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A VLT/FORS2 Narrowband Imaging Search for MgII Emission Around z ~ 0.7 GalaxiesMay 14 2019We perform a Very Large Telescope FOcal Reducer and low dispersion Spectrograph 2 (VLT/FORS2) narrowband imaging search around 5 star-forming galaxies at redshift z=0.67-0.69 in the Great Observatories Origins Deep Survey South (GOODS-S) field to constrain ... More

Topological Approaches to Deep LearningNov 02 2018We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed up computations ... More

Synthesis of titanium-oxide nanoparticles with size and stoichiometry controlApr 17 2015Ti-O nanoparticles have been synthesized via hollow cathode sputtering in an Ar-O2 atmosphere using high power pulsing. It is shown that the stoichiometry and the size of the nanoparticles can be varied independently, the former through controlling the ... More

A decomposition theorem for higher rank Coxeter groupsJul 21 2010In this paper, we show that any Coxeter graph which defines a higher rank Coxeter group must have disjoint induced subgraphs each of which defines a hyperbolic or higher rank Coxeter group. We then use this result to demonstrate several classes of Coxeter ... More

Spectrally-Precoded OFDM for 5G Wideband Operation in Fragmented sub-6GHz SpectrumJun 02 2016We consider spectrally-precoded OFDM waveforms for 5G wideband transmission in sub-6GHz band. In this densely packed spectrum, a low out-of-band (OOB) waveform is a critical 5G component to achieve the promised high spectral efficiency. By precoding data ... More

Partial regularity of weak solutions of the viscoelastic Navier-Stokes equations with dampingFeb 05 2011We prove an analog of the Caffarelli-Kohn-Nirenberg theorem for weak solutions of a system of PDE that model a viscoelastic fluid in the presence of an energy damping mechanism. The system was recently introduced as a possible method of establishing the ... More

The eigenvalue problem of singular ergodic controlFeb 05 2011Aug 30 2011We consider the problem of finding a real number lambda and a function u satisfying the PDE max{lambda -\Delta u -f,|Du|-1}=0, for all x in R^n. Here f is a convex, superlinear function. We prove that there is a unique lambda* such that the above PDE ... More

Induction and Analogy in a Problem of Finite SumsAug 13 2016What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from ... More

ExoData: A python package to handle large exoplanet catalogue dataOct 09 2015May 29 2016Exoplanet science often involves using the system parameters of real exoplanets for tasks such as simulations, fitting routines, and target selection for proposals. Several exoplanet catalogues are already well established but often lack a version history ... More

Finding paths of length k in O*(2^k) timeJul 18 2008Nov 09 2008We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2^k poly(n,k)) time.

Faster all-pairs shortest paths via circuit complexityDec 23 2013May 22 2014We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary ... More

Progress in leptonic and semileptonic decays in lattice QCDMay 04 1999The status of lattice calculations of heavy quark phenomenology is reviewed. Particular emphasis is placed on the understanding and control of the calculational uncertainties. The ensuing implications for constraining the CKM matrix elements are discussed. ... More

Automatically Segmenting Oral History TranscriptsSep 29 2015Dividing oral histories into topically coherent segments can make them more accessible online. People regularly make judgments about where coherent segments can be extracted from oral histories. But making these judgments can be taxing, so automated assistance ... More

Insights into Pre-Enrichment of Star Clusters and Self-Enrichment of Dwarf Galaxies from their Intrinsic Metallicity DispersionsSep 20 2012Star clusters are known to have smaller intrinsic metallicity spreads than dwarf galaxies due to their shorter star formation timescales. Here we use individual spectroscopic [Fe/H] measurements of stars in 19 Local Group dwarf galaxies, 13 Galactic open ... More

The Statistical Significance of the "Dark Flow"Oct 22 2009Feb 14 2013We revisit the statistical significance of the "dark flow" presented in Kashlinsky et al. (2009). We do not find a statistically significant detection of a bulk flow. Instead we find that CMB correlations between the 8 WMAP channels used in this analysis ... More

