Results for "Marcia Burton"

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Diffusion Anomaly in a three dimensional lattice gasApr 27 2007We investigate the relation between thermodynamic and dynamic properties of an associating lattice gas (ALG) model. The ALG combines a three dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of ... More
Stable Configurations of repelling Points on compact ManifoldsFeb 28 2012This is an expanded version of [arXiv:1107.4836v1 [math.DS]]. Using techniques from [Chapter XI, The Selberg Trace Formula, in Eigenvalues in Riemannian Geometry, by Isaac Chavel], in which a differential-geometrically intrinsic treatment of counterparts ... More
Naive entropy of dynamical systemsMar 21 2015Feb 20 2016We study an invariant of dynamical systems called naive entropy, which is defined for both measurable and topological actions of any countable group. We focus on nonamenable groups, in which case the invariant is two-valued, with every system having naive ... More
Efficient treatment of bilinear forms in global optimizationMar 20 2018We efficiently treat bilinear forms in the context of global optimization, by applying McCormick convexification and by extending an approach of Saxena, Bonami and Lee for symmetric quadratic forms to bilinear forms. A key application of our work is in ... More
Conventional Beams or Neutrino Factories: The Next Generation of Accelerator-Based Neutrino ExperimentsAug 21 2000The purpose of this paper is to provoke a discussion about the right next step in accelerator-based neutrino physics. In the next five years many experiments will be done to determine the neutrino mixing parameters. However, the small parameters $\theta_{13}\Delta ... More
Ecosystems, from life, to the Earth, to the GalaxyOct 31 2001Ecosystems are systems where energy flows and material cycles are maintained in an apparently stable, but non-equilibrium state through a process of self-regulation. Such a definition does just apply to biological systems, it can also apply to systems ... More
Growth of torsion of elliptic curves with odd-order torsion over quadratic cyclotomic fieldsApr 05 2016Apr 28 2016Let $K = \mathbb{Q}(\sqrt{-3})$ or $\mathbb{Q}(\sqrt{-1})$ and let $C_n$ denote the cyclic group of order $n$. We study how the torsion part of an elliptic curve over $K$ grows in a quadratic extension of $K$. In the case $E(K)[2] \approx C_1$ we investigate ... More
Stable Configurations of repelling points on compact hyperbolic ManifoldsJul 25 2011It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases
Unification of gravity and the harmonic oscillator on a quantum black hole horizon I: Nonperturbative particle scattering and Veneziano amplitudesJul 14 2003Nov 03 2003A relativistic quantum model of particle scattering near the horizon of a microscopic black hole unifies gravity and the harmonic-oscillator force. The model is obtained by modifying a harmonic-oscillator nonstandard Lagrangian for a closed system of ... More
Towards Alzheimer's Disease Classification through Transfer LearningNov 29 2017Detection of Alzheimer's Disease (AD) from neuroimaging data such as MRI through machine learning have been a subject of intense research in recent years. Recent success of deep learning in computer vision have progressed such research further. However, ... More
Assessment and OutlookJan 04 2000Jan 10 2000My assignment at this conference is to assess where we are in high-energy physics and speculate on where we might be going. This frees me from any obligation to summarize all that went on here and allows me to talk just about those topics that interest ... More
A Short Guide to Anyons and Modular FunctorsOct 17 2016To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to combine anyons, ... More
Spectra of Gauge Code HamiltoniansJan 10 2018We study the spectral gap of frustrated spin (qubit) Hamiltonians constructed from quantum subsystem (gauge) codes. Such a Hamiltonian can be block diagonalized, with blocks labelled by eigenvalues of extensively many integrals of motion (stabilizers ... More
A Hardy-type result on the average of the lattice point error term over long intervalsJul 31 2015Feb 04 2016Suppose $D$ is a suitably admissible compact subset of $\mathbb{R}^k$ having a smooth boundary with possible zones of zero curvature. Let \mbox{$R(T,\theta,x)= N(T,\theta,x) - T^{k}\mathrm{vol}(D)$,} where $N(T,\theta,x)$ is the number of integral lattice ... More
A topological semigroup structure on the space of actions modulo weak equivalenceJan 19 2015We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space of actions ... More
Gluon sivers and experimental considerations for TMDsDec 14 2012The study and characterisation of transverse-momentum-dependent distribution functions (TMDs) is a major goal of the Electron-Ion Collider (EIC) physics programme. The study of gluon TMDs poses a greater challenge than for quark TMDs in DIS measurements, ... More
