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Regular Polyhedra of Index Two, IINov 12 2010A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2 if it is combinatorially regular and its geometric symmetry group has index 2 in its combinatorial automorphism group; thus its automorphism group is flag-transitive but its symmetry ... More

A Littlewood-Richardson rule for the MacDonald inner product and bimodules over wreath productsSep 18 2013We prove a Littlewood-Richardson type formula for $(s_{\lambda/\mu},s_{\nu/\kappa})_{t^k,t}$, the pairing of two skew Schur functions in the MacDonald inner product at $q = t^k$ for positive integers $k$. This pairing counts graded decomposition numbers ... More

Nonlocality Without Inequalities for all Pure Entangled StatesJul 31 1998Aug 09 1999This paper has been withdrawn by the authors.

Optimum Unambiguous Discrimination Between Linearly Independent Symmetric StatesJul 08 1998The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can be discriminated. ... More

Nonholonomic Hamilton-Jacobi equation and IntegrabilityJun 18 2009Dec 18 2009We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton--Jacobi ... More

Universal Corrections to Black Hole Entropy in $\mathcal{N} \geq 2$ SupergravityMay 05 2015We embed general solutions to 4D Einstein-Maxwell theory into $\mathcal{N} \geq 2$ supergravity and study quadratic fluctuations of the supergravity fields around the background. We compute one-loop quantum corrections for all fields and show that the ... More

An Overview of the Security Concerns in Enterprise Cloud ComputingJan 28 2011Deploying cloud computing in an enterprise infrastructure bring significant security concerns. Successful implementation of cloud computing in an enterprise requires proper planning and understanding of emerging risks, threats, vulnerabilities, and possible ... More

A One-Loop Test of the near-AdS$_2$/near-CFT$_1$ CorrespondenceAug 09 2019We analyze quantum fluctuations around black hole solutions to the Jackiw-Teitelboim model. We use harmonic analysis on Euclidean AdS$_2$ to show that the logarithmic corrections to the partition function are determined entirely by quadratic holomorphic ... More

The Spherical Accretion Shock Instability in the Linear RegimeJul 07 2005We use time-dependent, axisymmetric, hydrodynamic simulations to study the linear stability of the stalled, spherical accretion shock that arises in the post-bounce phase of core-collapse supernovae. We show that this accretion shock is stable to radial ... More

Strategies and Networks for State-Dependent Quantum CloningDec 15 1998State-dependent cloning machines that have so far been considered either deterministically copy a set of states approximately, or probablistically copy them exactly. In considering the case of two equiprobable pure states, we derive the maximum global ... More

Quantum State Separation, Unambiguous Discrimination and Exact CloningAug 11 1998Unambiguous discrimination and exact cloning reduce the square-overlap between quantum states, exemplifying the more general type of procedure we term state separation. We obtain the maximum probability with which two equiprobable quantum states can be ... More

Regular Polyhedra of Index Two, IMay 26 2010A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2 if it is combinatorially regular but "fails geometric regularity by a factor of 2"; its combinatorial automorphism group is flag-transitive but its geometric symmetry group has ... More

The rolling sphere and the quantum spinJun 16 2009We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both rolling and spin ... More

An extension to the theory of controlled Lagrangians using the Helmholtz conditionsNov 19 2017The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand, matching conditions ... More

The friction of a mesh-like super-hydrophobic surfaceNov 16 2009When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to significant reduction ... More

Families of periodic orbits: closed 1-forms and global continuabilityJun 08 2019Jun 15 2019We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of Alexander, Alligood, ... More

Comparison of two unknown pure quantum statesFeb 15 2002Nov 01 2002We investigate the extent to which we can establish whether or not two quantum systems have been prepared in the same state. We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to conclusively identify ... More

Anything can happen, but only given half a chance: a quantum bound on large fluctuations away from equilibriumJun 23 2018We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be measured in a fixed ... More

