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    In this article, we consider the stochastic wave equation on $\mathbb{R}_{+} \times \mathbb{R}^d$, in spatial dimension $d=1$ or $d=2$, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structure are given by locally integrable functions $\gamma$ (in time) and $f$ (in space), which are the Fourier transforms of tempered measures $\nu$ on $\mathbb{R}$, respectively $\mu$ on $\mathbb{R}^d$. Our main result shows that the law of the solution $u(t,x)$ of this equation is absolutely continuous with respect to the Lebesgue measure, provided that the spatial spectral measure $\mu$ satisfies an integrability condition which ensures that the sample paths of the solution are Hölder continuous.
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    Entanglement has developed into an essential concept for the characterization of phases and phase transitions in ground states of quantum many-body systems. In this work, we use the logarithmic negativity to study the spatial entanglement structure in the transverse-field Ising chain both in the ground state and at nonzero temperatures. Specifically, we investigate the entanglement between two disjoint blocks as a function of their separation, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled, which holds even in the presence of long-ranged quantum correlations, i.e., at the system's quantum critical point. Using Time-Evolving Block Decimation (TEBD), we explore this feature as a function of temperature and size of the two blocks and present a simple model to describe our numerical observations.
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    We use a new mass modelling method, GravSphere, to measure the central dark matter density profile of the Draco dwarf spheroidal galaxy. Draco's star formation shut down long ago, making it a prime candidate for hosting a 'pristine' dark matter cusp, unaffected by stellar feedback during galaxy formation. We first test GravSphere on a suite of three tidally stripped mock 'Draco'-like dwarfs, placed on orbits similar to the real Draco around the Milky Way, containing realistic populations of binary stars, and with realistic foreground contamination. We show that we are able to correctly infer the dark matter density profile of both cusped and cored mocks within our 95% confidence intervals. While we obtain only a weak inference on the logarithmic slope of these density profiles, we are able to obtain a robust inference of the amplitude of the inner dark matter density at 150pc, $\rho_{\rm DM}(150\,{\rm pc})$. We show that, combined with constraints on the density profile at larger radii, this is sufficient to distinguish a $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cusp $-$ that has $\rho_{\rm DM}(150\,{\rm pc}) > 1.8 \times 10^8\,{\rm M}_\odot \,{\rm kpc}^{-3}$ $-$ from alternative dark matter models that have lower inner densities. We then apply GravSphere to the real Draco data. We find that Draco has an inner dark matter density of $\rho_{\rm DM}(150\,{\rm pc}) = 2.4_{-0.6}^{+0.5} \times 10^8\,{\rm M}_\odot \,{\rm kpc}^{-3}$, consistent with a $\Lambda$CDM cusp. Using a velocity independent SIDM model, calibrated on $\Lambda$SIDM cosmological simulations, we show that Draco's high central density gives an upper bound on the SIDM cross section of $\sigma/m < 0.57\,{\rm cm}^2\,{\rm g}^{-1}$ at 99% confidence. We conclude that the inner density of nearby dwarf galaxies like Draco provides a new and competitive probe of dark matter models.
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    This Final Report (FR) presents the results of the Enhanced direct imaging exoplanet detection with astrometry mass determination project, which was executed in support of NASA's Exoplanet Exploration Program and the ROSES Technology Development for Exoplanet Missions (TDEM). The first milestone is concerned with a demonstration of medium fidelity astrometry accuracy and the second milestone demonstrates high-contrast imaging utilizing the same astrometry-capable optics. We have met milestone #1 with a comfortable margin. The average accuracy obtained over the three datasets is 5.75e-5 L/D, which is 4 times better than the milestone requirement, or equivalent to 2.5microarcsec on 2.4m telescope, or 1.5microarcsec for a 4m telescope, working in the visible band. These results show the potential of this technique to enable detection and measure masses of Earth-like planets around nearby stars, hence bringing a real benefit to the astronomy community. We also met milestone #2 and demonstrated that it is possible to achieve high-contrast imaging utilizing a coronagraph fed by a telescope equipped with a DP, enabling dual use of the telescope. We performed three different high-contrast imaging runs and met the milestone #2 of 5e-7 raw contrast for all of them. On average, we obtained 3.33e-7 raw contrast considering all data sets. This result is 35% better than the milestone #2 requirement. We validated the stability of the high-contrast region by averaging frames and subtracting the average from single frames, which resulted in contrast improvement of approximately one order of magnitude, reaching 2.72e-8 contrast. The main achievement of this work was the medium fidelity demonstration and feasibility validation of performing astrometry and direct imaging using the same instrument, significantly enhancing the expected scientific yield of dedicated exoplanet characterization missions.
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    The variation of the work function upon carbon adsorption on the reconstructed Au(110) surface is measured experimentally and compared to density functional calculations. The adsorption dynamics is simulated with ab-initio molecular dynamics techniques. The contribution of various energetically available adsorption sites on the deposition process is analyzed, and the work function behavior with carbon coverage is explained by the resultant electron charge density distributions.
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    The digital economy is a highly relevant item on the European Union's policy agenda. Cross-border internet purchases are part of the digital economy, but their total value can currently not be accurately measured or estimated. Traditional approaches based on consumer surveys or business surveys are shown to be inadequate for this purpose, due to language bias and sampling issues, respectively. We address both problems by proposing a novel approach based on supply-side data, namely tax returns. The proposed data-driven record-linkage techniques and machine learning algorithms utilize two additional open data sources: European business registers and internet data. Our main finding is that the value of total cross-border internet purchases within the European Union by Dutch consumers was over EUR 1.3 billion in 2016. This is more than 6 times as high as current estimates. Our finding motivates the implementation of the proposed methodology in other EU member states. Ultimately, it could lead to more accurate estimates of cross-border internet purchases within the entire European Union.
