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Patching and the completed homology of locally symmetric spacesSep 22 2016Under an assumption on the existence of p-adic Galois representations, we carry out Taylor--Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated to GL(n) over a number field. We use our construction ... More

Patching and the completed homology of locally symmetric spacesSep 22 2016Dec 04 2016Under an assumption on the existence of p-adic Galois representations, we carry out Taylor--Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated to GL(n) over a number field. We use our construction ... More

Patching and the completed homology of locally symmetric spacesSep 22 2016Nov 08 2016Under an assumption on the existence of p-adic Galois representations, we carry out Taylor--Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated to GL(n) over a number field. We use our construction ... More

Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spacesDec 29 2014Oct 19 2015Both simplicial sets and simplicial spaces are used pervasively in homotopy theory as presentations of spaces, where in both cases we extract the "underlying space" by taking geometric realization. We have a good handle on the category of simplicial sets ... More

Model $\infty$-categories III: the fundamental theoremOct 16 2015We prove that a model structure on a relative $\infty$-category $(M,W)$ gives an efficient and computable way of accessing the hom-spaces $hom_{M[[W^{-1}]]}(x,y)$ in the localization. More precisely, we show that when the source $x \in M$ is *cofibrant* ... More

The universality of the Rezk nerveOct 12 2015We functorially associate to each relative $\infty$-category $(R,W)$ a simplicial space $N^R_\infty(R,W)$, called its Rezk nerve (a straightforward generalization of Rezk's "classification diagram" construction for relative categories). We prove the following ... More

Model $\infty$-categories II: Quillen adjunctionsOct 15 2015We prove that various structures on model $\infty$-categories descend to corresponding structures on their localizations: (i) Quillen adjunctions; (ii) two-variable Quillen adjunctions; (iii) monoidal and symmetric monoidal model structures; and (iv) ... More

A user's guide to co/cartesian fibrationsOct 08 2015We formulate a model-independent theory of co/cartesian morphisms and co/cartesian fibrations: that is, one which resides entirely *within the $\infty$-category of $\infty$-categories*. We prove this is suitably compatible with the corresponding quasicategorical ... More

Quillen adjunctions induce adjunctions of quasicategoriesJan 13 2015We prove that a Quillen adjunction of model categories (of which we do not require functorial factorizations and of which we only require finite bicompleteness) induces a canonical adjunction of underlying quasicategories.

Barnes-Hut Approximation for Point SetGeodesic ShootingJul 10 2019Geodesic shooting has been successfully applied to diffeo-morphic registration of point sets. Exact computation of the geodesicshooting between point sets, however, requiresO(N2) calculations each time step on the number of points in the point set. We ... More

Enhanced generative adversarial network for 3D brain MRI super-resolutionJul 10 2019Jul 15 2019Single image super-resolution (SISR) reconstruction for magnetic resonance imaging (MRI) has generated significant interest because of its potential to not only speed up imaging but to improve quantitative processing and analysis of available image data. ... More

Enhanced generative adversarial network for 3D brain MRI super-resolutionJul 10 2019Single image super-resolution (SISR) reconstruction for magnetic resonance imaging (MRI) has generated significant interest because of its potential to not only speed up imaging but to improve quantitative processing and analysis of available image data. ... More

The Sato-Tate conjecture for modular forms of weight 3Jun 02 2009Sep 03 2010We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place.

Companion Forms Over Totally Real Fields, IIJul 25 2005Sep 03 2010We prove a companion forms theorem for mod l Hilbert modular forms. This work generalises results of Gross and Coleman--Voloch for modular forms over Q, and gives a new proof of their results in many cases. The methods used are completely different to ... More

Abelian Surfaces over totally real fields are Potentially ModularDec 21 2018We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta functions. We furthermore ... More

On the weights of mod $p$ Hilbert modular formsJan 21 2006Sep 03 2010We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod $p$ Hilbert modular forms, by making use of modularity lifting theorems and computations in $p$-adic Hodge theory.

