Results for "Simon Watkins"

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High-Resolution, Three-Dimensional Reconstruction of the Outflow Tract Demonstrates Segmental Differences in Cleared EyesOct 28 2017Purpose: The rate of conventional aqueous humor outflow is the highest nasally. We hypothesized that this is reflected in regionally different outflow structures and analyzed the entire limbus by high-resolution, full-thickness ribbon-scanning confocal ... More
Bees with attitude: the effect of gusts on flight dynamicsFeb 10 2018Flight is a complicated task at small scales in part due to the ubiquitous unsteady air which contains it. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping ... More
Layer dependent role of collagen recruitment during loading of the rat bladder wallMay 09 2017In this work, we reevaluated long standing conjectures as to the source of the exceptionally large compliance of the bladder wall. Whereas, these conjectures were based on indirect measures of loading mechanisms, in this work we take advantage of advances ... More
Bounding the distinguishing number of infinite graphsFeb 18 2013A group of permutations G of a set V is k-distinguishable if there exists a partition of V into k parts such that only the identity permutation in G fixes setwise all of the cells of the partition. The least cardinal number k such that (G,V) is k-distinguishable ... More
Distinguishability of infinite groups and graphsJun 23 2011The {\em distinguishing number} of a group $G$ acting faithfully on a set $V$ is the least number of colors needed to color the elements of $V$ so that no non-identity element of the group preserves the coloring. The {\em distinguishing number} of a graph ... More
Faith in the Algorithm, Part 2: Computational EudaemonicsApr 01 2009Eudaemonics is the study of the nature, causes, and conditions of human well-being. According to the ethical theory of eudaemonia, reaping satisfaction and fulfillment from life is not only a desirable end, but a moral responsibility. However, in modern ... More
Infinite Motion and 2-Distinguishability of Graphs and GroupsApr 23 2013May 08 2013A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a ... More
The Higher Rank Rigidity Theorem for Manifolds With No Focal PointsNov 23 2011Jun 04 2012We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete, irreducible, ... More
Explicit lower bounds on the modular degree of an elliptic curveAug 10 2004We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the classical derivation ... More
A kinetic equation for linear fractional stable motion with applications to space plasma physicsMar 19 2008Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory seen in space physics and elsewhere. Natural time series frequently combine both effects, and Linear Fractional Stable Motion (LFSM) ... More
Some remarks on Heegner point computationsJun 16 2005Apr 05 2006We explain how to find a rational point on a rational elliptic curve of rank 1 using Heegner points. We give some examples, and list new algorithms that are due to Cremona and Delaunay. These are notes from a short course given at the Institut Henri Poincare ... More
The RMS Peculiar Velocity of ClustersOct 15 1997We study the rms peculiar velocity of clusters as a convenient statistic to put constraints on cosmological models. This statistic is easy to compute theoretically given a model for the power spectrum; we show that with some assumptions it can be directly ... More
The Red and Featureless Outer Disks of Nearby Spiral GalaxiesMay 17 2016We present results from deep, wide-field surface photometry of three nearby (D=4--7 Mpc) spiral galaxies: M94 (NGC 4736), M64 (NGC 4826), and M106 (NGC 4258). Our imaging reaches limiting surface brightnesses of $\mu_{B} \sim$ 28 -- 30 mag arcsec$^{-2}$ ... More
A parallel workload has extreme variabilityNov 13 2016Nov 18 2016In both high-performance computing (HPC) environments and the public cloud, the duration of time to retrieve or save your results is simultaneously unpredictable and important to your over all resource budget. It is generally accepted ("Google: Taming ... More
The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More
Longitudinal spin-relaxation of donor-bound electrons in direct bandgap semiconductorsMay 19 2016We measure the donor-bound electron longitudinal spin-relaxation time ($T_1$) as a function of magnetic field ($B$) in three high-purity direct-bandgap semiconductors: GaAs, InP, and CdTe, observing a maximum $T_1$ of $1.4~\text{ms}$, $0.4~\text{ms}$ ... More
Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Jul 07 2016One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More
Galactic substructure traced by RR Lyraes in SDSS Stripe 82Nov 18 2011Using a sample of 407 RR Lyrae stars extracted from SDSS Stripe 82, we study the degree of substructure in the Galactic halo. We identify overdensities associated with the known substructures of the Hercules-Aquila Cloud and the Sagittarius Stream, and ... More