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    It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new four-parameter statistical distribution which is a $\kappa$-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the $\kappa$-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter $\nu$, and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models. We also provide various associated statistical measures and inequality measures.
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    The measurement science in realizing and disseminating the unit for pressure in the International System of Units (SI), the pascal (Pa), has been the subject of much interest at the National Institute of Standards and Technology (NIST). Modern optical-based techniques for pascal metrology have been investigated, including multi-photon ionization and cavity ringdown spectroscopy. Work is ongoing to recast the pascal in terms of quantum properties and fundamental constants and in so doing, make vacuum metrology consistent with the global trend toward quantum-based metrology. NIST has ongoing projects that interrogate the index of refraction of a gas using an optical cavity for low vacuum, and count background particles in high vacuum to extreme high vacuum using trapped laser-cooled atoms.
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    For a pair of conjugate trigonometrical polynomials $C (t) = \sum_ { j = 1 } ^N { { a_j}\cos jt }, S(t) = \sum_ { j = 1 } ^N { { a_j}\sin jt }$ with real coefficients and normalization ${a_1} = 1 $ we solve the extremal problem \[ \sup_ a_2,...,a_N \left ( \min_t \left{ \Re \left ( F\left ( e^ it \right) \right): \Im \left ( F\left ( e^ it \right) \right) = 0 \right} \right) = -\frac14 \sec ^2\frac\piN + 2. \]We show that the solution is unique and is given by \[ a_j^ (0) = \frac 1 U'_N\left (\cos \frac\pi N + 2 \right) U' _ N - j + 1 \left (\cos \frac\pi N + 2 \right) U_ j - 1 \left (\cos \frac\pi N + 2 \right), \]where the $U_j(x)$ are the Chebyshev polynomials of the second kind, and the $U'_j(x)$ are their derivatives, $j = 1, \ldots, N.$ As a consequence, we obtain some theorems on covering of intervals by polynomial images of the unit disc. We formulate several conjectures on a number of extremal problems on classes of polynomials.
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    We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms, reminiscent to a problem posed by Fulton-Hansen.
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    In the paper we study applications of integral transforms composition method (ITCM) for obtaining transmutations via integral transforms. It is possible to derive wide range of transmutation operators by this method. Classical integral transforms are involved in the integral transforms composition method (ITCM) as basic blocks, among them are Fourier, sine and cosine-Fourier, Hankel, Mellin, Laplace and some generalized transforms. The ITCM and transmutations obtaining by it are applied to deriving connection formulas for solutions of singular differential equations and more simple non-singular ones. We consider well-known classes of singular differential equations with Bessel operators, such as classical and generalized Euler-Poisson-Darboux equation and the generalized radiation problem of A.Weinstein. Methods of this paper are applied to more general linear partial differential equations with Bessel operators, such as multivariate Bessel-type equations, GASPT (Generalized Axially Symmetric Potential Theory) equations of A.Weinstein, Bessel-type generalized wave equations with variable coefficients,ultra B-hyperbolic equations and others. So with many results and examples the main conclusion of this paper is illustrated: the integral transforms composition method (ITCM) of constructing transmutations is very important and effective tool also for obtaining connection formulas and explicit representations of solutions to a wide class of singular differential equations, including ones with Bessel operators.
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    The Near-Infrared Spectrograph (NIRSpec) is one of four instruments aboard the James Webb Space Telescope (JWST). NIRSpec is developed by ESA with AIRBUS Defence & Space as prime contractor. The calibration of its various observing modes is a fundamental step to achieve the mission science goals and provide users with the best quality data from early on in the mission. Extensive testing of NIRSpec on the ground, aided by a detailed model of the instrument, allow us to derive initial corrections for the foreseeable calibrations. We present a snapshot of the current calibration scheme that will be revisited once JWST is in orbit.
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    Changing-look quasars are a recently identified class of active galaxies in which the strong UV continuum and/or broad optical hydrogen emission lines associated with unobscured quasars either appear or disappear on timescales of months to years. The physical processes responsible for this behaviour are still debated, but changes in the black hole accretion rate or accretion disk structure appear more likely than changes in obscuration. Here we report on four epochs of spectroscopy of SDSS J110057.70-005304.5, a quasar at a redshift of $z=0.378$ whose UV continuum and broad hydrogen emission lines have faded, and then returned over the past $\approx$20 years. The change in this quasar was initially identified in the infrared, and an archival spectrum from 2010 shows an intermediate phase of the transition during which the flux below rest-frame $\approx$3400Å has decreased by close to an order of magnitude. This combination is unique compared to previously published examples of changing-look quasars, and is best explained by dramatic changes in the innermost regions of the accretion disk. The optical continuum has been rising since mid-2016, leading to a prediction of a rise in hydrogen emission line flux in the next year. Increases in the infrared flux are beginning to follow, delayed by a $\sim$3 year observed timescale. If our model is confirmed, the physics of changing-look quasars are governed by processes at the innermost stable circular orbit (ISCO) around the black hole, and the structure of the innermost disk. The easily identifiable and monitored changing-look quasars would then provide a new probe and laboratory of the nuclear central engine.
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    We report a new changing-look quasar, WISE~J105203.55+151929.5 at $z=0.303$, found by identifying highly mid-IR variable quasars in the WISE/NEOWISE data stream. Compared to multi-epoch mid-IR photometry of a large sample of SDSS-confirmed quasars, WISE J1052+1519 is an extreme photometric outlier, fading by more than a factor of two at $3.4$ and $4.6 \mu$m since 2009. Swift target-of-opportunity observations in 2017 show even stronger fading in the soft X-rays compared to the ROSAT detection of this source in 1995, with at least a factor of fifteen decrease. We obtained second-epoch spectroscopy with the Palomar telescope in 2017 which, when compared with the 2006 archival SDSS spectrum, reveals that the broad H$\beta$ emission has vanished and that the quasar has become significantly redder. The two most likely interpretations for this dramatic change are source fading or obscuration, where the latter is strongly disfavored by the mid-IR data. We discuss various physical scenarios that could cause such changes in the quasar luminosity over this timescale, and favor changes in the innermost regions of the accretion disk that occur on the thermal and heating/cooling front timescales. We discuss possible physical triggers that could cause these changes, and predict the multiwavelength signatures that could distinguish these physical scenarios.
