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Eight-cluster structure of chloroplast genomes differs from similar one observed for bacteriaFeb 08 2018Previously, a seven-cluster pattern claiming to be a universal one in bacterial genomes has been reported. Keeping in mind the most popular theory of chloroplast origin, we checked whether a similar pattern is observed in chloroplast genomes. Surprisingly, ... More

Efficient particle continuation model predictive controlSep 09 2015Continuation model predictive control (MPC), introduced by T. Ohtsuka in 2004, uses Krylov-Newton approaches to solve MPC optimization and is suitable for nonlinear and minimum time problems. We suggest particle continuation MPC in the case, where the ... More

Accelerated graph-based nonlinear denoising filtersDec 01 2015Apr 13 2016Denoising filters, such as bilateral, guided, and total variation filters, applied to images on general graphs may require repeated application if noise is not small enough. We formulate two acceleration techniques of the resulted iterations: conjugate ... More

Preconditioning for continuation model predictive controlSep 09 2015Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) deals with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses the GMRES iterative ... More

Conjugate Gradient Acceleration of Non-Linear Smoothing FiltersSep 04 2015The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often performed in practice by tuning filter parameters, such as by increasing the width of the local smoothing ... More

Sparse preconditioning for model predictive controlDec 01 2015Mar 11 2016We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov methods. The Continuation/GMRES ... More

Continuation model predictive control on smooth manifoldsSep 09 2015Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. Continuation MPC, suggested by T.~Ohtsuka in 2004, uses Krylov-Newton iterations. ... More

Accelerated graph-based spectral polynomial filtersSep 08 2015Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. ... More

Quasiperiodic AlGaAs superlattices for neuromorphic networks and nonlinear control systemsFeb 08 2015The application of quasiperiodic AlGaAs superlattices as a nonlinear element of the FitzHugh-Nagumo neuromorphic network is proposed and theoretically investigated on the example of Fibonacci and figurate superlattices. The sequences of symbols for the ... More

Fine structure of one-dimensional discrete point systemMay 31 2012We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in $N$ and $l$) ... More

Dynamical clusters of infinite particle dynamicsDec 16 2011For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,\tau]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff for some $t\in[0,\tau]$ ... More

Phase transitions in one-dimensional static Coulomb mediaNov 27 2014We consider configurations of $N$ charged particles on the interval with nearest neighbour Coulomb interaction and constant external force. For different values of external force we find 4 different phases of the asymptotic particle density for the configuration ... More

Preconditioned Continuation Model Predictive ControlJun 08 2015Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses ... More

Phase transitions in the time synchronization modelJan 17 2012We continue the study of the time synchronization model from arXiv:1201.2141 . There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any ... More

Towards the First Catalog of Fermi-LAT sources below 100 MeVFeb 08 2018Previous analyses of point sources in the gamma-ray range were done either below 30 MeV or above 100 MeV. Below 30 MeV, the imaging Compton telescope (COMPTEL) onboard NASA's Compton Gamma-Ray Observatory detected 26 steady sources in the energy range ... More

Del Pezzo singularities and SUSY breakingMay 23 2007Aug 25 2007An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the ... More

Non RG logarithms via RG equationsFeb 10 2004We compute complete leading logarithms in $\Phi^4$ theory with the help of Connes and Kreimer RG equations. These equations are defined in the Lie algebra dual to the Hopf algebra of graphs. The results are compared with calculations in parquet approximation. ... More

On discrepancy between ATIC and Fermi dataMay 18 2009Jul 04 2009Either ATIC or Fermi-LAT data can be fitted together with the PAMELA data by three components: primary background ~ E^{-3.3}, secondary background ~ E^{-3.6}, and an additional source of electrons ~ E^{-g_a} Exp(-E/E_{cut}). We find that the best fits ... More

Non-amenability of product replacement graphsMay 10 2013We prove non-amenability of the product replacement graphs \Gamma_n(G) for uniformly non-amenable groups. We also prove it for Z-large groups, when n is sufficiently large. It follows that \Gamma_n(G) is non-amenable when n is sufficiently large for hyperbolic ... More

A Modified Screw Dislocation With Non-Singular Core of Finite Radius From Einstein-Like Gauge Equation (Non-Linear Approach)Dec 30 2003A continual model of non-singular screw dislocation lying along a straight infinitely long circular cylinder is investigated in the framework of translational gauge approach with the Hilbert--Einstein gauge Lagrangian. The stress--strain constitutive ... More

