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Steiner triangular drop dynamicsJun 11 2019Steiner's circumellipse is the unique regularization of any triangle to a circumscribed ellipse with the same centroid, a regularization that motivates our introduction of the Steiner triangle as a minimal model of a liquid droplet. The center of mass ... More

An Asymptotic Analysis of Queues with Delayed Information and Time Varying Arrival RatesJan 19 2017Understanding how delayed information impacts queueing systems is an important area of research. However, much of the current literature neglects one important feature of many queueing systems, namely non-stationary arrivals. Non-stationary arrivals model ... More

Managing Information in Queues: The Impact of Giving Delayed Information to CustomersSep 23 2016Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the performance of ... More

Quantum-Mechanical Consequences of Five-Dimensional RelativityFeb 24 2011May 13 2011I outline a model where a massive particle in 4D spacetime follows a null (photon-like) path in 5D canonical (super-spherically-symmetric) space. This leads to wave-particle duality and quantization, along with other effects which show that it is possible ... More

The Equivalence Principle as a SymmetryFeb 22 2003It is shown that the extra coordinate of 5D induced-matter and membrane theory is related in certain gauges to the inertial rest mass of a test particle. This implies that the Weak Equivalence Principle is a geometric symmetry, valid only in the limit ... More

Classical and quantized aspects of dynamics in five dimensional relativityApr 15 2002A null path in 5D can appear as a timelike path in 4D, and for a certain gauge in 5D the motion of a massive particle in 4D obeys the usual quantization rule with an uncertainty-type relation. Generalizations of this result are discussed in regard to ... More

Particle Masses and the Cosmological 'Constant' in Five DimensionsNov 20 2011I give metrics and equations of motion in 5D general relativity, and use the conservation of momentum and conformal transformations to study the possible variability of particle masses and the cosmological 'constant'. It is feasible that all particles ... More

Quantum-Mechanical Waves in Closed Vacuum StatesDec 12 2010Campbell's theorem enables the embedding of 4D anti-deSitter space in 5D canonical space, so a particle becomes a wave in the extra dimension, running through spacetime. This model of wave-particle duality provides a new approach to particle mass.

Space-Time Uncertainty from Higher-Dimensional Determinism (or: How Heisenberg was right in 4D because Einstein was right in 5D)Sep 28 2003Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We here show that ... More

A Machian definition of particle mass in higher-dimensional gravityFeb 13 2016A new method involving the effective wave function is used to define the mass of a particle in a standard five-dimensional extension of general relativity. The mass is inversely proportional to the magnitude of the scalar field of the extra dimension. ... More

Particles, Waves and Vacuum in Five Dimensions: A Status ReportMay 20 2012Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several ways to ra-tionalize ... More

Physical Identifications for the Algebraic Quantities of Five-Dimensional RelativityJun 17 2010When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become widespread to view the ... More

The Scalar Field Of 5D Gravity And The Higgs Field Of 4D Particle Physics: A Possible ConnectionMar 12 2010The main results are reviewed of relating the scalar field of noncompactified Kaluza-Klein gravity to the Higgs field of particle physics. The embedding of 4D spacetime in a 5D manifold can result in a variable cosmological 'constant' and particle masses ... More

The Meaning of DimensionsDec 09 2007We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of book-keeping device, ... More

Einstein's Equations, Cosmology and AstrophysicsAug 15 2012I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for spherically-symmetric systems, ... More

General Relativity and Quantum Mechanics in Five DimensionsFeb 03 2011In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results effectively show how ... More

Time as an IllusionMay 01 2009We review the idea, due to Einstein, Eddington, Hoyle and Ballard, that time is a subjective label, whose primary purpose is to order events, perhaps in a higher-dimensional universe. In this approach, all moments in time exist simultaneously, but they ... More

Mass and Machian General RelativityNov 16 2008Jan 25 2009Mach's Principle is usually taken to mean that the mass of a particle as measured locally is determined in some way by the other matter in the universe. This is difficult to formalize in 4D,but is feasible in 5D if the scalar potential of non-compactified ... More