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    We introduce the notion of the difference quotient set of a real valued function $f$ on a set $E\subset[0,1]$, and compare this set to the range of $f$ on $E$. We discuss the measure theoretic properties of both the range and the difference quotient set of $f$ over $E$ under different assumptions on $f$ and $E$.
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    We observed comet C/2016 R2 (PANSTARRS) with the ARO 10-m SMT, and report the first detection of CO emission from this comet with amounts high enough to be the primary driver of activity. We obtained spectra and maps of the CO J=2-1 rotational line at 230 GHz between 2017 December and 2018 January. We calculated an average production rate of Q(CO)=(4.6+/-0.4)x10$^{28}$ mol s$^{-1}$ at r ~2.9 au and delta ~2.1 au. The CO line is thin FWHM ~ 0.8 km s$^{-1}$ with a slight blue-shift ~ -0.1 km s$^{-1}$ from the ephemeris velocity, and we derive a gas expansion velocity of V$_{exp}$ = 0.50+/-0.15 km s$^{-1}$. This comet produced approximately half the CO that comet C/1995 O1 (Hale-Bopp) did at 3 au. If CO production scales with nucleus surface area, then the radius need not exceed ~15 km. The spectra and mapping data are consistent with CO arising from a combination of a sunward-side active area and an isotropic source. For HCN, we calculated a 3-sigma upper limit production rate of Q(HCN) < 8x10$^{24}$ molecules s$^{-1}$, which corresponds to an extraordinarily high abundance ratio limit of Q(CO)/Q(HCN) > 5000. We inferred a production rate of molecular nitrogen of Q(N$_2$) ~2.8x10$^{27}$ molecules s$^{-1}$ using our CO data and the reported N$_2$/CO column density ratio (Cochran & MacKay 2018a,b). The comet does not show the typical nitrogen depletion seen in comets, and the CO-rich, N$_2$-rich and HCN-depleted values are consistent with formation in a cold environment of T < 50 K that may have provided significant N$_2$ shielding.
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    Extended narrow-line regions (NLRs) around active galactic nuclei (AGN) are shaped by the distribution of gas in the host galaxy and by the geometry of the circumnuclear obscuration, and thus they can be used to test the AGN unification model. In this work, we quantify the morphologies of the narrow-line regions in 308 nearby AGNs ($z=0-0.14$, \lbol $\sim 10^{42.4-44.1}$ \erg) from the MaNGA survey. Based on the narrow-line region maps, we find that a large fraction (81\%) of these AGN have bi-conical NLR morphology. The distribution of their measured opening angles suggests that the intrinsic opening angles of the ionization cones has a mean value of 85--98$^\circ$ with a finite spread of 39-44$^\circ$ (1-$\sigma$). Our inferred opening angle distribution implies a number ratio of type I to type II AGN of 1:1.6--2.3, consistent with other measurements of the type I / type II ratio at low AGN luminosities. Combining these measurements with the WISE photometry data, we find that redder mid-IR color (lower effective temperature of dust) corresponds to stronger and narrower photo-ionized bicones. This relation is in agreement with the unification model that suggests that the bi-conical narrow-line regions are shaped by a toroidal dusty structure within a few pc from the AGN. Furthermore, we find a significant alignment between the minor axis of host galaxy disks and AGN ionization cones. Together, these findings suggest that obscuration on both circumnuclear ($\sim $pc) and galactic ($\sim$ kpc) scales are important in shaping and orienting the AGN narrow-line regions.
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    Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding schemes. As proposed in Yuan and Lin [J. R. Statist. Soc. B, 68 (2006), 49-67], the group lasso is a natural and computationally convenient approach to perform variable selection in settings with categorical covariates. As pointed out by Simon and Tibshirani [Stat. Sin., 22 (2011), 983-1001], "standardization" by means of block-wise orthonormalization of column submatrices each corresponding to one group of variables can substantially boost performance. In this note, we study the aspect of standardization for the special case of categorical predictors in detail. The main result is that orthonormalization is not required; column-wise scaling of the design matrix followed by re-scaling and centering of the coefficients is shown to have exactly the same effect. Similar reductions can be achieved in the case of interactions. The extension to the so-called sparse group lasso, which additionally promotes within-group sparsity, is considered as well. The importance of proper standardization is illustrated via extensive simulations.
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    Information on the star-formation histories of cD galaxies and their extended stellar haloes lie in their spectra. Therefore, to determine whether these structures evolved together or through a two-phase formation, we need to spectroscopically separate the light from each component. We present a pilot study to use BUDDI to fit and extract the spectra of the cD galaxy NGC 3311 and its halo in an Integral Field Spectroscopy datacube, and carry out a simple stellar populations analysis to study their star-formation histories. Using MUSE data, we were able to isolate the light of the galaxy and its halo throughout the datacube, giving spectra representing purely the light from each of these structures. The stellar populations analysis of the two components indicates that, in this case, the bulk of the stars in both the halo and the central galaxy are very old, but the halo is more metal poor and less $\alpha$-enriched than the galaxy. This result is consistent with the halo forming through the accretion of much smaller satellite galaxies with more extended star formation. It is noteworthy that the apparent gradients in age and metallicity indicators across the galaxy are entirely consistent with the radially-varying contributions of galaxy and halo components, which individually display no gradients. The success of this study is promising for its application to a larger sample of cD galaxies that are currently being observed by IFU surveys.
