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Minimally Supervised Written-to-Spoken Text NormalizationSep 21 2016In speech-applications such as text-to-speech (TTS) or automatic speech recognition (ASR), \emph{text normalization} refers to the task of converting from a \emph{written} representation into a representation of how the text is to be \emph{spoken}. In ... More

Precipitation extremes under climate changeMar 25 2015The response of precipitation extremes to climate change is considered using results from theory, modeling, and observations, with a focus on the physical factors that control the response. Observations and simulations with climate models show that precipitation ... More

The Danger of a Big Data Episteme and the Need to Evolve GISOct 16 2013The emergence of "Big Data" as a dominant technology meme challenges Geography's technical underpinnings, found in GIS, while engaging the discipline in a conversation about the meme's impact on society. This allows scholars to engage collaboratively ... More

What Kind of Language Is Hard to Language-Model?Jun 11 2019How language-agnostic are current state-of-the-art NLP tools? Are there some types of language that are easier to model with current methods? In prior work (Cotterell et al., 2018) we attempted to address this question for language modeling, and observed ... More

Stable Adiabatic Times For A Continuous Evolution Of Markov ChainsJul 22 2015This paper continues the discussion on the stability of time-inhomogeneous Markov chains. In particular, this paper defines a time-inhomogeneous, discrete-time Markov chain governed by a continuous evolution in the appropriate martrix space. This matrix ... More

Digital Arroyos: An Examination of State Policy and Regulated Market Boundaries in Constructing Rural Internet AccessSep 25 2001This focused study on state-level policy and access patterns contributes to a fuller understanding of how these invisible barriers work to structure access and define rural communities. Combining both quantitative and qualitative data, this study examines ... More

A sufficient condition for finiteness of Frobenius test exponentsSep 26 2018Nov 05 2018The Frobenius test exponent $\operatorname{Fte}(R)$ of a local ring $(R,\mathfrak{m})$ of prime characteristic $p > 0$ is the smallest $e_0 \in \mathbb{N}$ such that for every ideal $\mathfrak{q}$ generated by a (full) system of parameters, the Frobenius ... More

"Cosmic Rays" from Quark MatterJun 04 2010Nov 30 2010I describe a dark matter candidate based in qcd physics in which the dark matter is composed of macroscopically large "nuggets" of quark and anti-quark matter. These objects may have a sufficiently massive low number density to avoid constraints from ... More

Generic fibrations around multiple fibersMay 25 2014Aug 18 2014Given some type of fibration on a 4-manifold $X$ with a torus regular fiber $T$, we may produce a new 4-manifold $X_T$ by performing torus surgery on $T$. There is a natural way to extend the fibration to $X_T$, but a multiple fiber (non-generic) singularity ... More

Surgery on tori in the 4-sphereFeb 24 2015Aug 13 2016We investigate the operation of torus surgery on tori embedded in $S^4$. Key questions include which 4-manifolds can be obtained in this way, and the uniqueness of such descriptions. As an application we construct embeddings of 3-manifolds into 4-manifolds ... More

State Classification of Cooking Objects Using a VGG CNNApr 21 2019In machine learning, it is very important for a robot to know the state of an object and recognize particular desired states. This is an image classification problem that can be solved using a convolutional neural network. In this paper, we will discuss ... More

Pairwise Rational Points on a ParabolaJul 30 2019This paper presents a solution to the following open problem in Number Theory and Geometry: How many points can you find on the (half) parabola $y=x^2$, $x>0$, so that the distance between any pair of them is rational? This problem sounds like a geometry ... More

Understanding decreases in land relative humidity with global warming: conceptual model and GCM simulationsMay 02 2016Climate models simulate a strong land-ocean contrast in the response of near-surface relative humidity to global warming: relative humidity tends to increase slightly over oceans but decrease substantially over land. Surface energy balance arguments have ... More

A Contribution to the Theory Behind the M0 Capture-Recapture Model: An Improved EstimatorDec 10 2012Feb 17 2014We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator ... More

Statistical Challenges for Searches for New Physics at the LHCNov 03 2005Jan 04 2006Because the emphasis of the LHC is on 5 sigma discoveries and the LHC environment induces high systematic errors, many of the common statistical procedures used in High Energy Physics are not adequate. I review the basic ingredients of LHC searches, the ... More

A Generalization of Plexes of Latin SquaresAug 01 2010A $k$-plex of a latin square is a collection of cells representing each row, column, and symbol precisely $k$ times. The classic case of $k=1$ is more commonly known as a transversal. We introduce the concept of a $k$-weight, an integral weight function ... More

