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The construction of thin film heterostructures has been a widely successful archetype for fabricating materials with emergent physical properties. This strategy is of particular importance for the design of multilayer magnetic architectures in which direct interfacial spin--spin interactions between magnetic phases in dissimilar layers lead to emergent and controllable magnetic behavior. However, crystallographic incommensurability and atomic-scale interfacial disorder can severely limit the types of materials amenable to this strategy, as well as the performance of these systems. Here, we demonstrate a method for synthesizing heterostructures comprising magnetic intercalation compounds of transition metal dichalcogenides (TMDs), through directed topotactic reaction of the TMD with a metal oxide. The mechanism of the intercalation reaction enables thermally initiated intercalation of the TMD from lithographically patterned oxide films, giving access to a new family of multi-component magnetic architectures through the combination of deterministic van der Waals assembly and directed intercalation chemistry.

In this paper, we describe the wide-field spectroscopic survey telescope (WST) project. WST is a 12-metre wide-field spectroscopic survey telescope with simultaneous operation of a large field-of-view (3 sq. degree), high-multiplex (20,000) multi-object spectrograph (MOS), with both a low and high-resolution modes, and a giant 3x3 arcmin2 integral field spectrograph (IFS). In scientific capability, these specifications place WST far ahead of existing and planned facilities. In only 5 years of operation, the MOS would target 250 million galaxies and 25 million stars at low spectral resolution, plus 2 million stars at high resolution. Without need for pre-imaged targets, the IFS would deliver 4 billion spectra offering many serendipitous discoveries. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work in synergy with future ground and space-based facilities. We show how it can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; the origin of stars and planets; and time domain and multi-messenger astrophysics. WST's uniquely rich dataset may yield unforeseen discoveries in many of these areas. The telescope and instruments are designed as an integrated system and will mostly use existing technology, with the aim to minimise the carbon footprint and environmental impact. We will propose WST as the next European Southern Observatory (ESO) project after completion of the 39-metre ELT., Comment: 15 pages, 15 figures

While small, Neptune-like planets are among the most abundant exoplanets, our understanding of their atmospheric structure and dynamics remains sparse. In particular, many unknowns remain on the way moist convection works in these atmospheres where condensable species are heavier than the non-condensable background gas. While it has been predicted that moist convection could shut-down above some threshold abundance of these condensable species, this prediction is based on simple linear analysis and relies on strong assumptions on the saturation of the atmosphere. To investigate this issue, we develop a 3D cloud resolving model for H2 atmospheres with large amounts of condensable species and apply this model to a prototypical temperate Neptune-like planet -- K2-18b. Our model confirms the shut-down of moist convection and the onset of a stably stratified layer in the atmosphere, leading to much hotter deep atmospheres and interiors. Our 3D simulations further provide quantitative estimates of the turbulent mixing in this stable layer, which is a key driver of the cycling of condensables in the atmosphere. This allows us to build a very simple, yet realistic 1D model that captures the most salient features of the structure of Neptune-like atmospheres. Our qualitative findings on the behavior of moist convection in hydrogen atmospheres go beyond temperate planets and should also apply to the regions where iron and silicates condense in the deep interior of H2-dominated planets. Finally, we use our model to investigate the likelihood of a liquid ocean beneath a H2 dominated atmosphere on K2-18b. We find that the planet would need to have a very high albedo (>0.5-0.6) to sustain a liquid ocean. However, due to the spectral type of the star, the amount of aerosol scattering that would be needed to provide such a high albedo is inconsistent with the latest observational data., Comment: Accepted for publication in Astronomy and Astrophysics

The High-Resolution Multi-Object Spectrograph (HRMOS) is a facility instrument that we plan to propose for the Very Large Telescope (VLT) of the European Southern Observatory (ESO), following the initial presentation at the VLT 2030 workshop held at ESO in June 2019. HRMOS provides a combination of capabilities that are essential to carry out breakthrough science across a broad range of active research areas from stellar astrophysics and exoplanet studies to Galactic and Local Group archaeology. HRMOS fills a gap in capabilities amongst the landscape of future instrumentation planned for the next decade. The key characteristics of HRMOS will be high spectral resolution (R = 60000 - 80000) combined with multi-object (20-100) capabilities and long term stability that will provide excellent radial velocity precision and accuracy (10m/s). Initial designs predict that a SNR~100 will be achievable in about one hour for a star with mag(AB) = 15, while with the same exposure time a SNR~ 30 will be reached for a star with mag(AB) = 17. The combination of high resolution and multiplexing with wavelength coverage extending to relatively blue wavelengths (down to 380\,nm), makes HRMOS a spectrograph that will push the boundaries of our knowledge and that is envisioned as a workhorse instrument in the future. The science cases presented in this White Paper include topics and ideas developed by the Core Science Team with the contributions from the astronomical community, also through the wide participation in the first HRMOS Workshop (https://indico.ict.inaf.it/event/1547/) that took place in Firenze (Italy) in October 2021., Comment: 88 pages, 39 figures. Comments and expressions of interest are welcome by contacting members of the Core Science Team

The next generation of space-based observatories will characterize the atmospheres of low-mass, temperate exoplanets with the direct-imaging technique. This will be a major step forward in our understanding of exoplanet diversity and the prevalence of potentially habitable conditions beyond the Earth. We compute a list of currently known exoplanets detectable with the mid-infrared Large Interferometer For Exoplanets (LIFE) in thermal emission. We also compute the list of known exoplanets accessible to a notional design of the Habitable Worlds Observatory (HWO), observing in reflected starlight. With a pre-existing method, we processed the NASA Exoplanet Archive and computed orbital realizations for each known exoplanet. We derived their mass, radius, equilibrium temperature, and planet-star angular separation. We used the LIFEsim simulator to compute the integration time ($t_{int}$) required to detect each planet with LIFE. A planet is considered detectable if a broadband signal-to-noise ratio $S/N$=7 is achieved over the spectral range $4-18.5\mu$m in $t_{int}\leq$100 hours. We tested whether the planet is accessible to HWO in reflected starlight based on its notional inner and outer working angles, and minimum planet-to-star contrast. LIFE's reference configuration (four 2-m telescopes with 5% throughput and a nulling baseline between 10-100 m) can detect 212 known planets within 20 pc. Of these, 55 are also accessible to HWO in reflected starlight, offering a unique opportunity for synergies in atmospheric characterization. LIFE can also detect 32 known transiting exoplanets. Furthermore, 38 LIFE-detectable planets orbit in the habitable zone, of which 13 with $M_p<5M_\oplus$ and 8 with $5M_\oplus

Traces of singular moduli can be approximated by exponential sums of quadratic irrationals. Recently Andersen and Duke used theory of Maass forms to estimate generalized twisted traces with power-saving error bounds. We establish an asymptotic formula with effective error bounds for such traces. Our methods depend on an explicit bound for sums of Kloosterman sums on $\Gamma_0(4)$.