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    Communications over power lines in the frequency range above 2 MHz, commonly referred to as broadband (BB) power line communications (PLC), has been the focus of increasing research attention and standardization efforts in recent years. BB-PLC channels are characterized by a dominant colored non-Gaussian additive noise, as well as by periodic variations of the channel impulse response and the noise statistics. In this work we study the fundamental rate limits for BB-PLC channels by bounding their capacity while accounting for the unique properties of these channels. We obtain explicit expressions for the derived bounds for several BB-PLC noise models, and illustrate the resulting fundamental limits in a numerical analysis.
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    We investigate the potential collider signatures of singly-charged and doubly-charged Higgs bosons such as those arising in minimal left-right symmetric models. Focusing on multileptonic probes in the context of the high-luminosity run of the Large Hadron Collider, we separately assess the advantages of the four-leptonic and trileptonic final states for a representative benchmark setup designed by considering a large set of experimental constraints. Our study establishes possibilities of identifying singly-charged and doubly-charged scalars at the Large Hadron Collider with a large significance, for luminosity goals expected to be reached during the high-luminosity phase of the Large Hadron Collider. We generalise our results and demonstrate that existing limits can in principle be pushed much further in the heavy mass regime.
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    While the width-luminosity relation among type Ia supernovae (slower is brighter) is one of the best studied properties of this type of events, its physical basis has not been identified convincingly. The 'luminosity' is known to be related to a clear physical quantity - the amount of $^{56}$Ni synthesised, but the 'width' has not been quantitatively linked yet to a physical time scale. In Paper I it was shown that the gamma-ray escape time $t_0$, which determines the long term evolution of the bolometric light curve, can be robustly inferred from observations, and its observed values span a narrow range of 30-45 days for the full range of observed $^{56}$Ni masses. In this paper we show that the recombination time of $^{56}$Fe and $^{56}$Co from doubly to singly ionized states causes the typical observed break in the color curve B-V due to a cliff in the mean opacities, and is a robust width measure of the light curve, which is insensitive to radiation transfer uncertainties. We show that a simple photospheric model can be used to calculate the recombination time to an accuracy of $\sim5$ days, allowing a quantitative understanding of the color WLR. The two physical times scales of the width luminosity relation are shown to be set by two (direction averaged and $^{56}$Ni weighted) column densities- the total column density which sets $t_0$ and the $^{56}$Ni column density which sets the recombination time. Central detonations of sub-$\rm M_{ch}$ WDs and direct WD collision models have gamma-ray escape times and recombination times which are consistent with observations across the luminosity range of type Ia's. Delayed detonation Chandrasekhar mass models have recombination times that are broadly consistent with observations, with tension at the bright end of the luminosity range and inconsistent gamma-ray escape times at the faint end.
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    We propose a phenomenological understanding of the recently discovered weak Mott insulator in the moiré superlattice of twisted bilayer graphene, especially the emergent superconductivity at low temperature within the weak Mott insulator phase, namely while lowering temperature, the longitudinal resistivity first grows below temperature $T_m$, but then rapidly drops to zero at even lower temperature $T_c$. An emergent superconductor in an insulator phase is very unusual. Here we propose that this phenomenon is due to the pure two-dimensional nature of the bilayer graphene moiré superlattice. We also compare our results with other theories proposed so far.
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    Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider the class of non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases in this class are classified by a topological invariant $\omega$ and a central charge $c$. Here we investigate the correlations of string operators in order to gain insight into the interplay between topology and criticality. In the gapped phases, these non-local operators are the string order parameters that allow us to extract $\omega$. More remarkable is that the correlation lengths of these operators show universal features, depending only on $\omega$. In the critical phases, the scaling dimensions of these operators serve as an order parameter, encoding both $\omega$ and $c$. More generally, we derive the exact long-distance asymptotics of these correlation functions using the theory of Toeplitz determinants. We include physical discussion in light of the mathematical results. This includes an expansion of the lattice operators in terms of the operator content of the relevant conformal field theory. Moreover, we discuss the spin chains which are dual to these fermionic systems.
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    We propose a way to generate tiny couplings of freeze-in massive particle dark matter with the Standard Model particles dynamically by considering an extension of the electroweak gauge symmetry. The dark matter is considered to be a singlet under this extended gauge symmetry which we have assumed to be the one in a very widely studied scenario called left-right symmetric model. Several heavy particles, that can be thermally inaccessible in the early Universe due to their masses being greater than the reheat temperature after inflation, can play the role of portals between dark matter and Standard Model particles through effective one loop couplings. Due to the loop suppression, one can generate the required non-thermal dark matter couplings without any need of highly fine tuned Yukawa couplings beyond that of electron Yukawa with the Standard Model like Higgs boson. We show that generic values of Yukawa couplings as large as $10^{-4}-10^{-3}$ can keep the dark matter out of thermal equilibrium in the early Universe and produce the correct relic abundance later through the freeze-in mechanism. Though the dark matter effective couplings are tiny as required by the freeze-in scenario, the associated rich particle sector of the model can be probed at ongoing and near future experiments. The allowed values of dark matter mass can remain in a wide range from keV to TeV order keeping the possibilities of warm and cold dark matter equally possible.
