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Nested colourings of graphsJun 01 2013A proper vertex colouring of a graph is \emph{nested} if the vertices of each of its colour classes can be ordered by inclusion of their open neighbourhoods. Through a relation to partially ordered sets, we show that the nested chromatic number can be ... More

Syzygy bundles and the weak Lefschetz property of almost complete intersectionsJun 06 2016Deciding the presence of the weak Lefschetz property often is a challenging problem. In this work an in-depth study is carried out in the case of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings ... More

The weak Lefschetz property, monomial ideals, and lozengesSep 18 2009We study the weak Lefschetz property and the Hilbert function of level Artinian monomial almost complete intersections in three variables. Several such families are shown to have the weak Lefschetz property if the characteristic of the base field is zero ... More

Some algebras with the weak Lefschetz propertyJun 06 2016Using a connection to lozenge tilings of triangular regions, we establish an easily checkable criterion that guarantees the weak Lefschetz property of a quotient by a monomial ideal. It is also shown that each such ideal also has a semistable syzygy bundle. ... More

Zombie Dice: An Optimal Play StrategyJun 02 2014We discuss the game of Zombie Dice, published by Steve Jackson Games. This game includes green, yellow, and red dice. Each die has brain, footprint, and shotgun symbols on it, with each color of dice having a different amount of each symbol. Out of the ... More

Partially ordered sets in Macaulay2Apr 30 2013We introduce the package Posets for Macaulay2. This package provides a data structure and the necessary methods for working with partially ordered sets, also called posets. In particular, the package implements methods to enumerate many commonly studied ... More

Infrared Period-Luminosity Relations of Evolved Variable Stars in the Large Magellanic CloudJul 28 2010We combine variability information from the MAssive Compact Halo Objects (MACHO) survey of the Large Magellanic Cloud (LMC) with infrared photometry from the Spitzer Space Telescope Surveying the Agents of a Galaxy's Evolution (SAGE) survey to create ... More

The structure of the Boij-Söderberg posetsJun 10 2010Boij and S\"oderberg made a pair of conjectures, which were subsequently proven by Eisenbud and Schreyer and then extended by Boij and S\"oderberg, about the structure of Betti diagrams of Graded modules. In the theory, a particular family of posets, ... More

The strong Lefschetz property in codimension twoJan 31 2013Feb 18 2013Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of monomial ideals. ... More

The uniform face ideals of a simplicial complexAug 06 2013We define the uniform face ideal of a simplicial complex with respect to an ordered proper vertex colouring of the complex. This ideal is a monomial ideal which is generally not squarefree. We show that such a monomial ideal has a linear resolution, as ... More

The Lefschetz properties of monomial complete intersections in positive characteristicNov 21 2011Stanley proved that, in characteristic zero, all artinian monomial complete intersections have the strong Lefschetz property. We provide a positive characteristic complement to Stanley's result in the case of artinian monomial complete intersections generated ... More

SimplicialDecomposability: a package for Macaulay 2Feb 11 2010Jun 10 2010We introduce a new Macaulay 2 package, SimplicialDecomposability, which works in conjunction with the extant package SimplicialComplexes in order to compute a shelling order, if one exists, of a specified simplicial complex. Further, methods for determining ... More

A Spectral Symplectic Algorithm for Cylindrical Electromagnetic Plasma SimulationsSep 16 2016Sep 23 2016Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend the symplectic ... More

On decomposing Betti tables and $O$-sequencesJul 15 2014The Boij-S\"oderberg characterization decomposes a Betti table into a unique positive integral linear combination of pure diagrams. Given a module with a pure resolution, we describe explicit formulae for computing the decomposition of the Betti table ... More

Nauty in Macaulay2Oct 29 2010Feb 24 2011We introduce a new Macaulay2 package, Nauty, which gives access to powerful methods on graphs provided by the software nauty by Brendan McKay. The primary motivation for accessing nauty is to determine if two graphs are isomorphic. We also implement methods ... More

