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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

The Algebra of Open and Interconnected SystemsSep 17 2016Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, ... 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

Analytical Methods for Squaring the DiscSep 21 2015Oct 27 2015We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region. Ideally, we want ... More

Revolvable Indoor Panoramas Using a Rectified Azimuthal ProjectionJun 10 2012May 02 2016We present an algorithm for converting an indoor spherical panorama into a photograph with a simulated overhead view. The resulting image will have an extremely wide field of view covering up to 4{\pi} steradians of the spherical panorama. We argue that ... More

Squircular CalculationsApr 08 2016Jun 02 2016The Fernandez-Guasti squircle is a plane algebraic curve that is an intermediate shape between the circle and the square. In this paper, we will analyze this curve and derive formulas for its area, arc length, and polar form. We will also provide several ... More

Decorated CospansFeb 03 2015Aug 11 2015Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor $F: (\mathcal ... 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

Second quantization of the elliptic Calogero-Sutherland modelFeb 07 2001We use loop group techniques to construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable ... More

Generalized Yang-Mills actions from Dirac operator determinantsApr 08 2001We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R^4 twisted by ... More

Source identity and kernel functions for elliptic Calogero-Sutherland type systemsMar 03 2010Jul 16 2010Kernel functions related to quantum many-body systems of Calogero-Sutherland type are discussed, in particular for the elliptic case. The main result is an elliptic generalization of an identity due to Sen that is a source for many such kernel functions. ... More

An explicit solution of the (quantum) elliptic Calogero-Sutherland modelJul 21 2004Sep 06 2004We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and ... 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

Anyons and the elliptic Calogero-Sutherland modelJul 27 2000Feb 07 2001We obtain a second quantization of the elliptic Calogero-Sutherland (eCS) model by constructing a quantum field theory model of anyons on a circle and at a finite temperature. This yields a remarkable identity involving anyon correlation functions and ... More

On anomalies and noncommutative geometryJul 17 1995I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.

Non--commutative Integration CalculusJan 20 1995We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. We consider the differential complex of forms $u_0\ccr{\eps}{u_1}\cdots\ccr{\eps}{u_n}$ with $\eps$ a grading operator ... More

Fermion Current Algebras and Schwinger Terms in 3+1 DimensionsApr 24 1993Apr 24 1993We discuss the restricted linear group in infinite dimensions modeled by the Schatten class of rank $2p=4$ which contains $(3+1)$-dimensional analog of the loop groups and is closely related to Yang-Mills theory with fermions in $(3+1)$-dimensions. We ... More

A two dimensional analogue of the Luttinger modelJun 17 2006Apr 14 2010We present a fermion model that is, as we suggest, a natural 2D analogue of the Luttinger model. We derive this model as a partial continuum limit of a 2D spinless lattice fermion system with local interactions and away from half filling. In this derivation, ... 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

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.

Quantum Gauge Theories and Noncommutative GeometryAug 01 1996I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from quantum field theory ... More

Cocycles for Boson and Fermion Bogoliubov TransformationsMay 05 1993Unitarily implementable Bogoliubov transformations for charged, relativistic bos\-ons and fermions are discussed, and explicit formulas for the 2-cocycles appearing in the group product of their implementers are derived. In the fermion case this provides ... More

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

MicroRNA Systems BiologyDec 20 2007Recently, microRNAs (miRNAs) have emerged as central posttranscriptional regulators of gene expression. miRNAs regulate many key biological processes, including cell growth, death, development and differentiation. This discovery is challenging the central ... 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

Understanding genomic alterations in cancer genomes using an integrative network approachSep 10 2014In recent years, cancer genome sequencing and other high-throughput studies of cancer genomes have generated many notable discoveries. In this review, Novel genomic alteration mechanisms, such as chromothripsis (chromosomal crisis) and kataegis (mutation ... 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

Coding Bounds for Multiple Phased-Burst Correction and Single Burst Correction CodesApr 07 2011Jun 23 2011In this paper, two upper bounds on the achievable code rate of linear block codes for multiple phased-burst correction (MPBC) are presented. One bound is constrained to a maximum correctable cyclic burst length within every subblock, or equivalently a ... 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

