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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

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

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

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

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

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.

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.

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

Multiple ionisation sources in HII regions and their effect on derived nebular abundancesSep 18 2009We present a theoretical investigation of the effect of multiple ionisation sources in HII regions on the total elemental abundances derived from the analysis of collisionally excited emission lines. We focus on empirical methods based on direct temperature ... 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

An exact self-similar solution for an expanding ball of radiationFeb 10 2004Nov 28 2005We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation ... 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

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

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

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

Approximation of projections of random vectorsDec 10 2009Feb 15 2011Let $X$ be a $d$-dimensional random vector and $X_\theta$ its projection onto the span of a set of orthonormal vectors $\{\theta_1,...,\theta_k\}$. Conditions on the distribution of $X$ are given such that if $\theta$ is chosen according to Haar measure ... More

Linear instability criteria for ideal fluid flows subject to two subclasses of perturbationsJan 14 2011In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and those in the ... More

Moduli of bundles on the blown-up planeOct 16 1998Let M(j) denote the moduli space of bundles on the blown-up plane which restrict to the exceptional divisor as O(j)+O(-j). We show that there is a topological embedding of M(j) into M(j+1).

Heavy Meson Masses in Chiral Perturbation Theory with Heavy Quark SymmetryDec 21 1992The $SU(3)$ and hyperfine mass splittings of mesons containing a single heavy quark are computed to one-loop order in chiral perturbation theory with heavy quark spin symmetry. Electromagnetic contributions of order $\alpha_em$ are included. The observed ... More

On weighted Bochner-Martinelli residue currentsOct 05 2009We study the weighted Bochner-Martinelli residue current R^p(f) associated with a sequence f=(f_1,...,f_m) of holomorphic germs at the origin in C^n, whose common zero set equals the origin, and p=(p_1,..., p_m)\in N^n. Our main results are a description ... More

Residue currents of monomial idealsNov 15 2005We compute residue currents of Bochner-Martinelli type associated with a monomial ideal $I$, by methods involving certain toric varieties. In case the variety of $I$ is the origin, we give a complete description of the annihilator of the currents in terms ... More

Black holes, TeV-scale gravity and the LHCJun 23 2013Jun 28 2013Over the past 15 years models with large extra space-time dimensions have been extensively studied. We have learned from these models that the energy scale of quantum gravity may be many orders of magnitude smaller than the conventional value of 10^19 ... More

Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie TypesNov 13 2013Jun 04 2014A Peterson variety is a subvariety of the flag variety $G/B$ which appears in the construction of the quantum cohomology of partial flag varieties. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert ... More

$K$-theory and homotopies of 2-cocycles on transformation groupsFeb 13 2014Sep 08 2014This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G}$ induces an isomorphism of the $K$-theory ... More

$K$-theory and homotopies of 2-cocycles on group bundlesAug 06 2014Oct 27 2014This paper continues the author's program to investigate the question of when a homotopy of 2-cocycles $\Omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G}$ induces an isomorphism of the $K$-theory groups of the twisted ... More

$K$-theory and homotopies of 2-cocycles on higher-rank graphsMar 15 2014May 19 2015This paper continues our investigation into the question of when a homotopy $\omega = \{\omega_t\}_{t \in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of the twisted ... More

On the Cohomology Ring of Real Moment-Angle ComplexesMay 30 2019Jun 11 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

Holomorphic Rank Two Vector Bundles on Blow-upsJan 12 1996In this paper we study holomorphic rank two vector bundles on the blow up of $ {\bf C}^2$ at the origin. A classical theorem of Birchoff and Grothendieck says that any holomorphic vector bundle on the projective plane ${\bf P}^1$ splits into a sum of ... More

Holomorphic bundles on O(-k) are algebraicAug 23 1996Sep 10 1996We show that holomorphic bundles on O(-k) for k > 0 are algebraic. We also show holomorphic bundles on O(-1) are trivial outside the zero section.

Linear functions on the classical matrix groupsSep 20 2005Jun 12 2006Let $M$ be a random matrix in the orthogonal group $\O_n$, distributed according to Haar measure, and let $A$ be a fixed $n\times n$ matrix over $\R$ such that $\tr(AA^t)=n$. Then the total variation distance of the random variable $\tr(AM)$ to standard ... More

The Spatial Context of Residential SegregationSep 11 2015Feb 15 2016Residential segregation is defined in a variety of ways to address a common concern: to what extent do social groups reside in separate or distinct places. The spatial pattern of segregation varies widely across cities, and distinct spatial patterns can ... More

Baryon Magnetic Moments in the 1/N_c Expansion with Flavor Symmetry BreakingNov 08 2011Nov 29 2011The magnetic moments and transition magnetic moments of the ground state baryons are analyzed in an expansion in 1/N_c, SU(3) flavor symmetry breaking and isospin symmetry breaking. There is clear evidence in the experimental data for the hierarchy of ... More

The Rare Top Decays $t \to b W^+ Z$ and $t \to c W^+ W^-$Nov 30 1996Dec 20 1996The large value of the top quark mass implies that the rare top decays $t \rightarrow b W^+ Z, s W^+ Z$ and $d W^+ Z$, and $t \rightarrow c W^+ W^-$ and $u W^+ W^-$, are kinematically allowed decays so long as $m_t \ge m_W + m_Z + m_{d_i} \approx 171.5 ... More

Update of Heavy Baryon Mass PredictionsSep 18 1996Predictions of unknown heavy baryon masses based on an expansion in $1/m_Q$, $1/N_c$ and $SU(3)$ breaking are updated to take into account a recent measurement of the $\Sigma_c^*$ mass. Values are given for the two remaining unknown charm baryon masses ... More

Fractal dimensions of subfractals induced by sofic subshiftsJan 19 2016In this paper, we will consider subfractals of hyperbolic iterated function systems which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a subshift of finite type or sofic subshift on the symbolic ... More

Source Code for Computing Giambelli's Formula for Type $E$ Peterson VarietiesNov 12 2013This document is a companion to the paper "Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie Types." We provide the source code for computing the Giambelli's formula in types $E_6$ $E_7$ and $E_8$.

The Containment Poset of Type $A$ Hessenberg VarietiesOct 15 2017Flag varieties are well-known algebraic varieties with many important geometric, combinatorial, and representation theoretic properties. A Hessenberg variety is a subvariety of a flag variety identified by two parameters: an element $X$ of the Lie algebra ... More

Quadrisecants and essential secants of knots: with applications to the geometry of knotsAug 08 2016A quadrisecant line is one which intersects a curve in at least four points, while an essential secant captures something about the knottedness of a knot. This survey article gives a brief history of these ideas, and shows how they may be applied to questions ... More

A note on the singularities of residue currents of integrally closed idealsJan 05 2019Feb 25 2019Given a free resolution of an ideal $\mathfrak a$ of holomorpic functions there is an associated residue current $R$ that coincides with the classical Coleff-Herrera product if $\mathfrak a$ is a complete intersection ideal and whose annihilator ideal ... More

Spectral bounds on orbifold isotropyJan 30 2003We first show that a Laplace isospectral family of Riemannian orbifolds, satisfying a lower Ricci curvature bound, contains orbifolds with points of only finitely many isotropy types. If we restrict our attention to orbifolds with only isolated singularities, ... 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

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

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

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

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

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