Magnetic materials with noncollinear spin textures are promising for spintronic applications. To realize practical devices, control over the length and energy scales of such spin textures is imperative. The chiral helimagnets Cr1/3NbS2 and Cr1/3TaS2 exhibit analogous magnetic phase diagrams with different real-space periodicities and field dependence, positioning them as model systems for studying the relative strengths of the microscopic mechanisms giving rise to exotic spin textures. Here, we carry out a comparative study of the electronic structures of Cr1/3NbS2 and Cr1/3TaS2 using angle-resolved photoemission spectroscopy and density functional theory. We show that bands in Cr1/3TaS2 are more dispersive than their counterparts in Cr1/3NbS2 and connect this result to bonding and orbital overlap in these materials. We also unambiguously distinguish exchange splitting from surface termination effects by studying the dependence of their photoemission spectra on polarization, temperature, and beam size. We find strong evidence that hybridization between intercalant and host lattice electronic states mediates the magnetic exchange interactions in these materials, suggesting that band engineering is a route toward tuning their spin textures. Overall, these results underscore how the modular nature of intercalated transition metal dichalcogenides translates variation in composition and electronic structure to complex magnetism., Comment: 46 pages, 18 figures, 5 tables

Neptune's tropospheric winds are among the most intense in the Solar System, but the dynamical mechanisms that produce them remain uncertain. Measuring wind speeds at different pressure levels may help understand the atmospheric dynamics of the planet. The goal of this work is to directly measure winds in Neptune's stratosphere with ALMA Doppler spectroscopy. We derived the Doppler lineshift maps of Neptune at the CO(3-2) and HCN(4-3) lines at 345.8 GHz ($\lambda$~0.87 mm) and 354.5 GHz (0.85 mm), respectively. For that, we used spectra obtained with ALMA in 2016 and recorded with a spatial resolution of ~0.37" on Neptune's 2.24" disk. After subtracting the planet solid rotation, we inferred the contribution of zonal winds to the measured Doppler lineshifts at the CO and HCN lines. We developed an MCMC-based retrieval methodology to constrain the latitudinal distribution of wind speeds. We find that CO(3-2) and HCN(4-3) lines probe the stratosphere of Neptune at pressures of $2^{+12}_{-1.8}$ mbar and $0.4^{+0.5}_{-0.3}$ mbar, respectively. The zonal winds at these altitudes are less intense than the tropospheric winds based on cloud tracking from Voyager observations. We find equatorial retrograde (westward) winds of $-180^{+70}_{-60}$ m/s for CO, and $-190^{+90}_{-70}$ m/s for HCN. Wind intensity decreases towards mid-latitudes, and wind speeds at 40$^\circ$S are $-90^{+50}_{-60}$ m/s for CO, and $-40^{+60}_{-80}$ m/s for HCN. Wind speeds become 0 m/s at about 50$^\circ$S, and we find that the circulation reverses to a prograde jet southwards of 60$^\circ$S. Overall, our direct stratospheric wind measurements match previous estimates from stellar occultation profiles and expectations based on thermal wind equilibrium. These are the first direct Doppler wind measurements performed on the Icy Giants, opening a new method to study and monitor their stratospheric dynamics., Comment: Accepted for publication in A&A Letters on 10/05/2023. 8 pages, 1 Table, 5 Figures

Transition metal-intercalated transition metal dichalcogenides (TMDs) are promising platforms for next-generation spintronic devices based on their wide range of electronic and magnetic phases, which can be tuned by varying the host lattice or the identity of the intercalant, along with its stoichiometry and spatial order. Some of these compounds host a chiral magnetic phase in which the helical winding of magnetic moments propagates along a high-symmetry crystalline axis. Previous studies have demonstrated that variation in intercalant concentrations can have a dramatic impact on the formation of chiral domains and ensemble magnetic properties. However, a systematic and comprehensive study of how atomic-scale order and disorder impacts collective magnetic behavior are so far lacking. Here, we leverage a combination of imaging modes in the (scanning) transmission electron microscope (S/TEM) to directly probe (dis)order across multiple length scales and show how subtle changes in the atomic lattice can be leveraged to tune the mesoscale spin textures and bulk magnetic response, with direct implications for the fundamental understanding and technological implementation of such compounds.

In Paper I we showed that clumps in high-redshift galaxies, having a high star formation rate density (\Sigma_SFR), produce disks with two tracks in the [Fe/H]-[\alpha/Fe] chemical space, similar to that of the Milky Way's (MW's) thin + thick disks. Here we investigate the effect of clumps on the bulge's chemistry. The chemistry of the MW's bulge is comprised of a single track with two density peaks separated by a trough. We show that the bulge chemistry of an N-body + smoothed particle hydrodynamics clumpy simulation also has a single track. Star formation within the bulge is itself in the high-\Sigma_SFR clumpy mode, which ensures that the bulge's chemical track follows that of the thick disk at low [Fe/H] and then extends to high [Fe/H], where it peaks. The peak at low metallicity instead is comprised of a mixture of in-situ stars and stars accreted via clumps. As a result, the trough between the peaks occurs at the end of the thick disk track. We find that the high-metallicity peak dominates near the mid-plane and declines in relative importance with height, as in the MW. The bulge is already rapidly rotating by the end of the clump epoch, with higher rotation at low [\alpha/Fe]. Thus clumpy star formation is able to simultaneously explain the chemodynamic trends of the MW's bulge, thin + thick disks and the Splash., Comment: 25 pages, in press at ApJ

Since 2005 ESO has been working with its community and industry to develop an extremely large optical/infrared telescope. ESO's Extremely Large Telescope, or ELT for short, is a revolutionary ground-based telescope that will have a 39-metre main mirror and will be the largest visible and infrared light telescope in the world. To address specific topics that are needed for the science operations and calibrations of the telescope, thirteen specific working groups were created to coordinate the effort between ESO, the instrument consortia, and the wider community. We describe here the goals of these working groups as well as their achievements so far., Comment: 8 pages, 4 figures

