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Alternating distances of knots and linksJun 26 2014An alternating distance is a link invariant that measures how far away a link is from alternating. We study several alternating distances and demonstrate that there exist families of links for which the difference between certain alternating distances ... More

Chromatic homology, Khovanov homology, and torsionSep 12 2016Mar 14 2017In the first few homological gradings, there is an isomorphism between the Khovanov homology of a link and the categorification of the chromatic polynomial of a graph related to the link. In this article, we show that the categorification of the chromatic ... More

Chromatic homology, Khovanov homology, and torsionSep 12 2016In the first few homological gradings, there is an isomorphism between the Khovanov homology of a link and the categorification of the chromatic polynomial of a graph related to the link. In this article, we show that the categorification of the chromatic ... More

The Jones polynomial of an almost alternating linkJul 18 2017Dec 14 2017A link is almost alternating if it is non-alternating and has a diagram that can be transformed into an alternating diagram via one crossing change. We give formulas for the first two and last two potential coefficients of the Jones polynomial of an almost ... More

The Khovanov width of twisted links and closed 3-braidsJan 15 2009Jan 16 2009Khovanov homology is a bigraded Z-module that categorifies the Jones polynomial. The support of Khovanov homology lies on a finite number of slope two lines with respect to the bigrading. The Khovanov width is essentially the largest horizontal distance ... More

On knot Floer width and Turaev genusSep 05 2007To each knot $K\subset S^3$ one can associated its knot Floer homology $\hat{HFK}(K)$, a finitely generated bigraded abelian group. In general, the nonzero ranks of these homology groups lie on a finite number of slope one lines with respect to the bigrading. ... More

Turaev genus, knot signature, and the knot homology concordance invariantsFeb 04 2010We give bounds on knot signature, the Ozsvath-Szabo tau invariant, and the Rasmussen s invariant in terms of the Turaev genus of the knot.

The 2-Factor Polynomial Detects Even Perfect MatchingsDec 26 2018In this paper, we prove that the 2-factor polynomial, an invariant of a planar trivalent graph with a perfect matching, counts the number of 2- factors that contain the the perfect matching as a subgraph. Consequently, we show that the polynomial detects ... More

Turaev genus and alternating decompositionsJul 10 2015Aug 08 2016We prove that the genus of the Turaev surface of a link diagram is determined by a graph whose vertices correspond to the boundary components of the maximal alternating regions of the link diagram. Furthermore, we use these graphs to classify link diagrams ... More

A Turaev surface approach to Khovanov homologyJul 12 2011Jan 30 2013We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology of the link (after a grading shift). We also present a spanning ... More

Invariants for Turaev genus one linksApr 12 2016Sep 30 2016The Turaev genus defines a natural filtration on knots where Turaev genus zero knots are precisely the alternating knots. We show that the signature of a Turaev genus one knot is determined by the number of components in its all-A Kauffman state, the ... More

Extremal Khovanov homology of Turaev genus one linksDec 29 2018The Turaev genus of a link can be thought of as a way of measuring how non-alternating a link is. A link is Turaev genus zero if and only if it is alternating, and in this viewpoint, links with large Turaev genus are very non-alternating. In this paper, ... More

Cube diagrams and 3-dimensional Reidemeister-like moves for knotsNov 03 2008May 23 2012In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under two types of cube diagram operations. A knot homology is ... More

Torsion in thin regions of Khovanov homologyMar 13 2019In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are known to only contain $\mathbb{Z}_2$ torsion. In this paper, we ... More

On the Turaev genus of torus knotsMar 07 2017The Turaev genus and dealternating number of a link are two invariants that measure how far away a link is from alternating. We determine the Turaev genus of a torus knot with five or fewer strands either exactly or up to an error of at most one. We also ... More

Multiplicity Amongst Wide Brown Dwarf Companions to Nearby Stars: Gliese 337CDMar 17 2005We present Lick Natural Guide Star Adaptive Optics observations of the L8 brown dwarf Gliese 337C, which is resolved for the first time into two closely separated (0"53+/-0"03), nearly equal magnitude components with a K_s flux ratio of 0.93+/-0.10. Companionship ... More

