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Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory PhysicsMar 13 2019Mar 18 2019What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence between formal ... More

The impact of epistemology on learning: A case study from introductory physicsOct 31 2004Nov 11 2004We discuss a case study of the influence of epistemology on learning for a student in an introductory college physics course. An analysis of videotaped class work, written work, and interviews indicates that many of the student's difficulties were epistemological ... More

Incorporating Disciplinary Practices Into Characterizations of Progress in Responsive TeachingFeb 16 2015Responsive teaching, in which teachers adapt instruction based on close attention to the substance of students' ideas, is typically characterized along two dimensions: the level of detail at which teachers attend and respond to students' ideas, and the ... More

How substance-based ontologies for gravity can be productive: A case studyMay 06 2013Many science education researchers have argued that learners' commitment to a substance (matter-based) ontology impedes the learning of scientific concepts that scientists typically conceptualize as processes or interactions, such as such as force, electric ... More

Toward affect-inclusive models of cognitive dynamics: Coupling epistemological resources and emotionsJul 04 2013Many prominent lines of research on student's reasoning and conceptual change within learning sciences and physics education research have not attended to the role of learners' affect or emotions in the dynamics of their conceptual reasoning. This is ... More

"Classical-ish": Negotiating the boundary between classical and quantum particlesJul 02 2015Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we examine video ... More

'Because math': Epistemological stance or defusing social tension in QM?Jul 02 2015In collaborative small-group work, physics students need to both manage social conflict and grapple with conceptual and epistemological differences. In this paper, we document several outlets that students use as tools for managing social conflict when ... More

Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory PhysicsMar 13 2019What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence between formal ... More

How students blend conceptual and formal mathematical reasoning in solving physics problemsFeb 16 2011Dec 05 2013Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving expertise in ... More

"Bring it on": Explaining persistence in science at the intersection of identity and epistemologyFeb 16 2015Research has documented a sharp decline in students' interest and persistence in science, starting in middle school, particularly among students from underrepresented populations. In working to address this problem, we can learn a great deal from positive ... More

Logical Modelling of Physarum PolycephalumMay 20 2011We propose a novel model of unconventional computing where a structural part of computation is presented by dynamics of plasmodium of Physarum polycephalum, a large single cell. We sketch a new logical approach combining conventional logic with process ... More

Non-Abelian Cut Constructions and Hyperkähler ModificationsFeb 09 2010We discuss a general framework for cutting constructions and reinterpret in this setting the work on non-Abelian symplectic cuts by Weitsman. We then introduce two analogous non-Abelian modification constructions for hyperk\"ahler manifolds: one modifies ... More

Bigness in compatible systemsAug 13 2009Apr 21 2010Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if rho is an l-adic representation of the absolute Galois group of a number field for which the residual representation rho-bar comes from a modular ... More

Quaternionic Kähler Manifolds of Cohomogeneity OneAug 21 1998Nov 24 1998Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group preserving each ... More

On Creativity of Elementary Cellular AutomataMay 11 2013We map cell-state transition rules of elementary cellular automata (ECA) onto the cognitive control versus schizotypy spectrum phase space and interpret cellular automaton behaviour in terms of creativity. To implement the mapping we draw analogies between ... More

Modifying hyperkaehler manifolds with circle symmetryOct 24 2005Oct 25 2005A construction is introduced for modifying hyperkaehler manifolds with tri-Hamiltonian circle action, that in favourable situations increases the second Betti number by one. This is based on the symplectic cut construction of Lerman. In 4 or 8 dimensions ... More

Hypertoric manifolds and hyperKähler moment mapsJul 14 2016We discuss various aspects of moment map geometry in symplectic and hyperK\"ahler geometry. In particular, we classify complete hyperK\"ahler manifolds of dimension $4n$ with a tri-Hamiltonian action of a torus of dimension $n$, without any assumption ... More

Toric Hypersymplectic QuotientsApr 30 2004May 06 2004We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The image of the hypersymplectic moment ... More

A Gaussian distribution for refined DT invariants and 3D partitionsMar 15 2013We show that the refined Donaldson-Thomas invariants of C3, suitably normalized, have a Gaussian distribution as limit law. Combinatorially these numbers are given by weighted counts of 3D partitions. Our technique is to use the Hardy-Littlewood circle ... More

