Results for "Charles L. Fefferman"

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Waves in Honeycomb StructuresDec 30 2012We review recent work of the authors on the non-relativistic Schr\"odinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V=-\Delta+V$ ... More
The Brenner-Hochster-Kollár and Whitney Problems for Vector-valued Functions and JetsSep 11 2012Sep 15 2012In this paper, we give analytic methods for finding m (and m+\omega) times continuously differentiable solutions of a finite system of linear equations. Along the way, we also solve a generalized Whitney problem for vector-valued functions and jets.
Honeycomb Lattice Potentials and Dirac PointsFeb 17 2012Jun 08 2012We prove that the two-dimensional Schroedinger operator with a potential having the symmetry of a honeycomb structure has dispersion surfaces with conical singularities (Dirac points) at the vertices of its Brillouin zone. No assumptions are made on the ... More
Non-conservation of dimension in divergence-free solutions of passive and active scalar systemsMay 14 2019For any $h\in(1,2]$, we give an explicit construction of a compactly supported, uniformly continuous, and (weakly) divergence-free velocity field in $\mathbb{R}^2$ that weakly advects a measure whose support is initially the origin but for positive times ... More
The Structure of Sobolev Extension OperatorsJun 09 2012Nov 12 2012Let $L^{m,p}(\R^n)$ denote the Sobolev space of functions whose $m$-th derivatives lie in $L^p(\R^n)$, and assume that $p>n$. For $E \subset \R^n$, denote by $L^{m,p}(E)$ the space of restrictions to $E$ of functions $F \in L^{m,p}(\R^n)$. It is known ... More
Edge states in honeycomb structuresJun 19 2015Sep 06 2016An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge states are edge ... More
Topologically Protected States in One-Dimensional SystemsMay 19 2014Apr 08 2015We study a class of periodic Schr\"odinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by ... More
Sobolev Extension By Linear OperatorsMay 11 2012May 21 2012Let $L^{m,p}(\R^n)$ be the Sobolev space of functions with $m^{th}$ derivatives lying in $L^p(\R^n)$. Assume that $n< p < \infty$. For $E \subset \R^n$, let $L^{m,p}(E)$ denote the space of restrictions to $E$ of functions in $L^{m,p}(\R^n)$. We show ... More
Simultaneous approximation in Lebesgue and Sobolev norms via eigenspacesApr 06 2019We show how to approximate functions defined on smooth bounded domains by elements of eigenspaces of linear operators (e.g. the Laplacian or the Stokes operator) in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue ... More
Defect modes for dislocated periodic mediaOct 13 2018We study defect modes in a one-dimensional periodic medium with a dislocation. The model is a periodic Schrodinger operator on $\mathbb{R}$, perturbed by an adiabatic dislocation of amplitude $\delta\ll 1$. If the periodic background admits a Dirac point ... More
Fitting a Sobolev function to dataNov 06 2014We exhibit an algorithm to solve the following extension problem: Given a finite set $E \subset \mathbb{R}^n$ and a function $f: E \rightarrow \mathbb{R}$, compute an extension $F$ in the Sobolev space $L^{m,p}(\mathbb{R}^n)$, $p>n$, with norm having ... More
Scalars convected by a 2D incompressible flowJan 30 2001We provide a test for numerical simulations, for several two dimensional incompressible flows, that appear to develop sharp fronts. We show that in order to have a front the velocity has to have uncontrolled velocity growth.
Sharp finiteness principles for Lipschitz selections: long versionAug 02 2017Oct 21 2017Let $({\mathcal M},\rho)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$, let $F$ be a set-valued mapping from ${\mathcal M}$ into the family of all compact convex subsets of $Y$ of dimension at most $m$. In this paper we ... More
Ambient metric construction of Q-curvature in conformal and CR geometriesMar 16 2003Aug 21 2003We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to a large class ... More
Growth of solutions for QG and 2D Euler equationsJan 30 2001We study the rate of growth of sharp fronts of the Quasi-geostrophic equation and 2D incompressible Euler equations.. The development of sharp fronts are due to a mechanism that piles up level sets very fast. Under a semi-uniform collapse, we obtain a ... More
Continuous linear combinations of polynomialsMar 04 2011We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
Sharp finiteness principles for Lipschitz selectionsDec 31 2017Aug 03 2018Let $(M,\rho)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$, let $F$ be a set-valued mapping from $M$ into the family of all compact convex subsets of $Y$ of dimension at most $m$. In this paper we prove a finiteness principle ... More
Juhl's Formulae for GJMS Operators and Q-CurvaturesMar 02 2012Direct proofs are given of Juhl's formulae for GJMS operators and Q-curvatures starting from the original construction of GJMS.
