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On the diffraction measure of $k$-free integersJul 10 2019Jul 11 2019We show that the scaling of the total diffraction intensity for the set of $k$-free integers near the origin is asymptotically approximated by a power law. This considerably improves on recent work by Baake and Coons whose main result provides upper and ... More

The Hasse Norm Principle For Biquadratic ExtensionsJul 03 2017Aug 01 2018We give an asymptotic formula for the number of biquadratic extensions of the rationals of bounded discriminant that fail the Hasse norm principle.

A Positive Proportion of Hasse Principle Failures in a Family of Châtelet SurfacesMar 19 2018Feb 22 2019We investigate the family of surfaces defined by the affine equation $$Y^2 + Z^2 = (aT^2 + b)(cT^2 +d)$$ where $\vert ad-bc \vert=1$ and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly ... More

Fields of definition of curves of a given degreeJan 31 2019Kontsevich and Manin gave a formula for the number $N_e$ of rational plane curves of degree $e$ through $3e-1$ points in general position in the plane. When these $3e-1$ points have coordinates in the rational numbers, the corresponding set of $N_e$ rational ... More

On the diffraction measure of $k$-free integersJul 10 2019We show that the scaling of the total diffraction intensity for the set of $k$-free integers near the origin is asymptotically approximated by a power law. This considerably improves on recent work by Baake and Coons whose main result provides upper and ... More

Near field imaging of small isotropic and extended anisotropic scatterersJan 12 2016Jan 17 2017In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic scatterers via the ... More

Probing texture zeros with scaling ansatz in inverse seesawJan 05 2015May 21 2015We investigate neutrino mass matrix phenomenology involving scaling ansatz and texture zeros adhering inverse seesaw mechanism. It is seen that four is the maximum number of zeros in $m_D$ and $\mu$ to obtain viable phenomenology. Depending upon the generic ... More

Near field imaging of small isotropic and extended anisotropic scatterersJan 12 2016Sep 11 2016In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic scatterers via the ... More

Extended scaling and residual flavor symmetry in the neutrino Majorana mass matrixApr 22 2016Jul 01 2016The residual symmetry approach, along with a complex extension for some flavor invariance, is a powerful tool to uncover the flavor structure of the $3\times3$ neutrino Majorana mass matrix $M_\nu$ towards gaining insights into neutrino mixing. We utilize ... More

Representing seesaw neutrino models and their motion in lepton flavour spaceDec 19 2018Feb 14 2019We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular ... More

Probing relic neutrino decays with 21 cm cosmologyMay 29 2018Sep 20 2018We show how 21 cm cosmology can test relic neutrino radiative decays into sterile neutrinos. Using recent EDGES results, we derive constraints on the lifetime of the decaying neutrinos. If the EDGES anomaly will be confirmed, then there are two solutions, ... More

Inflationary Attractors and Perturbation Spectra in Generally Coupled GravityMar 19 1993A generic outcome of theories with scalar-tensor coupling is the existence of inflationary attractors, either power-law or de Sitter. The fluctuations arising during this phase are Gaussian and their spectrum depends on the wavenumber $k$ according to ... More

Quarticles and the Identity of IndiscerniblesAug 01 2002Aug 11 2004The principle of the identity of indiscernibles (PII) states that if two systems are qualitatively identical then they are logically identical. French and Redhead (1988) and Butterfield (1993) have shown the sense in which bosons and fermions violate ... More

Weak Lensing and CosmologyOct 16 1996We explore the dependence of weak lensing phenomena on the background cosmology. We first generalise the relation between $P_\psi(\omega)$, the angular power spectrum of the distortion, and the power spectrum of density fluctuations to non-flat cosmologies. ... More

Weak Gravitational Lensing: Current Status and Future ProspectsSep 05 1995In this review I will describe progress that has been made in determining masses of galaxy clusters using `weak lensing' and how this technique my be applied in the future to determine the dark matter distribution both on supercluster scales and on the ... More

