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MMT Hypervelocity Star SurveyAug 19 2008Sep 15 2008We describe a new survey for unbound hypervelocity stars (HVSs), stars traveling with such extreme velocities that dynamical ejection from a massive black hole (MBH) is their most likely origin. We investigate the possible contribution of unbound runaway ... More

Do the nearby BHB stars belong to the Thick Disk or the Halo?Nov 12 2008We study the Milky Way region Z<3.0 kpc, where the thick disk and inner halo overlap, by using the kinematics of local blue horizontal branch (BHB) stars (within 1 kpc) and new samples of BHB stars and A-type stars from the Century Survey. We derive Galactic ... More

Accurate Masses for the Primary and Secondary in the Eclipsing White Dwarf Binary NLTT 11748Aug 05 2010We measure the radial velocity curve of the eclipsing detached white dwarf binary NLTT 11748. The primary exhibits velocity variations with a semi-amplitude of 273 km/s and an orbital period of 5.641 hr. We do not detect any spectral features from the ... More

Gaia and the Galactic Center Origin of Hypervelocity StarsMay 10 2018Aug 17 2018We use new Gaia measurements to explore the origin of the highest velocity stars in the Hypervelocity Star Survey. The measurements reveal a clear pattern in the B-type stars. Halo stars dominate the sample at speeds about 100 km/s below Galactic escape ... More

The DECam Minute Cadence Survey II: 49 Variables but No Planetary Transits of a White DwarfFeb 11 2019We present minute cadence photometry of 31732 point sources observed in one 3 $deg^{2}$ DECam pointing centred at RA = 09:03:02 and Dec = -04:35:00 over eight consecutive half-nights. We use these data to search for eclipse-like events consistent with ... More

Impact of the Galactic Disk and Large Magellanic Cloud on the Trajectories of Hypervelocity Stars Ejected from the Galactic CenterJun 26 2018Aug 20 2018We consider how the gravity of the Galactic disk and the Large Magellanic Cloud (LMC) modifies the radial motions of hypervelocity stars (HVSs) ejected from the Galactic Center. For typical HVSs ejected towards low (high) Galactic latitudes, the disk ... More

The Origin of HVS17, an Unbound Main Sequence B Star at 50 kpcAug 19 2013We analyze Keck ESI spectroscopy of HVS17, a B-type star traveling with a Galactic rest frame radial velocity of +445 km/s in the outer halo of the Milky Way. HVS17 has the projected rotation of a main sequence B star and is chemically peculiar, with ... More

The Nature of Hypervelocity Stars and the Time Between Their Formation and EjectionJun 18 2012We obtain Keck HIRES spectroscopy of HVS5, one of the fastest unbound stars in the Milky Way halo. We show that HVS5 is a 3.62 +- 0.11 Msun main sequence B star at a distance of 50 +- 5 kpc. The difference between its age and its flight time from the ... More

Today a Duo, But Once a Trio? The Double White Dwarf HS 2220$+$2146 May Be A Post-Blue Straggler BinaryJul 01 2016For sufficiently wide orbital separations {\it a}, the two members of a stellar binary evolve independently. This implies that in a wide double white dwarf (DWD), the more massive WD should always be produced first, when its more massive progenitor ends ... More

A Refined Search for Pulsations in White Dwarf Companions to Millisecond PulsarsJun 10 2018We present optical high-speed photometry of three millisecond pulsars with low-mass ($< 0.3 M_{\odot}$) white dwarf companions, bringing the total number of such systems with follow-up time-series photometry to five. We confirm the detection of pulsations ... More

New Halo White Dwarf Candidates in the Sloan Digital Sky SurveyAug 25 2016We present optical spectroscopy and near-infrared photometry of 57 faint ($g= 19-22$) high proper motion white dwarfs identified through repeat imaging of $\approx3100$ square degrees of the Sloan Digital Sky Survey footprint by Munn et al. (2014). We ... More

