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Results for "Colin Poole"

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Constraints on 3- and 4-loop $β$-functions in a general four-dimensional Quantum Field TheoryJun 11 2019The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the $\beta$-functions by parametrizing ... More
Constraints on 3- and 4-loop $β$-functions in a general four-dimensional Quantum Field TheoryJun 11 2019Jun 12 2019The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the $\beta$-functions by parametrizing ... More
On Weak Hamiltonicity of a Random HypergraphOct 27 2014A {\it weak (Berge) cycle} is an alternating sequence of vertices and (hyper)edges $C=(v_0, e_1, v_1, ..., v_{\ell-1}, e_\ell, v_{\ell}=v_0)$ such that the vertices $v_0, ..., v_{\ell-1}$ are distinct with $v_k, v_{k+1} \in e_{k}$ for each $k$, but the ... More
Consistency of non-minimal renormalisation schemesMar 23 2016Non-minimal renormalisation schemes such as the momentum subtraction scheme (MOM) have frequently been used for physical computations. The consistency of such a scheme relies on the existence of a coupling redefinition linking it to MSbar. We discuss ... More
The use of conflicts in searching Bayesian networksMar 06 2013This paper discusses how conflicts (as used by the consistency-based diagnosis community) can be adapted to be used in a search-based algorithm for computing prior and posterior probabilities in discrete Bayesian Networks. This is an "anytime" algorithm, ... More
Representing Bayesian Networks within Probabilistic Horn AbductionMar 20 2013This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions ... More
The homotopy operator method for symbolic integration by parts and inversion of divergences with applicationsAug 04 2009Aug 20 2009Using standard calculus, explicit formulas for one-, two- and three-dimensional homotopy operators are presented. A derivation of the one-dimensional homotopy operator is given. A similar methodology can be used to derive the multi-dimensional versions. ... More
A Framework for Decision-Theoretic Planning I: Combining the Situation Calculus, Conditional Plans, Probability and UtilityFeb 13 2013This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is essentially ... More
Robust split-step Fourier methods for simulating the propagation of ultra-short pulses in single- and two-mode optical communication fibersApr 06 2015Extensions of the split-step Fourier method (SSFM) for Schr\"odinger-type pulse propagation equations for simulating femto-second pulses in single- and two-mode optical communication fibers are developed and tested for Gaussian pulses. The core idea of ... More
Symmetric Collaborative Filtering Using the Noisy Sensor ModelJan 10 2013Collaborative filtering is the process of making recommendations regarding the potential preference of a user, for example shopping on the Internet, based on the preference ratings of the user and a number of other users for various items. This paper ... More
Efficient Inference in Large Discrete DomainsOct 19 2012In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables that have as ... More
The generalised Fitting subgroup of a profinite groupApr 02 2009The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, ... More
Hyperbolic KnotsSep 29 2003In 1978, W. Thurston revolutionized low diemsional topology with his work on hyperbolic 3-manifolds. In this paper, we discuss what is currently known about knots in the 3-sphere with hyperbolic complements. Then focus is on geometric invariants coming ... More
350 micron observations of local IRAS galaxies using SHARC-IIDec 12 2003The cosmologically significant population of dusty galaxies detected at sub-mm and mm wavelengths by SCUBA and MAMBO have played a central part in many of the discussions at this workshop. Obtaining their redshifts is critical in understanding their role ... More
The Top Quark and other Fermion MassesMar 28 1996Recent developments on approaches to the quark lepton mass problem are reviewed. In particular we discuss dynamical calculations of the top quark mass at (a) the infrared quasifixed point of the Minimal Supersymmetric Standard Model renormalisation group ... More
Approaches to threshold meson productionOct 15 1998Near-threshold data on meson production in nucleon-nucleon scattering are analysed in the short-range limit which permits a quantitative comparison of the production in two and three-body final states. The relative strengths of different meson productions ... More
eta meson production in nucleon-nucleon collisionsAug 03 2010New experimental data are presented on the energy dependence of the total cross sections for the np -> d eta and quasi-two-body pp -> pp eta reactions, where the final diproton is detected at very low excitation energy. Differential cross sections of ... More
SaturnalesJun 24 1998Un choix personnel a ete fait d'evenements memorables du programme de physique realise a Saturne-2 pendant les derniers 20 ans.