Solutions to A System of Equations for $C^m$ FunctionsFeb 11 2019Fix $m\geq 0$, and let $A=\left( A_{ij}\left( x\right) \right) _{1\leq i\leq N,1\leq j\leq M}$ be a matrix of semialgebraic functions on $\mathbb{R}^{n}$ or on a compact subset $E \subset \mathbb{R}^n$. Given $f=\left( f_{1},\cdots ,f_{N}\right) \in C^{\infty ... More
On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$Nov 10 2014Nov 26 2017Let $D\geq 2$, $S\subset \mathbb R^D$ be finite and let $\phi:S\to \mathbb R^D$ with $\phi$ a small distortion on $S$. We solve the Whitney extension-interpolation-alignment problem of how to understand when $\phi$ can be extended to a function $\Phi:\mathbb ... More
On Smooth Whitney Extensions of almost isometries with small distortion, Interpolation and Alignment in $\Bbb R^D$-Part 1Nov 10 2014Jan 13 2018In this paper, we study the following problem: Let $D\geq 2$ and let $E\subset \mathbb R^D$ be finite satisfying certain conditions. Suppose that we are given a map $\phi:E\to \mathbb R^D$ with $\phi$ a small distortion on $E$. How can one decide whether ... More
Q-Curvature and Poincare MetricsOct 24 2001This article presents a new definition of Branson's Q-curvature in even-dimensional conformal geometry. We derive the Q-curvature as a coefficient in the asymptotic expansion of the formal solution of a boundary problem at infinity for the Laplacian in ... More
Efficient Algorithms for Approximate Smooth SelectionMay 08 2019In this paper we provide efficient algorithms for approximate $\mathcal{C}^m(\mathbb{R}^n, \mathbb{R}^D)-$selection. In particular, given a set $E$, constants $M_0 > 0$ and $0 <\tau \leq \tau_{\max}$, and convex sets $K(x) \subset \mathbb{R}^D$ for $x ... More
Local existence for the non-resistive MHD equations in nearly optimal Sobolev spacesFeb 08 2016This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $\mathbb{R}^d$, $d=2,3$, with initial data $B_0\in H^s(\mathbb{R}^d)$ and $u_0\in H^{s-1+\varepsilon}(\mathbb{R}^d)$ ... More
Testing the Manifold HypothesisOct 01 2013Dec 19 2013The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning. The goal of this paper is to develop an algorithm (with accompanying complexity guarantees) for fitting a manifold to ... More
On the absence of "splash" singularities in the case of two-fluid interfacesDec 10 2013Dec 16 2013We show that "splash" singularities cannot develop in the case of locally smooth solutions of the two-fluid interface in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro-C\'{o}rdoba-Fefferman-Gancedo-G\'{o}mez-Serrano ... More
Finiteness Principles for Smooth SelectionNov 16 2015Nov 27 2015In this paper we prove finiteness principles for $C^{m}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, and for $C^{m-1,1}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, in particular providing a proof for a conjecture of Brudyni-Shvartsman ... More
Photonic realization of topologically protected bound states in domain-wall waveguide arraysFeb 12 2016Mar 11 2016We present an analytical theory of topologically protected photonic states for the two-dimensional Maxwell equations for a class of continuous periodic dielectric structures, modulated by a domain wall. We further numerically confirm the applicability ... More
Breakdown of smoothness for the Muskat problemJan 12 2012Jan 29 2012In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down i.e. no longer belongs to $C^4$.
