Results for "Jeffrey Cummings"

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A Novel Approach to Constrain Rotational Mixing & Convective-Core Overshoot in Stars Using the Initial-Final Mass RelationJan 09 2019The semi-empirical initial-final mass relation (IFMR) connects spectroscopically analyzed white dwarfs in star clusters to the initial masses of the stars that formed them. Most current stellar evolution models, however, predict that stars will evolve ... More
Uncovering Multiple Populations in NGC 7099 (M 30) using Washington PhotometrySep 04 2017Over the last decade, the classical definition of Globular Clusters (GCs) as simple stellar populations was revolutionized due to the discovery of "Multiple Populations" (MPs). However, our knowledge of this phenomenon and its characteristics is still ... More
Magnetic Field Evolution During Neutron Star RecyclingApr 27 2004I describe work on two aspects of magnetic field evolution relevant for the "recycling" scenario for making millisecond radio pulsars. First, many of the theoretical ideas for bringing about accretion-induced field decay rely on dissipation of currents ... More
Detectability of Extrasolar Planets in Radial Velocity SurveysAug 25 2004Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long periods and low ... More
The delayed evolution of high-mass white dwarfs: the Q branch and double-white-dwarf mergersMay 29 2019Jun 07 2019Studying high-mass white dwarfs (WDs) can shed light on the progenitors of Type Ia supernovae. Recently, the unprecedented power of Gaia Data Release 2 (DR2) has revealed an enhancement of high-mass WDs on the H-R diagram, called the Q branch. This branch ... More
The delayed evolution of high-mass white dwarfs: the Q branch and double-white-dwarf mergersMay 29 2019Studying high-mass white dwarfs (WDs) can shed light on the progenitors of Type Ia supernovae. Recently, the unprecedented power of Gaia Data Release 2 (DR2) has revealed an enhancement of high-mass WDs on the H-R diagram, called the Q branch. This branch ... More
Multiple Populations in NGC 1851: Abundance Variations and UV Photometric Synthesis in the Washington and HST/WFC3 SystemsApr 07 2017The analysis of multiple populations (MPs) in globular clusters, both spectroscopically and photometrically, is key in understanding their formation and evolution. The relatively narrow Johnson U, F336W, and Stromgren and Sloan u filters have been crucial ... More
Improved Main Sequence Turnoff Ages of Young Open Clusters: Multicolor UBV Techniques & the Challenges of RotationJul 27 2018Main sequence turnoff ages in young open clusters are complicated by turnoffs that are sparse, have high binarity fractions, can be affected by differential reddening, and typically include a number of peculiar stars. Furthermore, stellar rotation can ... More
Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud: III. Horizontal Branch MorphologyDec 29 2017We leverage new high-quality data from Hubble Space Telescope program GO-14164 to explore the variation in horizontal branch morphology among globular clusters in the Large Magellanic Cloud (LMC). Our new observations lead to photometry with a precision ... More
On Pattern and EvolutionApr 20 2009May 10 2009A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss curvature'K'enters. ... More
Helium-rich thermonuclear bursts and the distance to the accretion-powered millisecond pulsar SAX J1808.4-3658Jul 11 2006We analysed Rossi X-ray Timing Explorer observations of the accretion-powered 401 Hz pulsar SAX J1808.4-3658, in order to precisely determine the source distance. While the fluences for the five transient outbursts observed from 1996 were constant to ... More
Uncovering Multiple Populations with Washington Photometry: I. The Globular Cluster NGC 1851Jun 02 2014The analysis of multiple populations (MPs) in globular clusters (GCs) has become a forefront area of research in astronomy. Multiple red giant branches (RGBs), subgiant branches (SGBs), and even main sequences (MSs) have now been observed photometrically ... More
