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Pushing Automated Abundance Derivations Into the Cool Star Regime: A Test Using Three G and Two K Stars in PraesepeDec 07 2018We present the results of an abundance analysis of three G and two K dwarfs in the Praesepe open cluster based on high-resolution, moderate signal-to-noise-ratio spectra obtained with the ARC 3.5-m Telescope at Apache Point Observatory. Using a Principle ... More

The Solar Benchmark: Rotational Modulation of the Sun Reconstructed from Archival Sunspot RecordsJan 14 2019We use archival daily spot coverage measurements from Howard et al. (1984) to study the rotational modulation of the Sun as though it were a distant star. A quasi-periodic Gaussian process measures the solar rotation period $P_\mathrm{rot} = 26.3 \pm ... More

astroquery: An Astronomical Web-Querying Package in PythonJan 14 2019astroquery is a collection of tools for requesting data from databases hosted on remote servers with interfaces exposed on the internet, including those with web pages but without formal application program interfaces (APIs). These tools are built on ... More

Optimal Actuator Design for Semi-linear SystemsFeb 16 2018Oct 22 2018Actuator location and design are important choices in controller design for distributed parameter systems. Semi-linear partial differential equations model a wide spectrum of physical systems with distributed parameters. It is shown that under certain ... More

Cosmic microwave background constraints on coupled dark matterJun 16 2014Dec 16 2014We study CMB constraints on a model with a cosmological constant and a fraction of dark matter non-minimally coupled to a massless scalar field. In this scenario, there is an extra gravity-like fifth force which can affect the evolution of the Universe ... More

Phase field methods for binary recoveryOct 17 2013We consider the inverse problem of recovering a binary function from blurred and noisy data. Such problems arise in many applications, for example image processing and optimal control of PDEs. Our formulation is based on the Mumford-Shah model, but with ... More

Stability and Well-posedness of a Nonlinear Railway Track ModelMar 08 2018Jul 03 2018Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in presence of ... More

Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithmMar 30 2016The Douglas-Rachford splitting algorithm was originally proposed in 1956 to solve a system of linear equations arising from the discretization of a partial differential equation. In 1979, Lions and Mercier brought forward a very powerful extension of ... More

Constraining Stellar Photospheres as an Essential Step for Transmission Spectroscopy of Small ExoplanetsMar 14 2019Transmission spectra probe the atmospheres of transiting exoplanets, but these observations are also subject to signals introduced by magnetic active regions on host stars. Here we outline scientific opportunities in the next decade for providing useful ... More

Tropical gluing formulae for Gromov-Witten invariantsMar 16 2017We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula ... More

On rotationally invariant shrinking gradient Ricci solitonsFeb 20 2007In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$, $\R{n}$ and $\R{}\times S^{n-1}$ are, respectively, ... More

Time-analyticity of solutions to the Ricci flowOct 10 2012Oct 15 2012In this paper, we prove that if $g(t)$ is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on $M\times[0, \Omega]$, then the correspondence $t\mapsto g(t)$ is real-analytic at each $t_0\in (0, \Omega)$. The analyticity is a ... More

Holomorphic curves in exploded manifolds: virtual fundamental classDec 17 2015This paper defines Gromov-Witten invariants of exploded manifolds using embedded Kuranishi structures, constructed in arXiv:1301.4748. The technical heart of this paper is a construction of a virtual fundamental class $[\mathcal K]$ of any Kuranishi category ... More

Gluing formula for Gromov-Witten invariants in a triple productNov 03 2015We present a gluing formula for Gromov-Witten invariants in the case of a triple product. This gluing formula is a simple case of a much more general gluing formula proved and stated using exploded manifolds. We present this simple case because it is ... More

Backwards uniqueness of the Ricci flowJun 26 2009In this paper, we prove a unique continuation or ``backwards-uniqueness'' theorem for solutions to the Ricci flow. A particular consequence is that the isometry group of a solution cannot expand within the lifetime of the solution.

