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A note on the definition of small overlap monoidsOct 23 2009Small overlap conditions are simple and natural combinatorial conditions on semigroup and monoid presentations, which serve to limit the complexity of derivation sequences between equivalent words in the generators. They were introduced by J.H.Remmers, ... More

Free adequate semigroupsFeb 02 2009May 08 2009We give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The morphisms of the free adequate semigroup onto the free ample semigroup ... More

Free left and right adequate semigroupsApr 06 2009May 08 2009Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there are natural ... More

Multiplicative structure of 2x2 tropical matricesJul 02 2009We study the algebraic structure of the semigroup of all $2 \times 2$ tropical matrices under multiplication. Using ideas from tropical geometry, we give a complete description of Green's relations and the idempotents and maximal subgroups of this semigroup. ... More

A strong geometric hyperbolicity property for directed graphs and monoidsJan 03 2014Oct 13 2014We introduce and study a strong "thin triangle"' condition for directed graphs, which generalises the usual notion of hyperbolicity for a metric space. We prove that finitely generated left cancellative monoids whose right Cayley graphs satisfy this condition ... More

Green's J-order and the rank of tropical matricesFeb 14 2011Jan 04 2012We study Green's J-order and J-equivalence for the semigroup of all n-by-n matrices over the tropical semiring. We give an exact characterisation of the J-order, in terms of morphisms between tropical convex sets. We establish connections between the ... More

Idempotent tropical matrices and finite metric spacesMar 12 2012There is a well known correspondence between the triangle inequality for a distance function on a finite set, and idempotency of an associated matrix over the tropical semiring. Recent research has shed new light on the structure (algebraic, combinatorial ... More

Face monoid actions and tropical hyperplane arrangementsApr 11 2016We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in ... More

Wreath product decompositions for triangular matrix semigroupsDec 01 2005We consider wreath product decompositions for semigroups of triangular matrices. We exhibit an explicit wreath product decomposition for the semigroup of all n-by-n upper triangular matrices over a given field k, in terms of aperiodic semigroups and affine ... More

On cogrowth, amenability and the spectral radius of a random walk on a semigroupJun 05 2017We introduce two natural notions of cogrowth for finitely generated semigroups --- one local and one global --- and study their relationship with amenability and random walks. We establish the minimal and maximal possible values for cogrowth rates, and ... More

Linear isomorphisms preserving Green's relations for matrices over semiringsSep 15 2017In this paper we characterize those linear bijective maps on the monoid of all $n \times n$ square matrices over an anti-negative semifield which preserve and strongly preserve each of Green's equivalence relations $\mathcal{L}, \mathcal{R}, \mathcal{D}, ... More

Identities in Upper Triangular Tropical Matrix Semigroups and the Bicyclic MonoidDec 13 2016Jun 13 2017We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of $n\times n$ upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for checking whether ... More

On the rational subset problem for groupsFeb 21 2006We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products ... More

Pure Dimension and Projectivity of Tropical PolytopesJun 22 2011Oct 03 2016We study how geometric properties of tropical convex sets and polytopes, which are of interest in many application areas, manifest themselves in their algebraic structure as modules over the tropical semiring. Our main results establish a close connection ... More

Automatic Rees matrix semigroups over categoriesSep 14 2005We consider the preservation of the properties of automaticity and prefix-automaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the single-object case of Rees matrix ... More

The loop problem for Rees matrix semigroupsFeb 23 2007We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which the loop problem ... More

On commuting elements and embeddings of graph groups and monoidsJan 03 2006Feb 03 2006We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Gamma is any graph not containing a four-cycle without chords, then the group G(Gamma) does not contain four elements whose commutation graph is ... More

The loop problem for monoids and semigroupsSep 11 2006We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial group theory. ... More

Anisimov's Theorem for inverse semigroupsMar 21 2013The idempotent problem of a finitely generated inverse semigroup is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent problem is ... More

A large class of sofic monoidsJan 28 2014We prove that a monoid is sofic, in the sense recently introduced by Ceccherini-Silberstein and Coornaert, whenever the J-class of the identity is a sofic group, and the quotients of this group by orbit stabilisers in the rest of the monoid are amenable. ... More

Free objects in triangular matrix varieties and quiver algebras over semiringsApr 12 2019We study the free objects in the variety of semigroups and variety of monoids generated by the monoid of all $n \times n$ upper triangular matrices over a commutative semiring. We obtain explicit representations of these, as multiplicative subsemigroups ... More

Small overlap monoids: the word problemDec 03 2007We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis of words which ... More

