cssi/SciSciGPT-SciSciNet huggingface dataset:
Atomic Scale Elastic Textures Coupled to Electrons in Superconductors

We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and can describe elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplar textures. We clarify the microscopic origin of anisotropic gradient terms, some of which are included phenomenologically in Landau–Ginzburg theory. The obtained elastic textures are used to investigate the effects of elasticity-driven lattice deformation on the nanoscale electronic structure in superconductor by solving the Bogliubov–de Gennes equations with the electronic degrees of freedom coupled to the lattice ones. It is shown that the order parameter is depressed in the regions where the lattice deformation takes place. The calculated local density of states suggests the electronic structure is strongly modulated as a response to the lattice deformation—the elasticity propagates the electronic response over long distances. In particular, the trapping of low-lying quasiparticle states around the defects is possible. These predictions could be directly tested by STM experiments in superconducting materials.
Two-photon optical frequency reference with active AC stark shift cancellation

In some embodiments, two light beams having different frequencies can be counter-propagated through an atomic absorber having an atomic transition frequency approximately equal to the sum of the frequencies of the two beams. When the beams are appropriately tuned, the atomic absorber absorbs significant amount of light of at least the lower power beam. The amount of light remaining after the absorber is an indication of how well the frequencies are tuned to the absorber. At least one of the beam frequencies has an FM modulation applied prior to the absorber. This means the phase of the remaining light compared to the FM modulation, along with the intensity of the remaining light, can be used to provide a first feedback signal to adjust the frequencies of the beams to match the absorber frequency. Finally, both beams have amplitude modulation applied before the absorber. Comparing the response of the first feedback signal to the AM modulation frequency generates an intensity ratio feedback signal used to adjust the power of at least one of the beams and realize the zero light shift condition.
Noncommutative aspects of open/closed strings via foliations

We give a brief summary of algebraic aspects of string theory arising in the noncommutative geometry setting of foliations called string diagrammatics which we introduced jointly with Bob Penner. We furthermore discuss how this gives rise to actions on the Hochschild complex of a Frobenius algebra. We then explain how this leads to new quantum chains for loop spaces and a stabilization in the semi-simple case.
Computing symmetric determinantal representations

We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our algorithms are geared towards speed and robustness, employing linear algebra and numerical algebraic geometry, without genericity assumptions on the polynomials.
Crossover from shear-driven to thermally activated drainage of liquid-infused microscale capillaries

Surface roughness can play a critical role in dynamic wetting processes like imbibition and drainage of capillaries. In the presence of nanoscale roughness, The shear-driven drainage of microscale capillary grooves exhibits regimes that cannot be described by solely considering hydrodynamic and capillary effects. Thermal motion and nanoscale surface roughness ``characterized by AFM'' induce drainage rates predicted by Kramers theory of thermally activated transitions.
Nearby Gas-rich Low Surface Brightness Galaxies

We examine the Fisher-Tully cz < 1000 km s-1 galaxy sample to determine whether it is a complete and representative sample of all galaxy types, including low surface brightness populations, as has been recently claimed. We find that the sample is progressively more incomplete for galaxies with (1) smaller physical diameters at a fixed isophote and (2) lower H I masses. This is likely to lead to a significant undercounting of nearby gas-rich low surface brightness galaxies. However, through comparisons to other samples, we can understand how the nearby galaxy counts need to be corrected, and we see some indications of environmental effects that probably result from the local high density of galaxies.
Type Ia Supernova Colors and Ejecta Velocities: Hierarchical Bayesian Regression with Non-Gaussian Distributions

We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocity (NV) supernovae exhibit significant discrepancies for B – V and B – R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B – V and B – R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of –0.021 ± 0.006 and –0.030 ± 0.009 mag (10{sup 3} km s{sup –1}){sup –1} for intrinsic B – V and B – R colors versus velocity, respectively. Because the ejecta velocity more » distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to A{sub V} extinction estimates as large as –0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances. « less
Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the...
Learning Credible Models