Hamilton's gradient estimate for the heat kernel on complete manifoldsJan 12 2007In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \geq -Kg$. We accomplish this extension via a maximum ... More

Kepler's Optical Secondary Eclipse of HAT-P-7b and Probable Detection of Planet-Induced Stellar Gravity DarkeningJan 18 2013We present observations spanning 355 orbital phases of HAT-P-7 observed by Kepler from May 2009 to March 2011 (Q1-9). We find a shallower secondary eclipse depth than initially announced, consistent with a low optical albedo and detection of nearly exclusively ... More

Kählerity of shrinking gradient Ricci solitons asymptotic to Kähler conesJan 30 2017Dec 07 2017We prove that a shrinking gradient Ricci soliton which is asymptotic to a K\"ahler cone along some end is itself K\"ahler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally K\"ahler.

Short-time persistence of bounded curvature under the Ricci flowJul 29 2015We use a first-order energy quantity to prove a strengthened statement of uniqueness for the Ricci flow. One consequence of this statement is that if a complete solution on a noncompact manifold has uniformly bounded Ricci curvature, then its sectional ... More

Field Theories Without a Holographic DualJun 08 2016Oct 24 2016In applying the gauge-gravity duality to the quark-gluon plasma, one models the plasma using a particular kind of field theory with specified values of the temperature, magnetic field, and so forth. One then assumes that the bulk, an asymptotically AdS ... More

Non-uniform covering array with symmetric forbidden edge constraintsJan 08 2019It has been conjectured that whenever an optimal covering array exists there is also a uniform covering array with the same parameters and this is true for all known optimal covering arrays. When used as a test suite, the application context may have ... More

Large Starspot Groups on HAT-P-11 in Activity Cycle 1Jan 30 2018HAT-P-11 is a planet-hosting K4V star in the Kepler field, with an activity cycle that bear similarities to the Sun's. The chromospheric activity of HAT-P-11 indicates that a new activity cycle is beginning. We report ground-based observations with holographic ... More

Robust Transiting Exoplanet Radii in the Presence of Starspots from Ingress and Egress DurationsJul 13 2018We typically measure the radii of transiting exoplanets from the transit depth, which is given by the ratio of cross-sectional areas of the planet and star. However, if a star has dark starspots (or bright regions) distributed throughout the transit chord, ... More

An Interesting IdentityMar 13 2015This purpose of this paper is to note an interesting identity derived from an integral in Gradshteyn and Ryzhik using techniques from George Boros'(deceased) Ph.D thesis. The idenity equates a sum to a product by evaluating an integral in two different ... More

Statistical Equilibrium of the Korteweg-de Vries and Benjamin-Ono Unidirectional Soliton ModelsFeb 09 2019The Korteweg-de Vries and Benjamin-Ono nonlinear wave equations can describe solitary waves, all of which propagate in the same direction and which emerge from collisions with their shapes unchanged. There are technical challenges to giving a description ... More

Faster Kernels for Graphs with Continuous Attributes via HashingOct 01 2016While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we present hash ... More

A procedure for making high dynamic-range radio images: Deep imaging of the kiloparsec-scale radio structures of a distant blazar, NRAO 530, with JVLA dataMar 20 2019Using JVLA data of Sgr A* and NRAO 530 (as a calibrator) at 5.5, 9 and 33 GHz, we developed a procedure for the reduction of wideband data. We have demonstrated that, correcting for residual interferometer errors such as residual delays, astronomers can ... More

Optimal actuator design for vibration control based on LQR performance and shape calculusMar 18 2019Optimal actuator design for a vibration control problem is calculated. The actuator shape is optimized according to the closed-loop performance of the resulting linear-quadratic regulator and a penalty on the actuator size. The optimal actuator shape ... More

Unseen companions of V Hya inferred from periodic ejectionsFeb 21 2019Recent Hubble Space Telescope observations found periodic, high-speed, collimated ejections (or "bullets") from the star V Hya (Sahai et al. 2016). The proposed model associated these bullets with the periastron passage of an unseen, substellar companion ... More

Productive Dialog During Collaborative Problem SolvingJun 03 2008Collaboration is an important problem-solving skill; however, novice collaboration generally benefits from some kind of support. One possibility for supporting productive conversations between collaborators is to encourage pairs of students to provide ... More