The coloring problem for classes with two small obstructionsJul 01 2013The coloring problem is studied in the paper for graph classes defined by two small forbidden induced subgraphs. We prove some sufficient conditions for effective solvability of the problem in such classes. As their corollary we determine the computational ... More

Spectral components analysis of diffuse emission processesFeb 06 2012We develop a novel method to separate the components of a diffuse emission process based on an association with the energy spectra. Most of the existing methods use some information about the spatial distribution of components, e.g., closeness to an external ... More

Expanders are order diameter non-hyperbolicJan 30 2015Feb 25 2015We show that expander graphs must have Gromov-hyperbolicity at least proportional to their diameter, with a constant of proportionality depending only on the expansion constant and maximal degree. In other words, expanders contain geodesic triangles which ... More

Time-dependent transport of a localized surface plasmon through a linear array of metal nanoparticles: Precursor and normal mode contributionsFeb 08 2018We theoretically investigate the time-dependent transport of a localized surface plasmon excitation through a linear array of identical and equidistantly spaced metal nanoparticles. Two different signals propagating through the array are found: one traveling ... More

XX Heisenberg Spin Chain and an Example of Path Integral with "Automorphic" Boundary ConditionsApr 01 2002New representation for the generating function of correlators of third components of spins in the XX Heisenberg spin chain is considered in the form given by the fermionic Gaussian path integrals. A part of the discrete anti-commuting integration variables ... More

Hopf algebra of ribbon graphs and renormalizationDec 17 2001Apr 24 2002Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is naturally defined ... More

The Integral Representation for the Product of Two Parabolic Cylinder Functions $D_ν(x) D_ν(-x)$ at $Re ν<0$ by Means of the Fundamental Solution of a Landau-Type OperatorJun 17 2001Dec 04 2001The fundamental solution (Green's function) of a first order matrix ordinary differential equation arising in a Landau-type problem is calculated by two methods. The coincidence of the two representations results in the integral formula for the product ... More

Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the meltingDec 07 2014The behavior of the shear modulus caused by proliferation of dipoles of non-singular screw dislocations with finite-sized core is considered. The representation of two-dimensional Coulomb gas with smoothed-out coupling is used, and the stress-stress correlation ... More

Optical bistability in artificial composite nanoscale molecules: Towards all optical processing at the nanoscaleDec 28 2010Optical response of artificial composite nanoscale molecules comprising a closely spaced noble metal nanoparticle and a semiconductor quantum dot have been studied theoretically. We consider a system composed of an Au particle and CdSe or CdSe/ZnSe quantum ... More

Engineering molecular aggregate spectraSep 16 2008We show that optical properties of linear molecular aggregates undergo drastic changes when aggregates are deposited on a metal surface. The dipole-dipole interactions of monomers with their images can result in strong {re-structuring of both the exciton ... More

Statistics of low-energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical studyFeb 03 2001Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i. e. those determining optical response. We found that the distribution ... More

Optical bistability and hysteresis of hybrid metal-semiconductor nano-dimerJun 08 2011Optical response of an artificial composite nano-dimer comprising a semiconductor quantum dot and a metal nanosphere is analyzed theoretically. We show that internal degrees of freedom of the system can manifest bistability and optical hysteresis as functions ... More

D-branes at Singularities and String PhenomenologyNov 15 2007In these notes we give an introduction to some of the concepts involved in constructing SM-like gauge theories in systems of branes at singularities of CY manifolds. These notes are an expanded version of lectures given by Herman Verlinde at the Cargese ... More

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

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

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

Fixed Points for Stochastic Open Chemical SystemsDec 16 2011In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for Boltzman equation. ... More

On the ambiguity of determination of interfering resonances parametersApr 17 2015The general form of solutions for parameters of interfering Breit-Wigner resonances is found. The number of solutions is determined by the properties of roots of corresponding characteristic equation and does not exceed $2^{N-1}$, where $N$ is the number ... More

Analytic dynamics of one-dimensional particle system with strong interactionMar 08 2012We study here the small time dynamics of $N$ electrons on the circle with Coul;omb repulsive interaction and study the series for the velocities (initially zero). The main result is the estimates of the convergence radius from below. We explain how this ... More