On the Density of Ranges of Generalized Divisor Functions with Restricted DomainsJul 09 2015We begin by defining functions $\sigma_{t,k}$, which are generalized divisor functions with restricted domains. For each positive integer $k$, we show that, for $r>1$, the range of $\sigma_{-r,k}$ is a subset of the interval $\displaystyle{\left[1,\frac{\zeta(r)}{\zeta((k+1)r)}\right)}$. ... More
Postorder PreimagesApr 06 2016Aug 06 2016Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$ and all permutations ... More
Writing Commutators of Commutators as Products of CubesJul 29 2015It is known that commutators of commutators can be written as products of cubes, with the current upper bound on the number of cubes being 60. We discuss how proofs extracted via coset enumeration can be used to investigate this problem, and exhibit a ... More
On Sparsely Schemmel Totient NumbersDec 09 2014For each positive integer $r$, let $S_r$ denote the $r^{th}$ Schemmel totient function, a multiplicative arithmetic function defined by \[S_r(p^{\alpha})=\begin{cases} 0, & \mbox{if } p\leq r; \\ p^{\alpha-1}(p-r), & \mbox{if } p>r \end{cases}\] for all ... More
A General Approach for Producing Hamiltonian Numerical Schemes for Fluid EquationsJan 26 2005Feb 24 2005Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical Hamiltonian system; this ... More
How to detect a genuine quantum pump effect in graphene?Apr 30 2013Jul 10 2013Quantum pumping in graphene has been predicted in recent years. Till date there have been no experiments indicating a graphene based quantum pump. This is not uncommon as in case of other non-Dirac behavior showing materials it has not yet been unambiguously ... More
Can dephasing generate non-local spin correlations?Oct 24 2011Jan 07 2012By examining the full counting statistics of a non adiabatic pure spin pump with particular emphasis on the second and third moments, it is shown that incoherent or sequential transport, in contrast to coherent transport, can change non-local spin shot ... More
Incoherence induced sign change in noise cross-correlations: A case study in the full counting statistics of a pure spin pumpAug 27 2008Oct 12 2009The full counting statistics of a non adiabatic pure spin pump are calculated with particular emphasis on the second and third moments. We show that incoherence can change the sign of spin shot noise cross-correlations from negative to positive, implying ... More
Resonances on some geometrically finite hyperbolic manifoldsDec 02 2004We prove the meromorphic extension to C for the resolvent of the Laplacian on a class of geometrically finite hyperbolic manifolds with infinite volume and we give a polynomial bound on the number of resonances. This class notably contains the geometrically ... More
Meromorphic properties of the resolvent on asymptotically hyperbolic manifoldsNov 24 2003Mar 29 2004We show that the resolvent of the Laplacian on asymptotically hyperbolic spaces extends meromorphically with finite rank poles to the complex plane if and only if the metric is `even' (in a sense). If it is not even, there exist some cases where the resolvent ... More
Random graphs from a weighted minor-closed classOct 09 2012There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a more general ... More
Connectivity for random graphs from a weighted bridge-addable classMar 15 2012Aug 01 2012There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable structured class, such as the class of all planar graphs. Here we consider a general 'bridge-addable' class of graphs - if a graph is in the ... More
On Arithmetic Functions Related to Iterates of the Schemmel Totient FunctionsJun 17 2015We begin by introducing an interesting class of functions, known as the Schemmel totient functions, that generalizes the Euler totient function. For each Schemmel totient function $L_m$, we define two new functions, denoted $R_m$ and $H_m$, that arise ... More
A new proof of Harish-Chandra's integral formulaDec 11 2017Jul 02 2018We present a new proof of Harish-Chandra's formula $$\Pi(h_1) \Pi(h_2) \int_G e^{\langle \mathrm{Ad}_g h_1, h_2 \rangle} dg = \frac{ [ \! [ \Pi, \Pi ] \!] }{|W|} \sum_{w \in W} \epsilon(w) e^{\langle w(h_1),h_2 \rangle},$$ where $G$ is a compact, connected, ... More
