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    A key feature of neural networks, particularly deep convolutional neural networks, is their ability to "learn" useful representations from data. The very last layer of a neural network is then simply a linear model trained on these "learned" representations. Despite their numerous applications in other tasks such as classification, retrieval, clustering etc., a.k.a. transfer learning, not much work has been published that investigates the structure of these representations or whether structure can be imposed on them during the training process. In this paper, we study the dimensionality of the learned representations by models that have proved highly succesful for image classification. We focus on ResNet-18, ResNet-50 and VGG-19 and observe that when trained on CIFAR10 or CIFAR100 datasets, the learned representations exhibit a fairly low rank structure. We propose a modification to the training procedure, which further encourages low rank representations of activations at various stages in the neural network. Empirically, we show that this has implications for compression and robustness to adversarial examples.
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    X-ray catalogues provide a wealth of information on many source types, ranging from compact objects to galaxies, clusters of galaxies, stars, and even planets. Thanks to the huge volume of X-ray sources provided in the 3XMM catalogue, along with many source specific products, many new examples from rare classes of sources can be identified. Through visualising spectra and lightcurves from about 80 observations included in the incremental part of the 3XMM catalogue, 3XMM-DR5, as part of the quality control of the catalogue, we identified two new X-ray sources, 3XMM J183333.1+225136 and 3XMM J184916.1+652943, that were highly variable. This work aims to investigate their nature. Through simple model fitting of the X-ray spectra and analysis of the X-ray lightcurves of 3XMM J183333.1+225136 and 3XMM J184916.1+652943, along with complementary photometry from the XMM-Newton Optical Monitor, Pan-Starrs and the Stella/WiFSIP and Large Binocular Telescope (LBT) spectra, we suggest that the two sources might be magnetic cataclysmic variables (CVs) of the polar type and we determine some of their properties. Both CVs have very hard spectra, showing no soft excess. They are both situated in the local neighbourhood, located within $\sim$1 kpc. 3XMM J183333.1+225136 has an orbital period of 2.15 hours. It shows features in the lightcurve that may be a total eclipse of the white dwarf. 3XMM J184916.1+652943 has an orbital period of 1.6 hours. Given that only a small sky area was searched to identify these CVs, future sensitive all sky surveys such as the eROSITA project should be very successful at uncovering large numbers of such sources.
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    An ordered set partition of $\{1,2,\ldots,n\}$ is a partition with an ordering on the parts. let $\OP_{n,k}$ be the set of ordered set partitions of $[n]$ with $k$ blocks, Godbole, Goyt, Herdan and Pudwell defined $\OP_{n,k}(\sigma)$ to be the set of ordered set partitions in $\OP_{n,k}$ avoiding a permutation pattern $\sigma$ and obtained the formula for $|\OP_{n,k}(\sigma)|$ when the pattern $\sigma$ is of length $2$. Later, Chen, Dai and Zhou found a formula algebraically for $|\OP_{n,k}(\sigma)|$ when the pattern $\sigma$ is of length $3$. In this paper, we define a new pattern avoidance for the set $\OP_{n,k}$, called $\WOP_{n,k}(\sigma)$, which includes the questions proposed by Godbole \textitet al. We obtain formulas for $|\WOP_{n,k}(\sigma)|$ combinatorially for any $\sigma$ of length $\leq 3$. We also define 3 kinds of descent statistics on ordered set partitions and study the distribution of the descent statistics on $\WOP_{n,k}(\sigma)$ for $\sigma$ of length $\leq 3$.
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    We cross-match objects from several different astronomical catalogs to determine the absolute proper proper motions of stars within the 30-arcmin radius fields of 115 Milky-Way globular clusters with the accuracy of 1--2~mas/yr. The proper motions are based on positional data recovered from the USNO-B1, 2MASS, URAT1, ALLWISE, UCAC5, and GAIA DR1 surveys with up to 10 positions spanning an epoch difference of up to $\sim$~65~years, and reduced to GAIA DR1 TGAS frame using UCAC5 as the reference catalog. Cluster members are photometrically identified by selecting horizontal- and red-giant branch stars on color-magnitude diagrams, and the mean absolute proper motions of the clusters with a typical formal error of $\sim$~0.4~mas/yr are computed by averaging the proper motions of selected members. The inferred absolute proper motions of clusters are combined with available radial-velocity data and heliocentric distance estimates to compute the cluster orbits in terms of the Galactic potential models based on Miyamoto and Nagai disk, Hernquist spheroid, and modified isothermal dark-matter halo (axisymmetric model without a bar) and the same model + rotating Ferre's bar (non-axisymmetric). Five distant clusters have higher-than-escape velocities, most likely due to large errors of computed transversal velocities, whereas the computed orbits of all other clusters remain bound to the Galaxy. Unlike previously published results, we find the bar to affect substantially the orbits of most of the clusters, even those at large Galactocentric distances, bringing appreciable chaotization, especially in the portions of the orbits close to the Galactic center, and stretching out the orbits of some of the thick-disk clusters.