Ultrafilters on singular cardinals of uncountable cofinalityJul 26 2019We prove that consistently there is a singular cardinal $\kappa$ of uncountable cofinality such that $2^\kappa$ is weakly inaccessible, and every regular cardinal strictly between $\kappa$ and $2^\kappa$ is the character of some uniform ultrafilter on ... More
$^3$He Transport in the Sun and the Solar Neutrino ProblemAug 20 1996Recent solar neutrino experiments have shown that both $\phi(^8$B) and the neutrino flux ratio $\phi(^7$Be)/$\phi(^8$B) are substantially below their standard solar model values, leading some to discount the possibility of an astrophysical solution to ... More
TESS reveals that the nearby Pisces-Eridanus stellar stream is only 120 Myr oldMay 25 2019Pisces-Eridanus (Psc-Eri), a nearby ($d$ $\simeq$ 80-226 pc) stellar stream stretching across $\approx$120 degrees of the sky, was recently discovered with Gaia data. The stream was claimed to be $\approx$1 Gyr old, which would make it an exceptional ... More
A Massive Magnetic Helium Atmosphere White Dwarf Binary in a Young Star ClusterJun 11 2019We have searched the Gaia DR2 catalogue for previously unknown hot white dwarfs in the direction of young open star clusters. The aim of this experiment was to try and extend the initial-final mass relation (IFMR) to somewhat higher masses, potentially ... More
An Ultramassive 1.28 M$_\odot$ White Dwarf in NGC 2099Mar 01 2016With the Keck I Low-Resolution Imaging Spectrometer we have observed nine white dwarf candidates in the very rich open cluster NGC 2099 (M37). The spectroscopy shows seven to be DA white dwarfs, one to be a DB white dwarf, and one to be a DZ white dwarf. ... More
Initial-Final Mass Relation for 3 to 4 M$_\odot$ Progenitors of White Dwarfs from the Single Cluster NGC 2099May 25 2015We have expanded the sample of observed white dwarfs in the rich open cluster NGC 2099 (M37) with the Keck Low-Resolution Imaging Spectrometer. Of 20 white dwarf candidates, the spectroscopy shows 19 to be true white dwarfs with 14 of these having high ... More
WIYN Open Cluster Study. LXXV. Testing the Metallicity Dependence of Stellar Lithium Depletion Using Hyades-Aged Clusters. 1. Hyades & PraesepeFeb 13 2017WIYN/Hydra spectroscopy (at R~15,000) of the moderately metal-rich Praesepe and Hyades open clusters was used to study their main sequence (MS) iron ([Fe/H]) and lithium (A(Li)) abundances. Self-consistent [Fe/H] and Li analyses of these clusters of consistent ... More
Lithium Abundances of the Super-Metal-Rich Open Cluster NGC 6253Sep 25 2012High-resolution CTIO 4-m/HYDRA spectroscopy of the super-metal-rich open cluster NGC 6253 ([Fe/H]=+0.43+/-0.01) has been used to study the stellar lithium (Li) abundances near the cluster's turnoff. NGC 6253 greatly expands the range of [Fe/H] for clusters ... More
Rollercoasters and CaterpillarsJan 25 2018A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence, that is increasing or decreasing, has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as ... More
Two Massive White Dwarfs from NGC 2323 and the Initial-Final Mass Relation for Progenitors of 4 to 6.5 M$_\odot$Jan 12 2016We have observed a sample of 10 white dwarf candidates in the rich open cluster NGC 2323 (M50) with the Keck Low-Resolution Imaging Spectrometer. The spectroscopy shows eight to be DA white dwarfs, with six of these having high S/N appropriate for our ... More
The White Dwarf Initial-Final Mass Relation for Progenitor Stars From 0.85 to 7.5 M$_\odot$Sep 05 2018We present the initial-final mass relation (IFMR) based on the self-consistent analysis of Sirius B and 79 white dwarfs from 13 star clusters. We have also acquired additional signal on eight white dwarfs previously analyzed in the NGC 2099 cluster field, ... More
Magnetars: Time Evolution, Superfluid Properties, and Mechanism of Magnetic Field DecayJan 27 2004We calculate the coupled thermal evolution and magnetic field decay in relativistic model neutron stars threaded by superstrong magnetic fields (B > 10^{15} G). Our main goal is to evaluate how such ``magnetars'' evolve with time and how field decay modifies ... More
