Results for "Andrew M. Dai"

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Adversarial Training Methods for Semi-Supervised Text ClassificationMay 25 2016May 06 2017Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations ... More
MaskGAN: Better Text Generation via Filling in the______Jan 23 2018Mar 01 2018Neural text generation models are often autoregressive language models or seq2seq models. These models generate text by sampling words sequentially, with each word conditioned on the previous word, and are state-of-the-art for several machine translation ... More
Adversarial Training Methods for Semi-Supervised Text ClassificationMay 25 2016Nov 07 2016Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations ... More
MaskGAN: Better Text Generation via Filling in the ______Jan 23 2018Neural text generation models are often autoregressive language models or seq2seq models. These models generate text by sampling words sequentially, with each word conditioned on the previous word, and are state-of-the-art for several machine translation ... More
The supervised hierarchical Dirichlet processDec 17 2014We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another ... More
Improved Patient Classification with Language Model Pretraining Over Clinical NotesSep 06 2019Clinical notes in electronic health records contain highly heterogeneous writing styles, including non-standard terminology or abbreviations. Using these notes in predictive modeling has traditionally required preprocessing (e.g. taking frequent terms ... More
Virtual Adversarial Training for Semi-Supervised Text ClassificationMay 25 2016Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations ... More
Semi-supervised Sequence LearningNov 04 2015We present two approaches that use unlabeled data to improve sequence learning with recurrent networks. The first approach is to predict what comes next in a sequence, which is a conventional language model in natural language processing. The second approach ... More
Document Embedding with Paragraph VectorsJul 29 2015Paragraph Vectors has been recently proposed as an unsupervised method for learning distributed representations for pieces of texts. In their work, the authors showed that the method can learn an embedding of movie review texts which can be leveraged ... More
Millimeter Dust Emission in the GQ Lup SystemDec 12 2009We present Submillimeter Array observations of the GQ Lup system at 1.3 millimeters wavelength with $0\farcs4$ ($\sim$60 AU) resolution. Emission is detected from the position of the primary star, GQ Lup A, and is marginally resolved. No emission is detected ... More
Phospholipid-Dextran with a Single Coupling Point: a Useful Amphiphile for Functionalization of NanomaterialsJan 31 2009Nanomaterials hold much promise for biological applications, but they require appropriate functionalization to provide biocompatibility in biological environments. For non-covalent functionalization with biocompatible polymers, the polymer must also remain ... More
Learning Longer-term Dependencies in RNNs with Auxiliary LossesMar 01 2018Jun 13 2018Despite recent advances in training recurrent neural networks (RNNs), capturing long-term dependencies in sequences remains a fundamental challenge. Most approaches use backpropagation through time (BPTT), which is difficult to scale to very long sequences. ... More
Who Said What: Modeling Individual Labelers Improves ClassificationMar 26 2017Jan 04 2018Data are often labeled by many different experts with each expert only labeling a small fraction of the data and each data point being labeled by several experts. This reduces the workload on individual experts and also gives a better estimate of the ... More
Generating Sentences from a Continuous SpaceNov 19 2015May 12 2016The standard recurrent neural network language model (RNNLM) generates sentences one word at a time and does not work from an explicit global sentence representation. In this work, we introduce and study an RNN-based variational autoencoder generative ... More
Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every StepOct 23 2017Feb 20 2018Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative model) and a discriminator ... More
Graph Convolutional Transformer: Learning the Graphical Structure of Electronic Health RecordsJun 11 2019Jun 28 2019Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that utilizing the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) ... More
HyperNetworksSep 27 2016This work explores hypernetworks: an approach of using a small network, also known as a hypernetwork, to generate the weights for a larger network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between ... More
HyperNetworksSep 27 2016Oct 28 2016This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between ... More
HyperNetworksSep 27 2016Dec 01 2016This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between ... More
