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Supersolvable simplicial arrangementsDec 05 2017Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane arrangements ... More

Supersolvable simplicial arrangementsDec 05 2017Jun 24 2019Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane arrangements ... More

MAT-free reflection arrangementsApr 12 2019We introduce the class of MAT-free hyperplane arrangements which is based on the Multiple Addition Theorem by Abe, Barakat, Cuntz, Hoge, and Terao. We also investigate the closely related class of MAT2-free arrangements based on a recent generalization ... More

Automorphisms of $\mathscr{P}(λ)/\mathscr{I}_κ$Jun 10 2015Aug 27 2015We study conditions on automorphisms of Boolean algebras of the form $P(\lambda)/I_\kappa$ (where $\lambda$ is an uncountable cardinal and $I_\kappa$ is the ideal of sets of cardinality less than $\kappa$) which allow one to conclude that a given automorphism ... More

The dynamics of domain wall SkyrmionsMay 13 2013It has recently been shown that Skyrmions with a fixed size can exist in theories without a Skyrme term, providing the Skyrmion is located on a domain wall. Here we numerically compute domain wall Skyrmions of this type, in a (2+1)-dimensional O(3) sigma ... More

Time, Space, and Energy in Reversible ComputingApr 20 2005We survey results of a quarter century of work on computation by reversible general-purpose computers (in this setting Turing machines), and general reversible simulation of irreversible computations, with respect to energy-, time- and space requirements. ... More

On Liftings of Projective Indecomposable $G_{(1)}$-ModulesJun 19 2015Jul 17 2015Let $G$ be a simple simply connected algebraic group over an algebraically closed field $k$ of characteristic $p$, with Frobenius kernel $G_{(1)}$. It is known that when $p\ge 2h-2$, where $h$ is the Coxeter number of $G$, the projective indecomposable ... More

Module Invariants and Blocks of Finite Group SchemesJan 13 2012Sep 26 2012We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the representation-theoretic constructions ... More

Causal diagrams for physical modelsSep 03 2015I present a scheme of drawing causal diagrams based on physically motivated mathematical models expressed in terms of temporal differential equations. They provide a means of better understanding the processes and causal relationships contained within ... More

A result of Lemmermeyer on class numbersSep 21 2010I present Franz Lemmermeyer's proof that if p is a prime congruent to 9 mod 16 then the class number of Q(p^(1/4)) is congruent to 2 mod 4.

A Hecke algebra attached to mod 2 modular forms of level 3Aug 30 2015Oct 09 2016Let $D$ in $Z/2[[x]]$ be $\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show ... More

A memo on chains and their topologiesDec 07 2013We summarize some facts on chains (totally ordered sets), from an order-theoretic and from a topological point of view. We highlight the fact that many classical theorems that are true for partially ordered sets under some completeness assumption remain ... More

Finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules from the equitable point of viewMar 25 2013We consider the quantum algebra $U_q(\mathfrak{sl}_2)$ with $q$ not a root of unity. We describe the finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules from the point of view of the equitable presentation.

A Functional Hitchhiker's Guide to Hereditarily Finite Sets, Ackermann Encodings and Pairing FunctionsAug 06 2008The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available at http://logic.csci.unt.edu/tarau/research/2008/fSET.zip ... More

Ranking Catamorphisms and Unranking Anamorphisms on Hereditarily Finite DatatypesAug 06 2008Using specializations of unfold and fold on a generic tree data type we derive unranking and ranking functions providing natural number encodings for various Hereditarily Finite datatypes. In this context, we interpret unranking operations as instances ... More

Logic Engines as InteractorsAug 05 2008We introduce a new programming language construct, Interactors, supporting the agent-oriented view that programming is a dialog between simple, self-contained, autonomous building blocks. We define Interactors as an abstraction of answer generation and ... More

A Generic Numbering System based on Catalan Families of Combinatorial ObjectsJun 06 2014We study novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects. Our algorithms work on a generic representation that we illustrate on instances like ordered binary and multiway trees, balanced ... More

A Prolog Specification of Giant Number ArithmeticJul 17 2013The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their bitsizes. ... More

Executable Set Theory and Arithmetic Encodings in PrologAug 05 2008The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip ... More

Properties of Dust in Giant Elliptical Galaxies: The role of the EnvironmentNov 22 1999The properties of dust in giant elliptical galaxies are reviewed, with particular emphasis on the influence of the environment. After normalizing by the optical luminosities, a strong anti-correlation between the masses of dust and hot gas in X-ray bright ... More