WEAVE, the new wide-field, massively multiplexed spectroscopic survey facility for the William Herschel Telescope, will see first light in late 2022. WEAVE comprises a new 2-degree field-of-view prime-focus corrector system, a nearly 1000-multiplex fibre positioner, 20 individually deployable 'mini' integral field units (IFUs), and a single large IFU. These fibre systems feed a dual-beam spectrograph covering the wavelength range 366$-$959\,nm at $R\sim5000$, or two shorter ranges at $R\sim20\,000$. After summarising the design and implementation of WEAVE and its data systems, we present the organisation, science drivers and design of a five- to seven-year programme of eight individual surveys to: (i) study our Galaxy's origins by completing Gaia's phase-space information, providing metallicities to its limiting magnitude for $\sim$3 million stars and detailed abundances for $\sim1.5$ million brighter field and open-cluster stars; (ii) survey $\sim0.4$ million Galactic-plane OBA stars, young stellar objects and nearby gas to understand the evolution of young stars and their environments; (iii) perform an extensive spectral survey of white dwarfs; (iv) survey $\sim400$ neutral-hydrogen-selected galaxies with the IFUs; (v) study properties and kinematics of stellar populations and ionised gas in $z<0.5$ cluster galaxies; (vi) survey stellar populations and kinematics in $\sim25\,000$ field galaxies at $0.3\lesssim z \lesssim 0.7$; (vii) study the cosmic evolution of accretion and star formation using $>1$ million spectra of LOFAR-selected radio sources; (viii) trace structures using intergalactic/circumgalactic gas at $z>2$. Finally, we describe the WEAVE Operational Rehearsals using the WEAVE Simulator., Comment: 41 pages, 27 figures, accepted for publication by MNRAS; updated version including information on individual grants in a revised Acknowledgements section, corrections to the affiliation list, and an updated references list

We use natural-language-processing algorithms on a novel dataset of over 900 presidential speeches from ten Latin American countries spanning two centuries to study the dynamics and determinants of presidential policy priorities. We show that most speech content can be characterized by a compact set of policy issues whose relative composition exhibited slow yet substantial shifts over 1819-2022. Presidential attention initially centered on military interventions and the development of state capacity. Attention gradually evolved towards building physical capital through investments in infrastructure and public services and finally turned towards building human capital through investments in education, health, and social safety nets. We characterize the way in which president-level characteristics, like age and gender, predict the main policy issues. Our findings offer novel insights into the dynamics of presidential attention and the factors that shape it, expanding our understanding of political agenda-setting., Comment: JEL codes: D78, I32, D72, N16

We study low-lying zeroes of $L$-functions and their $n$-level density, which relies on a smooth test function $\phi$ whose Fourier transform $\widehat\phi$ has compact support. Assuming the generalized Riemann hypothesis, we compute the $n^\text{th}$ centered moments of the $1$-level density of low-lying zeroes of $L$-functions associated with weight $k$, prime level $N$ cuspidal newforms as $N \to \infty$, where ${\rm supp}(\widehat\phi) \subset \left(-2/n, 2/n\right)$. The Katz-Sarnak density conjecture predicts that the $n$-level density of certain families of $L$-functions is the same as the distribution of eigenvalues of corresponding families of orthogonal random matrices. We prove that the Katz-Sarnak density conjecture holds for the $n^\text{th}$ centered moments of the 1-level density for test functions with $\widehat{\phi}$ supported in $\left(-2/n, 2/n\right)$, for families of cuspidal newforms split by the sign of their functional equations. Our work provides better bounds on the percent of forms vanishing to a certain order at the central point. Previous work handled the 1-level for support up to 2 and the $n$-level up to $\min(2/n, 1/(n-1))$; we are able to remove the second restriction on the support and extend the result to what one would expect, based on the 1-level, by finding a tractable vantage to evaluate the combinatorial zoo of terms which emerge., Comment: 57 pages, updated acknowledgements

We investigate congruence relations of the form $p_r(\ell m n + t) \equiv 0 \pmod{\ell}$ for all $n$, where $p_r(n)$ is the number of $r$-colored partitions of $n$ and $m,\ell$ are distinct primes.

Let $E_k$ be the normalized Eisenstein series of weight $k$ on $\mathrm{SL}_{2}(\mathbb{Z})$. Let $\varphi_k$ be the polynomial that encodes the $j$-invariants of non-elliptic zeros of $E_k$. In 2001, Gekeler observed that the polynomials $\varphi_k$ seem to be irreducible (and verified this claim for $k\leq 446$). We show that $\varphi_k$ is irreducible for infinitely many $k$.

We use an $N$-body+smoothed particle hydrodynamics simulation of an isolated barred galaxy to study the age dependence of bulge longitudinal proper motion ($\mu_l$) rotation curves. We show that close to the minor axis ($|l| \sim 0^\circ$) the relatively young stars rotate more rapidly than the old stars, as found by Hubble Space Telescope in the Milky Way's (MW's) bulge. This behaviour would be expected also if the MW were unbarred. At larger $|l|$ a different behaviour emerges. Because younger stars trace a strong bar, their galactocentric radial motions dominate their $\mu_l$ at $|l| \sim 6^\circ$, leading to a reversal in the sign of $\left< \mu_l \right>$. This results in a rotation curve with forbidden velocities (negative $\left< \mu_l \right>$ at positive longitudes, and positive $\left< \mu_l \right>$ at negative longitudes). The old stars, instead, trace a much weaker bar and thus their kinematics are more axisymmetric, resulting in no forbidden velocities. We develop metrics of the difference in the $\left< \mu_l \right>$ rotation curves of young and old stars, and forbidden velocities. We use these to predict the locations where rotation curve reversals can be observed by HST and the Vera Rubin Telescope. Such measurements would represent support for the amplitude of the bar being a continuous function of age, as predicted by kinematic fractionation, in which the bar strength variations are produced purely by differences in the random motions of stellar populations at bar formation., Comment: 20 pages, 18 figures, 2 tables, published in MNRAS

The theory of remote sensing shows that observing a planet at multiple phase angles ($\alpha$) is a powerful strategy to characterize its atmosphere. Here, we analyse how the information contained in reflected-starlight spectra of exoplanets depends on the phase angle, and the potential of multi-phase measurements to better constrain the atmospheric properties and the planet radius ($R_p$). We simulate spectra (500-900 nm) at $\alpha$=37$^\circ$, 85$^\circ$ and 123$^\circ$ with spectral resolution $R$~125-225 and signal-to-noise ratio $S/N$=10. Assuming a H$_2$-He atmosphere, we use a seven-parameter model that includes the atmospheric methane abundance ($f_{CH_4}$), the optical properties of a cloud layer and $R_p$. All these parameters are assumed unknown a priori and explored with an MCMC retrieval method. We find that no single-phase observation can robustly identify whether the atmosphere has clouds or not. A single-phase observation at $\alpha$=123$^\circ$ and $S/N$=10 can constrain $R_p$ with a maximum error of 35%, regardless of the cloud coverage. Combining small (37$^\circ$) and large (123$^\circ$) phase angles is a generally effective strategy to break multiple parameter degeneracies. This enables to determine the presence or absence of a cloud and its main properties, $f_{CH_4}$ and $R_p$ in all the explored scenarios. Other strategies, such as doubling $S/N$ to 20 for a single-phase observation or combining small (37$^\circ$) and moderate (85$^\circ$) phase angles, fail to achieve this. We show that the improvements in multi-phase retrievals are associated with the shape of the scattering phase function of the cloud aerosols and that the improvement is more modest for isotropically-scattering aerosols. We finally discuss that misidentifying the background gas in the retrievals of super-Earth observations leads to a systematic underestimate of the absorbing gas abundance., Comment: Accepted for publication in A&A. 14 pages + 7 of Appendix, 3 Tables, 9 Figures + 6 in Appendix

