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Precolouring extension of Vizing's theoremNov 28 2016Fix a palette $\mathcal K$ of $\Delta+1$ colours, a graph with maximum degree $\Delta$, and a matching $M$ with minimum distance between edges at least $9$. If the edges of $M$ are arbitrarily precoloured from $\mathcal K$, then there is guaranteed to ... More

Decomposition of bounded degree graphs into $C_4$-free subgraphsAug 08 2014Sep 23 2014We prove that every graph with maximum degree $\Delta$ admits a partition of its edges into $O(\sqrt{\Delta})$ parts (as $\Delta\to\infty$) none of which contains $C_4$ as a subgraph. This bound is sharp up to a constant factor. Our proof uses an iterated ... More

Distance colouring without one cycle lengthJan 26 2017We consider distance colourings in graphs of maximum degree at most $d$ and how excluding one fixed cycle length $\ell$ affects the number of colours required as $d\to\infty$. For vertex-colouring and $t\ge 1$, if any two distinct vertices connected by ... More

A precolouring extension of Vizing's theoremNov 28 2016Dec 27 2018Fix a palette $\mathcal K$ of $\Delta+1$ colours, a graph with maximum degree $\Delta$, and a subset $M$ of the edge set with minimum distance between edges at least $9$. If the edges of $M$ are arbitrarily precoloured from $\mathcal K$, then there is ... More

List colouring with a bounded paletteJul 13 2015Nov 27 2015Kr\'al' and Sgall (2005) introduced a refinement of list colouring where every colour list must be subset to one predetermined palette of colours. We call this $(k,\ell)$-choosability when the palette is of size at most $\ell$ and the lists must be of ... More

The distance-t chromatic index of graphsMay 18 2012Sep 03 2013We consider two graph colouring problems in which edges at distance at most $t$ are given distinct colours, for some fixed positive integer $t$. We obtain two upper bounds for the distance-$t$ chromatic index, the least number of colours necessary for ... More

The t-improper chromatic number of random graphsSep 26 2008Apr 16 2009We consider the $t$-improper chromatic number of the Erd{\H o}s-R{\'e}nyi random graph $G(n,p)$. The t-improper chromatic number $\chi^t(G)$ of $G$ is the smallest number of colours needed in a colouring of the vertices in which each colour class induces ... More

Rapid mixing of subset Glauber dynamics on graphs of bounded tree-widthFeb 17 2011Motivated by the `subgraphs world' view of the ferromagnetic Ising model, we develop a general approach to studying mixing times of Glauber dynamics based on subset expansion expressions for a class of graph polynomials. With a canonical paths argument, ... More

Bounded monochromatic components for random graphsJul 14 2014Jul 18 2017We consider vertex partitions of the binomial random graph $G_{n,p}$. For $np\to\infty$, we observe the following phenomenon: in any partition into asymptotically fewer than $\chi(G_{n,p})$ parts, i.e. $o(np/\log np)$ parts, one part must induce a connected ... More

Squared chromatic and stability numbers without claws or large cliquesSep 27 2016Let $G$ be a claw-free graph on $n$ vertices with clique number $\omega$. We prove the following for the square $G^2$ of $G$. If $\omega\le 3$, then its chromatic number satisfies $\chi(G^2)\le 10$ while its stability number satisfies $\alpha(G^2)\ge ... More

VC dimension and a union theorem for set systemsAug 07 2018Oct 15 2018Fix positive integers $k$ and $d$. We show that, as $n\to\infty$, any set system $\mathcal{A} \subset 2^{[n]}$ for which the VC dimension of $\{ \triangle_{i=1}^k S_i \mid S_i \in \mathcal{A}\}$ is at most $d$ has size at most $(2^{d\bmod{k}}+o(1))\binom{n}{\lfloor ... More

Squared chromatic number without claws or large cliquesSep 27 2016May 17 2018Let $G$ be a claw-free graph on $n$ vertices with clique number $\omega$, and consider the chromatic number $\chi(G^2)$ of the square $G^2$ of $G$. Writing $\chi'_s(d)$ for the supremum of $\chi(L^2)$ over the line graphs $L$ of simple graphs of maximum ... More

Packing graphs of bounded codegreeMay 18 2016Two graphs $G_1$ and $G_2$ on $n$ vertices are said to pack if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\'as and Eldridge and, independently, ... More