Hard spectrum of cosmic rays in the Disks of Milky Way and Large Magellanic CloudMay 28 2015The slope of the locally measured spectrum of cosmic rays varies from 2.8 for protons with energies below 200 GeV down to 2.5 for heavy nuclei with energies in the TeV-PeV range. It is not clear if the locally measured slope values are representative ... More

Local level statistics for optical and transport properties of disordered systems at finite temperatureOct 06 2006It is argued that the (traditional) global level statistics which determines localization and coherent transport properties of disordered systems at zero temperature (e.g. the Anderson model) becomes inappropriate when it comes to incoherent transport. ... More

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

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

ATIC, PAMELA, HESS, Fermi and nearby Dark Matter subhalosApr 22 2009Jun 25 2009We study the local flux of electrons and positrons from annihilating Dark Matter (DM), and investigate how its spectrum depends on the choice of DM model and inhomogeneities in the DM distribution. Below a cutoff energy, the flux is expected to have a ... More

Macrodimension - an invariant of local dynamicsJan 20 2012We define a Markov process on the set of countable graphs with spins. Transitions are local substitutions in the graph. It is proved that the scaling macrodimension is an invariant of such dynamics.

Lifts, derandomization, and diameters of Schreier graphs of Mealy automataJul 17 2014It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and present a class of ... More

Growth in product replacement graphsApr 19 2013Aug 01 2014We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.

On the resonant optical bistability conditionNov 16 2012We address a two level system in an environment interacting with the electromagnetic field in the dipole approximation. The resonant optical bistability induced by local-field effects is studied by considering the relationship between the population difference ... More

A complexity dichotomy for the dominating set problemMay 31 2015We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.

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

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

The laws of Newton and Coulomb as information transmission by virtual particlesMay 14 2016In elementary particle physics the philosophy of virtual particles is widely used. We use this philosophy to obtain the famous inverse square law of classical physics. We define a formal model without fields or forces, but with virtual particle - information ... More

KMS states on Quantum GrammarsJun 09 1999We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is called quantum ... More

Self-organized circular flow of classical point particlesSep 11 2012We consider newtonian dynamics of $N$ charged particles on the circle with nearest neigbour interaction with Coulomb repulsive potential $r^{-1}$ . Also there is an external accelerating force which is nonzero only on a small part of the circle. We construct ... More

Critical states of strongly interacting many-particle systems on a circleFeb 05 2012In multicomponent systems with strong local interaction one can encounter some phenomena absent in the standard systems of statistical physics and other multicomponent systems. Namely, a system with $N$ components in the bounded volume of order 1 (macroscale) ... More

Very high energy Fermi/LAT detection of HESS J0632+057Jan 29 2016Feb 02 2016We report on the results of ~7 yrs of the very-high energy (10-600 GeV) observations of HESS J0632+057 with FERMI/LAT. In the highest energy band, 200-600 GeV, the source is clearly detected with the statistical significance >3.6sigma at orbital phases ... More

Point Source Detection and Flux Determination with PGWaveOct 05 2016One of the largest uncertainties in the Point Source (PS) studies, at Fermi-LAT energies, is the uncertainty in the diffuse background. In general there are two approaches for PS analysis: background-dependent methods, that include modeling of the diffuse ... More

Resonance Features of the Conductance of Open Billiards with the Spin-Orbit InteractionJan 30 2013Feb 01 2013The transport properties of a circular billiard with attached channels, which is an open system, have been studied in the presence of the Dresselhaus and Rashba spin-orbit interactions. It has been shown that this interaction leads to the appearance of ... More

DNA double helices for single molecule electronicsMar 09 2007The combination of self-assembly and electronic properties as well as its true nanoscale dimensions make DNA a promising candidate for a building block of single molecule electronics. We argue that the intrinsic double helix conformation of the DNA strands ... More

On the size scaling of the nearest level spacing at criticalityOct 20 2003Oct 21 2003It is conjectured that the size scaling of the nearest level spacing in the critical spectral region, $S(N)\propto N^{-\lambda}$, remains qualitatively the same within phases of extended and critical states. The exponent $\lambda$ is therefore identical ... More

Probability around the Quantum Gravity. Part 1: Pure Planar GravitySep 18 1998In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the existence and properties ... More

Fixed points for one-dimensional particle system with strong interactionFeb 01 2012We consider hamiltonian $N$ particle system on the finite segment with nearest-neighbor Coulomb interaction and external force $F$. We study the fixed points of such system and show that the distances between neighbors are asymptotically, for large $N$, ... More

