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Fingerprints of giant planets in the photospheres of Herbig starsSep 09 2015Around 2% of all A stars have photospheres depleted in refractory elements. This is hypothesized to arise from a preferential accretion of gas rather than dust, but the specific processes and the origin of the material -- circum- or interstellar -- are ... More

Estimating magnetic filling factors from Zeeman-Doppler magnetogramsMar 13 2019Low-mass stars are known to have magnetic fields that are believed to be of dynamo origin. Two complementary techniques are principally used to characterise them. Zeeman-Doppler imaging (ZDI) can determine the geometry of the large-scale magnetic field ... More

Age dependence of wind properties for solar type stars: a 3d studySep 21 2016Young and rapidly rotating stars are known for intense, dynamo generated magnetic fields. Spectropolarimetric observations of those stars in precisely aged clusters are key input for gyrochronology and magnetochronology. We use ZDI maps of several young ... More

On the Structure of Dark Matter Halos at the Damping Scale of the Power Spectrum with and without Relict VelocitiesSep 25 2007We report a series of high-resolution cosmological N-body simulations designed to explore the formation and properties of dark matter halos with masses close to the damping scale of the primordial power spectrum of density fluctuations. We further investigate ... More

Entropy Production in Collisionless Systems. III. Results from SimulationsMar 24 2015The equilibria formed by the self-gravitating, collisionless collapse of simple initial conditions have been investigated for decades. We present the results of our attempts to describe the equilibria formed in $N$-body simulations using thermodynamically-motivated ... More

Embeddings of quotient division algebras of rings of differential operatorsNov 13 2014Let $k$ be an algebraically closed field of characteristic zero, let $X$ and $Y$ be smooth irreducible algebraic curves over $k$, and let $D(X)$ and $D(Y)$ denote respectively the quotient division rings of the ring of differential operators of $X$ and ... More

The Evolving Magnetic Topology of $τ$ BoötisApr 08 2016We present six epochs of spectropolarimetric observations of the hot-Jupiter-hosting star $\tau$ Bo\"otis that extend the exceptional previous multi-year data set of its large-scale magnetic field. Our results confirm that the large-scale magnetic field ... More

Magnetic topologies of young suns: The weak-line T Tauri stars TWA 6 and TWA 8AFeb 15 2019Feb 19 2019We present a spectropolarimetric study of two weak-line T Tauri stars (wTTSs), TWA 6 and TWA 8A, as part of the MaTYSSE (Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets) program. Both stars display significant Zeeman signatures ... More

The Surface Magnetic Activity of the Weak-Line T Tauri Stars TWA 9A and V1095 ScoJul 20 2018We present a detailed analysis of high-resolution spectropolarimetric observations of the weak-line T Tauri stars (wTTSs) TWA 9A and V1095 Sco as part of a wider sur- vey of magnetic properties and activity in weak-line T Tauri stars, called MaTYSSE (Magnetic ... More

From solar to stellar corona: the role of wind, rotation and magnetismSep 23 2015Observations of surface magnetic fields are now within reach for many stellar types thanks to the development of Zeeman-Doppler Imaging. These observations are extremely useful for constraining rotational evolution models of stars, as well as for characterizing ... More

Discovery of a weak magnetic field in the photosphere of the single giant PolluxJul 09 2009Aims: We observe the nearby, weakly-active single giant, Pollux, in order to directly study and infer the nature of its magnetic field. Methods: We used the new generation spectropolarimeters ESPaDOnS and NARVAL to observe and detect circular polarization ... More

The Upper Atmospheres of Terrestrial Planets: Carbon Dioxide Cooling and the Earth's Thermospheric EvolutionJun 18 2018Context: The thermal and chemical structures of the upper atmospheres of planets crucially influence losses to space and must be understood to constrain the effects of losses on atmospheric evolution. Aims: We develop a 1D first-principles hydrodynamic ... More

Quantum Clock Synchronization Based on Shared Prior EntanglementApr 27 2000Jun 30 2000We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In contrast to classical synchronization schemes, the accuracy ... More