Worldtube conservation laws for the null-timelike evolution problemMay 17 2011I treat the worldtube constraints which arise in the null-timelike initial-boundary value problem for the Bondi-Sachs formulation of Einstein's equations. Boundary data on a worldtube and initial data on an outgoing null hypersurface determine the exterior ... More
Higgs boson mass from maximally nonlinear superconductive quantum gravityJul 31 2019Presented is a quantum gravity theory that is a quantum mechanical generalization of Einstein's vierbein field-based approach, where the classical metric tensor field is promoted to a quantum mechanical metric tensor field operator. The quantum gravity ... More
Categorified Algebra and Quantum MechanicsJan 19 2006Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding a combinatorial ... More
Deforming Representations of SL(2,R)Jan 20 2017The spherical principal series representations $\pi(\nu)$ of SL(2,$\mathbb R$) is a family of infinite dimensional representations parametrized by $\nu\in\mathbb C$. The representation $\pi(\nu)$ is irreducible unless $\nu$ is an odd integer, in which ... More
The Real Chevalley InvolutionMar 08 2012Feb 13 2014We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate ... More
An equivalence between two approaches to limits of local fieldsNov 18 2015Nov 20 2015Marc Krasner proposed a theory of limits of local fields in which one relates the extensions of a local field to the extensions of a sequence of related local fields. The key ingredient in his approach was the notion of valued hyperfields, which occur ... More
Lifting images of standard representations of symmetric groupsMar 14 2019May 02 2019We investigate closed subgroups $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$ whose modulo-$2$ images coincide with the image $\mathfrak{S}_{2g + 1} \subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g + 1}$ or the image $\mathfrak{S}_{2g + 2} \subseteq ... More
The diffeomorphism group of a K3 surface and Nielsen realizationMay 31 2007Nov 12 2017The Nielsen Realization problem asks when the group homomorphism from Diff(M) to pi_0 Diff(M) admits a section. For M a closed surface, Kerckhoff proved that a section exists over any finite subgroup, but Morita proved that if the genus is large enough ... More
More Examples of Pseudo-Collars on High-Dimensional ManifoldsApr 07 2018In a previous paper, we developed general techniques for constructing a variety of pseudo-collars, as defined by Guilbault and Tinsley, with roots in earlier work by Chapman and Siebenmann. As an application of our techniques, we exhibited an uncountable ... More
Small Seifert fibered surgery on hyperbolic pretzel knotsOct 29 2012Jul 23 2013We complete the classification of hyperbolic pretzel knots admitting Seifert fibered surgeries. This is the final step in understanding all exceptional surgeries on hyperbolic pretzel knots. We also present results toward similar classifications for non-pretzel ... More
Markov Chains, Tensor Products, and Quantum Random WalksDec 12 2012We provide two new constructions of Markov chains which had previously arisen from the representation theory of the infinite-dimensional unitary group. The first construction uses the combinatorial rule for the Littlewood-Richardson coefficients, which ... More
Disembodied boundary data for Einstein's equationsSep 10 2009Nov 12 2009A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld conditions have been ... More
A New Way to Make WavesMar 08 2000I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other systems described ... More
The characteristic treatment of black holesNov 26 1999The characteristic initial value problem has been implemented as a robust computational algorithm (the PITT NULL CODE), with direct application to binary black holes. The event horizon can be analyzed by characteristic techniques as a stand-alone object ... More
The six-point remainder function to all loop orders in the multi-Regge limitSep 24 2012We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric N=4 Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree with an integral ... More
