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Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior BootstrapFeb 08 2019Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, ... More

A proposal for measuring photon temporal coherence in continuum radiationOct 24 2013Oct 06 2015A technique complementary to those for spectral lines is proposed for the observation of continuum radiation. As, quantum mechanically, the radiation is a mixture of pure states, it should be possible to measure the temporal coherence of the states as ... More

Methods for Accelerating Conway's Doomsday Algorithm (part 1)Jun 20 2010Jan 27 2011We propose a modification of a key component in the Doomsday Algorithm for calculating the day of the week of any calendar date. In particular, we propose to replace the calculation of the required term: \lfloor \frac{x}{12} \rfloor + x \bmod 12 + \lfloor ... More

Elliptification of Rectangular ImagerySep 22 2017We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We will focus primarily on methods that use mathematical mappings with explicit and invertible equations. We will also present different post-processing ... More

Waterfilling Theorems in the Time-Frequency Plane for the Heat Channel and a Related SourceApr 02 2014Apr 28 2014The capacity of the heat channel, a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN), is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source is ... More

Astrometric asteroid masses: a simultaneous determinationFeb 18 2014Using over 89 million astrometric observations of 349,737 numbered minor planets, an attempt was made to determine the masses of 230 of them by simultaneously solving for corrections to all orbital elements and the masses. For 132 minor planets an acceptable ... More

Coulomb and spin-orbit interaction matrix elements in d^2d' configurationSep 10 1998Oct 10 1998The $d^2d'$ configuration is analysed in group-theoretical terms. Starting from the table given by Condon and Odabasi (1980) for the configuration $d^2d'$, we determine a set of convenient group-theoretical basis states, and rewrite the Coulomb matrix ... More

Waterfilling Theorems for Linear Time-Varying Channels and Related Nonstationary SourcesSep 18 2015Sep 30 2016The capacity of the linear time-varying (LTV) channel, a continuous-time LTV filter with additive white Gaussian noise, is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source ... More

Initial conditions to cosmological N-body simulations, or how to run an ensemble of simulationsMar 04 2005Jun 11 2005The conventional method of generating initial conditions for cosmological N-body simulations introduces a significant error in the real-space statistical properties of the particles. More specifically, the finite box size leads to a significant underestimate ... More

On the Capacity of the Heat Channel, Waterfilling in the Time-Frequency Plane, and a C-NODE RelationshipDec 31 2010Jan 27 2014The heat channel is defined by a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN) at the filter output. The continuous-time LTV filter is related to the heat kernel of the quantum mechanical harmonic oscillator, so the name of ... More

Design of Pulse Shapes and Digital Filters Based on Gaussian FunctionsJul 14 2009Two new pulse shapes for communications are presented. The first pulse shape is ISI-free and identical with the interpolating function (or ISI-free kernel) of a reconstruction formula in shift-invariant spaces with Gaussian generator. Several closed form ... More

Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular OnesFeb 26 2007There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense) set of exact ... More

Bosons and fermions in external fieldsJul 12 2005Contribution to the Encyclopedia of Mathematical Physics (Elsevier, 2006): a brief and (hopefully) pedagogical introduction to quantum field theory models describing particles in external fields is presented. Following the instructions, the only references ... More

Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensionsMay 28 2002I present a novel class of exactly solvable quantum field theories. They describe non-relativistic fermions on even dimensional flat space, coupled to a constant external magnetic field and a four point interaction defined with the Groenewold-Moyal star ... More

Exactly solvable models for 2D correlated fermionsJun 04 2002Jun 06 2003I discuss many-body models for interacting fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: 2D fermions in a constant magnetic field and a particular non-local 4-point ... More

Correction to "A Note on Gallager's Capacity Theorem for Waveform Channels"Jul 19 2012Nov 04 2013We correct an alleged contradiction to Gallager's capacity theorem for waveform channels as presented in a poster at the 2012 IEEE International Symposium on Information Theory.