Reflected starlight measurements will open a new path in the characterization of directly imaged exoplanets. However, we still lack a population study of known targets amenable to this technique. Here, we investigate which of the about 4300 exoplanets confirmed to date are accessible to the Roman Space Telescope's coronagraph (CGI) in reflected starlight at reference wavelengths $\lambda$=575, 730 and 825 nm. We carry out a population study and also address the prospects for phase-curve measurements. We used the NASA Exoplanet Archive as a reference for planet and star properties, and explored the impact of their uncertainties on the exoplanet's detectability by applying statistical arguments. We define a planet as Roman-accessible on the basis of the instrument inner and outer working angles and its minimum planet-to-star constrast (IWA, OWA, $C_{min}$). We adopt for these technical specifications three plausible configurations labeled as pessimistic, intermediate and optimistic. Our key outputs for each exoplanet are its probability of being Roman-accessible ($P_{access}$), the range of observable phase angles, the evolution of its equilibrium temperature, the number of days per orbit that it is accessible and its transit probability. In the optimistic scenario, we find 26 Roman-accessible exoplanets with $P_{access}$>25% and host stars brighter than $V$=7 mag. This population is biased towards planets more massive than Jupiter but also includes the super-Earths tau Cet e and f which orbit near their star's habitable zone. A total of 13 planets are part of multiplanet systems, 3 of them with known transiting companions, offering opportunities for contemporaneous characterization. The intermediate and pessimistic scenarios yield 10 and 3 Roman-accessible exoplanets, respectively. We find that inclination estimates (e.g. with astrometry) are key for refining the detectability prospects., Comment: Accepted for publication in A&A. 34 pages, 12 Tables, 24 Figures

Exoplanetary science continues to excite and surprise with its rich diversity. We discuss here some key aspects potentially influencing the range of exoplanetary terrestrial-type atmospheres which could exist in nature. We are motivated by newly emerging observations, refined approaches to address data degeneracies, improved theories for key processes affecting atmospheric evolution and a new generation of atmospheric models which couple physical processes from the deep interior through to the exosphere and consider the planetary-star system as a whole. Using the Solar System as our guide we first summarize the main processes which sculpt atmospheric evolution then discuss their potential interactions in the context of exoplanetary environments. We summarize key uncertainties and consider a diverse range of atmospheric compositions discussing their potential occurrence in an exoplanetary context.

We give a substantial improvement for the error term in the asymptotic formula for the smallest parts function $\mathrm{spt}(n)$ of Andrews. Our methods depend on an explicit bound for sums of Kloosterman sums of half integral weight on the full modular group.

We have investigated the information content in reflected-starlight spectra of exoplanets. We specify our analysis to Barnard's Star b candidate super-Earth, for which we assume a radius 0.6 times that of Neptune, an atmosphere dominated by H$_2$-He, and a CH$_4$ volume mixing ratio of 5$\cdot$10$^{-3}$. The main conclusions of our study are however planet-independent. We set up a model of the exoplanet described by seven parameters including its radius, atmospheric methane abundance and basic properties of a cloud layer. We generate synthetic spectra at zero phase (full disk illumination) from 500 to 900 nm and spectral resolution R$\sim$125-225. We simulate a measured spectrum with a simplified, wavelength-independent noise model at Signal-to-Noise ratio S/N=10. With an MCMC-based retrieval methodology, we analyse which planet/atmosphere parameters can be inferred from the measured spectrum and the theoretical correlations amongst them. We consider limiting cases in which the planet radius is either known or completely unknown, and intermediate cases in which the planet radius is partly constrained. If the planet radius is known, we can generally discriminate between cloud-free and cloudy atmospheres, and constrain the methane abundance to within two orders of magnitude. If the planet radius is unknown, new correlations between model parameters occur and the accuracy of the retrievals decreases. Without a radius determination, it is challenging to discern whether the planet has clouds, and the estimates on methane abundance degrade. However, we find the planet radius is constrained to within a factor of two for all the cases explored. Having a priori information on the planet radius, even if approximate, helps improve the retrievals. We urge exoplanet detection efforts to extend the population of long-period planets with mass and radius determinations., Comment: Accepted for publication in A&A. 22 pages, 6 Tables, 16 figures. The abstract has been shortened to meet arXiv requirements

Windows of low extinction in the Milky Way (MW) have been used along the past decades for the study of the Galactic structure and the stellar population across the inner bulge and disk. Here we report the analysis of another low extinction near-IR window discovered by the VISTA Variables in the V\'ia L\'actea Survey. VVV WIN 1733$-$3349 is about half a degree in size and is conveniently located right in the MW plane, at Galactic coordinates $(l, b) = (-5.2, -0.3)$. The mean extinction of VVV WIN 1733$-$3349 is $A_{Ks} = 0.61\pm0.08$ mag, which is much smaller than the extinction in the surrounding area. The excess in the star counts is consistent with the reduced extinction, and complemented by studying the distribution of red clump (RC) stars. Thanks to the strategic low-latitude location of VVV WIN 1733$-$3349, we are able to interpret their RC density fluctuations with the expected overdensities due to the presence of the spiral arms beyond the bulge. In addition, we find a clear excess in the number of microlensing events within the window, which corroborates our interpretation that VVV WIN 1733$-$3349 is revealing the far side of the MW bulge., Comment: 5 pages, 4 figures. Accepted for publication in MNRAS Letters

A new all-sky visible and Near-InfraRed (NIR) space astrometry mission with a wavelength cutoff in the K-band is not just focused on a single or small number of key science cases. Instead, it is extremely broad, answering key science questions in nearly every branch of astronomy while also providing a dense and accurate visible-NIR reference frame needed for future astronomy facilities. For almost 2 billion common stars the combination of Gaia and a new all-sky NIR astrometry mission would provide much improved proper motions, answering key science questions -- from the solar system and stellar systems, including exoplanet systems, to compact galaxies, quasars, neutron stars, binaries and dark matter substructures. The addition of NIR will result in up to 8 billion newly measured stars in some of the most obscured parts of our Galaxy, and crucially reveal the very heart of the Galactic bulge region. In this white paper we argue that rather than improving on the accuracy, a greater overall science return can be achieved by going deeper than Gaia and by expanding the wavelength range to the NIR., Comment: arXiv admin note: substantial text overlap with arXiv:1609.07325

We recommend configuring the LSST coverage of the inner Galactic plane to allow the production of the definitive age/metallicity map of the Galactic bulge from LSST data, matched to external surveys where appropriate. This will allow the formation history of the Galactic bulge to be reconstructed, as well as furnishing a huge legacy dataset to support one of the key LSST science goals (Mapping the Milky Way). We recommend precise multi-color $grizy$~photometry as deeply as spatial crowding will allow (ideally completing early in the project), complemented by a single-filter survey spread over the entire 10-year time baseline. Both strands should cover as broad an area within the Bulge as possible, with image quality sufficient to reach at least the bulge main sequence turn-off in seeing-limited observations. We specify metrics and a figure of merit by which candidate observing strategies could be evaluated with respect to `static' bulge science (proper motions and photometry), Comment: White Paper submitted to the 2018 call for LSST cadence proposals