Fertility NumbersSep 11 2018A nonnegative integer is called a fertility number if it is equal to the number of preimages of a permutation under West's stack-sorting map. We prove structural results concerning permutations, allowing us to deduce information about the set of fertility ... More
Enumerating Cliques in Direct Product GraphsJul 17 2017Nov 19 2018The unitary Cayley graph of $\mathbb Z/n\mathbb Z$, denoted $G_{\mathbb Z/n\mathbb Z}$, is the graph with vertices $0,1,\ldots,$ $n-1$ in which two vertices are adjacent if and only if their difference is relatively prime to $n$. These graphs are central ... More
Catalan Intervals and Uniquely Sorted PermutationsApr 04 2019For each positive integer $k$, we consider five well-studied posets defined on the set of Dyck paths of semilength $k$. We establish bijections between uniquely sorted permutations that avoid various patterns and intervals in these posets. We end with ... More
Tutorial models of the climate and habitability of Proxima Centauri b: a thin atmosphere is sufficient to distribute heat given low stellar fluxAug 25 2016Proxima Centauri b, an Earth-size planet in the habitable zone of our nearest stellar neighbour, has just been discovered. A theoretical framework of synchronously rotating planets, in which the risk of a runaway greenhouse on the sunlight side and atmospheric ... More
Number and Luminosity Evolution of Interacting Galaxies as a Natural explanation for the Galaxy CountsMay 23 1995A newly developed isochrone synthesis algorithm for the photometric evolution of galaxies is described. Two initial mass functions, IMFs, in particular, the recent IMF determined by Kroupa, Tout, and Gilmore, three photometric transformations, and a 1-Gyr-burst ... More
SaturnaliaJun 24 1998A personal choice is made of the highlights of the physics programme carried out at the Saturne-2 facility over the last twenty years.
An Examination of Possible Gravitational Perturbations in the Transit Timing Variations of Exoplanet WASP-3bJun 21 2011Maciejewski et al. (2010) claim to have detected a possible sinusoidal variation in the transit timing variations of exoplanet WASP-3b, which is currently the only known planet orbiting the star WASP-3. According to Maciejewski's analysis, this signal ... More
Quadruple crossing number of knots and linksNov 12 2012Jan 28 2013A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, ... More
Hybrid mesons from lattice QCDSep 27 2000Recent lattice simulation studies of heavy-quark hybrid mesons in which the quark and antiquark are bound together by an excited gluon field are summarized.
Bayesian curve fitting for lattice gauge theoristsDec 17 2001A new method of extracting the low-lying energy spectrum from Monte Carlo estimates of Euclidean-space correlation functions which incorporates Bayesian inference is described and tested. The procedure fully exploits the information present in the correlation ... More
Detecting a true quantum pump effectAug 06 2005Oct 30 2006Even though quantum pumping is a very promising field, it has unfortunately not been unambiguously experimentally detected. The reason being that in the experiments the rectification effect overshadows the pumped current. One of the better known ways ... More
Spiders and Generalized ConfluenceSep 27 2018Sep 28 2018Given a semisimple Lie algebra $\mathfrak{g}$, we can represent invariants of tensor products of fundamental representations of the quantum enveloping algebra $U_q(\mathfrak{g})$ using particular directed graphs called webs. In particular webs are trivalent ... More
Resonances and scattering poles on asymptotically hyperbolic manifoldsMar 31 2004On an asymptotically hyperbolic manifold (X,g), we show that the resolvent resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for the special points n/2-k (with k>0 integer) where an additional term ... More
A univalent universe in finite order arithmeticDec 21 2014Jan 10 2015Homotopy Type Theory with a univalent universe $\,\mathcal{U}_0$ is interpreted at the strength of finite order arithmetic. We eliminate Grothendieck universes, avoid the axiom of replacement, and bound all uses of separation.