Spectral gap for the zero range process with constant rateMay 10 2004Nov 20 2006We solve an open problem concerning the relaxation time (inverse spectral gap) of the zero range process in $\mathbf {Z}^d/L\mathbf {Z}^d$ with constant rate, proving a tight upper bound of $O((\rho +1)^2L^2)$, where $\rho$ is the density of particles. ... More

The CI problem for infinite groupsFeb 21 2015A finite group $G$ is a DCI-group if, whenever $S$ and $S'$ are subsets of $G$ with the Cayley graphs Cay$(G,S)$ and Cay$(G,S')$ isomorphic, there exists an automorphism $\varphi$ of $G$ with $\varphi(S)=S'$. It is a CI-group if this condition holds under ... More

Cosmological effects of coupled dark matterApr 08 2013Oct 15 2013Many models have been studied that contain more than one species of dark matter and some of these couple the Cold Dark Matter (CDM) to a light scalar field. In doing this we introduce additional long range forces, which in turn can significantly affect ... More

Zero-temperature Glauber dynamics on Z^dSep 02 2008Nov 26 2009We study zero-temperature Glauber dynamics on \Z^d, which is a dynamic version of the Ising model of ferromagnetism. Spins are initially chosen according to a Bernoulli distribution with density p, and then the states are continuously (and randomly) updated ... More

Automorphism groups of circulant graphs -- a surveyNov 13 2004A circulant (di)graph is a (di)graph on n vertices that admits a cyclic automorphism of order n. This paper provides a survey of the work that has been done on finding the automorphism groups of circulant (di)graphs, including the generalisation in which ... More

Elementary proof that $\mathbb Z_p^4$ is a DCI-groupMar 18 2014A finite group $R$ is a DCI-group if, whenever $S$ and $T$ are subsets of $R$ with the Cayley graphs ${\rm Cay}(R,S)$ and ${\rm Cay}(R,T)$ isomorphic, there exists an automorphism $\varphi$ of $R$ with $S^\varphi=T$. Elementary abelian groups of order ... More

Nonstationary open dynamical systemsAug 16 2018This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as the holes) may ... More

Sequence variations of the 1-2-3 Conjecture and irregularity strengthNov 02 2012Karonski, Luczak, and Thomason (2004) conjectured that, for any connected graph G on at least three vertices, there exists an edge weighting from {1,2,3} such that adjacent vertices receive different sums of incident edge weights. Bartnicki, Grytczuk, ... More

Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formulaNov 14 2007In the first part of this paper, we prove local interior and boundary gradient estimates for p-harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for ... More

Classification of Reconfiguration Graphs of Shortest Path Graphs With No Induced $4$-cyclesAug 28 2018For any graph $G$ with $a,b\in V(G)$, a shortest path reconfiguration graph can be formed with respect to $a$ and $b$; we denote such a graph as $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths from $a$ to $b$ in $G$ while two ... More

On congruent primes and class numbers of imaginary quadratic fieldsOct 27 2011Apr 30 2012We consider the problem of determining whether a given prime p is a congruent number. We present an easily computed criterion that allows us to conclude that certain primes for which congruency was previously undecided, are in fact not congruent. As a ... More

Beam Extraction From The Recycler Ring To P1 Line At FermilabFeb 16 2017The transfer line for beam extraction from the Recycler ring to P1 line provides a way to deliver 8 GeV kinetic energy protons from the Booster to the Delivery ring, via the Recycler, using existing beam transport lines, and without the need for new civil ... More

Nonstationary open dynamical systemsAug 16 2018Mar 16 2019This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as the holes) may ... More

Arithmetic aspects of the Burkhardt quartic threefoldMay 25 2017May 29 2018We show that the Burkhardt quartic threefold is rational over any field of characteristic distinct from 3. We compute its zeta function over finite fields. We realize one of its moduli interpretations explicitly by determining a model for the universal ... More

Locating Patterns in the De Bruijn TorusMay 15 2015Nov 23 2015The de Bruijn torus (or grid) problem looks to find an $n$-by-$m$ binary matrix in which every possible $j$-by-$k$ submatrix appears exactly once. The existence and construction of these binary matrices was determined in the 70's, with generalizations ... More