Explicit Salem sets and applications to metrical Diophantine approximationApr 01 2016Let $Q$ be an infinite subset of $\mathbb{Z}$, let $\Psi: \mathbb{Z} \rightarrow [0,\infty)$ be positive on $Q$, and let $\theta \in \mathbb{R}$. Define $$ E(Q,\Psi,\theta) = \{ x \in \mathbb{R} : \| q x - \theta \| \leq \Psi(q) \text{ for infinitely ... More

Estimating Forces of Robotic Pouring Using a LSTM RNNApr 21 2019May 02 2019In machine learning, it is very important for a robot to be able to estimate dynamics from sequences of input data. This problem can be solved using a recurrent neural network. In this paper, we will discuss the preprocessing of 10 states of the dataset, ... More

Conformal dimension and boundaries of planar domainsJul 16 2015Jun 14 2016Building off of techniques that were recently developed by M. Carrasco, S. Keith, and B. Kleiner to study the conformal dimension of boundaries of hyperbolic groups, we prove that uniformly perfect boundaries of John domains in the Riemann sphere have ... More

Lower bounds for codimension-1 measure in metric manifoldsFeb 20 2016We establish Euclidean-type lower bounds for the codimension-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in the setting ... More

Complex Random Matrices have no Real EigenvaluesSep 24 2016Let $\zeta = \xi + i\xi'$ where $\xi, \xi'$ are iid copies of a mean zero, variance one, subgaussian random variable. Let $N_n$ be a $n \times n$ random matrix with iid entries $\zeta_{ij} = \zeta$. We prove that there exists a $c \in (0,1)$ such that ... More

Shortest Non-trivial Cycles in Directed and Undirected Surface GraphsNov 29 2011Sep 19 2012Let G be a graph embedded on a surface of genus g with b boundary cycles. We describe algorithms to compute multiple types of non-trivial cycles in G, using different techniques depending on whether or not G is an undirected graph. If G is undirected, ... More

Upper Bounds for Maximally Greedy Binary Search TreesFeb 24 2011Apr 29 2011At SODA 2009, Demaine et al. presented a novel connection between binary search trees (BSTs) and subsets of points on the plane. This connection was independently discovered by Derryberry et al. As part of their results, Demaine et al. considered GreedyFuture, ... More

Practical Statistics for the LHCMar 26 2015This document is a pedagogical introduction to statistics for particle physics. Emphasis is placed on the terminology, concepts, and methods being used at the Large Hadron Collider. The document addresses both the statistical tests applied to a model ... More

$2^3$ Quantified Boolean Formula Games and Their ComplexitiesJan 15 2014Dec 29 2014Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this paper, three common ... More

A Contribution to the Theory Behind the M0 Capture-Recapture Model: An Improved EstimatorDec 10 2012Nov 28 2018We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator ... More

Recent Advances on Estimating Population Size with Link-Tracing SamplingSep 22 2017A new approach to estimate population size based on a stratified link-tracing sampling design is presented. The method extends on the Frank and Snijders (1994) approach by allowing for heterogeneity in the initial sample selection procedure. Rao-Blackwell ... More

Primes from sums of two squares and missing digitsJun 07 2018Let $\mathcal{A}'$ be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for counting primes of the form $p = m^2 + \ell^2$, with $\ell \in \mathcal{A}'$. ... More

Gallai MultigraphsJun 30 2007A complete edge-colored graph or multigraph is called Gallai if it lacks rainbow triangles. We give a construction of all finite Gallai multigraphs.

Rao-Blackwellization to give Improved Estimates in Multi-List StudiesSep 26 2017Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented. As Rao-Blackwellization ... More

Quark Matter Induced Extensive Air ShowersNov 15 2010May 03 2011If the dark matter of our galaxy is composed of nuggets of quarks or antiquarks in a colour superconducting phase there will be a small but non-zero flux of these objects through the Earth's atmosphere. A nugget of quark matter will deposit only a small ... More

Powers of Elements in Jordan LoopsAug 04 2010A Jordan loop is a commutative loop satisfying the Jordan identity $(x^2 y) x = x^2 (y x)$. We establish several identities involving powers in Jordan loops and show that there is no nonassociative Jordan loop of order $9$.

