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Astro2020 Decadal Science White Paper: The state of gravitational-wave astrophysics in 2020Mar 11 2019While still in its infancy, the budding field of gravitational-wave astronomy has so far exceeded most expectations, and the achievements that have already been made bode well for the decade to come. While the discoveries made possible by LIGO have captured ... More

Astro2020 Decadal Science White Paper: Gravitational Wave Survey of Galactic Ultra Compact BinariesMar 13 2019Ultra-compact binaries (UCBs) are systems containing compact or degenerate stars with orbital periods less than one hour. Tens of millions of UCBs are predicted to exist within theGalaxy emitting gravitational waves (GWs) at mHz frequencies. Combining ... More

Determination of meteor showers on other planets using comet ephemeridesDec 23 1999Dec 04 2000Meteor showers on the Earth occur at well known times, and are associated with the decay of comets or other minor bodies whose orbital paths pass close to the Earth's trajectory. On the surface, determining the closest proximity of two orbital paths appears ... More

Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domainJan 28 2019We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first ... More

The LISA Time-Delay Interferometry Zero-Signal Solution. I: Geometrical PropertiesMay 30 2004Time-Delay Interferometry (TDI) is the data processing technique needed for generating interferometric combinations of data measured by the multiple Doppler readouts available onboard the three LISA spacecraft. Within the space of all possible interferometric ... More

Can gravitational waves be detected in quasar microlensing?Jul 11 2000Studies of the lensed quasar ${\rm Q}0957+561 {\rm A,B}$ have shown evidence for microlensing in the brightness history of the quasar images. It had been suggested that a frequency offset between the brightness fluctuations in each of the two images might ... More

Gravitational wave bursts from the Galactic massive black holeDec 13 2006The Galactic massive black hole (MBH), with a mass of Mbh=3.6\times10^6 Solar masses, is the closest known MBH, at a distance of only 8 kpc. The proximity of this MBH makes it possible to observe gravitational waves from stars with periapse in the observational ... More

LISA data analysis: Source identification and subtractionJan 28 2003Jan 28 2003The Laser Interferometer Space Antenna (LISA) will operate as an AM/FM receiver for gravitational waves. For binary systems, the source location, orientation and orbital phase are encoded in the amplitude and frequency modulation. The same modulations ... More

Astrophysical Bounds on Global StringsApr 09 1997Global topological defects produce nonzero stress-energy throughout spacetime, and as a result can have observable gravitational influence on surrounding matter. Gravitational effects of global strings are used to place bounds on their cosmic abundance. ... More

Space missions to detect the cosmic gravitational-wave backgroundMar 21 2001Mar 24 2001It is thought that a stochastic background of gravitational waves was produced during the formation of the universe. A great deal could be learned by measuring this Cosmic Gravitational-wave Background (CGB), but detecting the CGB presents a significant ... More

Using binary stars to bound the mass of the gravitonDec 23 1999Interacting white dwarf binary star systems, including helium cataclysmic variable (HeCV) systems, are expected to be strong sources of gravitational radiation, and should be detectable by proposed space-based laser interferometer gravitational wave observatories ... More

Revealing black holes with GaiaOct 12 2017Nov 14 2017We estimate the population of black holes with luminous stellar companions (BH-LCs) in the Milky Way (MW) observable by Gaia. We evolve a realistic distribution of BH-LC progenitors from zero-age to the current epoch taking into account relevant physics, ... More

Null-stream pointing with pulsar timing arraysJul 12 2016Locating sources on the sky is one of the largest challenges in gravitational wave astronomy, owing to the omni-directional nature of gravitational wave detection techniques, and the often intrinsically weak signals being observed. Ground-based detectors ... More

Competing Process Hazard Function Models for Player Ratings in Ice HockeyAug 03 2012Feb 28 2013Evaluating the overall ability of players in the National Hockey League (NHL) is a difficult task. Existing methods such as the famous "plus/minus" statistic have many shortcomings. Standard linear regression methods work well when player substitutions ... More

