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Piecewise linear approximation of smooth functions of two variablesMay 09 2013Jun 19 2013Given a piecewise linear (PL) function $p$ defined on an open subset of $\R^n$, one may construct by elementary means a unique polyhedron with multiplicities $\D(p)$ in the cotangent bundle $\R^n\times \R^{n*}$ representing the graph of the differential ... More

Constraints on dark energy dynamics and spatial curvature from Hubble parameter and baryon acoustic oscillation dataMay 16 2018Jun 24 2018We use all available baryon acoustic oscillation distance measurements and Hubble parameter data to constrain the cosmological constant $\Lambda$, dynamical dark energy, and spatial curvature in simple cosmological models. We find that the consensus spatially ... More

Baryon acoustic oscillation, Hubble parameter, and angular size measurement constraints on the Hubble constant, dark energy dynamics, and spatial curvatureFeb 08 2019Jul 19 2019In this paper we use all available baryon acoustic oscillation, Hubble parameter, and quasar angular size data to constrain six dark energy cosmological models, both spatially flat and non-flat. Depending on the model and data combination considered, ... More

Baa.pl: A tool to evaluate de novo genome assemblies with RNA transcriptsSep 09 2013Feb 07 2014Assessing the correctness of genome assemblies is an important step in any genome project. Several methods exist, but most are computationally intensive and, in some cases, inappropriate. Here I present baa.pl, a fast and easy-to-use program that uses ... More

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

Rotationally Aligned Hexagonal Boron Nitride on Sapphire by High-Temperature Molecular Beam EpitaxyJun 17 2019Hexagonal boron nitride (hBN) has been grown on sapphire substrates by ultra-high temperature molecular beam epitaxy (MBE). A wide range of substrate temperatures and boron fluxes have been explored, revealing that high crystalline quality hBN layers ... More

The Atmosphere and Interior Structure of HAT-P-13b from Spitzer Secondary EclipsesJan 03 2017We present {\em Spitzer} secondary-eclipse observations of the hot Jupiter HAT-P-13 b in the 3.6 {\micron} and 4.5 {\micron} bands. HAT-P-13 b inhabits a two-planet system with a configuration that enables constraints on the planet's second Love number, ... More

Symmetrised Characterisation of Noisy Quantum ProcessesJul 04 2007A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme fragility of quantum ... More

Scaling simulation-to-real transfer by learning composable robot skillsSep 26 2018Nov 13 2018We present a novel solution to the problem of simulation-to-real transfer, which builds on recent advances in robot skill decomposition. Rather than focusing on minimizing the simulation-reality gap, we learn a set of diverse policies that are parameterized ... More

Zero-Shot Skill Composition and Simulation-to-Real Transfer by Learning Task RepresentationsOct 04 2018Nov 13 2018Simulation-to-real transfer is an important strategy for making reinforcement learning practical with real robots. Successful sim-to-real transfer systems have difficulty producing policies which generalize across tasks, despite training for thousands ... More

Necessity of negativity in quantum theoryOct 16 2009Oct 15 2010A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require negative probability ... More

The New Nitrides: Layered, Ferroelectric, Magnetic, Metallic and Superconducting Nitrides to Boost the GaN Photonics and Electronics Eco-SystemMay 18 2019The nitride semiconductor materials GaN, AlN, and InN, and their alloys and heterostructures have been investigated extensively in the last 3 decades, leading to several technologically successful photonic and electronic devices. Just over the past few ... More

Electronic and Rovibrational Quantum Chemical Analysis of C$_3$P$^-$: The Next Interstellar Anion?Aug 10 2015C$_3$P$^-$ is analogous to the known interstellar anion C$_3$N$^-$ with phosphorus replacing the nitrogen in a simple step down the periodic table. In this work, it is shown that C$_3$P$^-$ is likely to possess a dipole-bound excited state. It has been ... More

Baryon acoustic oscillation, Hubble parameter, and angular size measurement constraints on the Hubble constant, dark energy dynamics, and spatial curvatureFeb 08 2019In this paper we use all available baryon acoustic oscillation and Hubble parameter data to constrain six dark energy cosmological models, both spatially flat and non-flat. These data mildly favor (at 1.3-1.4$\sigma$) closed spatial hypersurfaces in the ... More

On the Progenitor and Supernova of the SN 2002cx-like Supernova 2008geAug 03 2010Sep 05 2010We present observations of supernova (SN) 2008ge, which is spectroscopically similar to the peculiar SN 2002cx, and its pre-explosion site that indicate that its progenitor was probably a white dwarf. NGC 1527, the host galaxy of SN 2008ge, is an S0 galaxy ... More