Trees, Forests, and Stationary States of Quantum Lindblad SystemsOct 26 2018In this paper, we study the stationary orbits of quantum Lindblad systems. We show that they can be characterized in terms of trees and forests on a directed graph with edge weights that depend on the Lindblad operators and the eigenbasis of the density ... More

Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random MatricesFeb 04 2010This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation frequency. The development ... More

Hill's Equation with Random Forcing Parameters: The Limit of Delta Function BarriersJun 10 2009This paper considers random Hill's equations in the limit where the periodic forcing function becomes a Dirac delta function. For this class of equations, the forcing strength $q_k$, the oscillation frequency $\af_k$, and the period are allowed to vary ... More

Control of Squeezed StatesFeb 22 2000In this paper we consider the classical and quantum control of squeezed states of harmonic oscillators. This provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated systems in the stochastic ... More

IRAS 16293-2422: Evidence for Infall onto a Counter-Rotating Protostellar Accretion DiskDec 08 2005We report high spatial resolution VLA observations of the low-mass star-forming region IRAS 16293-2422 using four molecular probes: ethyl cyanide (CH$_3$CH$_2$CN), methyl formate (CH$_3$OCHO), formic acid (HCOOH), and the ground vibrational state of silicon ... More

Viscous Marangoni propulsionDec 05 2012Marangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous regime. ... More

Geometric transition in friction for flow over a bubble mattressDec 10 2008Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid and along the ... More

Hydrodynamic friction of fakir-like super-hydrophobic surfacesMay 20 2010A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, ... More

Flag-Based Control of Quantum Purity for $n=2$ SystemsFeb 05 2016Feb 16 2016This paper investigates the fast Hamiltonian control of $n=2$ density operators by continuously varying the flag as one moves away from the completely mixed state. In general, the critical points and zeros of the purity derivative can only be solved analytically ... More

Towards Precision LSST Weak-Lensing Measurement - I: Impacts of Atmospheric Turbulence and Optical AberrationNov 08 2010Mar 22 2011The weak-lensing science of the LSST project drives the need to carefully model and separate the instrumental artifacts from the intrinsic lensing signal. The dominant source of the systematics for all ground based telescopes is the spatial correlation ... More

Discrete Hamilton-Jacobi TheoryNov 11 2009Jun 08 2011We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and also prove ... More

Baryonic Collapse within Dark Matter Halos and the Formation of Gaseous Galactic DisksSep 12 2006This paper constructs an analytic framework for calculating the assembly of galactic disks from the collapse of gas within dark matter halos, with the goal of determining the surface density profiles. Gas parcels (baryons) fall through the potentials ... More

Evolution of Planetary Orbits with Stellar Mass Loss and Tidal DissipationOct 09 2013Intermediate mass stars and stellar remnants often host planets, and these dynamical systems evolve because of mass loss and tides. This paper considers the combined action of stellar mass loss and tidal dissipation on planetary orbits in order to determine ... More

Flag-based Control of Orbit Dynamics in Quantum Lindblad SystemsFeb 20 2016In this paper, we demonstrate that the dynamics of an $n$-dimensional Lindblad control system can be separated into its inter- and intra-orbit dynamics when there is fast controllability. This can be viewed as a control system on the simplex of density ... More

Electroweak Phase Transition in Two Higgs Doublet ModelsSep 03 1996Aug 23 2007We reexamine the strength of the first order phase transition in the electroweak theory supplemented by an extra Higgs doublet. The finite-temperature effective potential, $V_{eff}$, is computed to one-loop order, including the summation of ring diagrams, ... More

Computing automorphism groups of shifts using atypical equivalence classesMay 11 2015Feb 01 2017We study the automorphism group of an infinite minimal shift $(X,\sigma)$ such that the complexity difference function, $p(n+1)-p(n)$, is bounded. We give some new bounds on $\mbox{Aut}(X,\sigma)/\langle \sigma \rangle$ and also study the one-sided case. ... More

Families of periodic orbits: closed 1-forms and global continuabilityJun 08 2019Jul 17 2019We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of Alexander, Alligood, ... More