In many settings, it is important that a model be capable of providing reasons for its predictions (ie, the model must be interpretable). However, the model's reasoning may not conform with well-established knowledge. In such cases, while interpretable, the model lacks credibility. In this work, we formally define credibility in the linear setting and focus on techniques for learning models that are both accurate and credible. In particular, we propose a regularization penalty, expert yielded estimates (EYE), that incorporates expert knowledge about well-known relationships among covariates and the outcome of interest. We give both theoretical and empirical results comparing our proposed method to several other regularization techniques. Across a range of settings, experiments on both synthetic and real data show that models learned using the EYE penalty are significantly more credible than those learned using other penalties. Applied to two large-scale patient risk stratification task, our proposed technique results in a model whose top features overlap significantly with known clinical risk factors, while still achieving good predictive performance.
EARLY-TYPE GALAXY ARCHEOLOGY: AGES, ABUNDANCE RATIOS, AND EFFECTIVE TEMPERATURES FROM FULL-SPECTRUM FITTING

The stellar populations of galaxies hold vital clues to their formation histories. In this paper we present results based on modeling stacked spectra of early-type galaxies drawn from the Sloan Digital Sky Survey as a function of velocity dispersion, σ, from 90 km s–1 to 300 km s–1. The spectra are of extremely high quality, with typical signal-to-noise ratio of 1000 A–1, and a wavelength coverage of 4000 A –8800 A. Our population synthesis model includes variation in 16 elements from C to Ba, a two-component star formation history, the shift in effective temperature, Δ T eff, of the stars with respect to a solar metallicity isochrone, and the stellar initial mass function, among other parameters. In our approach we fit the full optical spectra rather than a select number of spectral indices and are able to, for the first time, measure the abundances of the elements V, Cr, Mn, Co, and Ni from the integrated light of distant galaxies. Our main results are as follows: (1) light-weighted stellar ages range from 6-12 Gyr from low to high σ; (2) [Fe/H] varies by less than 0.1 dex across the entire sample; (3) Mg closely tracks O, and both increase from ≈0.0 at low σ to ~0.25 at high σ; Si and Ti show a shallower rise with σ, and Ca tracks Fe rather than O; (4) the iron peak elements V, Cr, Mn, and Ni track Fe, while Co tracks O, suggesting that Co forms primarily in massive stars; (5) C and N track O over the full sample and [C/Fe] and [N/Fe] exceed 0.2 at high σ; and (6) the variation in Δ T eff with total metallicity closely follows theoretical predictions based on stellar evolution theory. This last result is significant because it implies that we are robustly solving not only for the detailed abundance patterns but also the detailed temperature distributions (i.e., isochrones) of the stars in these galaxies. A variety of tests reveal that the systematic uncertainties in our measurements are probably 0.05 dex or less. Our derived [Mg/Fe] and [O/Fe] abundance ratios are 0.05-0.1 dex lower than most previous determinations. Under the conventional interpretation that the variation in these ratios is due to star formation timescale variations, our results suggest longer star formation timescales for massive early-type galaxies than previous studies. Detailed chemical evolution models are necessary in order to translate the abundance ratio distributions of these galaxies into constraints on their formation histories. Alternatively, these data may provide useful constraints on the nucleosynthetic pathways for elements whose production is not well understood.
Model-independent Plotting of the Cosmological Scale Factor as a Function of Lookback Time

In this work we describe a model-independent method of developing a plot of scale factor a(t) versus lookback time t{sub L} from the usual Hubble diagram of modulus data against redshift. This is the first plot of this type. We follow the model-independent methodology of Daly and Djorgovski used for their radio-galaxy data. Once the a(t)data plot is completed, any model can be applied and will display as described in the standard literature. We then compile an extensive data set to z = 1.8 by combining Type Ia supernovae (SNe Ia) data from SNLS3 of Conley et al., high-z SNe data of Riess et al., and radio-galaxy data of Daly and Djorgovski to validate the new plot. We first display these data on a standard Hubble diagram to confirm the best fit for ΛCDM cosmology, and thus validate the joined data set. The scale factor plot is then developed from the data and the ΛCDM model is again displayed from a least-squares fit. The fit parameters are in agreement with the Hubble diagram fit confirming the validity of the new plot. Of special interest is the transition time of the universe, which in the scale factor plot will appear asmore » an inflection point in the data set. Noise is more visible in this presentation, which is particularly sensitive to inflection points of any model displayed in the plot, unlike on a modulus-z diagram, where there are no inflection points and the transition-z is not at all obvious by inspection. We obtain a lower limit of z ≥ 0.6. It is evident from this presentation that there is a dearth of SNe data in the range z = 1-2, exactly the range necessary to confirm a ΛCDM transition-z around z = 0.76. We then compare a 'toy model' wherein dark matter is represented as a perfect fluid with an equation of state p = –(1/3) ρ to demonstrate the plot sensitivity to model choice. Its density varies as 1/t {sup 2} and it enters the Friedmann equations as Ω{sub dark}/t {sup 2}, replacing only the Ω{sub dark}/a {sup 3} term. The toy model is a close match to ΛCDM, but separates from it on the scale factor plot for similar ΛCDM density parameters. It is described in the Appendix. A more complete transition time analysis will be presented in a future paper.« less
Light quark masses using domain wall fermions