Infrared Observations of the Quintuplet Proper Members using SOFIA/FORCAST and Gemini/TReCSJul 10 2016Since their discovery, the Quintuplet proper members (QPMs) have been somewhat mysterious in nature. Originally dubbed the "cocoon stars" due to their cool featureless spectra, high-resolution near-infrared imaging observations have shown that at least ... More

Probing hyperbolic polaritons using infrared attenuated total reflectance micro-spectroscopyOct 01 2018Hyperbolic polariton modes are highly appealing for a broad range of applications in nanophotonics, including surfaced enhanced sensing, sub-diffractional imaging and reconfigurable metasurfaces. Here we show that attenuated total reflectance micro-spectroscopy ... More

Updated Core Libraries of the ALPS ProjectNov 19 2018The open source ALPS (Algorithms and Libraries for Physics Simulations) project provides a collection of physics libraries and applications, with a focus on simulations of lattice models and strongly correlated electron systems. The libraries provide ... 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

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

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.

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

Extremal Behavior in Exponential Random GraphsJun 03 2019Yin, Rinaldo, and Fadnavis classified the extremal behavior of the edge-triangle exponential random graph model by first taking the network size to infinity, then the parameters diverging to infinity along straight lines. Lubetzky and Zhao proposed an ... 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

Offensive Language Analysis using Deep Learning ArchitectureMar 12 2019Mar 19 2019SemEval-2019 Task 6 (Zampieri et al., 2019b) requires us to identify and categorise offensive language in social media. In this paper we will describe the process we took to tackle this challenge. Our process is heavily inspired by Sosa (2017) where he ... More

Combinatorial spin structures on triangulated manifoldsJun 20 2013Nov 08 2017This 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

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

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

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

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

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

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

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

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

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

Tree modules and counting polynomialsDec 20 2011Aug 25 2012We give a formula for counting tree modules for the quiver S_g with g loops and one vertex in terms of tree modules on its universal cover. This formula, along with work of Helleloid and Rodriguez-Villegas, is used to show that the number of d-dimensional ... More

Noisy Corruption DetectionAug 20 2019We answer a question of Alon, Mossel, and Pemantle about the corruption detection model on graphs in the noisy setting.

Analogs of the Shapiro Shapiro Conjecture in Positive CharacteristicMay 19 2016Motivated by the Shapiro Shapiro conjecture, we consider the following: given a field $k$, under what conditions must a rational function with only $k$-rational ramification points be equivalent (after post-composition with a fractional linear transformation) ... 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

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

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

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

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

On the image of the Lawrence-Krammer representationFeb 23 2002Nov 14 2005A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant ... 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

Benford's Law and Continuous Dependent Random VariablesSep 22 2013Mar 09 2018Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known as Benford's ... More

Uncovering the Origin of Divergence in the CsM(CrO$_4$)$_2$ (M = La, Pr, Nd, Sm, Eu; Am) Family through Examination of the Chemical Bonding in a Molecular Cluster and by Band Structure AnalysisMar 20 2018A series of f-block chromates, CsM(CrO$_4$)$_2$ (M = La, Pr, Nd, Sm, Eu; Am), were prepared revealing notable differences between the AmIII derivatives and their lanthanide analogs. While all compounds form similar layered structures, the americium compound ... More

Ground-state properties of artificial bosonic atoms, Bose interaction blockade and the single-atom pipetteJul 31 2003Aug 05 2003We analyze the ground-state properties of an artificial atom made out of repulsive bosons attracted to a center for the case that all the interactions are short-ranged. Such bosonic atoms could be created by optically trapping ultracold particles of alkali ... More

Variability Properties of 4 Million Sources in the $TESS$ Input Catalog Observed with the Kilodegree Extremely Little Telescope SurveyNov 09 2017The Kilodegree Extremely Little Telescope (KELT) has been surveying more than $70\%$ of the celestial sphere for nearly a decade. While the primary science goal of the survey is the discovery of transiting, large-radii planets around bright host stars, ... More

A multi-wavelength study of nearby millisecond pulsar PSR J1400$-$1431: improved astrometry & an optical detection of its cool white dwarf companionAug 30 2017In 2012, five high school students involved in the Pulsar Search Collaboratory discovered the millisecond pulsar PSR J1400$-$1431 and initial timing parameters were published in Rosen et al. (2013) a year later. Since then, we have obtained a phase-connected ... More