Is Mass Quantized?Sep 20 2003The cosmological constant combined with Planck's constant and the speed of light implies a quantum of mass of approximately 2 x 10^{-65}g. This follows either from a generic dimensional analysis, or from a specific analysis where the cosmological constant ... More

On Higher-Dimensional DynamicsMay 17 2001Technical results are presented on motion in N(>4)D manifolds to clarify the physics of Kaluza-Klein theory, brane theory and string theory. The so-called canonical or warp metric in 5D effectively converts the manifold from a coordinate space to a momentum ... More

Vacuum WavesDec 11 2012As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in nature, the waves ... More

Five dimensional relativity and two timesMay 28 2002It is possible that null paths in 5D appear as the timelike paths of massive particles in 4D, where there is an oscillation in the fifth dimension around the hypersurface we call spacetime. A particle in 5D may be regarded as multiply imaged in 4D, and ... More

The Dispersion Relation for Matter Waves in a Two-Phase VacuumNov 01 2014The cosmological constant (lambda) of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional theory of the type needed for unification. The exact 5D solution for lambda less than 0 shows waves in ordinary 3D space ... More

The Physical Nature of Five-Dimensional Solutions: A SurveyApr 16 2011The basic quasi-Schwarzschild 5D objects known as solitons have a long history, which is reviewed. Then some material is added, leading to the inference that a soliton is a singularity in the geometry which represents a bivalent source of gravitational ... More

The Embedding of General Relativity in Five-Dimensional Canonical Space: A Short History and a Review of Recent Physical ProgressOct 31 2010Einstein theory can be embedded in Kaluza-Klein theory, and in particular all 4D vacuum solutions can be embedded in 5D (pure) canonical space where spacetime is independent of the extra coordinate. The uniqueness of 5D canonical space is quickly reproven, ... More

Consequences of Kaluza-Klein CovarianceMay 01 2009The group of coordinate transformations for 5D noncompact Kaluza-Klein theory is broader than the 4D group for Einstein's general relativity. Therefore, a 4D quantity can take on different forms depending on the choice for the 5D coordinates. We illustrate ... More

Wave Mechanics and General Relativity: A RapprochementJan 16 2006Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.

Vacuum InstabilityJul 09 2004Mar 30 2005Following fresh attempts to resolve the problem of the energy density of the vacuum, we reconsider the case where the cosmological constant is derived from a higher-dimensional version of general relativity, and interpret the gauge-dependence of $\Lambda ... More

Dynamical Implications of Adjustments to Proper Time Caused by Higher Dimensions: A NoteNov 11 2010When the proper time of general relativity is adjusted to reflect the possible existence of higher dimensions, small dynamical effects appear in spacetime of the sort usually associated with the cosmological constant, Hubble's Law and Heisenberg's relation. ... More

The Status of Modern Five-Dimensional GravityNov 10 2014Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such theories smoothly ... More

Transformity: The Dependence of the Laws of Physics on Higher-Dimensional Coordinate TransformationsJun 28 2013In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in (say) five ... More

Astronomy and the Fifth DimensionJan 01 2013Astronomy is a precise and relatively simple science because objects accelerate in a gravitational field at the same rate, irrespective of their composition. Galileo knew this, and Einstein took it as the basis for general relativity. Surprisingly, it ... More

Classical Universes and Quantized Particles from Five-Dimensional Null PathsMar 15 2009All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a quantized particle. ... More

Quantization in Spacetime from Null Paths in Higher DimensionsDec 11 2008Jan 25 2009Massive particles on timelike paths in spacetime can be viewed as moving on null paths in a higher-dimensional manifold. This and other consequences follow from the use of Campbell's theorem to embed 4D general relativity in non-compactified 5D Kaluza-Klein ... More

An Embedding for General Relativity and its Implications for New PhysicsMay 01 2007We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological "constant" that is a specific function of ... More

In Defense of Campbell's Theorum as a Frame for New PhysicsJul 25 2005The Campbell-Magaard theorem is widely seen as a way of embedding Einstein's 4D theory of general relativity in a 5D theory of the Kaluza-Klein type. We give a brief history of theorem, present a short account of it, and show that it provides a geometrical ... More

