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Effect of Pressure Broadening on Molecular Absorption Cross Sections in Exoplanetary AtmospheresFeb 02 2016Spectroscopic observations of exoplanets are leading to unprecedented constraints on their atmospheric compositions. However, molecular abundances derived from spectra are degenerate with the absorption cross sections which form critical input data in ... More

The selection monad as a CPS transformationMar 20 2015A computation in the continuation monad returns a final result given a continuation, ie. it is a function with type $(X \to R) \to R$. If we instead return the intermediate result at $X$ then our computation is called a selection function. Selection functions ... More

Monad Transformers for Backtracking SearchJun 09 2014This paper extends Escardo and Oliva's selection monad to the selection monad transformer, a general monadic framework for expressing backtracking search algorithms in Haskell. The use of the closely related continuation monad transformer for similar ... More

Limits of bimorphic lensesAug 16 2018Bimorphic lenses are a simplification of polymorphic lenses that (like polymorphic lenses) have a type defined by 4 parameters, but which are defined in a monomorphic type system (i.e. an ordinary category with finite products). We show that the category ... More

Coherence for lenses and open gamesApr 07 2017Sep 15 2017Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ways. Specifically they have a family of morphisms ... More

A generalisation of Nash's theorem with higher-order functionalsJan 21 2013The recent theory of sequential games and selection functions by Mar- tin Escardo and Paulo Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalised to games ... More

Discovery of New Dipper Stars with K2: A Window into the Inner Disk Region of T Tauri StarsFeb 01 2018In recent years a new class of Young Stellar Object has been defined, referred to as dippers, where large transient drops in flux are observed. These dips are too large to be attributed to stellar variability, last from hours to days and can reduce the ... More

Four Small Planets Buried in K2 Systems: What Can We Learn for TESS?Jul 18 2019The Kepler, K2, and Transiting Exoplanet Survey Satellite (TESS) missions have provided a wealth of confirmed exoplanets, benefiting from a huge effort from the planet-hunting and follow-up community. With careful systematics mitigation, these missions ... More

Morphisms of open gamesNov 19 2017Nov 23 2017We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings between strategy ... More

From open learners to open gamesFeb 22 2019The categories of open learners (due to Fong, Spivak and Tuy\'eras) and open games (due to the present author, Ghani, Winschel and Zahn) bear a very striking and unexpected similarity. The purpose of this short note is to prove that there is a faithful ... More

Dialectica models of additive-free linear logicJan 18 2014Sep 25 2014This paper presents a construction which transforms categorical models of additive-free propositional linear logic, closely based on de Paiva's dialectica categories and Oliva's functional interpretations of classical linear logic. The construction is ... More

String diagrams for game theoryMar 20 2015This paper presents a monoidal category whose morphisms are games (in the sense of game theory, not game semantics) and an associated diagrammatic language. The two basic operations of a monoidal category, namely categorical composition and tensor product, ... More

The game semantics of game theoryApr 25 2019We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq 0$ noncooperative ... More

Backward Induction for Repeated GamesApr 19 2018Jul 11 2018We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad viewed as a notion ... More

Oscillations and Surface Rotation of Red Giant StarsAug 03 2013More than 15000 red giants observed by Kepler for a duration of almost one year became public at the beginning of this year. We analysed a subsample of 416 stars to determine the global properties of acoustic modes (mean large separation and frequency ... More

Kepler-62f: Kepler's First Small Planet in the Habitable Zone, but Is It Real?May 14 2019Kepler-62f is the first exoplanet small enough to plausibly have a rocky composition orbiting within the habitable zone (HZ) discovered by the Kepler Mission. The planet is 1.4 times the size of the Earth and has an orbital period of 267 days. At the ... More

Kepler-62f: Kepler's First Small Planet in the Habitable Zone, but Is It Real?May 14 2019May 15 2019Kepler-62f is the first exoplanet small enough to plausibly have a rocky composition orbiting within the habitable zone (HZ) discovered by the Kepler Mission. The planet is 1.4 times the size of the Earth and has an orbital period of 267 days. At the ... More

A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with BialgebrasFeb 04 2016Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural ... More