Uniform decision problems and abstract properties of small overlap monoidsOct 26 2009We study the way in which the abstract structure of a small overlap monoid is reflected in, and may be algorithmically deduced from, a small overlap presentation. We show that every C(2) monoid admits an essentially canonical C(2) presentation; by counting ... More

On generic properties of finitely presented monoids and semigroupsJul 08 2008We study the generic properties of finitely presented monoids and semigroups. We show that for positive integers a > 1, k and m, the generic a-generator k-relation monoid and semigroup presentation (defined in any of several definite statistical senses) ... More

Small overlap monoids II: automatic structures and normal formsJun 24 2008Oct 31 2008We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular language of normal ... More

Word problems recognisable by deterministic blind monoid automataJun 08 2005Jul 27 2005We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class including groups, ... More

Formal languages and groups as memoryJan 04 2006Oct 19 2007We present an exposition of the theory of finite automata augmented with a multiply-only register storing an element of a given monoid or group. Included are a number of new results of a foundational nature. We illustrate our techniques with a group-theoretic ... More

Tropical matrix duality and Green's D relationOct 01 2010We give a complete description of Green's D relation for the multiplicative semigroup of all n-by-n tropical matrices. Our main tool is a new variant on the duality between the row and column space of a tropical matrix (studied by Cohen, Gaubert and Quadrat ... More

Graph products of right cancellative monoidsMar 14 2008Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then ... More

Convexity of tropical polytopesNov 06 2014We study the relationship between min-plus, max-plus and Euclidean convexity for subsets of $\mathbb{R}^n$. We introduce a construction which associates to any max-plus convex set with compact projectivisation a canonical matrix called its dominator. ... More

Uniform decision problems in automatic semigroupsSep 15 2005We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which seem to be necessary to make the problem well-defined, ... More

A Svarc-Milnor lemma for monoids acting by isometric embeddingsApr 30 2010We continue our programme of extending key techniques from geometric group theory to semigroup theory, by studying monoids acting by isometric embeddings on spaces equipped with asymmetric, partially-defined distance functions. The canonical example of ... More

Rational semigroup automataAug 07 2007We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such family arises ... More

Rational subsets of polycyclic monoids and valence automataOct 19 2007We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that ... More

The word problem for free adequate semigroupsNov 29 2013We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and compute normal ... More

Groups acting on semimetric spaces and quasi-isometries of monoidsJun 02 2009We study groups acting by length-preserving transformations on spaces equipped with asymmetric, partially-defined distance functions. We introduce a natural notion of quasi-isometry for such spaces and exhibit an extension of the Svarc-Milnor Lemma to ... More

Quasi-isometry and finite presentations of left cancellative monoidsApr 11 2012We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our main tool is an elementary, but useful, geometric characterisation of ... More

Amenability and geometry of semigroupsMay 22 2015We study the connection between amenability, F{\o}lner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left cancellative semigroups, ... More

NP-completeness in the gossip monoidJun 03 2016Gossip monoids form an algebraic model of networks with exclusive, transient connections in which nodes, when they form a connection, exchange all known information. They also arise naturally in pure mathematics, as the monoids generated by the set of ... More

On groups and counter automataNov 07 2006We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this ... More

Exact rings and semiringsDec 21 2012May 08 2013We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn-Banach-type separation property on modules. Our motivation comes from the tropical semiring, and in particular a desire to understand the often surprising ... More

Tropical matrix groupsMar 12 2012We study the subgroup structure of the semigroup of finitary tropical matrices under multiplication. We show that every maximal subgroup is isomorphic to the full linear automorphism group of a related tropical polytope, and that each of these groups ... More

The Spectra of Lamplighter Groups and Cayley MachinesDec 20 2004Sep 09 2005We calculate the spectra and spectral measures associated to random walks on restricted wreath products of finite groups with the infinite cyclic group, by calculating the Kesten-von Neumann-Serre spectral measures for the random walks on Schreier graphs ... More

Thermal stability of cold clouds in galaxy halosJul 02 1999Oct 14 1999We consider the thermal properties of cold, dense clouds of molecular hydrogen and atomic helium. For cloud masses below 10^-1.7 Msun, the internal pressure is sufficient to permit the existence of particles of solid or liquid hydrogen at temperatures ... More

The Cloudy UniverseJul 20 1999Modelling of Extreme Scattering Events suggests that the Galaxy's dark matter is an undetected population of cold, AU-sized, planetary-mass gas clouds. None of the direct observational constraints on this picture -- thermal/non-thermal emission, extinction ... More

A Probabilistic Model of Compound NounsSep 06 1994Compound nouns such as example noun compound are becoming more common in natural language and pose a number of difficult problems for NLP systems, notably increasing the complexity of parsing. In this paper we develop a probabilistic model for syntactically ... More