Companion forms over totally real fieldsAug 12 2004Sep 03 2010We show that if F is a totally real field in which p splits completely and f is a mod p Hilbert modular form with parallel weight 2<k<p, which is totally ordinary at p and has tamely ramified Galois representation at all primes dividing p, then there ... More

Automorphic lifts of prescribed typesOct 10 2008Sep 03 2010We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings of local Galois representations, and deduce from this and ... More

A modularity lifting theorem for weight 2 Hilbert modular formsJan 21 2006Oct 10 2008We prove a modularity lifting theorem for potentially Barostti-Tate representations over totally real fields, generalising recent results of Kisin. Unfortunately, there was an error in the original version of this paper, meaning that we can only obtain ... More

Hammocks and fractions in relative $\infty$-categoriesOct 14 2015We study the *homotopy theory* of $\infty$-categories enriched in the $\infty$-category $sS$ of simplicial spaces. That is, we consider $sS$-enriched $\infty$-categories as presentations of ordinary $\infty$-categories by means of a "local" geometric ... More

Companion forms for unitary and symplectic groupsJan 13 2010We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce ... More

The Breuil--Mezard conjecture for quaternion algebrasAug 30 2013We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL_2. In the course of the proof we establish a mod p analogue of the Jacquet--Langlands correspondence for ... More

Explicit reduction modulo p of certain 2-dimensional crystalline representations, IIApr 06 2012Apr 11 2016We complete the calculations begun in [BG09], using the p-adic local Langlands correspondence for GL2(Q_p) to give a complete description of the reduction modulo p of the 2-dimensional crystalline representations of G_{Q_p} of slope less than 1, when ... More

The Breuil-Mézard conjecture for potentially Barsotti-Tate representationsAug 15 2012Sep 18 2013We prove the Breuil-M\'ezard conjecture for 2-dimensional potentially Barsotti-Tate representations of the absolute Galois group G_K, K a finite extension of Q_p, for any p>2 (up to the question of determining precise values for the multiplicities that ... More

Serre weights for quaternion algebrasSep 07 2009Aug 31 2010We study the possible weights of an irreducible two-dimensional mod p representation of the absolute Galois group of F which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified ... More

Explicit reduction modulo $p$ of certain crystalline representationsApr 08 2008Sep 03 2010We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms.

"Scheme-theoretic images" of morphisms of stacksJun 19 2015Oct 07 2015We give criteria for certain morphisms from an algebraic stack to a (not necessarily algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our criteria to show that certain natural moduli stacks of local Galois representations ... More

The conjectural connections between automorphic representations and Galois representationsSep 03 2010Sep 07 2015We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.

Goerss--Hopkins obstruction theory for $\infty$-categoriesDec 18 2018Goerss--Hopkins obstruction theory is a powerful tool for constructing structured ring spectra from purely algebraic data. Using the formalism of model $\infty$-categories, we provide a generalization that applies in an arbitrary presentably symmetric ... More

$\mathbb{E}_\infty$ automorphisms of motivic Morava $E$-theoriesJan 17 2019We apply Goerss--Hopkins obstruction theory for motivic spectra to study the motivic Morava $E$-theories. We find that they always admit $\mathbb{E}_\infty$ structures, but that these may admit "exotic" $\mathbb{E}_\infty$ automorphisms not coming from ... More

Arthur's multiplicity formula for GSp$_4$ and restriction to Sp$_4$Jul 11 2018We prove the classification of discrete automorphic representations of GSp$_4$ explained in [Art04], as well as a compatibility between the local Langlands correspondences for GSp$_4$ and Sp$_4$ .