A compositional approach to economic game theoryMar 15 2016This paper aims to significantly impact the way we conceive of, reason about, and construct software for economic game theory. We achieve this by building an new and original model of economic games based upon the computer science idea of compositionality: ... More

Towards Functorial Language-GamesJul 20 2018Nov 08 2018In categorical compositional semantics of natural language one studies functors from a category of grammatical derivations (such as a Lambek pregroup) to a semantic category (such as real vector spaces). We compositionally build game-theoretic semantics ... More

Scaling of earthquake waiting times and the Olami-Feder-Christensen modelMay 02 2005Waiting-time statistics are generated from the Olami-Feder-Christensen model and shown to mimic some aspects of real seismicity. Preliminary analysis of the model data implies a recently proposed universal scaling law for the distribution in seismicity ... More

An $L^2-$stability estimate for periodic nonuniform sampling in higher dimensionsOct 31 2016We consider sampling strategies for a class of multivariate bandlimited functions $f$ that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating $f$ to the samples $f(y), ... More

Barycentric subdivisions and derangement polynomials for the even-signed permutation groupsDec 06 2012Jan 21 2013The derangement polynomial for the symmetric group enumerates derangements by the number of excedances. It can be interpreted as the local $h$-polynomial, in the sense of Stanley, of the barycentric subdivision of the simplex. Motivated by this interpretation, ... More

An $L^2-$stability estimate for periodic nonuniform sampling in higher dimensionsOct 31 2016Apr 16 2018We consider sampling strategies for a class of multivariate bandlimited functions $f$ that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating $f$ to the samples $f(y), ... More

An extension and trace theorem for functions of H-bounded variation in Carnot groups of step 2Oct 17 2005This paper provides an extension for a function $u \in BV_H(\Omega)$ to a function $u_0 \in BV_H(G)$ when $\Omega$ is ``H-admissible,'' and G is a step 2 Carnot group. It is shown that H-admissible domains include non-characteristic domains and domains ... More

Critical random hypergraphs: The emergence of a giant set of identifiable verticesJan 16 2004Aug 30 2005We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase transition takes various ... More

Faulhaber's Problem Revisited: Alternate Methods for Deriving the Bernoulli Numbers--Part IDec 27 2018This paper sets the groundwork for the consideration of families of recursively defined polynomials and rational functions capable of describing the Bernoulli numbers. These families of functions arise from various recursive definitions of the Bernoulli ... More

Scalar Curvature and Intrinsic Flat ConvergenceJun 29 2016Aug 03 2016Herein we present open problems and survey examples and theorems concerning sequences of Riemannian manifolds with uniform lower bounds on scalar curvature and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought to have certain ... More

Soft QCD Results from CDFJun 15 2011We review the latest underlying event and minimum bias results and discuss the associated problematics with the idea of establishing a solid baseline for the LHC experiments. These measurements include study of the underlying event in Drell-Yan and dijet ... More

How Riemannian Manifolds Converge: A SurveyJun 02 2010Oct 06 2011This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic notions which ... More

Lambda(1520) production in d+Au collisions at RHICMar 30 2006Recent results of $\Lambda$(1520) resonance production in d+Au collisions at $\sqrt{s_{\rm NN}} = $ 200 GeV are presented and discussed in terms of the evolution and freeze-out conditions of a hot and dense fireball medium. Yields and spectra are compared ... More

Convergence and the Length SpectrumFeb 14 2006The author defines and analyzes the $1/k$ length spectra, $L_{1/k}(M)$, whose union, over all $k\in \NN$ is the classical length spectrum. These new length spectra are shown to converge in the sense that $\lim_{i\to\infty} L_{1/k}(M_i) \subset \{0\}\cup ... More

Nonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groupsSep 23 1998In 1968, Milnor conjectured that a complete noncompact manifold with nonnegative Ricci curvature has a finitely generated fundamental group. The author applies the Excess Theorem of Abresch and Gromoll (1990), to prove two theorems. The first states that ... More

Generalization of Algebraic Operations via EnrichmentNov 12 2014In this dissertation we examine enrichment relations between categories of dual structure and we sketch an abstract framework where the theory of fibrations and enriched category theory are appropriately united. We initially work in the context of a monoidal ... More

