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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 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

Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimatorApr 12 2019May 22 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

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

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

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

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

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

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

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 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

Restricted eigenvalue property for corrupted Gaussian designsMay 21 2018Nov 30 2018Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is suitable for ... 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

Emergence of a Dynamic Super-Structural Order Integrating Antiferroelectric and Antiferrodistortive Competing Instabilities in EuTiO3Jun 23 2012Microscopic structural instabilities of EuTiO3 single crystal were investigated by synchrotron x-ray diffraction. Antiferrodistortive (AFD) oxygen octahedral rotational order was observed alongside Ti derived antiferroelectric (AFE) distortions. The competition ... 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

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

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

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

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

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

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

Invariants of curves in RP^2 and R^2Feb 01 2006Jun 30 2009There is an elegant relation found by Fabricius-Bjerre [Math. Scand 40 (1977) 20--24] among the double tangent lines, crossings, inflections points, and cusps of a singular curve in the plane. We give a new generalization to singular curves in RP^2. We ... More

A Thermodynamic Definition of Topological Pressure for Non-Compact SetsJul 14 2008Feb 11 2010We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an equilibrium state. ... 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

Magnetic vortex dynamics in a 2D easy plane ferromagnetOct 16 2005In this thesis, we consider the dynamics of vortices in the easy plane insulating ferromagnet in two dimensions. In addition to the quasiparticle excitations, here spin waves or magnons, this magnetic system admits a family of vortex solutions carrying ... 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

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

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

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

Functional inequalities for Feynman-Kac semigroupsNov 08 2018Apr 15 2019Using the tools of 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 ... 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

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

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

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

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

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

Curves of equiharmonic solutions, and problems at resonanceSep 19 2016We consider the semilinear Dirichlet problem \[ \Delta u+kg(u)=\mu _1 \varphi _1+\cdots +\mu _n \varphi _n+e(x) \;\; \mbox{for $x \in \Omega$}, \;\; u=0 \;\; \mbox{on $\partial \Omega$}, \] where $\varphi _k$ is the $k$-th eigenfunction of the Laplacian ... More

Extending the Lambda Calculus to Express Randomized and Quantumized AlgorithmsDec 31 1996Jan 09 1997This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification of classical ... More

Regulation SimulationFeb 11 2010A deterministic trading strategy by a representative investor on a single market asset, which generates complex and realistic returns with its first four moments similar to the empirical values of European stock indices, is used to simulate the effects ... 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

Derivation of Quantum Theory from Feynman's RulesMar 14 2014Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most of the fundamental ... 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.

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

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.

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

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

Integrable systems associated with the Bruhat Poisson structuresFeb 26 2001Jun 26 2001The purpose of this note is to give a simple description of a (complete) family of functions in involution on certain hermitian symmetric spaces. This family, obtained via bi-hamiltonian approach using the Bruhat Poisson structure, is especially simple ... 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 remark on Pinney's equationFeb 07 2019We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.

Topology of the Stokes phenomenonMar 29 2019May 30 2019Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate category between ... 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

Contemporary Infinitesimalist Theories of Continua and their late 19th- and early 20th-century forerunnersAug 09 2018Dec 27 2018The purpose of this paper is to provide a historical overview of some of the contemporary infinitesimalist alternatives to the Cantor-Dedekind theory of continua. Among the theories we will consider are those that emerge from nonstandard analysis, nilpotent ... More

A Bijection Between the Adjoint and Coadjoint Orbits of a Semidirect ProductJun 21 2018Mar 25 2019We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgroups. We also show that under certain conditions the homotopy types of any ... More

The Slope of the Upper End of the IMF and the Upper Mass Limit: An Observer's PerspectiveAug 05 2010Aug 08 2010There are various ways of measuring the slope of the upper end of the IMF. Arguably the most direct of these is to place stars on the H-R diagram and compare their positions with stellar evolutionary models. Even so, the masses one infers from this depend ... More

Massive Stars in the Local Group: Star Formation and Stellar EvolutionJul 30 2003The galaxies of the Local Group that are currently forming stars can serve as our laboratories for understanding star formation and the evolution of massive stars. In this talk I will summarize what I think we've learned about these topics over the past ... More

