Results for "Ian Melbourne"

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Disintegration of Invariant Measures for Hyperbolic Skew ProductsMar 14 2015Nov 22 2016We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable $v$ on the skew product to an observable $\bar v$ on the ... More
Decay of correlations for slowly mixing flowsNov 06 2006We show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of a class of nonuniformly hyperbolic diffeomorphisms for which Young proved polynomial decay of correlations. ... More
Mixing for invertible infinite measure systemsApr 19 2014May 01 2016In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of noninvertible maps preserving ... More
Operator renewal theory and mixing rates for dynamical systems with infinite measureAug 24 2010Apr 11 2015We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This ... More
Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flowsMay 20 2008Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick succession, it is ... More
Statistical properties for flows with unbounded roof function, including the Lorenz attractorMar 06 2018Jun 24 2018For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We also obtain ... More
Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and SingularitiesAug 30 2011Apr 23 2013We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem ... More
Rate of Convergence in the Weak Invariance Principle for Deterministic SystemsJun 04 2018Oct 23 2018We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. Our results hold for uniformly expanding/hyperbolic (Axiom A) systems, as ... More
Almost Sure Invariance Principle For Nonuniformly Hyperbolic SystemsMar 29 2005We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the ... More
Operator renewal theory for continuous time dynamical systems with finite and infinite measureApr 09 2014May 10 2016We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic rational ... More
Deterministic homogenization for fast-slow systems with chaotic noiseSep 19 2014Consider a fast-slow system of ordinary differential equations of the form $\dot x=a(x,y)+\varepsilon^{-1}b(x,y)$, $\dot y=\varepsilon^{-2}g(y)$, where it is assumed that $b$ averages to zero under the fast flow generated by $g$. We give conditions under ... More
Moment bounds and concentration inequalities for slowly mixing dynamical systemsApr 02 2014Sep 16 2014We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit theorem with ... More
First and higher order uniform dual ergodic theorems for dynamical systems with infinite measureMay 25 2011We generalize the proof of Karamata's Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of \emph{uniform dual ergodicity} for a very large class of dynamical systems with infinite measure, ... More
Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measureNov 30 2015We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on nonexistence of ... More
Weak Convergence to Stable Lévy Processes for Nonuniformly Hyperbolic Dynamical SystemsSep 25 2013We consider weak invariance principles (functional limit theorems) in the domain of a stable law. A general result is obtained on lifting such limit laws from an induced dynamical system to the original system. An important class of examples covered by ... More
A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansionNov 28 2014Mar 10 2016We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time function is ... More
Deterministic homogenization for discrete-time fast-slow systems under optimal moment assumptionsMar 25 2019We consider discrete-time fast-slow systems of the form $$ X^{(n)}_{k+1} = X^{(n)}_k + n^{-1}a_n(X_k^{(n)},Y_k^{(n)}) + n^{-1/2}b_n(X_k^{(n)},Y_k^{(n)})\;, \quad Y_{k+1}^{(n)} = T_nY_k^{(n)}\;.$$ We give conditions under which the dynamics of the slow ... More
Disintegration of Invariant Measures for Hyperbolic Skew ProductsMar 14 2015Oct 13 2015We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable $v$ on the skew product to an observable $\bar v$ on the ... More
Exponential decay of correlations for nonuniformly hyperbolic flows with a C^{1+α} stable foliation, including the classical Lorenz attractorApr 16 2015Apr 10 2016We prove exponential decay of correlations for a class of $C^{1+\alpha}$ uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric ... More
Mixing for continuous time dynamical systems with infinite measureJul 30 2013Apr 10 2014We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic ... More
Decay of correlations for nonuniformly expanding systems with general return timesAug 27 2011We give a unified treatment of decay of correlations for nonuniformly expanding systems with a good inducing scheme. In addition to being more elementary than previous treatments, our results hold for general integrable return time functions under fairly ... More
Dynamics on unbounded domains; co-solutions and inheritance of stabilityAug 30 2006We consider the dynamics of semiflows of patterns on unbounded domains that are equivariant under a noncompact group action. We exploit the unbounded nature of the domain in a setting where there is a strong `global' norm and a weak `local' norm. Relative ... More
Smooth approximation of stochastic differential equationsMar 28 2014Feb 09 2016Consider an It\^{o} process $X$ satisfying the stochastic differential equation $dX=a(X)\,dt+b(X)\,dW$ where $a,b$ are smooth and $W$ is a multidimensional Brownian motion. Suppose that $W_n$ has smooth sample paths and that $W_n$ converges weakly to ... More
Convergence to a Lévy process in the Skorohod $M_1$ and $M_2$ topologies for nonuniformly hyperbolic systems, including billiards with cuspsSep 18 2018Nov 23 2018We prove convergence to a Levy process for a class of dispersing billiards with cusps. For such examples, convergence to a stable law was proved by Jung & Zhang. For the corresponding functional limit law, convergence is not possible in the usual Skorohod ... More
A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical SystemsJun 21 2006We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom~A diffeomorphisms and flows as ... More
On the detection of superdiffusive behaviour in time seriesJul 25 2016We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data and relies on one realisation (ie one sample path) ... More
On the Validity of the 0-1 Test for ChaosJun 08 2009In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics.
