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    Recently, penalties promoting signals that are sparse within and across groups have been proposed. In this letter, we propose a generalization that allows to encode more intricate dependencies within groups. However, this complicates the realization of the threshold function associated with the penalty, which hinders the use of the penalty in energy minimization. We discuss how to sidestep this problem, and demonstrate the use of the modified penalty in an energy minimization formulation for an inverse problem.
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    This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This long standing problem is related to homogenization theory on the one hand, and to regularization theory on the other hand. Here, a novel approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming preassigned values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.
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    Our study exploits the Constant Intensity Cut principles applied simultaneously to muonic and electromagnetic detectors of cosmic rays. We use the fact that the ordering of events according to their signal sizes induced in different types of surface detectors provides information about the mass composition of primary cosmic-ray beam, with low sensitivity to details of hadronic interactions. Composition analysis at knee energies is performed using Monte Carlo simulations for extensive air showers having maxima located far away from a hypothetical observatory. Another type of a hypothetical observatory is adopted to examine composition of ultra-high energy primaries which initiate vertical air showers with maxima observed near surface detectors.
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    The existence of neutron stars with $2M_\odot$ requires the strong stiffness of the equation of state (EoS) of neutron-star matter. We introduce a multi-pomeron exchange potential (MPP) working universally among 3- and 4-baryons to stiffen the EoS. Its strength is restricted by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The EoSs are derived using the Brueckner-Hartree-Fock (BHF) and the cluster variational method (CVM) with the nuclear interactions ESC and AV18. The mass-radius relations are derived by solving the Tolmann-Oppenheimer-Volkoff (TOV) equation, where the maximum masses over $2M_\odot$ are obtained on the basis of the terrestrial data. Neutron-star radii $R$ at a typical mass $1.5M_\odot$ are predicted to be $12.3\!\sim\!13.0$ km. The uncertainty of calculated radii is mainly from the ratio of 3- and 4-pomeron coupling constants, which cannot be fixed by any terrestrial experiment. Though values of $R(1.5M_\odot)$ are not influenced by hyperon-mixing effects, finely-observed values for them indicate degrees of EoS softening by hyperon mixing in the region of $M\!\sim\!2M_\odot$. If $R(1.5M_\odot)$ is less than about 12.4 km, the softening of EoS by hyperon mixing has to be weak. Useful information can be expected by the space mission NICER offering precise measurements for neutron-star radii within $\pm 5\%$.
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    We study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on an $AA$-stacked bilayer honeycomb lattice. In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor antiferromagnetic (AFM) exchange couplings $J_{1}$, $J_{2}$, and $J_{3}$, respectively. The two layers are coupled with an AFM NN exchange coupling $J_{1}^{\perp}\equiv\delta J_{1}$. The model is studied for arbitrary values of $\delta$ along the line $J_{3}=J_{2}\equiv\alpha J_{1}$ that includes the most highly frustrated point at $\alpha=\frac{1}{2}$, where the classical ground state is macroscopically degenerate. The coupled cluster method is used at high orders of approximation to calculate the magnetic order parameter and the triplet spin gap. We are thereby able to give an accurate description of the quantum phase diagram of the model in the $\alpha\delta$ plane in the window $0 \leq \alpha \leq 1$, $0 \leq \delta \leq 1$. This includes two AFM phases with Néel and striped order, and an intermediate gapped paramagnetic phase that exhibits various forms of valence-bond crystalline order. We obtain accurate estimations of the two phase boundaries, $\delta = \delta_{c_{i}}(\alpha)$, or equivalently, $\alpha = \alpha_{c_{i}}(\delta)$, with $i=1$ (Néel) and 2 (striped). The two boundaries exhibit an "avoided crossing" behavior with both curves being reentrant.
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    The $R_{K^{(*)}}$ anomaly can be explained by tree level exchange of leptoquarks. We study the consequences of subjecting these models to the principle of minimal flavor violation (MFV). We consider MFV in the linear regime, and take the charged lepton Yukawa matrix to be the only spurion that violates lepton flavor universality. We find that a combination of constraints from a variety of processes -- $b\to s\mu\mu$, $b\to s\tau\tau$, $b\to s\nu\nu$, $b\bar b\to\tau\tau$, $b\to c\tau\nu$ and (for scalar leptoquarks) $B_s-\overline{B_s}$ mixing -- excludes MFV in these models.
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    The memory-type control charts, such as EWMA and CUSUM, are powerful tools for detecting small quality changes in univariate and multivariate processes. Many papers on economic design of these control charts use the formula proposed by Lorenzen and Vance (1986) [Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics, 28(1), 3-10, DOI: 10.2307/1269598]. This paper shows that this formula is not correct for memory-type control charts and its values can significantly deviate from the original values even if the ARL values used in this formula are accurately computed. Consequently, the use of this formula can result in charts that are not economically optimal. The formula is corrected for memory-type control charts, but unfortunately the modified formula is not a helpful tool from a computational perspective. We show that simulation-based optimization is a possible alternative method.