The fundamental group of the harmonic archipelagoJan 24 2005The harmonic archipelago HA is obtained by attaching a large pinched annulus to every pair of consecutive loops of the Hawaiian earring. We clarify the fundamental group pi1(HA) as a quotient of the Hawaiian earring group, provide a precise description ... More

On affine interest rate modelsNov 14 2009Oct 27 2011Bernstein processes are Brownian diffusions that appear in Euclidean Quantum Mechanics. Knowledge of the symmetries of the Hamilton-Jacobi-Bellman equation associated with these processes allows one to obtain relations between stochastic processes (Lescot-Zambrini, ... More

QSO LifetimesApr 01 2003The QSO lifetime t_Q is one of the most fundamental quantities for understanding black hole and QSO evolution, yet it remains uncertain by several orders of magnitude. If t_Q is long, then only a small fraction of galaxies went through a luminous QSO ... More

Axiomatic Foundations for a Class of Generalized Expected Utility: Algebraic Expected UtilityJun 27 2012Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty representation is supposed ... More

Stable D-branes, calibrations and generalized Calabi-Yau geometryJun 18 2005We introduce generalized calibrations that take into account the gauge field on the D-brane so that calibrated submanifolds minimize the Dirac-Born-Infeld energy. We establish the calibration bound and show that the calibration form is closed in a supersymmetric ... More

Abelian and Non-abelian D-brane Effective ActionsMay 25 2004Nov 21 2015In this Ph.D. thesis we review and elaborate on a method to find the D-brane effective action, based on BPS equations. Firstly, both for the Yang-Mills action and the Born-Infeld action it is shown that these configurations are indeed BPS, i.e. solutions ... More

Falling flavors in AdS/CFTDec 10 2012Jul 01 2013We consider the behavior of D7 probes of supersymmetric warped geometries that are perturbed by the presence of anti-D3-branes. Such constructions are the gravitational duals of non-supersymmetric states in supersymmetric flavored gauge theories. Although ... More

Constructing new ample divisors out of old onesMay 21 1997May 25 1997We prove a gluing theorem which allows to construct an ample divisor on a rational surface from two given ample divisors on simpler surfaces. This theorem combined with the Cremona action on the ample cone gives rise to an algorithm for constructing new ... More

Effects on quantum physics of the local availability of mathematics and space time dependent scaling factors for number systemsOct 06 2011Oct 14 2011The work is based on two premises: local availability of mathematics to an observer at any space time location, and the observation that number systems, as structures satisfying axioms for the number type being considered, can be scaled by arbitrary, ... More

Use of Mathematical Logical Concepts in Quantum Mechanics: An ExampleJun 27 2001Feb 22 2002The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple ... More

Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum ComputersMay 15 1996Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$ is investigated ... More

Effects of gauge theory based number scaling on geometryJun 19 2013Effects of local availability of mathematics (LAM) and space time dependent number scaling on physics and, especially, geometry are described. LAM assumes separate mathematical systems as structures at each space time point. Extension of gauge theories ... More

A Representation of Real and Complex Numbers in Quantum TheoryAug 29 2005Apr 09 2007A quantum theoretic representation of real and complex numbers is described here as equivalence classes of Cauchy sequences of quantum states of finite strings of qubits. There are 4 types of qubits each with associated single qubit annihilation creation ... More

The Representation of Numbers in Quantum MechanicsMar 14 2001Sep 24 2001Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, ... More

The Representation of Natural Numbers in Quantum MechanicsMar 16 2000Dec 08 2000This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a ... More

Quantum Robots Plus EnvironmentsJul 13 1998A quantum robot is a mobile quantum system including an on bord quantum computer and ancillary systems, that interact with an environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements and physical experiments ... More

Differential Geometry on Hopf Algebras and Quantum Groups (Ph.D. Thesis)Dec 17 1994The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and ... More

q-holonomic formulas for colored HOMFLY polynomials of 2-bridge linksOct 14 2014We compute q-holonomic formulas for the HOMFLY polynomials of 2-bridge links colored with one-column (or one-row) Young diagrams.