Gravitational radiation timescales for extreme mass ratio inspiralsAug 11 2005Nov 17 2005The capture and inspiral of compact stellar masses into massive black holes is an important source of low-frequency gravitational waves (with frequencies of ~1-100mHz), such as those that might be detected by the planned Laser Interferometer Space Antenna ... More

Constraining the properties of the proposed supermassive black hole system in 3c66b: Limits from pulsar timingOct 09 2003Oct 10 2003Data from long term timing observations of the radio pulsar PSR B1855+09 have been searched for the signature of Gravitational waves (G-waves) emitted by the proposed supermassive binary black hole system in 3C66B. For the case of a circular orbit, the ... More

Unequal arm space-borne gravitational wave detectorsJun 26 2002Unlike ground-based interferometric gravitational wave detectors, large space-based systems will not be rigid structures. When the end-stations of the laser interferometer are freely flying spacecraft, the armlengths will change due to variations in the ... More

Specific Angular Momentum of Extrasolar Planetary SystemsAug 13 2007Sep 02 2011As the number of known planetary systems increases, the ability to follow-up and characterize the extent of any system becomes limited. This paper considers the use of specific angular momentum as a metric to prioritize future observations. We analyze ... More

Semiclassical effects in black hole interiorsJan 03 1997First-order semiclassical perturbations to the Schwarzschild black hole geometry are studied within the black hole interior. The source of the perturbations is taken to be the vacuum stress-energy of quantized scalar, spinor, and vector fields, evaluated ... More

Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction FunctionNov 21 2008Apr 30 2009Detection of a gravitational-wave stochastic background via ground or space-based gravitational-wave detectors requires the cross-correlation of the response of two or more independent detectors. The cross-correlation involves a frequency-dependent factor ... More

Null geodesics in the Alcubierre warp drive spacetime: the view from the bridgeJul 06 1999The null geodesic equations in the Alcubierre warp drive spacetime are numerically integrated to determine the angular deflection and redshift of photons which propagate through the distortion of the ``warp drive'' bubble to reach an observer at the origin ... More

Contribution of Compact Mass Transferring Systems to the Galactic Gravitational Wave BackgroundOct 25 2005Nov 01 2008Compact object binaries, mostly double with dwarfs, are believed to be a potential source of confusion-limited noise for the Laser Interferometer Space Antenna (LISA). In a specific frequency range, this noise may rise above the instrumental noise sources ... More

Detecting circumbinary exoplanets and hierarchical stellar triples with the LISA gravitational radiation missionDec 09 2018We investigate the possibility of detecting planetary or stellar companions orbiting white dwarf binaries using the LISA gravitational radiation detector. Specifically, we consider the acceleration of the barycenter of the white dwarf binary due to the ... More

Sensitivity curves for spaceborne gravitational wave interferometersSep 26 1999Jan 10 2000To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted (after ... More

Integrated Sachs-Wolfe Effect for Gravitational RadiationMay 12 2009Apr 15 2010Gravitational waves are messengers carrying valuable information about their sources. For sources at cosmological distances, the waves will contain also the imprint left by the intervening matter. The situation is in close analogy with cosmic microwave ... More

Semi-relativistic approximation to gravitational radiation from encounters with nonspinning black holesAug 11 2005Jan 04 2007The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic ... More

LISA, binary stars, and the mass of the gravitonSep 26 2002We extend and improve earlier estimates of the ability of the proposed LISA (Laser Interferometer Space Antenna) gravitational wave detector to place upper bounds on the graviton mass, m_g, by comparing the arrival times of gravitational and electromagnetic ... More

Limiting alternative theories of gravity using gravitational wave observations across the spectrumNov 13 2013Nov 13 2014The advent of gravitational wave astronomy provides new proving grounds for testing theories of gravity. Recent work has reinvigorated the study of bimetric theories of gravity and massive gravity theories. One of the most interesting predictions of these ... More