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    The initial mass function for the stars is often modeled by a lognormal distribution. This paper is devoted to demonstrating the advantage of introducing a left and right truncated lognormal probability density function, which is characterized by four parameters. Its normalization constant, mean, the variance, second moment about the origin and distribution function are calculated. The chi-square test and the Kolmogorov--Smirnov test are performed on four samples of stars.
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    We suggest a novel approach for wide-field imaging of the neural network dynamics of brain slices that uses highly sensitivity magnetometry based on nitrogen-vacancy (NV) centers in diamond. In-vitro recordings in brain slices is a proven method for the characterization of electrical neural activity and has strongly contributed to our understanding of the mechanisms that govern neural information processing. However, traditional recordings can only acquire signals from a few positions simultaneously, which severely limits their ability to characterize the dynamics of the underlying neural networks. We suggest to radically extend the scope of this method using the wide-field imaging of the neural magnetic fields across the slice by means of NV magnetometry. Employing comprehensive computational simulations and theoretical analyses, we characterize the spatiotemporal characteristics of the neural magnetic fields and derive the required key performance parameters of an imaging setup based on NV magnetometry. In particular, we determine how the technical parameters determine the achievable spatial resolution for an optimal reconstruction of the neural currents from the measured field distributions. Finally, we compare the imaging of neural slice activity with that of a single planar pyramidal cell. Our results suggest that imaging of neural slice activity will be possible with the upcoming generation of NV magnetic field sensors, while imaging of the activity of a single planar cell remains more challenging.
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    In this work, we explore the long-term variability properties of the blazar PKS 0219-164 in the radio and the $\gamma$-ray regime, utilizing the OVRO 15 GHz and the \fermi/LAT observations from the period 2008--2017. We found that $\gamma$-ray emission is more variable than the radio emission implying that $\gamma$ ray emission possibly originated in more compact regions while the radio emission represented continuum emission from the large scale jets. Also, in $\gamma$-ray the source exhibited spectral variability characterized by the \emph softer-when-brighter trend, a less frequently observed feature in the high energy emission by BL Lacs. In radio, using Lomb-Scargle periodogram and weighted wavelet z-transform, we detected a strong signal of quasi-periodic oscillation (QPO) with a periodicity of 270 $\pm$ 26 days with possible harmonics of 550 $\pm$ 42 and 1150 $\pm$ 157 days periods. At a time when the issue of the detection of QPOs in blazars is still under debate, the observed QPO with high statistical significance ( $\sim$ 97\% -- 99\% global significance over underlying red-noise processes) and persistent over nearly 10 oscillations could make one of the strongest cases for the detection of QPOs in blazar light curves. We discuss various blazar models that might lead to the $\gamma$-ray and radio variability, QPO, and the achromatic behavior seen in the high energy emission from the source.
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    We present a search for optical bursts from the repeating fast radio burst FRB 121102 using simultaneous observations with the high-speed optical camera ULTRASPEC on the 2.4-m Thai National Telescope and radio observations with the 100-m Effelsberg Radio Telescope. A total of 13 radio bursts were detected, but we found no evidence for corresponding optical bursts in our 70.7-ms frames. The 5-sigma upper limit to the optical flux density during our observations is 0.33 mJy at 767nm. This gives an upper limit for the optical burst fluence of 0.046 Jy ms, which constrains the broadband spectral index of the burst emission to alpha < -0.2. Two of the radio pulses are separated by just 34 ms, which may represent an upper limit on a possible underlying periodicity (a rotation period typical of pulsars), or these pulses may have come from a single emission window that is a small fraction of a possible period.
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    NGC6217 is a nearby spiral galaxy with a starburst region near its center. Evidence for a low luminosity Active Galactic Nucleus (AGN) in its core has also been found in optical spectra. Intriguingly, X-ray observations by ROSAT revealed three knots aligned with the galaxy center, resembling a jet structure. This paper presents a study of XMM-Newton observations made to assess the hypothesis of a jet emitted from the center of NGC6217. The XMM data confirm the knots found with ROSAT and our spectral analysis shows that they have similar spectral properties with a hard photon index Gamma~1.7. The core of NGC6217 is well fitted by a model with an AGN and a starburst component, where the AGN contributes at most 46% of the total flux. The candidate jet has an apparent length ~15 kpc and a luminosity of ~5 X 10^38 erg/s. It stands out by being hosted by a spiral galaxy, since jets are more widely associated with ellipticals. To explain the jet launching mechanism we consider the hypothesis of an advection dominated accretion flow with a low accretion rate. The candidate jet emitted from NGC6217 is intriguing since it represents a challenge to the current knowledge of the connection between AGN, jets and host galaxies.
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    We study the motion of an electron bubble in the zero temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wavefunction is coupled to a Schrödinger equation for the electron wavefunction, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^4$He at a pressure of one bar. By performing fully 3D spatio-temporal simulations of the superfluid coupled to an electron, that is modelled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex-nucleation limited mobility of the ion to recover values in reasonable agreement with measured data.