Notations Around the World: Census and ExploitationApr 28 2010Mathematical notations around the world are diverse. Not as much as requiring computing machines' makers to adapt to each culture, but as much as to disorient a person landing on a web-page with a text in mathematics. In order to understand better this ... More

Normal Limits of Nilpotents in C*-AlgebrasMay 16 2012Dec 02 2013We will investigate the intersection of the normal operators with the closure of the nilpotent and quasinilpotent operators in various C*-algebras. A complete characterization will be given for type I and type III von Neumann algebras with separable predual ... More

A Model of Late Long-Term Potentiation Simulates Aspects of Memory MaintenanceApr 27 2007Late long-term potentiation (L-LTP) appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not ... More

Skyrmions, instantons and holographyFeb 26 2010Sep 21 2010Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by proving that ... More

Vortex rings in ferromagnetsJul 10 2007Vortex ring solutions are presented for the Landau-Lifshitz equation, which models the dynamics of a three-dimensional ferromagnet. The vortex rings propagate at constant speed along their symmetry axis and are characterized by the integer-valued Hopf ... More

BPS MonopolesJul 01 1997We review classical BPS monopoles, their moduli spaces, twistor descriptions and dynamics. Particular emphasis is placed upon symmetric monopoles, where recent progress has been made. Some remarks on the role of monopoles in S-duality and Seiberg-Witten ... More

Skyrmions in a truncated BPS theoryJan 12 2011Recently, it has been shown that (4+1)-dimensional Yang-Mills theory may be written as a (3+1)-dimensional BPS Skyrme model, in which the Skyrme field is coupled to an infinite tower of vector mesons. Truncating this tower to a single vector meson yields ... More

Instanton Moduli and Topological Soliton DynamicsAug 30 1994It has been proposed by Atiyah and Manton that the dynamics of Skyrmions may be approximated by motion on a finite dimensional manifold obtained from the moduli space of SU(2) Yang-Mills instantons. Motivated by this work we describe how similar results ... More

The moduli space metric for tetrahedrally symmetric 4-monopolesJul 31 1995The metric on the moduli space of SU(2) charge four BPS monopoles with tetrahedral symmetry is calculated using numerical methods. In the asymptotic region, in which the four monopoles are located on the vertices of a large tetrahedron, the metric is ... More

Structure Functions are not Parton ProbabilitiesSep 26 2002Parton distributions given by deep inelastic lepton scattering (DIS) are not equal to the probabilities of finding those partons in the parent wave function. Soft rescattering of the struck parton within the coherence length of the hard process influences ... More

Physics at ELFEMar 31 1997I review some central physics opportunities at the 15 ... 30 GeV continuous beam electron accelerator ELFE, proposed to be built in conjunction with the DESY linear collider. Our present detailed knowledge of single parton distributions in hadrons and ... More

New QCD Effects at Large xOct 27 1992In heavy quark production at large Feynman $x$ there are two hardness scales, one given by the heavy quark pair mass $\M^2$\ and the other by $\Lambda_{QCD}^2/(1-x)$. When these two scales are comparable, the twist expansion of Perturbative QCD breaks ... More

Introduction to QCD - a bound state perspectiveJun 07 2011These lecture notes focus on the bound state sector of QCD. Motivated by data which suggests that the strong coupling \alpha_s(Q) freezes at low Q, and by similarities between the spectra of hadrons and atoms, I discuss if and how QCD bound states may ... More

QCD Effects in Particle Production on NucleiOct 04 1993I discuss some questions related to hard scattering processes in nuclei and corrections to the leading twist approximation. The QCD factorization theorem requires that high energy partons do not lose energy while traversing the nucleus. I explain the ... More

Heitmann's proof of the direct summand conjecture in dimension 3Dec 05 2002We discuss Ray Heitmann's recent proof of the Direct Summand Conjecture in dimension 3 in mixed characteristic. This paper contains a discussion of his methods, a proof of the theorem, and a direct proof of the Canonical Element Conjecture in dimension ... More

Implications of space-momentum correlations and geometric fluctuations in heavy-ion collisionsFeb 25 2010Mar 25 2010The standard picture of heavy-ion collisions includes a collective expansion. If the initial energy density in the collisions is lumpy, then a collective expansion can convert that spatial lumpiness into correlations between final-state particles. Correlations ... More

Elliptic flow fluctuations in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeVDec 19 2006Jul 13 2007Please note that after these results were reported at Quark Matter 2006 and posted on the preprint server it was found that what is reported here as \textit{elliptic flow fluctuations}, should rather be taken as an upper limit on the fluctuations. Further ... More