An algorithm to assign musical prime commas to every prime number to allow construction of a complete notation for frequencies in free Just IntonationDec 05 2016Musical frequencies in Just Intonation are comprised of rational numbers. The structure of rational numbers is determined by prime factorisations. Just Intonation frequencies can be split into two components. The larger component uses only integer powers ... More

Plemelj Projection Operators over Domain ManifoldsMay 07 1998Plemelj projection operators are introduced for spaces of square integrable functions defined over the boundaries of a class of compact real n-dimensional manifolds lying in C^n. These manifolds posses many properties similar to domains in R^n, and are ... More

Monge-Ampère IterationDec 07 2017In a recent paper, Darvas-Rubinstein proved a convergence result for the Kahler-Ricci iteration, which is a sequence of recursively defined complex Monge-Ampere equations. We introduce the Monge-Ampere iteration to be an analogous, but more general, sequence ... More

A Model Explanation System: Latest Updates and ExtensionsJun 30 2016We propose a general model explanation system (MES) for "explaining" the output of black box classifiers. This paper describes extensions to Turner (2015), which is referred to frequently in the text. We use the motivating example of a classifier trained ... More

Localization for Chern-Simons on Circle Bundles via Loop GroupsJul 06 2015Nov 03 2017We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate ... More

The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric SurfaceJul 25 2016Let $\xi$ be a stable Chern character on $\mathbb{P}^1 \times \mathbb{P}^1$, and let $M(\xi)$ be the moduli space of Gieseker semistable sheaves on $\mathbb{P}^1 \times \mathbb{P}^1$ with Chern character $\xi$. In this paper, we provide an approach to ... More

New algorithms and lower bounds for circuits with linear threshold gatesJan 10 2014Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen as a "midpoint" ... More

Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO DynamicsAug 26 2016Broadly speaking, this thesis is about nonlinear optics, quantum mechanics, and computing. More specifically, it covers four main topics: Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO Dynamics. Tying them all together ... More

Trapezoid Order ClassificationDec 11 1996We show the nonequivalence of combinations of several natural geometric restrictions on trapezoid representations of trapezoid orders. Each of the properties unit parallelogram, unit trapezoid and proper parallelogram, unit trapezoid and parallelogram, ... More

Random sets and exact confidence regionsFeb 08 2013Oct 15 2013An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold approximately, for ... More

Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular controlFeb 05 2011Sep 03 2011We study the partial differential equation max{Lu - f, H(Du)}=0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations ... More

Ramsey Numbers of Odd Cycles Versus Larger Even WheelsSep 13 2016Sep 14 2016The generalized Ramsey number $R(G_1, G_2)$ is the smallest positive integer $N$ such that any red-blue coloring of the edges of the complete graph $K_N$ either contains a red copy of $G_1$ or a blue copy of $G_2$. Let $C_m$ denote a cycle of length $m$ ... More

A New Look at Chern-Simons on Circle Bundles I: The Caloron CorrespondenceJul 06 2015We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate ... More

Training Neural Networks with Stochastic Hessian-Free OptimizationJan 16 2013May 01 2013Hessian-free (HF) optimization has been successfully used for training deep autoencoders and recurrent networks. HF uses the conjugate gradient algorithm to construct update directions through curvature-vector products that can be computed on the same ... More

Mathematical Harmony AnalysisMar 29 2016Mar 30 2016Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by whole positive ... More

The independent discovery of planet candidates around low mass stars and astrophysical false positives from the first two TESS sectorsDec 19 2018Continuous data releases throughout the TESS primary mission will provide unique opportunities for the exoplanet community at large to contribute to maximizing TESS's scientific return via the discovery and validation of transiting planets. This paper ... More

Source Coding Optimization for Distributed Average ConsensusOct 04 2017Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored at all the ... More

Estimation of the Szlenk index of Banach Spaces via Schreier spacesDec 21 2012Aug 25 2013For each ordinal $\alpha<\omega_1$, we prove the existence of a space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of spaces with Szlenk index not exceeding $\omega^\alpha$. Our proof involves developing a characterization ... More

