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On variance reduction for stochastic smooth convex optimization with multiplicative noiseMay 08 2017May 24 2017We propose dynamic sampled stochastic approximation (SA) methods for stochastic optimization with a heavy-tailed distribution (with finite 2nd moment). The objective is the sum of a smooth convex function with a convex regularizer. Typically, it is assumed ... More

Sample average approximation with heavier tails II: localization in stochastic convex optimization and persistence results for the LassoNov 13 2017Oct 07 2018We present exponential finite-sample nonasymptotic deviation inequalities for the SAA estimator's near-optimal solution set over the class of stochastic optimization problems with heavy-tailed random \emph{convex} functions in the objective and constraints. ... More

Sample average approximation with heavier tails I: non-asymptotic bounds with weak assumptions and stochastic constraintsMay 02 2017Oct 07 2018We derive exponential finite-sample nonasymptotic deviation inequalities for the sample average approximation (SAA) estimator's near-optimal solution set and optimal value. In that respect, we give three contributions. First, our bounds do not require ... More

Stable pair compactification of moduli of K3 surfaces of degree 2Mar 23 2019We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces ... More

Stable pair compactification of moduli of K3 surfaces of degree 2Mar 23 2019Apr 16 2019We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces ... More

Incremental constraint projection methods for monotone stochastic variational inequalitiesMar 01 2017Mar 02 2017We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines stochastic approximation ... More

Tukey's transformational ladder for portfolio managementMar 19 2016Aug 06 2017Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted Standard and Poor's ... More

Portfolio Selection: The Power of Equal WeightFeb 02 2016Aug 07 2017We empirically show the superiority of the equally weighted S\&P 500 portfolio over Sharpe's market capitalization weighted S\&P 500 portfolio. We proceed to consider the MaxMedian rule, a non-proprietary rule designed for the investor who wishes to do ... More

Variance-based stochastic extragradient methods with line search for stochastic variational inequalitiesMar 01 2017Aug 24 2017A dynamic sampled stochastic approximated (DS-SA) extragradient method for stochastic variational inequalities (SVI) is proposed that is \emph{robust} with respect to an unknown Lipschitz constant $L$. To the best of our knowledge, it is the first provably ... More

Interference between independent photonic integrated devices for quantum key distributionJan 17 2019Advances in quantum computing are a rapidly growing threat towards modern cryptography. Quantum key distribution (QKD) provides long-term security without assuming the computational power of an adversary. However, inconsistencies between theory and experiment ... More

Extragradient method with variance reduction for stochastic variational inequalitiesMar 01 2017We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an unbounded feasible set, unbounded operator, ... More

Reanalysis of bubble chamber measurements of muon-neutrino induced single pion productionNov 17 2014There exists a longstanding disagreement between bubble chamber measurements of the single pion production channel $\nu_{\mu}p\rightarrow \mu^{-}p\pi^{+}$ from the Argonne and Brookhaven National Laboratories. We digitize and reanalyse data from both ... More

Sample average approximation with heavier tails I: non-asymptotic bounds with weak assumptions and stochastic constraintsMay 02 2017Nov 13 2017We give statistical guarantees for the sample average approximation (SAA) of stochastic optimization problems. Precisely, we derive exponential non-asymptotic finite-sample deviation inequalities for the approximate optimal solutions and optimal value ... More

Sample average approximation with heavier tails II: localization in stochastic convex optimization and persistence results for the LassoNov 13 2017We present exponential finite-sample nonasymptotic deviation inequalities for the SAA estimator's near-optimal solution set over the class of \emph{convex} stochastic optimization problems with heavy-tailed random H\"older continuous functions in the ... More

Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimatorApr 12 2019We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\ell_1$-penalized Huber's ... More

A SOI Integrated Quantum Random Number Generator Based on Phase fluctuations from a Laser DiodeApr 13 2018Random numbers are a fundamental resource in science and technology. Among the different approaches to generating them, random numbers created by exploiting the laws of quantum mechanics have proven to be reliable and can be produced at enough rates for ... More

Tukey's Transformational Ladder for Portfolio ManagementMar 19 2016May 23 2016Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted Standard and Poor's ... More

Portfolio Selection: The Power of Equal WeightFeb 02 2016Feb 08 2016We empirically show the power of the equally weighted S&P 500 portfolio over Sharpe's market capitalization weighted S&P 500 portfolio. We proceed to consider the MaxMedian rule, a nonproprietary rule which was designed for the investor who wishes to ... More