Behrend's function is constant on Hilb^n(C^3)Dec 15 2012May 15 2013We prove that Behrend's function is constant on Hilb^n(C^3). A calculation of motivic zeta functions shows the relevant Milnor fibers have zero Euler characteristic. As a corollary we see that Hilb^n(C^3) is generically reduced. These results extend to ... More

Counterexamples To Bertini Theorems for Test IdealsAug 29 2016In algebraic geometry, Bertini theorems are an extremely important tool. A generalization of the classical theorem to multiplier ideals show that multiplier ideals restrict to a general hyperplane section. In characteristic $p > 0$, the test ideal can ... More

Obstructions to compatible splittingsJan 07 2015Suppose one has a map of split short exact sequences in a category of modules, or more generally, in any abelian category. Do the short exact sequences split compatibly, i.e., does there exist a splitting of each short exact sequence which commutes with ... More

Towards plant wiresJan 17 2014In experimental laboratory studies we evaluate a possibility of making electrical wires from living plants. In scoping experiments we use lettuce seedlings as a prototype model of a plant wire. We approximate an electrical potential transfer function ... More

Patterns of conductivity in excitable automata with updatable intervals of excitationsFeb 25 2013We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's neighbourhood. ... More

Simulating strange attraction of acellular slime mould Physarum polycephaum to herbal tabletsDec 11 2012Plasmodium of acellular slime mould Physarum polycephalum exhibits traits of wave-like behaviour. The plasmodium's behaviour can be finely tuned in laboratory experiments by using herbal tablets. A single tablet acts as a fixed attractor: plasmodium propagates ... More

On growing connected beta-skeletonsApr 07 2013A $\beta$-skeleton, $\beta \geq 1$, is a planar proximity undirected graph of an Euclidean points set, where nodes are connected by an edge if their lune-based neighbourhood contains no other points of the given set. Parameter $\beta$ determines the size ... More

Slime mould logical gates: exploring ballistic approachMay 13 2010Plasmodium of \emph{Physarum polycephalum} is a single cell visible by unaided eye. On a non-nutrient substrate the plasmodium propagates as a traveling localization, as a compact wave-fragment of protoplasm. The plasmodium-localization travels in its ... More

Bayesian Statistical PragmatismJun 16 2011Discussion of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]

Rejoinder: Struggles with Survey Weighting and Regression ModelingOct 26 2007Rejoinder: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]

Stability in the homology of congruence subgroupsJan 23 2012Feb 10 2015The homology groups of many natural sequences of groups $\{G_n\}_{n=1}^{\infty}$ (e.g. general linear groups, mapping class groups, etc.) stabilize as $n \rightarrow \infty$. Indeed, there is a well-known machine for proving such results that goes back ... More

Small generating sets for the Torelli groupJun 16 2011Nov 02 2011Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup of the mapping class group has a finite generating set whose size grows cubically with respect to the genus of the surface. Our main tool is a new space called the handle graph ... More

Absolute Whitehead torsionFeb 16 2005We refine the Whitehead torsion of a chain equivalence of finite chain complexes in an additive category $\bA$ from an element of $\widetilde{K}^{iso}_1(\bA)$ to an element of the absolute group $K_1^{iso}(\bA)$. We apply this invariant to symmetric Poincar\'e ... More

Anisotropic Structures and Wormholes with Loop Quantum Gravity Holonomy CorrectionsJul 30 2011Oct 19 2011Anisotropic spherically symmetric systems are studied in the connection and densitized triad variables used in loop quantum gravity. The material source is an anisotropic fluid, which is arguably the most commonly used source term in anisotropic studies ... More

Integration in General RelativityFeb 14 1998This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial space-time geometry. ... More

Magnetic Field Evolution During Neutron Star RecyclingApr 27 2004I describe work on two aspects of magnetic field evolution relevant for the "recycling" scenario for making millisecond radio pulsars. First, many of the theoretical ideas for bringing about accretion-induced field decay rely on dissipation of currents ... More

Detectability of Extrasolar Planets in Radial Velocity SurveysAug 25 2004Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long periods and low ... More

Bounds to unitary evolutionMay 13 2007Upper and lower bounds are established for the survival probability $|<\psi(0)|\psi(t)>|^{2}$ of a quantum state, in terms of the energy moments $<\psi(0)|H^{n}|\psi(0)>$. Introducing a cut-off in the energy generally enables considerable improvement ... More

The evolution of oscillator wave functionsSep 20 2015We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical period of oscillation. ... More

