Results for "Jacob Boyd"

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Homological stability for Artin monoidsAug 23 2018We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the $K(\pi,1)$ conjecture holds for the associated family of Artin groups this establishes homological stability for these ... More
The low dimensional homology of finite rank Coxeter groupsNov 01 2018We give formulas for the second and third integral homology of an arbitrary finitely generated Coxeter group, solely in terms of the corresponding Coxeter diagram. The first of these calculations refines a theorem of Howlett, while the second is entirely ... More
Heavy quarkonium suppression beyond the adiabatic limitMay 14 2019Many prior studies of in-medium quarkonium suppression have implicitly made use of an adiabatic approximation in which it was assumed that the heavy quark potential is a slowly varying function of time. In the adiabatic limit, one can separately determine ... More
Toward a 6/5 Bound for the Minimum Cost 2-Edge Connected Spanning Subgraph ProblemDec 26 2015Feb 01 2016Given a complete graph $K_{n}=(V, E)$ with non-negative edge costs $c\in {\mathbb R}^{E}$, the problem $2EC$ is that of finding a 2-edge connected spanning multi-subgraph of $K_{n}$ of minimum cost. The integrality gap $\alpha\text{2EC}$ of the linear ... More
Providing better confidentiality and authentication on the Internet using Namecoin and MinimaLTJul 24 2014In this paper, we introduce a duo of improvements for the Internet that would lead to better security. The authentication model on the Internet is broken and TLS connections have a considerable overhead. We try to address those issues with changes in ... More
Graph-Guided Banding of the Covariance MatrixJun 01 2016Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix ... More
Intermediate asymptotics for critical and supercritical aggregation equations and Patlak-Keller-Segel modelsSep 30 2010Mar 27 2011We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose of this work is to identify when solutions decay to the self-similar ... More
A proof of the Andre-Oort conjecture for A_gJun 04 2015Dec 01 2015We give a proof of the Andr\'e-Oort conjecture for $\mathcal{A}_g$ - the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven `averaged' version of the Colmez conjecture yields lower bounds for Galois ... More
Symmetries in LDDMM with higher order momentum distributionsJun 14 2013Jul 17 2013In some implementations of the Large Deformation Diffeomorphic Metric Mapping formulation for image registration we consider the motion of particles which locally translate image data. We then lift the motion of the particles to obtain a motion on the ... More
Extended AIGER Format for SynthesisMay 22 2014May 26 2014We extend the AIGER format, as used in HWMCC, to a format that is suitable to define synthesis problems with safety specifications. We recap the original format and define one format for posing synthesis problems and one for solutions of synthesis problems ... More
gadfly: A pandas-based Framework for Analyzing GADGET Simulation DataMar 16 2016We present the first public release (v0.1) of the open-source GADGET Dataframe Library: gadfly. The aim of this package is to leverage the capabilities of the broader python scientific computing ecosystem by providing tools for analyzing simulation data ... More
Ultra-high field enhancing in Split Ring Resonators by azimuthally polarized excitationNov 25 2011We study the field enhancement and resonance frequencies in split-ring resonators (SRR) illuminated by azimuthally polarized light. We find that compared to linearly polarized illumination, the azimuthally polarized illumination increase the intensity ... More
Ikehara-type theorem involving boundednessJul 03 2008Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s_N, the paper gives the following necessary and sufficient condition in ... More
Orthomodular lattices, Foulis Semigroups and Dagger Kernel CategoriesDec 04 2009Jun 18 2010This paper is a sequel to arXiv:0902.2355 and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups. The relation between the latter two ... More
Simulating many-body lattice systems on a single nano-mechanical resonatorSep 12 2012We show that lattice systems, such as the Bose-Hubbard model, can be simulated on a single nano- or micro-mechanical resonator, by exploiting its many modes. The on-site Hamiltonians are engineered by coupling the mechanical modes to the modes of a pair ... More