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    Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. A vertex separator set in a graph is a set of vertices that disconnects two vertices. In this paper we study the relation between vertex separator sets, some chordality properties which are natural generalizations of being chordal and the hyperbolicity of the graph. We also give a characterization of being quasi-isometric to a tree in terms of chordality and prove that this condition also characterizes being hyperbolic, when restricted to triangles, and having stable geodesics, when restricted to bigons.
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    Inference from fMRI data faces the challenge that the hemodynamic system, that relates the underlying neural activity to the observed BOLD fMRI signal, is not known. We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD time series, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way. The prior mean function may be generated from a standard LTI system, based on a canonical hemodynamic response function, or a more elaborate physiological model such as the Balloon model. This gives us the nonparametric flexibility of the GP, but allows the posterior to fall back on the physiologically based prior when the data are weak. Results on simulated data show that even with an erroneous prior for the GP, the proposed model is still able to discriminate between active and non-active voxels in a satisfactory way. The proposed model is also applied to real fMRI data, where our Gaussian process model in several cases finds brain activity where a baseline model with fixed hemodynamics does not.
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    The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic algorithms - or by repeatedly kernelizing recursively in the branch-and-reduce paradigm. It is of critical importance for these algorithms that kernelization is fast and returns a small kernel. Current algorithms are either slow but produce a small kernel, or fast and give a large kernel. We attempt to accomplish both of these goals simultaneously, by giving an efficient parallel kernelization algorithm based on graph partitioning and parallel bipartite maximum matching. We combine our parallelization techniques with two techniques to accelerate kernelization further: dependency checking that prunes reductions that cannot be applied, and reduction tracking that allows us to stop kernelization when reductions become less fruitful. Our algorithm produces kernels that are orders of magnitude smaller than the fastest kernelization methods, while having a similar execution time. Furthermore, our algorithm is able to compute kernels with size comparable to the smallest known kernels, but up to two orders of magnitude faster than previously possible. Finally, we show that our kernelization algorithm can be used to accelerate existing state-of-the-art heuristic algorithms, allowing us to find larger independent sets faster on large real-world networks and synthetic instances.
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    It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Robin boundary conditions, are unique up to multiplication by a positive constant.
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    In this paper we study the asymptotic and qualitative properties of least energy radial sign-changing solutions of the fractional Brezis--Nirenberg problem ruled by the s-laplacian, in a ball of $\mathbb{R}^n$, when $s \in (0,1)$ and $n > 6s$. As usual, $\lambda$ is the (positive) parameter in the linear part in $u$, and we consider $\lambda$ close to zero. We prove that if such solutions vanish at the center of the ball then they vanish everywhere, we establish a bound on the number of sign-changes and, when $s$ is close to $1$, for a suitable value of the parameter $\lambda$ such solutions change sign exactly once. Moreover, for any $s \in (0,1)$ and $\lambda$ sufficiently small we prove that the number of connected components of the complement of the nodal set corresponds to the number of sign-changes plus one. In addition, for any $s \in (\frac{1}{2},1)$, we prove that least energy nodal solutions which change sign exactly once have the limit profile of a "tower of bubbles", as $\lambda \to 0^+$, i.e. the positive and negative parts concentrate at the same point (which is the center of the ball) with different concentration speeds.
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    Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. We investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI) in a magnetized Taylor-Couette flow using direct numerical simulations. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter plays a special role for its dynamics and determines its growth rate. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear states remain in all cases nearly axisymmetric suggesting that HMRI turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.
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    The MAGIC telescopes, located at the Roque de los Muchachos Observatory (2200 a.s.l.) in the Canary Island of La Palma, are placed on the top of a mountain, from where a window of visibility of about 5 deg in zenith and 80 deg in azimuth is open in the direction of the surrounding ocean. This permits to search for a signature of particle showers induced by earth-skimming cosmic tau neutrinos in the PeV to EeV energy range arising from the ocean. We have studied the response of MAGIC to such events, employing Monte Carlo simulations of upward-going tau neutrino showers. The analysis of the shower images shows that air showers induced by tau neutrinos can be discriminated from the hadronic background coming from a similar direction. We have calculated the point source acceptance and the expected event rates, assuming an incoming tau neutrino flux consistent with IceCube measurements, and for a sample of generic neutrino fluxes from photo-hadronic interactions in AGNs. The analysis of about 30 hours of data taken toward the sea leads to a point source sensitivity for tau neutrinos at the level of the down-going point source analysis of the Pierre Auger Observatory.
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    The aim of this article is to start a study of Jordan derivations in finite endomorphism semirings.