Largest sparse subgraphs of random graphsMar 01 2012For the Erd\H{o}s-R\'enyi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t = t(n) is not too ... More

Separation choosability and dense bipartite induced subgraphsFeb 11 2018Dec 04 2018We study a restricted form of list colouring, for which every pair of lists that correspond to adjacent vertices may not share more than one colour. The optimal list size such that a proper list colouring is always possible given this restriction, we ... More

The t-stability number of a random graphAug 31 2008Oct 26 2010Given a graph G = (V,E), a vertex subset S is called t-stable (or t-dependent) if the subgraph G[S] induced on S has maximum degree at most t. The t-stability number of G is the maximum order of a t-stable set in G. We investigate the typical values that ... More

Tree-like distance colouring for planar graphs of sufficient girthMay 06 2018Feb 06 2019Given a multigraph $G$ and a positive integer $t$, the distance-$t$ chromatic index of $G$ is the least number of colours needed for a colouring of the edges so that every pair of distinct edges connected by a path of fewer than $t$ edges must receive ... More

The Bollobás-Eldridge-Catlin conjecture for even girth at least $10$Mar 15 2017Two graphs $G_1$ and $G_2$ on $n$ vertices are said to \textit{pack} if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\'as and Eldridge and, ... More

Colouring squares of claw-free graphsSep 27 2016Is there some absolute $\varepsilon > 0$ such that for any claw-free graph $G$, the chromatic number of the square of $G$ satisfies $\chi(G^2) \le (2-\varepsilon) \omega(G)^2$, where $\omega(G)$ is the clique number of $G$? Erd\H{o}s and Ne\v{s}et\v{r}il ... More

A precise threshold for quasi-Ramsey numbersMar 14 2014Jul 14 2015We consider a variation of Ramsey numbers introduced by Erd\H{o}s and Pach (1983), where instead of seeking complete or independent sets we only seek a $t$-homogeneous set, a vertex subset that induces a subgraph of minimum degree at least $t$ or the ... More

On a Ramsey-type problem of Erdős and PachNov 17 2014Feb 22 2016In this paper we show that there exists a constant $C>0$ such that for any graph $G$ on $Ck\ln k$ vertices either $G$ or its complement $\bar{G}$ has an induced subgraph on $k$ vertices with minimum degree at least $\frac12(k-1)$. This affirmatively answers ... More

Strong cliques and forbidden cyclesMar 14 2019Given a graph $G$, the strong clique number $\omega_2'(G)$ of $G$ is the cardinality of a largest collection of edges every pair of which are incident or connected by an edge in $G$. We study the strong clique number of graphs missing some set of cycle ... More

Least conflict choosabilityMar 29 2018Given a multigraph, suppose that each vertex is given a local assignment of $k$ colours to its incident edges. We are interested in whether there is a choice of one local colour per vertex such that no edge has both of its local colours chosen. The least ... More

Seshadri constants on symmetric products of curvesAug 09 2006Sep 05 2006Let X_g=C^{(2)}_g be the second symmetric product of a very general curve of genus g. We reduce the problem of describing the ample cone on X_g to a problem involving the Seshadri constant of a point on X_{g-1}. Using this we recover a result of Ciliberto-Kouvidakis ... More

Occupancy fraction, fractional colouring, and triangle fractionDec 28 2018Given $\varepsilon>0$, there exists $f_0$ such that, if $f_0 \le f \le \Delta^2+1$, then for any graph $G$ on $n$ vertices of maximum degree $\Delta$ in which the neighbourhood of every vertex in $G$ spans at most $\Delta^2/f$ edges, (i) an independent ... More

Colouring triangle-free graphs with local list sizesDec 04 2018We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs. In both our results, we permit the amount of colour made available to ... More

Discrepancy and large dense monochromatic subsetsOct 20 2016Jan 10 2018Erd\H{o}s and Pach (1983) introduced the natural degree-based generalisations of Ramsey numbers, where instead of seeking large monochromatic cliques in a $2$-edge coloured complete graph, we seek monochromatic subgraphs of high minimum or average degree. ... More

Forecasting Transformative AI: An Expert SurveyJan 24 2019Transformative AI technologies have the potential to reshape critical aspects of society in the near future. However, in order to properly prepare policy initiatives for the arrival of such technologies accurate forecasts and timelines are necessary. ... More