The parametrized probabilistic finite-state transducer probe game player fingerprint modelJan 29 2014Fingerprinting operators generate functional signatures of game players and are useful for their automated analysis independent of representation or encoding. The theory for a fingerprinting operator which returns the length-weighted probability of a ... More
The diffeomorphism group of a K3 surface and Nielsen realizationMay 31 2007Jan 15 2009The Nielsen Realization problem asks when the group homomorphism from Diff(M) to pi_0 Diff(M) admits a section. For M a closed surface, Kerckhoff proved that a section exists over any finite subgroup, but Morita proved that if the genus is large enough ... More
Finite-dimensional spaces in resolving classesMay 03 2012Using the theory of resolving classes, we show that if $X$ is a CW complex of finite type such that $\map_*(X, S^{2n+1})\sim *$ for all sufficiently large $n$, then $\map_*(X, K) \sim *$ for every simply-connected finite-dimensional CW complex $K$; and ... More
Signalizers and balance in groups of finite Morley rankNov 27 2007Nov 28 2008We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has Prufer 2-rank at most two. This article covers the signalizer functor theory and identifies the groups of Lie rank at least ... More
Strong Homology, Derived Limits, and Set TheorySep 30 2015We consider the question of the additivity of strong homology. This entails isolating the set-theoretic content of the higher derived limits of an inverse system indexed by the functions from $\mathbb{N}$ to $\mathbb{N}$. We show that this system governs, ... More
Repulsive behavior in an exceptional familyAug 31 2011Mar 05 2012The existence of a Landau-Siegel zero leads to the Deuring-Heilbronn phenomenon, here appearing in the 1-level density in a family of quadratic twists of a fixed genus character L-function. We obtain explicit lower order terms describing the vertical ... More
Josephine: Using JavaScript to safely manage the lifetimes of Rust dataJun 29 2018This paper is about the interface between languages which use a garbage collector and those which use fancy types for safe manual memory management. Garbage collection is the traditional memory management scheme for functional languages, whereas type ... More
Hamming Distance for ConjugatesOct 05 2007Aug 15 2008Let x, y be strings of equal length. The Hamming distance h(x,y) between x and y is the number of positions in which x and y differ. If x is a cyclic shift of y, we say x and y are conjugates. We consider f(x,y), the Hamming distance between the conjugates ... More
Simultaneous avoidance of large squares and fractional powers in infinite binary wordsApr 29 2003In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where `4' is replaced ... More
How large is large? Estimating the critical disorder for the Anderson modelMay 30 2013Oct 17 2014Complete localization is shown to hold for the $d$-dimensional Anderson model with uniformly distributed random potentials provided the disorder strength $\lambda >\lambda_{And}$ where $\lambda_{\text{And}}$ satisfies $\lambda_{\text{And}}=\mu_d e \ln ... More
On the theorem of Conrey and IwaniecJul 02 2013An exposition on "Spacing of zeros of Hecke L-functions and the class number problem" by Conrey and Iwaniec; any errors are my own.
Computing $L$-functions with large conductorJun 05 2003May 05 2006An algorithm is given to efficiently compute $L$-functions with large conductor in a restricted range of the critical strip. Examples are included for about 21000 dihedral Galois representations with conductor near $10^7$. The data shows good agreement ... More
Extended TQFT's and Quantum GravitySep 29 2007This paper gives a definition of an extended topological quantum field theory (TQFT) as a weak 2-functor Z: nCob_2 -> 2Vect, by analogy with the description of a TQFT as a functor Z: nCob -> Vect. We also show how to obtain such a theory from any finite ... More
A Correction Note: Attractive Nearest Neighbor Spin Systems on the IntegersSep 19 2014In this note, we discuss a proof in T. Liggett's work on attractive translation invariant nearest neighbor spin systems on the integers. A correction to a wrong estimate is provided.