An ergodic algorithm for generating knots with a prescribed injectivity radiusMar 09 2016May 08 2017The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a ... More

Discrete length-volume inequalities and lower volume bounds in metric spacesOct 21 2014Feb 22 2016A theorem of W. Derrick ensures that the volume of any Riemannian cube $([0,1]^n,g)$ is bounded below by the product of the distances between opposite codimension-1 faces. In this paper, we establish a discrete analog of Derrick's inequality for weighted ... More

Rigidity for Quasi-Möbius Actions on Fractal Metric SpacesAug 02 2013Jan 15 2016In \cite{BK02}, M. Bonk and B. Kleiner proved a rigidity theorem for expanding quasi-M\"obius group actions on Ahlfors $n$-regular metric spaces with topological dimension $n$. This led naturally to a rigidity result for quasi-convex geometric actions ... More

Legendrian ribbons and strongly quasipositive links in an open bookOct 17 2017We show that a link in an open book can be realized as a strongly quasipositive braid if and only if it bounds a Legendrian ribbon with respect to the associated contact structure. This generalizes a result due to Baader and Ishikawa for links in the ... More

Jif: Language-based Information-flow Security in JavaDec 30 2014In this report, we examine Jif, a Java extension which augments the language with features related to security. Jif adds support for security labels to Java's type system such that the developer can specify confidentiality and integrity policies to the ... More

An ergodic algorithm for generating knots with a prescribed injectivity radiusMar 09 2016The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a ... More

A Contribution to the Theory Behind the Capture-Recapture M0 Model: An Improved EstimatorNov 21 2012Feb 17 2014We explore the use of a sufficient statistic based on the data of samples that are selected under the M_0 capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statistic ... More

Loop-Erased Random SurfacesNov 16 2015Jul 13 2016Loop-erased random walk and it's scaling limit, Schramm--Loewner evolution, have found numerous applications in mathematics and physics. We present a 2 dimensional analogue of LERW, the loop erased random surface. We do this by defining a 2 dimensional ... More

Estimating Forces of Robotic Pouring Using a LSTM RNNApr 21 2019In machine learning, it is very important for a robot to be able to estimate dynamics from sequences of input data. This problem can be solved using a recurrent neural network. In this paper, we will discuss the preprocessing of 10 states of the dataset, ... More

Equivariant Solutions to a System of Nonlinear Wave Equations with Ginzburg-Landau Type PotentialJan 11 2016It is known that there exist solutions with interfaces to various scalar nonlinear wave equations. In this paper, we look for solutions of a two-component system of nonlinear wave equations where one of the components has an interface and and where the ... More

A Language for Function Signature RepresentationsMar 31 2018Apr 18 2018Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being learned in these ... More

On the Sobolev stability threshold of 3D Couette flow in a homogeneous magnetic fieldDec 30 2018We study the stability of the Couette flow $(y,0,0)^T$ in the 3D incompressible magnetohydrodynamic (MHD) equations for a conducting fluid on $\mathbb{T} \times \mathbb{R} \times \mathbb{T} $ in the presence of a homogeneous magnetic field $\alpha(\sigma, ... More

Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjectureAug 04 2010For a finite loop $Q$, let $P (Q)$ be the set of elements that can be represented as a product containing each element of $Q$ precisely once. Motivated by the recent proof of the Hall-Paige conjecture, we prove several universal implications between the ... More

Avocado: Photometric Classification of Astronomical Transients with Gaussian Process AugmentationJul 09 2019Jul 11 2019Upcoming astronomical surveys such as the Large Synoptic Survey Telescope (LSST) will rely on photometric classification to identify the majority of the transients and variables that they discover. We present a set of techniques for photometric classification ... More

Constant Rate Distributions on Partially Ordered SetsOct 13 2008Apr 06 2010We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich ... More

Minimal braid representatives of quasipositive linksMay 05 2016We show that every quasipositive link has a quasipositive minimal braid representative, partially resolving a question posed by Orevkov. These quasipositive minimal braids are used to show that the maximal self-linking number of a quasipositive link is ... More

Cross-sections of unknotted ribbon disks and algebraic curvesJan 16 2018Feb 28 2018We resolve parts (A) and (B) of Problem 1.100 from Kirby's list by showing that many nontrivial links arise as cross-sections of unknotted holomorphic disks in the four-ball. The techniques can be used to produce unknotted ribbon surfaces with prescribed ... More

Lower bounds for codimension-1 measure in metric manifoldsFeb 20 2016Oct 21 2016We establish Euclidean-type lower bounds for the codimension-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in the setting ... More