Formulas for Partition $k$-Tuples with $t$-CoresOct 25 2015Feb 04 2016Let $A_{t,k}(n)$ denote the number of partition $k$-tuples of $n$ where each partition is $t$-core. In this paper, we establish formulas of $A_{t,k}(n)$ for some values of $t$ and $k$ by employing the method of modular forms, which extends Wang's result ... More

LISA data analysis I: Doppler demodulationJun 06 2002Jun 13 2002The orbital motion of the Laser Interferometer Space Antenna (LISA) produces amplitude, phase and frequency modulation of a gravitational wave signal. The modulations have the effect of spreading a monochromatic gravitational wave signal across a range ... More

On the power mean of a sum analogous to the Kloosterman sumDec 05 2017In this paper, we study the power mean of a sum analogous to the Kloosterman sum by using analytic methods for character sums.

Remarks on the distribution of the primitive roots of a primeMar 08 2016Let $\mathbb{F}_p$ be a finite field of size $p$ where $p$ is an odd prime. Let $f(x)\in\mathbb{F}_p[x]$ be a polynomial of positive degree $k$ that is not a $d$-th power in $\mathbb{F}_p[x]$ for all $d\mid p-1$. Furthermore, we require that $f(x)$ and ... More

Combinatorial proof of an identity of Andrews and YeeOct 28 2017May 22 2018Recently, Andrews and Yee studied two-variable generalizations of two identities involving partition functions $p_\omega(n)$ and $p_\nu(n)$ introduced by Andrews, Dixit and Yee. In this paper, we present a combinatorial proof of an interesting identity ... More

An overpartition analogue of partitions with bounded differences between largest and smallest partsFeb 11 2017We study the generating function for overpartitions with bounded differences between largest and smallest parts, which is analogous to a result of Breuer and Kronholm on integer partitions. We also connect this problem with over $q$-binomial coefficients ... More

On a conjecture of George BeckMay 30 2017May 22 2018In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.

Distribution of reducible polynomials with a given coefficient setFeb 24 2016Jul 04 2017For a given set of integers $\mathcal{S}$, let $\mathcal{R}_n^*(\mathcal{S})$ denote the set of reducible polynomials $f(X)=a_nX^n+a_{n-1}X^{n-1}+\cdots+a_1X+a_0$ over $\mathbb{Z}[X]$ with $a_i\in\mathcal{S}$ and $a_0a_n\ne 0$. In this note, we shall ... More

New congruences for 2-color partitionsNov 01 2015Feb 09 2016Let $p_k(n)$ denote the number of $2$-color partitions of $n$ where one of the colors appears only in parts that are multiples of $k$. We will prove a conjecture of Ahmed, Baruah, and Dastidar on congruences modulo $5$ for $p_k(n)$. Moreover, we will ... More

Science Icebreaker Activities: An Example from Gravitational Wave AstronomyMar 25 2005Sep 26 2005At the beginning of a class or meeting an icebreaker activity is often used to help loosen the group and get everyone talking. Our motivation is to develop activities that serve the purpose of an icebreaker, but are designed to enhance and supplement ... More

Hands-on Gravitational Wave Astronomy: Extracting astrophysical information from simulated signalsOct 04 2006In this paper we introduce a hands-on activity in which introductory astronomy students act as gravitational wave astronomers by extracting information from simulated gravitational wave signals. The process mimics the way true gravitational wave analysis ... More

Gravitational Waves: new observatories for new astronomySep 23 2005This article reviews the current status of gravitational wave astronomy and explains why astronomers are excited about the new generation of gravitational wave detectors. As part of the review we compare and contrast gravitational radiation to the more ... More

Coefficients of McKay-Thompson series and distributions of the moonshine moduleAug 15 2015Jan 03 2016In a recent paper, Duncan, Griffin and Ono provide exact formulas for the coefficients of McKay-Thompson series and use them to find asymptotic expressions for the distribution of irreducible representations in the moonshine module $V^\natural = \bigoplus_n ... More