Feedback and the Initial Mass functionOct 04 2004I describe a turbulence-inspired model for the stellar initial mass function which includes feedback and self-regulation via protostellar outflows. A new aspect of the model provides predictions of the star formation rate in molecular clouds and gas complexes. ... More

Supermassive Black Holes and Galaxy FormationSep 19 2001The formation of supermassive black holes (SMBH) is intimately related to galaxy formation, although precisely how remains a mystery. I speculate that formation of, and feedback from, SMBH may alleviate problems that have arisen in our understanding of ... More

String theory to the rescueDec 08 2015Dec 16 2015The search for a theory of quantum gravity faces two great challenges: the incredibly small scales of the Planck length and time, and the possibility that the observed constants of nature are in part the result of random processes. A priori, one might ... More

Cosmic Superstrings RevisitedOct 08 2004Dec 21 2004It is possible that superstrings, as well as other one-dimensional branes, could have been produced in the early universe and then expanded to cosmic size today. I discuss the conditions under which this will occur, and the signatures of these strings. ... More

Brane/antibrane dynamics and KKLT stabilitySep 18 2015Sep 25 2015String theory has few or no stable nonsupersymmetric or de Sitter vacua, only metastable ones. Antibranes are a simple source of supersymmetry breaking, as in the KKLT model, but various arguments have been given that these fail to produce the desired ... More

What is String Theory?Nov 04 1994The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: 1. Conformal Field Theory 2. String Theory 3. Vacua and ... More

The Specification of SugarscapeMay 22 2015Nov 07 2016Sugarscape is a well known and influential Agent Based Social Simulation (ABSS). Various parts of Sugarscape are supplied as examples in almost all Agent Based Model (ABM) toolkits. It has been used for demonstrating the applicability of different approaches ... More

Moduli spaces of semitoric systemsFeb 25 2015Recently Pelayo-V\~{u} Ngoc classified semitoric integrable systems in terms of five symplectic invariants. Using this classification we define a family of metrics on the space of semitoric integrable systems. The family is parameterized by two choices. ... More

Is the aether entrained by the motion of celestial bodies? What do the experiments tell us?Mar 20 2012Dec 17 2013Even though the concept has evolved and if the designation as aether is improperly regarded as outdated, nobody today considers that the vacuum is empty. However, the nature and the properties of the substratum, which permeates the entire universe, remain ... More

New normality constructions for continued fraction expansionsJul 01 2015Adler, Keane, and Smorodinsky showed that if one concatenates the finite continued fraction expansions of the sequence of rationals \[ \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{1}{5}, \cdots \] into an infinite ... More

A BQP-complete problem related to the Ising model partition function via a new connection between quantum circuits and graphsJan 31 2008Apr 02 2008We present a simple construction that maps quantum circuits to graphs and vice-versa. Inspired by the results of D.A. Lidar linking the Ising partition function with quadratically signed weight enumerators (QWGTs), we also present a BQP-complete problem ... More

Tropical analytic geometry, Newton polygons, and tropical intersectionsJul 15 2010In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: ... More

The length classification of threefold flops via noncommutative algebrasSep 08 2017Smooth threefold flops with irreducible centres are classified by the length invariant, which takes values 1, 2, 3, 4, 5 or 6. This classification by Katz and Morrison identifies 6 possible partial resolutions of Kleinian singularities that can occur ... More

Maps with symplectic graphsJul 13 2004Oct 22 2004We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use this to show that ... More

Higher-level canonical subgroups for p-divisible groupsOct 17 2009Mar 16 2011Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is said to have a level-n canonical subgroup if there is a K-subgroup of G\tensor_R ... More

An Ansatz for Hyperkähler $8$-Manifolds with two Commuting Rotating Killing FieldsSep 27 2014We consider a hyperk\"{a}hler $8$-manifold admitting either a $U(1) \times \mathbb{R}$, or a $U(1) \times U(1)$ action, where the first factor preserves $g$ and $I$, and acts on $\omega_2+i\omega_3$ by multiplying it by itself, while the second factor ... More

Trans-Gaussian Kriging in a Bayesian framework : a case studyMay 23 2018In the context of Gaussian Process Regression or Kriging, we propose a full-Bayesian solution to deal with hyperparameters of the covariance function. This solution can be extended to the Trans-Gaussian Kriging framework, which makes it possible to deal ... More

Indicators of Bismash Products from Exact Symmetric Group FactorizationsDec 15 2014Jul 22 2015We prove that all irreducible representations of the bismash product $H = \mathbb{k} ^G \# \mathbb{k} S_{n-k}$ have Frobenius-Schur indicators +1 or 0 where $\mathbb{k}$ is an algebraically closed field and $S_n = S_{n-k}\cdot G$ is an exact factorization. ... More