Annular Khovanov-Lee homology, braids, and cobordismsDec 18 2016We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A x I, has the structure of a bifiltered complex whose filtered chain homotopy type is an invariant of the isotopy class of L in A x I. Using ideas of Ozsvath-Stipsicz-Szabo ... More

A Review on Recommendation Systems: Context-aware to Social-basedNov 28 2018The number of Internet users had grown rapidly enticing companies and cooperations to make full use of recommendation infrastructures. Consequently, online advertisement companies emerged to aid us in the presence of numerous items and users. Even as ... More

Constraining Axion Mass through Gamma-ray Observations of PulsarsAug 09 2019We analyze 9 years of PASS 8 $\textit{Fermi}$-LAT data in the 60$-$500 MeV range and determine flux upper limits (UL) for 17 gamma-ray dark pulsars as a probe of axions produced by nucleon-nucleon Bremsstrahlung in the pulsar core. Using a previously ... More

Localising the gamma-ray emission region during the June 2014 outburst of 3C 454.3Jan 26 2016In May - July 2014, the flat spectrum radio quasar 3C 454.3 exhibited strong flaring behaviour. Observations with the Large Area Telescope detector on-board the Fermi Gamma-ray Space Telescope captured the $\gamma$-ray flux at energies 0.1 $\leq E_{\gamma}\leq$ ... More

Annular Khovanov homology and knotted Schur-Weyl representationsMay 17 2015Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov ... More

Icosahedral Skeletal Polyhedra Realizing Petrie Relatives of Gordan's Regular MapOct 07 2012Every regular map on a closed surface gives rise to generally six regular maps, its "Petrie relatives", that are obtained through iteration of the duality and Petrie operations (taking duals and Petrie-duals). It is shown that the skeletal polyhedra in ... More

Brain Damage and Motor Cortex Impairment in Chronic Obstructive Pulmonary Disease: Implication of Nonrapid Eye Movement Sleep DesaturationOct 25 2017Nonrapid eye movement (NREM) sleep desaturation may cause neuronal damage due to the withdrawal of cerebrovascular reactivity. The current study (1) assessed the prevalence of NREM sleep desaturation in nonhypoxemic patients with chronic obstructive pulmonary ... More

The Role of Data Analysis in Uncertainty Quantification: Case Studies for Materials ModelingDec 05 2017In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that can propagate ... More

Entanglement and Collective Quantum OperationsMar 16 2000Jun 16 2000We show how shared entanglement, together with classical communication and local quantum operations, can be used to perform an arbitrary collective quantum operation upon N spatially-separated qubits. A simple teleportation-based protocol for achieving ... More

Global consensus Monte CarloJul 24 2018For Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by ... More

Anytime Monte CarloDec 10 2016Jun 07 2017A Monte Carlo algorithm typically simulates some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, so that the number of ... More

Improved Volterra Kernel Methods with Applications to the Visual SystemDec 05 2008Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input interactions. ... More

W-algebras from Heisenberg categoriesJan 03 2015The trace (or zeroth Hochschild homology) of Khovanov's Heisenberg category is identified with a quotient of the algebra W_{1+\infty}. This induces an action of W_{1+\infty} on symmetric functions.

Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion ResonanceNov 05 2010Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into ... More

Uncertainty Quantification for Airfoil Icing using Polynomial Chaos ExpansionsNov 13 2014The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a large amount of ... More

Hamel's Formalism and Variational Integrators on a SphereNov 19 2012This paper discusses Hamel's formalism and its applications to structure-preserving integration of mechanical systems. It utilizes redundant coordinates in order to eliminate multiple charts on the configuration space as well as nonphysical artificial ... More

Enhanced Habitability on High Obliquity Bodies near the Outer Edge of the Habitable Zone of Sun-like StarsMay 22 2019High obliquity planets represent potentially extreme limits of terrestrial climate, as they exhibit large seasonality, a reversed annual-mean pole-to-equator gradient of stellar heating, and novel cryospheres. A suite of 3-D global climate model simulations ... More