We compute the one—loop self—energy correction to the massive domain wall quark propagator. Combining this calculation with simulations at several gauge couplings, we estimate the strange quark mass in the continuum limit. The perturbative one—loop mass renormalization is comparable to that for Wilson quarks and considerably smaller than that for Kogut—Susskind quarks. Also, scaling violations appear mild in comparison to other errors at present. Given their good chiral behavior and these features, domain wall quarks are attractive for evaluating the light quark masses. Our preliminary quenched result is ms(2 GeV) = 82(15) MeV in the MS scheme.
Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics

The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first- principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular-momentum sums to yield a robust holographic outcome.
Colored Khovanov–Rozansky homology for infinite braids

We show that the limiting unicolored sl(N) Khovanov–Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we show that the results hold in the case of colored homfly–pt Khovanov–Rozansky homology as well. An application of this result is given in finding a partial isomorphism between the homfly–pt homology of any braid positive link and the stable homfly–pt homology of the infinite torus knot as computed by Hogancamp.
TWO-DIMENSIONAL YANG-MILLS THEORIES ARE STRING THEORIES

We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold ℳ can be associated with maps from a string worldsheet onto ℳ. These maps are unbranched and branched covers of ℳ with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in ℳ. These string theories differ from SU(N) Yang-Mills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets.
AN EXTENDED AND MORE SENSITIVE SEARCH FOR PERIODICITIES IN ROSSI X-RAY TIMING EXPLORER/ALL-SKY MONITOR X-RAY LIGHT CURVES

We present the results of a systematic search in {approx}14 years of Rossi X-ray Timing Explorer All-Sky Monitor (ASM) data for evidence of periodicities. Two variations of the commonly used Fourier analysis search method have been employed to significantly improve upon the sensitivity achieved by Wen et al. in 2006, who also searched for periodicities in ASM data. In addition, the present search is comprehensive in terms of sources studied and frequency range covered, and has yielded the detection of the signatures of the orbital periods of eight low-mass X-ray binary systems and of ten high-mass X-ray binaries not listed in the tables of Wen et al. Orbital periods, epochs, signal amplitudes, modulation fractions, and folded light curves are given for each of these systems. Seven of the orbital periods are the most precise reported to date. In the course of this work, the 18.545 day orbital period of IGR J18483-0311 was co-discovered, and the first detections in X-rays were made of the {approx}3.9 day orbital period of LMC X-1 and the {approx}3.79 hr orbital period of 4U 1636-536. The results inform future searches for orbital and other periodicities in X-ray binaries.
A TEST OF COSMOLOGICAL MODELS USING HIGH- z MEASUREMENTS OF H ( z )

The recently constructed Hubble diagram using a combined sample of SNLS and SDSS-II SNe Ia, and an application of the Alcock–Paczynski (AP) test using model-independent Baryon Acoustic Oscillation (BAO) data, have suggested that the principal constraint underlying the cosmic expansion is the total equation-of-state of the cosmic fluid, rather than that of its dark energy. These studies have focused on the critical redshift range (0 ≲ z ≲ 2) within which the transition from decelerated to accelerated expansion is thought to have occurred, and they suggest that the cosmic fluid has zero active mass, consistent with a constant expansion rate. The evident impact of this conclusion on cosmological theory calls for an independent confirmation. In this paper, we carry out this crucial one-on-one comparison between the R{sub h} = ct universe (a Friedmann–Robertson–Walker cosmology with zero active mass) and wCDM/ΛCDM, using the latest high-z measurements of H(z). Whereas the SNe Ia yield the integrated luminosity distance, while the AP diagnostic tests the geometry of the universe, the Hubble parameter directly samples the expansion rate itself. We find that the model-independent cosmic chronometer data prefer R{sub h} = ct over wCDM/ΛCDM with a Bayes Information Criterion likelihood of ∼95% versus onlymore » ∼5%, in strong support of the earlier SNe Ia and AP results. This contrasts with a recent analysis of H(z) data based solely on BAO measurements which, however, strongly depend on the assumed cosmology. We discuss why the latter approach is inappropriate for model comparisons, and emphasize again the need for truly model-independent observations to be used in cosmological tests.« less
Multifaceted dynamics of janus oscillator networks