Completely positive entropy actions of sofic groups with $\mathbb{Z}$ in their centerSep 06 2015Mar 31 2016Let $\Gamma$ be a sofic group with a copy of $\mathbb{Z}$ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving $\Gamma$ actions with completely positive entropy, none of which is a factor of a Bernoulli shift. ... More
Topology and convexity in the space of actions modulo weak equivalenceJan 16 2015Jan 05 2016We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex combination. We show ... More
Phase-Boundaries near Critical End points: Applications to Cross-linked CopolymersDec 17 1997The phase behavior of a cross-linked polymer blend made of two incompatible species, $A$ and $B$, of different chemical nature is analyzed. Besides a homogeneous phase, this system also exhibits two microphases and a phase of total segregation. The transition ... More
On the periodic "good" Boussinesq equationJun 22 2009Aug 07 2009We study the well-posedness of the initial-value problem for the periodic nonlinear "good" Boussinesq equation. We prove that this equation is local well-posed for initial data in Sobolev spaces \textit{$H^s(\T)$} for $s>-1/4$, the same range of the real ... More
Uniform mixing and completely positive sofic entropyMar 30 2016Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to produce an ... More
Modelling collisions in a relativistic plasmaOct 22 2009Generalising the work of Lenard and Bernstein, we introduce a new, fully relativistic model to describe collisional plasmas. Like the Fokker-Planck operator, this equation represents velocity diffusion and conserves particle number. However, unlike the ... More
Molecular Hydrogen in the Lagoon: H2 line emission from Messier 8Jan 30 2002The 2.12 micron v=1-0 S(1) line of molecular hydrogen has been imaged in the Hourglass region of M8. The line is emitted from a roughly bipolar region, centred around the O7 star Herschel 36. The peak H2 1-0 S(1) line intensity is 8.2 x 10E-15 erg s-1 ... More
Points of order 13 on elliptic curvesAug 30 2016Oct 15 2016We pick up the study of 13-torsion in elliptic curves where Mazur and Tate left off 45 years ago. We consider various questions concerning elliptic curves defined over the maximal totally real subfield of the 13th cyclotomic field (where J_1(13) acquires ... More
Failure of the $L^1$ pointwise ergodic theorem for $\mathrm{PSL}_2(\mathbb{R})$Jan 04 2019Mar 23 2019Amos Nevo established the pointwise ergodic theorem in $L^p$ for measure-preserving actions of $\mathrm{PSL}_2(\mathbb{R})$ on probability spaces with respect to ball averages and every $p>1$. This paper shows by explicit example that Nevo's Theorem cannot ... More
Improved Upper Bounds for the Information Rates of the Secret Sharing Schemes Induced by the Vamos MatroidSep 17 2008An access structure specifying the qualified sets of a secret sharing scheme must have information rate less than or equal to one. The Vamos matroid induces two non-isomorphic access structures V1 and V6, which were shown by Marti-Farre and Padro to have ... More
The Pachner graph and the simplification of 3-sphere triangulationsNov 18 2010Feb 23 2011It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can ... More
The cusped hyperbolic census is completeMay 12 2014From its creation in 1989 through subsequent extensions, the widely-used "SnapPea census" now aims to represent all cusped finite-volume hyperbolic 3-manifolds that can be obtained from <= 8 ideal tetrahedra. Its construction, however, has relied on inexact ... More
Approximation of Measures on S^n by discrete MeasuresJan 10 2006We study the asymptotic behavior of discrete measures on S^{n-1} that are induced by radially projecting point masses concentrated on the integral lattice-points within dilates of a compact body D, for various classes of D. The results depend sensitively ... More
Combinatorial Seifert fibred spaces with transitive cyclic automorphism groupApr 11 2014Jul 10 2015In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of 3-manifolds with ... More
Uniform mixing and completely positive sofic entropyMar 30 2016Nov 02 2016Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to produce an ... More
Computational topology with Regina: Algorithms, heuristics and implementationsAug 13 2012Feb 22 2013Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structures, census enumeration, combinatorial recognition of triangulations, and ... More
Detecting genus in vertex links for the fast enumeration of 3-manifold triangulationsJan 16 2011Mar 16 2011Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they ... More
Searching a bitstream in linear time for the longest substring of any given densityOct 19 2009Jun 07 2010Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) ... More
A duplicate pair in the SnapPea censusNov 29 2013Feb 18 2014We identify a duplicate pair in the well-known Callahan-Hildebrand-Weeks census of cusped finite-volume hyperbolic 3-manifolds. Specifically, the six-tetrahedron non-orientable manifolds x101 and x103 are homeomorphic.