Constructing Reducible Brill--Noether CurvesMar 07 2016Sep 18 2018It was recently determined exactly through how many general points a nondegenerate curve with nonspecial hyperplane section can pass. This gives rise to a method of constructing reducible curves $C_1 \cup_\Gamma C_2 \to \mathbb{P}^r$ with general nodes: ... More

Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg groupMar 04 2016We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by ... More

LISA sources in Milky Way globular clustersFeb 15 2018May 30 2018We explore the formation of double-compact-object binaries in Milky Way (MW) globular clusters (GCs) that may be detectable by the Laser Interferometer Space Antenna (LISA). We use a set of 137 fully evolved GC models that, overall, effectively match ... More

Distinguishing Between Formation Channels for Binary Black Holes with LISAJun 30 2016Sep 22 2016The recent detections of GW150914 and GW151226 imply an abundance of stellar-mass binary-black-hole mergers in the local universe. While ground-based gravitational-wave detectors are limited to observing the final moments before a binary merges, space-based ... More

Observing IMBH-IMBH Binary Coalescences via Gravitational RadiationMay 30 2006Jun 21 2006Recent numerical simulations have suggested the possibility of forming double intermediate mass black holes (IMBHs) via the collisional runaway scenario in young dense star clusters. The two IMBHs formed would exchange into a common binary shortly after ... More

Prospects for observing ultra-compact binaries with space-based gravitational wave interferometers and optical telescopesJul 20 2012Aug 24 2012Space-based gravitational wave interferometers are sensitive to the galactic population of ultra-compact binaries. An important subset of the ultra-compact binary population are those stars that can be individually resolved by both gravitational wave ... More

The Testbed for LISA Analysis ProjectFeb 05 2006The Testbed for LISA Analysis (TLA) Project aims to facilitate the development, validation and comparison of different methods for LISA science data analysis, by the broad LISA Science Community, to meet the special challenges that LISA poses. It includes ... More

Low Frequency Gravitational Waves from White Dwarf MACHO BinariesMay 31 2000The possibility that Galactic halo MACHOs are white dwarfs has recently attracted much attention. Using the known properties of white dwarf binaries in the Galactic disk as a model, we estimate the possible contribution of halo white dwarf binaries to ... More

Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave DetectorsDec 21 2012Sep 13 2013We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ~0.01mHz - 1Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional ... More

Constraining the Black Hole Mass Spectrum with Gravitational Wave Observations I: The Error KernelMar 11 2009Oct 15 2009Many scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many of these formation scenarios predict a high-redshift population of intermediate-mass black holes (IMBHs), with ... More

Addressing LISA Science Analysis ChallengesJun 21 2006The principal goal of the \emph{LISA Science Analysis Workshop} is to encourage the development and maturation of science analysis technology in preparation for LISA science operations. Exactly because LISA is a pathfinder for a new scientific discipline ... More

The LISA Optimal SensitivitySep 12 2002Jun 04 2003The multiple Doppler readouts available on the Laser Interferometer Space Antenna (LISA) permit simultaneous formation of several interferometric observables. All these observables are independent of laser frequency fluctuations and have different couplings ... More

On certain weighted 7-colored partitionsJun 26 2017Nov 28 2017Inspired by Andrews' 2-colored generalized Frobenius partitions, we consider certain weighted 7-colored partition functions and establish some interesting Ramanujan-type identities and congruences. Moreover, we provide combinatorial interpretations of ... More

Busting Up Binaries: Encounters Between Compact Binaries and a Supermassive Black HoleJan 26 2015Given the stellar density near the galactic center, close encounters between compact object binaries and the supermassive black hole are a plausible occurrence. We present results from a numerical study of close to 13 million such encounters. Consistent ... More

Linear independence in the rational homology cobordism groupMar 21 2018We give simple homological conditions for a rational homology 3-sphere Y to have infinite order in the rational homology cobordism group, and for a collection of rational homology spheres to be linearly independent. These translate immediately to statements ... More