Cohen-Macaulay graphs and face vectors of flag complexesMar 23 2010Jun 13 2011We introduce a construction on a flag complex that, by means of modifying the associated graph, generates a new flag complex whose $h$-factor is the face vector of the original complex. This construction yields a vertex-decomposable, hence Cohen-Macaulay, ... More

Hyperplane sections and the subtlety of the Lefschetz propertiesDec 12 2010The weak and strong Lefschetz properties are two basic properties that Artinian algebras may have. Both Lefschetz properties may vary under small perturbations or changes of the characteristic. We study these subtleties by proposing a systematic way of ... More

Signed lozenge tilingsJul 06 2015It is well-known that plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in bijection. In this work we consider regions that are more general than ... More

Enumerations deciding the weak Lefschetz propertyMay 30 2011Dec 20 2011We introduce a natural correspondence between artinian monomial almost complete intersections in three variables and punctured hexagonal regions. We use this correspondence to investigate the algebras for the presence of the weak Lefschetz property. In ... More

Enumerations of lozenge tilings, lattice paths, and perfect matchings and the weak Lefschetz propertyMay 06 2013MacMahon enumerated the plane partitions in an $a \times b \times c$ box. These are in bijection to lozenge tilings of a hexagon, to certain perfect matchings, and to families of non-intersecting lattice paths. In this work we consider more general regions, ... More

The weak Lefschetz property for monomial ideals of small typeJul 14 2015Jul 15 2015In this work a combinatorial approach towards the weak Lefschetz property is developed that relates this property to enumerations of signed perfect matchings as well as to enumerations of signed families of non-intersecting lattice paths in certain triangular ... More

Theories for TC0 and Other Small Complexity ClassesMay 05 2005Mar 08 2006We present a general method for introducing finitely axiomatizable "minimal" two-sorted theories for various subclasses of P (problems solvable in polynomial time). The two sorts are natural numbers and finite sets of natural numbers. The latter are essentially ... More

A Theory For Particle Settling and Shear-Induced Migration in Thin Film FlowOct 16 2007Experiments of particle-laden inclined film flow [Zhou, Dupuy, Bertozzi, and Hosoi, Phys. Rev. Lett. 94 (2005)] have displayed different settling behaviors depending on the particle concentration $\phi$ and angle of inclination $\theta$, in which particles ... More

Homotopical Algebra in Categories with Enough ProjectivesMar 02 2017Mar 06 2018For a complete and cocomplete category $\mathcal{C}$ with a well-behaved class of `projectives' $\bar{\mathcal{P}}$, we construct a model structure on the category $s\mathcal{C}$ of simplicial objects in $\mathcal{C}$ where the weak equivalences, fibrations ... More

Ground-based Discovery of Cepheids and Miras in M101May 08 1995We have identified 4 Cepheids and 5 Miras using KPNO 4m BVRI images of an outer field in M101. The Cepheid and Mira periods range from 30 to 60 days and 350 to 800 days, respectively. We derive independent Cepheid and Mira distance moduli that agree within ... More

Infinite dimensional super Lie groupsOct 24 2006A super Lie group is a group whose operations are $G^{\infty}$ mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are $G^{\infty}$ functions. Moreover the images of our charts are open subsets ... More

The circular law for random regular digraphsMar 16 2017Aug 07 2017Let $\log^Cn\le d\le n/2$ for a sufficiently large constant $C>0$ and let $A_n$ denote the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices. We prove that as $n$ tends to infinity, the empirical spectral distribution of ... More

Laser frequency stabilization based on steady-state spectral-hole burning in Eu$^{3+}$:Y$_2$SiO$_5$Apr 09 2015We present and analyze a method of laser frequency stabilization via steady-state patterns of spectral holes in Eu$^{3+}$:Y$_2$SiO$_5$. Three regions of spectral holes are created, spaced in frequency by the ground state hyperfine splittings of $~^{151}$Eu$^{3+}$. ... More