The Runaway Binary LP 400-22 is Leaving the GalaxyJul 11 2013We present optical spectroscopy, astrometry, radio, and X-ray observations of the runaway binary LP 400-22. We refine the orbital parameters of the system based on our new radial velocity observations. Our parallax data indicate that LP 400-22 is significantly ... 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

A Deep Proper Motion Catalog Within the Sloan Digital Sky Survey Footprint. II. The White Dwarf Luminosity FunctionNov 18 2016A catalog of 8472 white dwarf (WD) candidates is presented, selected using reduced proper motions from the deep proper motion catalog of Munn et al. 2014. Candidates are selected in the magnitude range 16 < r < 21.5 over 980 square degrees, and 16 < r ... More

Visitors from the Halo: 11 Gyr old White Dwarfs in the Solar NeighborhoodApr 06 2010We report the discovery of three nearby old halo white dwarf candidates in the Sloan Digital Sky Survey (SDSS), including two stars in a common proper motion binary system. These candidates are selected from our 2800 square degree proper motion survey ... More

A quantitative spectral analysis of 14 hypervelocity stars from the MMT surveyJun 22 2018Hypervelocity stars (HVSs) travel so fast that they may leave the Galaxy. The tidal disruption of a binary system by the supermassive black hole in the Galactic center is widely assumed to be their ejection mechanism. To test the hypothesis of an origin ... More

Least Squares Policy Iteration with Instrumental Variables vs. Direct Policy Search: Comparison Against Optimal Benchmarks Using Energy StorageJan 04 2014This paper studies approximate policy iteration (API) methods which use least-squares Bellman error minimization for policy evaluation. We address several of its enhancements, namely, Bellman error minimization using instrumental variables, least-squares ... More

Hypervelocity Stars and the Galactic CenterNov 04 2008A summary of the current knowledge on hypervelocity stars (HVSs). HVSs are fascinating because their properties are linked to Sgr A* and the stellar environment of the Galactic Center. Observing the distribution of HVSs can address: 1) the nature of the ... More

Statistical analysis of the spatial distribution of operons in the transcriptional regulation network of Escherichia coliOct 23 2003We have performed a statistical analysis of the spatial distribution of operons in the transcriptional regulation network of Escherichia coli. The analysis reveals that operons that regulate each other and operons that are coregulated tend to lie next ... More

Some new classes of complex symmetric operatorsJul 22 2009We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), ... More

Metallicities and Radial Velocities of Five Open Clusters Including a New Candidate Member of the Monoceros StreamNov 18 2008Near infrared spectra of 133 red giant stars from ten Galactic open clusters and two Galactic globular clusters spanning 2.2 dex in metallicity and 11 Gyr in age are presented. We combine this sample with ten clusters from Cole and collaborators to investigate ... More

Practicality of Nested Risk Measures for Dynamic Electric Vehicle ChargingMay 10 2016Oct 03 2017We consider the sequential decision problem faced by the manager of an electric vehicle (EV) charging station, who aims to satisfy the charging demand of the customer while minimizing cost. Since the total time needed to charge the EV up to capacity is ... More

An Approximate Dynamic Programming Algorithm for Monotone Value FunctionsJan 08 2014Sep 01 2015Many sequential decision problems can be formulated as Markov Decision Processes (MDPs) where the optimal value function (or cost-to-go function) can be shown to satisfy a monotone structure in some or all of its dimensions. When the state space becomes ... More

Complex symmetric partial isometriesJul 26 2009An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial ... More

Risk-Averse Approximate Dynamic Programming with Quantile-Based Risk MeasuresSep 07 2015May 09 2017In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs; we call the overall objective a dynamic quantile-based ... More

Optimal Hour-Ahead Bidding in the Real-Time Electricity Market with Battery Storage using Approximate Dynamic ProgrammingFeb 14 2014Aug 31 2015There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to exploit variations ... More

A Factor Stochastic Volatility Model with Markov-Switching Panic RegimesMar 05 2019The use of factor stochastic volatility models requires choosing the number of latent factors used to describe the dynamics of the financial returns process; however, empirical evidence suggests that the number and makeup of pertinent factors is time-varying ... More