Algebraic Poincare cobordismAug 30 2000This paper is an introduction to the use of the cobordism of chain complexes with Poincar\'e duality in surgery theory. It is a companion to the author's paper "An introduction to algebraic surgery" math.AT/0008071 (to appear in Volume 2 of Surveys in ... More

An introduction to algebraic surgeryAug 09 2000Browder-Novikov-Sullivan-Wall surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory (such as the Wall ... More

Active stabilisation, quantum computation and quantum state synthesisNov 16 1996Active stabilisation of a quantum system is the active suppression of noise (such as decoherence) in the system, without disrupting its unitary evolution. Quantum error correction suggests the possibility of achieving this, but only if the recovery network ... More

The Smooth Structure of the Space of Piecewise-Smooth LoopsMar 05 2008We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the action of the ... More

Generalizing the Kodama State I: ConstructionNov 14 2006The Kodama State is unique in being an exact solution to all the ordinary constraints of canonical quantum gravity that also has a well defined semi-classical interpretation as a quantum version of a classical spacetime, namely (anti)de Sitter space. ... More

Gauge Gravity: a forward-looking introductionOct 27 2010This article is a review of modern approaches to gravity that treat the gravitational interaction as a type of gauge theory. The purpose of the article is twofold. First, it is written in a colloquial style and is intended to be a pedagogical introduction ... More

A surgery formula for the 2-loop piece of the LMO invariant of a pairNov 04 2002Let \Theta (M,K) denote the 2-loop piece of (the logarithm of) the LMO invariant of a knot K in M, a ZHS^3. Forgetting the knot (by which we mean setting diagrams with legs to zero) specialises \Theta (M,K) to \lambda (M), Casson's invariant. This note ... More

Worst-case time decremental connectivity and k-edge witnessOct 30 2008We give a simple algorithm for decremental graph connectivity that handles edge deletions in worst-case time $O(k \log n)$ and connectivity queries in $O(\log k)$, where $k$ is the number of edges deleted so far, and uses worst-case space $O(m^2)$. We ... More

Cutoff for Extensions of Massive Gravity and Bi-GravityJun 01 2015Jun 25 2015Recently there has been interest in extending ghost-free massive gravity, bi-gravity, and multi-gravity by including non-standard kinetic terms and matter couplings. We first review recent proposals for this class of extensions, emphasizing how modifications ... More

Primitive prime factors in second order linear recurrence sequencesDec 27 2012For a class of Lucas sequences ${x_n}$, we show that if $n$ is a positive integer then $x_n$ has a primitive prime factor which divides $x_n$ to an odd power, except perhaps when $n = 1, 2, 3 or 6$. This has several desirable consequences.

Correlation Between GC-content and Palindromes in Randomly Generated Sequences and Viral GenomesFeb 24 2013GC-content, the ratio of guanine and cytosine bases in an entire nucleotide sequence, and palindromic sequences are unique for every organism due to genomic evolution. The goals of our research was to establish a correlation between GC-content and palindromic ... More

The AGN-starburst connection, Galactic superwinds, and M_BH - sigmaNov 01 2005Recent observations of young galaxies at redshifts z ~ 3 have revealed simultaneous AGN and starburst activity, as well as galaxy-wide superwinds. I show that there is probably a close connection between these phenomena by extending an earlier treatment ... More

Parameterizing solutions to any Galois embedding problem over Z/p^nZ with elementary p-abelian kernelSep 19 2011Mar 27 2014In this paper we use the Galois module structure for the classical parameterizing spaces for elementary p-abelian extensions of a field K to give necessary and sufficient conditions for the solvability of any embedding problem which is an extension of ... More

Strong Clustering in the Low Redshift Lyman-$α$ ForestMay 10 1996The two-point correlation function, $\xi$, of Lyman-alpha forest is found to be large, $\xi = 1.8^{+1.6}_{-1.2}$, > 90% confidence level, on the scale of 250-500 km/s for a sample of absorbers (0 < z < 1.3) assembled from HST Key Project Observations. ... More

Acyclic and Star Colorings of CographsMar 29 2011An \emph{acyclic coloring} of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of \emph{star coloring} requires that the union of any two color classes ... More

Luminosities, Masses and Star Formation Rates of Galaxies at High Redshift (IAU279 conference proceedings)Jan 09 2013There has been great progress in recent years in discovering star forming galaxies at high redshifts (z>5), close to the epoch of reionization of the intergalactic medium (IGM). The WFC3 and ACS cameras on the Hubble Space Telescope have enabled Lyman ... More