Applications of Feedback Control in Quantum SystemsMay 02 2006We give an introduction to feedback control in quantum systems, as well as an overview of the variety of applications which have been explored to date. This introductory review is aimed primarily at control theorists unfamiliar with quantum mechanics, ... More
A simple formula for pooling knowledge about a quantum systemMar 24 2005When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here we derive ... More
Fully Convolutional Networks for Text ClassificationFeb 14 2019In this work I propose a new way of using fully convolutional networks for classification while allowing for input of any size. I additionally propose two modifications on the idea of attention and the benefits and detriments of using the modifications. ... More
Assessment of electrical and infrastructure recovery in Puerto Rico following hurricane Maria using a multisource time series of satellite imageryJul 16 2018Puerto Rico suffered severe damage from the category 5 hurricane (Maria) in September 2017. Total monetary damages are estimated to be ~92 billion USD, the third most costly tropical cyclone in US history. The response to this damage has been tempered ... More
Algorithms for computing linear invariants if directed graphsMar 11 2005Call two pairs $(M,N)$ and $(M',N')$ of $m\times n$ matrices over a field $K$, \emph{simultaneously K-equivalent} if there exist square invertible matrices $S,T$ over K, with $M'=SMT$ and $N'=SNT$. Kronecker \cite{Kronecker} has given a complete set of ... More
Kähler-Einstein metrics on symmetric general arrangement varietiesJun 24 2019We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine ... More
Spaces of rational maps and the Stone-Weierstrass TheoremJul 08 2003Sep 30 2004It is shown that Segal's theorem on the spaces of rational maps from CP^1 to CP^n can be extended to the spaces of continuous rational maps from CP^m to CP^n for any m less than or equal to n. The tools are the Stone-Weierstrass Theorem and Vassiliev's ... More
Simplicity of finitely-aligned k-graph C*-algebrasOct 25 2008It is shown that no local periodicity is equivalent to the aperiodicity condition for arbitrary finitely-aligned k-graphs. This allows us to conclude that C*(\Lambda) is simple if and only if \Lambda is cofinal and has no local periodicity.
Derived Algebraic Geometry III: Commutative AlgebraMar 07 2007May 04 2009This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.
Near-group categoriesSep 07 2002Aug 27 2003We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules, and an explicit ... More
Schooling Choice, Labour Market Matching, and WagesMar 24 2018Jul 02 2019We develop inference for a two-sided matching model where the characteristics of agents on one side of the market are endogenous due to pre-matching investments. The model can be used to measure the impact of frictions in labour markets using a single ... More
Properties of the Secondary Hochschild HomologyMay 07 2017In this paper we study properties of the secondary Hochschild homology of the triple $(A,B,\varepsilon)$ with coefficients in $M$. We establish a type of Morita equivalence between two triples and show that $H_\bullet((A,B,\varepsilon);M)$ is invariant ... More
From Hierarchical to Relative HyperbolicityMay 29 2019Jul 15 2019We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically hyperbolic groups, ... More
Conditional least squares estimation in nonstationary nonlinear stochastic regression modelsJan 13 2010Let $\{Z_n\}$ be a real nonstationary stochastic process such that $E(Z_n|{\mathcaligr F}_{n-1})\stackrel{\mathrm{a.s.}}{<}\infty$ and $E(Z^2_n|{\mathcaligr F}_{n-1})\stackrel{\mathrm{a.s.}}{<}\infty$, where $\{{\mathcaligr F}_n\}$ is an increasing sequence ... More
Bost-Connes type systems for function fieldsFeb 24 2006May 01 2012We describe a construction which associates to any function field $k$ and any place $\infty$ of $k$ a $C^*$-dynamical system $(C_{k,\infty},\sigma_t)$ that is analogous to the Bost-Connes system associated to $\QQ$ and its archimedian place. Our construction ... More
Derived Algebraic Geometry V: Structured SpacesMay 04 2009In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.