Maximizing Volume Ratios for Shadow Covering by TetrahedraJan 09 2012Define a body A to be able to hide behind a body B if the orthogonal projection of B contains a translation of the corresponding orthogonal projection of A in every direction. In two dimensions, it is easy to observe that there exist two objects such ... More

Friedmann Cosmology and Almost IsotropyFeb 19 2003Mar 30 2004In the Friedmann Model of the universe, cosmologists assume that spacelike slices of the universe are Riemannian manifolds of constant sectional curvature. This assumption is justified via Schur's Theorem by stating that the spacelike universe is locally ... More

Volumes in Hyperbolic SpaceNov 10 2011This paper focuses on the investigation of volumes of large Coxeter hyperbolic polyhedron. First, the paper investigates the smallest possible volume for a large Coxeter hyperbolic polyhedron and then looks at the volume of pyramids with one vertex at ... More

On Loops Representing Elements of the Fundamental Group of a Complete Manifold with Nonnegative Ricci CurvatureApr 19 1999This paper concerns complete noncompact manifolds with nonnegative Ricci curvature. Roughly, we say that M has the loops to infinity property if given any noncontractible closed curve, C, and given any compact set, K, there exists a closed curve contained ... More

Intrinsic Flat Arzela-Ascoli TheoremsFeb 25 2014Jun 21 2014One of the most powerful theorems in metric geometry is the Arzela-Ascoli Theorem which provides a continuous limit for sequences of equicontinuous functions between two compact spaces. This theorem has been extended by Gromov and Grove-Petersen to sequences ... More

H2O abundances in the atmospheres of three hot JupitersJul 22 2014The core accretion theory for giant planet formation predicts enrichment of elemental abundances in planetary envelopes caused by runaway accretion of planetesimals, which is consistent with measured super-solar abundances of C, N, P, S, Xe, and Ar in ... More

A warm Jupiter-sized planet transiting the pre-main sequence star V1298 TauFeb 26 2019Jun 10 2019We report the detection of V1298 Tau b, a warm Jupiter-sized planet ($R_P$ = 0.91 $\pm$ 0.05~ $R_\mathrm{Jup}$, $P = 24.1$ days) transiting a young solar analog with an estimated age of 23 million years. The star and its planet belong to Group 29, a young ... More

K2SUPERSTAMP: The release of calibrated mosaics for the {\em Kepler/K2} MissionFeb 18 2018We describe the release of a new High Level Science Product (HLSP) available at the MAST archive. The HLSP, called K2Superstamp, consists of a series of FITS images for four open star clusters observed by the K2 Mission using so-called "superstamp" pixel ... More

Dynamic propensity in a kinetically constrained lattice gasOct 23 2006May 22 2007We apply the concept of dynamic propensity to a simple kinetically constrained model of glass formers, the two-vacancy assisted triangular lattice gas, or (2)-TLG. We find that the propensity field, defined in our case as the local root-mean square displacement ... More

Classifying Several Classes of Leibniz AlgebrasJan 25 2013We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of these algebras ... More

Dynamic facilitation explains democratic particle motion of metabasin transitionsJun 07 2007Jun 07 2007Transitions between metabasins in supercooled liquids seem to occur through rapid "democratic" collective particle rearrangements. Here we show that this apparent homogeneous particle motion is a direct consequence of dynamic facilitation. We do so by ... More

The algebra of predicting agentsMar 27 2018The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. More precisely it has counits with no corresponding units, and a partially defined duality. ... More

A catalog of 29 open clusters and associations observed by the Kepler and K2 MissionsOct 29 2018Over the past nine years, the Kepler and K2 Missions have carried out high precision photometric monitoring of more than half a million stars. Among these targets are 29 clusters and associations, with ages from 1 Myr to over 11 Gyr. We have generated ... More

Kepler's Discoveries Will Continue: 21 Important Scientific Opportunities with Kepler & K2 Archive DataOct 30 2018NASA's Kepler Space Telescope has collected high-precision, high-cadence time series photometry on 781,590 unique postage-stamp targets across 21 different fields of view. These observations have already yielded 2,496 scientific publications by authors ... More

Making recommendations bandwidth awareJul 13 2016This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommender systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth ... More