The Robustness of Cosmological Hydrodynamic Simulation Predictions to Changes in Numerics and Cooling PhysicsOct 30 2018We test and improve the numerical schemes in our smoothed particle hydrodynamics (SPH) code for cosmological simulations, including the pressure-entropy formulation (PESPH), a time-dependent artificial viscosity, a refined timestep criterion, and metal-line ... More

Magnetar Spindown, Hyper-Energetic Supernovae, and Gamma Ray BurstsJan 26 2004The Kelvin-Helmholtz cooling epoch, lasting tens of seconds after the birth of a neutron star in a successful core-collapse supernova, is accompanied by a neutrino-driven wind. For magnetar-strength ($\sim10^{15}$ G) large scale surface magnetic fields, ... More

An On-chip Homodyne Detector for Measuring Quantum States and Generating Random NumbersDec 14 2016Optical homodyne detection has found use in a range of quantum technologies as both a characterisation tool and as a way to post-selectively generate non-linearities. So far optical implementations have been limited to bulk optics. Here we present the ... More

The Small Scatter in BH-Host Correlations & The Case for Self-Regulated BH GrowthMar 23 2009Sep 10 2009Supermassive black holes (BHs) obey tight scaling relations between their mass and their host galaxy properties such as total stellar mass, velocity dispersion, and potential well depth. This has led to the development of self-regulated models for BH ... More

Solar and Stellar Activity: Diagnostics and IndicesJan 23 2012Jan 27 2012We summarize the fifty-year concerted effort to place the "activity" of the Sun in the context of the stars. As a working definition of solar activity in the context of stars, we adopt those globally-observable variations on time scales below thermal ... More

Functional inequalities for Feynman-Kac semigroupsNov 08 2018Using stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman-Kac semigroups with possibly unbounded potentials. One of the main results is a derivative formula which can be used to characterize a lower bound on Ricci ... More

Normaloid Weighted Composition Operators on $H^2$Nov 26 2017Jul 26 2018When \ph\ is an analytic self-map of the unit disk with Denjoy-Wolff point $a \in \D$, and $\rho(\W) = \psi(a)$, we give an exact characterization for when \W\ is normaloid. We also determine the spectral radius, essential spectral radius, and essential ... More

Astrophysics of the Soft Gamma Repeaters and Anomalous X-Ray PulsarsOct 02 2000I summarize the recent advances in our understanding of the Soft Gamma Repeaters: in particular their spin behavior, persistent emission and hyper-Eddington outbursts. The giant flares on 5 March 1979 and 27 August 1998 provide compelling physical evidence ... More

The spectrum of large unitarily invariant models with increasingly many spikesMar 29 2019Apr 02 2019In this paper we study random matrix models where the matrices in question contain infinitely many spikes. Recent work has characterized the possible outliers in the spectrum of large deformed unitarily invariant models when the number of spikes in the ... More

The Sum of Four Squares Over Real Quadratic Number FieldsOct 21 2016May 23 2018Well-known results of Lagrange and Jacobi prove that the every $m \in \mathbb N$ can be expressed as a sum of four integer squares, and the number $r(m)$ of such representations can be given by an explicit formula in $m$. In this paper, we prove that ... More

Degenerations of K3 Surfaces of Degree TwoOct 28 2010Dec 19 2011We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every fibre to either ... More

Explicit Models for Threefolds Fibred by K3 Surfaces of Degree TwoJan 25 2011Aug 17 2012We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative ... More

Electrodynamics of Magnetars IV: Self-Consistent Model of the Inner Accelerator, with Implications for Pulsed Radio EmissionFeb 19 2008We consider the voltage structure in the open-field circuit and outer magnetosphere of a magnetar. The standard polar-cap model for radio pulsars is modified significantly when the polar magnetic field exceeds 1.8x10^{14} G. Pairs are created by accelerated ... More

Detecting Cross-Lingual Plagiarism Using Simulated Word EmbeddingsDec 29 2017Jan 03 2018Cross-lingual plagiarism (CLP) occurs when texts written in one language are translated into a different language and used without acknowledging the original sources. One of the most common methods for detecting CLP requires online machine translators ... More

Khovanov complexes of rational tanglesJan 26 2017Dec 12 2018We show that the Khovanov complex of a rational tangle has a very simple representative whose backbone of non-zero morphisms forms a zig-zag. Furthermore, this minimal complex can be computed quickly by an inductive algorithm. (For example, we calculate ... More