Face pairing graphs and 3-manifold enumerationJul 30 2003Nov 20 2003The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible ... More
Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings via Transfer-ImpedancesApr 02 2004Let G be a finite graph or an infinite graph on which Z^d acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is infinite, known methods show that this still makes sense, ... More
Point Mutations and Transitions Between Cellular Automata Attractor BasinsJun 17 2003We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t sites in that state. Results of such mutations are described by a rule-dependent ... More
High-resolution imaging of compact high-velocity cloudsDec 20 1999Six examples of the compact, isolated high-velocity HI clouds (CHVCs) identified by Braun and Burton (1999) have been imaged with the WSRT. The 65 confirmed objects in this class define a dynamically cold system, with a global minimum for the velocity ... More
The Determinant and Volume of 2-Bridge Links and Alternating 3-BraidsApr 07 2017We examine the conjecture, due to Champanerkar, Kofman, and Purcell that $\text{vol}(K) < 2 \pi \log \det (K)$ for alternating hyperbolic links, where $\text{vol}(K) = \text{vol}(S^3\backslash K)$ is the hyperbolic volume and $\det(K)$ is the determinant ... More
Astronomy in AntarcticaJul 13 2010Antarctica provides a unique environment for astronomy. The cold, dry and stable air found above the high plateau, as well as the pure ice below, offers new opportunities across the photon & particle spectrum. The summits of the plateau provide the best ... More
Stable configurations of repelling points on compact manifolds IIOct 14 2014Nov 16 2017This paper describes, in the case of the unit circle, several applications of a geometrically intrinsic treatment of counterparts of classical electrostatics, previously developed in [4] and [5].
A new approach to crushing 3-manifold triangulationsDec 06 2012Jan 06 2014The crushing operation of Jaco and Rubinstein is a powerful technique in algorithmic 3-manifold topology: it enabled the first practical implementations of 3-sphere recognition and prime decomposition of orientable manifolds, and it plays a prominent ... More
Converting between quadrilateral and standard solution sets in normal surface theoryJan 17 2009Sep 03 2009The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds ... More
The Spectra of Volume and Determinant Densities of LinksJul 07 2015The $\textit{volume density}$ of a hyperbolic link $K$ is defined to be the ratio of the hyperbolic volume of $K$ to the crossing number of $K$. We show that there are sequences of non-alternating links with volume density approaching $v_8$, where $v_8$ ... More
Information Rates of Minimal Non-Matroid-Related Access StructuresJan 23 2008In a secret sharing scheme, shares of a secret are distributed to participants in such a way that only certain predetermined sets of participants are qualified to reconstruct the secret. An access structure on a set of participants specifies which sets ... More
Quadrilateral-octagon coordinates for almost normal surfacesApr 20 2009Sep 05 2009Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this ... More
Optimizing the double description method for normal surface enumerationAug 29 2008May 20 2009Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, ... More
Maximal admissible faces and asymptotic bounds for the normal surface solution spaceApr 15 2010Dec 09 2010The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and ... More
Targeted Fibonacci ExponentiationNov 05 2017A targeted exponentiation algorithm computes a group exponentiation operation $a^k$ with a reversible circuit in such a way that the initial state of the circuit consists of only the base $a$ and fixed values, and the final state consists of only the ... More
A water-like model under confinement for hydrophobic and hydrophilic particle-plate interaction potentialsSep 24 2013Molecular dynamic simulations were employed to study a water-like model confined between hydrophobic and hydrophilic plates. The phase behavior of this system is obtained for different distances between the plates and particle-plate potentials. For both ... More
Liquid Polymorphism and Density Anomaly in a Lattice Gas ModelJul 29 2004We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom ... More
