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Amenability and Ramsey TheoryJun 16 2011Oct 20 2011The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey theoretic reformulation of amenability constitutes a considerable weakening of the Folner criterion. As ... More

Set mapping reflectionJan 28 2005In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that L(P(omega_1)) satisfies ... More

Hindman's Theorem, Ellis's Lemma, and Thompson's group $F$Jun 23 2011Jul 16 2018The purpose of this article is to formulate conjectural generalizations of Hindman's Theorem and Ellis's Lemma for nonassociative binary systems and relate them to the amenability problem for Thompson's group $F$. Partial results are obtained for both ... More

Nonassociative Ramsey Theory and the amenability of Thompson's groupSep 10 2012Oct 01 2012The purpose of this article is prove that Thompson's group F is amenable. The methods developed will then be used to prove a generalization of Hindman's theorem for the free nonassociative binary system on one generator.

The method of forcingFeb 08 2019The purpose of this article is to give a presentation of the method of forcing aimed at someone with a minimal knowledge of set theory and logic. The emphasis will be on how the method can be used to prove theorems in ZFC.

There may be no minimal non $σ$-scattered linear ordersJul 18 2017In this paper we demonstrate that it is consistent, relative to the existence of a supercompact cardinal, that there is no linear order which is minimal with respect to being non $\sigma$-scattered. This shows that a theorem of Laver, which asserts that ... More

A brief introduction to amenable equivalence relationsSep 03 2018This is a short survey of amenable equivalence relations.

Hindman's Theorem, Ellis's Lemma, and Thompson's group FJun 23 2011Sep 11 2012The purpose of this article is to formulate generalizations of Hindman's Theorem and Ellis's Lemma for non associative groupoids. A relation between these conjectures is proved and it is shown that they imply the amenability of Thompson's group F. In ... More

A note on Shavgulidze's papers concerning the amenability problem for Thompson's group $F$Feb 03 2011Feb 09 2011This paper examines Shavgulidze's postings to the ArXiv and publications which concern his argument that Thompson's group F is amenable. In particular I list specific places where there are errors in each of the postings and publications and give a public ... More

Idempotent means on free binary systems do not existJul 15 2018Free binary systems are shown to not admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman's theorem to nonassociative binary systems formulated and conjectured by the author is false.

Forcing Axioms and the Continuum Hypothesis, part II: Transcending ω_1-sequences of real numbersOct 23 2011Aug 03 2012The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah. The corresponding completely proper forcing which can be constructed ... More

Fast growth in Folner sets for Thompson's group FMay 08 2009Aug 08 2012The purpose of this note is to prove a lower bound on the Folner function for Thompson's groups F.

The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals HypothesisJan 28 2005The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, ... More

A five element basis for the uncountable linear ordersJan 28 2005In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five ... More

A solution to the L space problem and related ZFC constructionsJan 28 2005In this paper I will construct a non-separable hereditarily Lindelof space (L space) without any additional axiomatic assumptions. I will also show that there is a function f from [omega_1]^2 to omega_1 such that if A,B, subsets of omega_1, are uncountable ... More

A Boolean action of C(M,U(1)) without a spatial model and a re-examination of the Cameron-Martin theoremJan 18 2012Aug 08 2012We will demonstrate that if M is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which preserves the measure and yet does not admit a point ... More

A finitely presented group of piecewise projective homeomorphismsAug 20 2013Aug 01 2014In this article we will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of R. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian ... More

Maximal unbalanced familiesSep 11 2012A family of subsets of the set {1,2,...,n} is said to be unbalanced if the convex hull of its characteristic vectors misses the diagonal in the n-cube.The purpose of this article is to develop the combinatorics of maximal unbalanced families. Specifically, ... More

Parametrized $\diamondsuit$ principlesAug 25 2006We will present a collection of guessing principles which have a similar relationship to $\diamond$ as cardinal invariants of the continuum have to $\CH$. The purpose is to provide a means for systematically analyzing $\diamond$ and its consequences. ... More

Complexity among the finitely generated subgroups of Thompson's groupNov 29 2017We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson's group $F$ which is strictly well-ordered by the embeddability relation in type $\epsilon_0 +1$. All except the maximum element of this family (which is $F$ ... More

An Attempt towards Interpretable Audio-Visual Video CaptioningDec 07 2018Automatically generating a natural language sentence to describe the content of an input video is a very challenging problem. It is an essential multimodal task in which auditory and visual contents are equally important. Although audio information has ... More