Higher-Dimensional Communication and S.E.T.IDec 24 2013Jun 07 2014In cosmologies with more than four dimensions, of the type required for unification, it is possible for signals to have velocities in excess of that of light. Using a five-dimensional model which otherwise agrees with observations, two subjects are reviewed: ... More

Panspermia, Past and Present: Astrophysical and Biophysical Conditions for the Dissemination of Life in SpaceOct 30 2010Astronomically, there are viable mechanisms for distributing organic material throughout the Milky Way. Biologically, the destructive effects of ultraviolet light and cosmic rays means that the majority of organisms arrive broken and dead on a new world. ... More

The Equivalence Principle as a Probe for Higher DimensionsJan 17 2006Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical ... More

Limiting the Oscillations in Queues with Delayed Information Through a Novel Type of Delay AnnouncementFeb 20 2019Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information might be delayed or customers might require time to travel to the queue ... More

Mach, the Universe, and Foundations of MechanicsAug 15 2011Feb 06 2012Barbour's response to our recent paper on "Mach's principle and higher-dimensional dynamics" describes an approach to Mach's principle in which the universe as a whole is involved in the definition of inertial frames of reference. Moreover, Barbour's ... More

The Cosmological Constant Problem and Kaluza-Klein TheoryApr 15 2001We present technical results which extend previous work and show that the cosmological constant of general relativity is an artefact of the reduction to 4D of 5D Kaluza-Klein theory (or 10D superstrings and 11D supergravity). We argue that the distinction ... More

Gauge-Dependent Cosmological "Constant"Jan 01 2004Jun 09 2004When the cosmological constant of spacetime is derived from the 5D induced-matter theory of gravity, we show that a simple gauge transformation changes it to a variable measure of the vacuum which is infinite at the big bang and decays to an astrophysically-acceptable ... More

Universe Models with a Variable Cosmological "Constant" and a "Big Bounce"Jul 28 2001We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and manifests itself ... More

Gravitational conformal invariance and coupling constants in Kaluza-Klein theoryMar 12 2000Dec 17 2000We introduce a generalized gravitational conformal invariance in the context of non-compactified 5D Kaluza-Klein theory. It is done by assuming the 4D metric to be dependent on the extra non-compactified dimension. It is then shown that the conformal ... More

Radiating sources in higher-dimensional gravityApr 03 2001Jul 04 2001We study a time-dependent 5D metric which contains a static 4D sub-metric whose 3D part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of spherically-symmetric solutions. ... More

The Big Bang as a Phase TransitionOct 13 2003Jan 13 2005We study a five-dimensional cosmological model, which suggests that the universe bagan as a discontinuity in a (Higgs-type) scalar field, or alternatively as a conventional four-dimensional phase transition.

Mach's Principle and Higher-Dimensional DynamicsJun 29 2011Dec 16 2011We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B experiment. Furthermore, ... More

An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansionMay 04 2005May 08 2005We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.

Universes encircling 5-dimensional black holesSep 01 2003Jan 07 2004We clarify the status of two known solutions to the 5-dimensional vacuum Einstein field equations derived by Liu, Mashhoon & Wesson (LMW) and Fukui, Seahra & Wesson (FSW), respectively. Both 5-metrics explicitly embed 4-dimensional Friedman-Lemaitre-Robertson-Walker ... More

Wave Mechanics and the Fifth DimensionJan 28 2013Replacing 4D Minkowski space by 5D canonical space leads to a clearer derivation of the main features of wave mechanics, including the wave function and the velocity of de Broglie waves. Recent tests of wave-particle duality could be adapted to investigate ... More

Roundness properties of ultrametric spacesJan 31 2012Feb 22 2013We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric spaces into Euclidean ... More

Null Geodesics in Five Dimensional ManifoldsMay 11 2001We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that ... More

The Structure of the Big Bang from Higher-Dimensional EmbeddingsFeb 04 2002We give relations for the embedding of spatially-flat Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat manifolds of the type used in Kaluza-Klein theory. We present embedding diagrams that depict different 4D universes as hypersurfaces ... More