Stanley-Wilf limits are typically exponentialOct 31 2013For a permutation $\pi$, let $S_{n}(\pi)$ be the number of permutations on $n$ letters avoiding $\pi$. Marcus and Tardos proved the celebrated Stanley-Wilf conjecture that $L(\pi)= \lim_{n \to \infty} S_n(\pi)^{1/n}$ exists and is finite. Backed by numerical ... More
A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurementsDec 01 2004Jan 24 2006The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the Holevo bound ... More
Topics in Quantum Measurement and Quantum NoiseOct 05 1998Oct 06 1998In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be described ... More
Lower Bounds for non-Archimedean Lyapunov ExponentsOct 08 2015Oct 18 2016Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\textbf{P}^1$ denote the Berkovich projective line over $K$. The Lyapunov exponent for a rational map $\phi\in K(z)$ of degree $d\geq 2$ measures the exponential rate ... More
An Equidistribution Result For Dynamical Systems on the Berkovich Projective LineSep 16 2014Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\phi\in K(z)$ with $\textrm{deg}(\phi) \geq 2$. In this paper we consider the functions $\textrm{ordRes}_{\phi^n}(x)$ that measure the resultant of $\phi$ at points in ... More
Feedback Control Using Only Quantum Back-ActionApr 24 2009The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum back-action of a continuous ... More
Feedback control for communication with non-orthogonal statesJan 24 2006Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this measurement ... More
Some properties of the Higgs sector of the Next-to Minimal SuperSymmetric ModelJun 16 2011The problems of the standard model are briefly reviewed and the motivations for introducing supersymmetry are discussed. Two realistic supersymmetric models; the Minimal SuperSymmetric Model, MSSM, and its proposed extension NMSSM are introduced briefly ... More
Understanding ACT-R - an Outsider's PerspectiveJun 01 2013The ACT-R theory of cognition developed by John Anderson and colleagues endeavors to explain how humans recall chunks of information and how they solve problems. ACT-R also serves as a theoretical basis for "cognitive tutors", i.e., automatic tutoring ... More
Holography Inspired Stringy HadronsFeb 01 2016Jun 30 2016Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons and glueballs as strings in four dimensional space time. The models are based on a "map" from stringy hadrons of holographic confining backgrounds. In ... More
Langevin process reflected on a partially elastic boundary IApr 12 2010Jul 22 2011Consider a Langevin process, that is an integrated Brownian motion, constrained to stay on the nonnegative half-line by a partially elastic boundary at 0. If the elasticity coefficient of the boundary is greater than or equal to a critical value (0.16), ... More
Jets in Nuclear Collisions: Status and PerspectiveMar 29 2005Apr 06 2005I review the status and future directions of jet-related measurements in high energy nuclear collisions and their application as a probe of QCD matter.
Measurements of High Density Matter at RHICNov 11 2002Nov 13 2002QCD predicts a phase transition between hadronic matter and a Quark Gluon Plasma at high energy density. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is a new facility dedicated to the experimental study of matter under ... More
Projective Connections and the Algebra of DensitiesAug 20 2008Projective connections first appeared in Cartan's papers in the 1920's. Since then they have resurfaced periodically in, for example, integrable systems and perhaps most recently in the context of so called projectively equivariant quantisation. We recall ... More
Renormalization of single-ion magnetic anisotropy in the absence of Kondo effectDec 04 2017Feb 21 2018Inelastic spin flip excitations associated with single-ion magnetic anisotropy of quantum spins, can be strongly renormalized by Kondo exchange coupling to the conduction electrons in the substrate, as shown recently for the case of Co adatoms on CuN$_2$ ... More
Local energy decay for Lipschitz wavespeedsJul 20 2017May 06 2018We prove a logarithmic local energy decay rate for the wave equation with a wavespeed that is a compactly supported Lipschitz perturbation of unity. The key is to establish suitable resolvent estimates at high and low energy for the meromorphic continuation ... More
Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov-Fokker-Planck equationApr 03 2017In this paper, we study Landau damping in the weakly collisional limit of a Vlasov-Fokker-Planck equation with nonlinear collisions in the phase-space $(x,v) \in \mathbb T_x^n \times \mathbb R^n_v$. The goal is four-fold: (A) to understand how collisions ... More