Not Alone: Tracing the Origins of Very Low Mass Stars and Brown Dwarfs Through Multiplicity StudiesFeb 06 2006Feb 09 2006The properties of multiple stellar systems have long provided important empirical constraints for star formation theories, enabling (along with several other lines of evidence) a concrete, qualitative picture of the birth and early evolution of normal ... More

A Sample of Very Young Field L Dwarfs and Implications for the Brown Dwarf "Lithium Test" at Early AgesAug 22 2008Using a large sample of optical spectra of late-type dwarfs, we identify a subset of late-M through L field dwarfs that, because of the presence of low-gravity features in their spectra, are believed to be unusually young. From a combined sample of 303 ... More

Deep Near-Infrared Imaging of the rho Oph Cloud Core: Clues to the Origin of the Lowest-Mass Brown DwarfsJun 13 2010A search for young substellar objects in the rho Oph cloud core region has been made using the deep-integration Combined Calibration Scan images of the 2MASS extended mission in J, H and Ks bands, and Spitzer IRAC images at 3.6, 4.5, 5.8 and 8.0 microns. ... More

$Extrasolar~Storms$: Pressure-dependent Changes In Light Curve Phase In Brown Dwarfs From Simultaneous $Hubble$ and $Spitzer$ ObservationsMay 09 2016We present $Spitzer$/IRAC Ch1 and Ch2 monitoring of six brown dwarfs during 8 different epochs over the course of 20 months. For four brown dwarfs, we also obtained simulataneous $HST$/WFC3 G141 Grism spectra during two epochs and derived light curves ... More

Discovery of a Very Young Field L Dwarf, 2MASS J01415823-4633574Nov 15 2005While following up L dwarf candidates selected photometrically from the Two Micron All Sky Survey, we uncovered an unusual object designated 2MASS J01415823-4633574. Its optical spectrum exhibits very strong bands of vanadium oxide but abnormally weak ... More

HST NICMOS Imaging of the Planetary-mass Companion to the Young Brown Dwarf 2MASS J1207334-393254Jul 21 2006Multi-band (0.9 to 1.6 um) images of the TW Hydrae Association (TWA) brown dwarf, 2MASS J1207334-393254 (also known as 2M1207), and its candidate planetary mass companion (2M1207b) were obtained on 2004 Aug 28 and 2005 Apr 26 with HST/NICMOS. The images ... More

Ensemble Prediction of a Halo Coronal Mass Ejection Using Heliospheric ImagersDec 01 2017The Solar TErrestrial RElations Observatory (STEREO) and its heliospheric imagers (HI) have provided us the possibility to enhance our understanding of the interplanetary propagation of coronal mass ejections (CMEs). HI-based methods are able to forecast ... More

Adaptive optics imaging survey of the Tucana-Horologium associationApr 07 2003We present the results of an adaptive optics (AO) imaging survey of the common associations of Tucana and Horologium, carried out at the ESO 3.6m telescope with the ADONIS/SHARPII system. Based on our observations of two dozen probable association members, ... More

Giant Planet Companion to 2MASSW J1207334-393254Apr 29 2005We report new VLT/NACO imaging observations of the young, nearby brown dwarf 2MASSW J1207334-393254 and its suggested planetary mass companion (2M1207 b). Three epochs of VLT/NACO measurements obtained over nearly one year show that the planetary mass ... More

A Giant Planet Candidate near a Young Brown DwarfSep 14 2004We present deep VLT/NACO infrared imaging and spectroscopic observations of the brown dwarf 2MASSWJ1207334-393254, obtained during our on-going adaptive optics survey of southern young, nearby associations. This 25 MJup brown dwarf, located 70 pc from ... More

A Study of the Diverse T Dwarf Population Revealed by WISEJan 16 2013Feb 17 2013We report the discovery of 87 new T dwarfs uncovered with the Wide-field Infrared Survey Explorer (WISE) and three brown dwarfs with extremely red near-infrared colors that exhibit characteristics of both L and T dwarfs. Two of the new T dwarfs are likely ... More

HST Rotational Spectral Mapping of Two L-Type Brown Dwarfs: Variability In and Out of Water Bands Indicates High-Altitude Haze LayersNov 11 2014We present time-resolved near-infrared spectroscopy of two L5 dwarfs, 2MASS J18212815+1414010 and 2MASS J15074759-1627386, observed with the Wide Field Camera 3 instrument on the Hubble Space Telescope (HST). We study the wavelength dependence of rotation-modulated ... More