Groups of fast homeomorphisms of the interval and the ping-pong argumentJan 28 2017We adapt the Ping-Pong Lemma, which historically was used to study free products of groups, to the setting of the homeomorphism group of the unit interval. As a consequence, we isolate a large class of generating sets for subgroups of $\mathrm{Homeo}_+(I)$ ... More

Countable Toronto spacesFeb 11 1999A space X is called an alpha-Toronto space if X is scattered of Cantor-Bendixson rank alpha and is homeomorphic to each of its subspaces of same rank. We answer a question of Steprans by constructing a countable alpha-Toronto space for each alpha<=omega. ... More

New Pulse Timing Measurements of the sdBV Star CS 1246Dec 06 2017CS 1246 is a hot subdwarf B star discovered in 2009 to exhibit a single, large-amplitude radial pulsation. An O-C diagram constructed from this mode revealed reflex motion due to the presence of a low-mass M dwarf, as well as a long-term trend consistent ... More

A search for rapidly pulsating hot subdwarf stars in the GALEX surveyAug 02 2017NASA's Galaxy Evolution Explorer (GALEX) provided near- and far-UV observations for approximately 77 percent of the sky over a ten-year period; however, the data reduction pipeline initially only released single NUV and FUV images to the community. The ... More

Blazars in Context in the Fermi EraMar 20 2013Blazars are the most plentiful gamma-ray source at GeV energies, and despite detailed study, there is much that is not known about these sources. In this review I explore some recent results on blazars, including the controversy of the "blazar sequence", ... More

Sheaves, Cosheaves and ApplicationsMar 13 2013Dec 17 2014This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science and engineering. To provide a theory that is computable, we focus on a combinatorial version of sheaves and cosheaves called cellular sheaves and cosheaves, ... More

Norm inequalities in generalized Morrey spacesMay 29 2012May 14 2014We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey ... More

Topological Data Analysis and CosheavesNov 03 2014Mar 04 2015This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.

The Mezard-Parisi equation for matchings in pseudo-dimension d>1Sep 09 2014We establish existence and uniqueness of the solution to the cavity equation for the random assignment problem in pseudo-dimension $d>1$, as conjectured by Aldous and Bandyopadhyay (Annals of Applied Probability, 2005) and W\"astlund (Annals of Mathematics, ... More

The interpolation method for random graphs with prescribed degreesApr 26 2014We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic convergence of a ... More

Matroids: A Macaulay2 packageNov 14 2015We give an overview of the Macaulay2 package Matroids, which contains functionality to create and compute with matroids. Examples highlighting the use of all major functions in the package are provided, along with explanations of some of the algorithms. ... More

Closed points on schemesAug 22 2017This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.

Topology of eigenspace posets for unitary reflection groupsAug 09 2012Apr 02 2013The eigenspace theory of unitary reflection groups, initiated by Springer and Lehrer, suggests that the following object is worthy of study: the poset of eigenspaces of elements of a unitary reflection group, for a fixed eigenvalue, ordered by the reverse ... More

Generating mapping class groups with elements of fixed finite orderOct 12 2017We show that for any $k$ at least $6$ and $g$ sufficiently large, the mapping class group of a surface of genus $g$ can be generated by three elements of order $k$. We also show that this can be done with four elements of order $5$. We additionally prove ... More

Invertible sums of matricesMar 22 2016Apr 19 2016We give an elementary proof of a Caratheodory-type result on the invertibility of a sum of matrices, due first to Facchini and Barioli. The proof yields a polynomial identity, expressing the determinant of a large sum of matrices in terms of determinants ... More

Mono: an algebraic study of torus closuresOct 12 2017Given an ideal I in a polynomial ring, we consider the largest monomial subideal contained in I, denoted mono(I). We study mono as an interesting operation in its own right, guided by questions that arise from comparing the Betti tables of I and mono(I). ... More

Brace Bar-Cobar DualitySep 11 2013Sep 12 2013Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) \Omega ... More

Satellite-Mounted Light Sources as Photometric Calibration Standards for Ground-Based TelescopesJan 27 2011A significant and growing portion of systematic error on a number of fundamental parameters in astrophysics and cosmology is due to uncertainties from absolute photometric and flux standards. A path toward achieving major reduction in such uncertainties ... More

Semi-Streaming Algorithms for Annotated Graph StreamsJul 13 2014Aug 10 2015Considerable effort has been devoted to the development of streaming algorithms for analyzing massive graphs. Unfortunately, many results have been negative, establishing that a wide variety of problems require $\Omega(n^2)$ space to solve. One of the ... More