The Nature of Low-Density Star FormationMar 13 2019How do stars manage to form within low-density, HI-dominated gas? Such environments provide a laboratory for studying star formation with physical conditions distinct from starbursts and the metal-rich disks of spiral galaxies where most effort has been ... More

Determining the dimension of iterative Hessian transformationAug 30 2005The central mean subspace (CMS) and iterative Hessian transformation (IHT) have been introduced recently for dimension reduction when the conditional mean is of interest. Suppose that X is a vector-valued predictor and Y is a scalar response. The basic ... More

K-Band Red Clump Distance to the Large Magellanic CloudMay 28 2002The Hipparcos I-band calibration of horizontal-branch red clump giants as standard candles has lead to controversial results for the distance to the Large Magellanic Cloud (LMC). In an attempt to properly ascertain the corrections for interstellar extinction ... More

Line arrangements and configurations of points with an unusual geometric propertyFeb 06 2016Mar 02 2017The SHGH conjecture proposes a solution to the question of how many conditions a general union of fat points imposes on the complete linear system of curves in $\mathbb P^2$ of fixed degree $d$, and it is known to be true in many cases. We propose a new ... More

Line arrangements and configurations of points with an unusual geometric propertyFeb 06 2016The SHGH conjecture proposes a solution to the question of how many conditions a general union of fat points imposes on the complete linear system of curves in $\mathbb P^2$ of fixed degree $d$, and it is known to be true in many cases. We propose a new ... More

An algebraic approach to finite projective planesMar 14 2015Oct 19 2015A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a careful study ... More

Chemical Abundances of the Leo II Dwarf GalaxyOct 03 2008We use previously-published moderate-resolution spectra in combination with stellar atmosphere models to derive the first measured chemical abundance ratios in the Leo II dSph galaxy. We find that for spectra with SNR > 24, we are able to measure abundances ... More

Lefschetz properties of balanced 3-polytopesJun 07 2016In this paper, we study Lefschetz properties of Artinian reductions of Stanley-Reisner rings of balanced simplicial $3$-polytopes. A $(d-1)$-dimensional simplicial complex is said to be balanced if its graph is $d$-colorable. If a simplicial complex is ... More

Degenerate Perturbation Theory Describing the Mixing of Orbital Angular Momentum Modes in Fabry-Pérot Cavity ResonatorsJan 02 2009We present an analytic perturbation theory which extends the paraxial approximation for a common cylindrically symmetric stable optical resonator and incorporates the differential, polarization-dependent reflectivity of a Bragg mirror. The degeneracy ... More

Relativizing Small Complexity Classes and their TheoriesApr 24 2012Existing definitions of the relativizations of \NCOne, \L\ and \NL\ do not preserve the inclusions $\NCOne \subseteq \L$, $\NL\subseteq \ACOne$. We start by giving the first definitions that preserve them. Here for \L\ and \NL\ we define their relativizations ... More

Stochastic Dynamics of Infrared Fluctuations in Accelerating UniverseAug 31 2015We extend investigations of infrared dynamics in accelerating universes. In the presence of massless and minimally coupled scalar fields, physical quantities may acquire growing time dependences through quantum fluctuations at super-horizon scales. From ... More

The Connection Between Galaxy Environment and the Luminosity Function Slopes of Star-Forming RegionsJul 13 2016Jul 29 2016We present the first study of GALEX far ultra-violet (FUV) luminosity functions of individual star-forming regions within a sample of 258 nearby galaxies spanning a large range in total stellar mass and star formation properties. We identify ~65,000 star-forming ... More

A Spectral Symplectic Algorithm for Cylindrical Electromagnetic Plasma SimulationsSep 16 2016Oct 05 2016Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend the symplectic ... More

Study of the preheating phase of chaotic inflationJan 04 2008Oct 14 2008Particle production and its effects on the inflaton field are investigated during the preheating phase of chaotic inflation using a model consisting of a massive scalar inflaton field coupled to N massless quantum scalar fields. The effects of spacetime ... More