Finite Lattice and Phenomenological Approximations for the Anomaly in the Density of a Water-like Lattice Gas ModelNov 18 2011We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite lattice, so to ... More
Ion-ion correlations: an improved one-component plasma correctionOct 22 1999Based on a Debye-Hueckel approach to the one-component plasma we propose a new free energy for incorporating ionic correlations into Poisson-Boltzmann like theories. Its derivation employs the exclusion of the charged background in the vicinity of the ... More
Including Uncertainty when Learning from Human CorrectionsJun 06 2018Sep 13 2018It is difficult for humans to efficiently teach robots how to correctly perform a task. One intuitive solution is for the robot to iteratively learn the human's preferences from corrections, where the human improves the robot's current behavior at each ... More
GPU accelerated Nature Inspired Methods for Modelling Large Scale Bi-Directional Pedestrian MovementDec 16 2014Pedestrian movement, although ubiquitous and well-studied, is still not that well understood due to the complicating nature of the embedded social dynamics. Interest among researchers in simulating pedestrian movement and interactions has grown significantly ... More
Points of order 13 on elliptic curvesAug 30 2016Sep 16 2016We pick up the study of 13-torsion in elliptic curves where Mazur and Tate left off 45 years ago. We consider various questions concerning elliptic curves defined over the maximal totally real subfield of the 13th cyclotomic field (where J_1(13) acquires ... More
Structures of small closed non-orientable 3-manifold triangulationsNov 07 2003Sep 15 2005A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by these 41 different ... More
Stable configurations of repelling points on compact manifolds IIOct 14 2014This paper describes, in the case of the unit circle, several applications of a geometrically intrinsic treatment of counterparts of classical electrostatics, previously developed in [4] and [5].
Complementary vertices and adjacency testing in polytopesFeb 18 2012Aug 26 2012Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency ... More
Enumeration of non-orientable 3-manifolds using face pairing graphs and union-findApr 27 2006Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning ... More
M51 Stripped To Its BonesApr 06 1993We present optical and IR surface photometry of M51 (NGC~5194) at B~V~R~I~J~K and CO$(2.3\mu )$. These data are used to establish whether K-band ($2.2\mu$) images of spiral galaxies provide reliable maps of stellar surface mass density features such as ... More
Supergravity from a Massive Superparticle and the Simplest Super Black HoleAug 24 1997Sep 20 1997We describe in superspace a theory of a massive superparticle coupled to a version of two dimensional N=1 dilaton supergravity. The (1+1) dimensional supergravity is generated by the stress-energy of the superparticle, and the evolution of the superparticle ... More
Sine-Gordon mean field theory of a Coulomb GasFeb 14 1997Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and three dimensions (3d) are obtained. When analyzed in terms ... More
A Neutral Polyampholyte in an ionic solutionMay 13 1996The behavior of a neutral polyampholyte ($PA$) chain with $N$ monomers, in an ionic solution, is analyzed in the framework of the full Debye-H$\ddot u $ckel-Bjerrum-Flory $(DHBjF)$ theory. A $PA$ chain, that in addition to the neutral monomers, also contains ... More
Charge renormalization and phase separation in colloidal suspensionsOct 23 2000We explore the effects of counterion condensation on fluid-fluid phase separation in charged colloidal suspensions. It is found that formation of double layers around the colloidal particles stabilizes suspensions against phase separation. Addition of ... More
Density anomaly in a competing interactions lattice gas modelSep 06 2004We study a very simple model of a short-range attraction and an outer shell repulsion as a test system for demixing phase transition and density anomaly. The phase-diagram is obtained by applying mean field analysis and Monte Carlo simulations to a two ... More
Potassium bromide, KBr/ε : New Force FieldNov 09 2016The correct description of the ionic interaction and stable equilibrium of the simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model of the monovalent ions is very important. The force field needs to reproduce ... More