We discuss the predicted performance of the HARMONI spectrograph and the ELT in the context of two specific science cases: resolved stellar populations of Local Volume galaxies and Galactic archaeology in dense environments. We have produced and analysed a set of simulated data-cubes using the HSIM software, mimicking observations across the giant elliptical galaxy Centaurus A and in the nuclear bulge of the Milky Way. We use our results to demonstrate the instruments capabilities to perform stellar absorption line spectroscopy in a large number of stars which will allow us to study the detailed kinematics and stellar population characteristics of these high density regions, Comment: Proc. IAUS347, 'Early Science with ELTs', Vienna, August 2018

Red clump stars are commonly used to map the reddening and morphology of the inner regions of the Milky Way. We use the new photometric catalogues of the VISTA Variables in the V\'ia L\'actea survey to achieve twice the spatial resolution of previous reddening maps for Galactic longitudes $-10^{\circ}

The inner regions of the Galaxy are severely affected by extinction, which limits our capability to study the stellar populations present there. The Vista Variables in the Via Lactea (VVV) ESO Public Survey has observed this zone at near-infrared wavelengths where reddening is highly diminished. By exploiting the high resolution and wide field-of-view of the VVV images we aim to produce a deep, homogeneous, and highly complete database of sources that cover the innermost regions of our Galaxy. To better deal with the high crowding in the surveyed areas, we have used point spread function (PSF)-fitting techniques to obtain a new photometry of the VVV images, in the ZYJHKs near-infrared filters available. Our final catalogs contain close to one billion sources, with precise photometry in up to five near-infrared filters, and they are already being used to provide an unprecedented view of the inner Galactic stellar populations. We make these catalogs publicly available to the community. Our catalogs allow us to build the VVV giga-CMD, a series of color-magnitude diagrams of the inner regions of the Milky Way presented as supplementary videos. We provide a qualitative analysis of some representative CMDs of the inner regions of the Galaxy, and briefly mention some of the studies we have developed with this new dataset so far., Comment: Accepted for publication in A&A, 13 pages, 8 Figures, 1 Table

We present the late-time evolution of m12m, a cosmological simulation of a Milky Way-like galaxy from the FIRE project. The simulation forms a bar after redshift z = 0.2. We show that the evolution of the model exhibits behaviours typical of kinematic fractionation, with a bar weaker in older populations, an X-shape traced by the younger, metal-rich populations and a prominent X-shape in the edge-on mean metallicity map. Because of the late formation of the bar in m12m, stars forming after 10 Gyr (z = 0.34) significantly contaminate the bulge, at a level higher than is observed at high latitudes in the Milky Way, implying that its bar cannot have formed as late as in m12m. We also study the model's vertex deviation of the velocity ellipsoid as a function of stellar metallicity and age in the equivalent of Baade's Window. The formation of the bar leads to a non-zero vertex deviation. We find that metal-rich stars have a large vertex deviation (~ 40 degrees), which becomes negligible for metal-poor stars, a trend also found in the Milky Way, despite not matching in detail. We demonstrate that the vertex deviation also varies with stellar age and is large for stars as old as 9 Gyr, while 13 Gyr old stars have negligible vertex deviation. When we exclude stars that have been accreted, the vertex deviation is not significantly changed, demonstrating that the observed variation of vertex deviation with metallicity is not necessarily due to an accreted population., Comment: Published in MNRAS, 485, 5073. This version includes a few additional figures and discussion requested by the referee. No fundamental changes in the results from the earlier version

The windows of low extinction in the Milky Way (MW) plane are rare but important because they enable us to place structural constraints on the opposite side of the Galaxy, which has hitherto been done rarely. We use the near-infrared (near-IR) images of the VISTA Variables in the V\'ia L\'actea (VVV) Survey to build extinction maps and to identify low extinction windows towards the Southern Galactic plane. Here we report the discovery of VVV WIN 1713$-$3939, a very interesting window with relatively uniform and low extinction conveniently placed very close to the Galactic plane. The new window of roughly 30 arcmin diameter is located at Galactic coordinates (l,b)= (347.4,-0.4) deg. We analyse the VVV near-IR colour-magnitude diagrams in this window. The mean total near-IR extinction and reddening values measured for this window are A_Ks=0.46 and E(J-Ks)=0.95. The red clump giants within the window show a bimodal magnitude distribution in the Ks band, with peaks at Ks=14.1 and 14.8 mag, corresponding to mean distances of D=11.0+/-2.4 and 14.8+/-3.6 kpc, respectively. We discuss the origin of these red clump overdensities within the context of the MW disk structure., Comment: Comments: 6 pages, 6 figures. Accepted for publication in A&A

In Debattista et al. (2015), we proposed that a kiloparsec-scale nuclear disc is responsible for the high-velocity secondary peak in the stellar line-of-sight velocity distributions (LOSVDs) seen at positive longitudes in the bulge by the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Here, we make further qualitative but distinctive predictions of the kinematic properties of a nuclear disc, including for the LOSVDs at negative longitudes (which APOGEE-2 will observe) and examine the proper motions throughout the disc. Since a nuclear ring is also able to produce similar high-velocity LOSVD peaks, we present predictions for the proper motion signatures which distinguish between a nuclear disc and a nuclear ring. We also demonstrate that the stars in a nuclear disc, which would be on x2 orbits perpendicular to the bar, can remain on these orbits for a long time and can therefore be old. We show that such (old) nuclear discs of comparable size exist in external galaxies., Comment: Accepted to MNRAS

Interstellar extinction towards the Galactic Center is large and significantly differential. Its reddening and dimming effects in red clump stars in the Galactic Bulge can be exploited to better constrain the extinction law towards the innermost Galaxy. By virtue of a deep and complete catalog of more than 30 million objets at $|l|\le2.7\deg$ and $|b|\le1.55\deg$ obtained from VVV survey observations, we apply the red clump method to infer the selective-to-total extinction ratios in the $Z$, $Y$, $J$, $H$ and $K_s$ broadband near-infrared filters. The measured values are smaller than previously reported, and are not constant, with mean values, e.g., $A_{K_S}/E(J-K_s)=0.428\pm0.005\pm0.04$ and $A_{K_S}/E(H-K_s)=1.104\pm0.022\pm0.2$. We also obtain a ratio $A_Z$:$A_Y$:$A_J$:$A_H$:$A_{K_S}$ of 7.74:5.38:3.30:1.88:1.0, implying extinction towards the Galactic Center to follow a distribution as a function of wavelength steeper than previously reported, consistent with a power law $A_{\lambda}\propto{\lambda}^{-2.47}$ in the near-infrared., Comment: Accepted for publication in ApJ Letters, 10 pages, 3 Figures, 2 Tables