Finding geodesics in a triangulated 2-sphereAug 25 2014Sep 09 2014Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be unstable, corresponding, ... More

Some Graftings of Complex Projective Structures with Schottky HolonomyDec 10 2010Jan 27 2013Let $\mathcal{G}^*(S,\rho)$ be the graph whose vertices are marked complex projective structures with holonomy $\rho$ and whose edges are graftings from one vertex to another. If $\rho$ is quasi-Fuchsian, a theorem of Goldman implies that $\mathcal{G}^*(S,\rho)$ ... More

An Unstable Change of Rings for Morava E-TheorySep 12 2014Mar 16 2018The Bousfield-Kan (or unstable Adams) spectral sequence can be constructed for various homology theories such as Brown-Peterson homology theory BP, Johnson-Wilson theory $E(n)$, or Morava $E$-theory $E_n$. For nice spaces the $E_2$-term is given by Ext ... More

The rate of escape of random walks on polycyclic and metabelian groupsOct 05 2010Sep 13 2011We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger ... More

A generalisation of Dickson's commutative division algebrasFeb 28 2019Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not restricting us to the ... More

Tori and Heegaard splittingsMar 27 2016Haken showed that the Heegaard splittings of reducible 3-manifolds are reducible, that is, a reducing 2-sphere can be found which intersects the Heegaard surface in a single simple closed curve. When the genus of the "interesting" surface increases from ... More

Dehn surgery on complicated fibered knots in the 3-sphereApr 17 2016Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K is sufficiently complicated, then Dehn surgery on K cannot yield a lens space. Work of Yi Ni shows that if K has a lens space surgery then it is fibered. Combining this with our ... More

MUFASA: Galaxy Formation Simulations With Meshless HydrodynamicsApr 05 2016Aug 04 2016We present the MUFASA suite of cosmological hydrodynamic simulations, which employs the GIZMO meshless finite mass (MFM) code including H2-based star formation, nine-element chemical evolution, two-phase kinetic outflows following scalings from the Feedback ... More

A Maximum Stellar Surface Density in Dense Stellar SystemsAug 27 2009Oct 23 2009We compile observations of the surface mass density profiles of dense stellar systems, including globular clusters in the Milky Way and nearby galaxies, massive star clusters in nearby starbursts, nuclear star clusters in dwarf spheroidals and late-type ... More

Shock Breakout in Core-Collapse Supernovae and its Neutrino SignatureNov 10 2002Apr 02 2003(Abridged) We present results from dynamical models of core-collapse supernovae in one spatial dimension, employing a newly-developed Boltzmann neutrino radiation transport algorithm, coupled to Lagrangean hydrodynamics and a consistent high-density nuclear ... More

Spectral Signatures of KiloHertz Quasi-Periodic Oscillations from Accreting Neutron StarsAug 28 2000Correlations discovered between millisecond timing properties and spectral properties in neutron star x-ray binaries are described and then interpreted in relation to accretion flows in the systems. Use of joint timing and spectral observations to test ... More

A Chandra High-Resolution Camera Observation of X-Ray Point Sources in M31Jun 21 2002We present results from a 47 ks observation of the Andromeda galaxy, M31, using the High-Resolution Camera of the Chandra X-Ray Observatory. We detect 142 point sources spanning three orders of magnitude in luminosity, from $L_X = 2\times 10^{35} \rm ... More

Chandra X-Ray Point Sources, including Supernova 1979C, in the Spiral Galaxy M100Jun 29 2001Six x-ray point sources, with luminosities of $4 \times 10^{38} - 2 \times 10^{39} \rm ergs s^{-1}$ in the 0.4--7 keV band, were detected in Chandra observations of the spiral galaxy M100. One source is identified with supernova SN 1979C and appears to ... More

Pulsar Radiation and Quantum GravityMar 30 1999Quantum gravity may lead to an energy dependence in the speed of light. The high energy radiation from gamma-ray pulsars can be used to place limits on such effects. We find that emission from the Crab pulsar at energies above 2 GeV trails that at 70-100 ... More

The Unidentified Galactic EGRET SourcesAug 01 1996The nature of the unidentified gamma-ray point sources in the galactic plane is a long standing puzzle of gamma-ray astronomy. Kaaret and Cottam (1996) showed that 16 of the 25 unidentified gamma-ray point sources near the galactic plane lie in or near ... More