A Scalar Field and the Einstein Vacuum in Modern Kaluza-Klein TheorySep 23 2012Jan 25 2013Five-dimensional relativity as an extension of general relativity has field equations that simplify considerably given the adoption of a new gauge. The result is a scalar field governed by the Klein-Gordon equation, in an empty spacetime with a cosmological ... More

Kaluza-Klein GravityMay 07 1998We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identified and contrasted: compactified, projective and noncompactified. We discuss the cosmological ... More

Application of the Campbell-Magaard theorem to higher-dimensional physicsFeb 05 2003Apr 10 2003Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and ... More

Spatial Boundaries and the Local Context of Residential SegregationSep 08 2015Spatial boundaries are a defining feature of a city's social and spatial organization. Rivers, highways, and train tracks create excess distance between nearby locations and often mark social separation -- they become dividing lines that are well known ... More

MasersApr 12 2011An astrophysical MASER (Microwave Amplification by Stimulated Emission of Radiation) is a source of stimulated spectral line emission. Maser emission is observed from the circumstellar envelopes of evolved stars, molecular clouds/star-forming regions, ... More

Homological stability of non-orientable mapping class groups with marked pointsJun 06 2008Wahl recently proved that the homology of the non-orientable mapping class group stabilizes as the genus increases. In this short note we analyse the situation where the underlying non-orientable surfaces have marked points.

Sparse effective membership problems via residue currentsMar 20 2009Aug 20 2010We use residue currents on toric varieties to obtain bounds on the degrees of solutions to polynomial ideal membership problems. Our bounds depend on (the volume of) the Newton polytope of the polynomial system and are therefore well adjusted to sparse ... More

Projections of probability distributions: A measure-theoretic Dvoretzky theoremFeb 16 2011Apr 21 2011Many authors have studied the phenomenon of typically Gaussian marginals of high-dimensional random vectors; e.g., for a probability measure on $\R^d$, under mild conditions, most one-dimensional marginals are approximately Gaussian if $d$ is large. In ... More

Quantitative asymptotics of graphical projection pursuitNov 17 2008Apr 20 2009There is a result of Diaconis and Freedman which says that, in a limiting sense, for large collections of high-dimensional data most one-dimensional projections of the data are approximately Gaussian. This paper gives quantitative versions of that result. ... More

Two multivariate central limit theoremsJun 06 2007In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a basis of the ... More

KermionsOct 18 2013Oct 30 2013In the framework of quantum field theory in curved space-time, we study the quantization of a massless fermion field on a non-extremal Kerr black hole. The key theme in this note is the fundamental difference between scalar and fermion fields for the ... More

On a representation of the fundamental class of an ideal due to Lejeune-JalabertApr 19 2013Feb 24 2016Lejeune-Jalabert showed that the fundamental class of a Cohen-Macaulay ideal $\mathfrak a\subset \mathcal O_0$ admits a representation as a residue, constructed from a free resolution of $\mathfrak a$, multiplied by a certain differential form coming ... More

Analysis of a data matrix and a graph: Metagenomic data and the phylogenetic treeFeb 27 2012In biological experiments researchers often have information in the form of a graph that supplements observed numerical data. Incorporating the knowledge contained in these graphs into an analysis of the numerical data is an important and nontrivial task. ... More

Subtraction Division GamesDec 30 2011Jun 01 2012A Subtraction-Division game is a two player combinatorial game with three parameters: a set S, a set D, and a number n. The game starts at n, and is a race to say the number 1. Each player, on their turn, can either move the total to n-s for some s in ... More

Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebraNov 13 2013It is shown that any generalized Kac-Moody Lie algebra g that has no mutually orthogonal imaginary simple roots can be written as the vector space direct sum of a Kac-Moody subalgebra and subalgebras isomorphic to free Lie algebras over certain modules ... More

Large-N_c QCDMay 07 2009Jul 30 2009A brief review of large-N_c QCD and the 1/N_c expansion is given. Important results for large-N_c mesons and baryons are highlighted.

Baryon Masses in the 1/N ExpansionNov 08 2000The masses of baryons and heavy quark baryons are studied analytically in an expansion in 1/N, SU(3) flavor symmetry breaking and heavy-quark symmetry breaking. The measured baryon masses are in striking agreement with the 1/N hierarchy.