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    In this work we present a non-standard model for microbial enhanced oil recovery including the oil-water interfacial area. Including the interfacial area in the model, we eliminate the hysteresis in the capillary pressure relationship. One of the characteristics that a surfactant should have, it is biological production at the oil-water interface. Therefore, we consider the production rate of surfactants not only as a function of the nutrient concentration, but also the interfacial area. To solve the model equations, we use an efficient and robust linearization scheme that considers a linear approximation of the capillary pressure gradient. A comprehensive, 1D implementation based on two-point flux approximation of the model is achieved. We consider different parameterizations for the interfacial tension and residual oil saturation reduction. Illustrative numerical simulations are presented, where we study the spatial distribution and evolution in time of the average pressure, water saturation, interfacial area, capillary pressure, residual oil saturation and bacterial, nutrient and surfactant concentrations. Inclusion of the interfacial area in the model leads to different predictions of oil recovery. The model can also be used to design new experiments contributing to a better understanding and optimization of MEOR.
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    We study dual strong coupling description of integrability-preserving deformation of the $O(N)$ sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the $\kappa-$deformed $O(N)$ sigma-model after $T-$duality transformation.
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    We present the relation between stellar specific angular momentum $j_*$, stellar mass $M_*$, and bulge-to-total light ratio $\beta$ for THINGS, CALIFA and Romanowsky \& Fall datasets, exploring the existence of a fundamental plane between these parameters as first suggested by Obreschkow \& Glazebrook. Our best-fit $M_*-j_*$ relation yields a slope of $\alpha = 1.03 \pm 0.11$ with a trivariate fit including $\beta$. When ignoring the effect of $\beta$, the exponent $\alpha = 0.56 \pm 0.06$ is consistent with $\alpha = 2/3$ predicted for dark matter halos. There is a linear $\beta - j_*/M_*$ relation for $\beta \lesssim 0.4$, exhibiting a general trend of increasing $\beta$ with decreasing $j_*/M_*$. Galaxies with $\beta \gtrsim 0.4$ have higher $j_*$ than predicted by the relation. Pseudobulge galaxies have preferentially lower $\beta$ for a given $j_*/M_*$ than galaxies that contain classical bulges. Pseudobulge galaxies follow a well-defined track in $\beta - j_*/M_*$ space, consistent with Obreschkow \& Glazebrook, while galaxies with classical bulges do not. These results are consistent with the hypothesis that while growth in either bulge type is linked to a decrease in $j_*/M_*$, the mechanisms that build pseudobulges seem to be less efficient at increasing bulge mass per decrease in specific angular momentum than those that build classical bulges.
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    We describe the combinatorics of the cell structure of the tensor category of bimodules over a radical square zero Nakayama algebra. This accounts to an explicit description of left, right, and two-sided cells.
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    Continuum emissions from dust grains are used as a general probe to constrain the initial physical conditions of molecular dense cores where new stars may born. To get as much information as possible from dust emissions, we have developed a tool, named as $COREGA$, which is capable of identifying positions of dense cores, optimizing a three-dimensional model for the dense cores with well characterized uncertainties. $COREGA$ can also estimate the physical properties of dense cores, such as density, temperature, and dust emissivity, through analyzing multi-wavelength dust continuum data sets. In the numerical tests on $COREGA$, the results of fitting simulated data are consistent with initial built-in parameters. We also demonstrate $COREGA$ by adding random gaussian noises with Monte Carlo methods and show that the results are stable against varying observational noise intensities within certain levels. A beam size $<$ 3 arcsec and rms $<$ 0.2mJy/pixel (1 pixel = 0.1") is needed for ALMA to distinguish different collapse models, such as power law and Bonner-Ebert sphere, during continuum observations of massive dense cores in Orion molecular cloud. Based on its advanced algorithm, $COREGA$ is capable of giving a quick and deep analysis on dust cores.