Dyadic torsion of 2-dimensional hyperelliptic JacobiansOct 29 2014Let $k$ be a field of characteristic $0$, and let $\alpha_{1}$, $\alpha_{2}$, ..., $\alpha_{5}$ be algebraically independent and transcendental over $k$. Let $K$ be the transcendental extension of $k$ obtained by adjoining the elementary symmetric functions ... More
Diffusion in the Mean for an Ergodic Schrödinger Equation Perturbed by a Fluctuating PotentialJun 19 2014May 14 2015Diffusive scaling of position moments and a central limit theorem are obtained for the mean position of a quantum particle hopping on a cubic lattice and subject to a random potential consisting of a large static part and a small part that fluctuates ... More
Distribution of Resonances in Scattering by Thin BarriersApr 14 2014Sep 14 2015We study high energy resonances for the operators $-\Delta +\delta_{\partial\Omega}\otimes V$ and $-\Delta+\delta_{\partial\Omega}'\otimes V\partial_\nu$ where $\Omega$ is strictly convex with smooth boundary, $V:L^2(\partial\Omega)\to L^2(\partial\Omega)$ ... More
Length of the continued logarithm algorithm on rational inputsJun 13 2016Jun 21 2016The continued logarithm algorithm was introduced by Gosper around 1978, and recently studied by Borwein, Calkin, Lindstrom, and Mattingly. In this note I show that the continued logarithm algorithm terminates in at most 2 log_2 p + O(1) steps on input ... More
Extension of valuations in characteristic oneMay 20 2016Aug 22 2016We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central results in the ... More
The Quantum Sabine Law for Resonances in Transmission ProblemsNov 16 2015We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering by transparent ... More
Obstruction criteria for modular deformation problemsSep 24 2014For a newform $f=\sum a_n q^n$ of weight $k \geq 3$ and a prime $\lambda$ of $\mathbf{Q}(a_n)$, the deformation problem for its associated mod $\lambda$ Galois representation is unobstructed for all primes outside some finite set. Previous results gave ... More
Boundary Conditions for the Gravitational FieldMar 09 2012Apr 24 2012A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation ... More
Geometrization of metric boundary data for Einstein's equationsApr 02 2009The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new formulation of ... More
Characteristic Evolution and MatchingOct 10 2008Jan 12 2012I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that ... More
An interacting particle system with geometric jump rates near a partially reflecting boundaryJan 20 2016This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the dynamics match ... More
Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank twoApr 27 2015May 22 2015We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that ... More
On the Relative Gain Array (RGA) with Singular and Rectangular MatricesMay 25 2018Mar 04 2019In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, we show that the conventional use of the Moore-Penrose pseudoinverse is ... More
The K-level crossings of a random algebraic polynomial with dependent coefficientsDec 21 2009For a random polynomial with standard normal coefficients, two cases of the K-level crossings have been considered by Farahmand. When the coefficients are independent, Farahmand was able to derive an asymptotic value for the expected number of level crossings, ... More
The real zeros of a random algebraic polynomial with dependent coefficientsJun 10 2009Jul 18 2010Mark Kac gave one of the first results analyzing random polynomial zeros. He considered the case of independent standard normal coefficients and was able to show that the expected number of real zeros for a degree n polynomial is on the order of (2/pi)log(n), ... More
Stark conjectures for CM curves over number fieldsAug 30 2001We present an elliptic curve analog of the Stark conjecture for the value of the $L$-function at $s=0$. Although implied by the general Beilinson conjectures, the approach here is very concrete. Several cases are proved.