A note on Positivity of the CM line bundleMay 11 2006Aug 09 2006We show that positivity of the CM line associated to a family of polarised varieties is intimately related to the stability of its members. We prove that the CM line is nef on any curve which meets the stable locus, and that it is pseudoeffective (i.e. ... More

Algebraic and Logical Methods in Quantum ComputationOct 08 2015This thesis contains contributions to the theory of quantum computation. We first define a new method to efficiently approximate special unitary operators. Specifically, given a special unitary U and a precision {\epsilon} > 0, we show how to efficiently ... More

Cyclotron effective masses in layered metalsMar 13 2000Many layered metals such as quasi-two-dimensional organic molecular crystals show properties consistent with a Fermi liquid description at low temperatures. The effective masses extracted from the temperature dependence of the magnetic oscillations observed ... More

Thermodynamics of a bad metal-Mott insulator transition in the presence of frustrationNov 07 2012Apr 26 2013We study a range of thermodynamic properties (charge susceptibility, specific heat, entropy and spin susceptibility) of the Hubbard model on the anisotropic triangular lattice at half filling by means of the numerical finite-temperature Lanczos method. ... More

Weighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metricsJul 30 2009Sep 25 2009We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli space of orbifolds. ... More

Phonon anomalies due to strong electronic correlations in layered organic metalsJul 11 2000We show how the coupling between the phonons and electrons in a strongly correlated metal can result in phonon frequencies which have a non-monotonic temperature dependence. Dynamical mean-field theory is used to study the Hubbard-Holstein model that ... More

An obstruction to the existence of constant scalar curvature Kähler metricsDec 29 2004Dec 05 2005We prove that polarised manifolds that admit a constant scalar curvature K\"ahler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope $\mu$ for a projective manifold and for each of its subschemes, and show that ... More

A construction of 2-filtered bicolimits of categoriesMay 11 2006We define the notion of 2-filtered 2-category}and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if and only if it is a filtered category, and our construction ... More

Comparison of methods for estimating continuous distributions of relaxation timesApr 18 2005The nonparametric estimation of the distribution of relaxation times approach is not as frequently used in the analysis of dispersed response of dielectric or conductive materials as are other immittance data analysis methods based on parametric curve ... More

Entropy of Some Models of Sparse Random Graphs With Vertex-NamesJan 02 2013Consider the setting of sparse graphs on N vertices, where the vertices have distinct "names", which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as cN log N for some model-dependent ... More

Improper choosability and Property BMay 19 2012A fundamental connection between list vertex colourings of graphs and Property B (also known as hypergraph 2-colourability) was already known to Erd\H{o}s, Rubin and Taylor. In this article, we draw similar connections for improper list colourings. This ... More

Probing the Structure of the PomeronDec 16 1998We suggest that the pseudo-rapidity cut dependence of diffractive deep-inelastic scattering events at HERA may provide a sensitive test of models of diffraction. A comparison with the experimental cross section shows that the Donnachie-Landshoff model ... More

Enhancing Magnetic Ordering in Cr-doped Bi2Se3 using High-TC Ferrimagnetic InsulatorMar 26 2015We report a study of enhancing the magnetic ordering in a model magnetically doped topological insulator (TI), Bi2-xCrxSe3, via the proximity effect using a high-TC ferrimagnetic insulator Y3Fe5O12. The FMI provides the TI with a source of exchange interaction ... More

Comment on the Coupling of Zero Sound to the $J=1^-$ Modes of $^3$He-BFeb 01 1993Features in the zero sound attenuation near the pair-breaking edge in superfluid $^3$He-B have been observed in large magnetic fields. Schopohl and Tewordt [{\sl J. Low Temp. Phys.} {\bf 57}, 601 (1984)] claim that the $J=1^-, M=\pm 1$ order-parameter ... More

Collective Modes and Nonlinear Acoustics in Superfluid 3He-BSep 24 2013We discuss the relationship of collisionless sound propagation and attenuation to the order parameter collective modes of superfluid 3He-B. These modes, which reflect the symmetries of the normal state as well as the broken gauge and relative rotational ... More