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    Aggregate location data is often used to support smart services and applications, such as generating live traffic maps or predicting visits to businesses. In this paper, we present the first study on the feasibility of membership inference attacks on aggregate location time-series. We introduce a game-based definition of the adversarial task, and cast it as a classification problem where machine learning can be used to distinguish whether or not a target user is part of the aggregates. We empirically evaluate the power of these attacks on both raw and differentially private aggregates using two real-world mobility datasets. We find that membership inference is a serious privacy threat, and show how its effectiveness depends on the adversary's prior knowledge, the characteristics of the underlying location data, as well as the number of users and the timeframe on which aggregation is performed. Although differentially private defenses can indeed reduce the extent of the attacks, they also yield a significant loss in utility. Moreover, a strategic adversary mimicking the behavior of the defense mechanism can greatly limit the protection they provide. Overall, our work presents a novel methodology geared to evaluate membership inference on aggregate location data in real-world settings and can be used by providers to assess the quality of privacy protection before data release or by regulators to detect violations.
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    Let $p>2$ be a prime, $k$ a finite field of characteristic $p$, and $G$ a nilpotent-by-finite compact $p$-adic analytic group. Write $kG$ for the completed group ring of $G$ over $k$. We show that $kG$ is a catenary ring.
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    We describe an OctTree algorithm for the MPI-parallel, adaptive mesh-refinement code \sc FLASH, which can be used to calculate the gas self-gravity, and also the angle-averaged local optical depth, for treating ambient diffuse radiation. The algorithm communicates to the different processors only those parts of the tree that are needed to perform the tree walk locally. The advantage of this approach is a relatively low memory requirement, important in particular for the optical depth calculation, which needs to process information from many different directions. This feature also enables a general tree-based radiation transport algorithm that will be described in a subsequent paper, and delivers excellent scaling up to at least 1500 cores. Boundary conditions for gravity can be either isolated or periodic, and they can be specified in each direction independently, using a newly developed generalisation of the Ewald method. The gravity calculation can be accelerated with the \em adaptive block update technique by partially re-using the solution from the previous time-step. Comparison with the \sc Flash internal multi-grid gravity solver shows that tree based methods provide a competitive alternative, particularly for problems with isolated or mixed boundary conditions. We evaluate several multipole acceptance criteria (MACs) and identify a relatively simple APE MAC which provides high accuracy at low computational cost. The optical depth estimates are found to agree very well with those of the \sc RADMC-3D radiation transport code, with the tree solver being much faster. Our algorithm is available in the standard release of the \sc FLASH code in version 4.0 and later.
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    In this paper, we prove the well-posedness and optimal regularity for the solution of stochastic evolution equations with Lipschitz-type coefficients driven by general multiplicative noises. To consider the well-posedness of the problem, the linear operator of the equations is only need to be a generator of a $C_0$-semigroup and the proposed noises are quite general, which include space-time white noise and rougher noises. When the linear operator generates an analytic semigroup, we derive the optimal spatial and trajectory regularity of the solution through a generalized criterion by factorization method.
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    We study $\beta$ decays within an effective theory that treats nuclei as a spherical collective core with an even number of neutrons and protons that can couple to an additional neutron and/or proton. First we explore Gamow-Teller $\beta$ decays of parent odd-odd nuclei into low-lying ground-, one-, and two-phonon states of the daughter even-even system. The low-energy constants of the effective theory are adjusted to data on $\beta$ decays to ground states or Gamow-Teller strengths. The corresponding theoretical uncertainty is estimated based on the power counting of the effective theory. For a variety of medium-mass and heavy isotopes the theoretical matrix elements are in good agreement with experiment within the theoretical uncertainties. We then study the two-neutrino double-$\beta$ decay into ground and excited states. The results are remarkably consistent with experiment within theoretical uncertainties, without the necessity to adjust any low-energy constants.
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    In both WMAP and Planck observations on the temperature anisotropy of cosmic microwave background (CMB) radiation a number of large-scale anomalies were discovered in the past years, including the CMB parity asymmetry in the low multipoles. By defining a directional statistics, we find that the CMB parity asymmetry is directional dependent, and the preferred axis is stable, which means that it is independent of the chosen CMB map, the definition of the statistic, or the CMB masks. Meanwhile, we find that this preferred axis strongly aligns with those of the CMB quadrupole, octopole, as well as those of other large-scale observations. In addition, all of them aligns with the CMB kinematic dipole, which hints to the non-cosmological origin of these directional anomalies in cosmological observations.