A Huygens principle for diffusion and anomalous diffusion in spatially extended systemsApr 12 2013May 09 2013We present a universal view on diffusive behaviour in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behaviour (Brownian motion with drift) and weak chaos leads to superdiffusive ... More
Testing for Chaos in Deterministic Systems with NoiseOct 15 2004Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent. In this paper, ... More
A New Test for ChaosAug 26 2002Jan 17 2003We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos (the output is ... More
On the detection of superdiffusive behaviour in time seriesJul 25 2016Nov 17 2016We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data (with no prior knowledge required of the nature ... More
On the Implementation of the 0-1 Test for ChaosJun 08 2009In this paper we address practical aspects of the implementation of the 0-1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method ... More
On the detection of superdiffusive behaviour in time seriesJul 25 2016Dec 21 2016We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data (with no prior knowledge required of the nature ... More
A test for a conjecture on the nature of attractors for smooth dynamical systemsNov 23 2013Mar 29 2014Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter include many classical ... More
Homogenization for Deterministic Maps and Multiplicative NoiseApr 23 2013Apr 29 2015A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential equation with additive ... More
Broadband nature of power spectra for intermittent Maps with summable and nonsummable decay of correlationsOct 31 2015Mar 30 2016We present results on the broadband nature of the power spectrum $S(\omega)$, $\omega\in(0,2\pi)$, for a large class of nonuniformly expanding maps with summable and nonsummable decay of correlations. In particular, we consider a class of intermittent ... More
Central limit theorems and suppression of anomalous diffusion for systems with symmetryApr 03 2014Feb 23 2015We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps. In ... More
Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gasJan 01 2019In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Holder observables satisfy statistical ... More
Rates of mixing for nonMarkov infinite measure semiflowsJul 29 2016We develop an abstract framework for obtaining optimal rates of mixing for infinite measure semiflows. Previously, such results were restricted to the Markov setting. As an illustration of the method, we consider mixing rates for suspensions over nonMarkov ... More
Sharp Statistical Properties for a Family of Multidimensional NonMarkovian Nonconformal Intermittent MapsApr 02 2019Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that up to now is ... More
Variance continuity for Lorenz flowsDec 21 2018The classical Lorenz flow, and any flow which is close to it in the $C^{1+\alpha}$-topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuously for this family of flows.
Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiardsNov 19 2018Gouezel and Sarig introduced operator renewal theory as a method to prove sharp results on polynomial decay of correlations for certain classes of nonuniformly expanding maps. In this paper, we apply the method to planar dispersing billiards and multidimensional ... More
Rates of mixing for nonMarkov infinite measure semiflowsJul 29 2016Nov 01 2018We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincar\'e map that is uniformly ... More
Polynomial decay of correlations for flows, including Lorentz gas examplesOct 07 2017Nov 11 2018We prove sharp results on polynomial decay of correlations for nonuniformly hyperbolic flows. Applications include intermittent solenoidal flows and various Lorentz gas models including the infinite horizon Lorentz gas.