Evidence that particle acceleration in hotspots of FR II galaxies is not constrained by synchrotron coolingMar 03 2017We study the hotspots of powerful radiogalaxies, where electrons accelerated at the jet termination shock emit synchrotron radiation. The turnover of the synchrotron spectrum is typically observed between infrared and optical frequencies, indicating that ... More

Particle acceleration and magnetic field amplification in hotspots of FR II galaxies: The case study 4C74.26Feb 25 2016Apr 30 2016It has been suggested that relativistic shocks in extragalactic sources may accelerate the most energetic cosmic rays. However, recent theoretical advances indicating that relativistic shocks are probably unable to accelerate particles to energies much ... More

Ubiquity of density slope oscillations in the central regions of galaxy and cluster-sized systemsApr 05 2016One usually thinks of a radial density profile as having a monotonically changing logarithmic slope, such as in NFW or Einasto profiles. However, in two different classes of commonly used systems, this is often not the case. These classes exhibit non-monotonic ... More

A variational problem on Stiefel manifoldsSep 01 2006In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class ... More

Diffusion-limited Reactions in Nanoscale ElectronicsOct 19 2017A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor surface (or biochemical ... More

Extreme fluctuations of entropies in quantum systemsAug 19 2019The intuition that we have about entropy -- coming largely from the Boltzmann entropy -- is that the maximum entropy state is very close to the equilibrium state, while low entropy is associated with highly non-equilibrium states. It this paper, we investigate ... More

Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systemsAug 30 2012The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are discussed. Different types of gradient flows that arise from different ... More

Turbulence in Extrasolar Planetary Systems Implies that Mean Motion Resonances are RareMay 12 2008This paper considers the effects of turbulence on mean motion resonances in extrasolar planetary systems and predicts that systems rarely survive in a resonant configuration. A growing number of systems are reported to be in resonance, which is thought ... More

CMB Anisotropy in COBE-DMR-Normalized Open CDM CosmogonyDec 22 1995We compute the CMB anisotropy in an open inflation CDM model which is normalized to the two-year DMR sky map. Presently available CMB data is consistent with $\Omega_0 \sim 0.3 - 0.4$, but does not strongly disfavour either $\Omega_0 \sim 0.1$ or $\Omega_0 ... More

Mean Motion Resonances in Exoplanet Systems: An Investigation Into Nodding BehaviorNov 13 2012Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes libration (oscillatory ... More

CMB lensing and primordial non-GaussianityMay 28 2009Jun 18 2010We study the effects of gravitational lensing on the estimation of non-Gaussianity from the bispectrum of the cosmic microwave background (CMB) temperature anisotropies. We find that the effect of lensing on the bispectrum may qualitatively be described ... More

The Effect of a Light Sterile Neutrino at NO$ν$A and DUNEApr 10 2018Aug 10 2018Now that the NOvA experiment is approaching two years run time and has released some preliminary data, some constraints for the oscillation parameters can be inferred. Currently the best fits for NOvA are three separate results, the reason they are indistinct ... More

Evaluating the Gamma-Ray Evidence for Self-Annihilating Dark Matter from the Virgo ClusterJul 26 2012Oct 09 2012Based on three years of Fermi Large Area Telescope (LAT) gamma-ray data of the Virgo cluster, evidence for an extended emission associated with dark matter pair annihilation in the b b-bar channel has been reported by Han et al. [1]. After an in depth ... More

Comptonization of an isotropic distribution in moving media: higher-order effectsMay 27 1998Aug 24 1998We consider the Comptonization of an isotropic radiation field by a thermal distribution of electrons with non-vanishing bulk velocity. We include all relativistic effects, including induced scattering and electron recoil, in the derivation of a kinetic ... More

The spin rates of O stars in WR + O binaries. I. Motivation, methodology and first results from SALTOct 30 2015Aug 26 2016The black holes (BH) in merging BH-BH binaries are likely progeny of binary O stars. Their properties, including their spins, will be strongly influenced by the evolution of their progenitor O stars. The remarkable observation that many single O stars ... More