Hopf algebra of graphs and the RG equationsAug 30 2004We study the renormalization group equations following from the Hopf algebra of graphs. Vertex functions are treated as vectors in dual to the Hopf algebra space. The RG equations on such vertex functions are equivalent to RG equations on individual Feynman ... More

Toward the full test of the nuMSM sterile neutrino dark matter model with AthenaSep 09 2015Mar 12 2016We discuss the potential of Athena X-ray telescope, in particular of its X-ray Integral Field Unit (X-IFU), for detection of the signal from the light-weight decaying dark matter with mass in the keV range. We show that high energy resolution and large ... More

Leading RG logs in $φ^4$ theoryJul 31 2003Aug 15 2003We find the leading RG logs in $\phi^4$ theory for any Feynman diagram with 4 external edges. We obtain the result in two ways. The first way is to calculate the relevant terms in Feynman integrals. The second way is to use the RG invariance based on ... More

Asymptotic behaviour in the time synchronization modelJan 10 2012There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with rates $N_{j}^{-1}\alpha_{ij}$. ... More

Monitoring the localization-delocalization transition within a 1D model with non-random long-range interactionMar 05 2003Dec 01 2004We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and {\it non-random} long-range inter-site interaction $J_{mn}=J/|m-n|^{\mu}$. The model is critical at $1<\mu<3/2$ and reveals the localization-delocalization ... More

Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random WalksJan 28 2014The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. ... More

The Torelli group and congruence subgroups of the mapping class groupJan 18 2012These are the lecture notes for my course at the 2011 Park City Mathematics Graduate Summer School. The first two lectures covered the basics of the Torelli group and the Johnson homomorphism, and the third and fourth lectures discussed the second cohomology ... More

Obtaining presentations from group actions without making choicesJan 26 2009Apr 07 2011Consider a group $G$ acting nicely on a simply-connected simplicial complex $X$. Numerous classical methods exist for using this group action to produce a presentation for $G$. For the case that $X/G$ is 2-connected, we give a new method that has the ... More

Restricting Specht modules of cyclotomic Hecke algebrasOct 30 2016This paper proves that the restriction of a Specht module for a (degenerate or non-degenerate) cyclotomic Hecke algebra, or KLR algebra, of type A has a Specht filtration.

Rejoinder to "Analysis of variance--why it is more important than ever" by A. GelmanAug 26 2005Rejoinder to ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]

Thoughts on new statistical procedures for age-period-cohort analysesJul 15 2009Age-period-cohort analysis is mathematically intractable because of fundamental nonidentifiability of linear trends. However, some understanding can be gained in the context of individual problems.

The Informal Logic of Mathematical ProofJun 19 2003Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more ... More

On Upper Bounds for the Tail Distribution of Geometric Sums of Subexponential Random VariablesMay 29 2008Mar 18 2009The approach used by Kalashnikov and Tsitsiashvili for constructing upper bounds for the tail distribution of a geometric sum with subexponential summands is reconsidered. By expressing the problem in a more probabilistic light, several improvements and ... More

Software for enumerative and analytic combinatoricsJan 11 2016We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, P\'olya theory, combinatorial ... More

Size-Separable Tile Self-Assembly: A Tight Bound for Temperature-1 Mismatch-Free SystemsApr 29 2014We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by the practical ... More

The Gromov-Witten Theory of Borcea-Voisin Orbifolds and Its Analytic ContinuationsJun 24 2015In the early 1990s, Borcea-Voisin orbifolds were some of the ear- liest examples of Calabi-Yau threefolds shown to exhibit mirror symmetry. However, their quantum theory has been poorly investigated. We study this in the context of the gauged linear sigma ... More

Physical maze solvers. All twelve prototypes implement 1961 Lee algorithmJan 18 2016We overview experimental laboratory prototypes of maze solvers. We speculate that all maze solvers implement Lee algorithm by first developing a gradient of values showing a distance from any site of the maze to the destination site and then tracing a ... More

Slime mould computes planar shapesJun 01 2011Computing a polygon defining a set of planar points is a classical problem of modern computational geometry. In laboratory experiments we demonstrate that a concave hull, a connected alpha-shape without holes, of a finite planar set is approximated by ... More

Physarum boats: If plasmodium sailed it would never leave a portJan 28 2009Plasmodium of \emph{Physarum polycephalum} is a single huge (visible by naked eye) cell with myriad of nuclei. The plasmodium is a promising substrate for non-classical, nature-inspired, computing devices. It is capable for approximation of shortest path, ... More