Near-Infrared Emission Line Searches for High-Redshift GalaxiesNov 19 1999In this article I review recent developments in near-infrared emission line searches for star-forming galaxies at high redshift. Using the J-, H- & K-bands we can potentially chart the history of star formation over the range 1<z<5 using the prominent ... More

Diversities and ConformitiesJul 07 2013Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform continuity, ... More

Q-ball Formation in Affleck-Dine Baryogenesis with Gravity-mediated SUSY BreakingDec 02 2004To date, the properties of Q-balls arising from an Affleck-Dine condensate in gravity-mediated SUSY breaking have been obtained primarily through numerical simulations. In this work, we will derive the expected charge of the Q-balls formed in such a scenario ... More

Approaches for Synthesis Conjectures in an SMT SolverNov 14 2014Oct 09 2015This report describes several approaches for handling synthesis conjectures within an Satisfiability Modulo Theories (SMT) solver. We describe approaches that primarily focus on determining the unsatisfiability of the negated form of synthesis conjectures ... More

A simple formula for gravitational MHV amplitudesApr 09 2012A simple formula is given for the n-field tree-level MHV gravitational amplitude, based on soft limit factors. It expresses the full S_n symmetry naturally, as a determinant of elements of a symmetric (n \times n) matrix.

The box integrals in momentum-twistor geometryApr 19 2010An account is given of how the 'box integrals', as used for one-loop calculations in massless field theory, appear in momentum-twistor geometry. Particular attention is paid to the role of compact contour integration in representing the Feynman propagator ... More

Eliminating spurious poles from gauge-theoretic amplitudesMay 11 2009This note addresses the problem of spurious poles in gauge-theoretic scattering amplitudes. New twistor coordinates for the momenta are introduced, based on the concept of dual conformal invariance. The cancellation of spurious poles for a class of NMHV ... More

Twistor diagrams for all tree amplitudes in gauge theory: a helicity-independent formalismDec 29 2005Jan 11 2006We give a new formalism for pure gauge-theoretic scattering at tree-amplitude level. We first describe a generalization of the Britto-Cachazo-Feng recursion relation in which a significant restriction is removed. We then use twistor diagrams to express ... More

A new Truncated Fourier Transform algorithmOct 17 2012Jan 29 2013Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring ... More

Upper bounds on the number of conjugacy classes in unitriangular groupsNov 19 2014Mar 30 2015We provide a new upper bound on the number of conjugacy classes in the group $U_n(q)$ of unitriangular matrices over a finite field. We also compute a similar upper bound for every group in the lower central series of $U_n(q)$.

Singularities of ordinary deformation ringsNov 15 2011Let R^univ be the universal deformation ring of a residual representation of a local Galois group. Kisin showed that many loci in MaxSpec(R^univ[1/p]) of interest are Zariski closed, and gave a way to study the generic fiber of the corresponding quotient ... More

Parametric Bounded Löb's Theorem and Robust Cooperation of Bounded AgentsFeb 12 2016Aug 24 2016L\"ob's theorem and G\"odel's theorems make predictions about the behavior of systems capable of self-reference with unbounded computational resources with which to write and evaluate proofs. However, in the real world, systems capable of self-reference ... More

The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifoldMay 30 2006A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an infinite sequence of penetrations into a neighborhood of a cone singularity, so that the sequence of depths of maximal penetration has a limiting distribution. The distribution function ... More

Generalized Microlensing Effective TimescaleDec 23 2013Dec 26 2013The microlensing effective timescale t_eff=beta*t_E is used frequently in high-magnification (beta << 1) microlensing events, because it is better constrained than either the impact parameter beta or the Einstein timescale t_E separately. It also facilitates ... More

WFIRST Ultra-Precise Astrometry I: Kuiper Belt ObjectsMar 17 2014Aug 02 2014I show that the WFIRST microlensing survey will enable detection and precision orbit determination of Kuiper Belt Objects (KBOs) down to H_=28.2 over an effective area of about 17 sq.deg. Typical fractional period errors will be about 1.5% x 10^(0.4(H-28.2)) ... More