A ring of ``Janus'' oscillators---oscillators made from two components with differing natural frequencies---can exhibit myriad synchronization patterns.
A quadratic refinement of the Grothendieck–Lefschetz–Verdier trace formula

We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the “Euler characteristic integral” of a certain cohomotopy class over its scheme of fixed points. When the base is a field and the fixed points are etale, we compute this integral in terms of Morel’s identification of the ring of endomorphisms of the motivic sphere spectrum with the Grothendieck‐Witt ring. In particular, we show that the Euler characteristic of an etale algebra corresponds to the class of its trace form in the Grothendieck‐Witt ring. 14F42; 47H10, 11E81
Notions of denseness

The notion of a completely saturated packing [Fejes Toth, Kuperberg and Kuperberg, Highly saturated packings and reduced coverings, Monats. Math. 125 (1998) 127-145] is a sharper version of maximum density, and the analogous notion of a completely reduced covering is a sharper version of minimum density. We define two related notions: uniformly recurrent and weakly recurrent dense packings, and diffusively dominant packings. Every compact domain in Euclidean space has a uniformly recurrent dense packing. If the domain self-nests, such a packing is limit-equivalent to a completely saturated one. Diffusive dominance is yet sharper than complete saturation and leads to a better understanding of n-saturation.
PAMELA, DAMA, INTEGRAL and signatures of metastable excited WIMPs

Models of dark matter with ~ GeV scale force mediators provide attractive explanations of many high energy anomalies, including PAMELA, ATIC, and the WMAP haze. At the same time, by exploiting the ~ MeV scale excited states that are automatically present in such theories, these models naturally explain the DAMA/LIBRA and INTEGRAL signals through the inelastic dark matter (iDM) and exciting dark matter (XDM) scenarios, respectively. Interestingly, with only weak kinetic mixing to hypercharge to mediate decays, the lifetime of excited states with ? < 2melectron is longer than the age of the universe. The fractional relic abundance of these excited states depends on the temperature of kinetic decoupling, but can be appreciable. There could easily be other mechanisms for rapid decay, but the consequences of such long-lived states are intriguing. We find that CDMS constrains the fractional relic population of ~ 100 keV states to be 10?2, for a 1 TeV WIMP with ?n = 10?40 cm2. Upcoming searches at CDMS, as well as xenon, silicon, and argon targets, can push this limit significantly lower. We also consider the possibility that the DAMA excitation occurs from a metastable state into the XDM state, which decays via e+e? emission, which allows lighter states to explain the INTEGRAL signal due to the small kinetic energies required. Such models yield dramatic signals from down-scattering, with spectra peaking at high energies, sometimes as high as ~ 1 MeV, well outside the usual search windows. Such signals would be visible at future Ar and Si experiments, and may be visible at Ge and Xe experiments, although ?-rays associated with nuclear excitations would complicate the signal for these heavier targets. We also consider other XDM models involving ~ 500 keV metastable states, and find they can allow lighter WIMPs to explain INTEGRAL as well.
OPPOSITE-SIGN KLOOSTERMAN SUM ZETA FUNCTION

We study the meromorphic continuation and the spectral expansion of the opposite-sign Kloosterman sum zeta function for positive integers, to all . There are poles of the function corresponding to zeros of the Riemann zeta function and the spectral parameters of Maass forms. The analytic properties of this function are rather delicate. It turns out that the spectral expansion of the zeta function converges only in a left half-plane, disjoint from the region of absolute convergence of the Dirichlet series, even though they both are analytic expressions of the same meromorphic function on the entire complex plane.
Six-vertex model with partial domain wall boundary conditions: Ferroelectric phase

We obtain an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase region. The proof is based on a formula for the partition function involving the determinant of a matrix of mixed Vandermonde/Hankel type. This determinant can be expressed in terms of a system of discrete orthogonal polynomials, which can then be evaluated asymptotically by comparison with the Meixner polynomials.
THE LINK BETWEEN THE FORMATION RATES OF CLUSTERS AND STARS IN GALAXIES