Pair Correlation for Fractional Parts of $αn^2$Apr 04 2009We construct real numbers $\alpha$ for which the pair correlation function \[N^{-1}#\{m<n\le N:||\alpha m^2-\alpha n^2||\le XN^{-1}\}\] tends to $X$ as $N$ grows. Moreover we show for any "Diophantine" $\alpha$ that the pair correlation function is $X+O(X^{7/8})+O((\log ... More

Schwinger pair production at nonzero temperatures or in compact directionsDec 17 2015Jan 27 2019Electric fields may decay by quantum tunneling: as calculated by Schwinger, an electron-positron pair may be summoned from the vacuum. In this paper I calculate the pair-production rate at nonzero temperatures. I find that at high temperatures the decay ... More

The decay of hot KK spaceAug 25 2014Apr 30 2015The non-perturbative instabilities of hot Kaluza-Klein spacetime are investigated. In addition to the known instability of hot space (the nucleation of 4D black holes) and the known instability of KK space (the nucleation of bubbles of nothing by quantum ... More

Boom and Bust Inflation: a Graceful Exit via Compact Extra DimensionsJul 03 2008A model of inflation is proposed in which compact extra dimensions allow a graceful exit without recourse to flat potentials or super-Planckian field values. Though bubbles of true vacuum are too sparse to uniformly reheat the Universe by colliding with ... More

Zero Zeros After All These (20) YearsSep 27 1999We celebrate two birthdays connected with the radiation zero phenomenon. First, a striking dip in the theoretical angular distributions of radiative weak-boson production was discovered twenty years ago. The key experimental interest is that this will ... More

Bounds for the Cubic Weyl SumMay 12 2009It is shown, subject to the abc-conjecture, that \[\sum_{n\le N}\exp(2\pi i\alpha n^3)\ll_{\epsilon,\alpha}N^{5/7+\epsilon}\] for any $\epsilon>0$ and any quadratic irrational $\alpha$.

Fractional Moments of Dirichlet $L$-FunctionsOct 12 2009Let $k$ be a positive real number, and let $M_k(q)$ be the sum of $|L(\tfrac12,\chi)|^{2k}$ over all non-principal characters to a given modulus $q$. We prove that $M_k(q)\ll_k \phi(q)(\log q)^{k^2}$ whenever $k$ is the reciprocal $n^{-1}$ of a positive ... More

Corrigendum --- Quadratic Class Numbers Divisible by 3Sep 23 2010An error in the author's paper (Functiones et Approximatio, 37 . pp. 203-211) is corrected.

Galois theory and a new homotopy double groupoid of a map of spacesAug 27 2002The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes constructions by ... More

Zeros of Systems of ${\mathfrak p}$-adic Quadratic FormsOct 07 2008Apr 24 2009It is shown that a system of $r$ quadratic forms over a ${\mathfrak p}$-adic field has a non-trivial common zero as soon as the number of variables exceeds $4r$, providing that the residue class field has cardinality at least $(2r)^r$.

Brane tunneling and virtual brane-antibrane pairsSep 24 2007Sep 24 2017We survey barrier penetration by quantum tunneling for four cases: nonrelativistic point particles, scalar fields, relativistic point particles, and DBI branes. We examine two novel features that arise for DBI brane tunneling: the rate can sometimes increase ... More

Tensile Strength and the Mining of Black HolesJul 13 2012There are a number of important thought experiments that involve raising and lowering boxes full of radiation in the vicinity of black hole horizons. This paper looks at the limitations placed on these thought experiments by the null energy condition, ... More

A Note on the Chevalley--Warning TheoremsSep 20 2010Sep 23 2016Let $f_1,\...,f_r$ be polynomials in $n$ variables over a finite field $F$ of cardinality $q$ and characteristic $p$. Let $f_i$ have total degree $d_i$ and define $d=d_1+\...+d_r$. Write $Z$ for the set of common zeros of the $f_i$, over the field $F$. ... More