Detection of Interstellar HC$_5$O in TMC-1 with the Green Bank TelescopeJun 29 2017We report the detection of the carbon-chain radical HC$_5$O for the first time in the interstellar medium toward the dark cloud TMC-1 using the 100 m Green Bank Telescope. We observe four hyperfine components of this radical in the $J = 17/2 \rightarrow ... More

Gamma-ray Novae: Rare or Nearby?Oct 31 2016Classical Novae were revealed as a surprise source of gamma-rays in Fermi LAT observations. During the first 8 years since the LAT was launched, 6 novae in total have been detected to > 5 sigma in gamma-rays, in contrast to the 69 discovered optically ... More

Probing the Mass and Structure of the Ring Nebula in Lyra with SOFIA/GREAT Observations of the [CII] 158 micron lineMar 28 2012We have obtained new velocity-resolved spectra of the [CII] 158 micron line towards the Ring Nebula in Lyra (NGC 6720), one of the best-studied planetary nebulae, in order to probe its controversial 3-dimensional structure and to estimate the mass of ... More

Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operatorsDec 23 2013Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator can be uniquely written of a particular form, which we call the Matsumoto-Amano normal form. In this mostly expository paper, we give a detailed and streamlined presentation ... More

Exact synthesis of multiqubit Clifford+T circuitsDec 03 2012Apr 02 2013We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local ancillas if and only if its entries are in the ring Z[1/sqrt(2),i]. Moreover, we show that one ancilla always suffices. These facts were conjectured by ... More

A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitonsDec 08 2017We prove that a shrinking gradient Ricci soliton which agrees to infinite order at spatial infinity with one of the standard cylindrical metrics on $S^k\times \RR^{n-k}$ for $k\geq 2$ along some end must be isometric to the cylinder on that end. When ... More

Isometries of asymptotically conical shrinking Ricci solitonsDec 31 2018We show that if a shrinking soliton is asymptotic to a cone along an end then the isometry group of the cross-section of the cone embeds in the isometry group of the end of the shrinker. We also provide sufficient conditions for the isometries of the ... More

Thresholds for contagious sets in random graphsNov 30 2016For fixed $r\geq 2$, we consider bootstrap percolation with threshold $r$ on the Erd\H{o}s-R\'enyi graph ${\cal G}_{n,p}$. We identify a threshold for $p$ above which there is with high probability a set of size $r$ which can infect the entire graph. ... More

HD 202772A B: A Transiting Hot Jupiter Around A Bright, Mildly Evolved Star In A Visual Binary Discovered By TessOct 04 2018We report the first confirmation of a hot Jupiter discovered by the Transiting Exoplanet Survey Satellite (TESS) mission: HD 202772A b. The transit signal was detected in the data from TESS Sector 1, and was confirmed to be of planetary origin through ... More

Turbulence velocity profiling for high sensitivity and vertical-resolution atmospheric characterization with Stereo-SCIDARJan 10 2017As telescopes become larger, into the era of ~40 m Extremely Large Telescopes, the high- resolution vertical profile of the optical turbulence strength is critical for the validation, optimization and operation of optical systems. The velocity of atmospheric ... More

A Massive Bipolar Outflow and a Dusty Torus with Large Grains in the Pre-Planetary Nebula IRAS 22036+5306Sep 15 2006We report high angular-resolution (~1") CO J=3--2 interferometric mapping, using the Submillimeter Array (SMA), of IRAS22036+5306 (I22036), a bipolar pre-planetary nebula (PPN) with knotty jets discovered in our HST SNAPshot survey of young PPNs. In addition, ... More

Heterogeneity in $^{12}$CO/$^{13}$CO Ratios Toward Solar-Type Young Stellar ObjectsSep 21 2015This study reports an unusual heterogeneity in [$^{12}$C$^{16}$O]/[$^{13}$C$^{16}$O] abundance ratios of carbon monoxide observed in the gas phase toward seven ~ solar-mass YSOs and three dense foreground clouds in the nearby star-forming regions, Ophiuchus, ... More