Aerial UAV-IoT Sensing for Ubiquitous Immersive Communication and Virtual Human TeleportationMar 12 2017Jul 21 2017We consider UAV IoT aerial sensing that delivers multiple VR/AR immersive communication sessions to remote users. The UAV swarm is spatially distributed over a wide area of interest, and each UAV captures a viewpoint of the scene below it. The remote ... More
Another Enumeration of Caterpillar TreesOct 28 2018A caterpillar tree is a connected, acyclic, graph in which all vertices are either a member of a central path, or joined to that central path by a single edge. In other words, caterpillar trees are the class of trees which become path graphs after removing ... More
Semiclassical resolvent bound for compactly supported $L^\infty$ potentialsFeb 25 2018May 06 2018We give an elementary proof of a weighted resolvent estimate for semiclassical Schr\"odinger operators in dimension $n \ge 1$. We require the potential belong to $L^\infty(\mathbb{R}^n)$ and have compact support, but do not require that it have derivatives ... More
Measuring Compositionality in Representation LearningFeb 19 2019Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this compositional ... More
Duality for ConvexityNov 19 2009This paper studies convex sets categorically, namely as algebras of a distribution monad. It is shown that convex sets occur in two dual adjunctions, namely one with preframes via the Boolean truth values {0,1} as dualising object, and one with effect ... More
A Bound on the Norm of Shortest Vectors in Lattices Arising from CM Number FieldsOct 29 2012This paper partially addresses the problem of characterizing the lengths of vectors in a family of Euclidean lattices that arise from any CM number field. We define a modified quadratic form on these lattices, the weighted norm, that contains the standard ... More
(Infinity,2)-Categories and the Goodwillie Calculus IMay 04 2009May 08 2009The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also considered). Our ... More
The Existence of an Abelian Variety over the Algebraic Numbers isogenous to no JacobianOct 11 2010We prove the existence of an Abelian variety $A$ of dimension $g$ over $\Qa$ which is not isogenous to any Jacobian, subject to the necessary condition $g>3$. Recently, C.Chai and F.Oort gave such a proof assuming the Andr\'e-Oort conjecture. We modify ... More
The Hopf monoid of coloring problemsNov 13 2016We study coloring problems, which are induced subposets P of a Boolean lattice, paired with an order ideal I from the poset of intervals, ordered by inclusion. We study a quasisymmetric function associated to coloring problems, called the chromatic quasisymmetric ... More
Quasisymmetric Functions from Combinatorial Hopf Monoids and Ehrhart TheoryMar 31 2016We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class ... More
Higher Topos TheoryAug 02 2006Jul 31 2008This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few ... More
Stable Infinity CategoriesAug 09 2006May 08 2009This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a variety of constructions. ... More
Generating Specials: The Zorro AlgorithmAug 14 2006The concept of a configuration graph associated to a primitive, aperiodic substitution is introduced in [1] as a convenient graphical representation of the infinite indeterminism of the shift space of the substitution. The main result of [1] is an algorithm ... More
Regarding a uniqueness property of singly-periodic Scherk surfacesMar 18 2013May 13 2013Inspired by an argument of Ros [15] -- we use the L\'{o}pez-Ros deformation to give another proof of the fact -- due to Meeks and Wolf [13] -- that the only smooth, connected, singly-periodic minimal surfaces in $\Real^3$ with the area growth of two planes ... More
Excursions of the integral of the Brownian motionJan 22 2009Jun 18 2009The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a ... More
Spin transport in nanocontacts and nanowiresDec 10 2007In this thesis we study electron transport through magnetic nanocontacts and nanowires with ab initio quantum transport calculations. The aim is to gain a thorough understanding of the interplay between electrical conduction and magnetism in atomic-size ... More
Global Minimizers for Free Energies of Subcritical Aggregation Equations with Degenerate DiffusionSep 27 2010We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on $\Real^d$. Such equations arise in mathematical biology as models for organism group dynamics which account ... More
Background Fluctuations in Heavy Ion Jet ReconstructionDec 10 2010Jan 03 2011We present a new study by the STAR Collaboration of background fluctuations in jet reconstruction in heavy ion collisions.