Electrical Networks with Prescribed Current and Applications to Random Walks on GraphsMar 07 2017Oct 14 2018We study the inverse problem of determining the conductivity matrix of an electrical network from the prescribed knowledge of the magnitude of the induced current along the edges coupled with the imposed voltage or injected current on the boundary nodes. ... More

Boundary Independent Broadcasts in GraphsJun 24 2019A broadcast on a nontrivial connected graph G is a function f from the vertices of G to the non-negative integers such that f(v) does not exceed e(v) (the eccentricity of v) for each vertex v. If G is disconnected, we define a broadcast on G as the union ... More

Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor orderMar 23 2018Jul 15 2019Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou to be in bijection with pyramidal sequences of consecutive differences. ... More

Robustification of Elliott's on-line EM algorithm for HMMsApr 07 2013In this paper, we establish a robustification of an on-line algorithm for modelling asset prices within a hidden Markov model (HMM). In this HMM framework, parameters of the model are guided by a Markov chain in discrete time, parameters of the asset ... More

Parking on a random treeOct 27 2016Consider a uniform random rooted tree on vertices labelled by $[n] = \{1,2,\ldots,n\}$, with edges directed towards the root. We imagine that each node of the tree has space for a single car to park. A number $m \le n$ of cars arrive one by one, each ... More

Efficiently Tracking Homogeneous Regions in Multichannel ImagesAug 16 2017We present a method for tracking Maximally Stable Homogeneous Regions (MSHR) in images with an arbitrary number of channels. MSHR are conceptionally very similar to Maximally Stable Extremal Regions (MSER) and Maximally Stable Color Regions (MSCR), but ... More

Witnessing quantum memory in non-Markovian processesNov 09 2018We present a method to detect a quantum memory in a non-Markovian process. We call a process Markovian when the environment does not provide a memory that retains correlations across consecutive system-environment interactions. We define two types of ... More

Skyrmions Driven by Intrinsic MagnonsMar 11 2018Jun 12 2018We study the dynamics of a skyrmion in a magnetic insulating nanowire in the presence of time-dependent oscillating magnetic field gradients. These ac fields act as a net driving force on the skyrmion via its own intrinsic magnetic excitations. In a microscopic ... More

Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor orderMar 23 2018Dec 20 2018Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou to be in bijection with pyramidal sequences of consecutive differences. ... More

Making recommendations bandwidth awareJul 13 2016Dec 05 2017This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommender systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth ... More

Mathematical analysis of a marine ecosystem model with nonlinear coupling terms and non-local boundary conditionsMar 18 2014Aug 24 2015We investigate the weak solvability of initial boundary value problems associated with an ecosystem model of the marine phosphorus cycle. The analysis covers the model equations themselves as well as their linearization which is important in the model ... More

Preservation of log-concavity on summationFeb 25 2005Oct 12 2005We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these conditions are natural ... More

A Boolean algebra and a Banach space obtained by push-out iterationDec 22 2010Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen model. We prove ... More

Numerical methods for multiscale inverse problemsJan 10 2014Oct 25 2016We consider the inverse problem of determining the highly oscillatory coefficient $a^\epsilon$ in partial differential equations of the form $-\nabla\cdot (a^\epsilon\nabla u^\epsilon)+bu^\epsilon = f$ from given measurements of the solutions. Here, $\epsilon$ ... More

Hybrid matrix compression for high-frequency problemsSep 12 2018Feb 04 2019Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for high-frequency problems. ... More

Global weak solutions to a strongly degenerate haptotaxis modelMar 14 2016We consider a one-dimensional version of a model obtained in [C. Engwer, A. Hunt, and C. Surulescu: Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings, IMA J. Math. Med. Biol. ... More

Dual random fragmentation and coagulation and an application to the genealogy of Yule processesAug 10 2004The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of ... More

The covering spectrum of a compact length spaceNov 22 2003We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers $\delta>0$ ... More

Universal Covers for Hausdorff Limits of Noncompact SpacesJul 02 2002We prove that if $Y$ is the Gromov-Hausdorff limit of a sequence of complete manifolds, $M^n_i$, with a uniform lower bound on Ricci curvature then $Y$ has a universal cover.

