Results for "Simon Watkins"

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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
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
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
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
Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Jun 27 2017One 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
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
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
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
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
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
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
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
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
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
Circumbinary Planets Orbiting the sdB Binary NY Virginis: An Updated Two Planet SolutionDec 04 2018We report 18 new primary minima timing observations of the short-period eclipsing binary system NY Virginis. We combined these minima with previously published primary minima to update circumbinary exoplanet models in this system based on O-C timing variations. ... 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
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
Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More
Defending the future: An MSc module in End User Computing Risk ManagementSep 28 2010This paper describes the rationale, curriculum and subject matter of a new MSc module being taught on an MSc Finance and Information Management course at the University of Wales Institute in Cardiff. Academic research on spreadsheet risks now has some ... More
Computing Cup-Products in integral cohomology of Hilbert schemes of points on K3 surfacesOct 30 2014Jan 18 2016We study cup products in integral cohomology of the Hilbert scheme of $n$ points on a K3 surface and present a computer program for this purpose. In particular, we deal with the question, which classes can be represented by products of lower degrees.
Singular cotangent bundle reduction and spin Calogero-Moser systemsNov 03 2004Oct 30 2008We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider Calogero-Moser ... More
On the remote interaction of biological objects with identical genetic structuresJul 03 2002The paper puts forward an unusual prediction that cultivating a clone can curtail the lifespan of the clone donor. Neither the arrangement of this suggested empirical study nor the analyses of the anticipated outcomes rely on the accompanying theoretical ... More
Empirical AUC for evaluating probabilistic forecastsAug 22 2015Scoring functions are used to evaluate and compare partially probabilistic forecasts. We investigate the use of rank-sum functions such as empirical Area Under the Curve (AUC), a widely-used measure of classification performance, as a scoring function ... More
The asymmetric sandwich theoremAug 29 2011Sep 22 2011We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel ... More
Quadrivariate existence theorems and strong representabilitySep 01 2008Feb 22 2011In this paper, we give conditions under which we can compute the conjugate of a convex function on the product of two Frechet spaces defined in terms of another convex function on the product of two (possibly different) Frechet spaces. We use this result ... More
Higher-Derivative Quantum CosmologyNov 06 1999Nov 10 1999The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques ... More
A Proof of the Odd Perfect Number ConjectureJan 08 2004May 31 2008It is sufficient to prove that there is an excess of prime factors in the product of repunits with odd prime bases defined by the sum of divisors of the integer $N=(4k+1)^{4m+1}\prod_{i=1}^\ell ~ q_i^{2\alpha_i}$ to establish that there do not exist any ... More
A new approach to inverse spectral theory, I. Fundamental formalismJun 17 1999Nov 01 1999We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr\"odinger operator determines the potential. Our approach is an analog ... More
Equilibrium measures and capacities in spectral theoryNov 16 2007This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to ... More
Weak convergence of CD kernels and applicationsJul 17 2007We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper bounds on $n\lambda_n(x)$, ... More
The Classical Moment Problem as a Self-Adjoint Finite Difference OperatorJun 08 1999This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence ... More
Four Fermion Models at Non-Zero DensityJun 22 1998I review the properties of the three-dimensional Gross-Neveu model formulated with non-zero chemical potential and temperature, focussing on results obtained by lattice Monte Carlo simulation.