On the Negative $K$-theory of Singular VarietiesJun 16 2013Let $X$ be an $n$-dimensional variety over a field $k$ of characteristic zero, regular in codimension 1 with singular locus $Z$. In this paper we study the negative $K$-theory of $X$, showing that when $Z$ is sufficiently nice, $K_{1-n}(X)$ is an extension ... More

Up-down asymmetric tokamaksNov 21 2016Bulk toroidal rotation has proven capable of stabilising both dangerous MHD modes and turbulence. In this thesis, we explore a method to drive rotation in large tokamaks: up-down asymmetry in the magnetic equilibrium. We seek to maximise this rotation ... More

An Alternative to Particle Dark MatterAug 29 2014Dec 11 2014We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state ... More

Dark Matter SuperfluidityMay 26 2016In this talk I summarize a novel framework that unifies the stunning success of MOND on galactic scales with the triumph of the $\Lambda$CDM model on cosmological scales. This is achieved through the rich and well-studied physics of superfluidity. The ... More

Geodesic deviation at higher orders via covariant bitensorsJul 25 2014We review a simple but instructive application of the formalism of covariant bitensors, to use a deviation vector field along a fiducial geodesic to describe a neighboring worldline, in an exact and manifestly covariant manner, via the exponential map. ... More

Modeling Fermi Large Area Telescope and Multiwavelength Data from BlazarsFeb 18 2016Blazars are active galactic nuclei with relativistic jets pointed at the Earth, making them extremely bright at essentially all wavelengths, from radio to gamma rays. I review the modeling of this broadband spectral energy distributions of these objects, ... More

The cavity method for counting spanning subgraphs subject to local constraintsMar 16 2011Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree-like graphs. ... More

The Two Dimensional Kondo Model with Rashba Spin-Orbit CouplingAug 17 2007Sep 11 2007We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T < T_K, is robust against ... More

Almost sure global well posedness for the BBM equation with infinite $L^{2}$ initial dataJan 12 2019We consider the probabilistic Cauchy problem for the Benjamin-Bona-Mahony equation (BBM) on the one-dimensional torus $\mathbb{T}$ with initial data below $L^{2}(\mathbb{T})$. With respect to random initial data of strictly negative Sobolev regularity, ... More

The initial-boundary value problem for the Korteweg-de Vries equationJul 08 2005Feb 23 2006We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on the right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary ... More

Moduli spaces of sheaves on K3 surfacesMar 02 2016In this survey article we describe moduli spaces of simple, stable, and semistable sheaves on K3 surfaces, following the work of Mukai, O'Grady, Huybrechts, Yoshioka, and others. We also describe some recent developments, including applications to the ... More

Intrinsic square functions on functions spaces including weighted Morrey spacesMay 01 2012Apr 16 2013We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators ... More

Product of functions in $\BMO$ and $\H^{1}$ in non-homogeneous spacesJun 27 2009Aug 11 2010Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular $BMO$ and the atomic block $\H^{1}$ in the sense of ... More

Unusual formulae for the Euler characteristicJan 18 2002Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial invariants, ... More

Interpolating factorizations for acyclic Donaldson--Thomas invariantsJul 05 2018Mar 04 2019We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rimanyi by counting codimensions of quiver loci, gives two extremal ... More

Rationality of motivic zeta-functions for curves with finite abelian group actionsMar 10 2011Let $\mathfrak{Var}_k^G$ denote the category of pairs $(X,\sigma)$, where $X$ is a variety over $k$ and $\sigma$ is a group action on $X$. We define the Grothendieck ring for varieties with group actions as the free abelian group of isomorphism classes ... More

Learning Convex Inference of MarginalsJun 13 2012Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference ... More

Les Houches Lectures on Physics Beyond the Standard Model of CosmologyDec 06 2013In these Lectures, I review various extensions of the Lambda-Cold Dark Matter model, characterized by additional light degrees of freedom in the dark sector. In order to reproduce the successful phenomenology of GR in the solar system, these fields must ... More

Maximum Likelihood Learning With Arbitrary Treewidth via Fast-Mixing Parameter SetsSep 30 2015Oct 30 2015Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. ... More

Unbounded and dominating reals in Hechler extensionsJan 13 2012We give results exploring the relationship between dominating and unbounded reals in Hechler extensions, as well as the relationships among the extensions themselves. We show that in the standard Hechler extension there is an unbounded real which is dominated ... More

Up-down asymmetric tokamaksNov 21 2016Nov 22 2016Bulk toroidal rotation has proven capable of stabilising both dangerous MHD modes and turbulence. In this thesis, we explore a method to drive rotation in large tokamaks: up-down asymmetry in the magnetic equilibrium. We seek to maximise this rotation ... More