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

Mottness: Identifying the Propagating Charge Modes in doped Mott InsulatorsJan 28 2010Mar 16 2010High-temperature superconductivity in the copper-oxide ceramics remains an unsolved problem because we do not know what the propagating degrees of freedom are in the normal state. As a result, we do not know what are the weakly interacting degrees of ... More

Origin of the Correspondence Rules of Quantum TheoryOct 13 2009Feb 14 2010To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the correspondence rules of ... More

An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum FormalismMay 19 2008In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few elementary features ... 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

Nonlinear elliptic equations and systems with linear part at resonanceMay 13 2016The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and no examples ... 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

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

Explicit solutions and multiplicity results for some equations with the $p$-LaplacianJun 24 2016We derive explicit ground state solutions for several equations with the $p$-Laplacian in $R^n$, including (here $\varphi (z)=z|z|^{p-2}$, with $p>1$) \[ \varphi \left(u'(r)\right)' +\frac{n-1}{r} \varphi \left(u'(r)\right)+u^M+u^Q=0 \,. \] The constant ... More

Hurwitz Theory of Elliptic Orbifolds, IISep 20 2018An elliptic orbifold is the quotient of an elliptic curve by a finite group. In 2001, Eskin and Okounkov proved that generating functions for the number of branched covers of an elliptic curve with specified ramification are quasimodular forms for $SL_2(\mathbb{Z}).$ ... More

Propagation and stability of flames in inhomogeneous mixturesFeb 07 2018We investigate the effect of thermal expansion and gravity on the propagation and stability of flames in inhomogeneous mixtures. We focus on laminar flames in the simple configuration of an infinitely long channel with rigid porous walls in order to understand ... 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

Diophantine Quadruples and Cayley's HyperdeterminantJul 28 2001Sep 09 2001A 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. Such Diophantine sets have been used to construct high rank elliptic curves. Here I demonstrate ... 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

Equivariant Motivic Homotopy TheoryDec 01 2013In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by Voevodsky and ... More

High magnification events by MOA in 2007May 13 2008Gravitational microlensing events of high magnification provide exceptional sensitivity to the presence of low-mass planets orbiting the lens star, including planets with masses as low as that of Earth. The essential requirement for the detection of such ... More

Detecting Earth-Like Extra-Solar Planets from Antarctica by Gravitational MicrolensingAug 29 2005Earth-like extra-solar planets may be detected with 1-2m class telescopes using the gravitational microlensing technique. The essential requirement is the ability to be able to carry out continuous observations of the galactic bulge. A telescope situated ... 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

2D ion crystals in radiofrequency traps for quantum simulationApr 28 2016Jul 01 2016The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. Experimental ion-trap quantum simulation is a promising approach for studying ... 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

Spin Flips: Variation in the Orientation of Dark Matter Halos over their Merger HistoriesDec 23 2009Semi-analytic models of galaxy formation typically form the spheroidal components of galaxies ("bulges"), solely through galactic major mergers. However, it is possible that non-merger events (e.g. a "fly-by" by a smaller halo) can perturb a galaxy--halo ... More

Quantum Mesh Dynamics (QMD)Jan 02 2019Mar 22 2019A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical inconsistencies, falsifiable ... 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

Newton's Hypotheses on the Structure of MatterJul 15 2018Aug 03 2018Isaac Newton's book 'Opticks' from the 18th century includes several hypotheses on the structure of matter. Most of the hypotheses were confirmed during the 19th and 20th centuries at the scale of atoms and molecules. Conflicts appear however with today's ... 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

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

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

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

Hölder Continuous Euler Flows in Three Dimensions with Compact Support in TimeNov 16 2012Feb 14 2014Building on the recent work of C. De Lellis and L. Sz\'{e}kelyhidi, we construct global weak solutions to the three-dimensional incompressible Euler equations which are zero outside of a finite time interval and have velocity in the H\"{o}lder class $C_{t,x}^{1/5 ... 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

A White Hole Model of the Big BangMar 04 1998A model of the universe as a very large white hole provides a useful alternative inhomogeneous theory to pit against the homogeneous standard FLRW big bang models. The white hole would have to be sufficiently large that we can fit comfortably inside the ... More