Sodium Chloride, NaCl/ε : New Force FieldAug 08 2015A new computational model for Sodium Chloride, the NaCl/{\epsilon}, is proposed. The Force Fields employed here for the description of the NaCl is based on a set of radial particle-particle pair potentials involving Lennard-Jones (LJ) and Coulombic forces. ... More
Density Anomaly in Core-Softened Lattice GasAug 12 2004Oct 25 2004A two dimensional lattice gas model with ''core-softened'' potential is investigated. Two liquid phases and density anomaly are found. The demixing phase transition between the two liquid phases end at a tricritical point that is also the terminus of ... More
Relation between occupation in the first coordination shells and Widom line in Core-Softened PotentialsDec 27 2012Three core-softened families of potentials are checked for the presence of density and diffusion anomalies. These potentials exhibit a repulsive core with a softening region and at larger distances an attractive well. We found that the region in the pressure-temperature ... More
The Implicitly Constructible UniverseFeb 25 2017We answer several questions posed by Hamkins and Leahy concerning the implicitly constructible universe, Imp. Specifically, we show that it is relatively consistent with ZFC that Imp satisfies the negation of CH, that Imp is not HOD, and that Imp satisfies ... More
Enabling Robots to Infer how End-Users Teach and Learn through Human-Robot InteractionFeb 02 2019During human-robot interaction (HRI), we want the robot to understand us, and we want to intuitively understand the robot. In order to communicate with and understand the robot, we can leverage interactions, where the human and robot observe each other's ... More
Quantum statistics of atoms in microstructuresNov 09 1998This paper proposes groove-like potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For non-interacting particles ... More
Flexible Bond and Angle, FBA/epsilon model of waterJul 10 2018We propose a new flexible force field for water. The model in addition to the Lennard-Jones and electrostatic parameters, includes the flexibility of the OH bonds and angles. The parameters are selected to give the experimental values of the density and ... More
Flexible Polyelectrolytes with Monovalent SaltJul 23 2004We present a model for describing flexible polyelectrolytes in a good solvent a nd in the presence of monovalent salt . The molecule composed by $N$ monomers is characterized by the end to end distanc e $R_e=b (Z-1)^\gamma$ and the number of associated ... More
Aspects of Symmetry for Sparse Reflexive Generalized InversesMar 13 2019Fundamental in matrix algebra and its applications, a \emph{generalized inverse} of a real matrix $A$ is a matrix $H$ that satisfies the Moore-Penrose (M-P) property $AHA=A$. If $H$ also satisfies the additional useful M-P property, $HAH=H$, it is called ... More
Potassium bromide, KBr/ε : New Force FieldNov 09 2016Nov 14 2016The correct description of the ionic interaction and stable equilibrium of the simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model of the monovalent ions is very important. The force field needs to reproduce ... More
Thermodynamic and dynamic anomalous behavior in the TIP4P/ε water modelAug 08 2015Aug 11 2015The model Tip4p/{\epsilon} for water is tested for the presence of thermodynamic and dy- namic anomalies. Molecular dynamic simulations for this model were performed and we show that for this system the density versus temperature at constant pressure ... More
Anomalies in a waterlike model confined between platesDec 14 2012Using molecular dynamic simulations we study a waterlike model confined between two fixed hydrophobic plates. The system is tested for density, diffusion and structural anomalous behavior and compared with the bulk results. Within the range of confining ... More
Diffusion anomaly and dynamic transitions in the Bell-Lavis water modelJun 07 2010In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The Bell-Lavis model is defined on a triangular lattice in which water molecules are represented by particles ... More
Connection Between Minimum of Solubility and Temperature of Maximum Density in an Associating Lattice Gas ModelMay 09 2012In this paper we investigate the solubility of a hard - sphere gas in a solvent modeled as an associating lattice gas (ALG). The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties ... More