Generalized augmented alternating links and hyperbolic volumeJun 09 2015Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split reduced non-2-braid prime alternating projections. These links are known to be hyperbolic. Here, we extend to show that generalized ... More
Upper Bounds for Stern's Diatomic Sequence and Related SequencesJun 25 2015Let $(s_2(n))_{n=0}^\infty$ denote Stern's diatomic sequence. For $n\geq 2$, we may view $s_2(n)$ as the number of partitions of $n-1$ into powers of $2$ with each part occurring at most twice. More generally, for integers $b,n\geq 2$, let $s_b(n)$ denote ... More
Flexible Toggles and Symmetric Invertible Asynchronous Elementary Cellular AutomataNov 22 2015May 24 2018A sequential dynamical system (SDS) consists of a graph $G$ with vertices $v_1,v_2,\ldots,v_n$, a state set $A$, a collection of "vertex functions" $\{f_{v_i}\}_{i=1}^n$, and a permutation $\pi\in S_n$ that specifies how to compose these functions to ... More
Generalized Krein formula and determinants for even dimensional Poincare-Einstein manifoldsDec 08 2005Aug 02 2007For a class of even dimensional conformally compact manifolds (X,g), we define a generalized Krein spectral function by applying a renormalized trace functional to the spectral measure of the Laplacian. We then show that this is the phase of the Kontsevich-Vishik ... More
Counting 3-Stack-Sortable PermutationsMar 21 2019May 07 2019We prove a "Decomposition Lemma" that allows us to count preimages of certain sets of permutations under West's stack-sorting map $s$. As a first application, we give a new proof of Zeilberger's formula for the number of 2-stack-sortable permutations ... More
Triple Crossing Number of Knots and LinksJul 31 2012Sep 04 2012A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot ... More
A new paradigm for the universeNov 03 2003Jan 25 2012A new paradigm for the universe is presented in which the universe is far older than current estimates and there is no big bang.
Observation of M87 with VERITASSep 23 2007The giant radio galaxy M87 is the only extragalactic non-blazar object which has been detected as a source of very high energy gamma-rays. It represents a unique opportunity to study the phenomena of gamma-ray emission from a nearby AGN. In this paper ... More
An introduction to mesic nucleiJan 14 2016There is much speculation and a modest amount of evidence that certain mesons might form quasi-bound states with nuclei to produce really exotic states of matter. For this to be a practical possibility, the interaction between the meson and nucleons at ... More
COSY-11 : How will we remember it ?Sep 03 2007A personal selection is made of the highlights of the COSY-11 physics program undertaken at the COoler SYnchrotron of the Forschungszentrum Juelich. This has been particularly rich in the field of strange and non-strange meson production in proton-proton ... More
On the structure of just infinite profinite groupsJun 09 2009Jun 26 2009A profinite group $G$ is just infinite if every closed normal subgroup of $G$ is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup $H$ of $G$, there are only finitely many open normal subgroups ... More
Mony a Mickle Maks a Muckle: Minor Body Observations with Optical Telescopes of All SizesMar 17 2009I review the current capabilities of small, medium and large telescopes in the study of minor bodies of the Solar System (MBOSS), with the goal of identifying those areas where the next generation of Extremely Large Telescopes (ELTs) are required to progress. ... More
Some Poset Pattern-Avoidance Problems Posed by YakoubovAug 13 2016Extending the work of Yakoubov, we enumerate the linear extensions of comb posets that avoid certain length-$3$ patterns. We resolve many of Yakoubov's open problems and prove both of the conjectures from her paper.