25 Years of Self-Organized Criticality: Concepts and ControversiesApr 20 2015Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role ... More
Fast and backward stable computation of the eigenvalues of matrix polynomialsNov 30 2016In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues. In this article we propose a new backward stable method for computing a factored ... More
Vortices In Circumstellar DisksJan 12 1995We discuss the physics of vortices in the circumstellar disks associated with young stellar objects. We elucidate the basic physical properties of these localized storm systems. In particular, we consider point vortices, linear vortices, the effects of ... More
Bound States Can Stabilize Electroweak StringsNov 20 1992Nov 23 1992We show that the electroweak $Z-$string can be stabilized by the presence of bound states of a complex scalar field. We argue that fermions coupled to the scalar field of the string can also make the string stable and discuss the physical case where the ... More
Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependenceFeb 29 2016The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian ... More
Modular Parametrizations of Neumann-Setzer Elliptic CurvesApr 19 2004Suppose $p$ is a prime of the form $u^2+64$ for some integer $u$, which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves $E_0$ and $E_1$ of prime conductor $p$, and both have Mordell--Weil group $\Z/2\Z$. There is a surjective ... More
A discrete chemo-dynamical model of the dwarf spheroidal galaxy Sculptor: mass profile, velocity anisotropy and internal rotationAug 29 2016We present a new discrete chemo-dynamical axisymmetric modeling technique, which we apply to the dwarf spheroidal galaxy Sculptor. The major improvement over previous Jeans models is that realistic chemical distributions are included directly in the dynamical ... More
Symmetric powers of elliptic curve L-functionsApr 05 2006Apr 17 2006The conjectures of Deligne, Be\u\i linson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their $L$-functions. We make a numerical study for symmetric power $L$-functions ... More
Avalanching and Self Organised Criticality, a paradigm for geomagnetic activity?Jul 07 2000Oct 20 2000The characterization of global energy storage and release in the coupled solar wind-magnetosphere system remains one of the fundamental problems of space physics.Recently, it has been realised that a new paradigm in physics, that of Self Organised Criticality ... More
Extreme-value statistics from Lagrangian convex hull analysis I. Validation for homogeneous turbulent Boussinesq convection and MHD convectionMay 19 2016Aug 30 2016We investigate the utility of the convex hull to analyze physical questions related to the dispersion of a group of many more than four Lagrangian tracer particles in a turbulent flow. Validation of standard dispersion behaviors is a necessary preliminary ... More
Book to the Future - a manifesto for book liberationJul 04 2015The Book Liberation Manifesto is an exploration of publishing outside of current corporate constraints and beyond the confines of book piracy. We believe that knowledge should be in free circulation to benefit humankind, which means an equitable and vibrant ... More
Particle Dark EnergyNov 11 2004Feb 23 2006We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from 1/3 to less than -1 and can lead to the observed cosmic acceleration. The particles ... More
Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More
Approximations of generating functions and a few conjecturesNov 25 2009This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of Integer Sequences ... More
Prediction of the Virgo axis anisotropy: CMB radiation illuminates the nature of thingsSep 25 2005Recent findings of the anisotropy in the Cosmic Microwave Background (CMB) radiation are confusing for standard cosmology. Remarkably, this fact has been predicted several years ago in the framework of our model of the physical world. Moreover, in exact ... More
Holomorphic horospherical duality "sphere-cone"Jan 02 2005We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.
Quantum entanglement analysis based on abstract interpretationJan 28 2008Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum ... More
Extending and Implementing the Stable Model SemanticsMay 08 2000An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of efficient implementation ... More
A Brezis-Browder theorem for SSDB spacesApr 24 2010Sep 26 2010In this paper, we show how the Brezis-Browder theorem for maximally monotone multifunctions with a linear graph on a reflexive Banach space, and a consequence of it due to Yao, can be generalized to SSDB spaces.
