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 2019Aug 27 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 the strength of connectedness of a random hypergraphSep 04 2014Mar 09 2015Bollob\'{a}s and Thomason (1985) proved that for each $k=k(n) \in [1, n-1]$, with high probability, the random graph process, where edges are added to vertex set $V=[n]$ uniformly at random one after another, is such that the stopping time of having minimal ... 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
On the applicability of the two-band model to describe transport across n-p junctions in bilayer grapheneJan 11 2010We extend the low-energy effective two-band Hamiltonian for electrons in bilayer graphene (E. McCann, V. I. Fal'ko, Phys. Rev. Lett. 96 (2006) 86805) to include a spatially dependent electrostatic potential. We find that this Hamiltonian contains additional ... 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
Exploiting the Rule Structure for Decision Making within the Independent Choice LogicFeb 20 2013This paper introduces the independent choice logic, and in particular the "single agent with nature" instance of the independent choice logic, namely ICLdt. This is a logical framework for decision making uncertainty that extends both logic programming ... More
Context-Specific Approximation in Probabilistic InferenceJan 30 2013There is evidence that the numbers in probabilistic inference don't really matter. This paper considers the idea that we can make a probabilistic model simpler by making fewer distinctions. Unfortunately, the level of a Bayesian network seems too coarse; ... More
Probabilistic Semantics and DefaultsMar 27 2013There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side effects. Rather ... 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
Linear structure of Lipschitz-free spaces over countable compact metric spacesMar 04 2016Jun 01 2016In this paper we show that the Lipschitz-free space over some compact metric spaces linearly embed into a l1-sum of finite dimensional subspaces of itself. We also prove that under natural conditions, the Lipschitz-free space over a compact metric space ... 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
Nondegenerate $2 \times k \times (k+1)$ HypermatricesJun 14 2016Jun 17 2016We construct an extension of Gaussian elimination to show that if $\mathbb{F}$ is a topological field, then there is a transitive, free, and continuous action of a natural quotient of $GL_k(\mathbb{F}) \times GL_{k+1}(\mathbb{F})$ on the set $M_k(\mathbb{F})$ ... 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
Exploring the spectrum of QCD using a space-time latticeSep 21 2005Some past and ongoing explorations of the spectrum of QCD using Monte Carlo simulations on a space-time lattice are described. Glueball masses in the pure-gauge theory are reviewed, and the energies of gluonic excitations in the presence of a static quark-antiquark ... 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
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
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
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
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
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
Lower Bounds in the Preprocessing and Query Phases of Routing AlgorithmsJan 18 2015Sep 07 2015In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension ... 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
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
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
On the Density of Ranges of Generalized Unitary Divisor FunctionsJul 09 2015For any integer $t$, the unitary divisor function $\sigma_t^*$ is the multiplicative arithmetic function defined by $\sigma_t^*(p^{\alpha})=1+p^{\alpha t}$ for all primes $p$ and positive integers $\alpha$. The range of the unitary divisor function $\sigma_{-1}^*$ ... 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
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 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
Improved effective estimates of Pólya's Theorem for quadratic formsApr 08 2018Apr 14 2018Following de Loera and Santos, the P\'olya exponent of a $n$-ary real form (i.e. a homogeneous polynomial in $n$ variables with real coefficients) $f$ is the infimum of the upward closed set of nonnegative integers $m$ such that $(x_1 + \cdots + x_n)^m ... More
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
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
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
Eventual positivity of Hermitian polynomials and integral operatorsDec 04 2014Quillen proved that, if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and ... More
Descents in $t$-Sorted PermutationsApr 04 2019Jun 30 2019Let $s$ denote West's stack-sorting map. A permutation is called $t-\textit{sorted}$ if it is of the form $s^t(\mu)$ for some permutation $\mu$. We prove that the maximum number of descents that a $t$-sorted permutation of length $n$ can have is $\left\lfloor\frac{n-t}{2}\right\rfloor$. ... 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
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
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
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
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
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
Connectivity for bridge-alterable graph classesNov 13 2013Mar 01 2016A collection of graphs is called bridge-alterable if, for each graph G with a bridge e, G is in the class if and only if G-e is. For example the class of forests is bridge-alterable. For a random forest $F_n$ sampled uniformly from the set of forests ... 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
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
The Harish-Chandra integralJun 28 2018This paper introduces Harish-Chandra's integral formula for compact, connected, semisimple Lie groups. It is intended for mathematicians and physicists who are familiar with the basics of Lie groups and Lie algebras but who may not be specialists in representation ... 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
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
Proofs of Conjectures about Pattern-Avoiding Linear ExtensionsMay 07 2019Sep 11 2019After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation. Some recent papers consider specific families of posets and ask how many linear extensions give ... 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
Postorder PreimagesApr 06 2016Jun 02 2018Given 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
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
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
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
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
The continuum limit of the Bell modelJan 22 2003In a paper entitled Beables for Quantum Field Theory, John Bell has shown that it was possible to build a realistic interpretation of any hamiltonian lattice quantum field theory involving Fermi fields. His model is stochastic but Bell thought that it ... 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
Forms and Rotational States of the Nuclei of Ecliptic CometsJan 12 2007In this thesis I present measurements of the physical properties of the nuclei of Jupiter Family comets (JFCs), based on time-series observations. From the time-series photometry rotation rates and elongations were measured, and from these constraints ... More
A new paradigm for the universeNov 03 2003May 29 2019This 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
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.