Imposed Magnetic Field and Hot Electron Propagation in Inertial Fusion HohlraumsAug 04 2015Oct 08 2015The effects of an imposed, axial magnetic field $B_{z0}$ on hydrodynamics and energetic electrons in inertial confinement fusion (ICF) indirect-drive hohlraums are studied. We present simulations from the radiation-hydrodynamics code HYDRA of a low-adiabat ... More

Event rate estimates for LISA extreme mass ratio capture sourcesMay 28 2004One of the most exciting prospects for the LISA gravitational wave observatory is the detection of gravitational radiation from the inspiral of a compact object into a supermassive black hole. The large inspiral parameter space and low amplitude of the ... More

Overpartitions with bounded part differencesApr 18 2017May 22 2018We generalize recent results of Breuer and Kronholm, and Chern on partitions and overpartitions with bounded differences between largest and smallest parts. We prove our generalization both analytically and combinatorially.

Scott processesJul 08 2014The Scott process of a relational structure $M$ is the sequence of sets of formulas given by the Scott analysis of $M$. We present axioms for the class of Scott processes of structures in a relational vocabulary $\tau$, and use them to give a proof of ... More

Determinants of Subquotients of Galois Representations Associated to Abelian VarietiesOct 03 2011Mar 30 2012Given an abelian variety $A$ of dimension $g$ over a number field $K$, and a prime $\ell$, the $\ell^n$-torsion points of $A$ give rise to a representation $\rho_{A, \ell^n} : \gal(\bar{K} / K) \to \gl_{2g}(\zz/\ell^n\zz)$. In particular, we get a mod-$\ell$ ... More

Synthesis and structure of Na+ intercalated WO3(4,4'-bipyridyl)0.5Sep 28 2009We have prepared single crystals of WO3(4,4'-bipyridyl)0.5 and doped these by Na-ion implantation. The structure of the resultant NaxWO3(4,4'-bipyridyl)0.5 was determined by single-crystal x-ray diffraction to comprise atomic layers of corner-shared WO5N ... More

Progress Towards Counting D_5 Quintic FieldsJul 20 2011Nov 06 2011Let $N(5,D_5,X)$ be the number of quintic number fields whose Galois closure has Galois group $D_5$ and whose discriminant is bounded by $X$. By a conjecture of Malle, we expect that $N(5,D_5,X) \sim C X^{1/2}$ for some constant $C$. The best known upper ... More

Knot concordance and homology sphere groupsMay 25 2016Apr 25 2017We study two homomorphisms to the rational homology sphere group. If $\psi$ denotes the inclusion homomorphism from the integral homology sphere group, then using work of Lisca we show that the image of $\psi$ intersects trivially with the subgroup of ... More

Asymptotic behaviour of cuboids optimising Laplacian eigenvaluesMar 29 2017Oct 10 2017We prove that in dimension $n \geq 2$, within the collection of unit measure cuboids in $\mathbb{R}^n$ (i.e. domains of the form $\prod_{i=1}^{n}(0, a_n)$), any sequence of minimising domains $R_k^\mathcal{D}$ for the Dirichlet eigenvalues $\lambda_k$ ... More

Admissible sequences for positive operatorsJan 14 2018A sequence of scalars is said to be admissible for a positive operator A on a Hilbert space if it is the diagonal of VAV* for some partial isometry V having as domain the closure of the range of A. When A is a projection, the celebrated Kadison's carpenter ... More

Coxeter Groups and Wavelet SetsOct 19 2007A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained ... More

Rank-One Decomposition of Operators and Construction of FramesSep 14 2003The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with particular properties ... More

Constructing real rational knots by gluingAug 13 2016We show that the problem of constructing a real rational knot of a reasonably low degree can be reduced to an algebraic problem involving the pure braid group: expressing an associated element of the pure braid group in terms of the standard generators ... More

Multimessenger science opportunities with mHz gravitational wavesMar 11 2019LISA will open the mHz band of gravitational waves (GWs) to the astronomy community. The strong gravity which powers the variety of GW sources in this band is also crucial in a number of important astrophysical processes at the current frontiers of astronomy. ... More