A new version of an old modal incompleteness theoremFeb 15 2012Thomason \cite{Thomason74} showed that a certain modal logic $\mathbf{L}\subset \mathbf{S4}$ is incomplete with respect to Kripke semantics. Later Gerson \cite{Gerson75} showed that $\mathbf{L}$ is also incomplete with respect to neighborhood semantics. ... More
Hyper Normalisation and Conditioning for Discrete Probability DistributionsJul 10 2016Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description ... More
Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired informationAug 08 2012Nov 03 2012The energy cost of measurement is an interesting fundamental question, and may have profound implications for quantum technologies. In the context of Maxwell's demon, it is often stated that measurement has no minimum energy cost, while information has ... More
The Second Law of Thermodynamics and Quantum Feedback Control: Maxwell's Demon with Weak MeasurementsJun 23 2009Aug 05 2009Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. They left open the question of whether this bound could be achieved for every measurement ... More
A Mathematical Account of Soft Evidence, and of Jeffrey's `destructive' versus Pearl's `constructive' updatingJul 15 2018Evidence in probabilistic reasoning may be `hard' or `soft', that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0,1]. Reasoning with soft, $[0,1]$-valued evidence is important in many situations but may lead ... More
How Does Knowledge of the AUC Constrain the Set of Possible Ground-truth Labelings?Sep 07 2017Sep 11 2017Recent work on privacy-preserving machine learning has considered how data-mining competitions such as Kaggle could potentially be "hacked", either intentionally or inadvertently, by using information from an oracle that reports a classifier's accuracy ... More
Charged String Tensor NetworksMar 03 2017Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial dimension. There ... More
Reduced Ideals in Pure Cubic FieldsMay 01 2019Reduced ideals have been defined in the context of integer rings in quadratic number fields, and they are closely tied to the continued fraction algorithm. The notion of this type of ideal extends naturally to number fields of higher degree. In the case ... More
Spin correlations in top physics at ATLAS and CMS in Run 2May 21 2019Measurements of $\mathrm{t\bar{t}}$ spin correlations are presented in events with top quarks produced in $\mathrm{pp}$ collisions at the LHC. The data correspond to an integrated luminosity of $36\:\mathrm{fb^{-1}}$ at $\sqrt{s}=13\:\mathrm{TeV}$ collected ... More
On the notion of lower central series for loopsOct 24 2004The commutator calculus is one of the basic tools in group theory. However, its extension to the non-associative context, based on the usual definition of the lower central series of a loop, is not entirely satisfactory. Namely, the graded abelian group ... More
Khovanov-Rozansky homology of two-bridge knots and linksAug 25 2005Aug 15 2006We compute the reduced version of Khovanov and Rozansky's sl(N) homology for two-bridge knots and links. The answer is expressed in terms of the HOMFLY polynomial and signature.
A Mathematical Account of Soft Evidence, and of Jeffrey's `destructive' versus Pearl's `constructive' updatingJul 15 2018Mar 03 2019Evidence in probabilistic reasoning may be `hard' or `soft', that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0,1]. Reasoning with soft, [0,1]-valued evidence is important in many situations but may lead ... More
The Briancon-Skoda number of analytic irreducible planar curvesJan 16 2012The Briancon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal I\subset R and r\geq 1, the integral closure of I^{k+r-1} is contained in I^r. We compute the Briancon-Skoda number of the local ring of any analytic irreducible ... More
On the Classification of Topological Field TheoriesMay 04 2009This paper provides an informal sketch of a proof of the Baez-Dolan cobordism hypothesis, which provides a classification for extended topological quantum field theories.
Greatest Lower Bounds on Ricci Curvature for Fano $T$-manifolds of Complexity $1$Mar 28 2018Sep 07 2018In this short note we determine the greatest lower bounds on Ricci curvature for all Fano $T$-manifolds of complexity one, generalizing the result of Chi Li. Our method of proof is based on the work of Datar and Sz\'ekelyhidi, using the description of ... More
Global Regularity for General Non-Linear Wave Equations I. (6+1) and Higher DimensionsFeb 12 2004We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative non-linearities ... More
Khovanov's invariant for closed surfacesFeb 24 2005We compute the Khovanov-Jacobsson number of an embedded torus in R^4. The answer is always 2, regardless of the embedding.