PEG Branched Polymer for Functionalization of Nanomaterials with Ultralong Blood CirculationJan 30 2009Nanomaterials have been actively pursued for biological and medical applications in recent years. Here, we report the synthesis of several new poly(ethylene glycol) grafted branched-polymers for functionalization of various nanomaterials including carbon ... More
Analyzing the Role of Model Uncertainty for Electronic Health RecordsJun 10 2019In medicine, both ethical and monetary costs of incorrect predictions can be significant, and the complexity of the problems often necessitates increasingly complex models. Recent work has shown that changing just the random seed is enough for otherwise ... More
ALMA Measurements of Circumstellar Material in the GQ Lup SystemNov 18 2016We present ALMA observations of the GQ Lup system, a young Sun-like star with a substellar mass companion in a wide-separation orbit. These observations of 870 $\mu$m continuum and CO J=3-2 line emission with beam size $\sim0.3''$ ($\sim45$ AU) resolve ... More
Music TransformerSep 12 2018Dec 12 2018Music relies heavily on repetition to build structure and meaning. Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure. The Transformer (Vaswani et al., 2017), ... More
Peptide-Spectra Matching from Weak SupervisionAug 20 2018Aug 22 2018As in many other scientific domains, we face a fundamental problem when using machine learning to identify proteins from mass spectrometry data: large ground truth datasets mapping inputs to correct outputs are extremely difficult to obtain. Instead, ... More
Gmail Smart Compose: Real-Time Assisted WritingMay 17 2019In this paper, we present Smart Compose, a novel system for generating interactive, real-time suggestions in Gmail that assists users in writing mails by reducing repetitive typing. In the design and deployment of such a large-scale and complicated system, ... More
Dynamics of a producer-parasite ecosystem on the brink of collapseJun 14 2013Ecosystems can undergo sudden shifts to undesirable states, but recent studies with simple single species ecosystems have demonstrated that advance warning can be provided by the slowing down of population dynamics near a tipping point. However, it is ... More
One-Parameter Scaling of the Conductivity of Si:B: A Temperature-Independent Variable-Range Hopping PrefactorSep 12 2001For insulating Si:B with dopant concentrations from 0.75 n_c to the critical concentration n_c, the conductivity ranging over five orders of magnitude collapses using a single scaling parameter T* onto a universal curve of the form $\sigma (T) =\sigma_0 ... More
Fully distributed PageRank computation with exponential convergenceMay 28 2017Oct 22 2018This work studies a fully distributed algorithm for computing the PageRank vector, which is inspired by the Matching Pursuit and features: 1) a fully distributed implementation 2) convergence in expectation with exponential rate 3) low storage requirement ... More
An Equivalent Presentation of the Bezem-Coquand-Huber Category of Cubical SetsJan 30 2014Staton has shown that there is an equivalence between the category of presheaves on (the opposite of) finite sets and partial bijections and the category of nominal restriction sets: see [2, Exercise 9.7]. The aim here is to see that this extends to an ... More
Minimal and irreducible links in the Shannon gameJan 28 2013We discuss weak and strong links (`virtual connections') in the Shannon game. General properties of these links are discussed, leading to a method to find all links of given size by a suitably pruned exhaustive search. This is applied to links on graphs ... More
Quantum computer architecture for fast entropy extractionMar 11 2002If a quantum computer is stabilized by fault-tolerant quantum error correction (QEC), then most of its resources (qubits and operations) are dedicated to the extraction of error information. Analysis of this process leads to a set of central requirements ... More
The Ion Trap Quantum Information ProcessorAug 08 1996Aug 09 1996An introductory review of the linear ion trap is given, with particular regard to its use for quantum information processing. The discussion aims to bring together ideas from information theory and experimental ion trapping, to provide a resource to workers ... More
Characterizing polynomial domains by their automorphism groupJun 25 2015In this paper we study the automorphism group of bounded convex domains with smooth boundary. In particular, we show that such a domain is biholomorphic to a weighted homogeneous polynomial domain if and only if the limit set of the automorphism group ... More
Graph reconstruction and generation from one card and the degree sequenceOct 05 2018Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the degree sequence ... More
On the relationship between continuous- and discrete-time quantum walkOct 01 2008Oct 21 2009Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. ... More
Observations of Solids in Protoplanetary DisksJul 16 2015This review addresses the state of research that employs astronomical (remote sensing) observations of solids ("dust") in young circumstellar disks to learn about planet formation. The intention is for it to serve as an accessible, introductory, pedagogical ... More