The goal of this paper is to test whether the formation rate of star clusters is proportional to the star formation rate (SFR) in galaxies. As a first step, we present the mass functions of compact clusters younger than 10 Myr in seven star-forming galaxies of diverse masses, sizes, and morphologies: the Large and Small Magellanic Clouds, NGC 4214, NGC 4449, M83, M51, and the Antennae. These cluster mass functions (CMFs) are well represented by power laws, , with similar exponents , but with amplitudes that differ by factors up to , corresponding to vast differences in the sizes of the cluster populations in these galaxies. We then normalize these CMFs by the SFRs in the galaxies, derived from dust-corrected Hα luminosities, and find that the spread in the amplitudes collapses, with a remaining rms deviation of only . This is close to the expected dispersion from random uncertainties in the CMFs and SFRs. Thus, the data presented here are consistent with exact proportionality between the formation rates of stars and clusters. However, the data also permit weak deviations from proportionality, at the factor of two level, within the statistical uncertainties. We find the same spread in amplitudes when we normalize the mass functions of much older clusters, with ages in the range 100–400 Myr, by the current SFR. This is another indication of the general similarity among the cluster populations of different galaxies.
Power index rankings in bicameral legislatures and the US legislative system

In this paper we study rankings induced by power indices of players in simple game models of bicameral legislatures. For a bicameral legislature where bills are passed with a simple majority vote in each house we give a condition involving the size of each chamber which guarantees that a member of the smaller house has more power than a member of the larger house, regardless of the power index used. The only case for which this does not apply is when the smaller house has an odd number of players, the larger house has an even number of players, and the larger house is less than twice the size of the smaller house. We explore what can happen in this exceptional case. These results generalize to multi-cameral legislatures. Using a standard model of the US legislative system as a simple game, we use our results to study power index rankings of the four types of players—the president, the vice president, senators, and representatives. We prove that a senator is always ranked above a representative and ranked the same as or above the vice president. We also show that the president is always ranked above the other players. We show that for most power index rankings, including the Banzhaf and Shapley–Shubik power indices, the vice president is ranked above a representative, however, there exist power indices ranking a representative above the vice president.
Vibrational spectroscopy of polar molecules with superradiance

We investigate cooperative phenomena and superradiance for vibrational transitions in polar molecule spectroscopy of high optical-depth samples. Such cooperativity comes from the build-up of inter-particle coherence through dipole–dipole interactions and leads to speed-up of decay processes. We compare our calculation to recent work and find very good agreement, suggesting that superradiant effects need to be taken into account in a wide variety of ultracold molecule experiments, including vibrational and rotational states.
Universal factorization spaces and algebras

We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a factorization algebra or space by an etale morphism of schemes, and hence to define the notion of a universal factorization space or algebra. This provides a generalization to higher dimensions and to non-linear settings of the notion of a vertex algebra.
Improved accent classification combining phonetic vowels with acoustic features

Researches have shown accent classification can be improved by integrating semantic information into pure acoustic approach. In this work, we combine phonetic knowledge, such as vowels, with enhanced acoustic features to build an improved accent classification system. The classifier is based on Gaussian Mixture Model-Universal Background Model (GMM-UBM), with normalized Perceptual Linear Predictive (PLP) features. The features are further optimized by Principle Component Analysis (PCA) and Hetroscedastic Linear Discriminant Analysis (HLDA). Using 7 major types of accented speech from the Foreign Accented English (FAE) corpus, the system achieves classification accuracy 54% with input test data as short as 20 seconds, which is competitive to the state of the art in this field.
The Role of Quasar Radiative Feedback on Galaxy Formation during Cosmic Reionization

Recent observations have found that many $z\sim 6$ quasar fields lack galaxies. This unexpected lack of galaxies may potentially be explained by quasar radiation feedback. In this paper I present a suite of 3D radiative transfer cosmological simulations of quasar fields. I find that quasar radiation suppresses star formation in low mass galaxies, mainly by photo-dissociating their molecular hydrogen. Photo-heating also plays a role, but only after $\sim$100 Myr. However, galaxies which already have stellar mass above $10^5 M_\odot$ when the quasar turns on will not be suppressed significantly. Quasar radiative feedback suppresses the faint end of the galaxy luminosity function (LF) within $1$ pMpc, but to a far lesser degree than the field-to-field variation of the LF. My study also suggests that by using the number of bright galaxies ($M_{1500}<-16$) around quasars, we can potentially recover the underlying mass overdensity, which allows us to put reliable constraints on quasar environments.
Modeling Human Visual Search Performance on Realistic Webpages Using Analytical and Deep Learning Methods