A Deterministic Algorithm for Pliable Index CodingJan 21 2016Pliable index coding considers a server with m messages, and n clients where each has as side information a subset of the messages. We seek to minimize the number of transmissions the server should make, so that each client receives (any) one message ... More

Various Covering Spectra for Complete Metric SpacesNov 30 2012Apr 29 2014We study various covering spectra for complete noncompact length spaces with universal covers (including Riemannian manifolds and the pointed Gromov Hausdorff limits of Riemannian manifolds with lower bounds on their Ricci curvature). We relate the covering ... More

Contrasting Various Notions of Convergence in Geometric AnalysisMar 17 2018We explore the distinctions between $L^p$ convergence of metric tensors on a fixed Riemannian manifold versus Gromov-Hausdorff, uniform, and intrinsic flat convergence of the corresponding sequence of metric spaces. We provide a number of examples which ... More

Monoidal Grothendieck ConstructionSep 03 2018Feb 18 2019We lift the standard equivalence between fibrations and indexed categories to an equivalence between monoidal fibrations and monoidal indexed categories, namely weak monoidal pseudofunctors to the 2-category of categories. In doing so, we investigate ... More

Boundary Independent Broadcasts in GraphsJun 24 2019Jul 06 2019A broadcast on a nontrivial connected graph G is a function f from the vertices of G to the non-negative integers such that f(v) does not exceed e(v) (the eccentricity of v) for each vertex v. If G is disconnected, we define a broadcast on G as the union ... More

A Polynomial-Time Algorithm for Pliable Index CodingOct 21 2016In pliable index coding, we consider a server with $m$ messages and $n$ clients where each client has as side information a subset of the messages. We seek to minimize the number of broadcast transmissions, so that each client can recover any one unknown ... More

Causal and causally separable processesJun 17 2015Sep 12 2016We develop rigorous notions of causality and causal separability in the process framework introduced in [Oreshkov, Costa, Brukner, Nat. Commun. 3, 1092 (2012)], which describes correlations between separate local experiments without a prior assumption ... More

Review of physics results from the Tevatron: QCD physicsSep 19 2014We present a summary of results from studies of quantum chromodynamics at the Fermilab Tevatron collider by the CDF and the D0 experiments. These include Run II results for the time period up to the end of Summer 2014. A brief description of Run I resultsis ... More

Fairness Under CompositionJun 15 2018Nov 20 2018Algorithmic fairness, and in particular the fairness of scoring and classification algorithms, has become a topic of increasing social concern and has recently witnessed an explosion of research in theoretical computer science, machine learning, statistics, ... More

The Architectural Implications of Microservices in the CloudMay 25 2018Cloud services have recently undergone a shift from monolithic applications to microservices, with hundreds or thousands of loosely-coupled microservices comprising the end-to-end application. Microservices present both opportunities and challenges when ... More

An isometrically universal Banach space induced by a non-universal Boolean algebraMay 18 2015Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$ and $K_B$ are the Stone ... More

Distinguishing graphs with zeta functions and generalized spectraOct 07 2014May 01 2015Conjecturally, almost all graphs are determined by their spectra. This problem has also been studied for variants such as the spectra of the Laplacian and signless Laplacian. Here we consider the problem of determining graphs with Ihara and Bartholdi ... More

On universal Banach spaces of density continuumMay 19 2010We consider the question whether there exists a Banach space $X$ of density continuum such that every Banach space of density not bigger than continuum isomorphically embeds into $X$ (called a universal Banach space of density $\cc$). It is well known ... More

Taking a shower in Youth Hostels: risks and delights of heterogeneityJan 10 2008Dec 13 2010Tuning one's shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite ... More

Revisiting Tietze-Nakajima - Local and Global Convexity for MapsJan 25 2007Nov 19 2009A theorem of Tietze and Nakamija, from 1928, asserts that if a subset X of R^n is closed, connected, and locally convex, then it is convex. We give an analogous "local to global convexity" theorem when the inclusion map of X to R^n is replaced by a map ... More

Determining both the source of a wave and its speed in a medium from boundary measurementsMar 18 2018May 29 2018We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography, and has important ... More

Determining both the source of a wave and its speed in a medium from boundary measurementsMar 18 2018Jun 17 2019We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography, and has important ... More