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    We theoretically investigate pumping of phonons by the dynamics of a magnetic film into a non-magnetic contact. The enhanced damping due to the loss of energy and angular momentum does not obey the Gilbert orthodoxy. The phonon pumping depends on magnetization direction as well as geometrical and material parameters and could be observable, e.g., in thin films of yttrium iron garnet on a thick dielectric substrate.
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    The allocation of a (treatment) condition-effect on the wrong principal component (misallocation of variance) in principal component analysis (PCA) has been addressed in research on event-related potentials of the electroencephalogram. However, the correct allocation of condition-effects on PCA components might be relevant in several domains of research. The present paper investigates whether different loading patterns at each condition-level are a basis for an optimal allocation of between-condition variance on principal components. It turns out that a similar loading shape at each condition-level is a necessary condition for an optimal allocation of between-condition variance, whereas a similar loading magnitude is not necessary.
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    Synchronous computation models simplify the design and the verification of fault-tolerant distributed systems. For efficiency reasons such systems are designed and implemented using an asynchronous semantics. In this paper, we bridge the gap between these two worlds. We introduce a (synchronous) round-based computational model and we prove a reduction for a class of asynchronous protocols to our new model. The reduction is based on properties of the code that can be checked with sequential methods. We apply the reduction to state machine replication systems, such as, Paxos, Zab, and Viewstamped Replication.
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    We analyze the origin of the structure observed in the reaction $J/\psi \to \gamma \eta'\pi^+\pi^-$ for $\eta'\pi^+\pi^-$ invariant masses close to the antiproton-proton ($\bar pp$) threshold, commonly associated with the $X(1835)$ resonance. Specifically, we explore the effect of a possible contribution from the two-step process $J/\psi \to \gamma \bar NN \to \gamma \eta'\pi^+\pi^-$. The calculation is performed in distorted-wave Born approximation which allows an appropriate inclusion of the $\bar NN$ interaction in the transition amplitude. The $\bar NN$ amplitude itself is generated from a corresponding potential recently derived within chiral effective field theory. We are able to reproduce the measured spectra for the reactions $J/\psi \to \gamma \bar pp$ and $J/\psi \to \gamma \eta'\pi^+\pi^-$ for invariant masses around the $\bar pp$ threshold. The structure seen in the $\eta'\pi^+\pi^-$ spectrum emerges as a threshold effect due to the opening of the $\bar pp$ channel.
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    Asymptotic approximations to the zeros of Jacobi polynomials are given, with methods to obtain the coefficients in the expansions. These approximations can be used as standalone methods for the non-iterative computation of the nodes of Gauss--Jacobi quadratures of high degree ($n\ge 100$). We also provide asymptotic approximations for functions related to the first order derivative of Jacobi polynomials which can be used to compute the weights of the Gauss--Jacobi quadrature. The performance of the asymptotic approximations is illustrated with numerical examples.
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    We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not possible for (HW) equation and that below the ground state energy there are solutions whose energy travels as a localised packet and which preserve this localisation in time. This behaviour for (HW) is in sharp contrast with classical NLS in any dimension and with fractional NLS with radial data. The second result addressed is the non existence of traveling waves moving at the speed of light. The main ingredients of the proof are commutator estimates and a careful study of spatial decay of traveling waves profile using the harmonic extension to the upper half space.
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    The Gauss-Manin equations are solved for a class of flat-metrics defined by Novikov algebras, this generalizing a result of Balinskii and Novikov who solved this problem in the case of commutative Novikov algebras (where the algebraic conditions reduce to those of a Frobenius algebra). The problem stems from the theory of first-order Hamiltonian operators and their reduction to a constant, or Darboux, form. The monodromy group associated with the Novikov algebra gives rise to an orbit space, which is, for a wide range of Novikov algebras, a cyclic quotient singularity.