Explicit solution of the (quantum) elliptic Calogero-Sutherland modelJan 14 2004Dec 09 2008We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic ... More

Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland systemNov 28 2004Aug 08 2005We review the construction of a conformal field theory model which describes anyons on a circle and at finite temperature, including previously unpublished results. This anyon model is closely related to the quantum elliptic Calogero-Sutherland (eCS) ... More

A Generalized Sampling Theorem for Frequency Localized SignalsJul 02 2007Apr 15 2009A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate reconstruction from ... More

Supersymmetric and non-supersymmetric Seiberg-like dualities for gauged Wess-Zumino-Witten theories, realised on branesJun 24 2015Oct 13 2015In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality) between gauged Wess-Zumino-Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based on the coset ... More

Descent equations of Yang--Mills anomalies in noncommutative geometryAug 02 1995Aug 01 1996Consistent Yang--Mills anomalies $\int\om_{2n-k}^{k-1}$ ($n\in\N$, $ k=1,2, \ldots ,2n$) as described collectively by Zumino's descent equations $\delta\om_{2n-k}^{k-1}+\dd\om_{2n-k-1}^{k}=0$ starting with the Chern character $Ch_{2n}=\dd\om_{2n-1}^{0}$ ... More

Exactly solvable two-level quantum systems and Landau-Zener interferometryDec 13 2012Jul 15 2013I present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions to the Schrodinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving ... More

A 2D Luttinger modelFeb 28 2009Apr 14 2010A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is ... More

Non-commutative geometry and exactly solvable systemsOct 31 2007I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system is a prototype ... More

On 4-Dimensional J-Invariant Shrinking Ricci SolitonsJan 19 2014As of today, there are very few known complete shrinking Ricci solitons in dimension 4, and all examples discovered so far are K\"ahler and/or Einstein. In this note, we prove that any four dimensional J-invariant gradient shrinking Ricci solitons satisfy ... More

Cut-Set Bounds for Multimessage Multicast Networks with Independent Channels and Zero-Delay EdgesJun 01 2015Apr 26 2016We consider a communication network consisting of nodes and directed edges that connect the nodes. The network may contain cycles. The communications are slotted where the duration of each time slot is equal to the maximum propagation delay experienced ... More

On the collapsing rate of the Kähler-Ricci flow with finite-time singularityDec 27 2011This short note studies the collapsing behavior of the K\"ahler-Ricci flow on a compact K\"ahler manifold X admitting a holomorphic submersion X -> B where B is a K\"ahler manifold of lower dimension than X. We give cohomological and curvature conditions ... More

Stability and Kinetics of Step Motion on Crystal SurfacesDec 01 1993The kinetics of monoatomic steps in diffusion-controlled crystal growth and evaporation processes are investigated analytically using a Green's function approach. Integro-differential equations of motion for the steps are derived; and a systematic linear ... More

Baryogenesis from Symmetry PrincipleAug 14 2015Dec 07 2015In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario ... More

A recipe for black box functorsDec 10 2018The task of constructing compositional semantics for network-style diagrammatic languages, such as electrical circuits or chemical reaction networks, has been dubbed the black boxing problem, as it gives semantics that describes the properties of each ... More

Boltzmann's Entropy and Kähler-Ricci SolitonsMay 25 2016We study a Boltzmann's type entropy functional (which appeared in existing literature) defined on K\"ahler metrics of a fixed K\"ahler class. The critical points of this functional are gradient K\"ahler-Ricci solitons, and the functional was known to ... More

Generalized Macaulay representations and the flag $f$-vectors of generalized colored complexesJun 07 2013Nov 20 2014A colored complex of type $\mathbf{a} = (a_1, \dots, a_n)$ is a simplicial complex ${\Delta}$ on a vertex set $V$, together with an ordered partition $(V_1, \dots, V_n)$ of $V$, such that every face $F$ of ${\Delta}$ satisfies $|F \cap V_i| \leq a_i$. ... More

Chemical Models of Collapsing EnvelopesOct 07 1999We discuss recent models of chemical evolution in the developing and collapsing protostellar envelopes associated with low-mass star formation. In particular, the effects of depletion of gas-phase molecules onto grain surfaces is considered. We show that ... More

Holographic Corrections to Meson Scattering AmplitudesNov 01 2016Nov 03 2016We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature ... More