Additional Fermion Families and Precision Electroweak DataAug 17 1994The S,T, and U formalism for studying electroweak precision data has recently been updated to include the effects of new light physics and within this analysis the latest LEP and SLC data tightly constrain models of physics beyond the Standard Model. ... More

Quark Condensates in Non-Supersymmetric MQCDJan 23 1998Jun 14 1998A set of non-supersymmetric minimal area embeddings of an M-theory 5-brane are considered. The field theories on the surface of the 5-brane have the field content of N=2 SQCD with fundamental representation matter fields. By suitable choice of curve parameters ... More

Dynamical Generation of the CKM MatrixOct 07 1994We argue that in dynamical models of fermion masses, which explain the three mass scales of the generations of fermions with three separate heavy scales above the electroweak symmetry breaking scale, the off diagonal CKM matrix elements must be generated ... More

Fermion Mass Postdictions in a Generalized Extended Technicolour ScenarioMay 23 1994We review the recent discussion in the literature of one family extended technicolour models with techni-fermion mass spectra compatible with the experimental data for the precision parameters S,T,U,V, W and X and ETC interactions compatible with the ... More

The iterated Carmichael lambda functionNov 15 2011The Carmichael lambda function $\lambda(n)$ is defined to be the smallest positive integer $m$ such that $a^m$ is congruent to 1 modulo $n,$ for all $a$ and $n$ relatively prime. The function $\lambda_k(n)$ is defined to be the $k$th iterate of $\lambda(n).$ ... More

Stability properties of some particle filtersSep 30 2011Dec 05 2013Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic, relative variance ... More

Tracing High Redshift Starformation in the Current and Next Generation of Radio SurveysNov 24 2009The current deepest radio surveys detect hundreds of sources per square degree below 0.1mJy. There is a growing consensus that a large fraction of these sources are dominated by star formation although the exact proportion has been debated in the literature. ... More

Some Applications of the Fractional Poisson Probability DistributionDec 05 2008Nov 17 2011Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have discovered ... More

Easily testable logical networks based on a 'widened long flip-flop'Aug 19 2008Aug 20 2008The article describes an attempt to solve at once three basic problems arising at testing a complex digital equipment for defects: 1) the problem of an exponential increasing of the complexity of testing the equipment with the complexity of the equipment; ... More

Knowledge TechnologiesFeb 26 2008Several technologies are emerging that provide new ways to capture, store, present and use knowledge. This book is the first to provide a comprehensive introduction to five of the most important of these technologies: Knowledge Engineering, Knowledge ... More

Exciton-Phonon Dynamics with Long-Range InteractionApr 07 2011Exciton-phonon dynamics on a 1D lattice with long-range exciton-exciton interaction have been introduced and elaborated. Long-range interaction leads to a nonlocal integral term in the motion equation of the exciton subsystem if we go from discrete to ... More

Biequivalences in tricategoriesFeb 04 2011We show that every internal biequivalence in a tricategory T is part of a biadjoint biequivalence. We give two applications of this result, one for transporting monoidal structures and one for equipping a monoidal bicategory with invertible objects with ... More

The PPW conjecture in curved spacesMar 24 2015Apr 06 2015In Euclidean and Hyperbolic space, and the hemisphere in $S^n$, geodesic balls maximize the gap $\lambda_2 - \lambda_1$ of Dirichlet eigenvalues, amoung domains with fixed $\lambda_1$. We prove an upper bound on $\lambda_2 - \lambda_1$ for domains in ... More

Versality in mirror symmetryApr 02 2018One of the attractions of homological mirror symmetry is that it not only implies the previous predictions of mirror symmetry (e.g., curve counts on the quintic), but it should in some sense be `less of a coincidence' than they are and therefore easier ... More

