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Massive, wide binaries as tracers of massive star formationFeb 13 2018Massive stars can be found in wide (hundreds to thousands AU) binaries with other massive stars. We use $N$-body simulations to show that any bound cluster should always have approximately one massive wide binary: one will probably form if none are present ... More

How do binary clusters form?Jul 10 2017Approximately 10 per cent of star clusters are found in pairs, known as binary clusters. We propose a mechanism for binary cluster formation; we use N-body simulations to show that velocity substructure in a single (even fairly smooth) region can cause ... More

Morphologies of Radio, X-Ray, and Mid-Infrared Selected AGNJun 05 2010We investigate the optical morphologies of candidate active galaxies identified at radio, X-ray, and mid-infrared wavelengths. We use the Advanced Camera for Surveys General Catalog (ACS-GC) to identify 372, 1360, and 1238 AGN host galaxies from the VLA, ... More

Finite depth gravity water waves in holomorphic coordinatesJul 08 2016Jul 11 2016In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second, we consider ... More

Microscopic Observation of the Light-Cone-Like Thermal Correlations in Cracking ExcitationsOct 01 2016Many seemingly intractable systems can be reduced to a system of interacting spins. Here, we introduce a system of artificial acoustic spins which are manipulated with ultrasound excitations associated with micro-cracking sources in thin sheets of crystals. ... More

Competition in growth and urnsOct 20 2016We study survival among two competing types in two settings: a planar growth model related to two-neighbour bootstrap percolation, and a system of urns with graph-based interactions. In the urn scheme, each vertex of a graph $G$ has an associated urn ... More

Noise Sensitivity in Continuum PercolationAug 01 2011May 23 2013We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \ne 1/2. Our proof ... More

Exterior Differential Systems and Euler-Lagrange Partial Differential EquationsJul 03 2002We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an introduction ... More

Quenched Voronoi percolationJan 16 2015We prove that the probability of crossing a large square in quenched Voronoi percolation converges to 1/2 at criticality, confirming a conjecture of Benjamini, Kalai and Schramm from 1999. The main new tools are a quenched version of the box-crossing ... More

Truth and memory: Linking instantaneous and retrospective self-reported cigarette consumptionJan 11 2013Studies of smoking behavior commonly use the time-line follow-back (TLFB) method, or periodic retrospective recall, to gather data on daily cigarette consumption. TLFB is considered adequate for identifying periods of abstinence and lapse but not for ... More

Dynamic Evolution of Microscopic Wet Cracking NoisesNov 14 2015Sep 06 2016Characterizing the interaction between water and microscopic defects is one of the long-standing challenges in understanding a broad range of cracking processes. Different physical aspects of microscopic events, driven or influenced by water, have been ... More

Vortex disruption by magnetohydrodynamic feedbackSep 10 2016In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to form strong current sheets on their edges. Associated with these current sheets are magnetic stresses, which are subsequently released through reconnection, ... More

Adaptive Sampling for Convex RegressionAug 14 2018Aug 26 2018In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of complexity ... More

Silicon-Chip Mid-Infrared Frequency Comb GenerationAug 05 2014Optical frequency combs represent a revolutionary technology for high precision spectroscopy due to their narrow linewidths and precise frequency spacing. Generation of such combs in the mid-infrared (IR) spectral region (2-20 um) is of great interest ... More

Half of the Most Luminous Quasars May Be Obscured: Investigating the Nature of WISE-Selected Hot, Dust-Obscured GalaxiesAug 05 2014Feb 19 2015The WISE mission has unveiled a rare population of high-redshift ($z=1-4.6$), dusty, hyper-luminous galaxies, with infrared luminosities $L_{\rm IR} > 10^{13}~L_{\odot}$, and sometimes exceeding $10^{14}~L_{\odot}$. Previous work has shown that their ... More

A panoramic view of the Milky Way HI gasOct 30 2009Imaging of galaxies to study the interstellar medium on scales of a few pc is difficult. However, for the Milky Way galaxy two major Galactic all sky HI 21-cm line surveys will become available soon with unprecedented quality. We present the Galactic ... More