A companion to AB Pic at the planet/brown dwarf boundaryApr 29 2005We report deep imaging observations of the young, nearby star AB Pic, a member of the large Tucana-Horologium as sociation. We have detected a faint, red source 5.5" South of the star with JHK colors compatible with that of a young substellar L dwarf. ... More

Cloud Atlas: Discovery of Rotational Spectral Modulations in a Low-mass, L-type Brown Dwarf Companion to a StarOct 23 2017Observations of rotational modulations of brown dwarfs and giant exoplanets allow the characterization of condensate cloud properties. As of now rotational spectral modulations have only been seen in three L-type brown dwarfs. We report here the discovery ... More

Cloud Atlas: Rotational Spectral Modulations and potential Sulfide Clouds in the Planetary-mass, Late T-type Companion Ross 458CMar 26 2019Measurements of photometric variability at different wavelengths provide insights into the vertical cloud structure of brown dwarfs and planetary-mass objects. In seven Hubble Space Telescope consecutive orbits, spanning $\sim$10 h of observing time}, ... More

Astrometric and Spectroscopic Confirmation of a Brown Dwarf Companion to GSC 08047-00232Dec 21 2004We report VLT/NACO imaging observations of the stars GSC 08047-00232 and HIP 6856, probable members of the large Tucana-Horologium association. During our previous ADONIS/SHARPII deep imaging survey, a substellar candidate companion was discovered around ... More

The Circumstellar Disk of HD 141569 Imaged with NICMOSSep 06 1999Coronagraphic imaging with the Near Infrared Camera and Multi Object Spectrometer on the Hubble Space Telescope reveals a large, ~400 AU (4'') radius, circumstellar disk around the Herbig Ae/Be star HD 141569. A reflected light image at 1.1 micron shows ... More

Cloud Atlas: Rotational Modulations in the L/T Transition Brown Dwarf Companion HN Peg BJan 29 2018Feb 17 2018Time-resolved observations of brown dwarfs' rotational modulations provide powerful insights into the properties of condensate clouds in ultra-cool atmospheres. Multi-wavelength light curves reveal cloud vertical structures, condensate particle sizes, ... More

Cloud Atlas: Hubble Space Telescope Near-Infrared Spectral Library of Brown Dwarfs, Planetary-mass companions, and hot JupitersDec 10 2018Bayesian atmospheric retrieval tools can place constraints on the properties of brown dwarfs and hot Jupiters atmospheres. To fully exploit these methods, high signal-to-noise spectral libraries with well-understood uncertainties are essential. We present ... More

Randomized Benchmarking of Clifford OperatorsNov 25 2018Randomized benchmarking is an experimental procedure intended to demonstrate control of quantum systems. The procedure extracts the average error introduced by a set of control operations. When the target set of operations is intended to be the set of ... More

A numerical method for variational problems with convexity constraintsJul 26 2011Aug 23 2012We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational problems, ... More

No disk needed around HD 199143 BSep 11 2002We present new, high angular resolution images of HD 199143 in the Capricornus association, obtained with the adaptive optics system ADONIS+SHARPII at the ESO 3.6m Telescope of La Silla Observatory. HD 199143 and its neighbour star HD 358623 (separation ... More

Cloud Atlas: Discovery of Patchy Clouds and High-amplitude Rotational Modulations In a Young, Extremely Red L-type Brown DwarfSep 15 2016Sep 19 2016Condensate clouds fundamentally impact the atmospheric structure and spectra of exoplanets and brown dwarfs but the connections between surface gravity, cloud structure, dust in the upper atmosphere, and the red colors of some brown dwarfs remain poorly ... More

Cloud Atlas: High-Contrast Time-Resolved Observations of Planetary-Mass CompanionsJan 31 2019Feb 20 2019Directly-imaged planetary-mass companions offer unique opportunities in atmospheric studies of exoplanets. They share characteristics of both brown dwarfs and transiting exoplanets, therefore, are critical for connecting atmospheric characterizations ... More

Infrared Views of the TW Hya DiskOct 15 2001The face-on disk around TW Hya is imaged in scattered light at wavelengths of 1.1 and 1.6 micron using the coronagraph in the Near Infrared Camera and Multi Object Spectrometer aboard the Hubble Space Telescope. Stellar light scattered from the optically ... More