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    Which mechanism(s) are mainly driving nuclear activity in the centres of galaxies is a major unsettled question. In this study, we investigate the statistical relevance of galaxy mergers for fuelling gas onto the central few kpc of a galaxy, potentially resulting in an active galactic nucleus (AGN). To robustly address that, we employ large-scale cosmological hydrodynamic simulations from the Magneticum Pathfinder set, adopting state-of-the-art models for BH accretion and AGN feedback. Our simulations predict that for luminous AGN ($L_{\rm AGN} > 10^{45} L_{\rm bol}$) at $z = 2$, more than 50 per cent of their host galaxies have experienced a merger in the last 0.5Gyr. These high merger fractions, however, merely reflect the intrinsically high merger rates of massive galaxies at $z=2$, in which luminous AGN preferentially occur. Apart from that, our simulation predictions disprove that merger events are the statistically dominant fuelling mechanism for nuclear activity over a redshift range $z=0-2$: irrespective of AGN luminosity, less than 20 per cent of AGN hosts have undergone a recent merger, in agreement with a number of observational studies. The central ISM conditions required for inducing AGN activity can be, but are not necessarily caused by a merger. Despite the statistically minor relevance of mergers, at a given AGN luminosity and stellar mass, the merger rates of AGN hosts can be by up to three times higher than that of inactive galaxies. Such elevated merger rates still point towards an intrinsic connection between AGN activity and mergers, consistent with our traditional expectation.
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    Most massive stars, if not all, are in binary configuration or higher multiples. These massive stars undergo supernova explosions and end their lives as either black holes or neutron stars. Recent observations have suggested that neutron stars and perhaps even black holes receive large velocity kicks at birth. Such natal kicks and the sudden mass loss can significantly alter the orbital configuration of the system. Here we derive general analytical expressions that describe the effects of natal kicks in binaries on hierarchical triple systems. We explore several proof-of-concept applications such as black hole and neutron stars binaries and X-ray binaries with either stellar or Supermassive Black Hole (SMBH) companions on a wide orbit. Kicks can disrupt the hierarchical configuration, although it is harder to escape the potential well of an SMBH. Some binary systems do escape the SMBH system resulting in hyper-velocity binary system. Furthermore, kicks can result in increasing or decreasing the orbital separations. Decreasing the orbital separation may have significant consequences in these astrophysical systems. For example, shrinking the separation post-supernova kick can lead to the shrinking of an inner compact binary that then may merge via Gravitational Wave (GW) emission. This process yields a supernova that is shortly followed by a possible GW-LIGO event. Interestingly, we find that the natal kick can result in shrinking the outer orbit, and the binary may cross the tertiary Roche limit, breaking up the inner binary. Thus, in the case of SMBH companion, this process can lead to either a tidal disruption event or a GW-LISA detection event with a supernova precursor.
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    Pebble accretion is a promising process for decreasing growth timescales of planetary cores, allowing gas giants to form at wide orbital separations. However, nebular turbulence can reduce the efficiency of this gas-assisted growth. We present an order of magnitude model of pebble accretion, which calculates the impact of turbulence on the average velocity of small bodies, the radius for binary capture, and the sizes of the small bodies that can be accreted. We also include the effect of turbulence on the particle scale height, which has been studied in previous works. We find that turbulence does not prevent rapid growth in the high-mass regime: the last doubling time to the critical mass to trigger runaway gas accretion ($M \sim 10 \, M_\oplus$) is well within the disk lifetime even for strong ($\alpha \gtrsim 10^{-2}$) turbulence. We find that while the growth timescale is quite sensitive to the local properties of the protoplanetary disk, over large regimes of parameter space large cores grow in less than the disk lifetime if appropriately-sized small bodies are present. Instead, the effects of turbulence are most pronounced for low planetary masses. For strong turbulence the growth timescale is longer than the gas disk lifetime until the core reaches masses $\gtrsim 10^{-2}-10^{-1} M_\oplus$. A "Flow Isolation Mass", at which binary capture ceases, emerges naturally from our model framework. We comment that the dependence of this mass on orbital separation is similar to the semi-major axis distribution of solar-system cores.
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    A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are the need for appropriate mathematical structure on Hilbert space, and correspondence with general relativity and quantum field theory in weak-gravity situations. A basic physical question is that of "Einstein separability:" how to define mutually independent subsystems, e.g. through localization. Standard answers via tensor products or operator algebras conflict with properties of gravity, as is seen in the correspondence limit; this connects with discussions of "soft hair." Instead, gravitational behavior suggests a networked Hilbert space structure. This structure plus unitarity provide important clues towards a quantum formulation of gravity.
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    Recent numerical simulations reveal that the isothermal collapse of pristine gas in atomic cooling haloes may result in stellar binaries of supermassive stars with $M_* \gtrsim 10^4\ \mathrm{M}_{\odot}$. For the first time, we compute the in-situ merger rate for such massive black hole remnants by combining their abundance and multiplicity estimates. For black holes with initial masses in the range $10^{4-6} \ \mathrm{M}_{\odot}$ merging at redshifts $z \gtrsim 15$ our optimistic model predicts that LISA should be able to detect 0.6 mergers per year. This rate of detection can be attributed, without confusion, to the in-situ mergers of seeds from the collapse of very massive stars. Equally, in the case where LISA observes no mergers from heavy seeds at $z \gtrsim 15$ we can constrain the combined number density, multiplicity, and coalesence times of these high-redshift systems. This letter proposes gravitational wave signatures as a means to constrain theoretical models and processes that govern the abundance of massive black hole seeds in the early Universe.