A Unifying View of Explicit and Implicit Feature Maps for Structured Data: Systematic Studies of Graph KernelsMar 02 2017Mar 10 2017Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. To this end, explicit feature maps of kernels for vectorial data have been extensively studied. ... More

$L^q$-spectra of self-affine measures: closed forms, counterexamples, and split binomial sumsNov 08 2018We study $L^q$-spectra of planar self-affine measures generated by diagonal systems with an emphasis on providing closed form expressions. We answer a question posed by Fraser in 2016 in the negative by proving that a certain natural closed form expression ... More

Spatially Resolved Observations of the Galactic Center Source, IRS 21Apr 22 2002We present diffraction-limited 2-25 micron images obtained with the W. M. Keck 10-m telescopes that spatially resolve the cool source, IRS 21, one of a small group of enigmatic objects in the central parsec of our Galaxy that have eluded classification. ... More

Population-calibrated multiple imputation for a binary/categorical covariate in categorical regression modelsMay 04 2018Multiple imputation (MI) has become popular for analyses with missing data in medical research. The standard implementation of MI is based on the assumption of data being missing at random (MAR). However, for missing data generated by missing not at random ... More

Nuclear Structure from the In-Medium Similarity Renormalization GroupMay 23 2018Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, ... More

Is Anyone Out There? Unpacking Q&A Hashtags on TwitterJul 06 2015In addition to posting news and status updates, many Twitter users post questions that seek various types of subjective and objective information. These questions are often labeled with "Q&A" hashtags, such as #lazyweb or #twoogle. We surveyed Twitter ... More

Hamiltonian cycles in (2,3,c)-circulant digraphsSep 30 2006Let D be the circulant digraph with n vertices and connection set {2,3,c}. (Assume D is loopless and has outdegree 3.) Work of S.C.Locke and D.Witte implies that if n is a multiple of 6, c is either (n/2) + 2 or (n/2) + 3, and c is even, then D does not ... More

Weak Factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of Multilinear Riesz TransformsMar 08 2016Mar 19 2016This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ ... More

Interstellar Carbodiimide (HNCNH) - A New Astronomical Detection from the GBT PRIMOS Survey via Maser Emission FeaturesSep 07 2012In this work, we identify carbodiimide (HNCNH), which is an isomer of the well-known interstellar species cyanamide (NH2CN), in weak maser emission, using data from the GBT PRIMOS survey toward Sgr B2(N). All spectral lines observed are in emission and ... More

Representative optical turbulence profiles for ESO Paranal by hierarchical clusteringSep 20 2018Knowledge of the optical turbulence profile is important in adaptive optics (AO) systems, particularly tomographic AO systems such as those to be employed by the next generation of 40 m class extremely large telescopes (ELTs). Site characterisation and ... More

Flows that are sums of hamiltonian cycles in Cayley graphs on abelian groupsSep 02 2003Feb 06 2004If X is any connected Cayley graph on any finite abelian group, we determine precisely which flows on X can be written as a sum of hamiltonian cycles. (This answers a question of Brian Alspach.) In particular, if the degree of X is at least 5, and X has ... More

Isomorphisms of Cayley graphs on nilpotent groupsMar 06 2016Mar 11 2016Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with multiplication ... More

Cyclic $m$-cycle systems of complete graphs minus a 1-factorNov 13 2015In this paper, we provide necessary and sufficient conditions for the existence of a cyclic $m$-cycle system of $K_n-I$ when $m$ and $n$ are even and $m \mid n$.