Discreteness and Large Scale SurjectionsAug 12 2015We study the concept of coarse disjointness and large scale $n$-to-$1$ functions. As a byproduct, we obtain an Ostrand-type characterization of asymptotic dimension for coarse structures. It is shown that properties like finite asymptotic dimension, coarse ... More

Moment Independent Expansion for Fourth-Order Corrections in Lattice Boltzmann MethodsOct 30 2017Jan 17 2018A expansion to fourth-order for lattice Boltzmann methods is presented. This expansion provides an easy model for finding fourth-order corrections to lattice Boltzmann methods for various physical systems. The fourth-order terms can give rise to improved ... More

Upward and Downward Runs on Partially Ordered SetsOct 13 2008Apr 06 2010We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant distributions. We study ... More

Lattices and correction termsJul 13 2018Feb 22 2019Let L be a nonunimodular definite lattice. Using a theorem of Elkies we show that whether L embeds in the standard definite lattice of the same rank is completely determined by a collection of lattice correction terms, one for each metabolizing subgroup ... More

Loewner chains and Hölder geometryOct 21 2014Feb 22 2016The Loewner equation provides a correspondence between continuous real-valued functions $\lambda_t$ and certain increasing families of half-plane hulls $K_t$. In this paper we study the deterministic relationship between specific analytic properties of ... More

Complex Random Matrices have no Real EigenvaluesSep 24 2016Oct 08 2017Let $\zeta = \xi + i\xi'$ where $\xi, \xi'$ are iid copies of a mean zero, variance one, subgaussian random variable. Let $N_n$ be a $n \times n$ random matrix with entries that are iid copies of $\zeta$. We prove that there exists a $c \in (0,1)$ such ... More

Blocks in ASEP with step-Bernoulli initial conditionMay 28 2019This paper extends work by Tracy and Widom on blocks in the asymmetric simple exclusion process (ASEP) to the case of step-Bernoulli initial condition. We consider the probability that a particle at site $x$ is the beginning of a block of $L$ consecutive ... More

A sufficient condition for finiteness of Frobenius test exponentsSep 26 2018Apr 18 2019The Frobenius test exponent $\operatorname{Fte}(R)$ of a local ring $(R,\mathfrak{m})$ of prime characteristic $p > 0$ is the smallest $e_0 \in \mathbb{N}$ such that for every ideal $\mathfrak{q}$ generated by a (full) system of parameters, the Frobenius ... More

Investigation of the Vertical Movement of an Isothermal Line at the Density Maximum in H2O and D2OMar 05 2008We studied the cooling of a column of water, primarily in a freezer, and analyzed the development and movement of an isothermal line at ~4 degC in H2O and ~11 degC in D2O. Our experiments show that the vertical velocity of the symmetrical isothermal line ... More

Charge-qubit operation of an isolated double quantum dotApr 18 2005Aug 02 2005We have investigated coherent time evolution of pseudo-molecular states of an isolated (leadless) silicon double quantum-dot, where operations are carried out via capacitively-coupled elements. Manipulation is performed by short pulses applied to a nearby ... More

Experimental Study of a Lorentz Actuated OrbitMay 21 2008This experimental study investigates a new technique to keep a satellite in orbit utilizing electrodynamics. The technique consists of establishing a charge on a satellite such that the body's motion through a planetary magnetic field induces acceleration ... More

Finite-range-scaling analysis of metastability in an Ising model with long-range interactionsFeb 02 1994We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the $N$$\times$$\infty$ quasi-one-dimensional Ising model. ... More

Achieving Efficient Strong Scaling with PETSc using Hybrid MPI/OpenMP OptimisationMar 21 2013The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on massively parallel ... More

Unstructured Overlapping Mesh Distribution in ParallelJun 20 2015We present a simple mathematical framework and API for parallel mesh and data distribution, load balancing, and overlap generation. It relies on viewing the mesh as a Hasse diagram, abstracting away information such as cell shape, dimension, and coordinates. ... More

The Gender Balance of the Australian Space Research Community: A Snapshot from the 16th ASRC, 2016Aug 13 2017In recent years, there has been significant debate and discussion about the glaring gender disparity in the physical sciences. To better understand and address this within the Australian Space Research Community, in 2015 we began the process of keeping ... More

A New Approach to Inference in Multi-Survey Studies with Unknown Population SizeJan 27 2014Nov 30 2015We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference. The complete ... More