On the Nature of Self-Consistency in Density Functional TheoryMar 05 2018A thesis providing a pedagogical introduction to the problem of achieving self-consistency in density functional theory. Contained is an introduction to the framework of Kohn-Sham density functional theory, leading then to the considerations required ... More

Generalized permutohedra in the kinematic spaceApr 16 2018In this note, we study the permutohedral geometry of the poles of a certain differential form introduced in recent work of Arkani-Hamed, Bai, He and Yan. There it was observed that the poles of the form determine a family of polyhedra which have the same ... More

Versality of the relative Fukaya categorySep 21 2017Seidel introduced the notion of a Fukaya category `relative to an ample divisor', explained that it is a deformation of the Fukaya category of the affine variety that is the complement of the divisor, and showed how the relevant deformation theory is ... More

Combinatorics and Representation Theory for Generalized Permutohedra I: Simplicial PlatesNov 21 2016In this paper, we announce results from our thesis, which studies for the first time the categorification of the theory of generalized permutohedra. The vector spaces in the categorification are tightly constrained by certain continuity relations which ... More

The free-boundary Brakke flowFeb 11 2016Nov 16 2017We develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must "pop" upon tangential contact with the barrier. We prove a compactness theorem for ... More

Search for Flavor Changing Non-standard Interactions with the MINOS+ ExperimentNov 01 2015A study of MINOS+ sensitivity to non-standard interactions and previously published results using MINOS data are presented.

The PPW conjecture in curved spacesMar 24 2015Dec 23 2016In Euclidean and Hyperbolic space, and the hemisphere in $S^n$, geodesic balls maximize the gap $\lambda_2 - \lambda_1$ of Dirichlet eigenvalues, amoung domains with fixed $\lambda_1$. We prove an upper bound on $\lambda_2 - \lambda_1$ for domains in ... More

On a conjecture of DegosFeb 11 2015Oct 20 2015In this note we use a result of Kantor to prove a conjecture of Degos. Specifically we prove the following: let $\mathbb{F}$ be a finite field of order $q$ and let $f, g\in\mathbb{F}[X]$ be distinct polynomials of degree $n$ such that $f$ is primitive, ... More

Astronomical Redshifts and the Expansion of SpaceDec 04 2013In homogeneous cosmological models the wavelength $\lambda$ of a photon exchanged between two fundamental observers changes in proportion to expansion of the space $D$ between them, so $\Delta\log(\lambda / D) = 0$. This is exactly the same as for a pair ... More

On the Absence of Broad Forbidden Emission Lines in the Low Luminosity Seyfert 1 Nucleus of NGC 3227Sep 29 2013Dec 22 2015The absence of broad [O III] ${\lambda\lambda}$4959,5007 forbidden emission lines is one of the key arguments cited in the published literature for the gas density exceeding the critical density; 7 ${\times}$ 10$^5$ cm$^{-3}$, in the broad line region ... More

Measuring Gravitational Redshifts in Galaxy ClustersMar 15 2013Jul 24 2013Wojtak {\it et al} have stacked 7,800 clusters from the SDSS survey in redshift space. They find a small net blue-shift for the cluster galaxies relative to the brightest cluster galaxies, which agrees quite well with the gravitational redshift from GR. ... More

Nilpotent Singer GroupsJun 10 2006Let $N$ be a nilpotent group normal in a group $G$. Suppose that $G$ acts transitively upon the points of a finite non-Desarguesian projective plane $\mathcal{P}$. We prove that, if $\mathcal{P}$ has square order, then $N$ must act semi-regularly on $\mathcal{P}$. ... More

Subordinated discrete semigroups of operatorsJan 29 2008Given a power-bounded linear operator T in a Banach space and a probability F on the non-negative integers, one can form a `subordinated' operator S = \sum_k F(k) T^k. We obtain asymptotic properties of the subordinated discrete semigroup (S^n: n=1,2,...) ... More

$PSL(3,q)$ and line-transitive linear spacesMar 13 2006Apr 03 2007We present a partial classification of those finite linear spaces $\mathcal{S}$ on which an almost simple group $G$ with socle $PSL(3,q)$ acts line-transitively.