Finite difference methods for the Infinity Laplace and p-Laplace equationsJul 26 2011Dec 05 2012We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and the game theoretical $p$-Laplacian. The discretizations simplify and generalize earlier ones. We prove convergence of the solution of the Wide Stencil finite ... More

Neutral strange particle production at mid unit rapidity in p+p collisions at sqrt(s) = 200 GeVMar 12 2004Mar 19 2004We briefly discuss the methods of analysing reconstructed neutral strange particles in p+p collision data measured at sqrt(s) = 200 GeV taken using the Solenoidal Tracker At RHIC (STAR) detector. We present spectra for K0 short, lambda and anti-lambda ... More

Lambda and Antilambda polarization from deep inelastic muon scatteringNov 04 1999Nov 18 1999We report results of the first measurements of Lambda and Antilambda polarization produced in deep inelastic polarized muon scattering on the nucleon. The results are consistent with an expected trend towards positive polarization with increasing x_F. ... More

Identification, Interpretability, and Bayesian Word EmbeddingsApr 02 2019Social scientists have recently turned to analyzing text using tools from natural language processing like word embeddings to measure concepts like ideology, bias, and affinity. However, word embeddings are difficult to use in the regression framework ... More

The generalized Levinger transformationDec 22 2007In this paper, we present new results relating the numerical range of a matrix $A$ with generalized Levinger transformation $\mathcal{L}(A,\alpha,\beta) = \alphaH_A +\betaS_A$, where $H_A$ and $S_A$, are respectively the Hermitian and skew-hermitian parts ... More

Reliability Conditions in Quadrature AlgorithmsMar 06 2003The detection of insufficiently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the profile of the integrand at the quadrature knots which allows ... More

Avoidance of Partitions of a Three-element SetMar 20 2006Feb 15 2007Klazar defined and studied a notion of pattern avoidance for set partitions, which is an analogue of pattern avoidance for permutations. Sagan considered partitions which avoid a single partition of three elements. We enumerate partitions which avoid ... More

Rigidity Sequences of Power Rationally Weakly Mixing TransformationsMar 19 2015We prove that a class of infinite measure preserving transformations, satisfying a "strong" weak mixing condition, generates all rigidity sequences of all conservative ergodic invertible measure preserving transformations defined on a Lebesgue $\sigma$-finite ... More

The Möbius Function of a Restricted Composition PosetJun 09 2008Apr 19 2012We study a poset of compositions restricted by part size under a partial ordering introduced by Bj\"{o}rner and Stanley. We show that our composition poset $C_{d+1}$ is isomorphic to the poset of words $A_d^*$. This allows us to use techniques developed ... More

Mixing sets for non-mixing transformationsApr 04 2016For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is positive. In particular, ... More

VLT/NACO Deep imaging survey of young, nearby austral starsJun 16 2009Since November 2002, we have conducted the largest deep imaging survey of the young, nearby associations of the southern hemisphere. Our goal is detection and characterization of substellar companions at intermediate (10--500 AU) physical separations. ... More

A Sensitive Search for Variability in Late L Dwarfs: The Quest for WeatherJul 24 2006We have conducted a photometric monitoring program of 3 field late-L brown dwarfs looking for evidence of non-axisymmetric structure or temporal variability in their photospheres. The observations were performed using Spitzer/IRAC 4.5 and 8 micron bandpasses ... More

Mechanical switching of ferro-electric rubberDec 09 2008At the A to C transition, smectic elastomers have recently been observed to undergo $\sim$35% spontaneous shear strains. We first explicitly describe how strains of up to twice this value could be mechanically or electrically induced in Sm-$C$ elastomers ... More

Distributions of Long-Lived Radioactive Nuclei Provided by Star Forming EnvironmentsOct 17 2015Radioactive nuclei play an important role in planetary evolution by providing an internal heat source, which affects planetary structure and helps facilitate plate tectonics. A minimum level of nuclear activity is thought to be necessary --- but not sufficient ... More

Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundariesDec 09 2014Nov 18 2015Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to low accuracy ... More