Solar system Deep Time-Surveys of atmospheres, surfaces, and ringsMar 15 2019Imaging and resolved spectroscopy reveal varying environmental conditions in our dynamic solar system. Many key advances have focused on how these conditions change over time. Observatory-level commitments to conduct annual observations of solar system ... More

Eclipsing binary stars in the Large and Small Magellanic Clouds from the MACHO project: The SampleNov 10 2007We present a new sample of 4634 eclipsing binary stars in the Large Magellanic Cloud (LMC), expanding on a previous sample of 611 objects and a new sample of 1509 eclipsing binary stars in the Small Magellanic Cloud (SMC), that were identified in the ... More

Measurements of Si Hybrid CMOS X-Ray Detector CharacteristicsSep 16 2009The development of Hybrid CMOS Detectors (HCDs) for X-Ray telescope focal planes will place them in con- tention with CCDs on future satellite missions due to their faster frame rates, flexible readout scenarios, lower power consumption, and inherent ... More

The Stellar Halo and Tidal Streams of Messier 63Oct 19 2015We present new near-infrared (NIR) observations of M63 from the Extended Disk Galaxy Exploration Science (EDGES) Survey. The extremely deep 3.6 $\mu$m mosaic reaches 29 AB mag arcsec$^{-2}$ at the outer reaches of the azimuthally-averaged surface brightness ... More

Kinematic Evidence for an Old Stellar Halo in the Large Magellanic CloudSep 12 2003The oldest and most metal-poor Milky Way stars form a kinematically hot halo, which motivates the two major formation scenarios for our galaxy: extended hierarchical accretion and rapid collapse. RR Lyrae stars are excellent tracers of old and metal-poor ... More

A Concrete View of Rule 110 ComputationJun 17 2009Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed ... More

Comments on Beckmann's Uniform ReductsJan 19 2006Jan 23 2006Arnold Beckmann defined the uniform reduct of a propositional proof system f to be the set of those bounded arithmetical formulas whose propositional translations have polynomial size f-proofs. We prove that the uniform reduct of f + Extended Frege consists ... More

Complexity Classes and Theories for the Comparator Circuit Value ProblemJun 21 2011Oct 04 2011Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem. He proved that several other problems are complete for CC, including the stable marriage problem, and finding the lexicographical ... More

Spatial InterpolantsJan 16 2015We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants with data ... More

An improved bound for the degree of smooth surfaces in P4 not of general type.Jan 16 1995This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound for the degree of a smooth surface in $\pfour$ not of general type. Using their construction and the regularity of curves in $\pthree$, one may lower the bound a little more. ... More

The Connectedness of Space Curve InvariantsJan 28 1994It is a result of Gruson and Peskine that the invariants of a set points in $\ptwo$ in general position are connected. Associated to a space curve there are sequences of invariants which generalize the invariants of points in $\ptwo$. The main result ... More

Relativized Propositional CalculusMar 09 2012Proof systems for the Relativized Propositional Calculus are defined and compared.

Interactive Graphics for Visually Diagnosing Forest Classifiers in RApr 08 2017This paper describes structuring data and constructing plots to explore forest classification models interactively. A forest classifier is an example of an ensemble, produced by bagging multiple trees. The process of bagging and combining results from ... More

A smooth surface in P4 not of general type has degree at most 46Jan 04 1997This is the continuation of papers by Braun and Floystad, Cook, Braun and Cook. We use Generic Initial Ideal Theory in conjunction with Liaison Theory to further restrict the possible generic initial ideals of hyperplane sections of smooth surfaces not ... More

Many-body dynamics of p-wave Feshbach molecule production: a mean-field approachOct 08 2012Jan 16 2013We study the mean-field dynamics of p-wave Feshbach molecule production in an ultra cold gas of Fermi atoms in the same internal state. We derive a separable potential to describe the low-energy scattering properties of such atoms, and use this potential ... More