Chiral Lagrangian for Baryons in the $1/N_c$ ExpansionOct 01 1995A $1/\N$ expansion of the chiral Lagrangian for baryons is formulated and used to study the low-energy dynamics of baryons interacting with the pion nonet $\pi$, $K$, $\eta$ and $\eta^\prime$ in a combined expansion in chiral symmetry breaking and $1/\N$. ... More

Multi-Model Cantor SetsFeb 19 2002In this paper we define a new class of metric spaces, called multi-model Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz map from one ... More

Products of residue currents of Cauchy-Fantappiè-Leray typeDec 02 2005With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy-Fantappi\`e-Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete ... More

Residue currents constructed from resolutions of monomial idealsFeb 27 2007Jul 05 2008Given a free resolution of an ideal $J$ of holomorphic functions, one can construct a vector valued residue current $R$, whose annihilator is precisely $J$. In this paper we compute $R$ in case $J$ is a monomial ideal and the resolution is a cellular ... More

Maximal Newton points and the quantum Bruhat graphJun 23 2016Jun 25 2018We discuss a surprising relationship between the partially ordered set of Newton points associated to an affine Schubert cell and the quantum cohomology of the complex flag variety. The main theorem provides a combinatorial formula for the unique maximum ... More

Threats of Human Error in a High-Performance Storage System: Problem Statement and Case StudyDec 17 2004System administration is a difficult, often tedious, job requiring many skilled laborers. The data that is protected by system administrators is often valued at or above the value of the institution maintaining that data. A number of ethnographic studies ... More

On the topology of holomorphic bundlesMar 24 1997In this work we study the topology of holomorphic rank two bundles over complex surfaces. We consider bundles that are constructed by glueing and show that under certain conditions the topology of the bundle does not depend on the glueing. We present ... More

Some variants of Macaulay's and Max Noether's theoremsAug 21 2010We use residue currents on toric varieties to obtain bounds on the support of solutions to polynomial ideal membership problems. Our bounds depend on the Newton polytopes of the polynomial systems and are therefore well adjusted to sparse systems of polynomials. ... More

Hawking radiation from rotating brane black holesAug 20 2007Aug 28 2007We review recent work on the Hawking radiation of rotating brane black holes, as may be produced at the LHC. We outline the methodology for calculating the fluxes of particles, energy and angular momentum by spin-0, spin-1/2 and spin-1 quantum fields ... More

Borcherds' proof of the Conway-Norton conjectureMar 25 2009We give a summary of R. Borcherds' solution (with some modifications) to the following part of the Conway-Norton conjectures: Given the Monster simple group and Frenkel-Lepowsky-Meurman's moonshine module for the group, prove the equality between the ... More

An open-closed cobordism category with background spaceFeb 04 2009In this paper we introduce an open-closed cobordism category with maps to a background space. We identify the classifying space of this category for certain classes of background space. The key ingredient is the homology stability of mapping class groups ... More

Atiyah Jones conjecture for blown-up surfacesMar 08 2004Mar 04 2008We show that if the Atiyah Jones conjecture holds for a surface $X,$ then it also holds for the blow-up of $X$ at a point. Since the conjecture is known to hold for ${\mathbb P}^2$ and for ruled surfaces, it follows that the conjecture is true for all ... More

Chern Classes of Bundles over Rational SurfacesNov 15 1997Jul 27 1998Consider the blow up $\pi: \widetilde{X} \to X$ of a rational surface $X$ at a point. Let $\widetilde{V}$ be a holomorphic bundle over $\widetilde{X}$ whose restriction to the exceptional divisor equals ${\cal{O}(j) \oplus {\cal O}(-j)$ and define $V ... More

Classical Yang-Mills black hole hair in anti-de Sitter spaceJan 03 2008The properties of hairy black holes in Einstein-Yang-Mills (EYM) theory are reviewed, focusing on spherically symmetric solutions. In particular, in asymptotically anti-de Sitter space (adS) stable black hole hair is known to exist for su(2) EYM. We review ... More