High energy gamma-ray properties of the FR I radio galaxy NGC 1275Jan 13 2011We report on our study of the high-energy $\gamma-$ray emission from the FR I radio galaxy NGC 1275, based on two years of observations with the Fermi-LAT detector. Previous Fermi studies of NGC 1275 had found evidence for spectral and flux variability ... More

Approximate homogenization of fully nonlinear elliptic PDEs: estimates and numerical results for Pucci type equationsOct 27 2017May 14 2018We are interested in the shape of the homogenized operator $\overline F(Q)$ for PDEs which have the structure of a nonlinear Pucci operator. A typical operator is $H^{a_1,a_2}(Q,x) = a_1(x) \lambda_{\min}(Q) + a_2(x)\lambda_{\max}(Q)$. Linearization of ... More

Atomic and Molecular Opacities for Brown Dwarf and Giant Planet AtmospheresJul 11 2006Sep 06 2006We present a comprehensive description of the theory and practice of opacity calculations from the infrared to the ultraviolet needed to generate models of the atmospheres of brown dwarfs and extrasolar giant planets. Methods for using existing line lists ... More

A partial differential equation for the rank one convex envelopeMay 10 2016May 11 2016In this article we introduce a Partial Differential Equation (PDE) for the rank one convex envelope. Rank one convex envelopes arise in non-convex vector valued variational problems \cite{BallElasticity, kohn1986optimal1, BallJames87, chipot1988equilibrium}. ... More

Density-functional study of oxygen adsorption on Mo(112)Nov 15 2004Atomic oxygen adsorption on the Mo(112) surface has been investigated by means of first-principles total energy calculations. Among the variety of possible adsorption sites it was found that the bridge sites between two Mo atoms of the topmost row are ... More

Modified Bernoulli Equation for Use with Combined Electro-Osmotic and Pressure-Driven MicroflowsJan 05 2012In this paper we present electro-osmotic (EO) flow within a more traditional fluid mechanics framework. Specifically, the modified Bernoulli equation (viz. the energy equation, the mechanical energy equation, the pipe flow equation, etc.) is shown to ... More

An algebraic construction of twin-like modelsSep 19 2011Oct 04 2011If the generalized dynamics of K field theories (i.e., field theories with a non-standard kinetic term) is taken into account, then the possibility of so-called twin-like models opens up, that is, of different field theories which share the same topological ... More

A partial differential equation for the rank one convex envelopeMay 10 2016Jan 12 2017In this article we introduce a Partial Differential Equation (PDE) for the rank one convex envelope. Rank one convex envelopes arise in non-convex vector valued variational problems \cite{BallElasticity, kohn1986optimal1, BallJames87, chipot1988equilibrium}. ... More

Stochastic Gradient Descent with Polyak's Learning RateMar 20 2019Stochastic gradient descent (SGD) for strongly convex functions converges at the rate O(1/k). However, achieving the rate with the optimal constant requires knowledge of parameters of the function which are usually not available. In practise, the step ... More

A Candidate Substellar Companion to CoD -33 7795 (TWA 5)Dec 09 1998We present the discovery of a candidate substellar object in a survey of young stars in the solar vicinity using the sensitivity and spatial resolution afforded by the NICMOS coronagraph on the Hubble Space Telescope. The H=12.1 mag object was discovered ... More

Simultaneous X-ray and Infrared Observations of Sagittarius A*'s VariabilityDec 14 2018Emission from Sgr A* is highly variable at both X-ray and infrared (IR) wavelengths. Observations over the last ~20 years have revealed X-ray flares that rise above a quiescent thermal background about once per day, while faint X-ray flares from Sgr A* ... More

Spitzer Space Telescope Mid-IR Light Curves of NeptuneAug 25 2016We have used the Spitzer Space Telescope in February 2016 to obtain high cadence, high signal-to-noise, 17-hour duration light curves of Neptune at 3.6 and 4.5 $\mu$m. The light curve duration was chosen to correspond to the rotation period of Neptune. ... More

Deep search for companions to probable young brown dwarfsAug 15 2012We have obtained high contrast images of four nearby, faint, and very low mass objects 2MASSJ04351455-1414468, SDSSJ044337.61+000205.1, 2MASSJ06085283-2753583 and 2MASSJ06524851-5741376 (here after 2MASS0435-14, SDSS0443+00, 2MASS0608-27 and 2MASS0652-57), ... More