Post-Decadal White Paper: A Dual-Satellite Dark-Energy/Microlensing NASA-ESA MissionSep 30 2010A confluence of scientific, financial, and political factors imply that launching two simpler, more narrowly defined dark-energy/microlensing satellites will lead to faster, cheaper, better (and more secure) science than the present EUCLID and WFIRST ... More

Wide Field Imager in Space for Dark Energy and PlanetsFeb 12 2009A wide-field imager in space could make remarkable progress in two very different frontiers of astronomy: dark energy and extra-solar planets. Embedding such an imager on a much larger and more complicated DE mission would be a poor science-approach under ... More

Optimal Microlensing ObservationsJul 31 1998One of the major limitations of microlensing observations toward the Large Magellanic Cloud (LMC) is the low rate of event detection. What can be done to improve this rate? Is it better to invest telescope time in more frequent observations of the inner ... More

Microlens Parallax Asymmetries Toward the LMCFeb 11 1998If the microlensing events now being detected toward the Large Magellanic Cloud (LMC) are due to lenses in the Milky Way halo, then the events should typically have asymmetries of order 1% due to parallax from the reflex motion of the Earth. By contrast, ... More

chi^2 and Linear FitsOct 20 2003The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the end provides ... More

Analytic Study of Grid Star and Reference Star Selection for the Space Interferometry MissionFeb 16 2001May 18 2001Grid stars and reference stars provide the fundamental global and local astrometric reference frames for observations by the Space Interferometry Mission. They must therefore be astrometrically stable at the ~1 uas level. I present simple formulae in ... More

A New Argument Against An Intervening Stellar Population Toward the LMCFeb 26 1999Mar 10 1999Zaritsky & Lin have claimed detection of an intervening population of stars toward the Large Magellanic Cloud (LMC) which, they believe, could account for a substantial fraction of the observed microlensing events. I show that the observed time scales ... More

Extreme MicrolensingMar 27 1996Extreme microlensing events, defined as events with maximum magnification $A_\max\gsim 200$ are a potentially powerful probe of the mass spectrum and spatial distribution of objects along lines of sight toward the Galactic bulge. About 75 yr${}^{-1}$ ... More

Self-Lensing By A Stellar DiskAug 01 1994I derive a general expression for the optical depth $\tau$ for gravitational lensing of stars in a disk by Massive Compact Objects (Machos) in the same disk. For the more restricted case where the disk is self-gravitating and the stars and Machos have ... More

The Hollywood Strategy for Microlensing Detection of PlanetsAug 09 1996Follow the big stars! I review the theory of detection and parameter measurement of planetary systems by follow-up observations of ongoing microlensing events. Two parameters can generically be measured from the event itself: the planet/star mass ratio, ... More

Microlensing Search of $10^6$ QuasarsApr 26 1995By monitoring $10^6$ quasars one could search for lensing by stars and Massive Compact Halo Objects (Machos) out to redshifts $z\sim 4$. If Machos have a present cosmological density $\Omega_{L,0}=1\%$, then the expected event rate is $\Gamma\sim 200\,\yr^{-1}$. ... More

A note on Gornik's perturbation of Khovanov-Rozansky homologyDec 13 2010Dec 26 2010We show that the information contained in the associated graded vector space to Gornik's version of Khovanov-Rozansky knot homology is equivalent to a single even integer s_n(K). Furthermore we show that s_n is a homomorphism from the smooth knot concordance ... More

Heat Equations in $\mathbb{R}\times\mathbb{C}$Aug 29 2005Jun 30 2006Let $p:\mathbb{C}\to\mathbb{R}$ be a subharmonic, nonharmonic polynomial and $\tau$ a real parameter. Define $\bar{Z}_{\tau p} = \partial_{\bar z} + \tau p_{\bar z}$, a closed, densely-defined operator on $L^2(\mathbb{C})$. If $\Box_{\tau p} = \bar{Z}_{\tau ... More

Diffraction at the TevatronOct 09 2007This article contains a summary of the recent results in diffractive physics at the Tevatron. Results from the CDF diffraction program include the single diffractive to non-diffractive ratio in dijet events, observation of exclusive $e^+e^-$ production ... More

Prospects of Forward Energy Flow and Low-x Physics at the LHCOct 09 2007The LHC will soon provide proton-proton collisions at the unprecedented center of mass energy, $\sqrt{s}=$14 TeV. This not only allows us to probe new regions of high-$p_T$ physics, but also low-$x$ and forward physics. A selection of potential measurements ... More