The Lorenz attractor is mixingOct 08 2004We study a class of geometric Lorenz flows, introduced independently by Afraimovic, Bykov & Sil'nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. As a consequence, we show that the classical Lorenz attractor ... More
Existence and convergence properties of physical measures for certain dynamical systems with holesMay 29 2007Sep 24 2008We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckmann maps with singularities. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure $\mu$ (a.c.c.i.m.) with ... More
Superdiffusive limits for deterministic fast-slow dynamical systemsJul 10 2019We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times Y$ of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)}) v(y_k)\;,\quad y_{k+1} = f(y_k)\;, \end{cases} \] where $\alpha\in(1,2)$. ... More
Multiscale systems, homogenization, and rough pathsDec 04 2017Mar 25 2019In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey ... More
Necessary and sufficient condition for $\cM_2$-convergence to a Lévy process for billiards with cusps at flat pointsFeb 24 2019We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding L\'evy process in the $\cM_1$ and $\cM_2$ Skorohod topologies has been studied in recent work. Here ... More
Tunnel conductance spectroscopy via harmonic generation in a hybrid capacitor deviceMar 19 2013Jul 30 2013We address the measurement of density of states within and beyond the superconducting gap in tunnel-coupled finite-size nanostructures using a capacitive method. Third-harmonic generation is used to yield the full differential conductance spectrum without ... More
Summary talk: Gauge Boson Self InteractionsApr 03 1995A review is given of the theoretical expectations of the self couplings of gauge bosons and of the present experimental information on the couplings. The possibilities for future measurements are also discussed.
On the semi-annual, 27 day, variation in geomagnetic activity, cloud cover and surface temperatureDec 03 2013We develop a basic model of the time variation of geomagnetic activity and show that the model predicts, with decreasing levels of exactitude, the time variation of the ~27 day period components of geomagnetic aa index, cloud cover and surface temperature ... More
The evolvability of business and the role of antitrustMar 06 2012In this paper, based on theories of complex adaptive systems, I argue that the main case for antitrust policy should be extended to include the criteria of "evolvability." To date, the main case focuses on economizing, including market power as a key ... More
Multiple Dirichlet Series for Affine Weyl GroupsJun 03 2014Let $W$ be the Weyl group of a simply-laced affine Kac-Moody Lie group, excepting $\tilde{A}_n$ for $n$ even. We construct a multiple Dirichlet series $Z(x_1, \ldots x_{n+1})$, meromorphic in a half-space, satisfying a group $W$ of functional equations. ... More
High-energy amplitudes in the next-to-leading orderApr 01 2010I review the calculation of the next-to-leading order behavior of high-energy amplitudes in N=4 SYM and QCD using the operator expansion in Wilson lines.
Scattering of shock waves in QCDSep 27 2004The cross section of heavy-ion collisions is represented as a double functional integral with the saddle point being the classical solution of the Yang-Mills equations with boundary conditions/sources in the form of two shock waves corresponding to the ... More
NS-NS fluxes in Hitchin's generalized geometryDec 12 2006Dec 17 2007The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number ... More
Relating branes and matricesJan 12 2005We construct a general map between a Dp-brane with magnetic flux and a matrix configuration of D0-branes, by showing how one can rewrite the boundary state of the Dp-brane in terms of its D0-brane constituents. This map gives a simple prescription for ... More
AGN astrophysics from comparing radio and Gaia optical astrometryJan 29 2013Gaia will open up a huge volume of new parameter space in which to explore the physics of AGN and black hole evolution. We address the question as to how far along the relativistic jets blazar radio, optical and gamma ray emission originated. In some ... More
A conjecture on the distribution of firm profitJul 27 2004Mar 23 2011A common assumption of political economy is that profit rates across firms or sectors tend to uniformity, and often models are formulated in which this tendency is assumed to have been realised. But in reality this tendency is never realised and the distribution ... More
Singular Isotonic Oscillator, Supersymmetry and SuperintegrabilitySep 19 2012In the case of a one-dimensional nonsingular Hamiltonian $H$ and a singular supersymmetric partner $H_a$, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate ... More
Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz SystemsDec 08 2010Dec 23 2010There exist a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude (SVPEM) and the Schrodinger equation. We obtain the relativistic energy spectrum for the four Smorodinsky-Winternitz systems from ... More
Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic ChainFeb 04 1998Feb 20 1998The exact amplitude for the asymptotic correlation function in the S=1/2 Heisenberg antiferromagnetic chain is determined: <S^a_0 S^b_r> goes to (-1)^r delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation functions for small xxz anisotropy ... More
Non-Fermi liquid behavior in Kondo modelsSep 07 2004Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees ... More
The Kondo Screening CloudNov 17 2001Renormalization group theory of the Kondo effect predicts that an impurity spin is screened by a conduction electron spread over a large distance of order >.1 to 1 micron. This review has the following sections: 1. The Kondo effect and the screening cloud, ... More
Evidence of a planetary influence on solar activity: Phase coherence of the variation in sunspot area with the tidal effect of MercuryOct 08 2015There have been numerous reports of quasiperiodicities in solar activity in the intermediate period range. However, no accepted explanation for the episodic occurrence of quasiperiodicities has emerged. This paper examines the possibility that the periodicities ... More
Metrizing the Chabauty topologyOct 24 2016Oct 25 2016We describe an explicit metric that induces the Chabauty topology on the space of closed subsets of a proper metric space M.