Improved gluonic actions on anisotropic latticesAug 05 1996The use of novel perturbatively-improved gluonic actions on anisotropic lattices in which the temporal spacing is much smaller than that in the spatial directions is discussed. Such actions permit more efficient measurements of noisy correlation functions, ... More
A new paradigm for the universeNov 03 2003Dec 21 2017This book provides a completely new approach to understanding the universe. The main idea is that the principal objects in the universe form a spectrum unified by the presence of a massive or hypermassive black hole. These objects are variously called ... More
Connected Components of Complex Divisor FunctionsNov 12 2017May 04 2018For any complex number $c$, define the divisor function $\sigma_c\colon\mathbb N\to\mathbb C$ by $\displaystyle\sigma_c(n)=\sum_{d\mid n}d^c$. Let $\overline{\sigma_c(\mathbb N)}$ denote the topological closure of the range of $\sigma_c$. Extending previous ... More
On Ranges of Variants of the Divisor Functions that are DenseJul 04 2015For a real number $t$, let $s_t$ be the multiplicative arithmetic function defined by $\displaystyle{s_t(p^{\alpha})=\sum_{j=0}^{\alpha}(-p^t)^j}$ for all primes $p$ and positive integers $\alpha$. We show that the range of a function $s_{-r}$ is dense ... More
Crossed Andreev reflection as a probe for the pairing symmetry of Ferromagnetic SuperconductorsSep 26 2005Oct 30 2006The coexistence of superconductivity and ferromagnetism has brought about the phenomena of ferromagnetic superconductors. The theory needed to understand the compatibility of such antagonistic phenomena cannot be built until the pairing symmetry of such ... More
On 2-powerfully Perfect Numbers in Three Quadratic RingsDec 09 2014Dec 11 2014Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call $n$-powerfully perfect numbers in these rings. This definition serves to extend the concept of perfect numbers that have been defined ... More
An Extension of the Abundancy Index to Certain Quadratic RingsJun 17 2015We begin by introducing an extension of the traditional abundancy index to imaginary quadratic rings with unique factorization. After showing that many of the properties of the traditional abundancy index continue to hold in our extended form, we investigate ... More
Unitary Multiperfect Numbers in Certain Quadratic RingsDec 09 2014A unitary divisor $c$ of a positive integer $n$ is a positive divisor of $n$ that is relatively prime to $\displaystyle{\frac{n}{c}}$. For any integer $k$, the function $\sigma_k^*$ is a multiplicative arithmetic function defined so that $\sigma_k^*(n)$ ... More
Binary Codes and Period-2 Orbits of Sequential Dynamical SystemsSep 13 2015Sep 30 2017Let $[K_n,f,\pi]$ be the (global) SDS map of a sequential dynamical system (SDS) defined over the complete graph $K_n$ using the update order $\pi\in S_n$ in which all vertex functions are equal to the same function $f\colon\mathbb F_2^n\to\mathbb F_2^n$. ... More
Anti-Power Prefixes of the Thue-Morse WordJul 20 2016Oct 08 2016Recently, Fici, Restivo, Silva, and Zamboni defined a $k$-anti-power to be a word of the form $w_1w_2\cdots w_k$, where $w_1,w_2,\ldots,w_k$ are distinct words of the same length. They defined $AP(x,k)$ to be the set of all positive integers $m$ such ... More