High velocity gas from the Galactic dark haloNov 13 1998We present the germ of a new model for High Velocity Clouds, derived from the idea that the dark matter halo of our Galaxy is in the form of cold, planetary-mass gas clouds. In this picture HVCs arise as a result of disruptive collisions between dark ... More

Order-Revealing Encryption and the Hardness of Private LearningMay 03 2015An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning ... More

Extreme scattering events and Galactic dark matterFeb 10 1998Mar 20 1998Extreme Scattering Events (ESEs) are attributed to radio-wave refraction by a cloud of free-electrons crossing the line-of-sight. We present a new model in which these electrons form the photo-ionized 'skin' of an underlying cool, self-gravitating cloud ... More

Continuity in Discrete SetsJan 30 2010Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and television programs. ... More

Some Results on the Functional Decomposition of PolynomialsApr 30 2010If g and h are functions over some field, we can consider their composition f = g(h). The inverse problem is decomposition: given f, determine the ex- istence of such functions g and h. In this thesis we consider functional decom- positions of univariate ... More

Full Square Rhomboids and Their Algebraic ExpressionsMay 12 2013The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a full square rhomboid that is an example of non-series-parallel graphs. Our intention is to simplify the expressions of full square rhomboids and ... More

Automatic Identification of Support Verbs: A Step Towards a Definition of Semantic WeightOct 25 1995Oct 26 1995Current definitions of notions of lexical density and semantic weight are based on the division of words into closed and open classes, and on intuition. This paper develops a computationally tractable definition of semantic weight, concentrating on what ... More

Resource Letter TF-1: Turbulence in FluidsJun 14 1999This Resource Letter provides a guide to the literature on fully developed turbulence in fluids. It is restricted to mechanically driven turbulence in an incompressible fluid described by the Navier-Stokes equations of hydrodynamics, and places greatest ... More

Theory of the Stark Effect for P donors in SiJan 11 2005May 09 2005We develop a multi-valley effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is treated perturbatively. We apply the theory to the Stark effect in Si:P. The method becomes more accurate at ... More

A Faster Tableau for CTL*Jul 17 2013There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau approach built upon ... 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

Infrared Behaviour, sources and the Schwinger action principleMay 28 1994Nov 07 1994The paper describes a dynamical analogy for the renormalization group which leads to insights into its structure.

Collisional excitation of OH(6049 MHz) masers in supernova remnant - molecular cloud interactionsMar 19 2007Apr 16 2007OH (1720 MHz) masers serve as indicators of SNR - molecular cloud interaction sites. These masers are collisionally excited in warm (50-100K) shocked gas with densities of order 1e5 cm^-3 when the OH column density is in the range 1e16-1e17 cm^-2. Here ... More

A Note on the Quantum Collision and Set Equality ProblemsDec 04 2013Dec 11 2013The results showing a quantum query complexity of $\Theta(N^{1/3})$ for the collision problem do not apply to random functions. The issues are two-fold. First, the $\Omega(N^{1/3})$ lower bound only applies when the range is no larger than the domain, ... More

Comments on the observation of high multiplicity events at the LHCMay 11 2011Aug 04 2011We analyze the structure of the high multiplicity events observed by the CMS collaboration at the LHC. We argue that the bulk of the observed correlations is due to the production of a pair of jets with p_t > 15 GeV/c. We also suggest that high multiplicity ... More

High-energy hadron physics at future facilitiesNov 11 2007We outline several directions for future investigations of the three-dimensional structure of nucleon, including multiparton correlations, color transparency, and branching processes at hadron colliders and at hadron factories. We also find evidence that ... More

On distance two in Cayley graphs of Coxeter groupsApr 05 2014Apr 28 2014We consider the Cayley graph ${\rm C}(W,S)$ of a Coxeter system $(W,S)$ and describe all maximal $2$-cliques in this graph, i.e. maximal subsets in the vertex set such that the distance between any two distinct elements is equal to $2$. As an application, ... More

Isometric embeddings of half-cube graphs in half-spin GrassmanniansJun 27 2011Jan 11 2014Let $\Pi$ be a polar space of type $\textsf{D}_{n}$. Denote by ${\mathcal G}_{\delta}(\Pi)$, $\delta\in \{+,-\}$ the associated half-spin Grassmannians and write $\Gamma_{\delta}(\Pi)$ for the corresponding half-spin Grassmann graphs. In the case when ... More