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    Globular clusters (GCs) and their dynamic interactions with the Galactic components provide an important insight into the structure and formation of the early Milky Way. Here, we present a kinematic study of two outer halo GCs based on a combination of VLT/FORS2, VLT/FLAMES, and Magellan/MIKE low- and high-resolution spectroscopy of 32 and 27 member stars, respectively. Although both clusters are located at Galactocentric distances of 15 kpc, they have otherwise very different properties. M 75 is a luminous and metal-rich system at [Fe/H] = $-1.2$ dex, a value that we confirm from the calcium triplet region. This GC shows mild evidence for rotation with an amplitude of A$_{\rm rot}\sim$5 km s$^{-1}$. One of the most metal-poor GCs in the Milky Way (at [FeII/H] = $-2.3$ dex), NGC 6426 exhibits marginal evidence of internal rotation at the 2 km s$^{-1}$ level. Both objects have velocity dispersions that are consistent with their luminosity. Although limited by small-number statistics, the resulting limits on their $A_{\rm rot}/\sigma_0$ ratios suggest that M 75 is a slow rotator driven by internal dynamics rather than being effected by the weak Galactic tides at its large distances. Here, M 75 ($A_{\rm rot}/\sigma=0.31$) is fully consistent with the properties of other, younger halo clusters. At $A_{\rm rot}/\sigma_0=0.8\pm0.4$, NGC 6426 appears to have a remarkably ordered internal motion for its low metallicity, but the large uncertainty does not allow for an unambiguous categorization as a fast rotator. An accretion origin of M 75 cannot be excluded, based on the eccentric orbit, which we derived from the recent data release 2 of Gaia, and considering its younger age.
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    We propose that the Ultra-Diffuse Galaxy (UDG) population represents a set of satellite galaxies born in $\sim10^{10}-10^{11}~{\rm M_\odot}$ halos, similar to field dwarfs, which suffer a dramatic reduction in surface brightness due to tidal stripping and heating. This scenario is observationally motivated by the radial alignment of UDGs in Coma as well as the significant dependence of UDG abundance on cluster mass. As a test of this formation scenario, we apply a semi-analytic model describing the change in stellar mass and half-light radius of dwarf satellites, occupying either cored or cuspy halos, to cluster subhalos in the Bolshoi simulation. Key to this model are results from simulations which indicate that galaxies in cored dark-matter halos expand significantly in response to tidal stripping and heating, whereas galaxies in cuspy halos experience limited size evolution. Our analysis indicates that a population of tidally-stripped dwarf galaxies, residing in cored halos (like that of low-surface brightness field dwarfs), is able to reproduce the observed sizes, stellar masses, and abundance of UDGs in clusters remarkably well.
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    Confocal Annular Josephson Tunnel Junctions (CAJTJs) which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise.
  • PDF
    We investigate cosmology of the influence of generalized and extended uncertainty principle (GEUP) whether it could provide an explanation of the dark energy. The consequence of GEUP is existence of minimum length and maximum length which can modify a entropy area law and also modify a Friedmann equation. Its cosmological consequences are studied by paying a particular attention to the role of minimum length and maximum length. We find that the theory allows cosmological evolution where the radiation and matter dominated epochs are followed by a long period of virtually constant dark energy that closely mimics $\Lambda$CDM model and the main source of the current acceleration is provided by the maximum length scale $\beta$ governed by the relation $\Lambda\sim -\beta^{-1}W(-\beta^{-1})$. Constraining the minimum length scale $\alpha$ and maximum length scale $\beta$ using the recent observational data consisting of the Hubble parameters, type Ia supernovae, and baryon acoustic oscillations, together with the Planck or WMAP 9-year data of the cosmic microwave background radiation, we find $\alpha \lesssim 10^{81}$ and $\beta \sim -10^{-2}$.
  • PDF
    In previous contributions, we have presented an analytical model describing the evolution of molecular clouds (MCs) undergoing global and hierarchical collapse. Here, we show that it can be used to estimate the ages of MCs for which pairs of parameters are known. The model cloud evolution is characterized by an initial increase in its mass, density, and star formation rate (SFR) and efficiency (SFE) as it contracts gravitationally, followed by a decrease of these quantities as newly formed massive stars begin to disrupt the cloud. The main controlling parameter of the model is the maximum mass reached by the cloud during its evolution. Thus, specifying the instantaneous mass and some other variable completely determines the cloud's evolutionary stage. We apply this capability of the model to interpret the observed scatter in SFEs of the cloud sample compiled by Lada et al. as an evolutionary effect. The model predicts that, although clouds such as California and Orion A have similar masses, they are in different evolutionary stages, causing them to have different SFRs and SFEs. Furthermore, the model predicts that the California cloud will eventually reach a significantly larger total mass than the Orion A cloud. Next, we apply the model to provide estimated ages of the clouds since the time when approximately 25\% of their mass had become molecular. We find ages ranging from $\sim 1.5$ to 27 Myr, with the most inactive clouds being the youngest. Another prediction is that clouds with low SFEs should have massive atomic envelopes that constitute the majority of their gravitational mass. Finally, we discuss the model prediction that low-mass clouds ($M \sim 10^3-10^4 M_\odot$) end their lives with a mini-burst of star formation, reaching SFRs $\sim 300-500\, M_\odot$ Myr$^{-1}$, at which time they have contracted to become compact massive star-forming clumps, embedded within larger GMCs.
  • PDF
    A new concise proof is given of a duality theorem connecting completely monotone relaxation functions with Bernstein class creep functions in one-dimensional and anisotropic 3D viscoelasticity. The proof makes use of the theory of complete Bernstein functions and Stieltjes functions and is based on a relation between these two function classes.