Modeling visual search not only offers an opportunity to predict the usability of an interface before actually testing it on real users but also advances scientific understanding about human behavior. In this work, we first conduct a set of analyses on a large-scale dataset of visual search tasks on realistic webpages. We then present a deep neural network that learns to predict the scannability of webpage content, i.e., how easy it is for a user to find a specific target. Our model leverages both heuristic-based features such as target size and unstructured features such as raw image pixels. This approach allows us to model complex interactions that might be involved in a realistic visual search task, which can not be achieved by traditional analytical models. We analyze the model behavior to offer our insights into how the salience map learned by the model aligns with human intuition.
HYDROGEN EMISSION from the IONIZED GASEOUS HALOS of LOW-REDSHIFT GALAXIES

NASA ADAP [NNX12AE27G]; NSF [AST-1311326]; Alfred P. Sloan Foundation; National Science Foundation; U.S. Department of Energy Office of Science; University of Arizona; Brazilian Participation Group; Brookhaven National Laboratory; Carnegie Mellon University; University of Florida; French Participation Group; German Participation Group; Harvard University; Instituto de Astrofisica de Canarias; Michigan State/Notre Dame/JINA Participation Group; Johns Hopkins University; Lawrence Berkeley National Laboratory; Max Planck Institute for Astrophysics; Max Planck Institute for Extraterrestrial Physics; New Mexico State University; New York University; Ohio State University; Pennsylvania State University; University of Portsmouth; Princeton University; Spanish Participation Group; University of Tokyo; University of Utah; Vanderbilt University; University of Virginia; University of Washington; Yale University; [NSF-1313302]
Spread of infectious disease and social awareness as parasitic contagions on clustered networks

This study models the interactions between spreading and social campaigns as a system of parasitic contagions and looks at their complex interplay with network structure.
EXTENDED STRUCTURE AND FATE OF THE NUCLEUS IN HENIZE 2-10

We investigate the structure and nuclear region of the black hole (BH) hosting galaxy Henize 2-10. Surface brightness profiles are analyzed using Magellan/Megacam g- and r-band images. Excluding the central starburst, we find a best-fit two-component Sersic profile with n {sub in} ∼ 0.6, r {sub eff,} {sub in} ∼ 260 pc and n {sub out} ∼ 1.8, r ∼ 1 kpc. Integrating out to our outermost data point (100'' ∼ 4.3 kpc), we calculate M{sub g} = –19.2 and M{sub r} = –19.8. The corresponding enclosed stellar mass is M {sub *} ∼ (10 ± 3) × 10{sup 9} M {sub ☉}, ∼3 × larger than previous estimates. Apart from the central ≲500 pc, with blue colors and an irregular morphology, the galaxy appears to be an early-type system. The outer color is quite red, (g – r){sub 0} = 0.75, suggesting a dominant old population. We study the nuclear region of the galaxy using archival Gemini/NIFS K-band adaptive optics spectroscopy and Hubble Space Telescope imaging. We place an upper limit on the BH mass of ∼10{sup 7} M {sub ☉} from the NIFS data, consistent with that from the M {sub BH}-radio-X-ray fundamental plane. No coronal lines aremore » seen, but a Brγ source is located at the position of the BH with a luminosity consistent with the X-ray emission. The starburst at the center of Henize 2-10 has led to the formation of several super star clusters, which are within ∼100 pc of the BH. We examine the fate of the nucleus by estimating the dynamical masses and dynamical friction timescales of the clusters. The most massive clusters (∼10{sup 6} M {sub ☉}) have τ{sub dyn} ≲ 200 Myr, and thus Henize 2-10 may represent a rare snapshot of nuclear star cluster formation around a preexisting massive BH.« less
The pillowcase and perturbations of traceless representations of knot groups