A biologically plausible computational model for color representation is introduced. We present a mechanistic hierarchical model of neurons that not only successfully encodes local hue, but also explicitly reveals how the contributions of each visual cortical layer participating in the process can lead to a hue representation. Our proposed model benefits from studies on the visual cortex and builds a network of single-opponent and hue-selective neurons. Local hue encoding is achieved through gradually increasing nonlinearity in terms of cone inputs to single-opponent cells. We demonstrate that our model's single-opponent neurons have wide tuning curves, while the hue-selective neurons in our model V4 layer exhibit narrower tunings, resembling those in V4 of the primate visual system. Our simulation experiments suggest that neurons in V4 or later layers have the capacity of encoding unique hues. Moreover, with a few examples, we present the possibility of spanning the infinite space of physical hues by combining the hue-selective neurons in our model., Comment: 16 pages, 15 figures, 3 tables

We use deep multi-epoch near-IR images of the VISTA Variables in the V\'ia L\'actea (VVV) Survey to search for RR Lyrae stars towards the Southern Galactic plane. Here we report the discovery of a group of RR Lyrae stars close together in VVV tile d025. Inspection of the VVV images and PSF photometry reveals that most of these stars are likely to belong to a globular cluster, that matches the position of the previously known star cluster FSR\,1716. The stellar density map of the field yields a $>100$ sigma detection for this candidate globular cluster, that is centered at equatorial coordinates $RA_{J2000}=$16:10:30.0, $DEC_{J2000}=-$53:44:56; and galactic coordinates $l=$329.77812, $b=-$1.59227. The color-magnitude diagram of this object reveals a well populated red giant branch, with a prominent red clump at $K_s=13.35 \pm 0.05$, and $J-K_s=1.30 \pm 0.05$. We present the cluster RR Lyrae positions, magnitudes, colors, periods and amplitudes. The presence of RR Lyrae indicates an old globular cluster, with age $>10$ Gyr. We classify this object as an Oosterhoff type I globular cluster, based on the mean period of its RR Lyrae type ab, $=0.540$ days, and argue that this is a relatively metal-poor cluster with $[Fe/H] = -1.5 \pm 0.4$ dex. The mean extinction and reddening for this cluster are $A_{K_s}=0.38 \pm 0.02$, and $E(J-K_s)=0.72 \pm 0.02$ mag, respectively, as measured from the RR Lyrae colors and the near-IR color-magnitude diagram. We also measure the cluster distance using the RR Lyrae type ab stars. The cluster mean distance modulus is $(m-M)_0 = 14.38 \pm 0.03$ mag, implying a distance $D = 7.5 \pm 0.2$ kpc, and a Galactocentric distance $R_G=4.3$ kpc., Comment: 7 pages, 4 figures. ApJL, in press

Deep near-IR images from the VISTA Variables in the V\'ia L\'actea (VVV) Survey were used to search for RR Lyrae stars in the Southern Galactic plane. A sizable sample of 404 RR Lyrae of type ab stars was identified across a thin slice of the 4$^{\rm th}$ Galactic quadrant ($295\deg < l < 350\deg$, $-2.24\deg < b < -1.05\deg$). The sample's distance distribution exhibits a maximum density that occurs at the bulge tangent point, which implies that this primarily Oosterhoff type I population of RRab stars does not trace the bar delineated by their red clump counterparts. The bulge RR Lyrae population does not extend beyond $l \sim340 \deg$, and the sample's spatial distribution presents evidence of density enhancements and substructure that warrants further investigation. Indeed, the sample may be employed to evaluate Galactic evolution models, and is particularly lucrative since half of the discovered RR Lyrae are within reach of Gaia astrometric observations., Comment: 10 pages, 13 figures. AJ, in press

This work presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these perturbations and Diophantine equations of the form $$ \sum_{l=0}^n \binom{n}{l} x_l=0,$$ where $x_j$ belongs to some fixed bounded subset $\Gamma$ of $\mathbb{Z}$. The concepts of trivially balanced symmetric Boolean function and sporadic balanced Boolean function are extended to this type of perturbations. An observation made by Canteaut and Videau for symmetric Boolean functions of fixed degree is extended. To be specific, it is proved that, excluding the trivial cases, balanced perturbations of fixed degree do not exist when the number of variables grows. Some sporadic balanced perturbations are presented. Finally, a beautiful but unexpected identity between perturbations of two very different symmetric Boolean functions is also included in this work.

Bulges of edge-on galaxies are often boxy/peanut-shaped (B/PS), and unsharp masks reveal the presence of an X shape. Simulations show that these shapes can be produced by dynamical processes driven by a bar which vertically thickens the centre. In the Milky Way, which contains such a B/PS bulge, the X-shaped structure is traced by the metal-rich stars but not by the metal-poor ones. Recently Debattista et al. (2016) interpreted this property as a result of the varying effect of the bar on stellar populations with different starting kinematics. This kinematic fractionation model predicts that cooler populations at the time of bar formation go on to trace the X shape, whereas hotter populations are more uniformly distributed. As this prediction is not specific to the Milky Way, we test it with MUSE observations of the B/PS bulge in the nearby galaxy NGC 4710. We show that the metallicity map is more peanut-shaped than the density distribution itself, in good agreement with the prediction. This result indicates that the X-shaped structure in B/PS bulges is formed of relatively metal-rich stars that have been vertically redistributed by the bar, whereas the metal-poor stars have a more uniform, box-shaped distribution., Comment: accepted for publication in MNRAS Letters, 5 pages, 3 Figures

We present a novel interpretation of the previously puzzling different behaviours of stellar populations of the Milky Way's bulge. We first show, by means of pure N-body simulations, that initially co-spatial stellar populations with different in-plane random motions separate when a bar forms. The radially cooler populations form a strong bar, and are vertically thin and peanut-shaped, while the hotter populations form a weaker bar and become a vertically thicker box. We demonstrate that it is the radial, not the vertical, velocity dispersion that dominates this evolution. Assuming that early stellar discs heat rapidly as they form, then both the in-plane and vertical random motions correlate with stellar age and chemistry, leading to different density distributions for metal-rich and metal-poor stars. We then use a high-resolution simulation, in which all stars form out of gas, to demonstrate that this is what happens. When we apply these results to the Milky Way we show that a very broad range of observed trends for ages, densities, kinematics and chemistries, that have been presented as evidence for contradictory paths to the formation of the bulge, are in fact consistent with a bulge which formed from a continuum of disc stellar populations which were kinematically separated by the bar. For the first time we are able to account for the bulge's main trends via a model in which the bulge formed largely in situ. Since the model is generic, we also predict the general appearance of stellar population maps of external edge-on galaxies., Comment: Updated version as published in MNRAS