Are current-based synapses an accurate enough approximation? A homotopic mapping between current-based and conductance-based synapses in a neural field model of epilepsyOct 01 2015The overwhelming majority of neural field and mass models use current-based synapses [1] unlike spiking models which typically use conductance-based synapses [2]. Although neural field models that employ conductance-based synapses have been studied [3,9], ... More

Superhumps and flickering in V1316 CygniOct 08 2007We present analysis and results of a coordinated CCD photometry campaign to observe the 2006 June superoutburst of the cataclysmic variable V1316 Cyg involving 8 longitudinally-distributed observers. The outburst peaked at magnitude 15.03 on June 10, ... More

Software Requirements Specification of the IUfA's UUIS -- a Team 3 COMP5541-W10 Project ApproachMay 04 2010The purpose of this document is to specify the requirements of the University Unified Inventory System, of the UIfA. The Team of Analysts used a Feedback Waterfall approach to collect the requirements. UML diagrams, such as Use case diagrams, Block Diagrams, ... More

Late metal-silicate separation on the IAB parent asteroid: Constraints from combined W and Pt isotopes and thermal modellingFeb 28 2018The short-lived $^{182}$Hf-$^{182}$W decay system is a powerful chronometer for constraining the timing of metal-silicate separation and core formation in planetesimals and planets. Neutron capture effects on W isotopes, however, significantly hamper ... More

Software Design Document, Testing, Deployment and Configuration Management of the IUfA's UUIS -- a Team 3 COMP5541-W10 Project ApproachMay 05 2010The purpose of this document is to provide technical specifications concerned to the Design of the University Unified Inventory System - Web Portal, of the UIfA. The Team of Developers used a Feedback Waterfall approach to build up the system, under an ... More

SPIRITS: Uncovering Unusual Infrared Transients With SpitzerJan 04 2017We present an ongoing, systematic search for extragalactic infrared transients, dubbed SPIRITS --- SPitzer InfraRed Intensive Transients Survey. In the first year, using Spitzer/IRAC, we searched 190 nearby galaxies with cadence baselines of one month ... More

Individual band with higher Chern numbers in double perovskite {001} monolayersAug 09 2016Aug 28 2016We show a tight-binding model for double perovskite monolayers grown in the {001} crystallographic direction can exhibit higher Chern numbers for the lowest band of the model dispersion in the absence of an applied magnetic field, including $\pm2$, $\pm4$, ... More

Initial Data for Numerical RelativityJul 31 2000Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data ... More

Bieri-Eckmann Criteria for Profinite GroupsDec 04 2014Jan 15 2015In this paper we derive necessary and sufficient homological and cohomological conditions for profinite groups and modules to be of type $\operatorname{FP}_n$ over a profinite ring $R$, analogous to the Bieri-Eckmann criteria for abstract groups. We use ... More

Ordinal analysis of intuitionistic power and exponentiation Kripke Platek set theoryMar 10 2016Until the 1970s, proof theoretic investigations were mainly concerned with theories of inductive definitions, subsystems of analysis and finite type systems. With the pioneering work of Gerhard Jaeger in the late 1970s and early 1980s, the focus switched ... More

Continuous Measurement and Stochastic Methods in Quantum Optical SystemsJan 25 2013This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the quantum measurement ... More

Fisher Lecture: Dimension Reduction in RegressionAug 28 2007Beginning with a discussion of R. A. Fisher's early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with descriptions ... More

Majorana Fermions in Proximity-coupled Topological Insulator NanowiresMay 09 2011Nov 08 2011A topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, is shown to realize a one-dimensional topological superconductor with unpaired Majorana fermions localized ... More

A smooth surface in P4 not of general type has degree at most 66Jan 04 1997We continue the work of Braun and Floystad, and Cook bounding the degree of smooth surfaces in P4 not of general type using generic initial ideal theory.