Log Triviality in the Nambu -- Jona-Lasinio ModelSep 15 1997Results are presented from a Monte Carlo simulation of the Nambu -- Jona-Lasinio model with SU(2)xSU(2) chiral symmetry and N_f=2 flavors of fermion. We show that fits to the equation of state are sensitive to the shape and extent of the assumed scaling ... More
O(1/N_f) Corrections to the Thirring Model in 2<d<4Nov 02 1994Nov 10 1994The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to ... More
Fusion Rules of the ${\cal W}_{p,q}$ Triplet ModelsJul 26 2009Jan 11 2010In this paper we determine the fusion rules of the logarithmic ${\calW}_{p,q}$ triplet theory and construct the Grothendieck group with subgroups for which consistent product structures can be defined. The fusion rules are then used to determine projective ... More
Radio Observations of Two Isolated Neutron Stars, RXJ0720.4-3125 and RX J0806.4-4132Feb 24 2003Radio observations of two isolated neutron stars, RXJ0720.4-3125 and RX J0806.4-4132, have been made with the Australia Telescope Compact Array at a frequency of 1.4 GHz. No continuum emission is detected from either object with a 3 sigma upper limit ... More
Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL_2Mar 12 2011We prove an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL_2 over any number field which is not totally real. Our proof involves the theory of p-adically completed cohomology ... More
Measure theory over boolean toposesNov 06 2014In this paper we develop a notion of measure theory over boolean toposes which is analogous to noncommutative measure theory, i.e. to the theory of von Neumann algebras. This is part of a larger project to study relations between topos theory and noncommutative ... More
Symmetrization of monoïds as hypergroupsSep 08 2013We adapt the construction of the Grothendieck group associated to a commutative mono\"id to handle idempotent mono\"ids. Our construction works for a restricted class of commutative mono\"ids, it agrees with the Grothendieck group construction in many ... More
The long history of the Rossiter-McLaughlin effect and its recent applicationsSep 08 2011Nov 21 2011In this paper I will review the Rossiter-McLaughlin (RM) effect; its history, how it manifests itself during stellar eclipses and planetary transits, and the increasingly important role its measurements play in guiding our understanding of the formation ... More
Rethinking Newton's $\textit{Principia}$Sep 20 2016It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I argue to the ... More
Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large DeviationsAug 17 2016Short blurb for invited talk at AMS annual meeting in Atlanta; will appear in January AMS Notices
Right Amenable Left Group Sets and the Tarski-Følner TheoremMar 21 2016Mar 24 2016We introduce right amenability, right F{\o}lner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-F{\o}lner theorem for left homogeneous spaces with finite stabilisers. It states that right amenability, the existence ... More
The Garden of Eden Theorem for Cellular Automata on Group SetsMar 21 2016Sep 05 2016We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective ... More
Resolved observations of transition disksFeb 21 2016Resolved observations are bringing new constraints on the origin of radial gaps in protoplanetary disks. The kinematics, sampled in detail in one case-study, are indicative of non-Keplerian flows, corresponding to warped structures and accretion which ... More
FreeSASA: An open source C library for solvent accessible surface area calculationsJan 25 2016Calculating solvent accessible surface areas (SASA) is a run-of-the-mill calculation in structural biology. Although there are many programs available for this calculation, there are no free-standing, open-source tools designed for easy tool-chain integration. ... More
High frequency dispersive estimates in dimension twoJul 25 2007Sep 13 2007We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrodinger groupes for a very large class of real-valued potentials.
RAMBO on dietAug 13 2013We describe a phase space generator which is flat for massless particles, and approximately flat for massive particles of masses much smaller than the typical mometum scales involved in the process. The same goal is achieved by the RAMBO algorithm, contrary ... More
Inclusive Cross Sections in ME+PS MergingJul 02 2013We discuss an extension of matrix element plus parton shower merging at leading and next-to-leading order. The algorithm does preserve inclusive cross sections at the respective input order. This constraint avoids potentially large logarithmic contributions, ... More
The exact number of r-regular elements in finite exceptional groupsJan 26 2013We calculate the precise number of r-regular elements in the finite exceptional groups. As a corollary we find that the proportion of r-regular elements is at least 3577/18432 and for all \epsilon>0, there are infinitely finite simple exceptional groups ... More
Zero-Bias States and the Mechanism of the Surface d->d+is TransitionAug 28 2000We study the physical mechanism of the surface d->d+is transition proposed as the interpretation of results of tunneling experiments into ab planes. We base our argument on first-order perturbation theory and show that the zero-bias states drive the transition. ... More
Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noiseFeb 14 2014Apr 05 2015We investigate the macroscopic behavior of the disordered harmonic chain of oscillators, through energy diffusion. The Hamiltonian dynamics of the system is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, we prove ... More
The Gradient Flow of O'Hara's Knot EnergiesJan 12 2016Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \in (0, \infty)$. We study the negative gradient flow of the sum of one of the energies $E^\alpha = E^{\alpha,1}$, $\alpha \in (2,3)$, and a positive multiple of the length. Showing that the ... More
Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)Sep 05 2013Apr 08 2014We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive interactive proofs ... More