Banach SSD spaces and classes of monotone setsAug 04 2009Jul 05 2010In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type ... More
The Evolution of Ellipticals, Spirals and Irregulars: Overcoming Selection BiasDec 07 2000The Hubble Deep Fields represent our best opportunity for probing galaxy evolution over a substantive look-back time. However as with any dataset the HDFs are prone to selection biases. These biases are extremely severe beyond z \~1.25 such that a meaningful ... More
Spin Structures on Riemann Surfaces and the Perfect NumbersDec 28 1998Dec 23 1999The equality between the number of odd spin structures on a Riemann surface of genus g, with $2^g - 1$ being a Mersenne prime, and the even perfect numbers, is an indication that the action of the modular group on the set of spin structures has special ... More
Modular Invariance and the Finiteness of Superstring TheoryApr 01 1995Apr 03 1996The genus-dependence of multi-loop superstring amplitudes is bounded at large orders in perturbation theory using the super-Schottky group parametrization of supermoduli space. Partial estimates of supermoduli space integrals suggest an exponential dependence ... More
Configurations of Handles and the Classification of Divergences in the String Partition FunctionApr 13 1994Apr 22 1994The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of infinities can be traced ... More
On the Closing Lemma problem for vector fields of bounded type on the torusNov 07 2008We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the $C^r$ Closing Lemma is verified for smooth vector fields that are area-preserving at all saddle points. ... More
Polar subspaces and automatic maximalityDec 11 2012Mar 28 2013This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and ... More
Space-Time and ProbabilityDec 14 2001Special relativity is most naturally formulated as a theory of space-time geometry, but within the space-time framework probability apears to be at best an epistemic notion - a matter of what can be known, not of the status of events in themselves. However, ... More
What is Probability?Dec 24 2004Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, ... More
Derivation of the Born Rule from Operational AssumptionsNov 21 2002Nov 21 2002The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to all the ... More
Prospects for Precision Higgs Physics at Linear CollidersNov 30 2012A linear e+e- collider provides excellent possibilities for precision measurements of the properties of the Higgs boson. At energies close to the Z-Higgs threshold, the Higgs boson can be studied in recoil against a Z boson, to obtain not only a precision ... More
Splitting the K-Terminal ReliabilityApr 18 2011Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article ... More
The sharp form of the strong Szego theoremFeb 06 2004Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the ... More
Sturm Oscillation and Comparison TheoremsNov 04 2003This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.
Simulating Dense MatterMar 19 2007I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I ... More
Lattice MatterSep 28 2001I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color ... More
The Phase Diagram of QCDMay 08 2001I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma ... More
Approximation properties of $β$-expansions IIJun 25 2015Given $\beta\in(1,2)$ and $x\in[0,\frac{1}{\beta-1}]$, a sequence $(\epsilon_{i})_{i=1}^{\infty}\in\{0,1\}^{\mathbb{N}}$ is called a $\beta$-expansion for $x$ if $$x=\sum_{i=1}^{\infty}\frac{\epsilon_{i}}{\beta^{i}}.$$ In a recent article the author studied ... More
Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon TheoremMar 21 2016Jun 13 2016We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic ... More
A First Look at the Impact of NNNLO Theory Uncertainties on Top Mass Measurements at the ILCMar 15 2016Aug 22 2016A scan of the top production threshold at a future electron-positron collider provides the possibility for a precise measurement of the top quark mass in theoretically well-defined mass schemes. With statistical uncertainties of 20 MeV or below, systematics ... More
Static perfect fluids with Pant-Sah equations of stateJan 17 2008Mar 31 2008We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the ... More
Criteria for (in)finite extent of static perfect fluidsApr 09 2002In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely ... More
Conformal positive mass theoremsMar 29 2000We show the following two extensions of the standard positive mass theorem (one for either sign): Let (N,g) and (N,g') be asymptotically flat Riemannian 3-manifolds with compact interior and finite mass, such that g and g' are twice Hoelder differentiable ... More
Minimum settling time control design through direct search optimizationSep 27 2011Dec 06 2011The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature ... More
ExSample -- A Library for Sampling Sudakov-Type DistributionsAug 31 2011Mar 19 2012Sudakov-type distributions are at the heart of generating radiation in parton showers as well as contemporary NLO matching algorithms along the lines of the POWHEG algorithm. In this paper, the C++ library ExSample is introduced, which implements adaptive ... More
Stability, birational transformations and the Kahler-Einstein problemJul 23 2010We define a new notion of "b-stability" for a polarised algebraic variety, adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.