Global solution curves for self-similar equationsOct 17 2016We consider positive solutions of a semilinear Dirichlet problem \[ \Delta u+\lambda f(u)=0, \;\; \mbox{for $|x|<1$}, \;\; u=0 , \;\; \mbox{when $|x|=1$} \] on a unit ball in $R^n$. For four classes of self-similar equations it is possible to parameterize ... More

Regularity in time along the coarse scale flow for the incompressible Euler equationsJul 02 2013Nov 18 2015One of the most remarkable features of known nonstationary solutions to the incompressible Euler equations is the phenomenon that coarse scale averages of the velocity carry the fine scale features of the flow. In this paper, we study time-regularity ... More

A Lower Bound for Primality of Finite LanguagesFeb 17 2019A regular language $L$ is said to be prime, if it is not the product of two non-trivial languages. Martens et al. settled the exact complexity of deciding primality for deterministic finite automata in 2010. For finite languages, Mateescu et al. and Wieczorek ... More

A note on Lagrangian loci of quotientsMar 26 2003Mar 15 2004We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding ... More

How Stands Collapse IINov 20 2006Oct 29 2007I review ten problems associated with the dynamical wave function collapse program, which were described in the first of these two papers. Five of these, the \textit{interaction, preferred basis, trigger, symmetry} and \textit{superluminal} problems, ... More

Relativistic Collapse Model With Tachyonic FeaturesFeb 10 1999A finite relativistic model for free particles, which describes the collapse of the statevector, is presented.

True Collapse and False CollapseMay 17 1998We emphasize that standard quantum theory (SQT) is incomplete because it doesn't describe what is experimentally observed, namely events, nor does it satisfactorily define the circumstances under which events may occur. Simple models are given (all of ... More

A Relativistic Dynamical Collapse ModelDec 21 2014A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schr\"odinger picture wave function depends upon space and time coordinates for each particle, as well as an inexorably ... More

Zeon Algebra, Fock Space, and Markov ChainsNov 11 2007Fock spaces over zeons are introduced. Trace identities and a noncommutative "integration-by-parts" formula are developed. As an application, we find a new criterion, without involving powers of the transition matrix, for a Markov chain to be ergodic. ... More

Countable Random Sets: Uniqueness in Law and ConstructivenessJun 27 2012Jul 23 2012The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two approaches on uniqueness ... More

General tax structures for a Lévy insurance risk process under the Cramér conditionJun 16 2018We investigate the Levy insurance risk model with tax under Cram\'er's condition. A direct analogue of Cram\'er's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin occurring, ... More

A Roadmap to Interstellar FlightApr 05 2016Oct 31 2016In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with ... More

Wild Character Varieties, points on the Riemann sphere and Calabi's examplesJan 05 2015Jul 19 2016We will give several descriptions of some basic examples of wild character varieties, including a discussion of links to work of Sibuya, Calabi and Euler, amongst others.

X-Ray PolarimetryAug 25 2014Jan 08 2016We review the basic principles of X-ray polarimetry and current detector technologies based on the photoelectric effect, Bragg reflection, and Compton scattering. Recent technological advances in high-spatial-resolution gas-filled X-ray detectors have ... More

A Generalised Stern-Brocot Tree from Regular Diophantine QuadruplesMar 06 1999Diophantine quadruples are sets of four distinct positive integers such that the product of any two is one less than a square. All known examples belong to an infinite set which can be constructed recursively. Some observations on these regular solutions ... More

Some Rational Diophantine SextuplesFeb 13 1999A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six such numbers are presented and the computational algorithm used to find them ... More

Synchrotron-radiation studies of topological insulatorsOct 09 2012Jun 28 2013Topological insulators (TIs) are a recently discovered class of quantum materials that are currently attracting considerable attention. The most interesting aspect of the TIs is, in fact, not that they are bulk insulators but that their surfaces support ... More

Completely Quantized Collapse and ConsequencesJun 21 2005Promotion of quantum theory from a theory of measurement to a theory of reality requires an unambiguous specification of the ensemble of realizable states (and each state's probability of realization). Although not yet achieved within the framework of ... More

Wavefunction Collapse and Conservation LawsApr 17 2000Jun 06 2000It is emphasized that the collapse postulate of standard quantum theory can violate conservation of energy-momentum and there is no indication from where the energy-momentum comes or to where it goes. Likewise, in the Continuous Spontaneous Localization ... More