Migrating super-Earths in low-viscosity discs: unveiling the roles of feedback, vortices, and laminar accretion flowsNov 30 2018Jan 13 2019We present the highest resolution study to date of super-Earths migrating in inviscid and low-viscosity discs, motivated by the connection to laminar, wind-driven models of protoplanetary discs. Our models unveil the critical role of vortices in determining ... More

Tutorial models of the climate and habitability of Proxima Centauri b: a thin atmosphere is sufficient to distribute heat given low stellar fluxAug 25 2016Proxima Centauri b, an Earth-size planet in the habitable zone of our nearest stellar neighbour, has just been discovered. A theoretical framework of synchronously rotating planets, in which the risk of a runaway greenhouse on the sunlight side and atmospheric ... More

Number and Luminosity Evolution of Interacting Galaxies as a Natural explanation for the Galaxy CountsMay 23 1995A newly developed isochrone synthesis algorithm for the photometric evolution of galaxies is described. Two initial mass functions, IMFs, in particular, the recent IMF determined by Kroupa, Tout, and Gilmore, three photometric transformations, and a 1-Gyr-burst ... More

Inner disk structure of the classical T Tauri star LkCa 15Nov 12 2018Magnetospheric accretion has been thoroughly studied in young stellar systems with full non-evolved accretion disks, but it is poorly documented for transition disk objects with large inner cavities. We aim at characterizing the star-disk interaction ... More

Cabling Conjecture for Small Bridge NumberJul 06 2015Let $k\subset S^3$ be a nontrivial knot. The Cabling Conjecture of Francisco Gonz\'alez-Acu\~na and Hamish Short posits that $\pi$-Dehn surgery on $k$ produces a reducible manifold if and only if $k$ is a $(p,q)$-cable knot and the surgery slope $\pi$ ... More

Bipyramids and bounds on volumes of hyperbolic linksNov 07 2015We utilize ideal bipyramids to obtain new upper bounds on volume for hyperbolic link complements in terms of the combinatorics of their projections.

Counting 3-Stack-Sortable PermutationsMar 21 2019We prove a "Decomposition Lemma" that allows us to count preimages of certain sets of permutations under West's stack-sorting map $s$. As a first application, we give a new proof of Zeilberger's formula for the number of 2-stack-sortable permutations ... More

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: II. Asymptotic AnalysisFeb 05 2019Electrochemical and equivalent-circuit modelling are the two most popular approaches to battery simulation, but the former is computationally expensive and the latter provides limited physical insight. A theoretical middle ground would be useful to support ... More

The generalised Fitting subgroup of a profinite groupApr 02 2009The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, ... More

Triple Crossing Number of Knots and LinksJul 31 2012Sep 04 2012A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot ... More

A new paradigm for the universeNov 03 2003Jan 25 2012A new paradigm for the universe is presented in which the universe is far older than current estimates and there is no big bang.

On 2-powerfully Perfect Numbers in Three Quadratic RingsDec 09 2014Dec 11 2014Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call $n$-powerfully perfect numbers in these rings. This definition serves to extend the concept of perfect numbers that have been defined ... More

An Extension of the Abundancy Index to Certain Quadratic RingsJun 17 2015We begin by introducing an extension of the traditional abundancy index to imaginary quadratic rings with unique factorization. After showing that many of the properties of the traditional abundancy index continue to hold in our extended form, we investigate ... More

Unitary Multiperfect Numbers in Certain Quadratic RingsDec 09 2014A unitary divisor $c$ of a positive integer $n$ is a positive divisor of $n$ that is relatively prime to $\displaystyle{\frac{n}{c}}$. For any integer $k$, the function $\sigma_k^*$ is a multiplicative arithmetic function defined so that $\sigma_k^*(n)$ ... More