The quantum potential: the breakdown of classical symplectic symmetry and the energy of localisation and dispersionMar 06 1997Feb 05 2002The composition of the quantum potential and its role in the breakdown of classical symplectic symmetry in quantum mechanics is investigated. General expressions are derived for the quantum potential in both configuration space and momentum space representations. ... More

Zeros of Pairs of Quadratic FormsApr 14 2013We prove the Hasse principle and weak approximation for varieties defined over number fields by the nonsingular intersection of pairs of quadratic forms in 8 variables. The argument develops work of Colliot-Thelene, Sansuc and Swinnerton-Dyer, and centres ... More

The Differences Between Consecutive Smooth NumbersAug 08 2018We show that large gaps between smooth numbers are infrequent. The key new tool is a novel mean value bound for a special type of Dirichlet polynomial.

Leakage mitigation for quantum error correction using a mixed qubit schemeApr 24 2019Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm ... More

Leakage mitigation for quantum error correction using a mixed qubit schemeApr 24 2019May 06 2019Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm ... More

Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: $^{174}$Yb$^{+}$ and $^{171}$Yb$^{+}$Mar 07 2018Apr 16 2018Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman ... More

A Serendipitous Pulsar Discovery in a Search for a Companion to a Low-Mass White DwarfJun 15 2018We report the discovery of a previously unidentified pulsar as part of a radio campaign to identify neutron star companions to low-mass white dwarfs (LMWDs) using the Robert C.\ Byrd Green Bank Telescope (GBT). PSR J0802-0955, which is coincident with ... More

Spatial isomorphisms of algebras of truncated Toeplitz operatorsNov 03 2010Apr 05 2011We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.

Model-based reinforcement learning in differential graphical gamesFeb 28 2017This paper seeks to combine differential game theory with the actor-critic-identifier architecture to determine forward-in-time, approximate optimal controllers for formation tracking in multi-agent systems, where the agents have uncertain heterogeneous ... More

Monte Carlo Tree Search with Sampled Information Relaxation Dual BoundsApr 20 2017Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the use of a heuristic, ... More

The two-loop n-point all-plus helicity amplitudeApr 22 2016Jul 19 2016We propose a compact analytic expression for the polylogarithmic part of the n-point two-loop all-plus helicity amplitude in gauge theory.

Two-Loop Gravity amplitudes from four dimensional UnitarityJan 11 2017Jan 24 2017We compute the polylogarithmic parts of the two-loop four and five-graviton amplitudes where the external helicities are positive and express these in a simple compact analytic form. We use these to extract the $\ln(\mu^2)$ terms from both the four and ... More

Chromospheric Evaporation in an M1.8 Flare Observed by the Extreme-ultraviolet Imaging Spectrometer on HinodeDec 17 2012We discuss observations of chromospheric evaporation for a complex flare that occurred on 9 March 2012 near 03:30 UT obtained from the Extreme-ultraviolet Imaging Spectrometer (EIS) on the Hinode spacecraft. This was a multiple event with a strong energy ... More

The inverse resonance problem for perturbations of algebro-geometric potentialsJun 02 2003We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues and resonances. ... More

Stability and Spectrum of Compactifications on Product ManifoldsOct 23 2013Dec 23 2014We study the spectrum and perturbative stability of Freund-Rubin compactifications on $M_p \times M_{Nq}$, where $M_{Nq}$ is itself a product of $N$ $q$-dimensional Einstein manifolds. The higher-dimensional action has a cosmological term $\Lambda$ and ... More

Populating the Whole LandscapeJul 31 2011Feb 19 2012Every de Sitter vacuum can transition to every other de Sitter vacuum despite any obstacle, despite intervening anti-de Sitter sinks, despite not being connected by an instanton. Eternal inflation populates the whole landscape.