Diophantine equations in the primesDec 21 2013Let $\mathfrak{p}=(\mathfrak{p}_1,...,\mathfrak{p}_r)$ be a system of $r$ polynomials with integer coefficients of degree $d$ in $n$ variables $\mathbf{x}=(x_1,...,x_n)$. For a given $r$-tuple of integers, say $\mathbf{s}$, a general local to global type ... More

The circular law for random regular digraphs with random edge weightsAug 02 2015Sep 08 2017We consider random $n\times n$ matrices of the form $Y_n=\frac1{\sqrt{d}}A_n\circ X_n$, where $A_n$ is the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices, with $d=\lfloor p n\rfloor$ for some fixed $p \in (0,1)$, and $X_n$ ... More

Efficient algorithms for Bayesian Nearest Neighbor Gaussian ProcessesFeb 01 2017Mar 03 2018We consider alternate formulations of recently proposed hierarchical Nearest Neighbor Gaussian Process (NNGP) models (Datta et al., 2016a) for improved convergence, faster computing time, and more robust and reproducible Bayesian inference. Algorithms ... More

Joint hierarchical models for sparsely sampled high-dimensional LiDAR and forest variablesMar 24 2016Dec 05 2016Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, ... More

A Note on Homology over Functor CategoriesDec 03 2014It is known that, for $C$ an abelian category and $I$ small, the functor category $C^I$ is again abelian; thus we can do homology in such categories, and examine how it relates to homology in $C$ itself. However, there does not seem to be any good reference ... More

Rejoinder: Fisher Lecture: Dimension Reduction in RegressionAug 28 2007Rejoinder: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]

Computing over the Reals: Foundations for Scientific ComputingSep 14 2005We give a detailed treatment of the ``bit-model'' of computability and complexity of real functions and subsets of R^n, and argue that this is a good way to formalize many problems of scientific computation. In the introduction we also discuss the alternative ... More

Random billiards with wall temperature and associated Markov chainsFeb 10 2012By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard domain, gives ... More

Power Law Distribution of the Frequency of Demises of U.S FirmsDec 09 2002Both theoretical and applied economics have a great deal to say about many aspects of the firm, but the literature on the extinctions, or demises, of firms is very sparse. We use a publicly available data base covering some 6 million firms in the US and ... More

Constellations in P^dOct 27 2010Nov 12 2010Let A be a subset of positive relative upper density of P^d, the d-tuples of primes. We prove that A contains an affine copy of any finite set of lattice points E, as long as E is in general position in the sense that it has at most one point on every ... More

Classifying the provably total set functions of KP and KP(P)Oct 07 2016This article is concerned with classifying the provably total set-functions of Kripke-Platek set theory, KP, and Power Kripke-Platek set theory, KP(P), as well as proving several (partial) conservativity results. The main technical tool used in this paper ... More

Complexity Theory for Operators in AnalysisMay 02 2013We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea is to use (a ... More

Discrepancy properties for random regular digraphsOct 21 2014Oct 26 2015For the uniform random regular directed graph we prove concentration inequalities for (1) codegrees and (2) the number of edges passing from one set of vertices to another. As a consequence, we can deduce discrepancy properties for the distribution of ... More

Dense random regular digraphs: singularity of the adjacency matrixMar 24 2014Aug 02 2015Fix $c\in (0,1)$ and let $\Gamma$ be a $\lfloor c n\rfloor$-regular digraph on $n$ vertices drawn uniformly at random. We prove that when $n$ is large, the (non-symmetric) adjacency matrix $M$ of $\Gamma$ is invertible with high probability. The proof ... More

On Profinite Groups of Type $\operatorname{FP}_\infty$Dec 05 2014Suppose $R$ is a profinite ring. We construct a large class of profinite groups $\widehat{{\scriptstyle\bf L}'{\scriptstyle\bf H}_R}\mathfrak{F}$, including all soluble profinite groups and profinite groups of finite cohomological dimension over $R$. ... More