Connected Components of Complex Divisor FunctionsNov 12 2017May 04 2018For any complex number $c$, define the divisor function $\sigma_c\colon\mathbb N\to\mathbb C$ by $\displaystyle\sigma_c(n)=\sum_{d\mid n}d^c$. Let $\overline{\sigma_c(\mathbb N)}$ denote the topological closure of the range of $\sigma_c$. Extending previous ... More

On Ranges of Variants of the Divisor Functions that are DenseJul 04 2015For a real number $t$, let $s_t$ be the multiplicative arithmetic function defined by $\displaystyle{s_t(p^{\alpha})=\sum_{j=0}^{\alpha}(-p^t)^j}$ for all primes $p$ and positive integers $\alpha$. We show that the range of a function $s_{-r}$ is dense ... More

Preimages under the Stack-Sorting AlgorithmNov 18 2015Jun 02 2018We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and $t$-stack sortable ... More

Stack-Sorting Preimages of Permutation ClassesSep 10 2018Feb 11 2019We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of Bousquet-M\'elou. ... More

Postorder PreimagesApr 06 2016Jun 02 2018Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$ and all permutations ... More

Deconvolution by simulationAug 08 2007Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution of Y. We present ... More

Binary Codes and Period-2 Orbits of Sequential Dynamical SystemsSep 13 2015Sep 30 2017Let $[K_n,f,\pi]$ be the (global) SDS map of a sequential dynamical system (SDS) defined over the complete graph $K_n$ using the update order $\pi\in S_n$ in which all vertex functions are equal to the same function $f\colon\mathbb F_2^n\to\mathbb F_2^n$. ... More

Why are some A stars magnetic, while most are not?Dec 21 2007A small fraction of intermediate-mass main sequence (A and B type) stars have strong, organised magnetic fields. The large majority of such stars, however, show no evidence for magnetic fields, even when observed with very high precision. In this paper ... More

Methane bursts as a trigger for intermittent lake-forming climates on post-Noachian MarsNov 06 2016Nov 23 2018Lakes existed on Mars later than 3.6 billion years ago, according to sedimentary evidence for deltaic deposition. The observed fluvio-lacustrine deposits suggest that individual lake-forming climates persisted for at least several thousand years (assuming ... More

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: I. Physical ModelFeb 05 2019An isothermal porous-electrode model of a discharging lead-acid battery is presented, which includes an extension of concentrated-solution theory that accounts for excluded-volume effects, local pressure variation, and a detailed microscopic water balance. ... More

Interaction of infalling solid bodies with primordial atmospheres of disk-embedded planetsSep 14 2018Planets that form early enough to be embedded in the circumstellar gas disk accumulate thick atmospheres of nebular gas. Models of these atmospheres need to specify the surface luminosity (i.e. energy loss rate) of the planet. This luminosity is usually ... More

The finiteness theorem for invariants of a finite group (translation of Emmy Noether's "Der Endlichkeitsatz der Invarianten endlicher Gruppen")Mar 22 2015A translation of Emmy Noether's paper "Der Endlichkeitsatz der Invarianten endlicher Gruppen" (Mathematische Annalen, vol. 77, 1920, pages 89--92). In Noether's words, the paper gives "an entirely elementary finiteness proof---using only the theory of ... More

Invariant distributions and X-ray transform for Anosov flowsAug 20 2014Dec 21 2015For Anosov flows preserving a smooth measure on a closed manifold $\mathcal{M}$, we define a natural self-adjoint operator $\Pi$ which maps into the space of invariant distributions in $\cap_{u<0} H^{u}(\mathcal{M})$ and whose kernel is made of coboundaries ... More

A search for Vega-like fields in OB starsOct 10 2014Very weak magnetic fields (with a longitudinal component below 1 Gauss) have recently been discovered in the A star Vega as well as in a few Am stars. According to fossil field scenarios, such weak fields should also exist in more massive stars. In the ... More

Measurement of air fluorescence light yield induced by an electromagnetic showerMar 09 2007Oct 20 2008For most of the Ultra-High-Energy-Cosmic-Ray (UHECR) experiments and projects (HiRes, AUGER, TA, JEM-EUSO, TUS,...), the detection technique of Extensive Air Showers is based, at least, on the measurement of the air-fluorescence-induced signal. The knowledge ... More