Chermak-Delgado Simple GroupsOct 14 2015This paper provides the first steps in classifying the finite solvable groups having Property A, which is a property involving abelian normal subgroups. We see that this classification is reduced to classifying the solvable Chermak-Delgado simple groups, ... More

Single-top Cross Section Measurements at ATLASNov 28 2008The single-top production cross section is one third that of the top-pair production cross section at the LHC. During a year of data-taking, assuming an average luminosity of 10^33 cm-2 s-1 and a CMS energy of 14 TeV, the determination of the major contributions ... More

A pathwise variation estimate for the sticky particle systemApr 25 2018Apr 30 2019We study collections of finitely many point masses that move freely in space and stick together when they collide via perfectly inelastic collisions. We establish a uniform bound on the mass average of the total variation of the velocities of particle ... More

An operad for splicingApr 22 2010Mar 31 2012A new topological operad is introduced, called the splicing operad. This operad acts on a broad class of spaces of self-embeddings N --> N where N is a manifold. The action of this operad on EC(j,M) (self embeddings R^j x M --> R^j x M with support in ... More

Topology of spaces of knots in dimension 3Jun 25 2005Aug 11 2009This paper is a computation of the homotopy type of K, the space of long knots in R^3, the same space of knots studied by Vassiliev via singularity theory. Each component of K corresponds to an isotopy class of long knot, and we `enumerate' the components ... More

JSJ-decompositions of knot and link complements in the 3-sphereJun 25 2005Oct 29 2007This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in the 3-sphere. Formulated in the language of graphs, the result is the construction of a bijective correspondence ... More

Projection Method for Solving Stokes FlowDec 06 2017Dec 20 2017Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the numerical solution ... More

Families and moduli of covers with specified ramificationDec 26 2013We study branched covers of curves with specified ramification points, under a notion of equivalence derived from linear series. In characteristic 0, no non-constant families of covers with fixed ramification points exist. In positive characteristic we ... More

Rank loci in representation spaces of quiversApr 12 2010Apr 19 2010Rank functors on a quiver $Q$ are certain additive functors from the category of representations of $Q$ to the category of finite-dimensional vector spaces. Composing with the dimension function on vector spaces gives a rank function on $Q$. These induce ... More

Natural Proofs Versus DerandomizationDec 09 2012Jul 21 2015We study connections between Natural Proofs, derandomization, and the problem of proving "weak" circuit lower bounds such as ${\sf NEXP} \not\subset {\sf TC^0}$. Natural Proofs have three properties: they are constructive (an efficient algorithm $A$ is ... More

A Casual Tour Around a Circuit Complexity BoundNov 04 2011I will discuss the recent proof that the complexity class NEXP (nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial size. The proof will be described from the perspective of someone trying to discover it.

Alternation-Trading Proofs, Linear Programming, and Lower BoundsJan 05 2010Feb 03 2010A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT, Majority-of-Majority-SAT, ... More

Applying Practice to TheoryNov 09 2008How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe how linear ... More

Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch EvaluationJan 18 2016We present an efficient proof system for Multipoint Arithmetic Circuit Evaluation: for every arithmetic circuit $C(x_1,\ldots,x_n)$ of size $s$ and degree $d$ over a field ${\mathbb F}$, and any inputs $a_1,\ldots,a_K \in {\mathbb F}^n$, $\bullet$ the ... More

Heavy quark physics from lattice QCDNov 08 2001Apr 07 2002I review the current status of lattice calculations of heavy quark quantities. Particular emphasis is placed on leptonic and semileptonic decay matrix elements.

Lattice determinations of the strange quark massAug 17 1999Aug 18 1999Lattice calculations of the mass of the strange quark are reviewed. In particular, the reason for the spread in values is explained with emphasis on the effects that recently implemented improvements have had on the lattice determinations.