G-valued local deformation rings and global liftsAug 16 2017Dec 30 2018We study G-valued Galois deformation rings with prescribed properties, where G is an arbitrary (not necessarily connected) reductive group over an extension of Z_l for some prime l. In particular, for the Galois groups of p-adic local fields (with p possibly ... More

p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varietiesMar 22 2012Apr 14 2015We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected range (at least ... More

Irreducibility of automorphic Galois representations of GL(n), n at most 5Apr 26 2011Oct 10 2016Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL_n(A_F), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic Galois representations associated to pi are irreducible, ... More

Automorphy lifting for small lSep 23 2012We prove a slight generalization of Theorem 4.2.1 of [BLGGT10], which weakens the assumption that $l\ge 2(n+1)$ to an adequacy hypothesis.

Serre weights for mod p Hilbert modular forms: the totally ramified caseApr 01 2009Sep 15 2010We study the possible weights of an irreducible 2-dimensional modular mod p representation of the absolute Galois group of F, where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the prime above ... More

A geometric perspective on the Breuil-Mézard conjectureSep 20 2011Mar 20 2013Let p > 2 be prime. We state and prove (under mild hypotheses on the residual representation) a geometric refinement of the Breuil-M\'ezard conjecture for 2-dimensional mod p representations of the absolute Galois group of Qp. We also state a conjectural ... More

All about the Grothendieck constructionOct 13 2015We provide, among other things: (i) a Bousfield--Kan formula for colimits in $\infty$-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) $\infty$-categorical generalizations of Barwick--Kan's ... More

Slopes of modular formsFeb 09 2015Apr 11 2016We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other related questions. ... More

Transparent Machine Education of Neural Networks for Swarm Shepherding Using Curriculum DesignJan 04 2019Swarm control is a difficult problem due to the need to guide a large number of agents simultaneously. We cast the problem as a shepherding problem, similar to biological dogs guiding a group of sheep towards a goal. The shepherd needs to deal with complex ... More

Every Graph Is Local Antimagic TotalJun 25 2019An antimagic labelling of a graph $G$ is a bijection $h : E(G) \to \{1, \ldots, |E(G)|\}$ such that the induced vertex label $h^+(v) = \sum_{uv\in E(G)}$ distinguish all vertices $v$. A well-known conjecture of Hartsfield and Ringel (1994) is that every ... More

QoE-aware Scalable Video Transmission in MIMO~SystemsOct 24 2016An important concept in wireless systems has been quality of experience (QoE)-aware video transmission. Such communications are considered not only connection-based communications but also content-aware communications, since the video quality is closely ... More

Brain network efficiency is influenced by pathological source of corticobasal syndromeJan 28 2016Multimodal neuroimaging studies of corticobasal syndrome using volumetric MRI and DTI successfully discriminate between Alzheimer's disease and frontotemporal lobar degeneration but this evidence has typically included clinically heterogeneous patient ... More

Potential automorphy over CM fieldsDec 25 2018Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and furthermore ... More

Companion Forms in Parallel Weight OneJun 28 2012Let $p>2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a mod $p$ Galois representation to arise from a mod $p$ Hilbert modular form of parallel weight one, by proving a "companion forms" ... More

Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal MethodSep 02 2016For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar ... More

Transit times of radiation through photonic bandgap materials: Pulse reshaping of classical and quantum fields in the time domainOct 17 2002Oct 21 2002We study the propagation of electromagnetic pulses through photonic bandgap materials and relate time-domain pulse reshaping to observable transit times. For layered dielectric mirrors we demonstrate how pulse reshaping of slowly varying classical fields ... More

Crystalline extensions and the weight part of Serre's conjectureJun 28 2011Let p>2 be prime. We complete the proof of the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the totally ramified case, by proving that any weight which occurs is a predicted weight. Our methods are a mixture ... More

The geometry of the cyclotomic traceOct 17 2017We provide a new construction of the topological cyclic homology $TC(C)$ of any spectrally-enriched $\infty$-category $C$, which affords a precise algebro-geometric interpretation of the cyclotomic trace map $K(X) \to TC(X)$ from algebraic K-theory to ... More

Congruences between Hilbert modular forms: constructing ordinary liftsJun 02 2010Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension F'/F such that ... More