Receiver Operating Characteristics for a Prototype Quantum Two-Mode Squeezing RadarFeb 28 2019We have built and evaluated a prototype quantum radar, which we call a quantum two-mode squeezing radar (QTMS radar), in the laboratory. It operates solely at microwave frequencies; there is no downconversion from optical frequencies. Because the signal ... More

Measurement of light and charge yield of low-energy electronic recoils in liquid xenonNov 30 2016The dependence of the light and charge yield of liquid xenon on the applied electric field and recoil energy is important for dark matter detectors using liquid xenon time projections chambers. Few measurements have been made of this field dependence ... More

Suppression of Reabsorption via Modulation of LightJul 24 2006Jul 24 2006Reabsorption, the multiple scattering of spontaneously emitted photons in optically thick gases, is a major limitation to efficient optical pumping and laser cooling in ultracold gases. We report mitigation of reabsorption using spatial and frequency ... More

The logic of the future in quantum theorySep 02 2014May 02 2016According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the ... More

Entangling capacity and distinguishability of two-qubit unitary operatorsFeb 14 2005Sep 02 2005We prove that the entangling capacity of a two-qubit unitary operator without local ancillas, both with and without the restriction to initial product states, as quantified by the maximum attainable concurrence, is directly related to the distinguishability ... More

Distinguishability Measures and Ensemble OrderingsSep 27 2001Nov 01 2002It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the maximum probabilities ... More

Top Production Properties at the TevatronNov 27 2000Nov 28 2000Following the confirmation of the top quark discovery at the Tevatron, the next step is to begin studying its properties. Because the scale of electroweak symmetry breaking is of the same order as the measured top mass, the top quark may be very sensitive ... More

Invariants topologiques des Espaces non commutatifsJul 24 2013In this thesis, we give a definition of topological K-theory of Kontsevich's noncommutative spaces (ie dg-categories) defined over the complex. The main motivation comes from noncommutative Hodge structures in the sense of Kontsevich--Katzarkov--Pantev ... More

Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct partsAug 07 2016Nov 23 2016For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give good evidence ... More

On the Riemann zeta-function, Part IIMay 18 2007An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. We determine the two-sided Laplace transform representation of f(s) on open vertical strips, V'(4w), disjoint from the (translated) critical strip. ... More

Hyperbolic diagram groups are freeMay 08 2015In this paper, we study the so-called diagram groups. Our main result is that diagram groups are free if and only if they do not contain any subgroup isomorphic to $\mathbb{Z}^2$. As an immediate corollary, we get that hyperbolic diagram groups are necessarily ... More

K^F-invariants in irreducible representations of G^F, when G=GL_nJul 24 2001Jan 25 2002Using a general result of Lusztig, we give explicit formulas for the dimensions of K^F-invariants in irreducible representations of G^F, when G=GL_n, F:G->G is a Frobenius map, and K is an F-stable subgroup of finite index in G^theta for some involution ... More

On the Riemann zeta-function, Part I: OutlineMay 14 2007Results of a multipart work are outlined. Use is made therein of the conjunction of the Riemann hypothesis, RH, and hypotheses advanced by the author. Let z(n) be the nth nonreal zero of the Riemann zeta-function with positive imaginary part in order ... More

Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formatsMay 02 2017Apr 19 2018This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a product set equipped ... More

Negative curvature of automorphism groups of graph products with applications to right-angled Artin groupsJul 02 2018Oct 29 2018Given a (freely irreducible) product graph of groups $\Gamma \mathcal{G}$, we introduce and study its \emph{product graph} $P(\Gamma, \mathcal{G})$, defined as the graph whose vertices are the maximal product subgroups of $\Gamma \mathcal{G}$ and whose ... More

The Eccentric Frame Decomposition of Central Force FieldsDec 20 2007The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body problem. In general, ... More