Reconstruction and interpolation of manifolds I: The geometric Whitney problemAug 04 2015Nov 17 2018We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold reconstruction where a smooth $n$-dimensional submanifold $S\subset {\mathbb ... More
Reconstruction of a Riemannian manifold from noisy intrinsic distancesMay 17 2019We consider reconstruction of a manifold, or, invariant manifold learning, where a smooth Riemannian manifold $M$ is determined from intrinsic distances (that is, geodesic distances) of points in a discrete subset of $M$. In the studied problem the Riemannian ... More
Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structuresSep 29 2015This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional honeycomb structures. We consider a family of Schr\"odinger Hamiltonians consisting of a bulk honeycomb potential ... More
Finite time singularities for the free boundary incompressible Euler equationsDec 09 2011Sep 29 2012In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks down in finite ... More
Turning waves and breakdown for incompressible flowsNov 27 2010We consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by $(\al,f_0(\al))$, ... More
Rayleigh-Taylor breakdown for the Muskat problem with applications to water wavesFeb 09 2011Jun 10 2011The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially ... More
Splash singularity for water wavesJun 10 2011Oct 03 2011We exhibit smooth initial data for the 2D water wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water ... More
Symbolic calculus for Toeplitz operators with half-formsFeb 08 2006This paper is devoted to the use of half-form bundles in the symbolic calculus of Berezin-Toeplitz operators on Kahler manifolds. We state the Bohr-Sommerfeld conditions and relate them to the functional calculus of Toeplitz operators, a trace formula ... More
Higher order commutator estimates and local existence for the non-resistive MHD equations and related modelsJan 20 2014This paper establishes the local-in-time existence and uniqueness of strong solutions in $H^{s}$ for $s > n/2$ to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $\mathbb{R}^{n}$, $n=2, 3$, as well as for a related model where the advection ... More
Wave packets in Honeycomb Structures and Two-Dimensional Dirac EquationsDec 25 2012In a recent article [10], the authors proved that the non-relativistic Schr\"odinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located ... More
Quantum vs Classical Proofs and Subset VerificationOct 22 2015We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, ... More
Quantum Merlin Arthur with Exponentially Small GapJan 08 2016We study the complexity of QMA proof systems with inverse exponentially small promise gap. We show that this class can be exactly characterized by PSPACE, the class of problems solvable with a polynomial amount of memory. As applications we show that ... More
Counting Exceptional Points for Rational Numbers Associated to the Fibonacci SequenceJul 07 2016If $\alpha$ is a non-zero algebraic number, we let $m(\alpha)$ denote the Mahler measure of the minimal polynomial of $\alpha$ over $\mathbb Z$. A series of articles by Dubickas and Smyth, and later by the author, develop a modified version of the Mahler ... More
Estimating heights using auxiliary functionsAug 18 2014Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to problems involving ... More
Lower bounds on the projective heights of algebraic pointsAug 21 2014If $\alpha_1,\ldots,\alpha_r$ are algebraic numbers such that $$N=\sum_{i=1}^r\alpha_i \ne \sum_{i=1}^r\alpha_i^{-1}$$ for some integer $N$, then a theorem of Beukers and Zagier gives the best possible lower bound on $$\sum_{i=1}^r\log h(\alpha_i)$$ where ... More
The finiteness of computing the ultrametric Mahler measureAug 21 2014Recent work of Fili and the author examines an ultrametric version of the Mahler measure, denoted $M_\infty(\alpha)$ for an algebraic number $\alpha$. We show that the computation of $M_\infty(\alpha)$ can be reduced to a certain search through a finite ... More
On Quantum ObfuscationFeb 04 2016Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerful means of obfuscating classical programs, so-called ``black-box ... More
The Power of Quantum Fourier SamplingJul 20 2015A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. ... More
Pseudorandom generators and the BQP vs. PH problemJul 02 2010Dec 22 2010It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool AC_0, with ... More
Metric Mahler measures over number fieldsMay 22 2017For an algebraic number $\alpha$, the metric Mahler measure $m_1(\alpha)$ was first studied by Dubickas and Smyth in 2001 and was later generalized to the $t$-metric Mahler measure $m_t(\alpha)$ by the author in 2010. The definition of $m_t(\alpha)$ involves ... More