Measurement of air and nitrogen fluorescence light yields induced by electron beam for UHECR experimentsDec 04 2006Most of the Ultra High Energy Cosmic Ray (UHECR) experiments and projects (HiRes, AUGER, TA, EUSO, TUS,...) use air fluorescence to detect and measure extensive air showers (EAS). The precise knowledge of the Fluorescence Light Yield (FLY) is of paramount ... More

Quantum mock modular forms arising from eta-theta functionsApr 04 2016In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta-theta functions by constructing mock modular forms from the eta-theta functions with even characters, such that the shadows of these mock modular ... More

Sensitivity analysis for the average treatment effect in paired observational studiesSep 07 2016A method for conducting a sensitivity analysis for the average treatment effect in a paired observational study is presented. It is shown that, in the limit, the power of a sensitivity analysis for the average treatment effect under a constant treatment ... More

Nonlocal pure spin current injection via quantum pumping and crossed Andreev reflectionFeb 24 2005Jul 12 2005A pure spin current injector is proposed based on adiabatic pumping and crossed normal/Andreev reflection. The device consists of a three-terminal ferromagnet-superconductor-semiconductor system in which the injection of a pure spin current is into the ... More

Quantum spin pumping with adiabatically modulated magnetic barrier'sMar 29 2003Dec 09 2003A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structure's is investigated. The device for dc- transport does not provide spin-polarized currents, but in the adiabatic regime, when one ... More

A Detailed Model of the Irish High Voltage Power Network for Simulating GICsNov 09 2018Constructing a power network model for geomagnetically induced current (GIC) calculations requires information on the DC resistances of elements within a network. This information is often not known, and power network models are simplified as a result, ... More

On Multilevel Monte Carlo Ensemble Forecasts and Their CalibrationMay 27 2016Jul 04 2016Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte Carlo. This paper ... More

Chern-Simons line bundle on Teichmüller spaceFeb 09 2011Jul 24 2011Let $X$ be a non-compact geometrically finite hyperbolic 3-manifold without cusps of rank 1. The deformation space $\mc{H}$ of $X$ can be identified with the Teichm\"uller space $\mc{T}$ of the conformal boundary of $X$ as the graph of a section in $T^*\mc{T}$. ... More

Quantum localization correction to chiral edge mode transportDec 31 2018We answer the question- Can chiral quantum Hall edge modes suffer localization? in the affirmative. Hitherto, only seen in quantum diffusive transport, a quantum localization correction arises in the calculation of the Hall and 2-terminal resistance. ... More

Identification of a connection from Cauchy data on a Riemann surface with boundaryJul 05 2010Aug 26 2010We consider a connection $\nabla^X$ on a complex line bundle over a Riemann surface with boundary $M_0$, with connection 1-form $X$. We show that the Cauchy data space of the connection Laplacian (also called magnetic Laplacian) $L:={\nabla^X}^*\nabla^X ... More

Conformal harmonic forms, Branson-Gover operators and Dirichlet problem at infinityAug 05 2008For odd dimensional Poincar\'e-Einstein manifolds $(X^{n+1},g)$, we study the set of harmonic $k$-forms (for $k<\ndemi$) which are $C^m$ (with $m\in\nn$) on the conformal compactification $\bar{X}$ of $X$. This is infinite dimensional for small $m$ but ... More

Reeb vector fields and open book decompositionsSep 29 2008We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux. We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For ... More

Stabilizing the monodromy of an open book decompositionJun 05 2007We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.

Mathematical models for passive imaging I: general backgroundOct 19 2006Passive imaging is a new technics which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields between different points is strongly related to the Green function of the wave propagation. The aim of this paper ... More

Tunneling on graphs: an approach "a la Helffer-Sjoestrand"Sep 13 2018We revisit a paper of Li-Gabor-Yau on quantum tunneling on graphs using the approach of Helffer-Sjoestrand for the study of tunneling for Schroedinger operators on manifolds.