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    Measuring the imprint of primordial gravitational waves in the cosmic microwave background (CMB) polarisation field is one of the main goals in modern cosmology. However, the so called $B$-mode polarisation can be generated by different sources besides the primary one predicted by inflationary theories, known as secondary $B$-mode signal. Among them, CMB lensing and astrophysical foregrounds play an important role. Moreover, a partial sky analysis leads to a leakage between $E$-modes and $B$-modes. In this article, we use the well known Minkowski functionals (MF) statistics to study the significance of this leakage in the CMB lensing $B$-mode signal. We find that the MF can detect the $E$-to-$B$ leakage contamination, thus it should not be neglected in future CMB data analysis.
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    We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors $\nu=\pm 2$, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.
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    We compute the tensor spectral index $n_t$, tensor-to-scalar ratio $r$, consistency relation and other inflation parameters in the general monomial multifield slow-roll inflation models with potentials $V \sim\sum_i\lambda_i \left|\phi_i\right|^{p_i}$ analytically. The general models give a novel relation that the tensor and scalar spectral index $n_t$, $n_s$ and also the consistency relation $n_t/r$ are all nearly proportional to the logarithm of the number of fields $N_f$ when $N_f$ is getting extremely large with the order of magnitude around $\mathcal{O}(10^{40})$. Requiring the slow variation parameter $\epsilon\lesssim 0.1$ then gives the upper bound of $N_f$ with $N_f\lesssim N_*e^{ZN_*}$ where $N_*$ is the number of e-foldings before the end of inflation and $Z$ is a value depends on the specific probability distributions of $\lambda_i$ and $p_i$. We also find a relation between the inflationary observables which is independent of the specific probability distributions. Besides, $n_t/r$ is differ from the single-field result $-1/8$ with substantial probability except for a few very special cases. In the end, we derive theoretical bounds for tensor-to-scalar ratio $r>2/N_*$ ($r\gtrsim0.03$) and for $n_t$ which can be tested by observation in the near future.
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    It is known that the classical limit of the second order BPZ null vector decoupling equation for the simplest two 5-point degenerate spherical conformal blocks yields: (i) the normal form of the Heun equation with the (holomorphic) accessory parameter determined by the 4-point classical block on the sphere, and (ii) a pair of the Floquet-type linearly independent solutions of the normal form Heun equation. A key point in a derivation of the above result is the classical asymptotic of the 5-point degenerate blocks in which the so-called heavy and light contributions decouple. In the present work the semi-classical heavy-light factorization of the 5-point degenerate conformal blocks is studied. In particular, a mechanism responsible for the decoupling of the heavy and light contributions is identified. Moreover, it is shown that the factorization property yields a practical method of computation of the Floquet-type Heun's solutions. Finally, it should be stressed that tools analyzed in this work have a broad spectrum of applications, in particular, in the studies of spectral problems with the Heun class of potentials, sphere-torus correspondence in 2d CFT, the KdV theory, the connection problem for the Heun equation and black hole physics. These applications are main motivations for the present work.
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    We consider a chain of coupled pendula pairs, where each pendulum is connected to the nearest neighbors in the longitudinal and transverse directions. The common strings in each pair are modulated periodically by an external force. In the limit of small coupling and near the 1:2 parametric resonance, we derive a novel system of coupled PT-symmetric discrete nonlinear Schrodinger equation, which has Hamiltonian symmetry but has no gauge symmetry. By using the conserved energy, we find the parameter range for the linear and nonlinear stability of the zero equilibrium. Numerical experiments illustrate how destabilization of the zero equilibrium takes place when the stability constraints are not satisfied. The central pendulum excites nearest pendula and this process continues until a dynamical equilibrium is reached where each pendulum in the chain oscillates at a finite amplitude.
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    We investigate the properties of a sunspot light-bridge, focusing on the changes produced by the impact of a plasma blob ejected from a C-class flare. We observed a sunspot in active region NOAA 12544 using spectropolarimetric raster maps of the four Fe I lines around 15655 Å with the GREGOR Infrared Spectrograph (GRIS), narrow-band intensity images sampling the Fe I 6173 Å line with the GREGOR Fabry-Pérot Interferometer (GFPI), and intensity broad band images in G-band and Ca II H band with the High-resolution Fast Imager (HiFI). All these instruments are located at the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. The data cover the time before, during, and after the flare event. The analysis is complemented with Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) data from the Solar Dynamics Observatory (SDO). The physical parameters of the atmosphere at differents heights were inferred using spectral-line inversion techniques. We identify photospheric and chromospheric brightenings, heating events, and changes in the Stokes profiles associated to the flare eruption and the subsequent arrival of the plasma blob to the light bridge, after traveling along an active region loop. The measurements suggest that these phenomena are the result of reconnection events driven by the interaction of the plasma blob with the magnetic field topology of the light bridge.
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    We modify the Fick's law for coordinate dependent diffusion from first principle. Based on this we show that Fick's law in its original (constant diffusion) and also in its modified form dictates that the equilibrium probability distribution of a Brownian particle with coordinate dependent damping cannot be the Boltzmann distribution. We show the modified Boltzmann distribution from the condition of balance of currents. We compare these results with existing results of our alternative model and give arguments as to why the Boltzmann distribution for such a system actually captures a non-equilibrium state.