Comment on "Phase-Shift Analysis of NN Scattering Below 160 Mev: Indication of a Strong Tensor Force"Dec 01 1993In his recent publication of a NN phase shift analysis below 160 MeV, Henneck reports relatively large values for the mixing parameter $\epsilon_1$. Based on these results, Henneck suggests that the strength of the $\rho$-meson tensor coupling to the ... More

The Complexity Geometry of a Single QubitMar 29 2019The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we demonstrate many ... More

Bubbles of Nothing and the Fastest Decay in the LandscapeOct 25 2010Sep 23 2011The rate and manner of vacuum decay are calculated in an explicit flux compactification, including all thick-wall and gravitational effects. For landscapes built of many units of a single flux, the fastest decay is usually to discharge just one unit. ... More

On 'Nothing'Nov 01 2011May 16 2012Nothing---the absence of spacetime---can be either an endpoint of tunneling, as in the bubble of nothing, or a starting point for tunneling, as in the quantum creation of a universe. We argue that these two tunnelings can be treated within a unified framework, ... More

Cubical abelian groups with connections are equivalent to chain complexesDec 11 2002The theorem of the title is deduced from the equivalence between crossed complexes and cubical $\omega$-groupoids with connections proved by the authors in 1981. In fact we prove the equivalence of five categories defined internally to an additive category ... More

Development and Evaluation of a Quantum Interactive Learning Tutorial on Larmor Precession Of SpinFeb 16 2016We conducted research on student difficulties and developed and evaluated a quantum interactive learning tutorial (QuILT) on Larmor precession of spin to help students learn about time-dependence of expectation values in quantum mechanics. The QuILT builds ... More

Magnetothermodynamics: measuring the equations of state of a compressible magnetized plasmaNov 16 2018Magnetothermodynamics (MTD) is the study of compression and expansion of magnetized plasma with an eye towards identifying equations of state for magneto-inertial fusion experiments. We present recent results from SSX experiments on the thermodynamics ... More

Study of Oxygen Diffusion and Clustering in Silicon using an Empirical Interatomic PotentialApr 25 1995The diffusion path and diffusivity of oxygen in crystalline silicon are computed using an empirical interatomic potential which was recently developed for modelling the interactions between oxygen and silicon atoms. The diffusion path is determined by ... More

Properties of Dark Matter Revealed by Astrometric Measurements of the Milky Way and Local GalaxiesFeb 17 2009The fact that dark matter (DM), thus far, has revealed itself only on scales of galaxies and larger, again thrusts onto astrophysics the opportunity and the responsibility to confront the age old mystery "What is the nature of matter?" By deriving basic ... More

A Spitzer Search for Substellar Companions to Low Mass White DwarfsNov 04 2009The formation scenarios for single low-mass (M < 0.45 Msol) white dwarfs include enhanced mass loss from a metal-rich progenitor star or a common envelope phase of a solar-like star with a close-in massive planet or a brown dwarf. Both scenarios suggest ... More

SN~2012cg: Evidence for Interaction Between a Normal Type Ia Supernova and a Non-Degenerate Binary CompanionJul 26 2015Mar 01 2016We report evidence for excess blue light from the Type Ia supernova SN 2012cg at fifteen and sixteen days before maximum B-band brightness. The emission is consistent with predictions for the impact of the supernova on a non-degenerate binary companion. ... More

The BHB stars in the Survey Fields of Rodgers et al. (1993): New Observations and Comparisons with other Recent SurveysMar 07 2011We study blue horizontal branch (BHB) and RR Lyrae stars in the Rogers et al. (1993a) fields and compare their velocity and density distributions with other surveys in the same part of the sky. Photometric data are given for 176 early-type stars in the ... More

Low-Amplitude Variables: Distinguishing RR Lyrae stars from Eclipsing BinariesMar 18 2010It is not easy to identify and classify low-amplitude variables, but it is important that the classification is done correctly. We use photometry and spectroscopy to classify low-amplitude variables in a 246 deg^2 part of the Akerlof et al. (2002) field. ... More

Handling Leakage with Subsystem CodesMar 10 2019Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during ... More