Computational topology of graphs on surfacesFeb 17 2017Sep 05 2017Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn on surfaces. ... More

The magnetic fields of intermediate-mass T Tauri stars : I. Magnetic detections and fundamental stellar parametersOct 30 2018Context. The origin of the fossil magnetic fields detected in 5 to 10% of intermediate-mass main sequence stars is still highly debated. Aims. We want to bring observational constraints to a large population of intermediate-mass pre-main sequence (PMS) ... More

Reconstruction formulas for X-ray transforms in negative curvatureNov 17 2015We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it $I_0$) and solenoidal vector fields on surfaces with negative curvature and strictly convex boundary. These formulas generalize the Pestov-Uhlmann formulas ... More

A sufficient condition for a locally compact almost simple group to have open monolithFeb 18 2019We obtain a sufficient condition, given a totally disconnected, locally compact group $G$ with a topologically simple monolith $S$, to ensure that $S$ is open in $G$ and abstractly simple.

Proof of the Matrix-valued Pólya Positivstellensatz via pure statesJun 18 2017Jun 27 2017Let $\Sigma$ denote the linear form $x_1 + \cdots + x_n$. By a classical Positivstellensatz of P\'olya, if a real form $f$ is strictly positive on the standard simplex, then $\Sigma^m f$ has strictly positive coefficients for some nonnegative integer ... More

General Bounds on Satisfiability Thresholds for Random CSPs via Fourier AnalysisJan 23 2017Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to variables passes certain ... More

Markov Chain Truncation for Doubly-Intractable InferenceOct 15 2016Mar 11 2017Computing partition functions, the normalizing constants of probability distributions, is often hard. Variants of importance sampling give unbiased estimates of a normalizer Z, however, unbiased estimates of the reciprocal 1/Z are harder to obtain. Unbiased ... More

Do the close binaries HD 22128 and HD 56495 contain Ap or Am stars?Jun 12 2013HD 22128 and HD 56495 are both double-lined spectroscopic binary systems with short orbital periods, which have been proposed to host magnetic Ap stars. Ap stars in short period binary systems are very rare, and may provide insight into the origin of ... More

Lenses as an Atom-Photon Interface: A Semiclassical ModelDec 03 2010Strong interaction between the light field and an atom is often achieved with cavities. Recent experiments have used a different configuration: a propagating light field is strongly focused using a system of lenses, the atom being supposed to sit at the ... More

A classification of spanning surfaces for alternating linksMay 24 2012A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating link, we determine all possible combinations of genus, orientability, and ... More

Phototactic Clustering of Swimming Micro-organisms in a Turbulent Velocity FieldFeb 05 2008We study the distribution of swimming micro-organisms advected by a model turbulent flow and attracted towards a localised light source through phototaxis. It is shown that particles aggregate along a dynamical attractor with fractal measure whose dimension ... More

Radiative forcings for 28 potential Archean greenhouse gasesSep 05 2014Despite reduced insolation in the late Archean, evidence suggests a warm climate which was likely sustained by a stronger greenhouse effect, the so-called Faint Young Sun Problem (FYSP). CO2 and CH4 are generally thought to be the mainstays of this enhanced ... More

Efficient glueball simulations on anisotropic latticesApr 22 1997Monte Carlo results for the low-lying glueball spectrum using an improved, anisotropic action are presented. Ten simulations at lattice spacings ranging from 0.2 to 0.4 fm and two different anisotropies have been performed in order demonstrate the advantages ... More

Wave 0-Trace and length spectrum on convex co-compact hyperbolic manifoldsJun 09 2006Apr 30 2012For quotients of the $n+1$-dimensional hyperbolic space by a convex co-compact group $\Gamma$, we obtain a formula relating the renormalized trace of the wave operator with the resonances of the Laplacian and some conformal invariants of the boundary, ... More