Infinitely many nonsolvable groups whose Cayley graphs are hamiltonianJul 17 2015This note shows there are infinitely many finite groups G, such that every connected Cayley graph on G has a hamiltonian cycle, and G is not solvable. Specifically, for every prime p that is congruent to 1, modulo 30, we show there is a hamiltonian cycle ... More

A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theoryJun 01 2009We use ergodic theory to prove a quantitative version of a theorem of M. A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a theorem asserting ... More

Nanodiamond in tellurite glass Part II: practical nanodiamond-doped fibersNov 06 2014Tellurite glass fibers with embedded nanodiamond are attractive materials for quantum photonics applications. Reducing the loss of these fibers in the 600-800 nm wavelength range of nanodiamond fluorescence is essential to exploit the unique properties ... More

Are Starspots and Plages Co-Located on Active G and K Stars?Sep 12 2018We explore the connection between starspots and plages of three main-sequence stars by studying the chromospheric and photospheric activity over several rotation periods. We present simultaneous photometry and high-resolution ($R\sim 31,500$) spectroscopy ... More

CSO and CARMA Observations of L1157. I. A Deep Search for Hydroxylamine (NH$_2$OH)Sep 12 2015A deep search for the potential glycine precursor hydroxylamine (NH$_2$OH) using the Caltech Submillimeter Observatory (CSO) at $\lambda = 1.3$ mm and the Combined Array for Research in Millimeter-wave Astronomy (CARMA) at $\lambda = 3$ mm is presented ... More

A Radio Survey of Galactic Center CloudsDec 20 2013We present a survey of molecules in a sample of Galactic center molecular clouds using the Karl G. Jansky Very large Array, which includes M0.25+0.01, the clouds near Sgr A, and Sgr B2. The molecules detected are primarily NH3 and HC3N; in Sgr B2-N we ... More

SiS in the circumstellar envelope of IRC +10126: maser and quasi-thermal emissionJun 08 2017We present new Effelsberg-100 m, ATCA, and VLA observations of rotational SiS transitions in the circumstellar envelope (CSE) of IRC +10216. Thanks to the high angular resolution achieved by the ATCA observations, we unambiguously confirm that the molecule's ... More

Efficient Computation of a Canonical Form for a Generalized P-matrixApr 27 2012We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.

Dutch book in simple multivariate normal prediction: Another lookMay 19 2008In this expository paper we describe a relatively elementary method of establishing the existence of a Dutch book in a simple multivariate normal prediction setting. The method involves deriving a nonstandard predictive distribution that is motivated ... More

The second term for two-neighbour bootstrap percolation in two dimensionsJun 23 2018In the $r$-neighbour bootstrap process on a graph $G$, vertices are infected (in each time step) if they have at least $r$ already-infected neighbours. Motivated by its close connections to models from statistical physics, such as the Ising model of ferromagnetism, ... More

A necessary and sufficient condition for a matrix equilibrium state to be mixingDec 06 2016Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to H\"older-continuous real-valued potentials. The construction of equilibrium states associated to matrix-valued potentials is much more recent, with a complete ... More

Ergodic properties of matrix equilibrium statesMar 05 2016Oct 05 2016Given a finite irreducible set of real $d \times d$ matrices $A_1,\ldots,A_M$ and a real parameter $s>0$, there exists a unique shift-invariant equilibrium state associated to $(A_1,\ldots,A_M,s)$. In this article we characterise the ergodic properties ... More

Most Rigid Representations and Cayley indexMar 27 2017For any finite group $G$, a natural question to ask is the order of the smallest possible automorphism group for a Cayley graph on $G$. A particular Cayley graph whose automorphism group has this order is referred to as an MRR (Most Rigid Representation), ... More

Dani's Work on Dynamical Systems on Homogeneous SpacesJul 25 2013In honor of S.G.Dani's 65th birthday, we describe some of his many contributions to the theory and applications of dynamical systems on homogeneous spaces, with emphasis on unipotent flows.

Classification of finite groups that admit an oriented regular representationJul 17 2017This is the third, and last, of a series of papers dealing with oriented regular representations. Here we complete the classification of finite groups that admit an oriented regular representation (or ORR for short), and give a complete answer to a 1980 ... More

A short proof that the number of division steps in the Euclidean algorithm is normally distributedFeb 26 2015D. Hensley showed in 1994 that the number of steps taken by the Euclidean algorithm to find the greatest common divisor of two natural numbers less than or equal to n follows a normal distribution in the limit as n tends to infinity. V. Baladi and B. ... More

Cayley graphs on groups with commutator subgroup of order 2p are hamiltonianMar 19 2017We show that if G is a finite group whose commutator subgroup [G,G] has order 2p, where p is an odd prime, then every connected Cayley graph on G has a hamiltonian cycle.