Beta Distribution of Human MTL Neuron Sparsity: A Sparse and Skewed CodeAug 18 2015Single unit recordings in the human medial temporal lobe (MTL) have revealed a population of cells with conceptually based, highly selective activity, indicating the presence of a sparse neural code. Building off previous work by the author and J.C. Collins, ... More

Weak amenability for dynamical systemsDec 06 2016Using the recently developed notion of a Herz--Schur multiplier of a C*-dynamical system we introduce weak amenability of C*- and W*-dynamical systems. As a special case we recover Haagerup's characterisation of weak amenability of a discrete group. We ... More

A fast C++ implementation of thermal functionsFeb 08 2018We provide a small C++ library with Mathematica and Python interfaces for computing thermal functions, defined $$ J_\text{B/F}(y^2) \equiv \Re \int_0^\infty x^2 \log\left[1 \mp e^{-\sqrt{x^2 + y^2}} \right] \,\text{d}x, $$ which appear in finite-temperature ... More

Electromagnetic self-force for axially symmetric charge on a spherical shellSep 26 2018Sep 27 2018We obtain the fields and electromagnetic self-force of a charge distributed on the surface of a sphere undergoing rigid motion at constant proper acceleration, where the charge distribution has axial symmetry about the direction of motion. A closed-form ... More

Classification of Certain Subgroups of G2Jan 14 2015May 19 2015We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type G2, focusing on the case of number fields and p-adic fields. In the same context we characterize the rational conjugacy classes of A2 subgroups of ... More

Generative complexity of Gray-Scott modelOct 28 2016In the Gray-Scott reaction-diffusion system one reactant is constantly fed in the system, another reactant is reproduced by consuming the supplied reactant and also converted to an inert product. The rate of feeding one reactant in the system and the ... More

Higher Commutator Theory for Congruence Modular VarietiesOct 22 2016Mar 04 2017We develop the basic properties of the higher commutator for congruence modular varieties.

Graphical methods establishing nontriviality of state cycle Khovanov homology classesJul 02 2009We determine when certain state cycles represent nontrivial Khovanov homology classes by analyzing features of the state graph. Using this method, we are able to produce hyperbolic knots with arbitrarily many diagonals containing nontrivial state cycle ... More

A note on the connectivity of certain complexes associated to surfacesDec 26 2006Nov 28 2007This note is devoted to a trick which yields almost trivial proofs that certain complexes associated to topological surfaces are connected or simply connected. Applications include new proofs that the complexes of curves, separating curves, nonseparating ... More

Yet More Smooth Mapping Spaces and Their Smoothly Local PropertiesJan 23 2013Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of smoothly local ... More

Delegating Custom Object Detection Tasks to a Universal Classification SystemDec 19 2013In this paper, a concept of multipurpose object detection system, recently introduced in our previous work, is clarified. The business aspect of this method is transformation of a classifier into an object detector/locator via an image grid. This is a ... More

Pointwise Estimates for Relative Fundamental Solutions of Heat Equations in $\mathbb{R}\times\mathbb{C}$May 12 2006Let $p:C\to R$ be a subharmonic, nonharmonic polynomial and $\tau\in R$ a parameter. Define $\bar Z_{\tau p} = \partial_{\bar z} + \tau p_{\bar z} = e^{-\tau p} p_{\bar z} e^{\tau p}$, a closed, densely defined operator on $L^2(C)$. If $\Box_{\tau p} ... More

Comparative SmootheologyFeb 15 2008May 21 2010We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Fr\"olicher, Sikorski, Smith, and Souriau. The method of comparison is to construct functors between the categories that enable us ... More

Using Dynamical Systems to Construct Infinitely Many PrimesAug 23 2017Euclid's proof can be reworked to construct infinitely many primes, in many different ways, using ideas from arithmetic dynamics. After acceptance Soundararajan noted the beautiful and fast converging formula: $$ \tau = a^{1/(d-1)} x_0 \cdot \lim_{n\to ... More

Tilting modules for cyclotomic Schur algebrasMay 14 2002This paper investigates the tilting modules of the cyclotomic q-Schur algebras, the Young modules of the Ariki-Koike algebras, and the interconnections between them. The main tools used to understand the tilting modules are contragredient duality, and ... More

Cycle groups for Artin stacksOct 28 1998We construct an algebraic homology functor for Artin stacks of finite type over a field, and we develop intersection-theoretic properties.