Observed Asymptotic Differences in Energies of Stable and Minimal Point Configurations on $\mathbb{S}^2$ and the Role of DefectsJul 01 2013Oct 02 2013Observations suggest that configurations of points on a sphere that are stable with respect to a Riesz potential distribute points uniformly over the sphere. Further, these stable configurations have a local structure that is largely hexagonal. Minimal ... More

A new limit on the permanent electric dipole moment of ^{199}HgDec 01 2000We present the first results of a new search for a permanent electric dipole moment of the ^{199}Hg atom using a UV laser. Our measurements give d(Hg)= - (1.06 +/- 0.49 +/- 0.40) 10^{-28} e cm. We interpret the result as an upper limit |d(Hg)| < 2.1 10^{-28} ... More

Shear instabilities in shallow-water magnetohydrodynamicsJan 31 2015Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as H{\o}iland's growth ... More

A Moran coefficient-based mixed effects approach to investigate spatially varying relationshipsJun 22 2016Aug 10 2016This study develops a spatially varying coefficient model by extending the random effects eigenvector spatial filtering model. The developed model has the following properties: its coefficients are interpretable in terms of the Moran coefficient; each ... More

A Comparison of Monte Carlo Tree Search and Mathematical Optimization for Large Scale Dynamic Resource AllocationMay 21 2014Dynamic resource allocation (DRA) problems are an important class of dynamic stochastic optimization problems that arise in a variety of important real-world applications. DRA problems are notoriously difficult to solve to optimality since they frequently ... More

Diffractive Scintillation of the Pulsar PSR B1259-63Nov 03 1997PSR B1259-63 is in a highly eccentric 3.4 yr orbit around the Be-star SS2883. The system is located in the direction of the Sagittarius-Carina spiral arm at a distance of $\sim$1.5 kpc. We have made scintillation observations of the pulsar far from periastron ... More

The importance of scale in spatially varying coefficient modelingSep 26 2017While spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the "spatial scale" of each data relationship ... More

Accuracy and Precision in Collider Event ShapesMay 20 2016In this thesis, we discuss and investigate the use of Soft-Collinear Effective Theory (SCET) for high precision calculations. In the first part of the work, we present an extraction of the strong coupling, $\alpha_s(m_Z)$ and the leading nonperturbative ... More

Multigraphs with $Δ\ge 3$ are Totally-$(2Δ-1)$-choosableAug 14 2013The \emph{total graph} $T(G)$ of a multigraph $G$ has as its vertices the set of edges and vertices of $G$ and has an edge between two vertices if their corresponding elements are either adjacent or incident in $G$. We show that if $G$ has maximum degree ... More

Acyclic edge-coloring of planar graphs: $Δ$ colors suffice when $Δ$ is largeMay 14 2017Jan 29 2019An \emph{acyclic edge-coloring} of a graph $G$ is a proper edge-coloring of $G$ such that the subgraph induced by any two color classes is acyclic. The \emph{acyclic chromatic index}, $\chi'_a(G)$, is the smallest number of colors allowing an acyclic ... More

Regular graphs of odd degree are antimagicMar 20 2013An antimagic labeling of a graph $G$ with $m$ edges is a bijection from $E(G)$ to $\{1,2,\ldots,m\}$ such that for all vertices $u$ and $v$, the sum of labels on edges incident to $u$ differs from that for edges incident to $v$. Hartsfield and Ringel ... More

Nomadic Decompositions of Bidirected Complete GraphsSep 05 2006We use $K^*_n$ to denote the bidirected complete graph on $n$ vertices. A nomadic Hamiltonian decomposition of $K^*_n$ is a Hamiltonian decomposition, with the additional property that ``nomads'' walk along the Hamiltonian cycles (moving one vertex per ... More

Reduction to first order of the Hamiltonian Constraint of General RelativityMar 28 2016Sep 19 2016In this work, a method for solving the constraints of general relativity is presented, where first all geometrical objects are written in terms of a set of orthonormal triads and a flat Weitzenbock connection, which depends on the triads and on a flat ... More

Density Estimation with Distribution Element TreesOct 02 2016The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. ... More

Antimagic labelings of regular bipartite graphs: An application of the Marriage TheoremAug 21 2007A labeling of a graph is a bijection from $E(G)$ to the set $\{1, 2,..., |E(G)|\}$. A labeling is \textit{antimagic} if for any distinct vertices $u$ and $v$, the sum of the labels on edges incident to $u$ is different from the sum of the labels on edges ... More