Calabi-Yau metrics on Kummer surfaces as a model glueing problemJul 23 2010This is an expository paper which aims to give a simple proof of the existence of Ricci-flat metrics on certain K3 surfaces, as an illustration of general "glueing" techniques.
Ricci Flow of regions with curvature bounded below in dimension threeJul 04 2014We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has curvature bounded from below by -1, then we prove estimates which show that ... More
Zero repulsion in families of elliptic curve L-functions and an observation of S. J. MillerSep 01 2011Oct 20 2011We provide a theoretical explanation for an observation of S. J. Miller that if L(s,E) is an elliptic curve L-function for which L(1/2, E) is nonzero, then the lowest lying zero of L(s,E) exhibits a repulsion from the critical point which is not explained ... More
Endoscopy and cohomology growth on U(3)Jan 30 2013We apply the endoscopic classification of automorphic forms on U(3) to prove a case of a conjecture of Sarnak and Xue on cohomology growth.
Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22Jul 08 2015In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic ... More
Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)Aug 29 2012May 29 2013We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises ... More
A Logic of Interactive Proofs (Formal Theory of Knowledge Transfer)Jan 17 2012Apr 05 2016We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as embedded into ... More
The 3/5-conjecture for weakly $S(K_{1,3})$-free forestsJul 10 2015The $3/5$-conjecture for the domination game states that the game domination numbers of an isolate-free graph $G$ on $n$ vertices are bounded as follows: $\gamma_g(G)\leq \frac{3n}5 $ and $\gamma_g'(G)\leq \frac{3n+2}5 $. Recent progress have been done ... More
Marginable functions on Fréchet spacesApr 20 2015Dec 11 2015This paper is about the technique of {\em shadow variables} that was used in the theory of monotone operators. In this paper, we use it to show that certain results that were originally proved for lower semicontinuous convex functions are in fact true ... More
Comment on "Separability of quantum states and the violation of Bell-type inequalities"Oct 05 2004The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. ... More
The Foundations of Quantum Information and Feasible ExperimentsMar 12 2001This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric down-conversion are analyzed ... More
Aizenman's Theorem for Orthogonal Polynomials on the Unit CircleNov 17 2004For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if \[ \mathbb{E} \biggl(\int\frac{d\theta}{2\pi} \biggl|\biggl(\frac{\mathcal{C} + e^{i\theta}}{\mathcal{C} ... More
Generalized regularity and solution concepts for differential equationsJun 09 2008As the title ``Generalized regularity and solution concepts for differential equations'' suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations, in particular first order hyperbolic partial ... More
Localic Metric spaces and the localic Gelfand dualityNov 04 2014In this paper we prove, as conjectured by B.Banachewski and C.J.Mulvey, that the constructive Gelfand duality can be extended into a duality between compact regular locales and unital abelian localic C*-algebras. In order to do so we develop a constructive ... More
Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg groupMar 04 2016We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by ... More
On the remainder term of the Berezin inequality on a convex domainSep 22 2015Nov 08 2016We study the Dirichlet eigenvalues of the Laplacian on a convex domain in $\mathbb{R}^n$, with $n\geq 2$. In particular, we generalize and improve upper bounds for the Riesz means of order $\sigma\geq 3/2$ established in an article by Geisinger, Laptev ... More
Regularized Newton methods for simultaneous Radon inversion and phase retrieval in phase contrast tomographyFeb 17 2015Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different incident angles of ... More
On the construction of solutions to the Yang-Mills equations in higher dimensionsFeb 10 2003Aug 13 2003We describe a glueing construction for the Yang-Mills equations in dimension $n > 4$. Our method is based on a construction of approximate solutions, and a detailed analysis of the linearized operator near an approximate solution.