Probabilistic Couplings for Probabilistic ReasoningOct 27 2017Nov 01 2017This thesis explores proofs by coupling from the perspective of formal verification. Long employed in probability theory and theoretical computer science, these proofs construct couplings between the output distributions of two probabilistic processes. ... More

A characterization of the 2-fusion system of L_4(q)Mar 24 2013Oct 25 2014We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F is 2-perfect with no nontrivial normal 2-subgroups, and the centralizer of the component is a cyclic 2-group, it is shown that ... More

Constraints on the Global Mass-to-Light Ratios and Extent of Dark Matter Halos in Globular Clusters and Dwarf SpheroidalsNov 29 1995The detection of stars in the process of being tidally removed from globular clusters and dwarf spheroidals in the Galaxy's halo provides a strong constraint on their mass to light ratios and on the extent of their possible dark matter halos. If a significant ... More

Some Comments on Branes, G-flux, and K-theoryDec 01 2000This is a summary of a talk at Strings2000 explaining three ways in which string theory and M-theory are related to the mathematics of K-theory.

Finite in All DirectionsMay 25 1993We study toroidal compactifications of string theories which include compactification of a timelike coordinate. Some new features in the theory of toroidal compactifications arise. Most notably, Narain moduli space does not exist as a manifold since the ... More

K-Theory from a physical perspectiveApr 02 2003This is an expository paper which aims at explaining a physical point of view on the K-theoretic classification of D-branes. We combine ideas of renormalization group flows between boundary conformal field theories, together with spacetime notions such ... More

Learning Graphical Model Parameters with Approximate Marginal InferenceJan 15 2013Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted marginals, ... More

A Dark Matter SuperfluidJul 10 2015In this talk we present a novel framework that unifies the stunning success of MOND on galactic scales with the triumph of the LambdaCDM model on cosmological scales. This is achieved through the rich and well-studied physics of superfluidity. The dark ... More

Acoustic detection of astrophysical neutrinos in South Pole iceDec 30 2011When high-energy particles interact in dense media to produce a particle shower, most of the shower energy is deposited in the medium as heat. This causes the medium to expand locally and emit a shock wave with a medium-dependent peak frequency on the ... More

Dualities between Cellular Sheaves and CosheavesJul 23 2016This paper affirms a conjecture of MacPherson: that the derived category of cellular sheaves is equivalent to the derived category of cellular cosheaves. We give a self-contained treatment of cellular sheaves and cosheaves and note that certain classical ... More

Another Path for the Emergence of Modified Galactic Dynamics from Dark Matter SuperfluidityFeb 18 2016Apr 20 2016In recent work we proposed a novel theory of dark matter (DM) superfluidity that matches the successes of the LambdaCDM model on cosmological scales while simultaneously reproducing MOdified Newtonian Dynamics (MOND) phenomenology on galactic scales. ... More

Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfacesSep 14 2012We study generalized complex structures on K3 surfaces, in the sense of Hitchin. For each real parameter t between one and infinity we exhibit two families of generalized K3 surfaces, (M,cal{I}_{zeta}) and (M,cal{J}_{zeta}), parametrized by zeta in CP^1, ... More

On Lagrangian fibrations by Jacobians IMar 07 2008Sep 16 2011Let Y->P^n be a flat family of integral Gorenstein curves, such that the compactified relative Jacobian X=\bar{J}^d(Y/P^n) is a Lagrangian fibration. We prove that the degree of the discriminant locus Delta in P^n is at least 4n+2, and we prove that X ... More

Rozansky-Witten invariants of hyperkähler manifoldsApr 20 2004We investigate invariants of compact hyperk{\"a}hler manifolds introduced by Rozansky and Witten: they associate an invariant to each graph homology class. It is obtained by using the graph to perform contractions on a power of the curvature tensor and ... More

A bound on the second Betti number of hyperkähler manifolds of complex dimension sixNov 29 2015Let M be an irreducible compact hyperk\"ahler manifold of complex dimension six. We prove that the second Betti number of M is at most 23.