Post-Newtonian Dynamics in Dense Star Clusters: Binary Black Holes in the LISA BandNov 28 2018The dynamical processing of black holes in the dense cores of globular clusters (GCs), makes them efficient factories for producing binary black holes (BBHs). Here we explore the population of BBHs that form dynamically in GCs and may be observable at ... More

Post-Newtonian Dynamics in Dense Star Clusters: Binary Black Holes in the LISA BandNov 28 2018Feb 26 2019The dynamical processing of black holes in the dense cores of globular clusters (GCs), makes them efficient factories for producing binary black holes (BBHs). Here we explore the population of BBHs that form dynamically in GCs and may be observable at ... More

Some remarks on 'superradiant' phase transitions in light-matter systemsDec 01 2016Mar 29 2017In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally the Jaynes-Cummings model. As the light-matter coupling is increased into the deep strong coupling ... More

MHz Gravitational Wave Constraints with Decameter Michelson InterferometersNov 17 2016A new detector, the Fermilab Holometer, consists of separate yet identical 39-meter Michelson interferometers. Strain sensitivity achieved is better than $10^{-21} /{\sqrt{\rm{Hz}}}$ between 1 to 13 MHz from a 130-hr dataset. This measurement exceeds ... More

Some inequalities for $k$-colored partition functionsSep 20 2017Dec 20 2017Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for $k$-colored partition functions $p_{-k}(n)$ for all $k\geq2$. This enables us to extend the $k$-colored partition function multiplicatively to a function on ... More

Discontinuous homomorphisms, selectors and automorphisms of the complex fieldMar 07 2018Jul 25 2018We show, assuming a weak form of the Axiom of Choice, that the existence of a discontinuous homomorphism of the additive group of real numbers induces a selector for the Vitali equivalence relation $\mathbb{R}/\mathbb{Q}$. In conjunction with a result ... More

Some inequalities for Garvan's bicrank function of 2-colored partitionsMay 17 2018In order to provide a unified combinatorial interpretation of congruences modulo $5$ for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted vector partitions. In this paper, we obtain some inequalities between the ... More

Anomalous Spin-Orbit Torques in Magnetic Single-Layer FilmsFeb 14 2019Spin-orbit interaction (SOI) couples charge and spin transport, enabling electrical control of magnetization. A quintessential example of SOI-induced transport is the anomalous Hall effect (AHE), first observed in 1880, in which an electric current perpendicular ... More

A re-analysis of the three-year WMAP temperature power spectrum and likelihoodJun 05 2006Oct 02 2006We analyze the three-year WMAP temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations ... More

Unveiling the Phase Transition of the Universe During the Reionization Epoch with Lyman-alphaMar 11 2019The epoch of reionization (6 < z < 10) marks the period in our universe when the first large galaxies grew to fruition, and began to affect the universe around them. Massive stars, and potentially accreting supermassive black holes, filled the universe ... More

Analysis of Finite Element Methods for Vector Laplacians on SurfacesOct 21 2016Nov 08 2018We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as elastic membranes ... More

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularizationSep 16 2016Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably ... More

Chirality at two-dimensional surfaces: A perspective from small molecule alcohol assembly on Au(111)Jul 18 2018The delicate balance between H-bonding and van der Waals interactions determine the stability,structure and chirality of many molecular and supramolecular aggregates weakly adsorbed on solid surfaces.Yet the inherent complexity of these systems makes ... More

Three-way tiling sets in two dimensionsOct 18 2007In this article we show that there exist measurable sets W in the plane with finite measure that tile the plane in a measurable way under the action of a expansive matrix A, an affine Weyl group W, and a full rank lattice G. This note is follow-up research ... More

Lieb-Thirring inequalities for wave functions vanishing on the diagonal setJan 15 2019We propose a general strategy to derive Lieb-Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb-Thirring inequality to wave functions vanishing on the diagonal set of the configuration ... More