Effects of Biases in Virial Mass Estimation on Cosmic Synchronization of Quasar AccretionApr 04 2011Recent work using virial mass estimates and the quasar mass-luminosity plane has yielded several new puzzles regarding quasar accretion, including a sub-Eddington boundary on most quasar accretion, near-independence of the accretion rate from properties ... More
Embedded, Self-Gravitating Equilibria in Sheetlike and Filamentary Molecular CloudsMay 13 2000Numerical solutions of the isothermal Lane-Emden equation are presented, corresponding to self-gravitating gaseous cores embedded within a finite density envelope of overall cylindrical symmetry. These structures may be members of a fragmentation hierarchy ... More
Entanglement entropy and Berezin-Toeplitz operatorsMar 08 2018Oct 28 2018We consider Berezin-Toeplitz operators on compact Kahler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a two-term Weyl law, the second term being proportional to the ... More
Constraints on Field Theoretical Models for Variation of the Fine Structure ConstantAug 26 2003Mar 18 2004Recent theoretical ideas and observational claims suggest that the fine structure constant alpha may be variable. We examine a spectrum of models in which alpha is a function of a scalar field. Specifically, we consider three scenarios: oscillating alpha, ... More
Anderson Localization, Non-linearity and Stable Genetic DiversityFeb 28 2006In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation ... More
Astrophysical Observations: Lensing and Eclipsing Einstein's TheoriesMar 15 2005Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these papers, Einstein ... More
Critical Comparison of 3-d Imaging Approaches for NGSTAug 22 1999Currently three imaging spectrometer architectures, tunable filter, dispersive, and Fourier transform, are viable for imaging the universe in three dimensions. There are domains of greatest utility for each of these architectures. The optimum choice among ... More
Continued fraction expansions in connection with the metric Mahler measureAug 07 2015Aug 01 2016The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer's conjecture in topological language. More recent work of the author examined a parametrized family of generalized metric Mahler measures that gives ... More
The Weil height in terms of an auxiliary polynomialAug 21 2014Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number $\alpha$ under certain assumptions on $\alpha$. We prove a theorem which introduces an auxiliary polynomial for giving ... More
Extensions in $\mathbb R^D$Nov 10 2014May 27 2015In this paper we consider the following interesting question. Suppose we are given an almost isometry $\phi:E\to \mathbb R^D$ where $E$ is a finite subset of $\mathbb R^D$. Can $\phi$ be extended to an almost isometry to the whole of $\mathbb R^D$? In ... More
Cobordism, Relative Indices and Stein FillingsMay 11 2007In this paper we build on the framework developed in "Subelliptic Boundary Value Problems for the Spin_C Dirac Operator, I, II, III" to obtain a more complete understanding of the gluing properties for indices of boundary value problems for the SpinC-Dirac ... More
Subelliptic SpinC Dirac Operators, IV Proof of the Relative Index ConjectureMar 25 2012We prove the relative index conjecture, which in turn implies that the set of embeddable deformations of a strictly pseudoconvex CR-structure on a compact 3-manifold is closed in the C\infty-topology.
Subelliptic Spin_c Dirac operators, III The Atiyah-Weinstein conjectureJul 26 2005May 11 2007In this paper we show that there is a well defined modified dbar-Neumann problem for a spin_c manifold with a strictly pseudoconvex boundary (in the contact geometry sense). We show that the index of the associated boundary value problem can be computed ... More
Metric Heights on an Abelian GroupNov 08 2012Aug 18 2014Suppose $m(\alpha)$ denotes the Mahler measure of the non-zero algebraic number $\alpha$. For each positive real number $t$, the author studied a version $m_t(\alpha)$ of the Mahler measure that has the triangle inequality. The construction of $m_t$ is ... More
A collection of metric Mahler measuresAug 21 2014Let $M(\alpha)$ denote the Mahler measure of the algebraic number $\alpha$. In a recent paper, Dubickas and Smyth constructed a metric version of the Mahler measure on the multiplicative group of algebraic numbers. Later, Fili and the author used similar ... More
The parametrized family of metric Mahler measuresAug 21 2014Let $M(\alpha)$ denote the (logarithmic) Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth, and later Fili and the author, examined metric versions of $M$. The author generalized these constructions in order to associate, to each point ... More
On the Collapse of Tubes Carried by 3D Incompressible FlowsJan 30 2001Feb 02 2001We povide a test for numerical simulations for the collapse of regular tubes carried by a 3D incompressible flow. In particular, we obtain necessary conditions for 3D Euler to have a vortex tube collapse in finite time.