The Identification of RR Lyrae and Delta Scuti Stars from Variable GALEX Ultraviolet SourcesAug 04 2014We identify the RR Lyrae and delta Scuti (DSCT) stars in three catalogs of GALEX variable sources. The NUV amplitude of RR Lyrae stars is about twice that in V-band, so we find a larger percentage of low amplitude variables than catalogs such as Abbas ... More

Numerical Conformal Mapping to One-Tooth Gear-Shaped Domains and ApplicationsMar 03 2015We study conformal mappings from the unit disk (or a rectangle) to one-tooth gear-shaped planar domains from the point of view of the Schwarzian derivative, with emphasis on numerical considerations. Applications are given to evaluation of a singular ... More

Gears, Pregears and Related DomainsMar 03 2015We study conformal mappings from the unit disk to one-toothed gear-shaped planar domains from the point of view of the Schwarzian derivative. Gear-shaped (or "gearlike") domains fit into a more general category of domains we call "pregears" (images of ... More

Conformal Mapping of Circular Quadrilaterals and Weierstrass Elliptic FunctionsDec 16 2010Numerical and theoretical aspects of conformal mappings from a disk to a circular-arc quadrilateral, symmetric with respect to the coordinate axes, are developed. The problem of relating the accessory parameters (prevertices together with coefficients ... More

Optimal Packing Behavior of some 2-block PatternsApr 06 2004In this paper, a result of Albert, Atkinson, Handley, Holton, and Stromquist [Electron. J. Combin. 9 (2002), #R5] which characterizes the optimal packing behavior of the pattern 1243 is generalized in two directions. The packing densities of layered patterns ... More

Calibrations associated to Monge-Ampere equationsFeb 10 2007Sep 15 2007We show the volume maximizing property of the special Lagrangian submanifolds of a pseudo-Euclidean space. These special Lagrangian submanifolds arise locally as gradient graphs of solutions to Monge-Ampere Equations.

Sticky Particles and Stochastic FlowsSep 24 2014Gaw\c{e}dzki and Horvai have studied a model for the motion of particles carried in a turbulent fluid and shown that in a limiting regime with low levels of viscosity and molecular diffusivity, pairs of particles exhibit the phenomena of stickiness when ... More

Dynamics and Endogeny for recursive processes on treesJun 02 2005We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some independent innovation. ... More

An improved proof of the Almost Stability TheoremNov 02 2018In 1989, Dicks and Dunwoody proved the Almost Stability Theorem, which has among its corollaries the Stallings-Swan theorem that groups of cohomological dimension one are free. In this article, we use a nestedness result of Bergman, Bowditch, and Dunwoody ... More

On free-group algorithms that sandwich a subgroup between free-product factorsJun 17 2013Let $F$ be a finite-rank free group and $H$ be a finite-rank subgroup of $F$. We discuss proofs of two algorithms that sandwich $H$ between an upper-layer free-product factor of $F$ that contains $H$ and a lower-layer free-product factor of $F$ that is ... More

Direct measurement of Bacon-Shor code stabilizersApr 03 2018A Bacon-Shor code is a subsystem quantum error-correcting code on an $L \times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually inferred from the measurements of $(L-1)^2$ weight-2 gauge operators. Here we show that the stabilizers can ... More

Density of rational points on a quadric bundle in $\mathbb{P}^3\times \mathbb{P}^3$May 27 2018An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface $x_1y_1^2+\dots+x_4y_4^2=0$ in $\mathbb{P}^3\times\mathbb{P}^3$. This confirms ... More

Forms in many variables and differing degreesMar 24 2014Feb 02 2015We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically ... More

Integral points on cubic hypersurfacesNov 03 2006Jun 19 2007Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines ... More

Estimates for the $L^q$-mixed problem in $C^{1,1}$-domainsFeb 23 2019We consider the $L^q$-mixed problem in domains in ${\bf R}^n$ with $C^ {1,1}$-boundary. We assume that the boundary between the sets where we specify Neumann and Dirichlet data is Lipschitz. With these assumptions, we show that we may solve the $L^q$-mixed ... More