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    In security-sensitive applications, the success of machine learning depends on a thorough vetting of their resistance to adversarial data. In one pertinent, well-motivated attack scenario, an adversary may attempt to evade a deployed system at test time by carefully manipulating attack samples. In this work, we present a simple but effective gradient-based approach that can be exploited to systematically assess the security of several, widely-used classification algorithms against evasion attacks. Following a recently proposed framework for security evaluation, we simulate attack scenarios that exhibit different risk levels for the classifier by increasing the attacker's knowledge of the system and her ability to manipulate attack samples. This gives the classifier designer a better picture of the classifier performance under evasion attacks, and allows him to perform a more informed model selection (or parameter setting). We evaluate our approach on the relevant security task of malware detection in PDF files, and show that such systems can be easily evaded. We also sketch some countermeasures suggested by our analysis.
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    We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other fields. In the process we introduce the notions of split-exchangeability and plane-invariance of a general Markov splitting model in order to readily obtain probabilities over various equivalence classes of trees that arise in statistics, phylogenetics, epidemiology and group theory.
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    In this paper, the fractional order Hegselmann-Krause type model with leadership is studied.We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics. Necessary optimality conditions are obtained by the use of a fractional counterpart of Pontryagin Maximum Principle. The effectiveness of the proposed control strategy is illustrated by numerical examples.
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    We propose to revisit knowledge transfer for training object detectors on target classes with only weakly supervised training images. We present a unified knowledge transfer framework based on training a single neural network multi-class object detector over all source classes, organized in a semantic hierarchy. This provides proposal scoring functions at multiple levels in the hierarchy, which we use to guide object localization in the target training set. Compared to works using a manually engineered class-generic objectness measure as a vehicle for transfer, our learned top-level scoring function for 'entity' is much stronger. Compared to works that perform class-specific transfer from a few most related source classes to the target class, our framework enables to explore a broad rage of generality of transfer. Experiments on 200 object classes in the ILSVRC 2013 dataset show that our technique (1) leads to much greater performance improvements than manually engineered objectness; (2) outperforms the best reported transfer learning results on this dataset by a wide margin (+40% correct localization on the target training set, and +14% mAP on the target test set).
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    The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability.
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    This paper presents a novel application to detect counterfeit identity documents forged by a scan-printing operation. Texture analysis approaches are proposed to extract validation features from security background that is usually printed in documents as IDs or banknotes. The main contribution of this work is the end-to-end mobile-server architecture, which provides a service for non-expert users and therefore can be used in several scenarios. The system also provides a crowdsourcing mode so labeled images can be gathered, generating databases for incremental training of the algorithms.
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    We consider inverse curvature flows in warped product manifolds, which are constrained subject to local terms of lower order, namely the radial coordinate and the generalized support function. Under various assumptions we prove longtime existence and smooth convergence to a coordinate slice. We apply this result to deduce a new Minkowski type inequality in the anti-de-Sitter Schwarzschild manifolds and a weighted isoperimetric type inequality in the hyperbolic space.
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    We construct a five-mode helical dynamo model containing three velocity and two magnetic modes and solve it analytically. This model exhibits dynamo transition via supercritical pitchfork bifurcation. We show that the critical magnetic Reynolds number for dynamo transition ($\mathrm{Rm}_c$) asymptotes to constant values for very low and very high magnetic Prandtl numbers ($\mathrm{Pm}$). Beyond dynamo transition, secondary bifurcations lead to periodic, quasi-periodic, and chaotic dynamo states as the forcing amplitude is increased and chaos appears through a quasi-periodic route.
  • PDF
    Mallinson's idea that some spin textures in planar magnetic structures could produce an enhancement of the magnetic flux on one side of the plane at the expense of the other gave rise to permanent magnet configurations known as Halbach magnet arrays. Applications range from wiggler magnets in particle accelerators and free electron lasers, to motors, to magnetic levitation trains, but exploiting Halbach arrays in micro- or nanoscale spintronics devices requires solving the problem of fabrication and field metrology below 100 \mum size. In this work we show that a Halbach configuration of moments can be obtained over areas as small as 1 x 1 \mum^2 in sputtered thin films with Néel-type domain walls of unique domain wall chirality, and we measure their stray field at a controlled probe-sample distance of 12.0 x 0.5 nm. Because here chirality is determined by the interfacial Dyzaloshinkii-Moriya interaction the field attenuation and amplification is an intrinsic property of this film, allowing for flexibility of design based on an appropriate definition of magnetic domains. 100 nm-wide skyrmions illustrate the smallest kind of such structures, for which our measurement of stray magnetic fields and mapping of the spin structure shows they funnel the field toward one specific side of the film given by the sign of the Dyzaloshinkii-Moriya interaction parameter D.