The masses of AGN host galaxies & the origin of radio loudnessMar 12 2002We highlight some of the principal results from our recent Hubble Space Telescope studies of quasars and radio galaxies. The hosts of these powerful AGN are normal massive ellipticals which lie on the region of the fundamental plane populated predominantly ... More

Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}Mar 27 2013Nov 02 2013The recent measurement of the third lepton mixing angle, \theta_{13}, has shown that, although small compared to \theta_{12} and \theta_{23}, it is much larger than anticipated in schemes that generate Tri-Bi-Maximal (TBM) or Golden Ratio (GR) mixing. ... More

Photon Structure Functions Beyind the SUSY ThresholdAug 25 2000We evolve virtual photon parton densities up to the SUSY threshold and higher using coupled inhomogeneous DGLAP differential equations. Reliable input parameterizations were available from the c-quark threshold. Limited $P^2$ ( target photon virtuality ... More

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse fieldDec 31 1998We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse field. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation ... More

Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductorsJul 30 2010Jan 14 2011We review the interplay of frustration and strong electronic correlations in quasi-two-dimensional organic charge transfer salts, such as k-(BEDT-TTF)_2X and Et_nMe_{4-n}Pn[Pd(dmit)2]2. These two forces drive a range of exotic phases including spin liquids, ... More

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetryJun 20 2000We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can ... More

Colouring powers and girthNov 27 2015Aug 08 2016Alon and Mohar (2002) posed the following problem: among all graphs $G$ of maximum degree at most $d$ and girth at least $g$, what is the largest possible value of $\chi(G^t)$, the chromatic number of the $t$th power of $G$? For $t\ge 3$, we provide several ... More

Bounded monochromatic components for random graphsJul 14 2014We consider vertex partitions of the binomial random graph $G_{n,p}$. For $np\to\infty$, we observe the following phenomenon: for any partition into asymptotically fewer than $\chi(G_{n,p})$ parts, i.e. $o(np/\log np)$ parts, there must be one part whose ... More

Evolution of the Clustering of Photometrically Selected SDSS GalaxiesFeb 08 2010Apr 26 2010We measure the angular auto-correlation functions (w) of SDSS galaxies selected to have photometric redshifts 0.1 < z < 0.4 and absolute r-band magnitudes Mr < -21.2. We split these galaxies into five overlapping redshift shells of width 0.1 and measure ... More

Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State SystemJul 16 2014Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal ... More

Ideal triangulations of 3--manifolds I: spun normal surface theoryOct 25 2004In this paper, we will compute the dimension of the space of spun and ordinary normal surfaces in an ideal triangulation of the interior of a compact 3-manifold with incompressible tori or Klein bottle components. Spun normal surfaces have been described ... More

The Information Content of Anisotropic Baryon Acoustic Oscillation Scale MeasurementsJan 22 2015Apr 29 2015Anisotropic measurements of the Baryon Acoustic Oscillation (BAO) feature within a galaxy survey enable joint inference about the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$. These measurements are typically obtained from moments of ... More

Normalization of the Matter Power Spectrum via Higher-Order Angular Correlations of Luminous Red GalaxiesApr 21 2008We present a novel technique to measure $\sigma_8$, by measuring the dependence of the second-order bias of a density field on $\sigma_8$ using two separate techniques. Each technique employs area-averaged angular correlation functions ($\bar{\omega}_N$), ... More

On the observed disc temperature of accreting intermediate mass black holesAug 17 2004Some ultraluminous X-ray sources in nearby galaxies show soft components resembling thermal disc emission. Calculations based on blackbody emission then indicate that the accreting black holes at the centres of these discs have masses of 100s to 1000s ... More

Iron line profiles including emission from within the innermost stable orbit of a black hole accretion discAug 10 1998Reynolds & Begelman (1997) have recently proposed a model in which the broad and extremely redshifted iron line seen during a deep minimum of the light curve of the Seyfert 1 galaxy MCG-6-30-15 originates from matter spiralling into a Schwarzschild black ... More

Solving the BFKL Equation with Running CouplingNov 03 2000Nov 30 2000We describe a formalism for solving the BFKL equation with a coupling that runs for momenta above a certain infrared cutoff. By suitably choosing matching conditions proper account is taken of the fact that the BFKL diffusion implies that the solution ... More