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    We present optical photometry of Hubble Space Telescope (HST) ACS/WFC data of the resolved stellar populations in the outer disc of the dwarf irregular galaxy DDO 154. The photometry reveals that young main sequence stars are almost absent from the outermost HI disc. Instead, most are clustered near the main stellar component of the galaxy. We constrain the stellar initial mass function (IMF) by comparing the luminosity function of the main sequence stars to simulated stellar populations assuming a constant star formation rate over the dynamical timescale. The best-fitting IMF is deficient in high mass stars compared to a canonical Kroupa IMF, with a best-fit slope $\alpha = -2.45$ and upper mass limit $M_U = 16\ M_{\odot}$. This top-light IMF is consistent with predictions of the Integrated Galaxy-wide IMF theory. Combining the HST images with HI data from The HI Nearby Galaxy Survey Treasury (THINGS) we determine the star formation law (SFL) in the outer disc. The fit has a power law exponent $N = 2.92 \pm0.22$ and zero point $A=4.47 \pm 0.65 \times 10^{-7} \ M_{\odot} \ \text{yr}^{-1} \ \text{kpc}^{-2}$. This is depressed compared to the Kennicutt-Schmidt Star Formation Law, but consistent with weak star formation observed in diffuse HI environments. Extrapolating the SFL over the outer disc implies that there could be significant star formation occurring that is not detectable in H$\alpha$. Last, we determine the Toomre stability parameter $Q$ of the outer disc of DDO 154 using the THINGS HI rotation curve and velocity dispersion map. 72% of the HI in our field has $Q\leq 4$ and this incorporates 96% of the observed MS stars. Hence 28% of the HI in the field is largely dormant.
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    A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an elegant and rigorous route to the evaluation of equivalent higher-order materials, but are often of difficult and awkward practical implementation. On the other hand, identification techniques, though relying on simplifying assumptions, are of straightforward use. A novel strategy for the identification of equivalent second-gradient Mindlin solids is proposed in an attempt to combine the accuracy of asymptotic techniques with the simplicity of identification approaches. Following the asymptotic homogenization scheme, the overall behaviour is defined via perturbation functions, which (differently from the asymptotic scheme) are evaluated on a finite domain obtained as the periodic repetition of cells and subject to quadratic displacement boundary conditions. As a consequence, the periodicity of the perturbation function is satisfied only in an approximate sense, nevertheless results from the proposed identification algorithm are shown to be reasonably accurate.
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    By combining ab initio simulations including an on-site Coulomb repulsion term and Boltzmann theory, we explore the thermoelectric properties of (LaNiO$_3$)$_n$/(LaAlO$_3$)$_n$(001) superlattices ($n=1,3$) and identify a strong dependence on confinement, spacer thickness, and epitaxial strain. While the system with $n=3$ shows modest values of the Seebeck coefficient and power factor, the simultaneous reduction of the LaNiO$_3$ region and the LaAlO$_3$ spacer thickness to single layers results in a strong enhancement, in particular of the in-plane values. This effect can be further tuned by using epitaxial strain as control parameter: Under tensile strain corresponding to the lateral lattice constant of SrTiO$_3$ we predict in- and cross-plane Seebeck coefficients of $\pm 600$ $\mu$V/K and an in-plane power factor of $11$ $\mu$W/K$^2$cm for an estimated relaxation time of $\tau = 4$ fs around room temperature. These values are comparable to some of the best performing oxide systems such as La-doped SrTiO$_3$ or layered cobaltates and are associated with the opening of a small gap ($0.29$ eV) induced by the concomitant effect of octahedral tilting and Ni-site disproportionation. This establishes oxide superlattices at the verge of a metal-to-insulator transition driven by confinement and strain as promising candidates for thermoelectric materials.
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    The aim of this paper is to study the laws of the exponential functionals of the processes $X$ with independent increments, namely $$I_t= ∫_0^t\exp(-X_s)ds, \,\,t≥0,$$ and also $$I_∞= ∫_0^∞\exp(-X_s)ds.$$ Under suitable conditions we derive the integro-differential equations for the density of $I_t$ and $I_{\infty}$. We give sufficient conditions for the existence of smooth density of the laws of these functionals. In the particular case of Levy processes these equations can be simplified and, in a number of cases, solved explicitly.
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    Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean-free-path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries of Migdal-Eliashberg approximation. An intimate connection between dilute superconductivity and aborted ferroelectricity is widely suspected. In this review, we will give a brief account of ongoing research on bulk strontium titanate as an insulator, a metal and a superconductor.