Lens rigidity for manifolds with hyperbolic trapped setDec 04 2014Dec 21 2015For a Riemannian manifold $(M,g)$ with strictly convex boundary $\partial M$, the lens data consists in the set of lengths of geodesics $\gamma$ with endpoints on $\partial M$, together with their endpoints $(x_-,x_+)\in \partial M\times \partial M$ and ... More
Deconvolution by simulationAug 08 2007Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution of Y. We present ... More
Stack-Sorting Preimages of Permutation ClassesSep 10 2018Feb 11 2019We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of Bousquet-M\'elou. ... More
Preimages under the Stack-Sorting AlgorithmNov 18 2015Jun 02 2018We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and $t$-stack sortable ... More
B MixingMar 13 2001The neutral $B$ mesons, $B^0$ and $B_s$, can oscillate between their particle and antiparticle states owing to flavor-changing weak interactions. In recent years, techniques to detect these oscillations as a function of the meson's decay time have been ... More
The inhabitance paradox: how habitability and inhabitancy are inseparableMar 03 2016The dominant paradigm in assigning "habitability"' to terrestrial planets is to define a circumstellar habitable zone: the locus of orbital radii in which the planet is neither too hot nor too cold for life as we know it. One dimensional climate models ... More
Subgroups of finite index and the just infinite propertyMay 11 2009A residually finite (profinite) group $G$ is just infinite if every non-trivial (closed) normal subgroup of $G$ is of finite index. This paper considers the problem of determining whether a (closed) subgroup $H$ of a just infinite group is itself just ... More
Near-Threshold Production of $η$-MesonsJan 11 1993It is shown that the striking energy variation in the $p\, d \rightarrow \mbox{$^{\, 3}{\rm He}$}\, \eta$ cross section near threshold is probably due to a final state interaction associated with a large (complex) $\eta -\mbox{$^{3}{\rm He}$}$ scattering ... More
The Continuing Outburst of V1647~Orionis: Winter/Spring 2011 ObservationsAug 06 2011Aug 10 2011We present optical and near-IR observations of the young eruptive variable star V1647 Orionis which illuminates McNeil's Nebula. In late 2003, V1647 Ori was observed to brightened by around 5 mag to r'=17.7. In early 2006 the star faded back to its quiescent ... More
V2492 Cygni: The Early Evolution of the 2010 OutburstMay 04 2011We present Gemini-North optical and near-IR observations of a young eruptive star in Cygnus, designated as V2492 Cyg in the General Catalog of Variable Stars. This object is one of two young stars, located within 2 degrees of each other, that recently ... More
Sub-Compton quantum non-equilibrium and Majorana systemsJun 05 2013We study the Majorana equation from the point of view of the de Broglie-Bohm pilot-wave theory (according to which a quantum ensemble of fermions is not only described by a spinor but also by a distribution of position configurations). Although the Majorana ... More
Complex Divisor FunctionsFeb 11 2015For any complex number $c$, let $\sigma_c\colon\mathbb N\rightarrow\mathbb C$ denote the divisor function defined by $\sigma_c(n)=\displaystyle{\sum_{d|n}d^c}$ for all $n\in\mathbb N$, and define $R(c)=\{\sigma_c(n)\in\mathbb C\colon n\in\mathbb N\}$ ... More
Unique ergodicity of the automorphism group of the semigeneric directed graphFeb 13 2019We prove that the automorphism group of the semigeneric directed graph (in the sense of Cherlin's classification) is uniquely ergodic.