Edge-choosability and total-choosability of planar graphs with no adjacent 3-cyclesDec 22 2005Jun 21 2008Let $G$ be a planar graph with no two 3-cycles sharing an edge. We show that if $\Delta(G)\geq 9$, then $\chi'_l(G) = \Delta(G)$ and $\chi''_l(G)=\Delta(G)+1.$ We also show that if $\Delta(G)\geq 6$, then $\chi'_l(G)\leq\Delta(G)+1$ and if $\Delta(G)\geq ... More

At most 27 length inequalities define Maskit's fundamental domain for the modular group in genus 2Nov 09 1998In recently published work Maskit constructs a fundamental domain D_g for the Teichmueller modular group of a closed surface S of genus g>1. Maskit's technique is to demand that a certain set of 2g non-dividing geodesics C_{2g} on S satisfies certain ... More

A Neutral Hydrogen Self-Absorption Cloud in the SGPSAug 26 2003Using data from the Southern Galactic Plane Survey (SGPS) we analyze an HI self-absorption cloud centered on l = 318.0 deg, b = -0.5 deg, and velocity, v = -1.1 km/s. The cloud was observed with the Australia Telescope Compact Array (ATCA) and the Parkes ... More

Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model resultsOct 15 2005Jan 30 2006We consider systems confined to a $d$-dimensional slab of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$ and are describable by an O(n) symmetrical Hamiltonian. Periodic ... More

Modularizing Contexted ConstraintsJun 08 1996This paper describes a method for compiling a constraint-based grammar into a potentially more efficient form for processing. This method takes dependent disjunctions within a constraint formula and factors them into non-interacting groups whenever possible ... More

Quasi-random oriented graphsJan 28 2011Aug 10 2011We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham and Wilson in the case of unoriented graphs, ... More

(k+1)-sums versus k-sumsNov 19 2010Jun 08 2012A $k$-sum of a set $A\subseteq \mathbb{Z}$ is an integer that may be expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of the number of $(k+1)$-sums to the number of $k$-sums be? Writing $k\wedge A$ for the set of $k$-sums of ... More

Quantifying synergistic information remains an unsolved problemDec 07 2011May 22 2012This paper has been withdrawn by the author. This paper is now obsolete. For a solution please see: arXiv:/1205.4265.

Characterization of protonated and deuterated Tetra-Phenyl Butadiene Film in a Polystyrene MatrixFeb 13 2013We study the effect of deuteration and annealing on the fluorescence spectrum shape and VUV to visible conversion efficiency of TPB films in a polystyrene matrix with input light from 120 to 220 nm. We observed no discernible difference in the fluorescence ... More

A 1.75 kpc/h Separation Dual AGN at z=0.36 in the COSMOS FieldJun 19 2009We present strong evidence for dual active galactic nuclei (AGN) in the z=0.36 galaxy COSMOS J100043.15+020637.2. COSMOS Hubble Space Telescope (HST) imaging of the galaxy shows a tidal tail, indicating that the galaxy recently underwent a merger, as ... More

XMM-Newton observations of the BL Lac MS 0737+7441Oct 31 2000We report on the XMM-Newton observations of the BL Lac object MS 0737.9+7441 during the performance verification phase. A simple power-law fit provides an adequate description of the integrated spectrum in the 0.2-10 keV energy band. The photon index ... More

Multitasking Capacity: Hardness Results and Improved ConstructionsSep 08 2018We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently introduced in ... More

Spectroscopic confirmation of a galaxy cluster associated with 7C1756+6520 at z=1.416Apr 18 2010We present spectroscopic follow-up of an overdensity of galaxies photometrically selected to be at 1.4<z<2.5 found in the vicinity of the radio galaxy 7C1756+6520 at z=1.4156. Using the DEIMOS optical multi-object spectrograph on the Keck 2 telescope, ... More

A Graph-Theoretic Approach to MultitaskingNov 08 2016Cognitive control -- the capacity to carry out goal-directed behavior in the face of compelling or distracting alternatives -- is a hallmark of human cognitive function. One of the defining, and best documented findings concerning cognitive control is ... More

A Principled Infotheoretic φ-like MeasureJan 06 2014Oct 09 2014Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $\phi$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we pinpoint three ... More