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    The phase diagrams of correlated systems like cuprates or pnictides high-temperature superconductors are characterized by a topological change of the Fermi surface under continuous variation of an external parameter, the so-called Lifshitz transition. However, the large number of low-temperature instabilities and the interplay of multiple energy scales complicate the study of this phenomenon. Here we first identify the optical signatures of a pressure-induced Lifshitz transition in a clean elemental system, black phosphorus. By applying external pressures above 1.5 GPa, we observe a change in the pressure dependence of the Drude plasma frequency due to the appearance of massless Dirac fermions. At higher pressures, optical signatures of two structural phase transitions are also identified. Our findings suggest that a key fingerprint of the Lifshitz transition in solid state systems, and in absence of structural phase transitions, is a discontinuity of the Drude plasma frequency due to the change of Fermi surface topology.
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    Kingman's coalescent is one of the most popular models in population genetics. It describes the genealogy of a population whose genetic composition evolves in time according to the Wright-Fisher model, or suitable approximations of it belonging to the broad class of Fleming-Viot processes. Ancestral inference under Kingman's coalescent has had much attention in the literature, both in practical data analysis, and from a theoretical and methodological point of view. Given a sample of individuals taken from the population at time $t>0$, most contributions have aimed at making frequentist or Bayesian parametric inference on quantities related to the genealogy of the sample. In this paper we propose a Bayesian nonparametric predictive approach to ancestral inference. That is, under the prior assumption that the composition of the population evolves in time according to a neutral Fleming-Viot process, and given the information contained in an initial sample of $m$ individuals taken from the population at time $t>0$, we estimate quantities related to the genealogy of an additional unobservable sample of size $m^{\prime}\geq1$. As a by-product of our analysis we introduce a class of Bayesian nonparametric estimators (predictors) which can be thought of as Good-Turing type estimators for ancestral inference. The proposed approach is illustrated through an application to genetic data.
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    In this paper we present the results of parallel numerical computations of the long-term dynamics of linked vortex filaments in a three-dimensional FitzHugh-Nagumo excitable medium. In particular, we study all torus links with no more than 12 crossings and identify a timescale over which the dynamics is regular in the sense that each link is well-described by a spinning rigid conformation of fixed size that propagates at constant speed along the axis of rotation. We compute the properties of these links and demonstrate that they have a simple dependence on the crossing number of the link for a fixed number of link components. Furthermore, we find that instabilities that exist over longer timescales in the bulk can be removed by boundary interactions that yield stable torus links which settle snugly at the medium boundary. The Borromean rings are used as an example of a non-torus link to demonstrate both the irregular tumbling dynamics that arises in the bulk and its suppression by a tight confining medium. Finally, we investigate the collision of torus links and reveal that this produces a complicated wrestling motion where one torus link can eventually dominate over the other by pushing it into the boundary of the medium.
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    Cosmological simulations are fundamental tools to study structure formation and the astrophysics of evolving structures, in particular clusters of galaxies. While hydrodynamical simulations cannot sample efficiently large volumes and explore different cosmologies at the same time, N-body simulations lack the baryonic physics that is crucial to determine the observed properties of clusters. One solution is to use (semi-)analytical models to implement the needed baryonic physics. In this way, we can generate the many mock universes that will be required to fully exploit future large sky surveys, such as that from the upcoming eROSITA X-ray telescope. We developed a phenomenological model based on observations of clusters to implement gas density and temperature information on the dark-matter-only halos of the MultiDark simulations. We generate several full-sky mock light-cones of clusters for the WMAP and Planck cosmologies, adopting different parameters in our phenomenological model of the intra-cluster medium. For one of these simulations and models, we also generate 100 light-cones corresponding to 100 random observers and explore the variance among them in several quantities. In this first paper on MultiDark mock galaxy cluster light-cones, we focus on presenting our methodology and discuss predictions for eROSITA, in particular, exploring the potential of angular power spectrum analyses of its detected (and undetected) cluster population to study X-ray scaling relations, the intra-cluster medium, and the composition of the cosmic X-ray background. We make publicly available on-line more than 400 GB of light-cones, which include the expected eROSITA count rate, on Skies & Universes (http://www.skiesanduniverses.org).