The Rise and Fall of the RidgeJan 10 2011Recent data from heavy ion collisions at RHIC show unexpectedly large near-angle correlations that broaden longitudinally with centrality. The amplitude of this ridge-like correlation rises rapidly with centrality, reaches a maximum, and then falls in ... More

Elliptic flow fluctuations and correlations in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeVAug 04 2008In this talk, we report an analysis of elliptic flow ($v_2$), non-flow ($\delta_{2}$), and $v_2$ fluctuations ($\sigma_{v_{2}}$) for the STAR collaboration at middle rapidity in $\sqrt{s_{_{NN}}}=200$ GeV Au+Au collisions. We compare the results to models ... More

Evidence from Identified Particles for Active Quark and Gluon Degrees of FreedomJan 23 2007Measurements of intermediate pT (1.5 < pT < 5.0 GeV/c) identified particle distributions in heavy ion collisions at SPS and RHIC energies display striking dependencies on the number of constituent quarks in the corresponding hadron. One finds that elliptic ... More

Heavy flavour results from ATLASJan 24 2012A selection of heavy-flavour physics results from the ATLAS experiment is presented, based on data collected in proton-proton collisions at the LHC during 2010. Differential cross-sections for the production of heavy flavours, charmonium and bottomonium ... More

NEUTRINO PHYSICSMar 14 1995The theoretical motivations, experimental searches/hints, and implications of neutrino mass are surveyed.

Five Phases of Weak Neutral Current Experiments from the Perspective of a TheoristMay 12 1993I give my personal perspective on the past, present, and future of weak neutral current experiments, emphasizing the experimental inputs; the theoretical difficulties and inputs; the role of model independent and global analyses; and the implications ... More

Particle Physics Summary, Where are We and Where are We Going?Jul 01 1992The XXVII$^{\rm th}$ Rencontres de Moriond featured approximately 84 talks on a wide range of topics. I will try to summarize the highlights under the hypothesis that $SU_3 \x SU_2 \x U_1$ is correct to first approximation, concentrating on probes for ... More

A Mechanism for Ordinary-Sterile Neutrino MixingMay 11 1998Jul 24 1998Efficient oscillations between ordinary (active) and sterile neutrinos can occur only if Dirac and Majorana mass terms exist which are both small and comparable. It is shown that this can occur naturally in a class of string models, in which higher-dimensional ... More

Implications of Solar and Atmospheric NeutrinosJan 15 1993The implications of the deficit of solar neutrinos are discussed. If all of the experiments are taken literally the relative suppressions render an astrophysical explanation unlikely. Allowing MSW conversions, the data simultaneously determine the temperature ... More

Proton DecayOct 15 1992The status of proton decay is described, including general motivations for baryon number violation, and the present and future experimental situation. Grand unification with and without supersymmetry is considered, including possible evidence from coupling ... More

Status and Phenomenology of the Standard ModelMar 07 2005Mar 10 2005The status of the new standard model is briefly surveyed, with emphasis on experimental tests, unique features, theoretical problems, necessary extensions, and possible TeV signatures of Planck scale physics.

Domain Directed Dialogs for Decision ProcessesMar 15 2007Mar 27 2007The search for a standardized optimum way to communicate using natural language dialog has involved a lot of research. However, due to the diversity of communication domains, we think that this is extremely difficult to achieve and different dialogue ... More

Automatic Annotation of XHTML Pages with Audio ComponentsMar 14 2007May 02 2007In this paper we present Deiush, a multimodal system for browsing hypertext Web documents. The Deiush system is based on our novel approach to automatically annotate hypertext Web documents (i.e. XHTML pages) with browsable audio components. It combines ... More

Software Engineering Process Theory: A Multi-Method Comparison of Sensemaking-CoevoIution-Implementation Theory and Function-Behavior-Structure TheoryJul 03 2013Many academics have called for increasing attention to theory in software engineering. Consequently, this paper empirically evaluates two dissimilar software development process theories - one expressing a more traditional, methodical view (FBS) and one ... More

Stress tensor for massive fields on flat spaces of spatial topology R^2\times{S^1}Apr 25 2005Sep 24 2005We calculate the expectation values of the energy-momentum tensor T_{{\mu}{\nu}} for massive scalar and spinor fields, in the Minkowski-like vacuum states on the two flat spaces which are quotients of Minkowski space under the discrete isometries (t,x,y,z)\mapsto(t,x,y,z+2a) ... More