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

Flavour in Soft LeptogenesisOct 02 2010Successful Soft Leptogenesis (SL) requires a relatively low mass scale for the SU(2) singlet neutrinos of $10^5-10^8$ GeV. However, conventional SL (unflavoured) requires an unnaturally small soft supersymmetry(SUSY)-breaking bilinear $B \ll \mathcal{O}({\rm ... More

Hilbert functions of colored quotient rings and a generalization of the Clements-Lindström theoremMar 13 2014Dec 02 2014Given a polynomial ring $S = \Bbbk[x_1, \dots, x_n]$ over a field $\Bbbk$, and a monomial ideal $M$ of $S$, we say the quotient ring $R = S/M$ is Macaulay-Lex if for every graded ideal of $R$, there exists a lexicographic ideal of $R$ with the same Hilbert ... More

Corelations are the prop for extraspecial commutative Frobenius monoidsJan 11 2016Jan 30 2016Just as binary relations between sets may be understood as jointly monic spans, so too may equivalence relations on the disjoint union of sets be understood as jointly epic cospans. With the ensuing notion of composition inherited from the pushout of ... More

Kähler-Ricci Flow on Projective Bundles over Kähler-Einstein ManifoldsApr 20 2011Oct 19 2011We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum profile, we ... 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

Ground-state fidelity in one-dimensional gapless modelJul 31 2007Nov 09 2007A general relation between quantum phase transitions and the second derivative of the fidelity (or the "fidelity susceptibility") is proposed. The validity and the limitation of the fidelity susceptibility in characterizing quantum phase transitions is ... More

Intermediate-Coupling Theory for the Spectral Weight of Spin PolaronJul 29 1996Within the intermediate-coupling theory, the quasiparticle weight $Z$ of one hole injected in the undoped antiferromagnetic ground state is studied. We find that, for the hole located at the quasiparticle band minimun with momentum ${\bf k}_0 = (\pm \frac{\pi}{2}, ... More

An application of liaison theory to the Eisenbud-Green-Harris conjectureNov 05 2013In this paper, we apply liaison theory to the Eisenbud-Green-Harris conjecture and prove that the conjecture holds for a certain subclass of homogeneous ideals in the linkage class of a complete intersection ideal. In the case of three variables, we prove ... More

The Locations of Short Gamma-ray Bursts as Evidence for Compact Object Binary ProgenitorsJul 02 2013We present a detailed investigation of Hubble Space Telescope (HST) rest-frame UV/optical observations of 22 short gamma-ray burst (GRB) host galaxies and sub-galactic environments. Utilizing the high angular resolution and depth of HST, we characterize ... 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

The Galactic and Sub-Galactic Environments of Short-Duration Gamma-Ray Bursts: Implications for the ProgenitorsDec 21 2009The study of short-duration gamma-ray bursts (GRBs) has undergone a revolution in recent years thanks to the discovery of the first afterglows and host galaxies in May 2005. In this review we summarize our current knowledge of the galactic and sub-galactic ... 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

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

Spontaneous breaking of the flavor symmetry avoids the strong CP problemMay 07 2013A promising approach to the Standard Model flavor puzzle is based on the idea that the $SU(3)^3$ quark-flavor symmetry is spontaneously broken by vacuum expectation values of `Yukawa fields' which minimize the symmetry invariant scalar potential at configurations ... More

On fast CP violating interactions in leptogenesisApr 15 2010May 09 2012We show that when the relevant CP violating interactions in leptogenesis are fast, the different matter density asymmetries are determined at each instant by a balance condition between the amount of asymmetry being created and destroyed. This fact allows ... 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

Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transportNov 19 2015May 25 2016We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the presence of ... More

Methods for Accelerating Conway's Doomsday Algorithm (part 2)Oct 05 2010Aug 08 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

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

Finding and solving Calogero-Moser type systems using Yang-Mills gauge theoriesSep 16 1999Sep 21 1999Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a Yang-Mills ... 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