Finite orbits in random subshifts of finite typeJun 08 2015Nov 15 2016For each $n, d \in \mathbb{N}$ and $0 < \alpha < 1$, we define a random subset of $\mathcal{A}^{\{1, 2, \dots, n\}^d}$ by independently including each element with probability $\alpha$ and excluding it with probability $1-\alpha$, and consider the associated ... More

Galactic Disc Rotation: Analytic models and asymptotic resultsJan 22 2013Jul 22 2013This paper outlines an exact analytic model for self-gravitating thin disc galaxies with flat rotation curves. It is shown that thin discs of matter alone can support perfectly flat rotation curves under Newtonian gravity, without needing extended halos ... More

An eigenvalue problem for fully nonlinear elliptic equations with gradient constraintsDec 27 2014Aug 30 2015We consider the problem of finding $\lambda\in \mathbb{R}$ and a function $u:\mathbb{R}^n\rightarrow\mathbb{R}$ that satisfy the PDE $$ \max\left\{\lambda + F(D^2u) -f(x),H(Du)\right\}=0, \quad x\in \mathbb{R}^n. $$ Here $F$ is elliptic, positively homogeneous ... More

Compactness methods for doubly nonlinear parabolic systemsOct 29 2014Aug 23 2015We study solutions of the system of PDE $D\psi({\bf v}_t)=\text{div}DF(D{\bf v})$, where $\psi$ and $F$ are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties of solutions ... More

A new Computer Friendly Notation for Musical Composition in Just Intonation allowing Easy Transposition by Multiplication of NotationsAug 31 2015Mar 11 2016Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve note tuning systems the frequency can be described using letters A to G with sharp or flat ... More

Proximity to $\ell_p$ and $c_0$ in Banach spacesFeb 20 2015We construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees. Among the applications of these trees and coloring theorems are quantification of the Bourgain $\ell_p$ and $c_0$ indices, dualization ... More

Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spacesAug 25 2013For each ordinal $\alpha< \omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the Szlenk indices ... More

On nonparametric estimation of a mixing density via the predictive recursion algorithmDec 05 2018Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion algorithm. After ... More

Incorrigibility in the CIRL FrameworkSep 19 2017Jun 03 2018A value learning system has incentives to follow shutdown instructions, assuming the shutdown instruction provides information (in the technical sense) about which actions lead to valuable outcomes. However, this assumption is not robust to model mis-specification ... More

A pathwise variation estimate for the sticky particle systemApr 25 2018Aug 04 2018We study collections of finitely many point masses that move freely in space and stick together when they collide via perfectly inelastic collisions. We establish a uniform bound on the mass average of the total variation of the velocities of particle ... More

Notes on Beilinson's "How to glue perverse sheaves"Feb 08 2010Jul 11 2010The titular, foundational work of Beilinson not only gives a technique for gluing perverse sheaves but also implicitly contains constructions of the nearby and vanishing cycles functors of perverse sheaves. These constructions are completely elementary ... More

Cauchy kernels for some conformally flat manifoldsMar 26 2003Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the n-dimensional sphere. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections tasking values in ... More

Edge-state instabilities of bosons in a topological bandAug 08 2013Feb 21 2014In this work, we consider the dynamics of bosons in bands with non-trivial topological structure. In particular, we focus on the case where bosons are prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory about the initial state ... More

Twisted Analytic Torsion and Adiabatic LimitsNov 26 2013We study an analogue of the analytic torsion for elliptic complexes that are graded by $\mathbb{Z}_2$, orignally constructed by Mathai and Wu. Motivated by topological T-duality, Bouwknegt an Mathai study the complex of forms on an odd-dimensional manifold ... More

Bridge number and tangle productsAug 29 2011We show that essential punctured spheres in the complement of links with distance three bridge spheres have bounded complexity. We define the operation of tangle product, a generalization of both connected sum and Conway product. Finally, we use the bounded ... More

The rank of a quiver representationNov 07 2007Mar 09 2009We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a quiver Q, which ... More

Security Landscape for RoboticsApr 05 2019In this paper, the current state of security in robotics is described to be in need of review. When we consider safety mechanisms implemented in an Internet-connected robot, the requirement of safety becomes a crucial security requirement. Upon review ... More