Lipschitz-free spaces and Schur propertiesMar 04 2016Apr 11 2017In this paper we study $\ell_1$-like properties for some Lipschitz-free spaces. The main result states that, under some natural conditions, the Lipschitz-free space over a proper metric space linearly embeds into an $\ell_1$-sum of finite dimensional ... More
A Note about Iterated Arithmetic FunctionsJan 24 2015Let $f\colon\mathbb{N}\rightarrow\mathbb{N}_0$ be a multiplicative arithmetic function such that for all primes $p$ and positive integers $\alpha$, $f(p^{\alpha})<p^{\alpha}$ and $f(p)\vert f(p^{\alpha})$. Suppose also that any prime that divides $f(p^{\alpha})$ ... More
Counting 3-Stack-Sortable PermutationsMar 21 2019We prove a "Decomposition Lemma" that allows us to count preimages of certain sets of permutations under West's stack-sorting map $s$. As a first application, we give a new proof of Zeilberger's formula for the number of 2-stack-sortable permutations ... More
The large structures of Grothendieck founded on finite order arithmeticFeb 09 2011Apr 30 2014Such large-structure tools of cohomology as toposes and derived categories stay close to arithmetic in practice, yet existing foundations for them go beyond the strong set theory ZFC. We formalize the practical insight by founding the theorems of EGA ... More
Strain designed Josephson $π$ junction qubits with topological insulatorsAug 15 2014Jun 23 2015A Josephson qubit is designed via the application of a tensile strain to a topological insulator surface sandwiched between two s-wave superconductors. The strain applied leads to a shift in the Dirac point without changing the pre-existing conducting ... More
Multiperfect Numbers in Certain Quadratic RingsJun 17 2015Using an extension of the abundancy index to imaginary quadratic rings that are unique factorization domains, we investigate what we call $n$-powerfully $t$-perfect numbers in these rings. This definition serves to extend the concept of multiperfect numbers ... More
Absence of resonance near the critical line on asymptotically hyperbolic spacesJun 24 2004Sep 02 2005As a consequence of a result of Cardoso and Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line. The case of non-trapping metrics with constant curvature ... More
Cabling Conjecture for Small Bridge NumberJul 06 2015Let $k\subset S^3$ be a nontrivial knot. The Cabling Conjecture of Francisco Gonz\'alez-Acu\~na and Hamish Short posits that $\pi$-Dehn surgery on $k$ produces a reducible manifold if and only if $k$ is a $(p,q)$-cable knot and the surgery slope $\pi$ ... More
Polyurethane TogglesApr 09 2019We consider the involutions known as "toggles," which have been used to give simplified proofs of the fundamental properties of the promotion and evacuation maps. We transfer these involutions so that they generate a group $\mathscr P_n$ that acts on ... More
Bipyramids and bounds on volumes of hyperbolic linksNov 07 2015We utilize ideal bipyramids to obtain new upper bounds on volume for hyperbolic link complements in terms of the combinatorics of their projections.
Waist size for cusps in hyperbolic 3-manifolds IIMar 03 2017The waist size of a cusp in an orientable hyperbolic 3-manifold is the length of the shortest nontrivial curve generated by a parabolic isometry in the maximal cusp boundary. Previously, it was shown that the smallest possible waist size, which is 1, ... More
Une infinite de structures de contact tendues sur les varietes toroidalesDec 12 2000We show that every closed toroidal irreducible orientable 3-manifold carries infinitely many universally tight contact structures.
Motzkin Intervals and Valid Hook ConfigurationsApr 23 2019We define a new natural partial order on Motzkin paths that serves as an intermediate step between two previously-studied partial orders. We provide a bijection between valid hook configurations of $312$-avoiding permutations and intervals in these new ... More
Habitability of waterworlds: runaway greenhouses, atmospheric expansion and multiple climate states of pure water atmospheresMar 16 2015There are four different stable climate states for pure water atmospheres, as might exist on so-called "waterworlds". I map these as a function of solar constant for planets ranging in size from Mars size to 10 Earth-mass. The states are: globally ice ... More
Finiteness properties of profinite groupsFeb 15 2010Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite groups are an important ... More
A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite groupOct 30 2008In this paper, we consider Problem 14.44 in the Kourovka notebook, which is a conjecture about the number of conjugacy classes of a finite group. While elementary, this conjecture is still open and appears to elude any straightforward proof, even in the ... More
Schur properties over some Lipschitz-free spacesMar 04 2016Nov 30 2016In this paper we show that the Lipschitz-free space over some proper metric spaces (every closed ball is compact) linearly embed into a $\ell_1$-sum of finite dimensional subspaces of itself. We also prove that under natural conditions, the Lipschitz-free ... More
Binary Codes and Period-$2$ Orbits of Sequential Dynamical SystemsSep 13 2015A sequential dynamical system (SDS) consists of an undirected simple graph $Y$ with vertices $v_1,v_2,\ldots,v_n$, a collection of vertex functions $\{f_{v_i}\}_{i=1}^n$, a permutation $\pi\in S_n$, and a collection of states $A$. The vertices update ... More