On Gauss-Bonnet black hole entropyFeb 10 2004Dec 10 2004We investigate the entropy of black holes in Gauss-Bonnet and Lovelock gravity using the Noether charge approach, in which the entropy is given as the integral of a suitable (n-2) form charge over the event horizon. We compare the results to those obtained ... More

Quantum Control Theory for State Transformations: Dark States and their EnlightenmentMar 22 2010Oct 05 2010For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an ... More

The galaxy UV luminosity function at z ~ 2 - 4; new results on faint-end slope and the evolution of luminosity densityJul 20 2015Mar 06 2016We present a new, robust measurement of the evolving rest-frame UV galaxy luminosity function (LF) over the key redshift range z = 2 - 4. Our results are based on the high dynamic range provided by combining the HUDF, CANDELS/GOODS-South, and UltraVISTA/COSMOS ... More

Modeling the reconstructed BAO in Fourier spaceNov 02 2015May 12 2016The density field reconstruction technique, which was developed to partially reverse the nonlinear degradation of the Baryon Acoustic Oscillation (BAO) feature in the galaxy redshift surveys, has been successful in substantially improving the cosmology ... More

A Proposed General Method for Parameter Estimation of Noise Corrupted Oscillator SystemsOct 10 2012This paper provides a proposed means to estimate parameters of noise corrupted oscillator systems. An application for a submarine combat control systems (CCS) rack is described as exemplary of the method.

Long distance chiral corrections in B meson amplitudesMay 16 2003Jun 13 2003We discuss the chiral corrections to f_B and B_B with particular emphasis on determining the portion of the correction that arises from long distance physics. For very small pion and kaon masses all of the usual corrections are truly long distance, while ... More

A random walker's view of networks whose growth it shapesNov 22 2018Jan 28 2019We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We demonstrate that ... More

Scaling and Balancing for High-Performance Computation of Optimal ControlsOct 25 2018It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We also show ... More

A Radial Measurement of the Galaxy Tidal Alignment Magnitude with BOSS DataFeb 21 2018The anisotropy of galaxy clustering in redshift space has long been used to probe the rate of growth of cosmological perturbations. However, if galaxies are aligned by large-scale tidal fields, then a sample with an orientation-dependent selection effect ... More

X-ray Scaling Properties of Early-type GalaxiesJan 09 2003We present an analysis of 39 X-ray luminous early-type galaxies observed with the ROSAT PSPC. Using multi-component spectral and spatial fits to these data we have measured halo abundance, temperature, luminosity and surface brightness profile. We compare ... More

Primordial non-Gaussianity in the bispectra of large-scale structureOct 28 2013May 16 2014The statistics of large-scale structure in the Universe can be used to probe non-Gaussianity of the primordial density field, complementary to existing constraints from the cosmic microwave background. In particular, the scale dependence of halo bias, ... More

Sensitivity of the photo-physical properties of organometallic complexes to small chemical changesMay 21 2010Jul 26 2010We investigate an effective model Hamiltonian for organometallic complexes that are widely used in optoelectronic devices. The two most important parameters in the model are $J$, the effective exchange interaction between the $\pi$ and $\pi^*$ orbitals ... More

Interplay of frustration, magnetism, charge ordering, and covalency in a model of Na0.5CoO2Aug 29 2008Jan 19 2009We investigate an effective Hamiltonian for Na0.5CoO2 that includes the electrostatic potential due to the ordered Na ions and strong electronic correlations. This model displays a subtle interplay between metallic and insulating phases and between charge ... More

Models of organometallic complexes for optoelectronic applicationsJul 02 2010Organometallic complexes have potential applications as the optically active components of organic light emitting diodes (OLEDs) and organic photovoltaics (OPV). Development of more effective complexes may be aided by understanding their excited state ... More

Quipper: Concrete Resource Estimation in Quantum AlgorithmsDec 01 2014Despite the rich literature on quantum algorithms, there is a surprisingly small amount of coverage of their concrete logical design and implementation. Most resource estimation is done at the level of complexity analysis, but actual concrete numbers ... More

Hyak Mortality Monitoring System: Innovative Sampling and Estimation Methods - Proof of Concept by SimulationApr 08 2015Traditionally health statistics are derived from civil registration and vital statistics (CRVS). CRVS in low- to middle-income countries varies from partial coverage to essentially nothing at all. Consequently the state of the art for public health information ... More