On interchanging the states of a pair of quditsNov 10 2008The qubit SWAP gate has been shown to be an integral component of quantum circuitry design. It permutes the states of two qubits and allows for the storage quantum information, teleportation of atomic or ionic states, and is a fundamental element in the ... More

Recognition of unipolar and generalised split graphsApr 04 2016A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the clique number, ... More

Random Perfect GraphsApr 04 2016Sep 05 2017We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are generalised ... More

Hamilton cycles, minimum degree and bipartite holesApr 04 2016Apr 19 2016We present a tight extremal threshold for the existence of Hamilton cycles in graphs with large minimum degree and without a large ``bipartite hole`` (two disjoint sets of vertices with no edges between them). This result extends Dirac's classical theorem, ... More

Entanglement renders free riding redundant in the thermodynamic limitAug 14 2018Jan 30 2019The free rider problem is one of the most well-studied problems in economics. The solution proposed mainly is punitive in order to deter people from free riding. In this work, we introduce quantum strategies and study the problem in the thermodynamic ... More

Marked boundary rigidity for surfacesFeb 09 2016Sep 12 2016We show that, on an oriented compact surface, two sufficiently $C^2$-close Riemannian metrics with strictly convex boundary, no conjugate points, hyperbolic trapped set for their geodesic flows, and same marked boundary distance, are isometric via a diffeomorphism ... More

The Algebra of Filters of a Cubic AlgebraJan 30 2009In this paper we discuss the inclusion ordering on the filters of a filter algebra, a special type of Metropolis-Rota algeba. Using embeddings into interval algebras we show that the notion of "untwisted" gives rise to a congruence relation on the group ... More

Enumerating the Derangements of an $n$-Cube via Möbius InversionFeb 05 2009Feb 06 2009In $\mathcal L$, the semilattice of faces of an $n$-cube, we count the number of automorphisms of $\mathcal L$ that fix a given subalgebra -- either pointwise or as a subalgebra. By using M\"obius inversion we get a formula for the number of derangements ... More

Warnaar's bijection and colored partition identities, IIFeb 04 2012Jan 17 2013In our previous paper, we determined a unified combinatorial framework to look at a large number of colored partition identities, and studied the five identities corresponding to the exceptional modular equations of prime degree of the Schroeter, Russell ... More

Dynamics of flat actions on totally disconnected, locally compact groupsMar 06 2015Feb 12 2016Let $G$ be a totally disconnected, locally compact group and let $H$ be a virtually flat (for example, polycyclic) group of automorphisms of $G$. We study the structure of, and relationships between, various subgroups of $G$ defined by the dynamics of ... More

An extension of the Duistermaat-Singer Theorem to the semi-classical Weyl algebraFeb 18 2009Motivated by many recent works (by L. Charles, V. Guillemin, T. Paul, J. Sj\"ostrand, A. Uribe, S. Vu Ngoc, S. Zelditch and others) on the semi-classical Birkhoff normal forms, we investigate the structure of the group of automorphisms of the graded semi-classical ... More

Resolvent at low energy and Riesz transform for Schroedinger operators on asymptotically conic manifolds. IIMar 12 2007Let $(M^\circ, g)$ be an asymptotically conic manifold, in the sense that $M^\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$ becomes a scattering metric on $M$. A special case of particular interest is that of asymptotically ... More

Homology stratifications and intersection homologyNov 21 1999A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [Intersection homology theory: II, Inventiones Mathematicae, 71 (1983) 77-129] in their proof of topological invariance ... More

Uniform Sobolev estimates for non-trapping metricsMay 18 2012We prove uniform Sobolev estimates $||u||_{L^{p'}} \leq C ||(\Delta-\alpha)u||_{L^{p}}$, where $p=2n/(n+2), p'=2n/(n-2)$, for the Laplacian $\Delta$ on non-trapping asymptotically conic manifolds of dimension $n$. Here C is independent of $\alpha$ which ... More