We introduce explicit holonomy perturbations of the Chern‐Simons functional on a 3‐ ball containing a pair of unknotted arcs. These perturbations give us a concrete local method for making the moduli spaces of flat singular SO.3/ connections relevant to Kronheimer and Mrowka’s singular instanton knot homology nondegenerate. The mechanism for this study is a (Lagrangian) intersection diagram which arises, through restriction of representations, from a tangle decomposition of a knot. When one of the tangles is trivial, our perturbations allow us to study isolated intersections of two Lagrangians to produce minimal generating sets for singular instanton knot homology. The (symplectic) manifold where this intersection occurs corresponds to the traceless character variety of the four-punctured 2‐sphere, which we identify with the familiar pillowcase. We investigate the image in this pillowcase of the traceless representations of tangles obtained by removing a trivial tangle from 2‐bridge knots and torus knots. Using this, we compute the singular instanton homology of a variety of torus knots. In many cases, our computations allow us to understand nontrivial differentials in the spectral sequence from Khovanov homology to singular instanton homology.
The untwisting number of a knot

The unknotting number of a knot is the minimum number of crossings one must change to turn that knot into the unknot. The algebraic unknotting number is the minimum number of crossing changes needed to transform a knot into an Alexander polynomial-one knot. We work with a generalization of unknotting number due to Mathieu and Domergue, which we call the untwisting number. The untwisting number is the minimum number (over all diagrams of a knot) of right- or left-handed twists on even numbers of strands of a knot, with half of the strands oriented in each direction, necessary to transform that knot into the unknot. We show that the algebraic untwisting number is equal to the algebraic unknotting number. However, we also exhibit several families of knots for which the difference between the unknotting and untwisting numbers is arbitrarily large, even when we only allow twists on a fixed number of strands or fewer.
A DISCRETIZED VERSION OF KALUZA–KLEIN THEORY WITH TORSION AND MASSIVE FIELDS

We consider an internal space of two discrete points in the fifth dimension of the Kaluza–Klein theory by using the formalism of noncommutative geometry — developed in a previous paper1 — of a spacetime supplemented by two discrete points. With the non-vanishing internal torsion two-form there are no constraints implied on the vielbeins. The theory contains a pair of tensor fields, a pair of vector fields and a pair of scalar fields. Using the generalized Cartan structure equation we are able to uniquely determine not only the Hermitian and metric-compatible connection one-forms, but also the nonvanishing internal torsion two-form in terms of vielbeins. The resulting action has a rich and complex structure, a particular feature being the existence of massive modes. Thus the nonvanishing internal torsion generates a Kaluza–Klein type model with zero and massive modes.
OBSERVATIONS OF CRAB GIANT PULSES IN 20-84 MHz USING LWA1

We report the detection and observed characteristics of giant pulses from the Crab Nebula pulsar (B0531+21) in four frequency bands covering 20-84 MHz using the recently completed Long Wavelength Array Station 1 (LWA1) radio telescope. In 10 hr of observations distributed over a 72 day period in fall of 2012, 33 giant pulses having peak flux densities between 400 Jy and 2000 Jy were detected. Twenty-two of these pulses were detected simultaneously in channels of 16 MHz bandwidth centered at 44 MHz, 60 MHz, and 76 MHz, including one pulse which was also detected in a channel centered at 28 MHz. We quantify statistics of pulse amplitude and pulse shape characteristics, including pulse broadening. Amplitude statistics are consistent with expectations based on extrapolations from previous work at higher and lower frequencies. Pulse broadening is found to be relatively high, but not significantly greater than expected. We present procedures that have been found to be effective for observing giant pulses in this frequency range.
QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.
Perron’s method for nonlocal fully nonlinear equations

This paper is concerned with the existence of viscosity solutions of nonlocal fully nonlinear equations that are not translation-invariant. We construct a discontinuous viscosity solution of such a nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Holder continuous and thus it is a viscosity solution.
The hidden assumptions behind counterfactual explanations and principal reasons