Lancaster distributions and Markov chains with Multivariate Poisson-Charlier, Meixner and Hermite-Chebycheff polynomial eigenfunctionsDec 12 2014Dec 18 2015This paper studies new Lancaster characterizations of bivariate multivariate Poisson, negative binomial and normal distributions which have diagonal expansions in multivariate orthogonal polynomials. The characterizations extend classical Lancaster characterizations ... More

Evidence for Galaxy Interactions/Mergers from Meduim-Deep Survey WFPC2 DataSep 12 1996We examine the morphological and statistical properties of close galaxy pairs from two sets of 28 WFPC2 fields, acquired for the Medium Deep Survey (MDS) and the Groth/Westphal Survey (GWS) in F606W (V) and F814W (I) passbands. In the GWS sample all fields ... More

"Missing Link" Clouds in the Southern Galactic Plane SurveyMar 24 2005We present an automated routine to search for HI self-absorption features within the Southern Galactic Plane Survey (SGPS). The data were taken with the Australia Telescope Compact Array (ATCA) and the Parkes Radio Telescope and encompass 3 deg by 105 ... More

Multivariate Krawtchouk polynomials and composition birth and death processesMar 01 2016May 03 2016This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined ... More

Asymptotically tight bounds on subset sumsMay 31 2008For a subset A of a finite abelian group G we define Sigma(A)={sum_{a\in B}a:B\subset A}. In the case that Sigma(A) has trivial stabiliser, one may deduce that the size of Sigma(A) is at least quadratic in |A|; the bound |Sigma(A)|>= |A|^{2}/64 has recently ... More

List-coloring claw-free graphs with $Δ$-1 colorsAug 14 2015We prove that if $G$ is a quasi-line graph with $\Delta(G)>\omega(G)$ and $\Delta(G)\ge 69$, then $\chi_{OL}(G)\le \Delta(G)-1$. Together with our previous work, this implies that if $G$ is a claw-free graph with $\Delta(G)>\omega(G)$ and $\Delta(G)\ge ... More

A note on coloring vertex-transitive graphsApr 25 2014We prove bounds on the chromatic number $\chi$ of a vertex-transitive graph in terms of its clique number $\omega$ and maximum degree $\Delta$. We conjecture that every vertex-transitive graph satisfies $\chi \le \max \left\{\omega, \left\lceil\frac{5\Delta ... More

Singlet-triplet decoherence due to nuclear spins in a double quantum dotJun 03 2005We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ... More

Quantum computing with spins in solidsJun 21 2006The ability to perform high-precision one- and two-qubit operations is sufficient for universal quantum computation. For the Loss-DiVincenzo proposal to use single electron spins confned to quantum dots as qubits, it is therefore sufficient to analyze ... More

Non-Markovian dynamics of a localized electron spin due to the hyperfine interactionNov 28 2004We review our theoretical work on the dynamics of a localized electron spin interacting with an environment of nuclear spins. Our perturbative calculation is valid for arbitrary polarization p of the nuclear spin system and arbitrary nuclear spin I in ... More

Kinematics of Protostellar Objects in the $ρ$ Ophiuchus A RegionMay 05 2006We present the detection of infall, rotation and outflow kinematic signatures towards both a protostellar source, VLA 1623 and what was initially thought to be a pre-protostellar core, SM1N, in the rho-Ophiuchus A region. The kinematic signatures of early ... More

Brooks' Theorem and BeyondMar 03 2014We collect some of our favorite proofs of Brooks' Theorem, highlighting advantages and extensions of each. The proofs illustrate some of the major techniques in graph coloring, such as greedy coloring, Kempe chains, hitting sets, and the Kernel Lemma. ... More

A peculiar two point boundary value problemOct 12 2007In this paper we consider a one-dimensional diffusion equation on the interval $[0,1]$ satisfying non-Feller boundary conditions. As a consequence, the initial value Cauchy problem fails to preserve nonnegativity or boundedness. Nonetheless, probability ... More

The Fractional Chromatic Number of the PlaneJan 07 2015The chromatic number of the plane is the chromatic number of the uncountably infinite graph that has as its vertices the points of the plane and has an edge between two points if their distance is 1. This chromatic number is denoted $\chi(\mathcal{R}^2)$. ... More