Source identity and kernel functions for Inozemtsev-type systemsFeb 16 2012The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BC_N trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural many-variable generalization of the Heun differential equation. ... More

Bachet's Problem: as few weights to weigh them allOct 26 2010A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 inclusive, if the weights can be placed in either of the scale pans ?" W.W. ... More

GeneNetMiner: accurately mining gene regulatory networks from literatureSep 06 2014GeneNetMiner is standalone software which parses the sentences of iHOP and captures regulatory relations. The regulatory relations are either gene gene regulations or gene biological processes relations. Capturing of gene biological process relations ... More

The Majid-Ruegg model and the Planck scalesJun 19 2013Nov 13 2013A novel differential calculus with central inner product is introduced for kappa-Minkowski space. The `bad' behaviour of this differential calculus is discussed with reference to symplectic quantisation and A-infinity algebras. Using this calculus in ... More

Classification of Minimal Polygons with Specified Singularity ContentMar 15 2017It is known that there are only finitely many mutation-equivalence classes with a given singularity content, and each of these equivalence classes contains only finitely many minimal polygons. We describe an efficient algorithm to classify these minimal ... More

An Explicit Formula for the Local zeta Function of a Laurent PolynomialFeb 21 2014Apr 08 2016In a recent paper Z\'u\~niga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a Laurent polynomial ... More

Noncommutative geodesics and the KSGNS constructionNov 19 2018We study parallel transport and geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel'fand, Naimark & Segal (KSGNS) construction. This is motivated from classical geometry, ... 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

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

A product formula for the eigenfunctions of a quartic oscillatorDec 12 2013Sep 12 2016We consider the Schr\"odinger operator on the real line with an even quartic potential. Our main result is a product formula of the type $\psi_k(x)\psi_k(y) = \int_{\mathbb{R}} \psi_k(z)\mathcal{K}(x,y,z)dz$ for its eigenfunctions $\psi_k$. The kernel ... 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

Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise caseSep 01 2008We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is H\"older continuous of index $\gamma>3/4$. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument ... More

Elementary Derivation of the Chiral AnomalyDec 15 1994Jan 24 1995An elementary derivation of the chiral gauge anomaly in all even dimensions is given in terms of noncommutative traces of pseudo-differential operators.

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

Chiral Schwinger models without gauge anomaliesApr 25 2000We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian models in ... 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

Construction by bosonization of a fermion-phonon modelMar 06 2015Dec 03 2015We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization. We present a ... More

Weak convergence of measure-valued processes and $r$-point functionsOct 16 2007We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions ... 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

Spectral triples from bimodule connections and Chern connectionsAug 19 2015Sep 03 2015We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators $D$ starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of $M_2(\Bbb C)$, and also applies to the standard ... More

A Semantics for Approximate Program TransformationsApr 19 2013An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power consumption, and memory ... 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

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

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

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

A Novel Approach for Modeling Complex Deep FuturesDec 02 2016Many large-scale, complex systems consist of interactions between humans, human-made systems and the environment. The approach developed in this paper is to partition the problem space into two fundamental layers and identify, parameterize and model the ... More

Minimal metrics on 6-dimensional complex nilmanifoldsSep 13 2013Sep 22 2013Let (N,J) be a real 2n-dimensional nilpotent Lie group endowed with an invariant complex structure. A left-invariant Riemannian metric on N compatible with J is said to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among ... 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

Quantum phase transitions of two-species bosons in square latticeSep 15 2010We investigate various quantum phase transitions of attractive two-species bosons in a square lattice. Using the algorithm based on the tensor product states, the phase boundaries of the pair superfluid states with nonzero pair condensate density \emph{and} ... More

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

Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy system modelling tumour growthAug 31 2016Oct 23 2016We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy's law. The system of equations arises from a mixture model for tumour ... More

Graphs attached to simple Frobenius-Perron dimensions of an integral fusion categoryMar 05 2014Nov 16 2014Let C be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category C, that extend the corresponding graphs associated to the irreducible ... 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