Pseudo-Anosov homeomorphisms and the lower central series of a surface groupFeb 21 2007Let Gamma_k be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on ... More

Flat maps to and from Noetherian ringsNov 14 2017We investigate flat maps where the source or target is a Noetherian ring, giving necessary and/or sufficient conditions on a ring for such maps to exist. Along the way, we develop some general facts about flat ring maps, and exhibit many examples, including ... More

A resolution of singularities for Drinfeld's compactification by stable mapsJun 05 2016Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting ... More

Derived equivalence of holomorphic symplectic manifoldsApr 20 2004We use twisted Fourier-Mukai transforms to study the relation between an abelian fibration on a holomorphic symplectic manifold and its dual fibration. Our reasoning leads to an equivalence between the derived category of coherent sheaves on one space ... More

Vahlen groups defined over commutative ringsJun 18 2015Jun 25 2015Elements of a Vahlen group are $2 \times 2$ matrices with entries in a Clifford algebra satisfying some conditions. Traditionally they have come in both ordinary and paravector type and have been defined (over Clifford algebras) over the real or complex ... More

Efficient estimation of the error distribution function in heteroskedastic nonparametric regression with missing dataOct 27 2016A residual-based empirical distribution function is proposed to estimate the distribution function of the errors of a heteroskedastic nonparametric regression with responses missing at random based on completely observed data, and this estimator is shown ... More

Steenrod coalgebrasJan 15 2014Mar 06 2015This paper shows that a functorial version of the "higher diagonal" of a space used to compute Steenrod squares actually contains far more topological information --- including (in some cases) the space's integral homotopy type.

Free Energy of Multiple Systems of Spherical Spin Glasses with Constrained OverlapsJun 26 2018The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper, we prove this ... More

Classical 6j-symbols and the tetrahedronDec 15 1998Mar 22 1999A classical 6j-symbol is a real number which can be associated to a labelling of the six edges of a tetrahedron by irreducible representations of SU(2). This abstract association is traditionally used simply to express the symmetry of the 6j-symbol, which ... More

Caustic Rings and Cold Dark MatterMar 06 2001The hierarchical cold dark matter (CDM) model for structure formation is a well defined and testable model. Direct detection is the best technique for confirming the model yet predictions for the energy and density distribution of particles on earth remain ... More

The Nature Of Dark MatterFeb 03 1994Collisionless particles, such as cold dark matter, interact only by gravity and do not have any associated length scale, therefore the dark halos of galaxies should have negligible core radii. This expectation has been supported by numerical experiments ... More

Evolutionary processes in clustersJun 27 2003Are the morphologies of galaxies imprinted during an early and rapid formation epoch or are they due to environmental processes that subsequently transform galaxies between morphological classes? Recent numerical simulations demonstrate that the cluster ... More

Beal's Conjecture vs. "Positive Zero", FightJan 07 2015This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most fundamental rules ... More

Source-LDA: Enhancing probabilistic topic models using prior knowledge sourcesJun 02 2016A popular approach to topic modeling involves extracting co-occurring n-grams of a corpus into semantic themes. The set of n-grams in a theme represents an underlying topic, but most topic modeling approaches are not able to label these sets of words ... More

Summary: Acoustic Detection of EHE NeutrinosNov 15 2006Neutrino astronomy was initiated primarily to search for TeV to PeV neutrinos from Active Galactic Nuclei, and the optical Cherenkov technique is well suited for this energy range. Interest has grown recently in detecting EeV neutrinos, particularly the ... More

Products of functions in $\BMO$ and $\H^{1}$ spaces on spaces of homogeneous typeFeb 18 2009We give an extension to certain \textit{RD-space} $\X$, i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in $\BMO(\X)$ and $\H^{1}(\X)$, ... More

On the Density of Happy NumbersOct 17 2011Mar 01 2015The happy function $H: \mathbb{N} \rightarrow \mathbb{N}$ sends a positive integer to the sum of the squares of its digits. A number $x$ is said to be happy if the sequence $\{H^n(x)\}^\infty_{n=1}$ eventually reaches one. A basic open question regarding ... More

Thermoacoustic Tomography in Elastic MediaMay 04 2011Oct 11 2011We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0,T] x \partial \Omega, where \Omega\subset\R^3 is some bounded domain containing ... More

Chameleon Field TheoriesJun 18 2013Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated ... More

Comparisons of polychromatic and monochromatic Ramsey theoryMar 06 2012May 17 2012We compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does the rainbow Ramsey theorem imply Ramsey's theorem over ZF. Extending the ... More

Structured Learning via Logistic RegressionJul 03 2014A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through ... More

Kirby calculus in manifolds with boundaryDec 15 1998Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the ... More

Grothendieck classes of quiver cycles as iterated residuesOct 14 2013In the case of Dynkin quivers we establish a formula for the Grothendieck class of a quiver cycle as the iterated residue of a certain rational function, for which we provide an explicit combinatorial construction. Moreover, we utilize a new definition ... More