Sylow 0-unipotent subgroups in groups of finite Morley rankNov 26 2007One of the central tools in the classification of simple algebraic groups is the distinction between semisimple subgroups and unipotent subgroups. It is not a priori clear how to make this distinction for torsion-free subgroups of a group of finite Morley ... More
A signalizer functor theorem for groups of finite Morley rankAug 06 2003There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik's trichotomy theorem. The "trichotomy" here is a case ... More
'Two Dogmas' ReduxJul 14 2019Jul 22 2019About ten years ago, Itamar Pitowsky and I wrote a paper, 'Two dogmas about quantum mechanics,' in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Here I revisit the paper ... More
Elementary Deuring-Heilbronn PhenomenonJan 03 2012Jul 02 2012Adapting a technique of Pintz, we give an elementary demonstration of the Deuring phenomenon: a zero of \zeta(s) off the critical line gives a lower bound on L(1,\chi). The necessary tools are Dirichlet's 'method of the hyperbola', Euler summation, summation ... More
Does Ten Have a Friend?Jun 05 2008Jun 06 2008Any positive integer $n$ other than 10 with abundancy index 9/5 must be a square with at least 6 distinct prime factors, the smallest being 5. Further, at least one of the prime factors must be congruent to 1 modulo 3 and appear with an exponent congruent ... More
Distinguished Cuspidal Representations over p-adic and Finite FieldsMar 26 2017May 12 2017The author's work with Murnaghan on distinguished tame supercuspidal representations is re-examined using a simplified treatment of Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups. This leads to a unification ... More
Stability of Critical p-Improper Interval GraphsMar 15 2019A $p$-improper interval graph is an interval graph that has an interval representation in which no interval contains more than $p$ other intervals. A critical $p$-improper interval graph is $p-1$ improper when any vertex is removed. In this paper we investigate ... More
Gromov-- Witten Invariants of Toric FibrationsJan 09 2009We prove a conjecture of Artur Elezi in a generalized form suggested by Givental. Namely, our main result relates genus-0 Gromov--Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric manifold. When the ... More
A Geometric Reverse To The Plus Construction And Some Examples Of Pseudo-Collars On High-Dimensional ManifoldsAug 14 2015In this paper, we develop a geometric procedure for producing a reverse to Quillen's plus construction, a construction called a 1-sided h-cobordism or semi-h-cobordism. We then use this reverse to the plus construction to produce uncountably many distinct ... More
The stable mapping class group of simply connected 4-manifoldsOct 27 2005Apr 10 2007We consider mapping class groups \Gamma(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains CP^2 (with either orientation) as a connected summand then ... More
Ideal triangulations and geometric transitionsMay 22 2013May 13 2014Thurston introduced a technique for finding and deforming three-dimensional hyperbolic structures by gluing together ideal tetrahedra. We generalize this technique to study families of geometric structures that transition from hyperbolic to anti de Sitter ... More
Time dilation relation for a Dirac Hamiltonian generator on a qubit arrayDec 08 2015Dec 13 2015Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum algorithm to model ... More
Images of 2-adic representations associated to hyperelliptic JacobiansOct 10 2014Let $k$ be a subfield of $\mathbb{C}$ which contains all $2$-power roots of unity, and let $K = k(\alpha_{1}, \alpha_{2}, ... , \alpha_{2g + 1})$, where the $\alpha_{i}$'s are independent and transcendental over $k$, and $g$ is a positive integer. We ... More
Global viscosity solutions of generalized Kahler-Ricci flowOct 06 2016We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth ... More
Characteristic Evolution and MatchingAug 23 2005Dec 08 2005I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations ... More
A Geometric transition from hyperbolic to anti de Sitter geometryFeb 22 2013We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe ... More
Quantum Correlations and the Measurement ProblemOct 23 2012Jan 14 2013The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. ... More