Painting Squares in $Δ^2-1$ ShadesNov 05 2013Jan 30 2014Cranston and Kim conjecture that if $G$ is a connected graph with maximum degree $\Delta$ and $G$ is not a Moore Graph, then $\chi_l(G^2) \le \Delta^2-1$; here $\chi_l$ is the list chromatic number. We prove their conjecture; in fact, this upper bound ... More

Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamicsMay 28 2004May 29 2004We have performed a systematic calculation for the non-Markovian dynamics of a localized electron spin interacting with an environment of nuclear spins via the Fermi contact hyperfine interaction. This work applies to an electron in the s -type orbital ... More

Bridge Hopping on Conducting Polymers in SolutionOct 06 2000Configurational fluctuations of conducting polymers in solution can bring into proximity monomers which are distant from each other along the backbone. Electrons can hop between these monomers across the "bridges" so formed. We show how this can lead ... More

Localization Effects in ac-driven Tight-Binding LatticesMar 02 1996We study coherent dynamics of tight-binding systems interacting with static and oscillating external fields. We consider Bloch oscillations and Wannier-Stark localization caused by dc fields, and compare these effects to dynamic localization that occurs ... More

Ac Stark Effects and Harmonic Generation in Periodic PotentialsSep 28 1993Sep 29 1993The ac Stark effect can shift initially nonresonant minibands in semiconductor superlattices into multiphoton resonances. This effect can result in strongly enhanced generation of a particular desired harmonic of the driving laser frequency, at isolated ... More

Critical Casimir amplitudes for $n$-component $φ^4$ models with O(n)-symmetry breaking quadratic boundary termsMay 19 2009Aug 05 2009Euclidean $n$-component $\phi^4$ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in films of thickness $L$. The boundary terms imply the Robin boundary conditions $\partial_n\phi_\alpha ... More

Markov counting models for correlated binary responsesMay 07 2013Aug 27 2014We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many previous models ... More

Coloring claw-free graphs with Δ-1 colorsJun 06 2012Dec 19 2012We prove that every claw-free graph $G$ that doesn't contain a clique on $\Delta(G) \geq 9$ vertices can be $\Delta(G) - 1$ colored.

Beyond Degree ChoosabilityNov 02 2015Let $G$ be a connected graph with maximum degree $\Delta$. Brooks' theorem states that $G$ has a $\Delta$-coloring unless $G$ is a complete graph or an odd cycle. A graph $G$ is \emph{degree-choosable} if $G$ can be properly colored from its lists whenever ... More

Short fans and the 5/6 bound for line graphsOct 13 2016In 2011, the second author conjectured that every line graph $G$ satisfies $\chi(G)\le \max\{\omega(G),\frac{5\Delta(G)+8}{6}\}$. This conjecture is best possible, as shown by replacing each edge in a 5-cycle by $k$ parallel edges, and taking the line ... More

A Constructive Approach for One-Shot Training of Neural Networks Using Hypercube-Based Topological CoveringsJan 09 2019In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in turn directly ... More

Planar Graphs have Independence Ratio at least 3/13Sep 20 2016The 4 Color Theorem (4CT) implies that every $n$-vertex planar graph has an independent set of size at least $\frac{n}4$; this is best possible, as shown by the disjoint union of many copies of $K_4$. In 1968, Erd\H{o}s asked whether this bound on independence ... More

Subcubic edge chromatic critical graphs have many edgesJun 13 2015Jun 16 2018We consider graphs $G$ with $\Delta=3$ such that $\chi'(G)=4$ and $\chi'(G-e)=3$ for every edge $e$, so-called \emph{critical} graphs. Jakobsen noted that the Petersen graph with a vertex deleted, $P^*$, is such a graph and has average degree only $\frac83$. ... More

Graphs with $χ=Δ$ have big cliquesMay 15 2013Aug 05 2015Brooks' Theorem states that if a graph has $\Delta\ge 3$ and $\omega \le \Delta$, then $\chi \le \Delta$. Borodin and Kostochka conjectured that if $\Delta\ge 9$ and $\omega\le \Delta-1$, then $\chi\le \Delta-1$. We show that if $\Delta\ge 13$ and $\omega ... More