Minimal Free Resolutions of $2\times n$ Domino TilingsAug 23 2017We introduce a squarefree monomial ideal associated to the set of domino tilings of a $2\times n$ rectangle and proceed to study the associated minimal free resolution. In this paper, we use results of Dalili and Kummini to show that the Betti numbers ... More

A Bernstein result and counterexample for entire solutions to Donaldson's equationMar 23 2015We show that convex entire solutions to Donaldson's equation are quadratic, using a result of Weiyong He. We also exhibit entire solutions to the Donaldson equation that are not of the form discussed by He. In the process we discover some non-trivial ... More

Regularity for a log-concave to log-concave mass transfer problem with near Euclidean costJul 22 2010If the cost function is not too far from the Euclidean cost, then the optimal map transporting Gaussians restricted to a ball will be regular. \ Similarly, given any cost function which is smooth in a neighborhood of two points on a manifold, there are ... More

A graph-theoretic proof for Whitehead's second free-group algorithmJun 29 2017J.H.C. Whitehead's second free-group algorithm determines whether or not two given elements of a free group lie in the same orbit of the automorphism group of the free group. The algorithm involves certain connected graphs, and Whitehead used three-manifold ... More

Continuum Nash Bargaining SolutionsDec 19 2017Nash`s classical bargaining solution suggests that n players in a non-cooperative bargaining situation should find a solution that maximizes the product of each player's utility functions. We consider a special case: Suppose that the players are chosen ... More

Non-polynomial entire solutions to $σ_{k}$ equationsMar 23 2015Apr 03 2015For $2k \leq n+1$, we exhibit non-polynomial solutions to the Hessian equation \[ \sigma_{k}(D^{2}u)=1 \] on all of $\mathbb{R}^{n}.$

Splitting: Tanaka's SDE revisitedNov 16 1999The weak solution of Tanaka's SDE is not a function of the driving Brownian motion, and therefore it has no Wiener chaos expansion. However in some sense explained here it has a generalised chaos expansion involving infinite products of stochastic differentials ... More

An elliptic pde with convex solutionsJul 15 2014Using a mixture of classical and probabilistic techniques we investigate the convexity of solutions to the elliptic pde associated with a certain generalized Ornstein-Uhlenbeck process.

A McLean Theorem for the moduli space of Lie solutions to mass transport equationsJun 07 2010Aug 24 2010On compact manifolds which are not simply connected, we prove the existence of "fake" solutions to the optimal transportion problem. These maps preserve volume and arise as the exponential of a closed 1 form, hence appear geometrically like optimal transport ... More

On slow escaping and non-escaping points of quasimeromorphic mappingsMar 21 2019We show that for any quasimeromorphic mapping with an essential singularity at infinity, there exist points whose iterates tend to infinity arbitrarily slowly. This extends a result by Nicks for quasiregular mappings, and Rippon and Stallard for transcendental ... More

On Solutions to Cournot-Nash Equilibria Equations on the SphereMar 28 2013We discuss equations associated to Cournot-Nash Equilibria as put forward recently by Blanchet and Carlier. These equations are related to an optimal transport problem in which the source measure is known, but the target measure is part of the problem. ... More

Co-Designing a Scalable Quantum Computer with Trapped Atomic IonsFeb 09 2016The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely ... More

Magic State Distillation and Gate Compilation in Quantum Algorithms for Quantum ChemistryJan 06 2015Jan 29 2015Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which implies the need ... More

Progress in compensating pulse sequences for quantum computationMar 28 2012The control of qubit states is often impeded by systematic control errors. Compensating pulse sequences have emerged as a resource efficient method for quantum error reduction. In this review, we discuss compensating composite pulse methods, and introduce ... More

Counting rational points on quadric surfacesJan 03 2018Sep 07 2018We give an upper bound for the number of rational points of height at most $B$, lying on a surface defined by a quadratic form $Q$. The bound shows an explicit dependence on $Q$. It is optimal with respect to $B$, and is also optimal for typical forms ... More