Exact information in N=2 theoriesMay 24 1993This is intended to be a simple discussion of work done in collaboration with S. Cecotti, K. Intriligator and C. Vafa; and with H. Saleur. I discuss how $ Tr F (-1)^F e^{-\beta H}$ can be computed exactly in any N=2 supersymmetric theory in two dimensions. ... More

Taking N to zero with S matricesNov 30 2001Interesting physical results can be obtained from sigma models by taking the number of fields N to zero. I discuss how one can make sense of this limit by using exact S matrix techniques. I review how this can be done for the case of self-avoiding polymers, ... More

Memory-Centred Cognitive Architectures for Robots Interacting Socially with HumansFeb 18 2016The Memory-Centred Cognition perspective places an active association substrate at the heart of cognition, rather than as a passive adjunct. Consequently, it places prediction and priming on the basis of prior experience to be inherent and fundamental ... More

Higher Derivative BLG: Lagrangian and Supersymmetry TransformationsJul 05 2012Working to lowest non-trivial order in fermions, we consider the four-derivative order corrected Lagrangian and supersymmetry transformations of the Euclidean Bagger-Lambert-Gustavsson theory. By demonstrating supersymmetric invariance of the Lagrangian ... More

Multiple M-branes and 3-algebrasNov 29 2012The purpose of this thesis is to explore the properties of multiple coincident M2- and M5-branes. We begin with a review of the BLG and ABJM models of multiple M2-branes and our focus will be on their formulation in terms of 3-algebras. We then examine ... More

Using Newton's Law for Dark EnergySep 24 2012A model is introduced in which Newton's law is modified between matter and dark energy corpuscles (DECs). The model predicts that the DEC component is presently decelerating in its expansion at 14% of the magnitude of the matter expansion acceleration. ... More

Structured Spreadsheet Modeling and ImplementationMar 10 2015Jun 06 2015Developing an error-free spreadsheet has been a problem since the beginning of end-user computing. In this paper, we present a methodology that separates the modeling from the implementation. Using proven techniques from Information Systems and Software ... More

Formule de caractère pour la série discrète de GL(N). Guide de l'utilisateur pour typistesMar 11 2015Ces notes en fran\c{c}ais sont un r\'esum\'e de la pr\'epublication arXiv:1402.2501, o\`u en collaboration avec Peter Schneider, nous \'etablissons des formules de caract\`ere pour la s\'erie discr\`ete de GL(N) d'un corps local non archim\'edien. Elles ... More

Eliminating the Coriols Effect in Liquid MirrorsAug 18 2001If uncorrected, the Coriolis force due to the rotation of the Earth causes significant aberration of images produced by large liquid-mirror telescopes. We show that this problem can be eliminated by a fixed compensating tilt of the liquid-mirror rotation ... More

A Technique for Photometric Detection and Measurement of Unresolved Binary SystemsNov 29 1997A technique is described for the detection and measurement of close binary systems whose images are unresolved. The method is based on analysis of the moment of inertia tensor of the image, from which the product of the binary flux ratio and square of ... More

Braids and symplectic four-manifolds with abelian fundamental groupFeb 14 2002We explain how a version of Floer homology can be used as an invariant of symplectic manifolds with $b_1>0$. As a concrete example, we look at four-manifolds produced from braids by a surgery construction. The outcome shows that the invariant is nontrivial; ... More

Symplectic Floer homology and the mapping class groupOct 30 2000Mar 04 2001We consider symplectic Floer homology in the lowest nontrivial dimension, that is to say, for area-preserving diffeomorphisms of surfaces. Particular attention is paid to the quantum cap product; we show that it distinguishes the trivial element of the ... More

More about vanishing cycles and mutationOct 03 2000The paper continues the discussion of symplectic aspects of Picard-Lefschetz theory begun in "Vanishing cycles and mutation" (this archive). There we explained how to associate to a suitable fibration over a two-dimensional disc a triangulated category, ... More

Some speculations on pairs-of-pants decompositions and Fukaya categoriesApr 06 2010Dec 07 2011These are notes from a 2010 talk. They concern possible ways in which Fukaya categories might be considered as "local", which means glued together from simpler pieces in a loosely sheaf-theoretic sense. As the title suggests, this is purely speculative. ... More

Vanishing cycles and mutationJul 19 2000Oct 02 2000This is the writeup of a talk given at the European Congress of Mathematics, Barcelona. It considers Picard-Lefschetz theory from the Floer cohomology viewpoint.