The Buzzard-Diamond-Jarvis conjecture for unitary groupsMar 12 2012Sep 02 2013Let p > 2 be prime. We prove the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard-Diamond-Jarvis conjecture for unitary groups), by proving that any Serre weight which ... More

The weight part of Serre's conjecture for GL(2)Sep 02 2013Dec 22 2014Let p > 2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call "pseudo-Barsotti-Tate representations", over arbitrary finite extensions of the p-adics. As a consequence, ... More

Lattices in the cohomology of Shimura curvesMay 07 2013Nov 19 2014We prove conjectures of Breuil and Breuil-Dembele (C. Breuil, "Sur un probleme de compatibilite local-global modulo p pour GL(2)"), including a generalisation from the principal series to the cuspidal case, subject to a mild global hypothesis that we ... More

A naive approach to genuine $G$-spectra and cyclotomic spectraOct 17 2017For any compact Lie group $G$, we give a description of genuine $G$-spectra in terms of the naive equivariant spectra underlying their geometric fixedpoints. We use this to give an analogous description of cyclotomic spectra in terms of naive $T$-spectra ... More

From fractions to complete Segal spacesSep 29 2014May 15 2015We show that the Rezk classification diagram of a relative category admitting a homotopical version of the two-sided calculus of fractions is a Segal space up to Reedy-fibrant replacement. This generalizes the result of Rezk and Bergner on the classification ... More

Congruences betwen Hilbert modular forms: constructing ordinary lifts IIMay 21 2012In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.

The Sato-Tate conjecture for Hilbert modular formsDec 05 2009Nov 04 2010We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of $\GL_2(\A_F)$, $F$ a totally real field, which are ... More

Weight cycling and Serre-type conjectures for unitary groupsJun 22 2011Jun 14 2013We prove that for forms of U(3) which are compact at infinity and split at places dividing a prime p, in generic situations the Serre weights of a mod p modular Galois representation which is irreducible when restricted to each decomposition group above ... More

Serre weights for rank two unitary groupsJun 28 2011We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights, agreeing with all ... More

General Serre weight conjecturesSep 08 2015Feb 26 2016We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these conjectures, and discuss ... More

Factorization homology of enriched $\infty$-categoriesOct 17 2017For an arbitrary symmetric monoidal $\infty$-category $V$, we define the factorization homology of $V$-enriched $\infty$-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case that $V$ is \textit{cartesian} symmetric ... More

Hierarchical Linear Modeling Approach to Measuring the Effects of Class Size and Other Classroom Characteristics on Student Learning in an Active-Learning Based Introductory Physics CourseSep 01 2018The effect of class size on student learning has numerous policy implications and has been a major subject of conversation and research for decades. Despite this, few studies have been done on class size in the context of university settings or physics ... More

Serre Weights for U(n)May 13 2014We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on unitary groups of rank n for odd primes l. Given a modular Galois representation, we use automorphy lifting ... More

A Relative Lubin-Tate Theorem via Meromorphic Formal GeometryAug 25 2013We formulate a theory of punctured affine formal schemes, suitable for certain problems within algebraic topology. As an application, we show that the Morava K-theoretic localizations of Morava E-theory corepresent a version of the Lubin-Tate moduli problem ... More

Considerations for Cloud Security OperationsJan 23 2016Information Security in Cloud Computing environments is explored. Cloud Computing is presented, security needs are discussed, and mitigation approaches are listed. Topics covered include Information Security, Cloud Computing, Private Cloud, Public Cloud, ... More

On embeddings of finite subsets of $\ell_2$Sep 28 2016We study finite subsets of $\ell_2$, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional Banach space contains ... More

Discrete analogue computing with rotor-routersJul 14 2010Aug 19 2010Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is ... More

R-symmetric High Scale SupersymmetryOct 17 2012Dec 07 2012Introducing an R-symmetry to models of high scale supersymmetry (SUSY) can have interesting consequences, and we focus on two aspects. If Majorana masses are forbidden by an R-symmetry and the main source of electroweak gaugino masses are Dirac terms, ... More