  • PDF
    The aim of this work is to use gamma-ray burst supernovae (GRB-SNe) as cosmological probes to measure the Hubble constant, $H_0$, in the local Universe. In the context of the Expanding Photosphere Method (EPM), I use empirically derived dilution factors of a sample of nearby SNe Ic, which were derived in Paper I of a two-paper series, as a proxy for the dilution factors of GRB-SNe. It is seen that the dilution factors as a function of temperature in $VI$ display the least amount of scatter, relative to $BVI$ and $BV$. A power-law function is fit to the former, and is used to derive model dilution factors which are then used to derive EPM distances to GRB-SNe 1998bw and 2003lw: $36.7\pm9.6$ and $372.2\pm137.1$ Mpc, respectively. In linear Hubble diagrams in filters $BVR$, I determine the offset of the Hubble ridge line, and armed with the peak absolute magnitudes in these filters for the two aforementioned GRB-SNe, I find a (weighted average) Hubble constant of $\bar{H_{0,\rm w}} = 61.9\pm12.3$ km s$^{-1}$ Mpc$^{-1}$ for GRB-SNe located at redshifts $z\le0.1$. The 20\% error is consistent with the value of $H_0$ calculated by Planck and SNe Ia within 1$\sigma$. I tested the fitting method on five nearby SNe Ic, and found that their EPM distances varied by 18-50\%, with smaller errors found for those SNe which had more numerous usable observations. For SN 2002ap, its EPM distance was overestimated by 18\%, and if the distance to SN 1998bw was similarly over-estimated by the same amount, the resultant value of the Hubble constant is $H_0 = 72$ km s$^{-1}$ Mpc$^{-1}$, which perfectly matches that obtained using SNe Ia. [abridged]
  • PDF
    We investigate the competition between the electron-vibron interaction (interaction with the Jahn-Teller phonons) and the Coulomb repulsion in a system with the local pairing of electrons on the 3-fold degenerate lowest unoccupied molecular orbital (LUMO). The el.-vib. interaction and the local pairing radically change conductivity and magnetic properties of alkali-doped fullerides $\texttt{A}_{n}\texttt{C}_{60}$, which would have to be antiferromagnetic Mott insulators: we have shown that materials with $n=1,2$ and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors but not superconductors; $n=3$ and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors and superconductors at low temperatures, but with $\texttt{A}=\texttt{Cs}$ they are Mott-Jahn-Teller insulators at normal pressure; $n=2,4$ are nonmagnetic Mott insulators. Thus superconductivity, conductivity and insulation of these materials have common nature. Using this approach we obtain the phase diagram of $\texttt{A}_{3}\texttt{C}_{60}$ analytically, which is the result of interplay between the local pairing, the el.-vib. interaction, Coulomb correlations, and formation of small radius polarons.
  • PDF
    A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and loss, in a combination with a photonic-crystal structure. The complex potential is built as a solution of the inverse problem, which predicts the potential supporting required periodic solutions. The main subject of the analysis is the spectral structure of the linear (in)stability for the stationary spatially periodic states in the periodic potentials. The stability and instability bands are calculated by means of the plane-wave-expansion method, and verified in direct simulations of the perturbed evolution. The results show that the periodic solutions may be stable against perturbations in specific Floquet-Bloch bands, even if they are unstable against small random perturbations.
  • PDF
    This paper deals with a new Bayesian approach to the two-sample problem. More specifically, let $x=(x_1,\ldots,x_{n_1})$ and $y=(y_1,\ldots,y_{n_2})$ be two independent samples coming from unknown distributions $F$ and $G$, respectively. The goal is to test the null hypothesis $\mathcal{H}_0:~F=G$ against all possible alternatives. First, a Dirichlet process prior for $F$ and $G$ is considered. Then the change of their Cramér-von Mises distance from a priori to a posteriori is compared through the relative belief ratio. Many theoretical properties of the procedure have been developed and several examples have been discussed, in which the proposed approach shows excellent performance.
  • PDF
    In this paper, we extend the `compact operator' part of D. Voiculescu's theorem on approximate equivalence of unital $*$-homomorphisms of an AF algebra when the range is in a semifinite von Neumann algebra. We also extend a result of D. Hadwin for approximate summands of representations into a finite von Neumann factor.
  • PDF
    Our goal in this paper is to find a characterization of $n$-dimensional bilinear Hardy inequalities \beginalign* \bigg\| \,\int_B(0,⋅) f ⋅\int_B(0,⋅) g \,\bigg\|_q,u,(0,∞) & ≤C \u2009\|f\|_p_1,v_1,\mathbb R^n \u2009\|g\|_p_2,v_2,\mathbb R^n, \quad f,\u2009g ∈\mathfrak M^+ (\mathbb R^n), \endalign* and \beginalign* \bigg\| \,\int_\,^^\mathsfc\!B(0,⋅) f ⋅\int_\,^^\mathsfc\!B(0,⋅) g \,\bigg\|_q,u,(0,∞) &≤C \u2009\|f\|_p_1,v_1,\mathbb R^n \u2009\|g\|_p_2,v_2,\mathbb R^n, \quad f,\u2009g ∈\mathfrak M^+ (\mathbb R^n), \endalign* when $0 < q \le \infty$, $1 \le p_1,\,p_2 \le \infty$ and $u$ and $v_1,\,v_2$ are weight functions on $(0,\infty)$ and ${\mathbb R}^n$, respectively. Since the solution of the first inequality can be obtained from the characterization of the second one by usual change of variables we concentrate our attention on characterization of the latter. The characterization of this inequality is easily obtained for the range of parameters when $p_1 \le q$ using the characterizations of multidimensional weighted Hardy-type inequalites while in the case when $q < p_1$ the problem is reduced to the solution of multidimensional weighted iterated Hardy-type inequality. To achieve the goal, we characterize the validity of multidimensional weighted iterated Hardy-type inequality $$ \left\|\left\|\int_\,^^\mathsfc\!B(0,⋅)h(z)dz\right\|_p,u,(0,t)\right\|_q,\mu,(0,∞)≤c \|h\|_\theta,v,(0,∞),~ h ∈\mathfrakM^+(\mathbb R^n) $$ where $0 < p,\,q < +\infty$, $1 \leq \theta \le \infty$, $u\in {\mathcal W}(0,\infty)$, $v \in {\mathcal W}({\mathbb R}^n)$ and $\mu$ is a non-negative Borel measure on $(0,\infty)$.