Experimental Demonstration of Optimal Unambiguous State DiscriminationJul 19 2000We present the first full demonstration of unambiguous state discrimination between non-orthogonal quantum states. Using a novel free space interferometer we have realised the optimum quantum measurement scheme for two non-orthogonal states of light, ... More

Structure of the $\mathbf{Λ(1405)}$ from Hamiltonian effective field theoryJul 20 2016Jan 09 2017The pole structure of the $\Lambda(1405)$ is examined by fitting the couplings of an underlying Hamiltonian effective field theory to cross sections of $K^- p$ scattering in the infinite-volume limit. Finite-volume spectra are then obtained from the theory, ... More

Condition for unambiguous state discrimination with local operations and classical communicationFeb 10 2003May 29 2004We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition is valid for ... More

Quantum Operations, State Transformations and ProbabilitiesSep 13 2001Sep 17 2001In quantum operations, probabilities characterise both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure-to-pure state transformations, ... More

Composable security proof for continuous-variable quantum key distribution with coherent statesAug 25 2014Feb 03 2015We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo ... More

Topological K-theory of complex noncommutative spacesNov 30 2012Jun 02 2015The purpose of this work is to give a definition of a topological K-theory for dg-categories over C and to prove that the Chern character map from algebraic K-theory to periodic cyclic homology descends naturally to this new invariant. This topological ... More

A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of densityJul 10 2012We study an initial boundary value problem for the 3D magnetohydrodynamics (MHD) equations of compressible fluids in $\R^3$. We establish a blow-up criterion for the local strong solutions in terms of the density and magnetic field. Namely, if the density ... More

On the Riemann zeta-function, Parts IV-VMay 31 2007Jul 12 2007In Part I an odd meromorphic function f(s) has been constructed from the Riemann zeta-function evaluated at one-half plus s. The conjunction of the Riemann hypothesis and hypotheses advanced by the author in Part I is assumed. In Part IV we derive the ... More

Hyperbolicities in CAT(0) cube complexesSep 26 2017Apr 26 2019This paper is a survey dedicated to the following question: given a group acting on some CAT(0) cube complex, how to exploit this action to determine whether or not the group is Gromov / relatively / acylindrically hyperbolic? As much as possible, the ... More

Convergence of finite-dimensional laws of the weighted quadratic variations process for some fractional Brownian sheetsJan 22 2008Feb 22 2008In this paper we state and prove a central limit theorem for the finite-dimensional laws of the quadratic variations process of certain fractional Brownian sheets. The main tool of this article is a method developed by Nourdin and Nualart based on the ... More

Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type AJan 05 2005The intersection cohomologies of closures of nilpotent orbits of linear (respectively, cyclic) quivers are known to be described by Kazhdan-Lusztig polynomials for the symmetric group (respectively, the affine symmetric group). We explain how to simplify ... More

Impossible configurations for geodesics on negatively-curved surfacesFeb 24 2019Hass and Scott's example of a 4-valent graph on the 3-punctured sphere that cannot be realized by geodesics in any metric of negative curvature is generalized to impossible configurations filling surfaces of genus $n$ with $k$ punctures for any $n$ and ... More

The symmetric group representation on cohomology of the regular elements of a maximal torus of the special linear groupNov 29 2003Mar 17 2006We give a formula for the character of the representation of the symmetric group $S_n$ on each isotypic component of the cohomology of the set of regular elements of a maximal torus of $SL_n$, with respect to the action of the centre.

Low-rank methods for high-dimensional approximation and model order reductionNov 04 2015Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply to many problems ... More

Power Values of Certain Quadratic PolynomialsJan 22 2009Mar 12 2010In this article we compute the $q$th power values of the quadratic polynomials $f$ with negative squarefree discriminant such that $q$ is coprime to the class number of the splitting field of $f$ over $\mathbb{Q}$. The theory of unique factorisation and ... More

Coning-off CAT(0) cube complexesMar 21 2016In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the characterization of ... More

Time, chance and quantum theoryJan 19 2016I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future ... More