On the approximate normality of eigenfunctions of the LaplacianMay 09 2007The main result of this paper is a bound on the distance between the distribution of an eigenfunction of the Laplacian on a compact Riemannian manifold and the Gaussian distribution. If $X$ is a random point on a manifold $M$ and $f$ is an eigenfunction ... More

The Spatial Proximity and Connectivity (SPC) Method for Measuring and Analyzing Residential SegregationSep 11 2015Aug 24 2017In recent years, there has been increasing attention to the spatial dimensions of residential segregation, such as the spatial arrangement of segregated neighborhoods and the geographic scale or relative size of segregated areas. However, the methods ... More

The Divergence Index: A Decomposable Measure of Segregation and InequalityAug 05 2015Dec 05 2016Decomposition analysis is a critical tool for understanding the social and spatial dimensions of inequality, segregation, and diversity. In this paper, I propose a new measure - the Divergence Index - to address the need for a decomposable measure of ... More

On Polyhedral Product Spaces over Polyhedral JoinsSep 21 2017The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler's $J$-construction and simplicial wedge construction. This article gives a cohomological decomposition of ... More

Instability of sphaleron black holes in asymptotically anti-de Sitter space-timeApr 05 2016May 12 2016We prove that sphaleron black holes in ${\mathfrak {su}}(2)$ Einstein-Yang-Mills-Higgs theory with a Higgs doublet in four-dimensional, asymptotically anti-de Sitter space-time are unstable.

Testing the Leptogenesis Mechanism of the Seesaw ModelMar 08 2004The seesaw theory, the leading theory for particle interactions, provides a viable mechanism for generating the matter-antimatter asymmetry of the universe. Testing the leptogenesis mechanism directly requires measurement of the d=6 operator of the low-energy ... More

Heavy Baryon Masses in the $1/m_Q$ and $1/N_c$ ExpansionsApr 01 1996Sep 02 1996The masses of baryons containing a single heavy quark are studied in a combined expansion in $1/m_Q$, $1/N_c$ and $SU(3)$ flavor symmetry breaking. Heavy quark baryon mass splittings are related to mass splittings of the octet and decuplet baryons. The ... More

Frobenius-Perron Theory of Modified ADE Bound Quiver AlgebrasJan 04 2018Sep 27 2018The Frobenius-Perron dimension for an abelian category was recently introduced. We apply this theory to the category of representations of the finite-dimensional radical squared zero algebras associated to certain modified ADE graphs. In particular, we ... More

A GIT Construction of Moduli Spaces of Stable Maps in Positive CharacteristicJul 13 2007Aug 27 2007In a previous paper, the author and David Swinarski constructed the moduli spaces of stable maps, \bar M_g,n(P^r,d), via geometric invariant theory (GIT). That paper required the base field to be the complex numbers, a restriction which this paper removes: ... More

On the Cohomology Ring of Real Moment-Angle ComplexesMay 30 2019In this article, we study the cohomology ring of real moment-angle complexes over a simplicial complex $K$. Combinatorial generators for the cohomology can be given in terms of $K$. For $K$ the boundary of an $n$-gon, we give a full description of the ... More

Folded ribbon knots in the planeJun 29 2018This survey reviews Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a ribbon, and the ribbonlength problem asks to minimize the ribbonlength for ... More

Interstitial Content DetectionAug 13 2017Interstitial content is online content which grays out, or otherwise obscures the main page content. In this technical report, we discuss exploratory research into detecting the presence of interstitial content in web pages. We discuss the use of computer ... More

Two applications of instanton numbersJul 08 2002The two applications are: 1. sometimes instanton numbers stratify moduli of bundles better than Chern numbers. 2. sometimes instanton numbers distinguish singularities better than the classical numerical invariants.

Measuring Inequality and SegregationAug 05 2015In this paper, I introduce the Divergence Index, a conceptually intuitive and methodologically rigorous measure of inequality and segregation. The index measures the difference between a distribution of interest and another empirical, theoretical, or ... More

Maximal Newton points and the quantum Bruhat graphJun 23 2016We discuss a surprising relationship between the partially ordered set of Newton points associated to an affine Schubert cell and the quantum cohomology of the complex flag variety. The main theorem provides a combinatorial formula for the unique maximum ... More