Conclusions from a NAIVE Bayes Operator Predicting the Medicare 2011 Transaction Data SetFeb 20 2014Introduction: The United States Federal Government operates one of the worlds largest medical insurance programs, Medicare, to ensure payment for clinical services for the elderly, illegal aliens and those without the ability to pay for their care directly. ... More

BPS Black Hole Horizons in N=2 Gauged SupergravityAug 06 2013Sep 12 2013We study static BPS black hole horizons in four dimensional N=2 gauged supergravity coupled to $n_v$-vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric and magnetic ... More

Missing Mirrors: Type IIA Supergravity on the Resolved ConifoldMar 10 2010We consider massive IIA supergravity on the resolved conifold with $SU(2)_L^2\times U(1)_R$ symmetry and $\N=1$ supersymmetry. A one dimensional family of such regular solutions was found by Brandhuber and we propose this to be the mirror to one dimension ... More

Directing Power Towards Sub-AlternativesJul 11 2019This paper proposes a novel test statistic for testing a potentially high-dimensional parameter vector. To derive the statistic, I generalize the Mahalanobis distance to measure length in a direction of interest. The test statistic is the sample analogue ... More

Second Order Operators Subject to Dirichlet Boundary Conditions in Weighted Triebel-Lizorkin Spaces: Parabolic ProblemsDec 13 2018In this paper we consider second order parabolic partial differential equations subject to the Dirichlet boundary condition on smooth domains. We establish weighted $L_{q}$-maximal regularity in weighted Triebel-Lizorkin spaces for such parabolic problems ... More

On the real spectrum of a product of Gaussian random matricesJan 31 2017Let $X_{m} = G_{1}\ldots G_{m}$ denote the product of $m$ independent random matrices of size $N \times N$, with each matrix in the product consisting of independent standard Gaussian variables. Denoting by $N_{\mathbb{R}}(m)$ the total number of real ... More

Orientable regular maps with Euler characteristic divisible by few primesMar 01 2012May 17 2012Let $G$ be a $(2,m,n)$-group and let $x$ be the number of distinct primes dividing $\chi$, the Euler characteristic of $G$. We prove, first, that, apart from a finite number of known exceptions, a non-abelian simple composition factor $T$ of $G$ is a ... More

Quasirandom group actionsFeb 05 2013Feb 19 2013Let $G$ be a finite group acting transitively on a set $\Omega$. We study what it means for this action to be {\it quasirandom}, thereby generalizing Gowers' study of quasirandomness in groups. We connect this notion of quasirandomness to an upper bound ... More

New Polynomials and Numbers Associated with Fractional Poisson Probability DistributionOct 14 2010Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.

STIS Spectroscopy of the Central 14 pc of NGC 3998: Evidence for an InflowAug 27 2010Nov 12 2010Prior imaging of the lenticular galaxy, NGC 3998, with the Hubble Space Telescope (HST) revealed a small, highly inclined, nuclear ionized gas disk, the kinematics of which indicate the presence of a 270 million solar mass black hole. Plausible kinematic ... More

The Size, Structure and Ionization of the Broad Line Region in NGC 3227Jun 06 2012Oct 25 2012Hubble Space Telescope (HST) spectroscopy of the Seyfert 1.5 galaxy, NGC 3227, confirms previous reports that the broad H-alpha emission line flux is time variable, decreasing by a modest ~ 11% between 1999 and 2000 in response to a corresponding ~ 37% ... More

A Spin Chain from String TheoryMay 28 2008We study the semiclassical spectrum of bosonic string theory on AdS_3 x S^1 in the limit of large AdS angular momentum. At leading semiclassical order, this is a subsector of the IIB superstring on AdS_5 x S^5. The theory includes strings with K spikes ... More