Contact structures on open 3-manifoldsAug 03 2004Sep 09 2004In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity. We first prove ... More

Regular Expression Subtyping for XML Query and Update LanguagesJan 04 2008XML database query languages such as XQuery employ regular expression types with structural subtyping. Subtyping systems typically have two presentations, which should be equivalent: a declarative version in which the subsumption rule may be used anywhere, ... More

Homotopy approximations to the space of knots, Feynman diagrams, and a conjecture of Scannell and SinhaJan 26 2006Aug 26 2010Scannell and Sinha considered a spectral sequence to calculate the rational homotopy groups of spaces of long knots in n-dimensional Euclidean space, for n greater than or equal to 4. At the end of their paper they conjecture that when n is odd, the terms ... More

Gropes and the rational lift of the Kontsevich integralApr 14 2004Oct 11 2004In this note, we calculate the leading term of the rational lift of the Kontsevich integral, introduced by Garoufalidis and Kricker, on the boundary of an embedded grope of class 2n. We observe that it lies in the subspace spanned by connected diagrams ... More

Presentations for rook partition monoids and algebras and their singular idealsJun 02 2016We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such ... More

Managing resonant trapped orbits in our GalaxyAug 04 2016Galaxy modelling is greatly simplified by assuming the existence of a global system of angle-action coordinates. Unfortunately, global angle-action coordinates do not exist because some orbits become trapped by resonances, especially where the radial ... More

Distribution functions for the Milky WayOct 08 2009Analytic distribution functions (DFs) for the Galactic disc are discussed. The DFs depend on action variables and their predictions for observable quantities are explored under the assumption that the motion perpendicular to the Galactic plane is adiabatically ... More

Actions for axisymmetric potentialsJul 20 2012We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits characteristic of ... More

The Cosmological Context of Extraplanar GasSep 27 2004I review evidence that galaxies form from gas that falls into potential wells cold, rather than from virialized gas, and that formation stops once an atmosphere of trapped virialized gas has accumulated. Disk galaxies do not have such atmospheres, so ... More

Black holes, cuspy atmospheres, and galaxy formationJul 12 2004In cuspy atmospheres, jets driven by supermassive black holes (BHs) offset radiative cooling. The jets fire episodically, but often enough that the cuspy atmosphere does not move very far towards a cooling catastrophe in the intervals of jet inactivity. ... More

Secular Evolution of the Galactic DiskSep 20 2000In the solar-neighbourhood, older stars have larger random velocities than younger ones. It is argued that the increase in velocity dispersion with time is predominantly a gradual process rather than one induced by discrete events such as minor mergers. ... More

Microlensing and Galactic StructureApr 26 2000Because we know little about the Galactic force-field away from the plane, the Galactic mass distribution is very ill-determined. I show that a microlensing survey of galaxies closer than 50 Mpc would enable us to map in three dimensions the Galactic ... More

Time-Integrated Gamma-Ray Burst Synchrotron Spectra from Blast Wave/Cloud InteractionsOct 15 1998We show that the spectral shape of the low energy tails found for the time-integrated spectra of gamma-ray bursts, even in the absence of strong synchrotron cooling, can be significantly softer than the $\nu F_\nu \propto \nu^{4/3}$ asymptote predicted ... More

An X-ray Reprocessing Model of Disk Thermal Emission in Type 1 Seyfert GalaxiesFeb 12 2002Using a geometry consisting of a hot central Comptonizing plasma surrounded by a thin accretion disk, we model the optical through hard X-ray spectral energy distributions of the type 1 Seyfert galaxies NGC 3516 and NGC 7469. As in the model proposed ... More

On tadpole relations via Verdier specializationNov 12 2015Feb 26 2016Using the construct of "Verdier specialization", we provide a purely mathematical derivation of Chern class identities which upon integration yield the D3-brane tadpole relations coming from the equivalence between F-theory and associated weakly coupled ... More