Three-dimensional initial data for the collision of two black holes II: Quasi-circular orbits for equal-mass black holesApr 25 1994The construction of initial-data sets representing binary black-hole configurations in quasi-circular orbits is studied in the context of the conformal-imaging formalism. An effective-potential approach for locating quasi-circular orbits is outlined for ... More

The Gravitational-Electromagnetic Analogy: A Possible Solution to the Vacuum-Energy and Dark-Energy ProblemsOct 24 2008Jan 29 2009There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers whether Mother ... More

Gauged Wess-Zumino Model in Noncommutative Minkowski SuperspaceMay 27 2005Jun 22 2005We develop a gauged Wess-Zumino model in noncommutative Minkowski superspace. This is the natural extension of the work of Carlson and Nazaryan, which extended N=1/2 supersymmetry written over deformed Euclidean superspace to Minkowski superspace. We ... More

Tournament Sequences and Meeussen SequencesFeb 25 2000Dec 01 2000A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative integer is ... More

On the singularity of adjacency matrices for random regular digraphsNov 02 2014Nov 09 2015We prove that the (non-symmetric) adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices is asymptotically almost surely invertible, assuming $\min(d,n-d)\ge C\log^2n$ for a sufficiently large constant $C>0$. The proof makes use ... More

Dynamic spatial regression models for space-varying forest stand tablesNov 03 2014Many forest management planning decisions are based on information about the number of trees by species and diameter per unit area. This information is commonly summarized in a stand table, where a stand is defined as a group of forest trees of sufficiently ... More

Percolation diffusion into self-assembled mesoporous silica microfibresJan 21 2014Mar 04 2014Percolation diffusion into long (11.5 cm) self-assembled, ordered mesoporous microfibres is studied using optical transmission and laser ablation inductive coupled mass spectrometry (LA-ICP-MS). Optical transmission based diffusion studies reveal rapid ... More

Computational and in vitro studies of blast-induced blood-brain barrier disruptionMar 31 2015Dec 17 2015There is growing concern that blast-exposed individuals are at risk of developing neurological disorders later in life. Therefore, it is important to understand the dynamic properties of blast forces on brain cells, including the endothelial cells that ... More

Empirical ugri-UBVRc Transformations for GalaxiesAug 05 2014We present empirical color transformations between Sloan Digital Sky Survey ugri and Johnson-Cousins UBVRc photometry for nearby galaxies (D < 11 Mpc). We use the Local Volume Legacy (LVL) galaxy sample where there are 90 galaxies with overlapping observational ... More

The Wyoming Survey for H-alpha. III. A Multi-wavelength Look at Attenuation by Dust in Galaxies out to z~0.4Jun 11 2010We report results from the Wyoming Survey for H-alpha (WySH), a comprehensive four-square degree survey to probe the evolution of star-forming galaxies over the latter half of the age of the Universe. We have supplemented the H-alpha data from WySH with ... More

The ACS Nearby Galaxy Survey Treasury. X. Quantifying the Star Cluster Formation Efficiency of Nearby Dwarf GalaxiesMar 21 2012Mar 27 2012We study the relationship between the field star formation and cluster formation properties in a large sample of nearby dwarf galaxies. We use optical data from the Hubble Space Telescope and from ground-based telescopes to derive the ages and masses ... More

Gravitational Space DilationFeb 17 2009We point out that, if one accepts the view that the standard second on an atomic clock is dilated at low gravitational potential (ordinary gravitational time dilation), then the standard meter must also be dilated at low gravitational potential and by ... More

The strength of replacement in weak arithmeticSep 08 2004The replacement (or collection or choice) axiom scheme asserts bounded quantifier exchange. We prove the independence of this scheme from various weak theories of arithmetic, sometimes under a complexity assumption.

Lower bounds for the smallest singular value of structured random matricesAug 26 2016Sep 18 2016We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider $n\times n$ matrices with complex entries of the form \[ M = A\circ X + B = (a_{ij}\xi_{ij} ... More