On excitable beta-skeletonsJul 01 2010A beta-skeleton is a planar proximity undirected graph of an Euclidean point set where nodes are connected by an edge if their lune-based neighborhood contains no other points of the given set. Parameter $\beta$ determines size and shape of the nodes' ... More

Latitudinal Shear Instabilities during Type I X-ray BurstsMay 04 2005Coherent oscillations have been observed during Type I X-ray bursts from 14 accreting neutron stars in low mass X-ray binaries, providing important information about their spin frequencies. However, the origin of the brightness asymmetry on the neutron ... More

A Framework for Specifying, Prototyping, and Reasoning about Computational SystemsOct 05 2009Oct 05 2009This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal systems, a mechanism ... More

An infinite presentation of the Torelli groupMar 19 2007Dec 02 2008In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all "separating twists", all "bounding pair maps", and all "commutators of simply intersecting ... More

Compressing Word EmbeddingsNov 19 2015May 16 2016Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale text analysis) ... More

Foundations of algebraic surgeryNov 30 2001An elementary introduction to the principles of algebraic surgery.

The differential topology of loop spacesOct 05 2005This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as the background notes to a series of seminars given at NTNU and subsequently at Sheffield. I am posting them ... More

Quantum Reed-Muller CodesAug 16 1996Aug 22 1996A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2 sum_{i=0}^{t-1} C(r,i), 2^t + 2^{t-1} ]].

Multiple Particle Interference and Quantum Error CorrectionJan 29 1996May 13 1996The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of ... More

Quantum ComputingAug 12 1997Sep 24 1997The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out ... More

$α$-admissibility of the right-shift semigroup on $L^2(\mathbb{R}_+)$Apr 28 2009It is shown that the right shift semigroup on $L^2(\mathbb{R}_+)$ does not satisfy the weighted Weiss conjecture for $\alpha \in (0,1)$. In other words, $\alpha$-admissibility of scalar valued observation operators cannot always be characterised by a ... More

The Geometry of the Loop Space and a Construction of a Dirac OperatorMay 04 2005We describe a construction of fibrewise inner products on the cotangent bundle of the smooth free loop space of a Riemannian manifold. Using this inner product, we construct an operator over the loop space of a string manifold which is directly analogous ... More

An Algebraic Weak Factorisation System on 01-Substitution Sets: A Constructive ProofSep 05 2014May 17 2016We will construct an algebraic weak factorisation system on the category of 01 substitution sets such that the R-algebras are precisely the Kan fibrations together with a choice of Kan filling operation. The proof is based on Garner's small object argument ... More

What is the best approach to counting primes?Jun 14 2014As long as people have studied mathematics, they have wanted to know how many primes there are. Getting precise answers is a notoriously difficult problem, and the first suitable technique, due to Riemann, inspired an enormous amount of great mathematics, ... More

Sequences and dynamical systems associated with canonical approximation by rationalsFeb 22 2011We study metrical properties of various subsequences associated to the sequence of rational approximants coming from the continued fraction of an irrational number. Our methods build upon Bosma, Jager and Wiedijk's proof of the Doblin-Lenstra conjecture ... More

Automorphism Groups of some Finite SemifieldsMay 22 2013We determine the automorphism group for some well known constructions of finite semifields. In particular, we compute the automorphism group of Sandler's semifields and in certain cases the automorphism groups of the Hughes-Kleinfeld and Knuth semifields. ... More

How Big Can a Black Hole Grow?Nov 26 2015Dec 09 2015I show that there is a physical limit to the mass of a black hole, above which it cannot grow through luminous accretion of gas, and so cannot appear as a quasar or active galactic nucleus. The limit is Mmax \simeq 5x10^{10}M_sun for typical parameters, ... More

Accretion and Outflow in Active GalaxiesFeb 09 2010Feb 10 2010I review accretion and outflow in active galactic nuclei. Accretion appears to occur in a series of very small--scale, chaotic events, whose gas flows have no correlation with the large--scale structure of the galaxy or with each other. The accreting ... More

Heating Cluster GasMar 09 2009It is now generally agreed that some process prevents the diffuse gas in galaxy clusters from cooling significantly, although there is less agreement about the nature of this process. I suggest that cluster gas may be heated by a natural extension of ... More