Krawtchouk-Griffiths Systems II: As Bernoulli SystemsDec 02 2016We call Krawtchouk-Griffiths systems, KG-systems, systems of multivariate polynomials orthogonal with respect to corresponding multinomial distributions. The original Krawtchouk polynomials are orthogonal with respect to a binomial distribution. Here ... More

Families of solution curves for some non-autonomous problemsMay 05 2016The paper studies families of positive solution curves for non-autonomous two-point problems \[ u"+\lambda f(u)-\mu g(x)=0, \;\; -1<x<1, \;\; u(-1)=u(1)=0 \] depending on two positive parameters $\lambda$ and $\mu$. We regard $\lambda$ as a primary parameter, ... More

On estimating the alphabet size of a discrete random sourceNov 20 2017We are concerned with estimating alphabet size $N$ from a stream of symbols taken uniformly at random from that alphabet. We define and analyze a memory-restricted variant of an algorithm that have been earlier proposed for this purpose. The alphabet ... More

Varieties with Ample Tangent SheavesApr 01 2017Sep 23 2017This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic to the complex ... More

Strict Local Martingales with JumpsJul 09 2013Mar 25 2014A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, ... More

Parallel Strands: A Preliminary Investigation into Mining the Web for Bilingual TextAug 07 1998Parallel corpora are a valuable resource for machine translation, but at present their availability and utility is limited by genre- and domain-specificity, licensing restrictions, and the basic difficulty of locating parallel texts in all but the most ... More

Evaluating Multilingual Gisting of Web PagesApr 07 1997We describe a prototype system for multilingual gisting of Web pages, and present an evaluation methodology based on the notion of gisting as decision support. This evaluation paradigm is straightforward, rigorous, permits fair comparison of alternative ... More

A Census of Massive Stars Across the Hertzsprung-Russell Diagram of Nearby Galaxies: What We Know and What We Don'tMar 02 2009Sep 21 2009When we look at a nearby galaxy, we see a mixture of foreground stars and bona fide extragalactic stars. I will describe what we need to do to get meaningful statistics on the massive star populations across the H-R diagram. Such a census provides the ... More

A UBVR CCD Survey of the Magellanic CloudsOct 24 2001We present photometry and a preliminary interpretation of a UBVR survey of the Large and Small Magellanic Clouds. We determine improved values for the relative number of blue and red supergiants. We also compare the relative number of Red Supergiants ... More

Extending cosmological tests of General Relativity with the Square Kilometre ArraySep 24 2015Jan 22 2016Tests of general relativity (GR) are still in their infancy on cosmological scales, but forthcoming experiments promise to greatly improve their precision over a wide range of distance scales and redshifts. One such experiment, the Square Kilometre Array ... More

A quarter century of astrophysics with JapanOct 19 2015On February 23 1987 a supernova (exploding star) was observed in the Large Cloud of Magellan, the brightest supernova in 400 years. It spurred the commencement of collaborative research in astrophysics between Japan and New Zealand that is still ongoing ... More

Electro-strong interaction and high Q^2 events at HERAMar 14 2001Jun 06 2002A previously proposed unified field theory of electro-strong interactions requires two scales of length within hadrons, $\sim10^{-15}m$ and $\sim10^{-18}m$ respectively, and the onset of new phenomena at the shorter scale. Studies at the HERA electron-proton ... More

Irreducibility of Polynomials over Number Fields is DiophantineJan 28 2016Mar 10 2016Given a number field $K$ and a positive integer $n$, we present a diophantine criterion for a polynomial in one variable of degree $n$ over $K$ not to have any root in $K$. This strengthens the known result that the set of non-$n$-th-powers in $K$ is ... More

Physics of the Pseudogap State: Spin-Charge LockingApr 18 2005The properties of the pseudogap phase above Tc of the high-Tc cuprate superconductors are described by showing that the Anderson-Nambu SU(2) spinors of an RVB spin gap 'lock' to those of the electron charge system because of the resulting improvement ... More

New Measurements of DNA Twist ElasticityAug 14 1997The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally-constrained single molecules give the first direct measurement of this new material ... More

Sequence Effects on DNA Entropic ElasticityNov 26 1997DNA stretching experiments are usually interpreted using the worm-like chain model; the persistence length A appearing in the model is then interpreted as the elastic stiffness of the double helix. In fact the persistence length obtained by this method ... More

Closed Unbounded classes and the Haertig Quantifier ModelMar 06 2019We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q$, $\langle L[P],\in ,P \rangle$ and $\langle L[Q],\in ... More