The $t$-metric Mahler measures of surds and rational numbersAug 18 2014A. Dubickas and C. Smyth introduced the metric Mahler measure $$ M_1(\alpha) = \inf\left\{\sum_{n=1}^N M(\alpha_n): N \in \mathbb N, \alpha_1 \cdots \alpha_N = \alpha\right\}, $$ where $M(\alpha)$ denotes the usual (logarithmic) Mahler measure of $\alpha ... More
On the Whitney distortion extension problem for $C^m(\mathbb R^n)$ and $C^{\infty}(\mathbb R^n)$ and its applications to interpolation and alignment of data in $\mathbb R^n$May 26 2015Nov 26 2017Let $n,m\geq 1$, $U\subset\mathbb R^n$ open. In this paper we provide a sharp solution to the following Whitney distortion extension problems: (a) Let $\phi:U\to \mathbb R^n$ be a $C^m$ map. If $E\subset U$ is compact (with some geometry) and the restriction ... More
The size of coefficients of certain polynomials related to the Goldbach conjectureAug 11 2010Recent work of Borwein, Choi, and the second author examined a collection of polynomials closely related to the Goldbach conjecture: the polynomial $F_N$ is divisible by the $N$th cyclotomic polynomial if and only if there is no representation of $N$ ... More
Harnack Inequalities and Heat-kernel Estimates for Degenerate Diffusion Operators Arising in Population BiologyJun 05 2014Aug 11 2014This paper continues the analysis, started in [2, 3], of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, ... More
Period derivative of the M15 X-ray Binary AC211/X2127+119Aug 28 1998We have combined Rossi X-ray Timing Explorer observations of X2127+119, the low-mass X-ray binary in the globular cluster M15, with archival X-ray lightcurves to study the stability of the 17.1 hr orbital period. We find that the data cannot be fit by ... More
Tempering the polylogarithmNov 08 2006We show that the function Li_s(e^x) extends to an entire function of the complex variable s, taking values in tempered distributions in x on the whole real line. That the classical polylogarithm extends similarly, as an entire function taking values in ... More
Debye Sources and the Numerical Solution of the Time Harmonic Maxwell EquationsAug 25 2008Mar 03 2009In this paper, we develop a new representation for outgoing solutions to the time harmonic Maxwell equations in unbounded domains in $\bbR^3.$ This representation leads to a Fredholm integral equation of the second kind for solving the problem of scattering ... More
Restricted Euler dynamics along trajectories of small inertial particles in turbulenceAug 08 2016The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple, low-dimensional ... More
Electromagnetic radiation from relativistic nuclear collisionsJun 11 2003Jun 16 2003We review some of the results obtained in the study of the production of electromagnetic radiation in relativistic nuclear collisions. We concentrate on the emission of real photons and dileptons from the hot and dense strongly interacting phases of the ... More
Properties of the phi meson at finite temperatureJan 06 1994We calculate the $\phi$-meson propagator at finite temperature at the one--loop order. The real and imaginary parts are studied separately in full kinematic ranges. From this activity we investigate how temperature affects such things as decay widths ... More
Determining the metric of the Cosmos: stability, accuracy, and consistencySep 06 2007Mar 28 2008The ultimate application of Einstein's field equations is to empirically determine the geometry of the Universe from its matter content, rather than simply assuming the Universe can be represented by a homogeneous model on all scales. Choosing an LTB ... More
On the non-Archimedean metric Mahler measureAug 21 2014Recently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metric na\"ive height on the multiplicative group of algebraic numbers. We give a non-Archimedean version of the metric Mahler measure, denoted $M_\infty$, and prove ... More
Generators for the $C^m$-closures of IdealsFeb 11 2019Let $\mathscr{R}$ denote the ring of real polynomials on $\mathbb{R}^{n}$. Fix $m\geq 0$, and let $A_{1},\cdots ,A_{M}\in \mathscr{R}$. The $ C^{m}$-closure of $\left( A_{1},\cdots ,A_{M}\right) $, denoted here by $ \left[ A_{1},\cdots ,A_{M};C^{m}\right] ... More
Hadronic interactions of the J/psiOct 04 2000Oct 18 2000We calculate the cross sections for reactions of the J/psi with light mesons. We also evaluate its finite temperature spectral function. We investigate separately the role of elastic and inelastic channels and we compare their respective importance. We ... More
A closure for Lagrangian velocity gradient evolution in turbulence using recent deformation mapping of initially Gaussian fieldsMar 09 2016The statistics of the velocity gradient tensor in turbulent flows are of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the velocity gradient ... More
Rotation Symmetries of Sequential Matrices with Applications to the Jacobi SymbolAug 18 2018Suppose that $p$ is an odd prime and $\genfrac{(}{)}{}{}{\cdot}{p}$ denotes the Legendre symbol modulo $p$. If $p$ is has the form $p= n^2+1$ then one easily verifies that $\genfrac{(}{)}{}{}{a}{p} = \genfrac{(}{)}{}{}{-a}{p}$ for all $a\in \mathbb Z/p\mathbb ... More