Sequential Monte Carlo samplers: error bounds and insensitivity to initial conditionsMar 21 2011This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end distributions in the ... More

Principles of Fractional Quantum MechanicsSep 28 2010A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity ... More

Magnon Bound States and the AdS/CFT CorrespondenceApr 24 2006Jun 12 2006We study the spectrum of asymptotic states in the spin-chain description of planar N=4 SUSY Yang-Mills. In addition to elementary magnons, the asymptotic spectrum includes an infinite tower of multi-magnon bound states with exact dispersion relation, ... More

The free-boundary Brakke flowFeb 11 2016Jun 10 2016We define a notion of Brakke flow with free-boundary in a barrier surface, and prove this class admits compactness. We find we must weaken the original notion of Brakke flows to allow the flow to "pop" at the barrier. We define a Gaussian monotonicity ... More

Strong Extended Technicolour Interactions and the $Zb\bar{b}$ VertexMar 21 1994LEP precision measurements of the $Zb\bar{b}$ vertex coupling are sufficiently accurate to see the non-oblique corrections from the heavy gauge boson responsible for the large top mass in standard extended tecnicolour models. If the ETC couplings are ... More

V,W and X in Technicolour ModelsNov 30 1993Light techni-fermions and pseudo Goldstone bosons that contribute to the electroweak radiative correction parameters V,W and X may relax the constraints on technicolour models from the experimental values of the parameters S and T. Order of magnitude ... More

Testing Models for Structure FormationSep 21 1993I review a number of tests of theories for structure formation. Large-scale flows and IRAS galaxies indicate a high density parameter $\Omega \simeq 1$, in accord with inflationary predictions, but it is not clear how this meshes with the uniformly low ... More

Logic Column 13: Reasoning Formally about Quantum Systems: An OverviewAug 01 2005This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for specification and analysis of quantum information systems, in particular, recent work by ... More

Maximal Regularity with Weights for Parabolic Problems with Inhomogeneous Boundary DataFeb 09 2017In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, ... More

A Finite Block Length Achievability Bound for Low Probability of Detection CommunicationJan 15 2018Jul 30 2018Low probability of detection (or covert) communication refers to the scenario where information must be sent reliably to a receiver, but with low probability of detection by an adversary. Recent works on the fundamental limits of this communication problem ... More

Canonical Bases for Permutohedral PlatesDec 22 2017Feb 01 2018We study three finite-dimensional quotient vector spaces constructed from the linear span of the set of characteristic functions of permutohedral cones by imposing two kinds of constraints: (1) neglect characteristic functions of higher codimension permutohedral ... More

Photoionization Modeling of the Low Luminosity Seyfert 1 Nucleus in NGC 3516Dec 14 2015Spectroscopic observations of the low luminosity Seyfert 1 nucleus in NGC 3516 obtained with the Hubble Space Telescope show that the visible spectrum is dominated by the Balmer emission lines of Hydrogen (H) and a continuum luminosity that rises into ... More

Skeptical Notes on a Physics of PassageAug 25 2015This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question of the paper ... More

Giant Broad Line Regions in Dwarf SeyfertsAug 18 2015High angular resolution spectroscopy obtained with the Hubble Space Telescope (HST) has revealed a remarkable population of galaxies hosting dwarf Seyfert nuclei with an unusually large broad-line region (BLR). These objects are remarkable for two reasons. ... More

Honeycomb tessellations and canonical bases for permutohedral bladesOct 08 2018Nov 27 2018This paper studies two families of piecewise constant functions which are determined by the $(n-2)$-skeleta of collections of honeycomb tessellations of $\mathbb{R}^{n-1}$ with standard permutohedra. The union of the codimension $1$ cones obtained by ... More

The monoidal structure of strictificationJan 25 2013We study the monoidal structure of the standard strictification functor $\textrm{st}:\mathbf{Bicat} \rightarrow \mathbf{2Cat}$. In doing so, we construct monoidal structures on the 2-category whose objects are bicategories and on the 2-category whose ... More