Fast approximation of the affinity dimension for dominated affine iterated function systemsJul 24 2018In 1988 K. Falconer introduced a formula which predicts the value of the Hausdorff dimension of the attractor of an affine iterated function system. The value given by this formula -- sometimes referred to as the affinity dimension -- is known to agree ... More

Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonianMay 01 2012We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamiltonian cycle.

Multiple-particle interaction in $1+1$ dimensional lattice modelAug 22 2018Finite volume multiple-particle interaction is studied in a two-dimensional complex $\phi^4$ lattice model. The existence of analytical solutions to the $\phi^4$ model in two-dimensional space and time makes it a perfect model for the numerical study ... More

Asymptotic enumeration of Cayley digraphsNov 19 2018In this paper we show that almost all Cayley digraphs have automorphism group as small as possible; that is, they are digraphical regular representations (DRRs). More precisely, we show that as $r$ tends to infinity, for every finite group $R$ of order ... More

$η$ Carinae's Dusty Homunculus Nebula from Near-Infrared to Submillimeter Wavelengths: Mass, Composition, and Evidence for Fading OpacityJun 15 2017Infrared observations of the dusty, massive Homunculus Nebula around the luminous blue variable $\eta$ Carinae are crucial to characterize the mass-loss history and help constrain the mechanisms leading to the Great Eruption. We present the 2.4 - 670 ... More

Observational evidence for high neutronization in supernova remnants: implications for Type Ia supernova progenitorsJan 24 2017Jun 28 2017The physical process whereby a carbon--oxygen white dwarf explodes as a Type Ia supernova (SN Ia) remains highly uncertain. The degree of neutronization in SN Ia ejecta holds clues to this process because it depends on the mass and the metallicity of ... More

2-generated Cayley digraphs on nilpotent groups have hamiltonian pathsMar 28 2011Jun 30 2011Suppose G is a nilpotent, finite group. We show that if {a,b} is any 2-element generating set of G, then the corresponding Cayley digraph Cay(G;a,b) has a hamiltonian path. This implies there is a hamiltonian path in every connected Cayley graph on G ... More

An inequality for the matrix pressure function and applicationsJul 02 2015Jul 28 2016We prove an a priori lower bound for the pressure, or $p$-norm joint spectral radius, of a measure on the set of $d \times d$ real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to give new proofs ... More

An explicit formula for the pressure of box-like affine iterated function systemsMar 27 2017Mar 29 2017In this article we investigate the pressure function and affinity dimension for iterated function systems associated to the "box-like" self-affine fractals investigated by D.-J. Feng, Y. Wang and J.M. Fraser. Combining previous results of V. Yu. Protasov, ... More

The Kato Square Root Problem on SubmanifoldsMar 25 2011We solve the Kato square root problem for divergence form operators on complete Riemannian manifolds that are embedded in Euclidean space with a bounded second fundamental form. We do this by proving local quadratic estimates for perturbations of certain ... More

The number of $C_{2l}$-free graphsSep 11 2013Nov 11 2015One of the most basic questions one can ask about a graph $H$ is: how many $H$-free graphs on $n$ vertices are there? For non-bipartite $H$, the answer to this question has been well-understood since 1986, when Erd\H{o}s, Frankl and R\"odl proved that ... More

Common zeroes of families of smooth vector fields on surfacesJun 06 2015Let Y and X denote C^k vector fields on a possibly noncompact surface with empty boundary, k >0. Say that Y tracks X if the dynamical system it generates locally permutes integral curves of X. Let K be a locally maximal compact set of zeroes of X. THEOREM ... More

Fixed points of local actions of nilpotent Lie groups on surfacesMay 09 2014Let $G$ be connected nilpotent Lie group acting locally on a real surface $M$. Let $\varphi$ be the local flow on $M$ induced by a $1$-parameter subgroup. Assume $K$ is a compact set of fixed points of $\varphi$ and $U$ is a neighborhood of $K$ containing ... More