Trapping planar Brownian motion in a non circular trapOct 30 2016Nov 01 2016Brownian motion in the plane in the presence of a "trap" at which motion is stopped is shown. If the trap $T$ is a connected compact set, it is shown that the probability for planar Brownian motion to hit this set before a given time $t$ is well approximated ... More
Two constructions of Markov chains on the dual of U(n)Dec 12 2012Apr 09 2017We provide two new constructions of Markov chains which had previously arisen from the representation theory of the infinite-dimensional unitary group. The first construction uses the combinatorial rule for the Littlewood-Richardson coefficients, which ... More
Lifting images of standard representations of symmetric groupsMar 14 2019We investigate closed subgroups $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$ whose modulo-$2$ images coincide with the image $\mathfrak{S}_{2g + 1} \subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g + 1}$ or the image $\mathfrak{S}_{2g + 2} \subseteq ... More
A Scale-Consistent Approach for Recommender SystemsApr 30 2019In this paper we propose and develop a relatively simple and efficient approach for estimating unknown elements of a user-rating matrix in the context of a recommender system (RS). The critical theoretical property of the method is its consistency with ... More
Minimally intersecting filling pairs on the punctured surface of genus twoJul 19 2018In this short note, we construct a minimally intersecting pair of simple closed curves that fill a genus 2 surface with an odd, greater than 3, number of punctures. This finishes the determination of minimally intersecting filling pairs for all surfaces ... More
Galois Cohomology of Real GroupsOct 29 2013Jul 01 2014Real forms of a complex reductive group are classified in terms of Galois cohomology $H^1(\Gamma,G_{ad})$ where $G_{ad}$ is the adjoint group. Alternatively, the theory of the Cartan involution gives a description in terms of cohomology with respect to ... More
Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating MetricsNov 14 2003Jan 09 2004We consider a family of manifolds with a class of degenerating warped product metrics $g_\epsilon=\rho(\epsilon,t)^{2a}dt^2 +\rho(\epsilon,t)^{2b}ds_M^2$, with $M$ compact, $\rho$ homogeneous degree one, $a \le -1$ and $b > 0$. We study the Laplace operator ... More
The computational complexity of the local postage stamp problemDec 22 2001The well-studied local postage stamp problem (LPSP) is the following: given a positive integer k, a set of postive integers 1 = a1 < a2 < ... < ak and an integer h >= 1, what is the smallest positive integer which cannot be represented as a linear combination ... More
Notes on $\log(ζ(s))^{\prime\prime}$Nov 21 2013Dec 22 2014Motivated by the connection to the pair correlation of the Riemann zeros, we investigate the second derivative of the logarithm of the Riemann zeta function, in particular the zeros of this function. Theorem 1 gives a zero-free region. Theorem 2 gives ... More
Quivers and Three-Dimensional Lie AlgebrasSep 23 2014We study a family of three-dimensional Lie algebras $L_\mu$ that depend on a continuous parameter $\mu$. We introduce certain quivers, which we denote by $Q_{m,n}$ $(m,n \in \mathbb{Z})$ and $Q_{\infty \times \infty}$, and prove that idempotented versions ... More
A note on 8-division fields of elliptic curvesApr 20 2017Aug 02 2017Let $K$ be a field of characteristic different from $2$ and let $E$ be an elliptic curve over $K$, defined either by an equation of the form $y^{2} = f(x)$ with degree $3$ or as the Jacobian of a curve defined by an equation of the form $y^{2} = f(x)$ ... More
Constraints on neutron star mass and radius in GS 1826-24 from sub-Eddington X-ray burstsNov 01 2011Feb 07 2012We investigate the constraints on neutron star mass and radius in GS 1826-24 from models of lightcurves and spectral evolution of type I X-ray bursts. This source shows remarkable agreement with theoretical calculations of burst energies, recurrence times, ... More
Error Bounds for Approximations of Geometrically Ergodic Markov ChainsFeb 24 2017May 20 2017A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the true kernel is slow to evaluate. A relatively limited set of quantitative tools exist to determine whether the performance ... More
A Lattice-Gas with Long-Range Interactions Coupled to a Heat BathMar 18 1994Introduced is a lattice-gas with long-range 2-body interactions. An effective inter-particle force is mediated by momentum exchanges. There exists the possibility of having both attractive and repulsive interactions using finite impact parameter collisions. ... More