Deterministically driven random walks in a random environment on ZJan 14 2013We introduce the concept of a deterministic walk in a deterministic environment on a countable state space (DWDE). For the deterministic walk in a fixed environment we establish properties analogous to those found in Markov chain theory, but for systems ... More

Deterministically driven random walks on a finite state spaceJan 14 2013We introduce the concept of a deterministic walk. Confining our attention to the finite state case, we establish hypotheses that ensure that the deterministic walk is transitive, and show that this property is in some sense robust. We also establish conditions ... More

Characterisation of a class of equations with solutions over torsion-free groupsOct 22 1998We study equations over torsion-free groups in terms of their `t-shape' (the occurences of the variable t in the equation). A t-shape is good if any equation with that shape has a solution. It is an outstanding conjecture that all t-shapes are good. In ... More

A Functional (Monadic) Second-Order Theory of Infinite TreesMar 14 2019This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results concerning the decidability ... More

A Short Proof of Hölder Continuity for Functions in DeGiorgi ClassesDec 15 2017The goal of this note is to give an alternative proof of local H\"older continuity for functions in DeGiorgi classes based on an idea of Moser.

On Anti-Powers in Aperiodic Recurrent WordsFeb 04 2019Fici, Restivo, Silva, and Zamboni define a $\textit{$k$-anti-power}$ to be a concatenation of $k$ consecutive words that are pairwise distinct and have the same length. They ask for the maximum $k$ such that every aperiodic recurrent word must contain ... More

Geomagnetically Induced Currents in the Irish Power Network during Geomagnetic StormsNov 23 2016Geomagnetically induced currents (GICs) are a well-known terrestrial space weather hazard. They occur in power transmission networks and are known to have adverse effects in both high and mid-latitude countries. Here, we study GICs in the Irish power ... More

Constraining the Dark Matter decay lifetime with very deep observations of the Perseus cluster with the MAGIC telescopesSep 14 2015We present preliminary results on Dark Matter searches from observations of the Perseus galaxy cluster with the MAGIC Telescopes. MAGIC is a system of two Imaging Atmospheric Cherenkov Telescopes located in the Canary island of La Palma, Spain. Galaxy ... More

An Overabundance of Low-density Neptune-like PlanetsNov 28 2016We present a uniform analysis of the atmospheric escape rate of Neptune-like planets with estimated radius and mass (restricted to $M_{\rm p}<30\,M_{\oplus}$). For each planet we compute the restricted Jeans escape parameter, $\Lambda$, for a hydrogen ... More

Independent sets in graphs with given minimum degreeOct 04 2012We consider numbers and sizes of independent sets in graphs with minimum degree at least $d$, when the number $n$ of vertices is large. In particular we investigate which of these graphs yield the maximum numbers of independent sets of different sizes, ... More

Ensemble filter techniques for intermittent data assimilation - a surveyAug 31 2012This survey paper is written with the intention of giving a mathematical introduction to filtering techniques for intermittent data assimilation, and to survey some recent advances in the field. The paper is divided into three parts. The first part introduces ... More

Strong exponent bounds for the local Rankin-Selberg convolutionMar 03 2016Let $F$ be a non-Archimedean locally compact field. Let $\sigma$ and $\tau$ be finite-dimensional semisimple representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of $\sigma\otimes\tau$ ... More

Efficiency and computability of MCMC with Langevin, Hamiltonian, and other matrix-splitting proposalsJan 13 2015We analyse computational efficiency of Metropolis-Hastings algorithms with AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HMC). By including the effect ... More

An infinite family of locally X graphs based on incidence geometriesNov 28 2018A graph ${\mathcal G}$ is locally X if the graphs induced on the neighbours of every vertex of ${\mathcal G}$ are isomorphic to the graph $X$. We prove that the infinite family of incidence graphs of the $r$-rank incidence geometries, $\Gamma(KG(n,k),r)$, ... More

Characterization of polynomials whose large powers have fully positive coefficientsFeb 09 2019We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a Laurent polynomial ... More