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
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
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
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.
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
Unitary Cayley Graphs of Dedekind Domain QuotientsDec 09 2014Mar 26 2017If $X$ is a commutative ring with unity, then the unitary Cayley graph of $X$, denoted $G_X$, is defined to be the graph whose vertex set is $X$ and whose edge set is $\{\{a,b\}\colon a-b\in X^\times\}$. When $R$ is a Dedekind domain and $I$ is an ideal ... 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
An Arithmetic Function Arising from the Dedekind $ψ$ FunctionJan 05 2015Jan 07 2015We define $\overline{\psi}$ to be the multiplicative arithemtic function that satisfies \[\overline{\psi}(p^{\alpha})=\begin{cases} p^{\alpha-1}(p+1), & \mbox{if } p\neq 2; \\ p^{\alpha-1}, & \mbox{if } p=2 \end{cases}\] for all primes $p$ and positive ... 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
The legacy of the experimental hadron physics programme at COSYNov 22 2016The experimental hadronic physics programme at the COoler SYnchrotron of the Forschungszentrum Juelich terminated at the end of 2014. After describing the accelerator and the associated facilities, a review is presented of the major achievements 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
Baryon spectroscopy on the lattice: recent resultsAug 08 2003Progress in determining the baryon spectrum using computer simulations of quarks and gluons in lattice QCD are summarized and some future plans are outlined.
The Monte Carlo method in quantum field theoryFeb 20 2007This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain ... More
The finiteness theorem for invariants of a finite group (translation of Emmy Noether's "Der Endlichkeitsatz der Invarianten endlicher Gruppen")Mar 22 2015A translation of Emmy Noether's paper "Der Endlichkeitsatz der Invarianten endlicher Gruppen" (Mathematische Annalen, vol. 77, 1920, pages 89--92). In Noether's words, the paper gives "an entirely elementary finiteness proof---using only the theory of ... More
Descents in $t$-Sorted PermutationsApr 04 2019Let $s$ denote West's stack-sorting map. A permutation is called $t-\textit{sorted}$ if it is of the form $s^t(\mu)$ for some permutation $\mu$. We prove that the maximum number of descents that a $t$-sorted permutation of length $n$ can have is $\left\lfloor\frac{n-t}{2}\right\rfloor$. ... More
Interpreting set theory in higher order arithmeticJul 26 2012Feb 15 2013A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.
Zariski cohomology in second order arithmeticJul 02 2012Jul 25 2012The cohomology of coherent sheaves and sheaves of Abelian groups on Noetherian schemes are interpreted in second order arithmetic by means of a finiteness theorem. This finiteness theorem provably fails for the etale topology even on Noetherian schemes. ... More
Complex Divisor FunctionsFeb 11 2015Jan 10 2018For 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
Enumeration of Stack-Sorting Preimages via a Decomposition LemmaApr 04 2019We give three applications of a recently-proven "Decomposition Lemma," which allows one to count preimages of certain sets of permutations under West's stack-sorting map $s$. We first enumerate the permutation class $s^{-1}(\text{Av}(231,321))=\text{Av}(2341,3241,45231)$, ... More