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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

Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressionsJul 17 2018While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC is considered. Given this background, this study develops a Moran's eigenvector-based ... More

Eigenvector spatial filtering for large data sets: fixed and random effects approachesFeb 21 2017Dec 09 2017Eigenvector spatial filtering (ESF) is a spatial modeling approach, which has been applied in urban and regional studies, ecological studies, and so on. However, it is computationally demanding, and may not be suitable for large data modeling. The objective ... More

Rapid Time Series Prediction with a Hardware-Based Reservoir ComputerJul 19 2018Nov 27 2018Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy and processing ... More

Low rank spatial econometric modelsOct 06 2018This article presents a re-structuring of spatial econometric models in a linear mixed model framework. To that end, it proposes low rank spatial econometric models that are robust to the existence of noise (i.e., measurement error), and can enjoy fast ... 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

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

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

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

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

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

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

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

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

Learning a face space for experiments on human identityMay 19 2018Generative models of human identity and appearance have broad applicability to behavioral science and technology, but the exquisite sensitivity of human face perception means that their utility hinges on the alignment of the model's representation to ... 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 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

Cognitive Model Priors for Predicting Human DecisionsMay 22 2019Human decision-making underlies all economic behavior. For the past four decades, human decision-making under uncertainty has continued to be explained by theoretical models based on prospect theory, a framework that was awarded the Nobel Prize in Economic ... 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

A Characterization of $(4,2)$-Choosable GraphsAug 18 2017Oct 04 2017A graph $G$ is \emph{$(a,b)$-choosable} if given any list assignment $L$ with $|L(v)|=a$ for each $v\in V(G)$ there exists a function $\varphi$ such that $\varphi(v)\in L(v)$ and $|\varphi(v)|=a$ for all $v\in V(G)$, and whenever vertices $x$ and $y$ ... More

A Characterization of $(4,2)$-Choosable GraphsAug 18 2017Apr 09 2019A graph $G$ is \emph{$(a,b)$-choosable} if given any list assignment $L$ with $|L(v)|=a$ for each $v\in V(G)$ there exists a function $\varphi$ such that $\varphi(v)\in L(v)$ and $|\varphi(v)|=b$ for all $v\in V(G)$, and whenever vertices $x$ and $y$ ... 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

(Un)Conditional Sample Generation Based on Distribution Element TreesNov 13 2017Jun 14 2018Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate random samples ... More

Density Estimation with Distribution Element TreesOct 02 2016May 03 2017The 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

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

Proper Distinguishing Colorings with Few Colors for Graphs with Girth at Least 5Jul 18 2017Oct 17 2018The distinguishing chromatic number, $\chi_D(G)$, of a graph $G$ is the smallest number of colors in a proper coloring, $\varphi$, of $G$, such that the only automorphism of $G$ that preserves all colors of $\varphi$ is the identity map. Collins and Trenk ... 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

The orbit space of groupoids whose $C^*$-algebras are GCRSep 08 2017Let $G$ be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem by Clark about GCR groupoid $C^*$-algebras. We show that if the groupoid $C^*$-algebra of $G$ is GCR then ... 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

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

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

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

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

"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

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

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

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

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

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

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

Spectroscopic Evidence of Low Energy Gaps Persisting Towards 120 Kelvin in Surface-Doped p-Terphenyl CrystalsApr 13 2017Mar 29 2018The possibility of high temperature superconductivity in organic compounds has been discussed since the pioneering work of Little in 1964, with unsatisfactory progress until the recent report of a weak Meissner shielding effect at 120 Kelvin in potassium-doped ... 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.

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

Capturing human category representations by sampling in deep feature spacesMay 19 2018Understanding how people represent categories is a core problem in cognitive science. Decades of research have yielded a variety of formal theories of categories, but validating them with naturalistic stimuli is difficult. The challenge is that human ... 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

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

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

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 2016Jun 09 2017A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off against the ... 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

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

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

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

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

The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4Mar 02 2017A simple graph $G$ is \emph{overfull} if $|E(G)|>\Delta\lfloor|V(G)|/2\rfloor$. By the pigeonhole principle, every overfull graph $G$ has $\chi'(G)>\Delta$. The \emph{core} of a graph, denoted $G_\Delta$, is the subgraph induced by its vertices of degree ... 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

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

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

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

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

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

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.

Clarifying the relationship between efficiency and resonance for flexible inertial swimmersJul 19 2018We study a linear inviscid model of a passively flexible swimmer, calculating its propulsive performance, eigenvalues, and eigenfunctions with an eye towards clarifying the relationship between efficiency and resonance. The frequencies of actuation and ... 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

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

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

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

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

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

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

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

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