Typal Heterogeneous Equality TypesJul 17 2019The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly different types. ... More
H-Matrix and Block Error TolerancesOct 12 2011We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels having singularity ... More
Characterizing the unit ball by its projective automorphism groupJun 30 2015In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary. ... More
An introduction to spinorsDec 13 2013We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some idea of what ... More
Efficient fault-tolerant quantum computingSep 17 1998Sep 18 1998Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes ... More
The Star Formation History of the UniverseNov 09 2006Strong constraints on the cosmic star formation history (SFH) have recently been established using ultraviolet and far-infrared measurements, refining the results of numerous measurements over the past decade. Taken together, the most recent and robust ... More
The fields and self-force of a constantly accelerating spherical shellJul 18 2013We present a partial differential equation describing the electromagnetic potentials around a charge distribution undergoing rigid motion at constant proper acceleration, and obtain a set of solutions to this equation. These solutions are used to find ... More
Refining enumeration schemes to count according to permutation statisticsJan 01 2014We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical and consecutive ... More
Compact asymptotically harmonic manifoldsMay 10 2012Oct 16 2012A complete Riemannian manifold without conjugate points is called asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotically harmonic manifolds include flat spaces and rank one locally symmetric ... More
Gromov hyperbolicity, the Kobayashi metric, and $\mathbb{C}$-convex setsFeb 03 2016In this paper we study the global geometry of the Kobayashi metric on domains in complex Euclidean space. We are particularly interested in developing necessary and sufficient conditions for the Kobayashi metric to be Gromov hyperbolic. For general domains, ... More
Gromov hyperbolicity and the Kobayashi metric on convex domains of finite typeMay 12 2014Aug 21 2015In this paper we prove necessary and sufficient conditions for the Kobayashi metric on a convex domain to be Gromov hyperbolic. In particular we show that for convex domains with $C^\infty$ boundary being of finite type in the sense of D'Angelo is equivalent ... More
Context, spacetime loops, and the interpretation of quantum mechanicsNov 03 2006Three postulates are discussed: first that well-defined properties cannot be assigned to an isolated system, secondly that quantum unitary evolution is atemporal, and thirdly that some physical processes are never reversed. It is argued that these give ... More
How to build a 300 bit, 1 Giga-operation quantum computerDec 21 2004Sep 01 2006Experimental methods for laser-control of trapped ions have reached sufficient maturity that it is possible to set out in detail a design for a large quantum computer based on such methods, without any major omissions or uncertainties. The main features ... More
Fast fault-tolerant filtering of quantum codewordsFeb 06 2002Apr 02 2004The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of symmetry. The required ... More
Boundaries of non-compact harmonic manifoldsAug 23 2012Dec 16 2012In this paper we consider non-compact non-flat simply connected harmonic manifolds. In particular, we show that the Martin boundary and Busemann boundary coincide for such manifolds. For any finite volume quotient we show that (up to scaling) there is ... More
UHECR Composition ModelsDec 31 2013In light of the increasingly heavy UHECR composition at the highest energies, as observed by the Pierre Auger Observatory, the implications of these results on the actual source composition and spectra are investigated. Depending on the maximum energy ... More
Shape-Wilf-equivalences for vincular patternsJan 23 2012Feb 02 2013We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as "generalized patterns" or "dashed patterns"). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilf-equivalence. When vincular patterns ... More
Characterizing domains by the limit set of their automorphism groupJun 25 2015Jan 14 2017In this paper we study the automorphism group of smoothly bounded convex domains. We show that such a domain is biholomorphic to a "polynomial ellipsoid" (that is, a domain defined by a weighted homogeneous balanced polynomial) if and only if the limit ... More
A new method of verification of security protocolsJun 01 2017In the paper we introduce a process model of security protocols, where processes are graphs with edges labelled by actions, and present a new method of specification and verification of security protocols based on this model.
A graph model of message passing processesJun 01 2017In the paper we consider a graph model of message passing processes and present a method verification of message passing processes. The method is illustrated by an example of a verification of sliding window protocol.