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    We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer; this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent.
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    Recently, low frequency, broadband radio emission has been observed accompanying bright meteors by the Long Wavelength Array (LWA). The broadband spectra between 20 and 60 MHz were captured for several events, while the spectral index (dependence of flux density on frequency, with $S_\nu \propto \nu^\alpha$) was estimated to be $-4\pm1$ during the peak of meteor afterglows. Here we present a survey of meteor emission and other transient events using the Murchison Widefield Array (MWA) at 72-103 MHz. In our 322-hour survey, down to a $5\sigma$ detection threshold of 3.5 Jy/beam, no transient candidates were identified as intrinsic emission from meteors. We derived an upper limit of -3.7 (95% confidence limit) on the spectral index in our frequency range. We also report detections of other transient events, like reflected FM broadcast signals from small satellites, conclusively demonstrating the ability of the MWA to detect and track space debris on scales as small as 0.1 m in low Earth orbits.
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    Real-world networks such as social and communication networks are too large to be observed entirely. Such networks are often partially observed such that network size, network topology, and nodes of the original network are unknown. In this paper we formalize the Adaptive Graph Exploring problem. We assume that we are given an incomplete snapshot of a large network and additional nodes can be discovered by querying nodes in the currently observed network. The goal of this problem is to maximize the number of observed nodes within a given query budget. Querying which set of nodes maximizes the size of the observed network? We formulate this problem as an exploration-exploitation problem and propose a novel nonparametric multi-arm bandit (MAB) algorithm for identifying which nodes to be queried. Our contributions include: (1) $i$KNN-UCB, a novel nonparametric MAB algorithm, applies $k$-nearest neighbor UCB to the setting when the arms are presented in a vector space, (2) provide theoretical guarantee that $i$KNN-UCB algorithm has sublinear regret, and (3) applying $i$KNN-UCB algorithm on synthetic networks and real-world networks from different domains, we show that our method discovers up to 40% more nodes compared to existing baselines.
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    We study truncated moment sequences of distribution mixtures, especially from Gaussian and log-normal distributions and their Carathéodory numbers. For $\mathsf{A} = \{a_1,\dots,a_m\}$ continuous (sufficiently differentiable) functions on $\mathbb{R}^n$ we give a general upper bound of $m-1$ and a general lower bound of $\left\lceil \frac{2m}{(n+1)(n+2)}\right\rceil$. For polynomials of degree at most $d$ in $n$ variables we find that the number of Gaussian and log-normal mixtures is bounded by the Carathéodory numbers in \citedidio17Cara. Therefore, for univariate polynomials $\{1,x,\dots,x^d\}$ at most $\left\lceil\frac{d+1}{2}\right\rceil$ distributions are needed. For bivariate polynomials of degree at most $2d-1$ we find that $\frac{3d(d-1)}{2}+1$ Gaussian distributions are sufficient. We also treat polynomial systems with gaps and find, e.g., that for $\{1,x^2,x^3,x^5,x^6\}$ 3 Gaussian distributions are enough for almost all truncated moment sequences. For log-normal distributions the number is bounded by half of the moment number. We give an example of continuous functions where more Gaussian distributions are needed than Dirac delta measures. We show that any inner truncated moment sequence has a mixture which contains any given distribution.
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    Using element-specific X-ray magnetic circular dichroism (XMCD) technique we have studied different magnetic sublattices in a multiferroic Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ single crystal. The XMCD measurements at the \emphL$_{2,3}$-edges of Ho and Nd, and at the Fe \emphK-edge have been performed at \emphT=2~K under a magnetic field up to 17~T applied along the trigonal \emphc-axis as well as in the basal \emphab-plane. All three magnetic sublattices are shown to undergo a spin-reorientation transition under magnetic field applied along the \emphc-axis. On the contrary, when magnetic field is applied in the \emphab-plane only the holmium atoms exhibit a magnetization jump. Thus, the element-specific magnetization curves revealed the Ho sublattice to be much stronger coupled to the Fe one than the Nd sublattice. The results demonstrate that the Ho$^{3+}$ subsystem plays even more dominant role in magnetic behavior of Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ crystal than in pure HoFe$_{3}$(BO$_{3}$)$_{4}$ crystal.