Counterfactual explanations are gaining prominence within technical, legal, and business circles as a way to explain the decisions of a machine learning model. These explanations share a trait with the long-established "principal reason" explanations required by U.S. credit laws: they both explain a decision by highlighting a set of features deemed most relevant---and withholding others. These "feature-highlighting explanations" have several desirable properties: They place no constraints on model complexity, do not require model disclosure, detail what needed to be different to achieve a different decision, and seem to automate compliance with the law. But they are far more complex and subjective than they appear. In this paper, we demonstrate that the utility of feature-highlighting explanations relies on a number of easily overlooked assumptions: that the recommended change in feature values clearly maps to real-world actions, that features can be made commensurate by looking only at the distribution of the training data, that features are only relevant to the decision at hand, and that the underlying model is stable over time, monotonic, and limited to binary outcomes. We then explore several consequences of acknowledging and attempting to address these assumptions, including a paradox in the way that feature-highlighting explanations aim to respect autonomy, the unchecked power that feature-highlighting explanations grant decision makers, and a tension between making these explanations useful and the need to keep the model hidden. While new research suggests several ways that feature-highlighting explanations can work around some of the problems that we identify, the disconnect between features in the model and actions in the real world---and the subjective choices necessary to compensate for this---must be understood before these techniques can be usefully implemented.
Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data

We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest. Under appropriate conditions on the quantile functions without requiring the existence of any moments, the new procedure is shown to enjoy the sure screening property in ultra-high dimensions. Furthermore, the quantile-adaptive framework can naturally handle censored data arising in survival analysis. We prove that the sure screening property remains valid when the response variable is subject to random right censoring. Numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantile-specific information from heteroscedastic data.
Restoring geometrical optics near caustics using sequenced metaplectic transforms

Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and, more generally, at caustics. We present a new formulation of GO, called metaplectic geometrical optics (MGO), that is free from these singularities and can be applied to any linear wave equation. MGO uses sequenced metaplectic transforms of the wavefield, corresponding to symplectic transformations of the ray phase space, such that caustics disappear in the new variables, and GO is reinstated. The Airy problem and the quantum harmonic oscillator are studied analytically using MGO for illustration. In both cases, the MGO solutions are remarkably close to the exact solutions and remain finite at cutoffs, unlike the usual GO solutions.
On actions of connected Hopf algebras

Let $H$ be a connected Hopf algebra acting on an algebra $A$. Working over a base field having characteristic $0$, we show that for a given prime (semi-prime, completely prime) ideal $I$ of $A$, the largest $H$-stable ideal of A contained in $I$ is also prime (semi-prime, completely prime). We also prove a similar result for certain subrings of convolution algebras.
An infinite-rank summand of topologically slice knots

Let CTS be the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that CTS contains an infinite-rank subgroup, and Livingston and Manolescu-Owens showed that CTS contains a Z 3 summand. We show that in fact CTS contains a Z 1 summand. The proof relies on the knot Floer homology package of Ozsvath‐Szabo and the concordance invariant ". 57N70, 57R58; 57M25
A comparison of two quantization procedures for lineal gravity

Abstract We consider two programs for quantizing gravity 1+1 dimensions, which have appeared in the literature: one using a gauge-theoretic approach and the other following a more conventional “geometric” approach. We compare the wave functionals produced by the two different programs by finding matrix elements between the variables of the two theories. We find that the wave functionals are equivalent.
PARTICLE TRANSPORT IN YOUNG PULSAR WIND NEBULAE

The model for pulsar wind nebulae (PWNe) as a result of the magnetohydrodynamic (MHD) downstream flow from a shocked, relativistic pulsar wind has been successful in reproducing many features of the nebulae observed close to central pulsars. However, observations of well-studied young nebulae like the Crab Nebula, 3C 58, and G21.5-0.9 do not show the toroidal magnetic field on a larger scale that might be expected in the MHD flow model; in addition, the radial variation of spectral index due to synchrotron losses is smoother than expected in the MHD flow model. We find that pure diffusion models can reproduce the basic data on nebular size and spectral index variation for the Crab, 3C 58, and G21.5-0.9. Most of our models use an energy-independent diffusion coefficient; power-law variations of the coefficient with energy are degenerate with variation in the input particle energy distribution index in the steady state, transmitting boundary case. Energy-dependent diffusion is a possible reason for the smaller diffusion coefficient inferred for the Crab. Monte Carlo simulations of the particle transport allowing for advection and diffusion of particles suggest that diffusion dominates over much of the total nebular volume of the Crab. Advection dominates close to the pulsarmore » and is likely to play a role in the X-ray half-light radius. The source of diffusion and mixing of particles is uncertain, but may be related to the Rayleigh-Taylor instability at the outer boundary of a young PWN or to instabilities in the toroidal magnetic field structure.« less