$π_1$ of symplectic automorphism groups and invertibles in quantum homology ringsNov 23 1995May 04 1997We define a homomorphism from (a certain extension of) the fundamental group of the Hamiltonian automorphism group of a symplectic manifold to the group of invertibles in its quantum cohomology ring. The manifold must satify a technical condition similar ... More

The almost product structure of Newton strata in the Deformation space of a Barsotti-Tate group with crystalline Tate tensorsJan 13 2016May 19 2016In this paper, we construct the almost product structure of the minimal Newton stratum in deformation spaces of {\BTTs}, similar to Oort's and Mantovan's construction for Shimura varieties of PEL-type. It allows us to describe the geometry of the Newton ... More

LIFO-search on digraphs: A searching game for cycle-rankMar 30 2011Aug 04 2011We consider the extension of the last-in-first-out graph searching game of Giannopoulou and Thilikos to digraphs. We show that all common variations of the game require the same number of searchers, and the minimal number of searchers required is one ... More

Light-Heavy Ion Collisions: A window into pre-equilibrium QCD dynamics?Feb 16 2015Relativistic collisions of light on heavy ions (p+Au at sqrt(s)=7.7 GeV, p+Au, d+Au,3He+Au at sqrt(s)=62.4 GeV and 200 GeV and p+Pb, 3He+Pb at sqrt(s)=5.02 TeV) are simulated using "superSONIC", a model that includes pre-equilibrium flow, viscous hydrodynamics ... More

Application of Model Derived Charge Transfer Inefficiency Corrections to STIS Photometric CCD DataOct 24 2003The STECF Calibration Enhancement effort for the Space Telescope Imaging Spectrograph (STIS) aims to improve data calibration via the application of physical modelling techniques. As part of this effort we have developed a model of the STIS CCD readout ... More

Magneto-elastic quantum fluctuations and phase transitions in the iron superconductorsFeb 22 2011Aug 01 2011We examine the relevance of magneto-elastic coupling to describe the complex magnetic and structural behaviour of the different classes of the iron superconductors. We model the system as a two-dimensional metal whose magnetic excitations interact with ... More

Comment on Dimensionless Units in the SIMay 27 2015The recent paper by Mohr and Phillips (arXiv:1409.2794) describes several problems relating to the treatment of angle measurement within SI, the unit hertz, and quantities that can be considered countable (rather than measureable). However, the proposals ... More

A Hiking Trip Through the Orders of Magnitude: Deriving Efficient Generators for Closed Simply-Typed Lambda Terms and Normal FormsAug 12 2016Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of {\em simply-typed ... More

The life and work of Major Percy Alexander MacMahonJul 05 2016My thesis describes the life and work of the mathematician Major Percy Alexander MacMahon (1854-1929). His early life as as a soldier in the Royal Artillery and the events which led to him embarking on a career in mathematical research and teaching are ... More

On $(p,r)$-Filtrations and Tilting ModulesOct 28 2016We study the relationship between Donkin's Tilting Module Conjecture and Donkin's Good $(p,r)$-Filtration Conjecture. Our main result was motivated by a result of Kildetoft and Nakano showing that the Tilting Module Conjecture implies one direction of ... More

2-categories and cyclic homologyMay 29 2016The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of ... More

The expected number of Z-eigenvalues of a real gaussian tensorApr 13 2016Aug 31 2016A real number $\lambda$ is called a Z-eigenvalue of a tensor $A$, if $\lambda$ is an eigenvalue of $A$ and the corresponding eigenvector $v$ is real and satisfies $v^Tv=1$. In this paper we compute the expected number of Z-eigenvalues of a real gaussian ... More

Rank Ordered AutoencodersMay 05 2016A new method for the unsupervised learning of sparse representations using autoencoders is proposed and implemented by ordering the output of the hidden units by their activation value and progressively reconstructing the input in this order. This can ... More

Developing a Repeating Model Using the Structured Spreadsheet Modelling and Implementation MethodologyFeb 20 2016Spreadsheets often have variables and formulas that are similar, differing only by the fact that they refer to different instances of an entity. For example, the calculation of the sales revenues of the South and East regions are Revenues South = Price ... More

Solving the Functional Schroedinger Equation: Yang-Mills String Tension and Surface Critical ScalingJun 25 2004Motivated by a heuristic model of the Yang-Mills vacuum that accurately describes the string-tension in three dimensions we develop a systematic method for solving the functional Schroedinger equation in a derivative expansion. This is applied to the ... More