  • PDF
    A review of recent state-of-the-art pulsed field experiments performed on URu$_2$Si$_2$ under a magnetic field applied along its easy magnetic axis $\mathbf{c}$ is given. Resistivity, magnetization, magnetic susceptibility, Shubnikov-de Haas, and neutron diffraction experiments are presented, permitting to emphasize the relationship between Fermi surface reconstructions, the destruction of the hidden-order and the appearance of a spin-density wave state in a high magnetic field.
  • PDF
    Given a set $U$ of alternatives, a choice (correspondence) on $U$ is a contractive map $c$ defined on a family $\Omega$ of nonempty subsets of $U$. Semantically, a choice $c$ associates to each menu $A \in \Omega$ a nonempty subset $c(A) \subseteq A$ comprising all elements of $A$ that are deemed selectable by an agent. A choice on $U$ is total if its domain is the powerset of $U$ minus the empty set, and partial otherwise. According to the theory of revealed preferences, a choice is rationalizable if it can be retrieved from a binary relation on $U$ by taking all maximal elements of each menu. It is well-known that rationalizable choices are characterized by the satisfaction of suitable axioms of consistency, which codify logical rules of selection within menus. For instance, WARP (Weak Axiom of Revealed Preference) characterizes choices rationalizable by a transitive relation. Here we study the satisfiability problem for unquantified formulae of an elementary fragment of set theory involving a choice function symbol $\mathtt{c}$, the Boolean set operators and the singleton, the equality and inclusion predicates, and the propositional connectives. In particular, we consider the cases in which the interpretation of $\mathtt{c}$ satisfies any combination of two specific axioms of consistency, whose conjunction is equivalent to WARP. In two cases we prove that the related satisfiability problem is NP-complete, whereas in the remaining cases we obtain NP-completeness under the additional assumption that the number of choice terms is constant.
  • PDF
    It is typically assumed that the kinetic and magnetic helicities play a crucial role in the growth of large-scale dynamo. In this paper we demonstrate that helicity is not essential for the amplification of large-scale magnetic field. For this purpose, we perform nonhelical magnetohydrodynamic (MHD) simulation, and show that the large-scale magnetic field can grow in nonhelical MHD when random external forcing is employed at scale $1/10$ the box size. The energy fluxes and shell-to-shell transfer rates computed using the numerical data show that the large-scale magnetic energy grows due to the energy transfers from the velocity field at the forcing scales.
  • PDF
    We report the first intensity correlation measured with star light since Hanbury Brown and Twiss' historical experiments. The photon bunching $g^{(2)}(\tau, r=0)$, obtained in the photon counting regime, was measured for 3 bright stars, $\alpha$ Boo, $\alpha$ CMi, and $\beta$ Gem. The light was collected at the focal plane of a 1~m optical telescope, was transported by a multi-mode optical fiber, split into two avalanche photodiodes and digitally correlated in real-time. For total exposure times of a few hours, we obtained contrast values around $2\times10^{-3}$, in agreement with the expectation for chaotic sources, given the optical and electronic bandwidths of our setup. Comparing our results with the measurement of Hanbury Brown et al. on $\alpha$ CMi, we argue for the timely opportunity to extend our experiments to measuring the spatial correlation function over existing and/or foreseen arrays of optical telescopes diluted over several kilometers. This would enable $\mu$as long-baseline interferometry in the optical, especially in the visible wavelengths with a limiting magnitude of 10.
  • PDF
    We present an approach for road segmentation that only requires image-level annotations at training time. We leverage distant supervision, which allows us to train our model using images that are different from the target domain. Using large publicly available image databases as distant supervisors, we develop a simple method to automatically generate weak pixel-wise road masks. These are used to iteratively train a fully convolutional neural network, which produces our final segmentation model. We evaluate our method on the Cityscapes dataset, where we compare it with a fully supervised approach. Further, we discuss the trade-off between annotation cost and performance. Overall, our distantly supervised approach achieves 93.8% of the performance of the fully supervised approach, while using orders of magnitude less annotation work.
  • PDF
    A finite-range separable pairing force is implemented in the tilted axis cranking covariant density functional theory for describing rotational bands in open shell nuclei. The developed method is used to investigate the yrast sequence of 109Ag for an example. The experimental energy spectrum, angular momenta, and electromagnetic transition probabilities are well reproduced by taking into account pairing correlations with the separable paring force. An abrupt transition of the rotational axis from the long-intermediate plane to the long-short one is obtained and discussed in detail.
  • PDF
    We present an effective (minimal) theory for chiral two-dimensional materials. These materials possess an electro-magnetic coupling without exhibiting a topological gap. As an example, we study the response of doped twisted bilayers, unveiling unusual phenomena in the zero frequency limit. An in-plane magnetic field induces a huge paramagnetic response at the neutrality point and, upon doping, also gives rise to a substantial longitudinal Hall response. The system also accommodates nontrivial longitudinal plasmonic modes which are associated with a longitudinal magnetic moment, thus endowing them with a chiral character. Finally, we note that the optical activity can be considerably enhanced upon doping.