Double Soft Theorems and Shift Symmetry in Nonlinear Sigma ModelsDec 03 2015We show both the leading and subleading double soft theorems of the nonlinear sigma model follow from a shift symmetry enforcing Adler's zero condition in the presence of an unbroken global symmetry. They do not depend on the underlying coset G/H and ... More
Compiling Process Networks to Interaction NetsSep 13 2016Kahn process networks are a model of computation based on a collection of sequential, deterministic processes that communicate by sending messages through unbounded channels. They are well suited for modelling stream-based computations, but are in no ... More
Superstring holography and integrability in AdS_5 x S^5May 03 2005May 31 2005The AdS/CFT correspondence provides a rich testing ground for many important topics in theoretical physics. The earliest and most striking example of the correspondence is the conjectured duality between the energy spectrum of type IIB superstring theory ... More
On the Integrability of String Theory in AdS_5 x S^5May 19 2004Jun 10 2004Integrability occupies an increasingly important role in direct tests of the AdS/CFT correspondence. Integrable structures have appeared in both planar N=4 super Yang-Mills theory and type IIB superstring theory on AdS_5 x S^5. A generalized statement ... More
Teaching cloud computing: a software engineering perspectiveSep 05 2012This short papers discusses the issues of teaching cloud computing from a software engineering rather than a business perspective. It discusses what topics might be covered in a senior course on cloud software engineering.
Particle-hole symmetry parameters for nucleiSep 12 2014Apr 27 2016Two new numbers, $\nu$ and $\zeta$, inspired by particle-hole symmetry are introduced. These numbers have extreme values at a closed shell and vanish mid-shell. A combination of even powers of these numbers has been used to model experimentally measured ... More
Matched Filters for Source Detection in the Poissonian Noise RegimeMar 14 2006A procedure is described for estimating an optimum kernel for the detection by convolution of signals among Poissonian noise. The technique is applied to the detection of x-ray point sources in XMM-Newton data, and is shown to yield an improvement in ... More
A new model in the Calogero-Ruijsenaars familyNov 19 2013Dec 22 2013Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of $SU(n,n)$, to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses $BC_n$ symmetry and is shown to be equivalent to the ... More
New Facts From the First Galaxy Distance EstimatesJan 28 2011A new database from the NASA/IPAC Extragalactic Database (NED) of galaxy Distances (NED-D), normally the source for the newest precision-based estimates, provides access to the oldest redshift-independent extragalactic distances in the publication record. ... More
Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motionAug 09 2009Jan 05 2010The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric quantum mechanics. ... More
Systoles of hyperbolic 4-manifoldsDec 11 2006We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.
Conjugacy growth series for wreath product finitary symmetric groupsDec 12 2016In recent work, Bacher and de la Harpe define and study conjugacy growth series for finitary permutation groups. In two subsequent papers, Cotron, Dicks, and Fleming study the congruence properties of some of these series. We define a new family of conjugacy ... More
On Reals with $Δ^{0}_{2}$-Bounded Complexity and Compressive PowerOct 14 2014The (prefix-free) Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This gives rise to some `standard' lowness notions for reals: A is K-trivial if its initial segments have the lowest possible complexity ... More
Lowness for Integer-Valued RandomnessOct 13 2014A real is called integer-valued random if no integer-valued martingale can win arbitrarily much capital betting against it. A real is low for integer-valued randomness if no integer-valued martingale recursive in A can succeed on an integer-valued random ... More
Bounds on exceptional Dehn fillingJun 27 1999Nov 15 2000We show that for a hyperbolic knot complement, all but at most 12 Dehn fillings are irreducible with infinite word-hyperbolic fundamental group.