Good-Enough Compositional Data AugmentationApr 21 2019We propose a simple data augmentation protocol aimed at providing a compositional inductive bias in conditional and unconditional sequence models. Under this protocol, synthetic training examples are constructed by taking real training examples and replacing ... More
Asymptotic structure of almost eigenfunctions of drift Laplacians on conical endsAug 23 2017Dec 13 2017We use a weighted variant of the frequency functions introduced by Almgren to prove sharp asymptotic estimates for almost eigenfunctions of the drift Laplacian associated to the Gaussian weight on an asymptotically conical end. As a consequence, we obtain ... More
Bases as CoalgebrasSep 03 2013Sep 20 2013The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated ... More
Dispersive Decay for the 1D Klein-Gordon Equation with Variable Coefficient NonlinearitiesJul 18 2013Jun 10 2014We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the solutions. In the ... More
The Simulator: An Engine to Streamline SimulationsJun 30 2016The simulator is an R package that streamlines the process of performing simulations by creating a common infrastructure that can be easily used and reused across projects. Methodological statisticians routinely write simulations to compare their methods ... More
Controllable Spin-Transfer Torque on an Antiferromagnet in a Dual Spin-ValveAug 23 2011We consider current-induced spin-transfer torque on an antiferromagnet in a dual spin-valve setup. It is demonstrated that a net magnetization may be induced in the AFM by partially or completely aligning the sublattice magnetizations via a current-induced ... More
On Coloring the Odd-Distance GraphAug 11 2009We present a proof, using spectral techniques, that there is no finite measurable coloring of the odd-distance graph.
Chirality Sensitive Domain Wall Motion in Spin-Orbit Coupled FerromagnetsFeb 19 2013Using the Lagrangian formalism, we solve analytically the equations of motion for current-induced domain-wall dynamics in a ferromagnet with Rashba spin-orbit coupling. An exact solution for the domain wall velocity is provided, including the effect of ... More
The Relative Lie Algebra Cohomology of the Weil RepresentationMay 01 2015May 15 2015We study the relative Lie algebra cohomology of $\mathfrak{so}(p,q)$ with values in the Weil representation $\varpi$ of the dual pair $\mathrm{Sp}(2k, \mathbb{R}) \times \mathrm{O}(p,q)$. Using the Fock model we filter this complex and construct the associated ... More
Universal Variational Quantum ComputationMar 11 2019Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimization [1], eigenvalue estimation [2] and machine learning [3]. Here we establish the quantum computational universality of variational quantum computation by developing ... More
The limit of the Yang-Mills flow on semi-stable bundlesApr 25 2011Aug 26 2013By the work of Hong and Tian it is known that given a holomorphic vector bundle E over a compact Kahler manifold X, the Yang-Mills flow converges away from an analytic singular set. If E is semi-stable, then the limiting metric is Hermitian-Einstein and ... More
The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifoldsSep 07 2011Oct 27 2014We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kahler manifold X . Along a solution of the flow, we show the curvature $i\Lambda F(A_t)$ approaches in $L^2$ an endomorphism with constant eigenvalues given by the slopes of ... More
Quantitative Logarithmic Equidistribution of the Crucial MeasuresJul 13 2015Let $K$ be a algebraically closed field of characteristic 0 that is complete with respect to a non-Archimedean absolute value. Let $\phi\in K(z)$ with $\textrm{deg}(\phi)\geq 2$. In this paper we establish uniform logarithmic equidistribution of the crucial ... More
Universal graphs at $\aleph_{ω_1+1}$May 02 2016Starting from a supercompact cardinal we build a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ but there is a jointly universal family of size $\aleph_{\omega_1+2}$ of graphs on $\aleph_{\omega_1+1}$. The same technique ... More
Tannaka Duality for Geometric StacksDec 14 2004Mar 23 2005We show that, under appropriate hypothesis, the groupoid of maps from S to an an algebraic stack X can be identified with a category of tensor functors from coherent sheaves on X to coherent sheaves on S. As an application, we show that if S is a proper ... More
Derived Algebraic Geometry VI: E_k AlgebrasOct 30 2009In this paper, we study algebras over the little cubes operads introduced by Boardman and Vogt, using the formalism of higher category theory.
Dagger Categories of Tame RelationsJan 05 2011Jul 16 2012Within the context of an involutive monoidal category the notion of a comparison relation is identified. Instances are equality on sets, inequality on posets, orthogonality on orthomodular lattices, non-empty intersection on powersets, and inner product ... More