Hydration and anomalous solubility of the Bell-Lavis model as solventJul 08 2012We address the investigation of the solvation properties of the minimal orientational model for water, originally proposed by Bell and Lavis. The model presents two liquid phases separated by a critical line. The difference between the two phases is the ... More
Liquid polymorphism, order-disorder transitions and anomalous behavior: a Monte Carlo study of the Bell-Lavis model for waterJul 10 2009The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density ... More
Palatini Variational Principle for $N$-Dimensional Dilaton GravityOct 31 1997We consider a Palatini variation on a general $N$-Dimensional second order, torsion-free dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter ... More
The Kinematic and Spatial Deployment of Compact, Isolated High-Velocity CloudsOct 27 1998We have identified a class of high-velocity clouds which are compact and apparently isolated. The clouds are compact in that they have angular sizes less than 2 degrees FWHM. They are isolated in that they are separated from neighboring emission by expanses ... More
CHVCs: Galactic Building Blocks at z = 0Feb 16 2000A distinct sub-class of anomalous velocity HI emission features has emerged from recent high quality surveys of the Local Group environment, namely the compact high velocity clouds (CHVCs). A program of high-resolution imaging with the Westerbork array ... More
Geometric estimates from spanning surfacesAug 17 2016May 09 2017We derive bounds on the length of the meridian and the cusp volume of hyperbolic knots in terms of the topology of essential surfaces spanned by the knot. We provide an algorithmically checkable criterion that guarantees that the meridian length of a ... More
How to Lose with Least ProbabilityDec 09 2011Dec 13 2011Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin the player going ... More
Fixed parameter tractable algorithms in combinatorial topologyFeb 17 2014May 05 2014To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time ... More
An edge-based framework for enumerating 3-manifold triangulationsDec 05 2014A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for mathematicians, constructing them is difficult: the best algorithms to ... More
Simulations of Coulombic Fission of Charged Inviscid DropsJan 15 2011We present boundary-integral simulations of the evolution of critically charged droplets. For such droplets, small ellipsoidal perturbations are unstable and eventually lead to the formation of a "lemon"-shaped drop with very sharp tips. For perfectly ... More
Compact High-Velocity Clouds at High ResolutionDec 22 1999Six examples of the compact, isolated high-velocity clouds catalogued by Braun & Burton (1999) and identified with a dynamically cold ensemble of primitive objects falling towards the barycenter of the Local Group have been imaged with the Westerbork ... More
Weak containment of measure preserving group actionsNov 23 2016We survey recent progress in the theory of weak containment of measure preserving group actions.
Embeddings of 3-manifolds in S^4 from the point of view of the 11-tetrahedron censusOct 14 2008Sep 26 2012This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed ... More
A fast branching algorithm for unknot recognition with experimental polynomial-time behaviourNov 05 2012Oct 09 2014It is a major unsolved problem as to whether unknot recognition - that is, testing whether a given closed loop in R^3 can be untangled to form a plain circle - has a polynomial time algorithm. In practice, trivial knots (which can be untangled) are typically ... More
A tree traversal algorithm for decision problems in knot theory and 3-manifold topologyOct 29 2010Mar 30 2012In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial ... More
On the entropy of radiation reactionOct 22 2013The inexorable development of ever more powerful laser systems has re-ignited interest in electromagnetic radiation reaction and its significance for the collective behaviour of charged matter interacting with intense electromagnetic fields. The classical ... More
Computing the crosscap number of a knot using integer programming and normal surfacesJul 12 2011Mar 06 2012The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known. We ... More
Geometric estimates from spanning surfacesAug 17 2016We derive bounds on the length of the meridian and the cusp volume of hyperbolic knots in terms of the topology of essential surfaces spanned by the knot. We provide an algorithmically checkable criterion that guarantees that the meridian length of a ... More