On the monodromy group of the family of smooth plane curvesOct 16 2016We consider the space of smooth complex projective plane curves of degree d. Defined over this is the tautological family of plane curves, and hence there is a monodromy representation into the mapping class group of the fiber. We show two results concerning ... More

Cup products in surface bundles, higher Johnson invariants, and MMM classesJan 28 2016In this paper we prove a family of results connecting the problem of computing cup products in surface bundles to various other objects that appear in the theory of the cohomology of the mapping class group $\operatorname{Mod}_g$ and the Torelli group ... More

Model-Based Reconstruction for Quantitative MRI using the Bloch EquationsMay 06 2019In this work a generic model-based reconstruction for the quantification of relaxation parameters is developed. In contrast to previous approaches that rely on simplified models derived from the Bloch equations, this work includes the Bloch equations ... More

A classification of the symmetries of uniform discrete defective crystalsOct 01 2013Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The geometrical ... More

On the comprehension schema in LP=>May 31 2013Sep 11 2013We construct a model of the comprehension schema in the logic LP=>.

An Exploratory Data Survey of Drug Name Incidence and Prevalence From the FDA's Adverse Event Reporting System, 2004 to 2012Q2Aug 31 2013Drug Names, Population Level Surveillance and the FDA's Adverse Event Reporting System: An Exploratory Data Survey of Drug Name Incidence and Prevalence, 2004-2012Q2 Purpose: To count and monitor the drug names reported in the publicly available version ... More

Surface bundles over surfaces with arbitrarily many fiberingsJul 08 2014Oct 11 2016In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a surface bundle ... More

Transitive projective planes and 2-rankNov 28 2007Mar 06 2008Suppose that a group $G$ acts transitively on the points of a non-Desarguesian plane, $\mathcal{P}$. We prove first that the Sylow 2-subgroups of $G$ are cyclic or generalized quaternion. We also prove that $\mathcal{P}$ must admit an odd order automorphism ... More

Transitive projective planesMar 11 2006Apr 03 2007A long-standing conjecture is that any transitive finite projective plane is Desarguesian. We make a contribution towards a proof of this conjecture by showing that a group acting transitively on the the points of a non-Desarguesianprojective plane must ... More

Entanglement Telegraphed Communication Avoiding Light-speed Limitation by Hong Ou Mandel EffectDec 15 2007Dec 19 2007Faster-than-light communication is possible via quantum entanglement in an EPR experiment if one can overcome nature's "quantum modesty" and gain knowledge concerning the quantum state of a single photon. Using a special EPR source that produces precisely ... More

Static BPS Black Holes in AdS4 with General Dyonic ChargesAug 12 2014Aug 20 2014We complete the study of static BPS, asymptotically AdS$_4$ black holes within N=2 FI-gauged supergravity and where the scalar manifold is a homogeneous very special Kahler manifold. We find the analytic form for the general solution to the BPS equations, ... More

Non-geometric String Backgrounds and Worldsheet AlgebrasMay 29 2008Jun 06 2008Using worldsheet Hamiltonian methods we derive a charge algebra which generalizes the Courant bracket to include fluxes of general index type. This is achieved by coupling a bi-vector to the Hamiltonian of the Polyakov model. This bracket is useful to ... More

Operads, tensor products, and the categorical Borel constructionAug 17 2015We show that every action operad gives rise to a notion of monoidal category via the categorical version of the Borel construction, embedding action operads into the category of 2-monads on $\mathbf{Cat}$. We characterize those 2-monads in the image of ... More

Finite asymptotic dimension for CAT(0) cube complexesApr 23 2010Jul 12 2010In this paper we prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is ... More

The half-integral weight eigencurveJun 17 2009In this paper we define Banach spaces of overconvergent half-integral weight $p$-adic modular forms and Banach modules of families of overconvergent half-integral weight $p$-adic modular forms over admissible open subsets of weight space. Both spaces ... More