On geometry of symplectic involutionsApr 20 2005Let $V$ be a $2n$-dimensional vector space over a field $F$ and $\Omega$ be a non-degenerate symplectic form on $V$. Denote by ${\mathfrak H}_{k}(\Omega)$ the set of all $2k$-dimensional subspaces $U\subset V$ such that the restriction $\Omega|_{U}$ is ... More

On embeddings of Grassmann graphs in polar Grassmann graphsMar 13 2015We establish that every embedding of a Grassmann graph in a polar Grassmann graph can be reduced to an embedding in a Grassmann graph or to an embedding in the collinearity graph of a polar space. Also, we consider $3$-embeddings, i.e. embeddings preserving ... More

The first galaxies: structure and stellar populationsApr 03 2000The Hubble Deep Fields continue to be a valuable resource for studying the distant universe, particularly at z>2 where their comoving volume becomes large enough to encompass several hundred L* galaxies or their progenitors. Here I present recent results ... More

Searches for High Redshift ClustersDec 18 1996High redshift galaxy clusters have traditionally been a fruitful place to study galaxy evolution. I review various search strategies for finding clusters at z > 1. Most efforts to date have concentrated on the environments of distant AGN. I illustrate ... More

Metrics of positive scalar curvature and generalised Morse functions, part IIOct 12 2009Jul 14 2011The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature ... More

Holographic Renormalisation and the Electroweak Precision ParametersMar 15 2010Oct 11 2010We study the effects of holographic renormalisation on an AdS/QCD inspired description of dynamical electroweak symmetry breaking. Our model is a 5D slice of AdS_5 geometry containing a bulk scalar and SU(2) times SU(2) gauge fields. The scalar field ... More

Astronomical Seeing from the Summits of the Antarctic PlateauDec 04 2001Jan 30 2002From the South Pole, microthermal turbulence within a narrow surface boundary layer some 200m thick provides the dominant contribution to the astronomical seeing. We present results for the seeing at a wavelength of 2.4um. The narrow turbulence layer ... More

Fluctuations and Bubble Dynamics in First-Order Phase TransitionsJun 28 1996Sep 26 1996We numerically examine the effect of thermal fluctuations on a first-order phase transition in 2+1 dimensions. By focusing on the expansion of a single bubble we are able to calculate changes in the bubble wall's velocity as well as changes in its structure ... More

Critical Exponents without the Epsilon ExpansionMar 22 1994We argue that the sharp-cutoff Wilson renormalization group provides a powerful tool for the analysis of second-order and weakly first-order phase transitions. In particular, in a computation no harder than the calculation of the 1-loop effective potential, ... More

Color superconducting quark matter in compact starsOct 11 2001When nuclear matter reaches a high enough density, we expect that the nucleons will overlap so much as to lose their separate identities, and merge into quark matter. In this talk I will review some theoretical expectations and speculations about quark ... More

Quantum Field Theory: Spin One HalfSep 02 2004This is a draft version of Part II of a three-part textbook on quantum field theory.

Axions: Past, Present, and FutureOct 17 2002I give a pedagogical and historical introduction to axion physics, and briefly review the present status of axions in our understanding of particle physics and cosmology. This is a contribution to Continuous Advances in QCD 2002/Arkadyfest, held in honor ... More

Is Purity Eternal?Jun 12 1992Jul 08 1993Phenomenological and formal restrictions on the evolution of pure into mixed states are discussed. In particular, it is argued that, if energy is conserved, loss of purity is incompatible with the weakest possible form of Lorentz covariance.

Thermal Abundances of Heavy ParticlesJan 11 2000Mar 23 2000Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop corrections to the number density of heavy particles (in thermal equilibrium with a gas of light particles) that are not Boltzmann suppressed by a factor of e^(-M/T) at temperatures ... More

Residual properties of 1-relator groupsJan 16 2010This is a survey of two papers joint with A. Borisov and a paper joint with I. Spakulova. It is based on my lectures at the conference "Groups St. Andrews 2009", Bath (August 2009). We prove that almost all 1-related groups with at least 3 generators ... More

The Rapid Decay property and centroids in groupsMay 05 2014Dec 17 2015This is a survey of methods of proving or disproving the Rapid Decay property in groups. We present a centroid property of group actions on metric spaces. That property is a generalized (and corrected) version of the property (**)-relative hyperbolicity" ... More

Aspherical groups and manifolds with extreme propertiesMar 20 2011Apr 26 2011We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional closed aspherical ... More

Algorithmic and asymptotic properties of groupsFeb 10 2006This is a survey of the recent work in algorithmic and asymptotic properties of groups. I discuss Dehn functions of groups, complexity of the word problem, Higman embeddings, and constructions of finitely presented groups with extreme properties (monsters). ... More