Taste symmetry breaking at finite temperatureJul 27 2012The breaking of the taste symmetry is studied in the temperature range between 140 MeV to 550 MeV. In order to investigate this violation we have calculated the screening masses of the various taste states fitting the exponential decay of the spatial ... More

Quantum Bianchi identities and characteristic classes via DG categoriesMay 23 2017Jun 14 2017We show how DG categories arise naturally in noncommutative differential geometry and use them to derive noncommutative analogues of the Bianchi identities for the curvature of a connection. We also give a derivation of formulae for characteristic classes ... More

Pointwise bounded asymptotic morphisms and Thomsen's non-stable k-theoryJan 08 2002In this paper I show that pointwise bounded asymptotic morphisms between separable metrisable locally convex *-algebras induce continuous maps between the quasi-unitary groups of the algebras, provided that the algebras support a certain amount of functional ... More

Astrobiology: An Astronomer's PerspectiveSep 18 2013In this review we explore aspects of the field of astrobiology from an astronomical viewpoint. We therefore focus on the origin of life in the context of planetary formation, with additional emphasis on tracing the most abundant volatile elements, C, ... More

The Chemistry of Dark Clouds: New Astrochemical Tools for Star Formation StudiesNov 26 2002The past decade has led to significant improvements in our understanding of the physical structure of the molecular cores of cold dark clouds. Observational efforts, in combination with improved knowledge of cloud structure, now provide clear evidence ... More

Deformed Calogero-Sutherland model and fractional Quantum Hall effectMar 19 2016Apr 29 2016The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which ... More

A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland typeMar 30 2007Jul 15 2009In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of Calogero-Sutherland ... More

Explicit formulas for the eigenfunctions of the N-body Calogero modelNov 10 2005We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle ... More

Series solutions of the non-stationary Heun equationSep 08 2016We consider the non-stationary Heun equation, also known as quantum Painlev\'e VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to ... More

Vacuum Polarization Renormalization and the Geometric PhaseDec 17 1996As an application of the renormalization method introduced by the second author we give a causal definition of the phase of the quantum scattering matrix for fermions in external Yang-Mills potentials. The phase is defined using parallel transport along ... More

Characterising and recognising game-perfect graphsOct 29 2018Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once the graph is ... More

Gravity induced from quantum spacetimeMay 10 2013Oct 21 2013We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a single real parameter ... More

A Leray spectral sequence for noncommutative differential fibrationsAug 25 2011This paper describes the Leray spectral sequence associated to a differential fibration. The differential fibration is described by base and total differential graded algebras. The cohomology used is noncommutative differential sheaf cohomology. For this ... More

M-partitions: Optimal partitions of weight for one scale panNov 14 2003An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so as to be able ... More

Series Solutions of the Non-Stationary Heun EquationSep 08 2016Feb 16 2018We consider the non-stationary Heun equation, also known as quantum Painlev\'e VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to ... More

Incremental Sequence LearningNov 09 2016Deep learning research over the past years has shown that by increasing the scope or difficulty of the learning problem over time, increasingly complex learning problems can be addressed. We study incremental learning in the context of sequence learning, ... More

Bethe-Salpeter Equation -- The OriginsNov 07 2008This article was originally written for scholarpedia.org. It describes the origins and related background of Bethe-Salpeter equation.

Nuclear Astrophysics Before 1957Nov 20 2007I discuss especially my summer with Willy Fowler at Kellogg Radiation in 1951, where I did my "triple-alpha" work. I also go back even earlier to Arthur Eddington and Hans Bethe. I also mention the 1953 summer school in Ann Arbor.