Polar spaces and embeddings of classical groupsMar 15 2006Given polar spaces $(V,\beta)$ and $(V,Q)$ where $V$ is a vector space over a field $K$, $\beta$ a reflexive sesquilinear form and $Q$ a quadratic form, we have associated classical isometry groups. Given a subfield $F$ of $K$ and an $F$-linear function ... More

Non-Linear Cluster Lens ReconstructionAug 29 1994We develop a method for general non-linear cluster lens reconstruction using the observable distortion of background galaxies. The distortion measures the combination $\gamma/(1-\kappa)$ of shear $\gamma$ and surface density $\kappa$. From this we obtain ... More

A New Shear Estimator for Weak Lensing ObservationsApr 01 1999We present a new shear estimator for weak lensing observations which properly accounts for the effects of a realistic point spread function (PSF). Images of faint galaxies are subject to gravitational shearing followed by smearing with the instrumental ... More

Instantons, Compactification and S-duality in N=4 SUSY Yang-Mills Theory IOct 14 2000We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all beta, ... More

A New Deconstruction of Little String TheoryJun 11 2004Jul 02 2004We present evidence for a new deconstruction of Little String Theory (LST). The starting point is a four-dimensional conformal field theory on its Higgs branch which provides a lattice regularization of six-dimensional gauge theory. We argue that the ... More

FERMION MASSES IN EXTENDED TECHNICOLOURJan 16 1995Talks presented at Beyond The Standard Model IV Conference, Lake Tahoe, Dec 94: NEW FERMION FAMILIES AND PRECISION ELECTROWEAK DATA: We highlight a trend in the precision electroweak data towards light new physics and argue that some spectra of strongly ... More

Levy Flights over Quantum PathsApr 14 2005An impact of integration over the paths of the Levy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox H-function. A new equation for the kernel of a partical ... More

A conservation approach to helicoidal surfaces of constant mean curvature in R^3, S^3 and H^3Oct 05 2011We develop a conservation law for constant mean curvature (CMC) surfaces introduced by Korevaar, Kusner and Solomon, and provide a converse, so as to characterize CMC surfaces by a conservation law. We work with `twizzler' construction, which applies ... More

Loop spaces, and coherence for monoidal and braided monoidal bicategoriesFeb 04 2011We prove a coherence theorem for braided monoidal bicategories and relate it to the coherence theorem for monoidal bicategories. We show how coherence for these structures can be interpretted topologically using up-to-homotopy operad actions and the algebraic ... More

Holographic QCD & PerfectionJan 25 2007A holographic description of chiral symmetry breaking in the pattern of QCD is reviewed. D7 brane probes are used to include quark fields in a simple non-supersymmetric deformation of the AdS/CFT Correspondence. The axial symmetry breaking is realized ... More

Asymptotics for the level set equation near a maximumJun 04 2018We give asymptotics for the level set equation for mean curvature flow on a convex domain near the point where it attains a maximum. It is known that solutions are not necessarily $C^3,$ and we recover this result and construct non-smooth solutions which ... More

Photoionization Modelling of the Giant Broad-Line Region in NGC 3998Oct 05 2017Prior high angular resolution spectroscopic observations of the Low-ionization nuclear emission-line region (Liner) in NGC 3998 obtained with the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope (HST) revealed a rich UV-visible ... More

Conjectures for Ehrhart $h^*$-vectors of Hypersimplices and Dilated SimplicesOct 26 2017We formulate conjectures giving combinatorial interpretations of the Ehrhart $h^*$-vector, for hypersimplices, for dilated simplices and for generic cross-sections of cubes, in terms of certain decorated ordered set partitions. All were formulated and ... More

Time Fractional Quantum MechanicsFeb 22 2017A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schr\"odinger equation has been launched. The introduced space-time fractional Schr\"odinger equation has a new scale parameter, ... More