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    Gog and Magog trapezoids are certain arrays of positive integers that generalize alternating sign matrices (ASMs) and totally symmetric self-complementary plane partitions (TSSCPPs) respectively. Zeilberger used constant term formulas to prove that there is the same number of (n,k)-Gog trapezoids as there is of (n,k)-Magog trapezoids, thereby providing so far the only proof for a weak version of a conjecture by Mills, Robbins and Rumsey from 1986. About 20 years ago, Krattenthaler generalized Gog and Magog trapezoids and formulated an extension of their conjecture, and, recently, Biane and Cheballah generalized Gog trapezoids further and formulated a related conjecture. In this paper, we derive constant term formulas for various refined enumerations of generalized Gog trapezoids including those considered by Krattenthaler and by Biane and Cheballah. For this purpose we employ a result on the enumeration of truncated monotone triangles which is in turn based in the author's operator formula for the number of monotone triangles with prescribed bottom row. As a byproduct, we also generalize the operator formula for monotone triangles by including the inversion number and the complementary inversion number for ASMs. Constant term formulas as well as determinant formulas for the refined Magog trapezoid numbers that appear in Krattenthaler's conjecture are also deduced by using the classical approach based on non-intersecting lattice paths and the Lindström-Gessel-Viennot theorem. Finally, we review and partly extend a few existing tools that may be helpful in relating constant term formulas for Gogs to those for Magogs to eventually prove the above mentioned conjectures.
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    Stretchcam is a thin camera with a lens capable of zooming with small actuations. In our design, an elastic lens array is placed on top of a sparse, rigid array of pixels. This lens array is then stretched using a small mechanical motion in order to change the field of view of the system. We present in this paper the characterization of such a system and simulations which demonstrate the capabilities of stretchcam. We follow this with the presentation of images captured from a prototype device of the proposed design. Our prototype system is able to achieve 1.5 times zoom when the scene is only 300 mm away with only a 3% change of the lens array's original length.
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    We use the SDSS-Gaia catalogue to search for material stripped off the atypical globular cluster $\omega$ Centauri. As actions are conserved under slow changes of the potential, this allows identification of groups of stars with a common accretion history. We devise a method to assess the significance of halo substructures based on their clustering in action space, using metallicity as a secondary check. This is validated against smooth models and numerically constructed stellar halos. We identify a number of new substructures in the SDSS-Gaia catalogue, including 7 high significance, high energy and retrograde ones. Using a simple model of the accretion of the progenitor of the $\omega$ Centauri, we argue for the possible association of up to 4 of our new substructures (labelled Rg1, Rg3, Rg4 and Rg6) with this event. This sets a minimum mass of $5 \times 10^8 M_\odot$ for the progenitor, so as to bring $\omega$ Centauri to its current location in action -- energy space. Our proposal can be tested by high resolution spectroscopy of the candidates to look for the unusual abundance patterns possessed by $\omega$ Centauri stars.
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    We used the Tycho-Gaia Astrometric Solution catalogue, part of the Gaia Data Release 1, to search for candidate astrometric microlensing events expected to occur within the remaining lifetime of the Gaia satellite. Our search yielded one promising candidate. We predict that the nearby DQ type white dwarf LAWD 37 (WD 1142-645) will lens a background star and will reach closest approach on November 11th 2019 ($\pm$ 4 days) with impact parameter $380\pm10$ mas. This will produce an apparent maximum deviation of the source position of $2.8\pm0.1$ mas. In the most propitious circumstance, Gaia will be able to determine the mass of LAWD 37 to $\sim3\%$. This mass determination will provide an independent check on atmospheric models of white dwarfs with helium rich atmospheres, as well as tests of white dwarf mass radius relationships and evolutionary theory.
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Recent comments