Recent work of Altu\u{g} continues the preliminary analysis of Langlands' Beyond Endoscopy proposal for $GL(2)$ by removing the contribution of the trivial representation to the trace formula using a Poisson summation formula. We show that Altu\u{g}'s method of smoothing real elliptic orbital integrals by an approximate functional equation extends to $GL(n)$. We also discuss the case of an arbitrary reductive group, and remaining obstructions for applying Poisson summation., Comment: To appear in Journal of Number Theory

Transmission spectroscopy facilitates the detection of molecules and/or clouds in the atmospheres of exoplanets. Such studies rely heavily on space-based or large ground-based observatories, as one needs to perform time- resolved, high signal-to-noise spectroscopy. The FORS2 instrument at ESO's Very Large Telescope is the obvious choice for performing such studies, and was indeed pioneering the field in 2010. After that, however, it was shown to suffer from systematic errors caused by the Longitudinal Atmospheric Dispersion Corrector (LADC). This was successfully addressed, leading to a renewed interest for this instrument as shown by the number of proposals submitted to perform transmission spectroscopy of exoplanets. We present here the context, the problem and how we solved it, as well as the recent results obtained. We finish by providing tips for an optimum strategy to do transmission spectroscopy with FORS2, in the hope that FORS2 may become the instrument of choice for ground-based transmission spectroscopy of exoplanets., Comment: Paper 9908-85 presented at SPIE 2016

We investigate interstellar extinction curve variations toward $\sim$4 deg$^{2}$ of the inner Milky Way in $VIJK_{s}$ photometry from the OGLE-III and $VVV$ surveys, with supporting evidence from diffuse interstellar bands and $F435W,F625W$ photometry. We obtain independent measurements toward $\sim$2,000 sightlines of $A_{I}$, $E(V-I)$, $E(I-J)$, and $E(J-K_{s})$, with median precision and accuracy of 2%. We find that the variations in the extinction ratios $A_{I}/E(V-I)$, $E(I-J)/E(V-I)$ and $E(J-K_{s})/E(V-I)$ are large (exceeding 20%), significant, and positively correlated, as expected. However, both the mean values and the trends in these extinction ratios are drastically shifted from the predictions of Cardelli and Fitzpatrick, regardless of how $R_{V}$ is varied. Furthermore, we demonstrate that variations in the shape of the extinction curve has at least two degrees of freedom, and not one (e.g. $R_{V}$), which we conform with a principal component analysis. We derive a median value of $=13.44$, which is $\sim$60% higher than the "standard" value. We show that the Wesenheit magnitude $W_{I}=I-1.61(I-J)$ is relatively impervious to extinction curve variations. Given that these extinction curves are linchpins of observational cosmology, and that it is generally assumed that $R_{V}$ variations correctly capture variations in the extinction curve, we argue that systematic errors in the distance ladder from studies of type Ia supernovae and Cepheids may have been underestimated. Moreover, the reddening maps from the Planck experiment are shown to systematically overestimate dust extinction by $\sim$100%, and lack sensitivity to extinction curve variations., Comment: 16 pages, 13 figures, 3 tables, accepted to MNRAS, small revisions due to editor's comments and suggestions from the international astronomical community

The Milky Way bulge offers a unique opportunity to investigate in detail the role that different processes such as dynamical instabilities, hierarchical merging, and dissipational collapse may have played in the history of the Galaxy formation and evolution based on its resolved stellar population properties. Large observation programmes and surveys of the bulge are providing for the first time a look into the global view of the Milky Way bulge that can be compared with the bulges of other galaxies, and be used as a template for detailed comparison with models. The Milky Way has been shown to have a box/peanut (B/P) bulge and recent evidence seems to suggest the presence of an additional spheroidal component. In this review we summarise the global chemical abundances, kinematics and structural properties that allow us to disentangle these multiple components and provide constraints to understand their origin. The investigation of both detailed and global properties of the bulge now provide us with the opportunity to characterise the bulge as observed in models, and to place the mixed component bulge scenario in the general context of external galaxies. When writing this review, we considered the perspectives of researchers working with the Milky Way and researchers working with external galaxies. It is an attempt to approach both communities for a fruitful exchange of ideas., Comment: Review article to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing. 36 pages, 10 figures

The VISTA Variables in the V\'ia L\'actea (VVV) survey is one of six public ESO surveys, and is now in its 4th year of observing. Although far from being complete, the VVV survey has already delivered many results, some directly connected to the intended science goals (detection of variables stars, microlensing events, new star clusters), others concerning more exotic objects, e.g. novae. Now, at the end of the fourth observing period, and comprising roughly 50% of the proposed observations, the actual status of the survey, as well some of the results based on the VVV data, are presented., Comment: 5 pages, 7 figures

Outskirts of large galaxies contain important information about the galaxy formation and assembly process, and resolved star count studies can probe the extremely low surface brightness of the outer halos. We use images obtained with the VISTA telescope to construct spatially resolved J vs Z-J colour-magnitude diagrams (CMDs) of NGC 253, a nearly edge-on disk galaxy in the Sculptor group. The very deep photometry, down to J ~ 23.5, and the wide area covered allows us to trace the red giant branch (RGB) and asymptotic giant branch (AGB) stars that belong to the outer disk and the halo of NGC 253, out to 50 kpc along the galaxy minor axis. We confirm the existence of an extra planar stellar component of the disk, with a very prominent southern shelf and a symmetrical feature on the north side. The only additional visible sub-structure is an overdensity in the north-west part of the halo at about 28 kpc from the plane and extending over ~ 20 kpc parallel with the disk of the galaxy. From the stellar count profile along the major axis we measure the transition from the disk to the halo at a radial distance of about 25 kpc, where a clear break appears in the number density profile. The isodensity contours show that the inner halo is a flattened structure that blends with a more extended, diffuse, rounder outer halo. Such external structure can be traced to the very edge of our image out to 50 kpc from the disk plane. The number density profile of the stars in the stellar halo follows a power law with index -1.6, as function of radius. The CMD shows a very homogeneous stellar population across the whole field; by comparison with theoretical isochrones we conclude that the RGB stars are ~ 8 Gyr old or more, while the AGB stars trace a population of about 2 x 10^8 Mo, formed from ~ 0.5 to a few Gyr ago. Surprisingly, part of this latter population appears scattered over a wide area., Comment: To appear on Astronomy and Astrophysics