On embeddings of finite subsets of $\ell_2$Sep 28 2016Sep 29 2016We study finite subsets of $\ell_2$, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional Banach space contains ... More

A perturbative quantized twist embedded in Minkowski spacetimeApr 28 2016Oct 31 2016In this article, spatially-structured gravitational waves are investigated. Drawing upon analogies between electrodynamics and general relativity, a new gauge is found. We investigate the polarization and degrees of freedom of the resulting radiation. ... More

Systematic Bias in 2MASS Galaxy PhotometryJul 08 2011We report the discovery of a serious bias in galaxy photometry reported in the 2MASS Extended Source Catalog (Jarrett et al. 2000). Due to an undetermined flaw in the 2MASS surface photometry routines, isophotal and total magnitudes calculated by their ... More

A lagrangian description of elastic motion in riemannian manifolds and an angular invariant of axially-symmetric elasticity tensorsDec 24 2013This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as the Euler-Lagrange ... More

Self-consistent solutions of canonical proper self-gravitating quantum systemsAug 24 2011Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have appropriate ... More

Quantum Behaviors on an Excreting Black HoleOct 24 2008Often, geometries with horizons offer insights into the intricate relationships between general relativity and quantum physics. However, some subtle aspects of gravitating quantum systems might be difficult to ascertain using static backgrounds, since ... More

A Model of Unified Gauge InteractionsMar 23 2016Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all particle types. ... More

Group Structure of an Extended Lorentz GroupSep 30 2003In a previous paper we extended the Lorentz group to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The group is particularly useful for developing ... More

XMM-Newton Observations of AGN Iron Line ProfilesNov 18 2002XMM-Newton observations of type I AGN are presented. The properties of the iron K emission line are reviewed, the majority of AGN observed by XMM-Newton show narrow, unresolved (by XMM) iron lines at 6.4 keV from cold matter that must originate far from ... More

Exactly Solvable Supercritical String Theories?Nov 25 2005By analytically continuing the string equations of the subcritical Type 0A (2, 4|m|) minimal string theories, we reveal a whole new family of differential and integro-differential equations associated with the naively supercritical (2, -4|m|) theories. ... More

Bistable Biorders: A Sequential Domain TheoryFeb 28 2007May 15 2007We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order -- the extensional order -- and a bistable coherence, which captures equivalence ... More

Casimir forces between spheresNov 13 2009We discuss the calculation of Casimir forces between a collection of $N$-dielectric spheres. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. Two and three body forces between ... More

Graphene membranes and the Dirac-Born-Infeld actionMay 03 2010Jul 08 2011We propose the use of the Dirac-Born-Infeld action in the phenomenological description of graphene sheet dynamics and interactions. Both the electronic properties of the Dirac fermions and the overall dynamics can be incorporated into this model. Classical ... More

Colourful antenna subtraction for gluon scatteringNov 24 2013In this talk I discuss the application and generalization of the antenna subtraction method to processes involving incoherent interferences of partial amplitudes, which are generically present for the sub-leading colour contributions to processes involving ... More

Feasibly Reducing KAT Equations to KA EquationsJan 15 2008Kleene algebra (KA) is the algebra of regular events. Familiar examples of Kleene algebras include regular sets, relational algebras, and trace algebras. A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Boolean subalgebra. The addition ... More

Stochastic Logic Programs: Sampling, Inference and ApplicationsJan 16 2013Algorithms for exact and approximate inference in stochastic logic programs (SLPs) are presented, based respectively, on variable elimination and importance sampling. We then show how SLPs can be used to represent prior distributions for machine learning, ... More

Simulations of superhumps and superoutburstsOct 22 1997We numerically study the tidal instability of accretion discs in close binary systems using a two-dimensional SPH code. We find that the precession rate of tidally unstable, eccentric discs does not only depend upon the binary mass ratio q. Although the ... More