Joel Wallman Apr 18 2018 13:34 UTC

A very nice approach! Could you clarify the conclusion a little bit though? The aspirational goal for a quantum benchmark is to test how well we approximate a *specific* representation of a group (up to similarity transforms), whereas what your approach demonstrates is that without additional knowle

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serfati philippe Mar 29 2018 14:07 UTC

see my 2 papers on direction of vorticity (nov1996 + feb1999) = https://www.researchgate.net/profile/Philippe_Serfati (published author, see also mendeley, academia.edu, orcid etc)

serfati philippe Mar 29 2018 13:34 UTC

see my 4 papers, 1998-1999, on contact and superposed vortex patches, cusps (and eg splashs), corners, generalized ones on lR^n and (ir/)regular ones =. http://www.researchgate.net/profile/Philippe_Serfati/ (published author).

Luis Cruz Mar 16 2018 15:34 UTC

Related Work:

- [Performance-Based Guidelines for Energy Efficient Mobile Applications](http://ieeexplore.ieee.org/document/7972717/)
- [Leafactor: Improving Energy Efficiency of Android Apps via Automatic Refactoring](http://ieeexplore.ieee.org/document/7972807/)

Dan Elton Mar 16 2018 04:36 UTC

Comments are appreciated. Message me here or on twitter @moreisdifferent

Code is open source and available at :
[https://github.com/delton137/PIMD-F90][1]

[1]: https://github.com/delton137/PIMD-F90

Danial Dervovic Mar 01 2018 12:08 UTC

Hello again Māris, many thanks for your patience. Your comments and questions have given me much food for thought, and scope for an amended version of the paper -- please see my responses below.

Please if any of the authors of [AST17 [arXiv:1712.01609](https://arxiv.org/abs/1712.01609)] have any fu

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igorot Feb 28 2018 05:19 UTC

The Igorots built an [online community][1] that helps in the exchange, revitalization, practice, and learning of indigenous culture. It is the first and only Igorot community on the web.

[1]: https://www.igorotage.com/

Beni Yoshida Feb 13 2018 19:53 UTC

This is not a direct answer to your question, but may give some intuition to formulate the problem in a more precise language. (And I simplify the discussion drastically). Consider a static slice of an empty AdS space (just a hyperbolic space) and imagine an operator which creates a particle at some

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Abhinav Deshpande Feb 10 2018 15:42 UTC

I see. Yes, the epsilon ball issue seems to be a thorny one in the prevalent definition, since the gate complexity to reach a target state from any of a fixed set of initial states depends on epsilon, and not in a very nice way (I imagine that it's all riddled with discontinuities). It would be inte

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Elizabeth Crosson Feb 10 2018 05:49 UTC

Thanks for the correction Abhinav, indeed I meant that the complexity of |psi(t)> grows linearly with t.

Producing an arbitrary state |phi> exactly is also too demanding for the circuit model, by the well-known argument that given any finite set of gates, the set of states that can be reached i

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