two papers is very general because they treat both DV and CV channels. However, things become "easier" and more specific if you restrict things to DVs. In this regard, let me point you at this paper https://arxiv.org/pdf/1706.05384.pdf , in particular to

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Marco Piani Jul 21 2017 16:33 UTC

Is it really the case for the general definition of teleportation-covariant channel given in https://arxiv.org/abs/1609.02160 or https://arxiv.org/abs/1510.08863 ? I understand that there special classes of teleportation-covariant channels are considered where what you say holds (that is, for pairs

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gae Jul 21 2017 15:51 UTC

If two channels are teleportation-covariant and between Hilbert spaces with the same dimension, then the correction unitaries are exactly the same. For instance, for any pair of Pauli channels (not just a Pauli and the identity), the corrections are Pauli operators.

Marco Piani Jul 21 2017 15:36 UTC

Is it more precisely that the result holds for any pair of *jointly* teleportation-covariant channels? The definition of teleportation-covariant channel (according to what I see in https://arxiv.org/abs/1609.02160 ) is such that the covariance can be achieved with a unitary at the output that depend

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gae Jul 21 2017 14:01 UTC

Thx Steve for pointing out this paper too, which is relevant as well. Let me just remark that the PRL mentioned in my previous comment [PRL 118, 100502 (2017), https://arxiv.org/abs/1609.02160 ] finds the result for any pair of teleportation-covariant channels (not just between a Pauli channel and t

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Steve Flammia Jul 21 2017 13:43 UTC

Actually, there is even earlier work that shows this result. In [arXiv:1109.6887][1], Magesan, Gambetta, and Emerson showed that for any Pauli channel the diamond distance to the identity is equal to the trace distance between the associated Choi states. They prefer to phrase their results in terms

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Stefano Pirandola Jul 21 2017 09:43 UTC

This is very interesting. In my reading list!

gae Jul 21 2017 09:00 UTC

In relation with the discussion at page 21 of this paper. Consider depolarizing channels (including the trivial case of the identity channel) which are teleportation covariant as in the definition Eq. (9) of https://arxiv.org/abs/1510.08863 [Nature Communications 8, 15043 (2017)]. The diamond norm b

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Chris Ferrie Jul 18 2017 02:32 UTC

Since arXiv now supports supplementary material, we did not host the source externally. The easiest way to view the code is using https://nbviewer.jupyter.org: https://nbviewer.jupyter.org/urls/arxiv.org/src/1707.05088v1/anc/specdens-est.ipynb.

By the way, if you are having difficulty navigating

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