Recent comments

Māris Ozols Aug 03 2017 09:34 UTC

If I'm not mistaken, what you describe here is equivalent to the [QR decomposition][1]. The matrices $R_{ij}$ that act non-trivially only in a two-dimensional subspace are known as [Givens rotations][2]. The fact that any $n \times n$ unitary can be decomposed as a sequence of Givens rotations is ex

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gae Jul 26 2017 21:19 UTC

For those interested in the literature on teleportation simulation of quantum channels, a detailed and *comprehensive* review is provided in Supplementary Note 8 of https://images.nature.com/original/nature-assets/ncomms/2017/170426/ncomms15043/extref/ncomms15043-s1.pdf
The note describes well the t

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Maciej Malinowski Jul 26 2017 15:56 UTC

In what sense is the ground state for large detuning ordered and antiferromagnetic? I understand that there is symmetry breaking, but other than that, what is the fundamental difference between ground states for large negative and large positive detunings? It seems to be they both exhibit some order

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Stefano Pirandola Jul 26 2017 15:28 UTC

The performance of the memory assisted MDI-QKD with "quasi-EPR" sources is remarkable. It improves the key rate by 5 orders of magnitude over the PLOB bound at about 600 km (take a look at Figure 4).

Māris Ozols Jul 26 2017 11:07 UTC

Conway's list still has four other $1000 problems left:

https://oeis.org/A248380/a248380.pdf

SHUAI ZHANG Jul 26 2017 00:20 UTC

I am still working on improving this survey. If you have any suggestions, questions or find any mistakes, please do not hesitate to contact me: shuai.zhang@student.unsw.edu.au.

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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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!