Publication Trends in Astronomy: The Lone AuthorFeb 21 2012In this short communication I highlight how the number of collaborators on papers in the main astronomy journals has evolved over time. We see a trend of moving away from single-author papers. This communication is based on data in the holdings of the ... More

Taste symmetry violation at finite temperatureJan 06 2013Symmetries play a distinctive role at the high temperature phase transition in QCD. Therefore the spectrum of screening masses has been investigated with emphasis on taste breaking. Although taste violation is an UV effect the relevant operators could ... More

Signatures of Nucleon Disappearance in Large Underground DetectorsJun 13 2002Mar 29 2003For neutrons bound inside nuclei, baryon instability can manifest itself as a decay into undetectable particles (e.g., $\it n \to \nu \nu \bar{\nu} $), i.e., as a disappearance of a neutron from its nuclear state. If electric charge is conserved, a similar ... More

Extrinsic curvature effects in brane-world scenariosMar 16 2011Mar 31 2011We consider models of bosons on curved 3+1 dimensional space-time embedded in a higher dimensional flat ambient space. We propose to derive (rather than postulate) equations of motions by assuming that a standard Klein-Gordon field on ambient space is ... More

(3+1)-Dimensional Schwinger Terms and Non-commutative GeometryJul 29 1994We discuss 2-cocycles of the Lie algebra $\Map(M^3;\g)$ of smooth, compactly supported maps on 3-dimensional manifolds $M^3$ with values in a compact, semi-simple Lie algebra $\g$. We show by explicit calculation that the Mickelsson-Faddeev-Shatashvili ... More

Meson Screening Masses at high Temperature in quenched QCD with improved Wilson QuarksMar 29 2001We report on a lattice investigation of improved quenched Wilson fermions above and below the confinement-deconfinement phase transition. Results on meson screening masses as well as spatial wave functions are presented. Moreover, the meson dispersion ... More

Bayesian Ensembles of Crowds and Deep Learners for Sequence TaggingNov 02 2018Current methods for sequence tagging, a core task in NLP, are data hungry. Crowdsourcing is a relatively cheap way to obtain labeled data, but the annotators are unreliable, so redundant labeling and aggregation techniques are required. We evaluate multiple ... More

A Topologically Stable Solution in Quantum ElectrodynamicsNov 30 1993This paper constructs exact classical solutions of the equations of QED. These are constructed in 4+2 dimensional space, which fibers over the usual 3+1 dimensional space-time. The solution is stationary and localised about a topological singularity in ... More

Divisibility Tests Unified: Stacking the Trimmings for SumsMar 12 2019Divisibility tests are algorithms that can quickly decide if one integer is divisible by another. There are many tests but most are either of the trimming or summing variety. Our goals are to present Zbikowski's family of trimming tests as one test and ... More

Quark masses, mixings, and CP violation from spontaneous breaking of flavor $SU(3)^{3}$Jul 16 2013Feb 25 2014A ${\cal G}_{\cal F}=SU(3)_{Q}\times SU(3)_{u}\times SU(3)_{d}$ invariant scalar potential breaking spontaneously the quark flavor symmetry can explain the standard model flavor puzzle. The approximate alignment in flavor space of the vacuum expectation ... More

Convergence to equilibrium for a bulk--surface Allen--Cahn system coupled through a Robin boundary conditionFeb 19 2019We consider a coupled bulk--surface Allen--Cahn system affixed with a Robin-type boundary condition between the bulk and surface variables. This system can also be viewed as a relaxation to a bulk--surface Allen--Cahn system with non-trivial transmission ... More

Thermodynamically Consistent Navier--Stokes--Cahn--Hilliard Models with Mass Transfer and ChemotaxisFeb 20 2017We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues of earlier Cahn--Hilliard--Darcy ... More

Making the small oblique parameters largeSep 14 1993We compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $. We show that, when ... More

A Noether Theorem for Markov ProcessesMar 09 2012Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the ... More

On the Angular Width of Diffractive Beam in Anisotropic MediaDec 15 20112-D diffraction patterns arising in the far-field region were investigated theoretically for the case, when the plane wave with non collinear group and phase velocities is incident on the wide slit in opaque screen with arbitrary orientation. This investigation ... More

Photoelectric cross-sections of gas and dust in protoplanetary disksJul 18 2011We provide simple polynomial fits to the X-ray photoelectric cross-sections (0.03 < E < 10keV) for mixtures of gas and dust found in protoplanetary disks. Using the solar elemental abundances of Asplund et al. (2009) we treat the gas and dust components ... More

The Chemical Evolution of Protoplanetary DisksAug 25 2009The origins of planets, and perhaps life itself, is intrinsically linked to the chemistry of planet formation. In this chapter we will attempt to explore the chemistry of planet-forming disks from the perspective of knowledge gained from decades of solar ... More