A covariant formalism of spin precession with respect to a reference congruenceAug 19 2007We derive an effectively three-dimensional relativistic spin precession formalism. The formalism is applicable to any spacetime where an arbitrary timelike reference congruence of worldlines is specified. We employ what we call a stopped spin vector which ... More

Inertial forces and the foundations of optical geometryAug 19 2007Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. ... More

Gyroscope precession in special and general relativity from basic principlesAug 18 2007In special relativity a gyroscope that is suspended in a torque-free manner will precess as it is moved along a curved path relative to an inertial frame S. We explain this effect, which is known as Thomas precession, by considering a real grid that moves ... More

An intuitive approach to inertial forces and the centrifugal force paradox in general relativityAug 18 2007As the velocity of a rocket in a circular orbit near a black hole increases, the outwardly directed rocket thrust must increase to keep the rocket in its orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we show that it follows ... More

Pathological abelian groups: a friendly exampleApr 19 2019We show that the group of bounded sequences of elements of $\mathbb{Z}[\sqrt 2]$ is an example of an abelian group with several well known, and not so well known, pathological properties. It appears to be simpler than all previously known examples for ... More

Option pricing in the large risk aversion, small transaction cost limitFeb 17 2011May 27 2014We characterize the price of a European option on several assets for a very risk averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic analysis of parabolic ... More

A statistical inference course based on p-valuesJun 07 2016Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach to teaching ... More

Concerning the Szlenk indexJan 27 2015We discuss pruning and coloring lemmas on regular families. We discuss several applications of these lemmas to computing the Szlenk index of certain $w^*$ compact subsets of the dual of a separable Banach space. Applications include estimates of the Szlenk ... More

Pick interpolation in several variablesOct 03 2011Oct 05 2011We investigate the Pick problem for the polydisk and unit ball using dual algebra techniques. Some factorization results for Bergman spaces are used to describe a Pick theorem for any bounded region in $\mathbb{C}^d$.

Asymptotic results on Klazar set partition avoidanceAug 07 2016We establish asymptotic bounds for the number of partitions of $[n]$ avoiding a given partition in Klazar's sense, obtaining the correct answer to within an exponential for the block case. This technique also enables us to establish a general lower bound. ... More

The Decrits Consensus Algorithm: Decentralized Agreement without Proof of WorkNov 04 2014Decrits is a cryptocurrency in development that makes use of a novel consensus algorithm that does not require proof-of-work. This paper describes how the Decrits Consensus Algorithm (DCA) is as trustless as a proof-of-work algorithm while offering superior ... More

Combinatorial spin structures on triangulated manifoldsJun 20 2013Oct 11 2014This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty ... More

A trajectory map for the pressureless Euler equationsFeb 12 2019We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide. The equations ... More

Attractors of sequences of iterated function systemsNov 03 2016If $F$ and $G$ are iterated function systems, then any infinite word $W$ in the symbols $F$ and $G$ induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single $C^{1 + \alpha}$ iterated function ... More

Foundations of a pathwise volatility framework with explicit fast reversion limitsFeb 05 2019Our first main results are the existence and uniqueness of solutions to a `generalised CIR initial-value problem', which originates from the classical Cox-Ingersoll-Ross (CIR) stochastic differential equation after a time-change. These results hold on ... More

A new proposal for group field theory I: the 3d caseNov 14 2006In this series of papers, we propose a new rendition of 3d and 4d state sum models based upon the group field theory (GFT) approach to non-perturbative quantum gravity. We will see that the group field theories investigated in the literature to date are, ... More

Introductory Clifford AnalysisMar 26 2003This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links to harmonic ... More

New inequalities for subspace arrangementsMay 11 2009Oct 26 2009For each positive integer $n \geq 4$, we give an inequality satisfied by rank functions of arrangements of $n$ subspaces. When $n=4$ we recover Ingleton's inequality; for higher $n$ the inequalities are all new. These inequalities can be thought of as ... More

Little cubes and long knotsSep 26 2003Dec 18 2006This paper gives a partial description of the homotopy type of K, the space of long knots in 3-dimensional Euclidean space. The primary result is the construction of a homotopy equivalence between K and the free little 2-cubes object over the space of ... More