Computer-Aided Discovery and Categorisation of Personality AxiomsMar 24 2014We propose a computer-algebraic, order-theoretic framework based on intuitionistic logic for the computer-aided discovery of personality axioms from personality-test data and their mathematical categorisation into formal personality theories in the spirit ... More
Correlated radiative electron capture in ion-atom collisionsAug 30 2010Radiative double electron capture (RDEC) is a one-step process where two free (or quasi-free) target electrons are captured into a bound state of the projectile, e.g. into an empty K-shell, and the energy excess is released as a single photon. This process ... More
The ring of coefficients for commutative complex $K$-theoryNov 11 2016We determine the integral coefficient ring for "commutative complex $K$-theory". This is a cohomology theory which was first defined by Adem and G\'omez and then generalised by Adem, G\'omez, Lind and Tillmann. We use the work of Lawson on unitary deformation ... More
A Feynman-Kac Formula for Unbounded SemigroupsJul 27 1999We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x) that obey (for all \epsilon > 0): V(x) \geq - \epsilon |x|^2 - C_\epsilon. Even though e^{-tH} is an unbounded operator, any \phi, \psi \in L^2 with compact support lie in D(e^{-tH}) ... More
Impact of Theory Uncertainties on the Precision of the Top Quark Mass in a Threshold Scan at Future e+e- CollidersNov 10 2016Future energy-frontier electron-positron colliders will be capable of high-precision studies of top quark properties. The measurement of the top-pair production cross section around the threshold provides access to the mass of the top quark in theoretically ... More
Molecular Labor Division: Its Cause and ConsequenceDec 04 2007Aug 21 2011Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More
An Illustrated Introduction to the Basic Biological PrinciplesDec 13 2007Dec 14 2009Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More
Topological constraints in magnetic field relaxationMar 17 2013Stability and reconnection of magnetic fields play a fundamental role in natural and man-made plasma. In these applications the field's topology determines the stability of the magnetic field. Here I will describe the importance of one topology quantifier, ... More
Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous DiffusionOct 13 2016We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ ... More
Small deviations in p-variation for stable processesMay 31 2003Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and $\k = \k (\alpha, p)\in (0, +\infty)$ such that $$\lim_{\ee\downarrow 0}\ee^{\gamma}\log\pb\lcr ... More
VC-sets and generic compact dominationFeb 16 2015Jan 26 2016Let X be a closed subset of a locally compact second countable group G whose family of translates has finite VC-dimension. We show that the topological border of X has Haar measure 0. Under an extra technical hypothesis, this also holds if X is constructible. ... More
In defence of non-ontic accounts of quantum statesApr 30 2012Feb 07 2013The paper discusses objections against non-hidden variable versions of the epistemic conception of quantum states - the view that quantum states do not describe the properties of quantum systems but reflect, in some way to be specified, the epistemic ... More
Gauge symmetry breaking in gauge theories---In search of clarificationJul 23 2011Aug 05 2012The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions ... More
The intersection ring of matroidsFeb 23 2016Aug 30 2016We study a particular graded ring structure on the set of all loopfree matroids on a fixed labeled ground set, which occurs naturally in tropical geometry. The product is given by matroid intersection and the additive structure is defined by assigning ... More
Singularity categories of deformations of Kleinian singularitiesOct 26 2016Let $G$ be a finite subgroup of $\text{SL}(2,\Bbbk)$ and let $R = \Bbbk[x,y]^G$ be the coordinate ring of the corresponding Kleinian singularity. In 1998, Crawley-Boevey and Holland defined deformations $\mathcal{O}^\lambda$ of $R$ parametrised by weights ... More
A general asymptotic decay lemma for elliptic problemsJun 03 2008We prove a general asymptotic decay lemma which is applicable in various contexts. As an example, the general theorem is shown to give lower growth estimates for entire and exterior solutions of the minimal surface equation.
Minimal generating sets of non-modular invariant rings of finite groupsMar 01 2007Apr 12 2007It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very ... More
Multiplicative strong unimodality for positive stable lawsFeb 26 2010It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation for the multiplicative ... More
One-sided asymptotically mean stationary channelsMar 26 2014This paper proposes an analysis of asymptotically mean stationary (AMS) communication channels. A hierarchy based on stability properties (stationarity, quasi-stationarity, recurrence and asymptotically mean stationarity) of channels is identified. Stationary ... More
Optimal eigenvalues estimate for the Dirac operator on domains with boundaryMar 21 2006We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.
An application of continuous logic to fixed point theoryOct 18 2016Jan 25 2019In aiming to apply to a broader class of examples the Avigad-Iovino "ultraproducts and metastability" approach to obtaining uniformity for convergence of sequences, we construct a framework using continuous logic that in particular is able to handle discontinuous ... More
OPUC on One FootFeb 23 2005We present an expository introduction to orthogonal polynomials on the unit circle.
Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two PicturesNov 17 2004Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large $n$. Motivated by two plots, we look at the finer structure for the case of random Verblunsky coefficients and for what we call the ... More
Categorical semantics of metric spaces and continuous logicJan 25 2019Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this "continuous semantics" is equivalent to the a priori ... 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