[abridged] The severe crowding in the direction of the inner Milky Way suggests that the census of stars within a few tens of parsecs in that direction may not be complete. We search for new nearby objects companions of known high proper motion (HPM) stars located towards the densest regions of the Southern Milky Way where the background contamination presented a major problem to previous works. The common proper motion (PM) method was used--we inspected the area around 167 known HPM (>=200 mas/yr) stars: 67 in the disk and 100 in the bulge. Multi-epoch images were provided by 2MASS and the VISTA Variables in Via Lactea (VVV). The VVV is a new on-going ZYJHKs plus multi-epoch Ks survey of ~562 deg^2 of Milky Way's bulge and inner Southern disk. Seven new co-moving companions were discovered around known HPM stars; six known co-moving pairs were recovered; a pair of stars that was thought to be co-moving was found to have different proper motions; published HPMs of eight stars were not confirmed; last but not least, spectral types ranging from G8V to M5V were derived from new infrared spectroscopy for seventeen stars, members of the co-moving pairs. The seven newly discovered stars constitute ~4% of the nearby HPM star list but this is not a firm limit on the HPM star incompleteness because our starting point--the HPM list assembled from the literature--is incomplete itself, missing many nearby HPM M and L type objects, and it is contaminated with non-HPM stars. We have demonstrated, that the superior sub-arcsec spatial resolution, with respect to previous surveys, allows the VVV to examine further the binary nature nature of known HPM stars. The >=5 yr span of VVV will provide sufficient baseline for finding new HPM stars from VVV data alone., Comment: Accepted for publication in A&A; 14 pages, 3 figures, 6 tables

In this paper we present an experimental study on the performance of spatial Interference Alignment (IA) in indoor wireless local area network scenarios that use Orthogonal Frequency Division Multiplexing (OFDM) according to the physical-layer specifications of the IEEE 802.11a standard. Experiments have been carried out using a wireless network testbed capable of implementing a 3-user MIMO interference channel. We have implemented IA decoding schemes that can be designed according to distinct criteria (e.g. zero-forcing or MaxSINR). The measurement methodology has been validated considering practical issues like the number of OFDM training symbols used for channel estimation or feedback time. In case of asynchronous users, a time-domain IA decoding filter is also compared to its frequency-domain counterpart. We also evaluated the performance of IA from bit error rate measurement-based results in comparison to different time-division multiple access transmission schemes. The comparison includes single- and multiple-antenna systems transmitting over the dominant mode of the MIMO channel. Our results indicate that spatial IA is suitable for practical indoor scenarios in which wireless channels often exhibit relatively large coherence times.

In this paper, we study the number of different interference alignment (IA) solutions in a K-user multiple-input multiple-output (MIMO) interference channel, when the alignment is performed via beamforming and no symbol extensions are allowed. We focus on the case where the number of IA equations matches the number of variables. In this situation, the number of IA solutions is finite and constant for any channel realization out of a zero-measure set and, as we prove in the paper, it is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of alignment solutions is the scaled average of the determinant of a certain Hermitian matrix related to the geometry of the problem. Interestingly, while the value of this determinant at an arbitrary point can be used to check the feasibility of the IA problem, its average (properly scaled) gives the number of solutions. For single-beam systems the asymptotic growth rate of the number of solutions is analyzed and some connections with classical combinatorial problems are presented. Nonetheless, our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user., Comment: Submitted to IEEE Transactions on Information Theory

We combine VI photometry from OGLE-III with VVV and 2MASS measurements of E(J-K_{s}) to resolve the longstanding problem of the non-standard optical extinction toward the Galactic bulge. We show that the extinction is well-fit by the relation A_{I} = 0.7465*E(V-I) + 1.3700*E(J-K_{s}), or, equivalently, A_{I} = 1.217*E(V-I)(1+1.126*(E(J-K_{s})/E(V-I)-0.3433)). The optical and near-IR reddening law toward the inner Galaxy approximately follows an R_{V} \approx 2.5 extinction curve with a dispersion {\sigma}_{R_{V}} \approx 0.2, consistent with extragalactic investigations of the hosts of type Ia SNe. Differential reddening is shown to be significant on scales as small as as our mean field size of 6', with the 1{\sigma} dispersion in reddening averaging 9% of total reddening for our fields. The intrinsic luminosity parameters of the Galactic bulge red clump (RC) are derived to be (M_{I,RC}, \sigma_{I,RC,0}, (V-I)_{RC,0}, \sigma_{(V-I)_{RC}}, (J-K_{s})_{RC,0}) = (-0.12, 0.09, 1.06, 0.121, 0.66). Our measurements of the RC brightness, brightness dispersion and number counts allow us to estimate several Galactic bulge structural parameters. We estimate a distance to the Galactic center of 8.20 kpc, resolving previous discrepancies in distance determinations to the bulge based on I-band observations. We measure an upper bound on the tilt {\alpha} \approx 40{\deg}. between the bar's major axis and the Sun-Galactic center line of sight, though our brightness peaks are consistent with predictions of an N-body model oriented at {\alpha} \approx 25{\deg}. The number of RC stars suggests a total stellar mass for the Galactic bulge of 2.0*10^{10} M_{\odot}, if one assumes a Salpeter IMF., Comment: 61 Pages, 21 Figures, 4 Tables, Submitted to The Astrophysical Journal and modified as per a referee report. Includes reddening, reddening law, differential reddening, mean distance, dispersion in distance, surface density of stars and errors thereof for ~9,000 bulge sightlines. For a brief video explaining the key result of this paper, see http://www.youtube.com/user/OSUAstronomy

A convergence theorem is proved for a class of Nystrom methods for weakly singular integral equations on surfaces in three dimensions. Fredholm equations of the second kind as arise in connection with linear elliptic boundary value problems for scalar and vector fields are considered. In contrast to methods based on product integration, coordinate transformations and singularity subtraction, the family of Nystrom methods studied here is based on a local polynomial correction determined by an auxiliary system of moment equations. The polynomial correction is shown to remove the weak singularity in the integral equation and provide control over the approximation error. Convergence results for the family of methods are established under minimal regularity assumptions consistent with classic potential theory. Rates of convergence are shown to depend on the regularity of the problem, the degree of the polynomial correction, and the order of the quadrature rule employed in the discretization. As a corollary, a simple method based on singularity subtraction which has been employed by many authors is shown to be convergent., Comment: submitted

In this paper, we consider the feasibility of linear interference alignment (IA) for multiple-input multiple-output (MIMO) channels with constant coefficients for any number of users, antennas and streams per user; and propose a polynomial-time test for this problem. Combining algebraic geometry techniques with differential topology ones, we first prove a result that generalizes those previously published on this topic. Specifically, we consider the input set (complex projective space of MIMO interference channels), the output set (precoder and decoder Grassmannians) and the solution set (channels, decoders and precoders satisfying the IA polynomial equations), not only as algebraic sets but also as smooth compact manifolds. Using this mathematical framework, we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective. If that mapping is not surjective, then the solution variety projects into the input space in a singular way and the projection is a zero-measure set. This result naturally yields a simple feasibility test, which amounts to checking the rank of a matrix. We also provide an exact arithmetic version of the test, which proves that testing the feasibility of IA for generic MIMO channels belongs to the bounded-error probabilistic polynomial (BPP) complexity class., Comment: To be published in IEEE Transactions on Information Theory