The weighted Fourier inequality, polarity, and reverse Hölder inequalityJul 23 2016Nov 17 2017We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to ... More

Möbius disjointness for homogeneous dynamicsJun 25 2015Oct 16 2016We prove Sarnak's M\"obius disjointness conjecture for all unipotent translations on homogeneous spaces of real connected Lie groups. Namely, we show that if $G$ is any such group, $\Gamma\subset G$ a lattice, and $u\in G$ an Ad-unipotent element, then ... More

Rank functions on rooted tree quiversJul 28 2008Mar 09 2009The free abelian group R(Q) on the set of indecomposable representations of a quiver Q, over a field K, has a ring structure where the multiplication is given by the tensor product. We show that if Q is a rooted tree (an oriented tree with a unique sink), ... More

Uniqueness of the measure of maximal entropy for the squarefree flowMay 13 2012Oct 07 2014The squarefree flow is a natural dynamical system whose topological and ergodic properties are closely linked to the behavior of squarefree numbers. We prove that the squarefree flow carries a unique measure of maximal entropy and express this measure ... More

On the optimal stacking of noisy observationsApr 14 2010Observations where additive noise is present can for many models be grouped into a compound observation matrix, adhering to the same type of model. There are many ways the observations can be stacked, for instance vertically, horizontally, or quadratically. ... More

Big Bang Nucleosynthesis and the Helium Isotope RatioOct 09 2015The conventional approach to search for departures from the standard model of physics during Big Bang Nucleosynthesis involves a careful, and subtle measurement of the mass fraction of baryons consisting of helium. Recent measurements of this quantity ... More

A Conversation with Nan LairdDec 11 2015Nan McKenzie Laird is the Harvey V. Fineberg Professor of Biostatistics at the Harvard T. H. Chan School of Public Health. She has made fundamental contributions to statistical methods for longitudinal data analysis, missing data and meta-analysis. In ... More

The weighted Fourier inequality, polarity, and reverse Hölder inequalityJul 23 2016Oct 05 2016We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to ... More

Dynamic Belief Fusion for Object DetectionFeb 26 2015Nov 12 2015A novel approach for the fusion of detection scores from disparate object detection methods is proposed. In order to effectively integrate the outputs of multiple detectors, the level of ambiguity in each individual detection score (called "uncertainty") ... More

Asymptotic results on Klazar set partition avoidanceAug 07 2016Mar 15 2018We establish asymptotic bounds for the number of partitions of $[n]$ avoiding a given partition in Klazar's sense, obtaining the correct answer to within an exponential for the block case. This technique also enables us to establish a general lower bound. ... More

Using the subspace theorem to bound unit distancesNov 21 2012Nov 29 2012We prove a special case of Erd\H{o}s' unit distance problem using a corollary of the subspace theorem bounding the number of solutions of linear equations from a multiplicative group. We restrict our attention to unit distances coming from a multiplicative ... More

A family of embedding spacesMay 02 2006Apr 02 2009Let Emb(S^j,S^n) denote the space of C^infty-smooth embeddings of the j-sphere in the n-sphere. This paper considers homotopy-theoretic properties of the family of spaces Emb(S^j,S^n) for n >= j > 0. There is a homotopy-equivalence of Emb(S^j,S^n) with ... More

The framed discs operad is cyclicJul 20 2006Mar 31 2007The operad of framed little discs is shown to be equivalent to a cyclic operad. This answers a conjecture of Salvatore in the affirmative, posed at the workshop `Knots and Operads in Roma,' at Universita di Roma ``La Sapienza'' in July of 2006.

A pointwise estimate for the Fourier transform and the number of maxima of a functionFeb 10 2009Nov 02 2009We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also ... More

Galois branched covers with fixed ramification locusOct 16 2013We examine conditions under which there exists a non-constant family of Galois branched covers of curves over an algebraically closed field $k$ of fixed degree and fixed ramification locus, under a notion of equivalence derived from considering linear ... More