The Topology of Open Manifolds with Nonnegative Ricci CurvatureJun 30 2006Nov 16 2006We survey all results concerning the topology of complete noncompact Riemannian manifolds with nonnegative Ricci curvature that have no additional conditions other than restrictions to the dimension, volume growth or diameter growth of the manifold. We ... More

A first step toward higher order chain rules in abelian functor calculusJul 15 2017One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy ... More

Content-type codingMay 13 2015Jun 03 2015This paper is motivated by the observation that, in many cases, we do not need to serve specific messages, but rather, any message within a content-type. Content-type traffic pervades a host of applications today, ranging from search engines and recommender ... More

The Brownian continuum random tree as the unique solution to a fixed point equationApr 21 2015Sep 07 2015In this note, we provide a new characterization of Aldous' Brownian continuum random tree as the unique fixed point of a certain natural operation on continuum trees (which gives rise to a recursive distributional equation). We also show that this fixed ... More

The scaling limit of a critical random directed graphMay 14 2019We consider the random directed graph $\vec{G}(n,p)$ with vertex set $\{1,2,\ldots,n\}$ in which each of the $n(n-1)$ possible directed edges is present independently with probability $p$. We are interested in the strongly connected components of this ... More

Enumerating Acyclic Digraphs by DescentsSep 02 2017A descent of a labeled acyclic digraph is a directed edge $x\to y$ with $x>y$. In this paper, we find a recurrence for the number of labeled acyclic digraphs with a given number of descents.

Intrinsic Flat Convergence of Covering SpacesSep 24 2014We examine the limits of covering spaces and the covering spectra of oriented Riemannian manifolds, $M_j$, which converge to a nonzero integral current space, $M_\infty$, in the intrinsic flat sense. We provide examples demonstrating that the covering ... More

Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis-haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more)Apr 25 2019We propose and study a class of parabolic-ODE models involving chemotaxis and haptotaxis of a species following signals indirectly produced by another, non-motile one. The setting is motivated by cancer invasion mediated by interactions with the tumor ... More

Part of Speech Based Term Weighting for Information RetrievalApr 05 2017Automatic language processing tools typically assign to terms so-called weights corresponding to the contribution of terms to information content. Traditionally, term weights are computed from lexical statistics, e.g., term frequencies. We propose a new ... More

Apollonian Equilateral TrianglesMar 01 2013Given an equilateral triangle with $a$ the square of its side length and a point in its plane with $b$, $c$, $d$ the squares of the distances from the point to the vertices of the triangle, it can be computed that $a$, $b$, $c$, $d$ satisfy $3(a^2+b^2+c^2+d^2)=(a+b+c+d)^2$. ... More

The Cut-off Covering SpectrumMay 25 2007Sep 17 2008We introduce the $R$ cut-off covering spectrum and the cut-off covering spectrum of a complete length space or Riemannian manifold. The spectra measure the sizes of localized holes in the space and are defined using covering spaces called $\delta$ covers ... More

Hausdorff Convergence and Universal CoversAug 29 2000We prove that if $Y$ is the Gromov-Hausdorff limit of a sequence of compact manifolds, $M^n_i$, with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then $Y$ has a universal cover. We then show that, for $i$ sufficiently ... More

Resonance production from jet fragmentationJul 17 2009Short lived resonances are sensitive to the medium properties in heavy-ion collisions. Heavy hadrons have larger probability to be produced within the quark gluon plasma phase due to their short formation times. Therefore heavy mass resonances are more ... More

Subwavelength Nanopatch Cavities for Semiconductor Plasmon LasersDec 09 2007We propose and analyze a family of nanoscale cavities for electrically-pumped surface-emitting semiconductor lasers that use surface plasmons to provide optical mode confinement in cavities which have dimensions in the 100-300 nm range. The proposed laser ... More

On the Measurement of D-meson Yield in Nucleus-Nucleus Collisions at the CERN SPSApr 23 1999Apr 25 1999We argue that the measurement of open charm gives a unique opportunity to test the validity of pQCD-based and statistical models of nucleus-nucleus collisions at high energies. We show that various approaches used to estimate D-meson multiplicity in central ... More