Sufficient sparseness conditions for G^2 to be (Δ+1)-choosable, when Δ\ge5Mar 21 2013Aug 17 2013We determine the list chromatic number of the square of a graph $\chil(G^2)$ in terms of its maximum degree $\Delta$ when its maximum average degree, denoted $\mad(G)$, is sufficiently small. For $\Delta\ge 6$, if $\mad(G)<2+\frac{4\Delta-8}{5\Delta+2}$, ... More

Hamiltonicity in connected regular graphsApr 29 2012In 1980, Jackson proved that every 2-connected $k$-regular graph with at most $3k$ vertices is Hamiltonian. This result has been extended in several papers. In this note, we determine the minimum number of vertices in a connected $k$-regular graph that ... More

Coloring a graph with $Δ-1$ colors: Conjectures equivalent to the Borodin-Kostochka conjecture that appear weakerMar 24 2012Aug 01 2013Borodin and Kostochka conjectured that every graph $G$ with maximum degree $\Delta \ge 9$ satisfies $\chi \le \max\{\omega, \Delta-1\}$. We carry out an in-depth study of minimum counterexamples to the Borodin-Kostochka conjecture. Our main tool is the ... More

Thermodynamic Casimir effects involving interacting field theories with zero modesOct 24 2007Mar 14 2008Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$. The effective forces induced ... More

Exchange-controlled single-electron-spin rotations in quantum dotsOct 16 2006Apr 23 2007We show theoretically that arbitrary coherent rotations can be performed quickly (with a gating time ~1 ns) and with high fidelity on the spin of a single confined electron using control of exchange only, without the need for spin-orbit coupling or ac ... More

Edge Lower Bounds for List Critical Graphs, via DischargingFeb 08 2016A graph $G$ is $k$-critical if $G$ is not $(k-1)$-colorable, but every proper subgraph of $G$ is $(k-1)$-colorable. A graph $G$ is $k$-choosable if $G$ has an $L$-coloring from every list assignment $L$ with $|L(v)|=k$ for all $v$, and a graph $G$ is ... More

Subcubic edge chromatic critical graphs have many edgesJun 13 2015We consider graphs $G$ with $\Delta=3$ such that $\chi'(G)=4$ and $\chi'(G-e)=3$ for every edge $e$, so-called \emph{critical} graphs. Jakobsen noted that the Petersen graph with a vertex deleted, $P^*$, is such a graph and has average degree only $2+\frac23$. ... More

List-coloring the Squares of Planar Graphs without 4-Cycles and 5-CyclesMay 13 2015Let $G$ be a planar graph without 4-cycles and 5-cycles and with maximum degree $\Delta\ge 32$. We prove that $\chi_{\ell}(G^2)\le \Delta+3$. For arbitrarily large maximum degree $\Delta$, there exist planar graphs $G_{\Delta}$ of girth 6 with $\chi(G_{\Delta}^2)=\Delta+2$. ... More

Observational Quantification of the Energy Dissipated by Alfvén Waves in a Polar Coronal Hole: Evidence that Waves Drive the Fast Solar WindFeb 21 2013Aug 29 2013We present a measurement of the energy carried and dissipated by Alfv\'en waves in a polar coronal hole. Alfv\'en waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease ... More

Identifying A-stars in the CoRoT-fields IRa01, LRa01 and LRa02Oct 13 2010Up to now, planet search programs have concentrated on main sequence stars later than spectral type F5. However, identifying planets of early type stars would be interesting. For example, the mass loss of planets orbiting early and late type stars is ... More

Edge-coloring via fixable subgraphsJul 20 2015Many graph coloring proofs proceed by showing that a minimal counterexample to the theorem being proved cannot contain certain configurations, and then showing that each graph under consideration contains at least one such configuration; these configurations ... More

Large Universe as the initial condition for a Collapsing UniverseJun 22 2002Using the extension of the standard Hawking-Hartle prescription for defining a wave function for the universe, we show that it is possible, given a suitable form for the scalar field potential, to have the universe begin at its largest size and thereafter ... More

Linear Choosability of Sparse GraphsJul 09 2010We study the linear list chromatic number, denoted $\lcl(G)$, of sparse graphs. The maximum average degree of a graph $G$, denoted $\mad(G)$, is the maximum of the average degrees of all subgraphs of $G$. It is clear that any graph $G$ with maximum degree ... More