Degenerate Diffusion Operators Arising in Population BiologySep 30 2011We analyze a class of partial differential equations that arise as "backwards Kolmogorov operators" in infinite population limits of the Wright-Fisher models in population genetics and in mathematical finance. These are degenerate elliptic operators defined ... More
Wright-Fisher Diffusion in One DimensionJul 22 2009We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are defined by a degenerate second order operator on the interval [0, 1], where the coefficient of the second order term vanishes simply at ... More
Analysis of Graphs for Digital Preservation SuitabilityApr 24 2010We investigate the use of autonomically created small-world graphs as a framework for the long term storage of digital objects on the Web in a potentially hostile environment. We attack the classic Erdos - Renyi random, Barab'asi and Albert power law, ... More
The ambient metricOct 04 2007Oct 22 2008This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. ... More
The 1.3 mm Full-Stokes Polarization System at CARMAJun 15 2015The CARMA 1.3 mm polarization system consists of dual-polarization receivers that are sensitive to right- (R) and left-circular (L) polarization, and a spectral-line correlator that measures all four cross polarizations (RR, LL, LR, RL) on each of the ... More
Connectivity Damage to a Graph by the Removal of an Edge or a VertexMar 16 2011The approach of quantifying the damage inflicted on a graph in Albert, Jeong and Barabsi's (AJB) report "Error and Attack Tolerance of Complex Networks" using the size of the largest connected component and the average size of the remaining components ... More
Solutions to a System of Equations for $C^m$ FunctionsFeb 11 2019Feb 12 2019Fix $m\geq 0$, and let $A=\left( A_{ij}\left( x\right) \right) _{1\leq i\leq N,1\leq j\leq M}$ be a matrix of semialgebraic functions on $\mathbb{R}^{n}$ or on a compact subset $E \subset \mathbb{R}^n$. Given $f=\left( f_{1},\cdots ,f_{N}\right) \in C^{\infty ... More
A BMO theorem for $ε$ distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ with applications to manifolds of speech and soundOct 26 2016Oct 27 2016This paper deals with a BMO Theorem for $\epsilon$ distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ with applications to manifolds of speech and sound.
A BMO theorem for $ε$ distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ with applications to manifolds of speech and soundOct 26 2016Aug 13 2017This paper deals with a BMO Theorem for $\epsilon$ distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ with applications to manifolds of speech and sound.
A BMO theorem for $ε$ distorted diffeomorphisms on $\mathbb R^D$ and an application to comparing manifolds of speech and soundOct 26 2016This paper deals with A BMO Theorem for $\epsilon$ distorted diffeomorphisms on $\mathbb R^D$ and an application comparing manifolds of speech and sound.
A Complete Characterization of Unitary Quantum SpaceApr 05 2016We give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-$n$ efficient encoding of a $2^{\mathcal{O}(k(n))} \times 2^{\mathcal{O}(k(n))}$ ... More
A Complete Characterization of Unitary Quantum SpaceApr 05 2016Nov 21 2016Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of a well-conditioned ... More
Direct Limits of Adèle Rings and Their CompletionsDec 21 2017Jun 13 2018If $\mathbb A_K$ and $\mathbb A_L$ are ad\`ele rings of global fields $K \subseteq L$, then $\mathbb A_K$ may be identified with a topological subring of $\mathbb A_L$ via the injection $\mathrm{con}_{L/K}:\mathbb A_K \to \mathbb A_L$. For a fixed global ... More
A class of phylogenetic networks reconstructable from ancestral profilesJan 13 2019May 01 2019Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set $X$ of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate processes (for example, ... More
Dissipative-regime measurements as a tool for confirming and characterizing near-room-temperature superconductivityJun 30 2019The search for new superconducting materials approaching room temperature benefits from having a variety of testing methodologies to confirm and characterize the presence of superconductivity. Often the first signatures of new superconducting species ... More
The Effect of Disease-induced Mortality on Structural Network PropertiesNov 02 2015As the understanding of the importance of social contact networks in the spread of infectious diseases has increased, so has the interest in understanding the feedback process of the disease altering the social network. While many studies have explored ... More
Transition probabilities for degenerate diffusions arising in population geneticsAug 06 2016We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The Markov processes ... More
Universal quantum dynamics from two 2-local HamiltoniansJan 29 2008In this paper, we show that the ability to switch globally between two 2-local Hamiltonians on n qubits is sufficient for achieving universal unitary dynamics on those n qubits. Of the two Hamiltonians used in the construction, one is comprised of nearest-neighbour ... More