Rigidity of complex convex divisible setsAug 19 2013An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are ... More
On Super-Resolution in Multirate Sampling SystemsSep 11 2016Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in ... More
Pascalutsa-Vanderhaeghen light-by-light sumrule from photon-photon collisionsJan 16 2017Light-by-light scattering sumrules based on general field theory principles relate cross-sections with different helicities. In this paper the simplest sumrule is tested for the $I=0$ and $2$ channels for "real" photon-photon collisions. Important contributions ... More
Pfaffian States in Coupled Atom-Cavity SystemsMar 08 2016Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings Hubbard model, have the potential to emulate a wide range of condensed matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect can ... More
Low RF-Complexity Technologies for 5G Millimeter-Wave MIMO Systems with Large Antenna ArraysJul 15 2016Millimeter-wave (mmWave) MIMO with large antenna array has attracted considerable interests from academic and industry, as it can simultaneously provide wider bandwidth and higher spectrum efficiency. However, with hundreds of antennas employed at mmWave ... More
On Super-Resolution in Multirate Sampling SystemsSep 11 2016Oct 06 2016Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in ... More
Production of the Extreme-Ultraviolet Late Phase of an X Class Flare in a Three-Stage Magnetic Reconnection ProcessJul 18 2013We report observations of an X class flare on 2011 September 6 by the instruments onboard the Solar Dynamics Observatory (SDO). The flare occurs in a complex active region with multiple polarities. The Extreme-Ultraviolet (EUV) Variability Experiment ... More
Low RF-Complexity Technologies to Enable Millimeter-Wave MIMO with Large Antenna Array for 5G Wireless CommunicationsJul 15 2016Oct 01 2017Millimeter-wave (mmWave) MIMO with large antenna array has attracted considerable interests from academic and industry communities, as it can provide larger bandwidth and higher spectrum efficiency. However, with hundreds of antennas, the number of radio ... More
$Suzaku$ Measurements of Hot Halo Emission at Outskirts for Two Poor Galaxy Groups: NGC 3402 and NGC 5129Apr 26 2017We present $Suzaku$ off-center observations of two poor galaxy groups, NGC 3402 and NGC 5129, with temperatures below 1 keV. Through spectral decomposition, we measure their surface brightnesses and temperatures out to 330 and 680 times the critical density ... More
Threat, support and dead edges in the Shannon gameOct 30 2012The notions of captured/lost vertices and dead edges in the Shannon game (Shannon switching game on nodes) are examined using graph theory. Simple methods are presented for identifying some dead edges and some captured sets of vertices, thus simplifying ... More
Overhead and noise threshold of fault-tolerant quantum error correctionJul 19 2002Jul 31 2003Fault tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of CSS codes, including large block ... More
Enlargement of Calderbank Shor Steane quantum codesFeb 24 1998Mar 31 1998It is shown that a classical error correcting code C = [n,k,d] which contains its dual, C^{\perp} \subseteq C, and which can be enlarged to C' = [n,k' > k+1, d'], can be converted into a quantum code of parameters [[ n, k+k' - n, min(d, 3d'/2) ]]. This ... More
Tracking the radiation reaction energy when charged bodies accelerateAug 06 2014We address some questions related to radiation and energy conservation in classical electromagnetism. We first treat the well-known problem of energy accounting during radiation from a uniformly accelerating particle. We present the problem in the form ... More
Secure assisted quantum computationNov 07 2001Jul 06 2005Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that ... More
Universal computation by quantum walkJun 12 2008In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be ... More
Matter-wave coherence limit owing to cosmic gravitational wave backgroundOct 16 2017We study matter-wave interferometry in the presence of a stochastic background of gravitational waves. It is shown that if the background has a scale-invariant spectrum over a wide bandwidth (which is expected in a class of inflationary models of Big ... More
Structural Optimisation: Biomechanics of the FemurOct 06 2011Feb 20 2012A preliminary iterative 3D meso-scale structural model of the femur was developed, in which bar and shell elements were used to represent trabecular and cortical bone respectively. The cross-sectional areas of the bar elements and the thickness values ... More
Asymptotically harmonic manifolds without focal pointsSep 12 2011Oct 06 2011In this note we show that a compact asymptotically harmonic manifold without focal points is either flat or a rank one locally symmetric space.
Applying the Cluster Method to Count Occurrences of Generalized Permutation PatternsMay 29 2009We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with three letters ... More
Π^0_1 classes, strong minimal covers and hyperimmune-free degreesNov 02 2007We investigate issues surrounding an old question of Yates' as to the existence of a minimal Turing degree with no strong minimal cover, specifically with respect to the hyperimmune-free degrees.
A New Method of Verification of Functional ProgramsApr 14 2016In the paper the problem of verification of functional programs (FPs) over strings is considered, where specifications of properties of FPs are defined by other FPs, and a FP S1 meets a specification defined by another FP S2 iff a composition of functions ... More
A theory of probabilistic automata, part 1Jul 18 2015In the book we present main concepts of probabilistic automata theory.