Numerical methods for motion of level sets by affine curvatureOct 27 2016Oct 28 2016We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite difference schemes, ... More

Empirical confidence estimates for classification by deep neural networksMar 21 2019How well can we estimate the probability that the classification, $C(f(x))$, predicted by a deep neural network is correct (or in the Top 5)? We consider the case of a classification neural network trained with the KL divergence which is assumed to generalize, ... More

Quantum families of invertible maps and related problemsMar 19 2015Aug 11 2015The notion of families of quantum invertible maps ($C^*$-algebra homomorphisms satisfying Podle\'s condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In particular ... More

Approximate homogenization of convex nonlinear elliptic PDEsOct 27 2017We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal invariant measure, which may be derived via Legendre-Fenchel duality. ... More

Subspace Restricted Boltzmann MachineJul 16 2014The subspace Restricted Boltzmann Machine (subspaceRBM) is a third-order Boltzmann machine where multiplicative interactions are between one visible and two hidden units. There are two kinds of hidden units, namely, gate units and subspace units. The ... More

Filtered schemes for Hamilton-Jacobi equations: a simple construction of convergent accurate difference schemesNov 12 2014We build a simple and general class of finite difference schemes for first order Hamilton-Jacobi (HJ) Partial Differential Equations. These filtered schemes are convergent to the unique viscosity solution of the equation. The schemes are accurate: we ... More

Approximate Convex Hulls: sketching the convex hull using curvatureFeb 27 2017Jun 14 2017Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this article we approximate ... More

Temperature dependence of the diffusive conductivity of bilayer grapheneDec 09 2009Sep 06 2010Assuming diffusive carrier transport and employing an effective medium theory, we calculate the temperature dependence of bilayer graphene conductivity due to Fermi-surface broadening as a function of carrier density. We find that the temperature dependence ... More

The Interstellar Line of Sight to the Interacting Galaxy NGC 5195Jan 14 2015We present moderately-high resolution echelle observations of the nucleus of NGC 5195, the line of sight to which samples intervening interstellar material associated with the outer spiral arm of M51. Our spectra reveal absorption from interstellar Na ... More

UV Radiation Fields Produced by Young Embedded Star ClustersDec 20 2007A large fraction of stars form within young embedded clusters, and these environments produce a substantial ultraviolet (UV) background radiation field, which can provide feedback on the star formation process. To assess the possible effects of young ... More

Discovery of gamma-ray emission from the Broad Line Radio Galaxy Pictor ADec 29 2011We report the discovery of high-energy \gamma-ray emission from the Broad Line Radio Galaxy (BLRG) Pictor A with a significance of ~5.8\sigma (TS=33.4), based on three years of observations with the Fermi Large Area Telescope (LAT) detector. The three-year ... More

The Dirichlet problem for the convex envelopeJul 05 2010The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified problem: the Dirichlet problem for the underlying PDE. The main result is ... More

Lipschitz regularized Deep Neural Networks converge and generalizeAug 28 2018Oct 03 2018Generalization of deep neural networks (DNNs) is an open problem which, if solved, could impact the reliability and verification of deep neural network architectures. In this paper, we show that if the usual fidelity term used in training DNNs is augmented ... More

Permutation Statistics and $q$-Fibonacci NumbersApr 02 2009Jul 07 2009In a recent paper, Goyt and Sagan studied distributions of certain set partition statistics over pattern restricted sets of set partitions that were counted by the Fibonacci numbers. Their study produced a class of $q$-Fibonacci numbers, which they related ... More

Preliminary Trigonometric Parallaxes of 184 Late-T and Y Dwarfs and an Analysis of the Field Substellar Mass Function into the "Planetary" Mass RegimeDec 04 2018We present preliminary trigonometric parallaxes of 184 late-T and Y dwarfs using observations from Spitzer (143), USNO (18), NTT (14), and UKIRT (9). To complete the 20-pc census of $\ge$T6 dwarfs, we combine these measurements with previously published ... More

Y dwarf Trigonometric Parallaxes from the Spitzer Space TelescopeSep 18 2018Sep 19 2018Y dwarfs provide a unique opportunity to study free-floating objects with masses $<$30 M$_{Jup}$ and atmospheric temperatures approaching those of known Jupiter-like exoplanets. Obtaining distances to these objects is an essential step towards characterizing ... More