Susceptibilities, the Specific Heat and a Cumulant in Two-Flavour QCDJun 13 1994We study the quark mass dependence of various response functions, which contribute to chiral susceptibilities and the specific heat in the staggered fermion formulation of two-flavour QCD. This yields information about the critical exponents $\alpha$, ... More

On the range of lattice models in high dimensions - extended versionJun 22 2018In this paper we investigate the scaling limit of the range (the set of visited vertices) for a class of critical lattice models, starting from a single initial particle at the origin. We give conditions on the random sets and an associated "ancestral ... More

Massive quark scattering at strong coupling from AdS/CFTNov 02 2009May 26 2010We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the N=2 hypermultiplets which arise when D7-brane probes are included in the AdS_5 ... More

Characterising and recognising game-perfect graphsOct 29 2018Mar 30 2019Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once the graph is ... More

Level-Rank Duality in Chern-Simons Theory from a Non-Supersymmetric Brane ConfigurationAug 20 2014We derive level-rank duality in pure Chern-Simons gauge theories from a non-supersymmetric Seiberg duality by using a non-supersymmetric brane configuration in type IIB string theory. The brane configuration consists of fivebranes, N D3 antibranes and ... More

The dimension of the boundary of super-Brownian motionNov 09 2017We show that the Hausdorff dimension of the boundary of $d$-dimensional super-Brownian motion is $0$, if $d=1$, $4-2\sqrt2$, if $d=2$, and $(9-\sqrt{17})/2$, if $d=3$.

Warping Peirce Quincuncial PanoramasNov 14 2010Sep 26 2015The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic applications. ... More

Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient FlowNov 05 2007In this paper, we propose an efficient and accurate numerical method for computing the ground state of spin-1 Bose-Einstein condensates (BEC) by using the normalized gradient flow or imaginary time method. The key idea is to find a third projection or ... More

Canonical Quantization of $(2+1)$ Dimensional Qed with Topological Mass TermMar 10 1992We discuss the canonical quantization of Quantum Electrodynamics in $2+1$ dimensions, with a Chern-Simons topological mass term and gauge-covariant coupling to a Dirac spinor field. A gauge-fixing term is used which generates a canonical momentum for ... More

Dynamical simulations of QCD at finite temperature with a truncated perfect actionSep 19 2006The Hypercube operator determines a variant of the approximate, truncated perfect fermion action. In this pilot study we are going to report on first experiences in dynamical QCD simulations with the Hypercube fermions. We apply this formulation in an ... More

The propagation of Lyman-alpha in evolving protoplanetary disksJul 18 2011We study the role resonant scattering plays in the transport of Lyman-alpha photons in accreting protoplanetary disk systems subject to varying degrees of dust settling. While the intrinsic stellar FUV spectrum of accreting T Tauri systems may already ... More

On the occurrence of large gaps in small contingency tablesDec 03 2009Examples of small contingency tables on binary random variables with large integer programming gaps on the lower bounds of cell entries were constructed by Sullivant. We argue here that the margins for which these constructed large gaps occur are rarely ... More

Astrochemistry and ObservationsNov 10 2003A major limitation and a continuing source of confusion in the interpretation of molecular line observations has been the large degree of chemical complexity that is observed in star-forming molecular cores. The past decade has seen dramatic improvements ... More

Holographic Corrections to the Veneziano AmplitudeJul 15 2016We propose a holographic computation of the $2\rightarrow 2$ meson scattering in a curved string background, dual to a QCD-like theory. We recover the Veneziano amplitude and compute a perturbative correction due to the background curvature. The result ... More

A fair comparison of many max-tree computation algorithms (Extended version of the paper submitted to ISMM 2013Dec 08 2012Jan 10 2013With the development of connected filters for the last decade, many algorithms have been proposed to compute the max-tree. Max-tree allows to compute the most advanced connected operators in a simple way. However, no fair comparison of algorithms has ... More

Diffusive Heat Waves in Random Conformal Field TheoryJul 26 2018Feb 14 2019We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random ... More