Circular Flows in Planar GraphsDec 24 2018For integers $a\ge 2b>0$, a \emph{circular $a/b$-flow} is a flow that takes values from $\{\pm b, \pm(b+1), \dots, \pm(a-b)\}$. The Planar Circular Flow Conjecture states that every $2k$-edge-connected planar graph admits a circular $(2+\frac{2}{k})$-flow. ... More

A Note on Bootstrap Percolation Thresholds in Plane Tilings using Regular PolygonsMar 24 2018In \emph{$k$-bootstrap percolation}, we fix $p\in (0,1)$, an integer $k$, and a plane graph $G$. Initially, we infect each face of $G$ independently with probability $p$. Infected faces remain infected forever, and if a healthy (uninfected) face has at ... More

Planar graphs are 9/2-colorableOct 27 2014Sep 20 2016We show that every planar graph $G$ has a 2-fold 9-coloring. In particular, this implies that $G$ has fractional chromatic number at most $\frac92$. This is the first proof (independent of the 4 Color Theorem) that there exists a constant $k<5$ such that ... More

A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal GridJun 18 2010Given a graph $G$, an identifying code $C \subseteq V(G)$ is a vertex set such that for any two distinct vertices $v_1,v_2\in V(G)$, the sets $N[v_1]\cap C$ and $N[v_2]\cap C$ are distinct and nonempty (here $N[v]$ denotes a vertex $v$ and its neighbors). ... More

Mid-Infrared Variability from the Spitzer Deep, Wide-Field SurveyFeb 18 2010May 28 2010We use the multi-epoch, mid-infrared Spitzer Deep, Wide-Field Survey to investigate the variability of 474,179 objects in 8.1 deg^2 of the NDWFS Bootes field. We perform a Difference Image Analysis of the four available epochs between 2004 and 2008, focusing ... More

Improved limit on the permanent electric dipole moment of 199HgJan 15 2009Mar 10 2009We report the results of a new experimental search for a permanent electric dipole moment of 199Hg utilizing a stack of four vapor cells. We find d(199Hg) = (0.49 \pm 1.29_stat \pm 0.76_syst) x 10^{-29} e cm, and interpret this as a new upper bound, |d(199Hg)| ... More

Glyph Sorting: Interactive Visualization for Multi-dimensional DataApr 10 2013Glyph-based visualization is an effective tool for depicting multivariate information. Since sorting is one of the most common analytical tasks performed on individual attributes of a multi-dimensional data set, this motivates the hypothesis that introducing ... More

XMM - Newton observations of Markarian 421Nov 09 2000The BL Lac object Mrk 421 was observed on May 25, 2000 during the XMM - Newton CAL/PV phase. The high throughput of the X-ray telescopes and the spectral capabilities of the instruments allow an uninterrupted temporal and spectral study of the source ... More

Measurement of Linear Stark Interference in 199HgNov 24 2010Jun 24 2011We present measurements of Stark interference in the 6$^1S_0$ $\rightarrow$ 6$^3P_1$ transition in $^{199}$Hg, a process whereby a static electric field $E$ mixes magnetic dipole and electric quadrupole couplings into an electric dipole transition, leading ... More

Dispersion in magnetostatic CoTaZr spin wave-guidesNov 03 2008Dec 29 2008Magnetostatic spin wave dispersion and loss are measured in micron scale spin wave-guides in ferromagnetic, metallic CoTaZr. Results are in good agreement with model calculations of spin wave dispersion and up to three different modes are identified. ... More

A ground-based near-infrared emission spectrum of the exoplanet HD 189733bFeb 12 2010Detection of molecules using infrared spectroscopy probes the conditions and compositions of exoplanet atmospheres. Water (H2O), methane (CH4), carbon dioxide (CO2), and carbon monoxide (CO) have been detected in two hot Jupiters. These previous results ... More

Proposal for a GHz count rate near-IR single-photon detector based on a nanoscale superconducting transition edge sensorFeb 21 2012We describe a superconducting transition edge sensor based on a nanoscale niobium detector element. This device is predicted to be capable of energy-resolved near-IR single-photon detection with a GHz count rate. The increased speed and sensitivity of ... More