  • PDF
    The supervisory control of probabilistic discrete event systems (PDESs) is investigated under the assumptions that the supervisory controller (supervisor) is probabilistic and has a partial observation. The probabilistic P-supervisor is defined, which specifies a probability distribution on the control patterns for each observation. The notions of the probabilistic controllability and observability are proposed and demonstrated to be a necessary and sufficient conditions for the existence of the probabilistic P-supervisors. Moreover, the polynomial verification algorithms for the probabilistic controllability and observability are put forward. In addition, the infimal probabilistic controllable and observable superlanguage is introduced and computed as the solution of the optimal control problem of PDESs. Several examples are presented to illustrate the results obtained.
  • PDF
    We show that the eccentricities (and thus the centrality indices) of all vertices of a $\delta$-hyperbolic graph $G=(V,E)$ can be computed in linear time with an additive one-sided error of at most $c\delta$, i.e., after a linear time preprocessing, for every vertex $v$ of $G$ one can compute in $O(1)$ time an estimate $\hat{e}(v)$ of its eccentricity $ecc_G(v)$ such that $ecc_G(v)\leq \hat{e}(v)\leq ecc_G(v)+ c\delta$ for a small constant $c$. We prove that every $\delta$-hyperbolic graph $G$ has a shortest path tree, constructible in linear time, such that for every vertex $v$ of $G$, $ecc_G(v)\leq ecc_T(v)\leq ecc_G(v)+ c\delta$. These results are based on an interesting monotonicity property of the eccentricity function of hyperbolic graphs: the closer a vertex is to the center of $G$, the smaller its eccentricity is. We also show that the distance matrix of $G$ with an additive one-sided error of at most $c'\delta$ can be computed in $O(|V|^2\log^2|V|)$ time, where $c'< c$ is a small constant. Recent empirical studies show that many real-world graphs (including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others) have small hyperbolicity. So, we analyze the performance of our algorithms for approximating centrality and distance matrix on a number of real-world networks. Our experimental results show that the obtained estimates are even better than the theoretical bounds.
  • PDF
    Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to $q$-series are discussed.
  • PDF
    There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons.
  • PDF
    The conversion between amplitude modulation and phase modulation as a modulated signal goes thrugh a filter is analyzed. The difference in how the modulated sideband ampitude experience the filter, and how AM and PM has opposite signs for one of their sidebands interact. The conversion between AM and PM is modelled, providing a scatter model and evaluation of two functions based on the linear filters transfer function. The system bandwidth effects is analyzed and rule of thumb developed to ensure AM and PM isolation.
  • PDF
    The thermoelectric transport through a benzene molecule with three metallic terminals is discussed. Using general local and non-local transport coeffcients, we investigated different conductance and thermopower coefficients within the linear response regime. Based on the Onsager coefficient which depend on the number of terminal efficiencies, efficiency at maximum power is also studied. In the three-terminal set up with tuning temperature differences, a great enhancement of the figure of merit is observed. Results also show that the third terminal model can be useful to improve the efficiency at maximum output power compared to the two-terminal model.
  • May 21 2018 math.HO arXiv:1805.06890v1
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    Walter Richard Talbot was the fourth African American to earn a PhD in Mathematics. His doctoral degree is from the University of Pittsburgh in 1934 in geometric group theory. A contemporary research program was the determination of fundamental domains of finite group actions on complex vector spaces. His thesis is not widely available, and this note gives a brief synopsis of the main results of his thesis, expressed using modern mathematical methods and language, and placed in general context.
  • PDF
    At the mesoscopic scales --- which interpolate between the macroscopic, classical, geometry and the microscopic, quantum, structure of spacetime --- one can identify the density of states of the geometry which arises from the existence of a zero-point length in the spacetime. This spacetime discreteness also associates an internal degree of freedom with each event, in the form of a fluctuating vector of constant norm. The equilibrium state, corresponding to the extremum of the total density of states of geometry plus matter, leads precisely to Einstein's equations. In fact, the field equation can now be reinterpreted as a zero-heat dissipation principle. The analysis of fluctuations around the equilibrium state (described by Einstein's equations), will provide new insights about quantum gravity.

Recent comments

Max Lu Apr 25 2018 22:08 UTC

"This is a very inspiring paper! The new framework (ZR = All Reality) it provided allows us to understand all kinds of different reality technologies (VR, AR, MR, XR etc) that are currently loosely connected to each other and has been confusing to many people. Instead of treating our perceived sens

...(continued)
Stefano Pirandola Apr 23 2018 12:23 UTC

The most important reading here is Sam Braunstein's foundational paper: https://authors.library.caltech.edu/3827/1/BRAprl98.pdf published in January 98, already containing the key results for the strong convergence of the CV protocol. This is a must-read for those interested in CV quantum informatio

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Mark M. Wilde Apr 23 2018 12:09 UTC

One should also consult my paper "Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels" https://arxiv.org/abs/1712.00145v4 posted in January 2018, in this context.

Stefano Pirandola Apr 23 2018 11:46 UTC

Some quick clarifications on the Braunstein-Kimble (BK) protocol for CV teleportation
and the associated teleportation simulation of bosonic channels.
(Disclaimer: the following is rather technical and CVs might not be so popular on this blog...so I guess this post will get a lot of dislikes :)

1)

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NJBouman Apr 22 2018 18:26 UTC

[Fredrik Johansson][1] has pointed out to me (the author) the following about the multiplication benchmark w.r.t. GMP. This will be taken into account in the upcoming revision.

Fredrik Johansson wrote:
> You shouldn't be comparing your code to `mpn_mul`, because this function is not actually th

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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