Spectral energy distributions of selfgravitating QSO discsSep 23 2002We calculate spectral energy distributions (SEDs) of steady accretion discs at high accretion rates, as appropriate for bright QSOs, under the assumption that the outer parts are heated sufficiently to maintain marginal gravitational stability, presumably ... More

Two-forms and Noncommutative Hamiltonian dynamicsJan 16 2001In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and Lie derivatives ... More

The fastest pulses that implement dynamically corrected gatesFeb 28 2018Mar 30 2018Dynamically correcting for unwanted interactions between a quantum system and its environment is vital to achieving the high-fidelity quantum control necessary for a broad range of quantum information technologies. In recent work, we uncovered the complete ... More

On the boundary of the zero set of super-Brownian motion and its local timeFeb 11 2018If $X(t,x)$ is the density of one-dimensional super-Brownian motion, we prove that $\text{dim}(\partial\{x:X(t,x)>0\})=2-2\lambda_0\in(0,1)$ a.s. on $\{X_t\neq 0\}$, where $-\lambda_0\in(-1,-1/2)$ is the lead eigenvalue of a killed Ornstein-Uhlenbeck ... More

A lower bound for $p_c$ in range-$R$ bond percolation in two and three dimensionsMar 14 2016We use the connection between bond percolation and SIR epidemics to establish lower bounds for the critical percolation probability in $2$ and $3$ dimensions as the range becomes large. The bound agrees with the conjectured asymptotics for the long range ... More

A Compositional Framework for Passive Linear NetworksApr 22 2015Sep 28 2016Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors. We describe a category where a morphism is a circuit of this sort with marked input ... More

Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxisApr 01 2016May 03 2017We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by healthy tissue. ... More

Parameter identification via optimal control for a Cahn--Hilliard-chemotaxis system with a variable mobilityJul 21 2017We consider the inverse problem of identifying parameters in a variant of the diffuse interface model for tumour growth model proposed by Garcke, Lam, Sitka and Styles (Math. Models Methods Appl. Sci. 2016). The model contains three constant parameters; ... More

Clustering Effects on Wireless Mobile Ad-Hoc Networks PerformancesMar 12 2014A new era is dawning for wireless mobile ad hoc networks where communication will be done using a group of mobile devices called cluster, hence clustered network. In a clustered network, protocols used by these mobile devices are different from those ... More

557 GHz Observations of Water Vapor Outflows from VY CMa and W HydraeDec 26 2001We report the first detection of thermal water vapor emission in the 557 GHz, $1_{10} - 1_{01}$ ground state transition of ortho-H$_2$O toward VY Canis Majoris. In observations obtained with the Submillimeter Wave Astronomy Satellite (SWAS), we measured ... More

Caustics, Critical Curves and Cross Sections for Gravitational Lensing by Disk GalaxiesFeb 10 1997Aug 28 1997We study strong gravitational lensing by spiral galaxies, modeling them as infinitely thin uniform disks embedded in singular isothermal spheres. We derive general properties of the critical curves and caustics analytically. The multiple-image cross section ... More

Towards a string representation of infrared SU(2) Yang-Mills theoryMay 20 1999We employ a heat kernel expansion to derive an effective action that describes four dimensional SU(2) Yang-Mills theory in the infrared limit. Our result supports the proposal that at large distances the theory is approximated by the dynamics of knotted ... More

Positive semiclassical states for a fractional Schrödinger-Poisson systemJan 04 2016We consider a fractional Schr\"odinger-Poisson system in the whole space $\mathbb R^{N}$ in presence of a positive potential and depending on a small positive parameter $\varepsilon.$ We show that, for suitably small $\varepsilon$ (i.e. in the "semiclassical ... More

Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge TheoryMay 10 2001May 25 2001We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on ... More

Maxwell-Chern-Simons Theory in Covariant and Coulomb GaugesSep 22 1994We quantize Quantum Electrodynamics in $2+1$ dimensions coupled to a Chern-Simons (CS) term and a charged spinor field, in covariant gauges and in the Coulomb gauge. The resulting Maxwell-Chern-Simons (MCS) theory describes charged fermions interacting ... More