Decoherent many-body dynamics of a nano- mechanical resonator coupled to charge qubitsMar 14 2010The dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multi partite entanglement ... More

Augmented Lagrangian finite element methods for contact problemsSep 12 2016We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, ... More

Quantitative Comparison of Statistical Methods for Analyzing Human Metabolomics DataOct 10 2017Feb 20 2018Background. Emerging technologies now allow for mass spectrometry based profiling of up to thousands of small molecule metabolites (metabolomics) in an increasing number of biosamples. While offering great promise for revealing insight into the pathogenesis ... More

A Single Visualization Technique for Displaying Multiple Metabolite-Phenotype AssociationsOct 12 2017More advanced visualization tools are needed to assist with the analyses and interpretation of human metabolomics data, which are rapidly increasing in quantity and complexity. Using a dataset of several hundred bioactive lipid metabolites profiled in ... More

Operator valued framesJul 22 2007We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to ... More

MHz Gravitational Wave Constraints with Decameter Michelson InterferometersNov 17 2016Jun 09 2017A new detector, the Fermilab Holometer, consists of separate yet identical 39-meter Michelson interferometers. Strain sensitivity achieved is better than $10^{-21} /{\sqrt{\rm{Hz}}}$ between 1 to 13 MHz from a 130-hr dataset. This measurement exceeds ... More

What we can learn from multi-band observations of black hole binariesMar 10 2019The LIGO/Virgo gravitational-wave (GW) interferometers have to-date detected ten merging black hole (BH) binaries, some with masses considerably larger than had been anticipated. Stellar-mass BH binaries at the high end of the observed mass range (with ... More

Rational cuspidal curves on del-Pezzo surfacesSep 21 2015We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler class computation ... More

Volume and geometry of homogeneously adequate knotsJun 01 2014Jun 17 2014We bound the hyperbolic volumes of a large class of knots and links, called homogeneously adequate knots and links, in terms of their diagrams. To do so, we use the decomposition of these links into ideal polyhedra, developed by Futer, Kalfagianni, and ... More

Understanding Agent Incentives using Causal Influence Diagrams. Part I: Single Action SettingsFeb 26 2019Mar 12 2019Agents are systems that optimize an objective function in an environment. Together, the goal and the environment induce secondary objectives, incentives. Modeling the agent-environment interaction in graphical models called influence diagrams, we can ... More

Saturation of the MRI in Strongly Radiation Dominated Accretion DisksMar 07 2013The saturation level of the magneto-rotational instability (MRI) in a strongly radiation dominated accretion disk is studied using a new Godunov radiation MHD code in the unstratified shearing box approximation. Since vertical gravity is neglected in ... More

Radiation Magneto-hydrodynamic Simulations of the Formation of Hot Accretion Disk CoronaeFeb 12 2014A new mechanism to form a magnetic pressure supported, high temperature corona above the photosphere of an accretion disk is explored using three dimensional radiation magneto-hydrodynamic (MHD) simulations. The thermal properties of the disk are calculated ... More

Super-Eddington Accretion Disks around Supermassive black HolesSep 08 2017We use global three dimensional radiation magneto-hydrodynamical simulations to study accretion disks onto a $5\times 10^8M_{\odot}$ black hole with accretion rates varying from $\sim 250L_{Edd}/c^2$ to $1500 L_{Edd}/c^2$. We form the disks with torus ... More

openWAR: An Open Source System for Evaluating Overall Player Performance in Major League BaseballDec 26 2013Mar 24 2015Within baseball analytics, there is substantial interest in comprehensive statistics intended to capture overall player performance. One such measure is Wins Above Replacement (WAR), which aggregates the contributions of a player in each facet of the ... More

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power SpectraMar 05 2008Oct 17 2008We present the temperature and polarization angular power spectra of the cosmic microwave background (CMB) derived from the first 5 years of WMAP data. The 5-year temperature (TT) spectrum is cosmic variance limited up to multipole l=530, and individual ... More