Global solution curves for several classes of singular periodic problemsMar 23 2016Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for three classes of periodically forced equations with singularities, including the equations arising in micro-electro-mechanical ... More

Dynamics of two-dimensional time-periodic Euler fluid flowsOct 05 2003This paper investigates the dynamics of time-periodic Euler flows in multi-connected, planar fluid regions which are ``stirred'' by the moving boundaries. The classical Helmholtz theorem on the transport of vorticity implies that if the initial vorticity ... More

Ultraproducts as a tool for first-order inexpressibility in the finite and infiniteOct 11 2013Ultraproducts are a well-known tool in the classical model theory of first-order logic. We explore their uses in the context of finite model theory.

On the local structure of doubly laced crystalsMar 22 2006Oct 14 2006Let $\mathfrak{g}$ be a Lie algebra all of whose regular subalgebras of rank 2 are type $A_{1}\times A_{1}$, $A_{2}$, or $C_{2}$, and let $B$ be a crystal graph corresponding to a representation of $\mathfrak{g}$. We explicitly describe the local structure ... More

Applications of Crystal Bases to Current Problems in Representation TheoryOct 24 2006Nov 30 2006This dissertation addresses several current problems in Representation Theory using crystal bases. It incorporates the results of arXiv:math.QA/0408113 and arXiv:math.RT/0603547, as well as previously unpublished results.

Relativistic Dynamical Collapse Model for a Scalar FieldApr 20 2014Apr 26 2014A natural generalization of the CSL (Continuous Spontaneous Localization) theory of dynamical collapse is applied to a relativistic quantum scalar field $\phi({\bf x},t)$. It is shown that the modified Schr\"odinger equation is relativistically invariant, ... More

Chronogenesis, Cosmogenesis and CollapseAug 13 2012A simple quantum model describing the onset of time is presented. This is combined with a simple quantum model of the onset of space. A major purpose is to explore the interpretational issues which arise. The state vector is a superposition of states ... More

Stress Tensor for Quantized Random Field and Wave Function CollapseApr 22 2008Aug 13 2008The continuous spontaneous localization (CSL) theory of dynamical wave function collapse is an experimentally testable alternative to non-relativistic quantum mechanics. In it, collapse occurs because particles interact with a classical random field. ... More

Dynamical Wave Function Collapse: Could It Have Cosmological Consequences?Oct 02 2007This talk was in response to the conference injunction to present "one bold but half-baked idea that you have been thinking about recently.. .". After a brief introduction to the ideas and formalism of the CSL theory of dynamical wave function collapse, ... More

How Stands Collapse INov 20 2006In this volume in honor of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo ... More

Book Review of Stephen L. Adler's, "Quantum theory as an emergent phenomenon."Feb 07 2006In Stephen Adler's book, "Quantum theory as an emergent phenomenon," the author starts from a classical mechanics structure and "derives" the formalism of quantum theory, together with wave function collapse dynamics, the latter providing the interpretation ... More

Tales and Tails and Stuff and NonsenseMay 17 1998In an informal way I review collapse models and my part in constructing them, and I recall some encounters with Abner Shimony. In particular, I address the question of the nature of spacetime reality in collapse models, stimulated by Abner's criticism ... More

The fifty-two icosahedral solutions to Painleve VIJun 14 2004Jun 10 2005The solutions of the (nonlinear) Painleve VI differential equation having icosahedral linear monodromy group will be classified up to equivalence under Okamoto's affine F4 Weyl group action and many properties of the solutions will be given. There are ... More

A Proof of Looijenga's Conjecture via Integral-affine GeometrySep 26 2014A cusp singularity is an elliptic surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. In 1981, Looijenga proved that whenever a cusp singularity is smoothable, ... More

SAX J1808.4-3658 and the origin of X-ray variability in X-ray binaries and active galactic nucleiNov 19 2003The aperiodic X-ray variability in neutron star and black hole X-ray binaries (XRBs), and active galactic nuclei (AGN) shows a characteristic linear relationship between rms amplitude and flux, implying a multiplying-together or `coupling' of variability ... More

A New Slant on Lebesgue's Universal Covering ProblemJan 29 2014Feb 19 2014Lebesgue's universal covering problem is re-examined using computational methods. This leads to conjectures about the nature of the solution which if correct could provide a blueprint for a complete solution. Empirical lower bounds for the minimal area ... More