On solutions to the Ginzburg-Landau equations in higher dimensionsFeb 06 2003Aug 13 2003We establish a glueing theorem for the Ginzburg-Landau equations in dimension $n > 2$. To this end, we consider a nondegenerate minimal submanifold of codimension 2, and construct a one-parameter family of solutions to the Ginzburg-Landau equations such ... More
Technical Report: Modelling Multiple Cell Types with Partial Differential EquationsSep 28 2015Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly. However, in case ... More
On the absolute continuity of multidimensional Ornstein-Uhlenbeck processesAug 26 2009Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular, the law of $X_1$ ... More
Completeness criteria for modular cohomology rings of non prime power groupsApr 05 2010Aug 31 2012We introduce a criterion for the completeness of ring approximations of modular cohomology rings of finite non prime power groups, and discuss how this criterion performs in practical computations, compared with other criteria.
Some remarks about equations defining coincident root lociAug 23 2011Consider the projective variety $X_\lambda$ of binary forms of degree $d$ whose linear factors are distributed according to the partition $\lambda$ of $d$. We determine minimal sets of local generators of the fiber product of $X_\lambda$ with its normalization, ... More
Equations describing the ramification of outer simple linear projectionsSep 03 2011We explain how to determine equations describing the ramification of an outer simple linear projection of a projective scheme in a way suited for explicit computations.
Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicityMar 18 2005We show that the parameters $a_n, b_n$ of a Jacobi matrix have a complete asymptotic series $ a_n^2 -1 &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n} + O(R^{-2n}) b_n &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n+1} + O(R^{-2n}) $ where $1 < |\mu_j| < R$ for $j\leq ... More
Geodesic restrictions of arithmetic eigenfunctionsApr 03 2012Aug 17 2013Let X be an arithmetic hyperbolic surface, \psi a Hecke-Maass form, and l a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of \psi restricted to l, by extending the technique of arithmetic ... More
Asymptotically tight bounds on subset sumsMay 31 2008For a subset A of a finite abelian group G we define Sigma(A)={sum_{a\in B}a:B\subset A}. In the case that Sigma(A) has trivial stabiliser, one may deduce that the size of Sigma(A) is at least quadratic in |A|; the bound |Sigma(A)|>= |A|^{2}/64 has recently ... More
Combinatorics of tropical Hurwitz cyclesJul 15 2014Jun 25 2015We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points ... More
Introduction to Gromov-Witten TheoryJul 04 2014The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference aimed at introducing ... More
Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular formsFeb 09 2012Apr 17 2012In this paper we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surfaces using the crepant resolution conjecture and the Yau-Zaslow formula. We present a formula to compute these in terms ... More
Linearised Higher Variational EquationsMar 30 2013Feb 10 2015This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and computationally ... More
Rigidity of compact Riemannian spin Manifolds with BoundaryMar 21 2008Oct 29 2008In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} ... More
A uniqueness result for propagation-based phase contrast imaging from a single measurementSep 16 2014Apr 27 2015Phase contrast imaging seeks to reconstruct the complex refractive index of an unknown sample from scattering intensities, measured for example under illumination with coherent X-rays. By incorporating refraction, this method yields improved contrast ... More
Hyperbolicity and Cubulability Are Preserved Under Elementary EquivalenceJan 29 2018The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated ... More
Azumaya skew group algebras and an application to quantum Kleinian singularitiesNov 23 2017Nov 27 2017We provide easily-verified necessary and sufficient conditions for a skew group ring, or more generally, a crossed product ring, to be an Azumaya algebra. We use our results to show that (suitable localisations of) skew group rings associated to the quantum ... More
La théorie de Hodge des bimodules de Soergel (d'après Soergel et Elias-Williamson)Nov 07 2017Soergel bimodules are certain bimodules over polynomial algebras, associated with Coxeter groups, and introduced by Soergel in the 1990's while studying the category O of complex semisimple Lie algebras. Even though their definition is algebraic and rather ... More
Tosio Kato's Work on Non--Relativistic Quantum MechanicsNov 01 2017We review the work of Tosio Kato on the mathematics of non--relativistic quantum mechanics and some of the research that was motivated by this. Topics include analytic and asymptotic eigenvalue perturbation theory, Temple--Kato inequality, self--adjointness ... More