Algebra properties for Besov spaces on unimodular Lie groupsMay 26 2015We consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an algebra property ... More

An indefinite system of equations governing the fractional quantum Hall effectOct 17 2018In this paper, we establish existence of solutions to an indefinite coupled non-linear system. We use partial coercivity to establish existence of a critical point to an indefinite functional and thus the existence of solutions on both bounded domains ... More

On the Atiyah problem on hyperbolic configurations of four pointsFeb 04 2015Aug 06 2015Given a configuration $\mathbf{x}$ of $n$ distinct points in hyperbolic $3$-space $H^3$, Michael Atiyah associated $n$ polynomials $p_1,\ldots,p_n$ of a variable $t \in \mathbb{C}P^1$, of degree $n-1$, and conjectured that they are linearly independent ... More

Category of fuzzy hyper BCK-algebrasJan 13 2011In this paper we first define the category of fuzzy hyper BCK- algebras. After that we show that the category of hyper BCK-algebras has equalizers, coequalizers, products. It is a consequence that this category is complete and hence has pullbacks.

Angle Bisectors of a Triangle in Lorentzian PlaneApr 24 2014In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates ... More

Statistical Mechanics of Amplifying ApparatusFeb 08 2005We implement Feynman's suggestion that the only missing notion needed for the puzzle of Quantum Measurement is the statistical mechanics of amplifying apparatus. We define a thermodynamic limit of quantum amplifiers which is a classically describable ... More

Hardy and BMO spaces on graphs, application to Riesz transformOct 24 2014Let $\Gamma$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $\Gamma$. We introduce $H^1$ Hardy spaces of functions and $1$-forms adapted to $P$ and prove various characterizations of these spaces. We ... More

Closed-Loop Control of a Delta-Wing Unmanned Aerial-Aquatic VehicleJun 04 2019We present a closed-loop control strategy for a delta-wing unmanned aerial aquatic-vehicle (UAAV) that enables autonomous swim, fly, and water-to-air transition. Our control system consists of a hybrid state estimator and a closed-loop feedback policy ... More

Infinite energy solutions to vortex equations governing the fractional quantum Hall effectOct 30 2018In this paper, we utilize weighted Sobolev spaces to establish an existence theory for infinite energy solutions to a coupled non-linear elliptic system. This system describes the fractional quantum Hall effect in two-dimensional double-layered systems. ... More

An invariance principle for the stochastic heat equationJun 17 2017We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d. mean zero random ... More

Logarithmic Poisson cohomology: example of calculation and application to prequantizationDec 21 2010Jan 19 2011In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, ... More

Introduction to effective Lagrangians for QCDDec 14 2001A brief introduction to the effective Lagrangian treatment of QCD (in the sense of using fields representing physical particles rather than quarks and gluons) will be given. The historical evolution of the subject will be discussed. Some background material ... More

Variant vector-tensor multiplets in supergravity: Classification and component reductionOct 31 2012Mar 11 2013The recent paper arXiv:1205.6881 has developed superform formulations for two versions of the vector-tensor multiplet and their Chern-Simons couplings in four-dimensional N = 2 conformal supergravity. One of them is the standard vector-tensor multiplet ... More

Homotopies in Grothendieck fibrationsMay 25 2019We define a natural 2-categorical structure on the base category of a large class of Grothendieck fibrations. Given any model category $\mathbf{C}$, we construct a fibration whose fibers are the homotopy categories of the slice categories $\mathbf{C}/A$, ... More

Moments of the Gaussian ChaosNov 09 2010This paper deals with Lata{\l}a's estimation of the moments of Gaussian chaoses. It is shown that his argument can be simplified significantly using Talagrand's generic chaining.

Deformations of algebras defined by tilting bundlesMay 15 2015In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformations ... More

A Center-Median Filtering Method for Detection of Temporal Variation in Coronal ImagesNov 13 2015Jan 29 2016Events in the solar corona are often widely separated in their timescales, which can allow them to be identified when they would otherwise be confused with emission from other sources in the corona. Methods for cleanly separating such events based on ... More

Sacler lecturesJan 31 1995The series of three lectures given at Tel-Aviv University in 1992: 1. Tensor categories. 2. Quantum groups. 3. Topological (quantum) field theories. Published as the preprint IAS 897-92 of Tel-Aviv University and The Mortimer and Raymond Sacler Institute ... More