Harmonic tori and generalised Jacobi varietiesJun 11 1999Jan 05 2000This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map off it. The ... More
The distinguishing number of the iterated line graphSep 14 2005We show that for all simple graphs G other than the cycles C_3,C_4,C_5, and the claw K_1,3 there exists a K > 0 such that whenever k > K the k-th iterate of the line graph can be distinguished by at most two colors. Additionally we determine, for trees, ... More
Knot Floer homology obstructs ribbon concordanceFeb 11 2019We prove that the map on knot Floer homology induced by a ribbon concordance is injective. As a consequence, we prove that the Seifert genus is monotonic under ribbon concordance. We also generalize a theorem of Gabai about the super-additivity of the ... More
Minimizing Closed Geodesics via Critical Points of the Uniform EnergyJun 02 2014Aug 26 2014In this paper we study 1/k-geodesics, those closed geodesics that minimize on any subinterval of length $l(\gamma)/k$. We employ energy methods to provide a relationship between the 1/k-geodesics and what we define as the balanced points of the uniform ... More
Volume change under drillingJan 17 2001Jan 11 2003Given a hyperbolic 3-manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable ... More
Sacks of dice with fair totalsNov 09 2014Jul 03 2017A fair sack is a finite set of independent dice, not required to be fair and allowed to have any number of sides, for which all totals are equally likely. These have been studied for over 60 years. Most results restrict the possible orders of dice in ... More
Moments of L'(1/2) in the Family of Quadratic TwistsAug 20 2012Nov 12 2012We prove the asymptotic formulae for several moments of derivatives of GL(2) L-functions over quadratic twists. The family of L-functions we consider has root number fixed to -1 and odd orthogonal symmetry. Assuming GRH we prove the asymptotic formulae ... More
Computer Network Defense Through Radial Wave FunctionsOct 06 2016The purpose of this research was to synthesize basic and fundamental findings in quantum computing, as applied to the attack and defense of conventional computer networks. The concept focuses on uses of radio waves as a shield for, and attack against ... More
Axial compression of a thin elastic cylinder: bounds on the minimum energy scaling lawApr 28 2016May 10 2016We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness and the magnitude ... More
Nielsen equivalence in mapping tori over the torusOct 24 2016We use the geometry of the Farey graph to give an alternative proof of the fact that if $A \in GL_2\mathbb Z$ and $G_A=\mathbb Z^2 \rtimes_A \mathbb Z$ is generated by two elements, there is a single Nielsen equivalence class of $2$-element generating ... More
A graph TQFT for hat Heegaard Floer homologyMar 19 2015Apr 02 2015In this paper we introduce an extension of the hat Heegaard Floer TQFT which allows cobordisms with disconnected ends. Our construction goes by way of sutured Floer homology, and uses some elementary results from contact geometry. We provide some model ... More
Revisiting 154-day periodicity in the occurrence of hard flares. A planetary influence?Nov 14 2016Rieger et al (1984) reported observations of a 154 day periodicity in flares during solar cycle 21. This paper discusses the observations in the light of a simple empirical planetary model of sunspot emergence. The planetary model predicts sunspot emergence ... More
Lower bounds on volumes of hyperbolic Haken 3-manifoldsJun 27 1999In this paper, we find lower bounds for volumes of hyperbolic 3-manifolds with various topological conditions. Let V_3 = 1.01494 denote the volume of a regular ideal simplex in hyperbolic 3-space. As a special case of the main theorem, if a hyperbolic ... More
High-enegy effective action from scattering of QCD shock wavesJul 20 2005At high energies, the relevant degrees of freedom are Wilson lines - infinite gauge links ordered along straight lines collinear to the velocities of colliding particles. The effective action for these Wilson lines is determined by the scattering of QCD ... More
Measuring the Shape of the Extra DimensionAug 27 2006Sep 03 2006We study the possibility of extracting geometric information on the shape of the extra dimension from four-dimensional data such as the mass of the Kaluza-Klein (KK) mode. Assuming one compact extra dimension whose geometry can be considered as perturbations ... More
The closed string tadpole in open string field theoryApr 07 2008We compute a class of gauge invariant observables for marginal solutions and the tachyon vacuum. In each case we find that the observables are related in a simple way to the closed-string tadpole on a disk with appropriate boundary conditions. We give ... More
Thermodynamic cycle in a cavity optomechanical systemFeb 16 2014A cavity optomechanical system is initiated by a radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as cooling its ... More
Quasi-lattice chains and multipartite entanglement in a cavityJun 12 2013Nov 12 2014Unlike atoms in a lattice, the spacings between neighboring qubits in a superconducting quantum circuit are mesoscopic and non-uniform. The strength of interaction between this quasi-lattice chain of qubits and a resonator mode in circuit transmission ... More