On the shard intersection order of a Coxeter groupAug 29 2011Jun 14 2013Introduced by Reading, the shard intersection order of a finite Coxeter group $W$ is a lattice structure on the elements of $W$ that contains the poset of noncrossing partitions $NC(W)$ as a sublattice. Building on work of Bancroft in the case of the ... More

Estimating the size and distribution of networked populations with snowball samplingFeb 18 2014Jan 22 2015A new strategy is introduced for estimating networked population characteristics. Sample selection is based on the one-wave snowball sampling design. A generalized stochastic block model is posited for the population's network topology. Inference is based ... More

Higson Compactification and Dimension RaisingAug 13 2016Let $X$ and $Y$ be proper metric spaces. We show that a coarsely $n$-to-$1$ map $f\colon X\to Y$ induces an $n$-to-$1$ map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large ... More

PSPACE-Complete Two-Color Placement GamesFeb 19 2016We show that three placement games, Col, NoGo, and Fjords, are PSPACE-complete on planar graphs. The hardness of Col and Fjords is shown via a reduction from Bounded 2-Player Constraint Logic and NoGo is shown to be hard directly from Col.

Fast Deep Stereo with 2D Convolutional Processing of Cost SignaturesMar 08 2019Modern neural network-based algorithms are able to produce highly accurate depth estimates from stereo image pairs, nearly matching the reliability of measurements from more expensive depth sensors. However, this accuracy comes with a higher computational ... More

Limit operator theory for groupoidsMar 20 2019We extend the symbol calculus and study the limit operator theory for $\sigma$-compact, \'{e}tale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact groups and discrete ... More

Fixed-Topology Lorentzian Triangulations: Quantum Regge Calculus in the Lorentzian DomainAug 24 2011Nov 09 2011A key insight used in developing the theory of Causal Dynamical Triangulations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path integral. By exploiting ... More

Similarity Renormalization Group Evolution of Three-Nucleon Forces in a Hyperspherical Momentum RepresentationApr 04 2013A new framework for computing the Similarity Renormalization Group (SRG) evolution of three-nucleon forces (3NF) in momentum representation is presented. The use of antisymmetric three-particle hyperspherical momentum states ensures unitary evolutions ... More

Realistic Traffic Generation for Web RobotsDec 15 2017Critical to evaluating the capacity, scalability, and availability of web systems are realistic web traffic generators. Web traffic generation is a classic research problem, no generator accounts for the characteristics of web robots or crawlers that ... More

Off-Lattice Random Walks with Excluded Volume: A New Method of Generation, Proof of Ergodicity and Numerical ResultsJun 15 2017We describe a new algorithm, the reflection method, to generate off-lattice random walks of specified, though arbitrarily large, thickness in $\mathbb{R}^3$ and prove that our method is ergodic on the space of thick walks. The data resulting from our ... More

Recovery Guarantees for Compressible Signals with Adversarial NoiseJul 15 2019We provide recovery guarantees for compressible signals that have been corrupted with noise and extend the framework introduced in [1] to defend neural networks against $\ell_0$-norm and $\ell_2$-norm attacks. Concretely, for a signal that is approximately ... More

Orbital minimization method with $\ell^1$ regularizationMay 03 2016We consider a modification of the OMM energy functional which contains an $\ell^1$ penalty term in order to find a sparse representation of the low-lying eigenspace of self-adjoint operators. We analyze the local minima of the modified functional as well ... More

Capturing an Evader in Polygonal Environments: A Complete Information GameOct 21 2011Suppose an unpredictable evader is free to move around in a polygonal environment of arbitrary complexity that is under full camera surveillance. How many pursuers, each with the same maximum speed as the evader, are necessary and sufficient to guarantee ... More

Motivic invariants of p-adic fieldsFeb 26 2010Nov 01 2012We provide a complete analysis of the motivic Adams spectral sequences converging to the bigraded coefficients of the 2-complete algebraic Johnson-Wilson spectra BPGL<n> over p-adic fields. These spectra interpolate between integral motivic cohomology ... More

Brieskorn spheres bounding rational ballsApr 25 2017Fintushel and Stern showed that the Brieskorn sphere $\Sigma(2,3,7)$ bounds a rational homology ball, while its non-trivial Rokhlin invariant obstructs it from bounding an integral homology ball. It is known that their argument can be modified to show ... More

Fibered ribbon disksOct 17 2014Oct 19 2015We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered ... More

Sparse Random Matrices have Simple SpectrumFeb 10 2018Feb 18 2018Let $M_n$ be a class of symmetric sparse random matrices, with independent entries $M_{ij} = \delta_{ij} \xi_{ij}$ for $i \leq j$. $\delta_{ij}$ are i.i.d. Bernoulli random variables taking the value $1$ with probability $p \geq n^{-1+\delta}$ for any ... More