Projective limits of quantum symmetry groups and the doubling construction for Hopf algebrasMay 20 2013The quantum symmetry group of the inductive limit of C*-algebras equipped with orthogonal filtrations is shown to be the projective limit of the quantum symmetry groups of the C*-algebras appearing in the sequence. Some explicit examples of such projective ... More

Computing the Spectrum of a Heterotic Flux VacuumAug 31 2009Jun 27 2012We compute the massless spectra of a set of flux vacua of the heterotic string. The vacua we study include well-known non-Kahler T^2-fibrations over K3 with SU(3) structure and intrinsic torsion. Following gauged linear sigma models of these vacua into ... More

Convergence and Rates for Fixed-Interval Multiple-Track Smoothing Using $k$-Means Type OptimizationJun 08 2015May 04 2016We address the task of estimating multiple trajectories from unlabelled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the reconstruction of the ... More

Twinlike models with identical linear fluctuation spectraDec 01 2011Recently, the possibility of so-called twinlike field theories has been demonstrated, that is, of different field theories which share the same topological defect solution with the same energy density. Further, purely algebraic conditions have been derived ... More

An efficient linear programming method for Optimal TransportationSep 11 2015An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for moderate grid ... More

Addressing the Fundamental Tension of PCGML with Discriminative LearningSep 10 2018Procedural content generation via machine learning (PCGML) is typically framed as the task of fitting a generative model to full-scale examples of a desired content distribution. This approach presents a fundamental tension: the more design effort expended ... More

Finite Sample Inference for the Maximum Score EstimandMar 04 2019We provide a finite sample inference method for the structural parameters of a semiparametric binary response model under a conditional median restriction originally studied by Manski (1975, 1985). Our inference method is valid for any sample size and ... More

Percolation thresholds on 2D Voronoi networks and Delaunay triangulationsJun 24 2009Sep 01 2009The site percolation threshold for the random Voronoi network is determined numerically for the first time, with the result p_c = 0.71410 +/- 0.00002, using Monte-Carlo simulation on periodic systems of up to 40000 sites. The result is very close to the ... More

Exchange and spin-fluctuation superconducting pairing in cupratesApr 12 2001Feb 06 2002We propose a microscopical theory of superconductivity in CuO$_2$ layer within the effective two-band Hubbard model in the strong correlation limit. By applying a projection technique for the matrix Green function in terms of the Hubbard operators, the ... More

Baryonic Collapse within Dark Matter Halos and the Formation of Gaseous Galactic DisksSep 12 2006This paper constructs an analytic framework for calculating the assembly of galactic disks from the collapse of gas within dark matter halos, with the goal of determining the surface density profiles. Gas parcels (baryons) fall through the potentials ... More

Evolution of Planetary Orbits with Stellar Mass Loss and Tidal DissipationOct 09 2013Intermediate mass stars and stellar remnants often host planets, and these dynamical systems evolve because of mass loss and tides. This paper considers the combined action of stellar mass loss and tidal dissipation on planetary orbits in order to determine ... More

Tack energy and switchable adhesion of liquid crystal elastomersAug 11 2012The mechanical properties of liquid crystal elastomers (LCEs) make them suitable candidates for pressure-sensitive adhesives (PSAs). Using the nematic dumbbell constitutive model, and the block model of PSAs, we study their tack energy and the debonding ... More

Exact Simulation of Noncircular or Improper Complex-Valued Stationary Gaussian Processes using Circulant EmbeddingMay 17 2016This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The ... More

Linear Models for Flux VacuaNov 08 2006We construct worldsheet descriptions of heterotic flux vacua as the IR limits of N=2 gauge theories. Spacetime torsion is incorporated via a 2d Green-Schwarz mechanism in which a doublet of axions cancels a one-loop gauge anomaly. Manifest (0,2) supersymmetry ... More

Single molecule narrowfield microscopy of protein-DNA binding dynamics in glucose signal transduction of live yeast cellsMay 25 2016Single-molecule narrowfield microscopy is a versatile tool to investigate a diverse range of protein dynamics in live cells and has been extensively used in bacteria. Here, we describe how these methods can be extended to larger eukaryotic, yeast cells, ... More