Nonlinear Harmonic Forms and an Indefinite Bochner FormulaNov 01 2014Oct 21 2015We introduce the study of nonlinear harmonic forms. These are forms which minimize the $L_2$ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence results. We also introduce ... More

Large Rapidity Gap Events in Deep Inelastic ScatteringJan 31 1997Large Rapidity Gap Events in Deep Inelastic Scattering are discussed in terms of lightcone wave functions for quarks and gluons inside the photon. It is shown that this approach is consistent with earlier, conventional Feynman diagram calculations. An ... More

Traceable 2D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonatorsNov 09 2006Mar 19 2007This paper explains how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate, efficiently, the frequencies and fields of the whispering-gallery ... More

The Deformation Space of Calabi-Yau n-folds with canonical singularities can be obstructedFeb 25 1994This paper gives a simple example of a family of Calabi-Yaus of any dimension with canonical singularities of dimension one, whose Kuranishi space is singular. Thus the Bogomolov-Tian-Todorov unobstructedness theorem is not true for Calabi-Yaus with canonical ... More

Motions of Classical Charged TachyonsMar 13 2002It is shown by numerical simulation that classical charged tachyons have self-orbiting helical solutions in a narrow neighborhood of certain discrete values for the velocity when the electromagnetic interaction is described by Feynman-Wheeler electrodynamics. ... More

The Lorentz-Dirac equation in complex space-timeSep 20 2011Aug 24 2012A hypothetical equation of motion is proposed for Kerr-Newman particles. It is obtained by analytic continuation of the Lorentz-Dirac equation into complex space-time. A new class of "runaway" solutions are found which are similar to Zitterbewegung. Electromagnetic ... More

A Dynamical Theory of Markovian DiffusionOct 08 2001A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order quantum effects ... More

Revstack sort, zigzag patterns, descent polynomials of $t$-revstack sortable permutations, and Steingrímsson's sorting conjectureApr 05 2014In this paper we examine the sorting operator $T(LnR)=T(R)T(L)n$. Applying this operator to a permutation is equivalent to passing the permutation reversed through a stack. We prove theorems that characterise $t$-revstack sortability in terms of patterns ... More

X-ray Constraints on Cluster Magnetic FieldsJul 05 1998Lower limits to the intracluster magnetic field are derived from modeling broad band X-ray spectra of 6 galaxy clusters with radio halos (A401, A754, A1367, Coma (A1656), A2256, and A2319). The 0.7 - 10 keV spectra for all clusters were obtained with ... More

Strangeness production in small and large collisions systems at RHICApr 13 2006We present measurements of strange and multi-strange hadrons in p+p collisions at $\sqrt{s}$= 200 GeV measured by STAR. We will compare these preliminary results to leading-order (LO) and next-to-leading order (NLO) perturbative QCD models widely believed ... More

Heavy flavor measurements using high-pt electrons in the ALICE EMCalJun 07 2010Heavy flavor hadrons, i.e. those containing charm and bottom quarks, will be abundantly produced at the LHC and are important probes of the Quark-Gluon Plasma (QGP). Of particular interest is the investigation of parton energy loss in the medium. Using ... More

Non-backtracking random walks and a weighted Ihara's theoremMar 17 2016We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara's Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking ... More

Battling the Digital Forensic Backlog through Data DeduplicationOct 02 2016In everyday life. Technological advancement can be found in many facets of life, including personal computers, mobile devices, wearables, cloud services, video gaming, web-powered messaging, social media, Internet-connected devices, etc. This technological ... More

Differential Geometry on SU(3) with Applications to Three State SystemsJul 28 1998The left and right invariant vector fields are calculated in an ``Euler angle'' type parameterization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This ... More

Modelling the Role of Nitric Oxide in Cerebral AutoregulationDec 30 2015Malfunction of the system which regulates the bloodflow in the brain is a major cause of stroke and dementia, costing many lives and many billions of pounds each year in the UK alone. This regulatory system, known as cerebral autoregulation, has been ... More

Visualising Large Datasets in TOPCAT v4Oct 24 2014TOPCAT is a widely used desktop application for manipulation of astronomical catalogues and other tables, which has long provided fast interactive visualisation features including 1, 2 and 3-d plots, multiple datasets, linked views, color coding, transparency ... More

The classification of Rank 3 Reflective Hyperbolic Lattices over Z[\sqrt{2}]Dec 03 2015There are 432 strongly squarefree symmetric bilinear forms of signature $(2,1)$ defined over $\Z[\sqrt{2}]$ whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on Nikulin's) ... More