Adiabatic times for Markov chains and applicationsAug 11 2010We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of Ising model over Z^d/nZ^d. The theorems derived in this paper describe a type of adiabatic dynamics for l^1(R_+^n) ... More

Tail bounds for gaps between eigenvalues of sparse random matricesJan 17 2019We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and error probability from the work of the second author and Vu. As an application ... More

Interlacing of zeros of weakly holomorphic modular formsAug 05 2013We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the space of weakly holomorphic modular forms of weight $k$ for $\SL_2(\mathbb{Z})$ ... More

Twisted index theory on orbifold symmetric products and the fractional quantum Hall effectFeb 04 2015We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples ... More

Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the $p$-adic numbersAug 18 2017We exhibit the first explicit examples of Salem sets in $\mathbb{Q}_p$ of every dimension $0 < \alpha < 1$ by showing that certain sets of well-approximable $p$-adic numbers are Salem sets. We construct measures supported on these sets that satisfy essentially ... More

A Geometric Consideration of the Erdős-Straus ConjectureNov 13 2014Dec 08 2014In this paper we will explore the solutions to the diophantine equation in the Erd\H{o}s-Straus conjecture. For a prime $p$ we are discussing the relationship between the values $x,y,z \in \mathbb{N}$ so that $$ \frac{4}{p} = \frac{1}{x} + \frac{1}{y} ... More

Spontaneous supersymmetry breaking in the two-dimensional N=1 Wess-Zumino modelOct 24 2014We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on the lattice using Wilson fermions and the fermion loop formulation. We give a complete nonperturbative determination of the ground state structure in the continuum and infinite ... More

RECAST: Extending the Impact of Existing AnalysesOct 12 2010Searches for new physics by experimental collaborations represent a significant investment in time and resources. Often these searches are sensitive to a broader class of models than they were originally designed to test. We aim to extend the impact of ... More

Frequentist Hypothesis Testing with Background UncertaintyOct 22 2003We consider the standard Neyman-Pearson hypothesis test of a signal-plus-background hypothesis and background-only hypothesis in the presence of uncertainty on the background-only prediction. Surprisingly, this problem has not been addressed in the recent ... More

Knot concordance and homology sphere groupsMay 25 2016We study two homomorphisms to the rational homology sphere group. If $\beta$ denotes the homomorphism from the knot concordance group $\mathcal{C}$ defined by taking double branched covers of knots, we show that the kernel of $\beta$ is infinitely generated ... More

Estimating the size and distribution of networked populations with snowball samplingFeb 18 2014Jul 26 2017A new strategy is introduced for estimating population size and networked population characteristics. Sample selection is based on the one-wave snowball sampling design. A generalized stochastic block model is posited for the population's network graph. ... More

Groupoid Models of $C^*$-algebras and Gelfand DualityApr 03 2018Aug 10 2018We construct a large class of morphisms, which we call partial morphisms, of groupoids that induce $*$-morphisms of maximal and minimal groupoid $C^*$-algebras. We show that the association of a groupoid to its maximal (minimal) groupoid $C^*$-algebra ... More

511 keV Line Emission from Nearby Spherical Dwarf GalaxiesNov 17 2016The observed galactic 511 keV line has been interpreted in a number of papers as a possible signal of dark matter annihilation within the galactic bulge. If this is the case then we should expect a similar spectral feature associated with nearby dwarf ... More

Enhancing Infrastructure Security in Real EstateNov 30 2015As a result of the increased dependency on obtaining information and connecting each computer together for ease of access or communication, organizations risk being attacked and losing private information through breaches or insecure business activities. ... More

Trackability with Imprecise LocalizationDec 19 2013Imagine a tracking agent $P$ who wants to follow a moving target $Q$ in $d$-dimensional Euclidean space. The tracker has access to a noisy location sensor that reports an estimate $\tilde{Q}(t)$ of the target's true location $Q(t)$ at time $t$, where ... More

An Explicit Formulation of the Earth Movers Distance with Continuous Road Map DistancesSep 27 2013Oct 14 2013The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of Demand-Responsive ... More

Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard modelAug 22 2018A lattice of interacting Majorana modes can occur in a superconducting film on a topological insulator in a magnetic field. The phase diagram as a function of interaction strength for the square lattice was analyzed recently using a combination of mean ... More