Theory of processesSep 12 2010The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of verification of processes. ... More
Achieving Super-Resolution in Multi-Rate Sampling Systems via Efficient Semidefinite ProgrammingApr 19 2016Aug 02 2016Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in ... More
Two photon couplings of the lightest isoscalars from BELLE dataMar 28 2014Jul 03 2014Amplitude Analysis of two photon production of $\pi\pi$ and ${\overline K}K$, using S-matrix constraints and fitting all available data, including the latest precision results from Belle, yields a single partial wave solution up to 1.4 GeV. The two photon ... More
Superfluid-Mott transitions and vortices in the Jaynes-Cummings-Hubbard lattices with time reversal symmetry breakingOct 20 2015We investigate the groundstate behaviour of Jaynes-Cummings-Hubbard lattices in the presence of a synthetic magnetic field, via a Gutzwiller ansatz. Specifically, we study the Mott-Superfluid transition, and the formation of vortex lattices in the superfluid ... More
Constraints on the Obliquities of Kepler Planet-Hosting StarsOct 12 2017Nov 24 2017Stars with hot Jupiters have obliquities ranging from 0-180 degrees, but relatively little is known about the obliquities of stars with smaller planets. Using data from the California-Kepler Survey, we investigate the obliquities of stars with planets ... More
Protein Microarrays with Carbon Nanotubes as Multi-Color Raman LabelsOct 31 2008Detection of biomolecules is important in proteomics and clinical diagnosis and treatment of diseases. Here, we apply functionalized, macromolecular, single walled carbon nanotubes SWNTs as multi-color Raman labels to protein arrays for highly sensitive, ... More
Fractal Location and Anomalous Diffusion Dynamics for Oil Wells from the KY Geological SurveyDec 13 2009Utilizing data available from the Kentucky Geonet ( the fossil fuel mining locations created by the Kentucky Geological Survey geo-locating oil and gas wells are mapped using ESRI ArcGIS in Kentucky single plain 1602 ft projection. This ... More
Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard LatticesFeb 23 2012Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard ... More
Analytic and Monte Carlo Studies of Jets with Heavy Mesons and QuarkoniaMar 22 2016Jun 16 2016We study jets with identified hadrons in which a family of jet-shape variables called angularities are measured, extending the concept of fragmenting jet functions (FJFs) to these observables. FJFs determine the fraction of energy, z, carried by an identified ... More
Explaining an increase in predicted risk for clinical alertsJul 10 2019Much work aims to explain a model's prediction on a static input. We consider explanations in a temporal setting where a stateful dynamical model produces a sequence of risk estimates given an input at each time step. When the estimated risk increases, ... More
Near field thermal memory deviceAug 25 2014Nov 03 2014We report the concept of a near-field memory device based on the radiative bistability effect in the system of two closely separated parallel plates of SiO$_2$ and VO$_2$ which exchange heat by thermal radiation in vacuum. We demonstrate that the VO$_2$ ... More
On the existence of crepant resolutions of Gorenstein Abelian quotient singularities in dimensions \geq 4Dec 28 2005Apr 03 2006For which finite subgroups G of SL(r,C), r \geq 4, are there crepant desingularizations of the quotient space C^r/G? A complete answer to this question (also known as "Existence Problem" for such desingularizations) would classify all those groups for ... More
Chiral Scale and Conformal Invariance in 2D Quantum Field TheoryJul 14 2011Sep 07 2011It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we consider a chiral ... More
Charge Relaxation and Dephasing in Coulomb Coupled ConductorsFeb 24 1999The dephasing time in coupled mesoscopic conductors is caused by the fluctuations of the dipolar charge permitted by the long range Coulomb interaction. We relate the phase breaking time to elementary transport coefficients which describe the dynamics ... More
Perturbative behaviour of a vortex in a trapped Bose-Einstein condensateFeb 29 2012We derive a set of equations that describe the shape and behaviour of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform a relation for a vortex's velocity, ... More
Analytic Solutions of Ultra-High Energy Cosmic Ray Nuclei RevisitedOct 14 2010The chemical composition of ultra-high energy cosmic rays is a key question in particle astrophysics. The measured composition, inferred from the elongation rates of cosmic ray showers, looks in general very different from the initial source composition: ... More
The Bayesian Approach To Inverse ProblemsFeb 27 2013Jul 02 2015These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification ... More
Uncertainty quantification and weak approximation of an elliptic inverse problemFeb 01 2011We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation ... More
A Markovian genomic concatenation model guided by persymmetric matricesMay 06 2018Sobottka and Hart (2011) made use of a Markovian concatenation model to observe novel statistical symmetries in the mononucleotide and dinucleotide distributions of a collection of bacterial chromosomes. The model roughly approximates the first-order ... More
Some Wilf-equivalences for vincular patternsSep 27 2013Aug 23 2014We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating functions for the number of permutations of length n avoiding ... More
Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensionsDec 04 2012Apr 08 2013We classify distinct types of quantum number fractionalization occurring in two-dimensional topologically ordered phases, focusing in particular on phases with Z2 topological order, that is, on gapped Z2 spin liquids. We find that the fractionalization ... More
Antiferromagnetic topological insulators in cold atomic gasesDec 27 2011May 10 2012We propose a spin-dependent optical lattice potential that realizes a three-dimensional antiferromagnetic topological insulator in a gas of cold, two-state fermions such as alkaline earths, as well as a model that describes the tight-binding limit of ... More