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave fieldOct 20 2010Nov 29 2010We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator ... More

Canonical forms for single-qutrit Clifford+T operatorsMar 13 2018We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit ... More

Squared chromatic number without claws or large cliquesSep 27 2016Oct 25 2016Let $G$ be a claw-free graph on $n$ vertices with clique number $\omega$. We prove the following for the chromatic number $\chi(G^2)$ of the square $G^2$ of $G$. If $\omega\le 3$, then $\chi(G^2)\le 10$. If $\omega \le 4$, then $\chi(G^2) \le 22$. This ... More

The universal $\ln^{2}s$ increase in total cross sectionsFeb 12 2003Feb 17 2003While it has long been known that many models of high energy scattering give cross sections which rise as $\ln^{2}s$, the determination of the coefficient of this term is rarely given. We show that in gaussian and exponential eikonal models an exact expression ... More

A microscopic theory of skyrmion excitations in the fractional quantum Hall systemAug 13 1996We present a microscopic theory of skyrmion and antiskyrmion excitations in fractional quantum Hall systems, and calculate in an analytical fashion their excitation energies. From the calculated net spins at various fractional filling factors, we find ... More

Massive and Red Objects predicted by a semianalytical model of galaxy formationJan 30 2006May 25 2006We study whether hierarchical galaxy formation in a concordance $\Lambda$CDM universe can produce enough massive and red galaxies compared to the observations. We implement a semi-analytical model in which the central black holes gain their mass during ... More

Pairing in the quantum Hall systemOct 14 1997We find an analogy between the single skyrmion state in the quantum Hall system and the BCS superconducting state and address that the quantum mechanical origin of the skyrmion is electronic pairing. The skyrmion phase is found to be unstable for magnetic ... More

GRATIS: GeneRAting TIme Series with diverse and controllable characteristicsMar 07 2019The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires a diverse collection of time series ... More

Granular gases under extreme drivingFeb 04 2010Aug 06 2010We study inelastic gases in two dimensions using event-driven molecular dynamics simulations. Our focus is the nature of the stationary state attained by rare injection of large amounts of energy to balance the dissipation due to collisions. We find that ... More

Resonant Nernst effect in the metallic and field-induced spin density wave states of (TMTSF)2ClO4Jan 26 2005We examine an unusual phenomenon where, in tilted magnetic fields near magic angles parallel to crystallographic planes, a "giant" resonant Nernst signal has been observed by Wu et al.[Phys. Rev. Lett. 91 56601(2003)] in the metallic state of an organic ... More

de Haas-van Alphen effect of correlated Dirac states in kagome metal Fe3Sn2Sep 28 2018Oct 16 2018The field of topological electronic materials has seen rapid growth in recent years, in particular with the increasing number of weakly interacting systems predicted and observed to host topologically non-trivial bands. Given the broad appearance of topology ... More

Semistability and CAT(0) GeometryMar 20 2017We explain why semistability of a one-ended proper CAT(0) space can be determined by the geodesic rays. This is applied to boundaries of CAT(0) groups.

The rigidity of periodic frameworks as graphs on a fixed torusFeb 29 2012We define periodic frameworks as graphs on the torus, using the language of gain graphs. We present some fundamental definitions and results about the infinitesimal rigidity of graphs on a torus of fixed size and shape, and find necessary conditions for ... More

Skew-closed categoriesMay 30 2012Sep 01 2012Spurred by the new examples found by Kornel Szlach\'anyi of a form of lax monoidal category, the author felt the time ripe to publish a reworking of Eilenberg-Kelly's original paper on closed categories appropriate to the laxer context. The new examples ... More

The core of adjoint functorsDec 01 2011Jan 03 2012There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, ... More

Monoidal categories in, and linking, geometry and algebraJan 14 2012Oct 04 2012This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a link between knot ... More

The rigidity of periodic body-bar frameworks on the three-dimensional fixed torusMar 29 2012We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.

Inductive constructions for frameworks on a two-dimensional fixed torusMar 29 2012Nov 06 2014An infinite periodic framework in the plane can be represented as a framework on a torus, using a $\mathbb Z^2$-labelled gain graph. We find necessary and sufficient conditions for the generic minimal rigidity of frameworks on the two-dimensional fixed ... More

Fast R-CNNApr 30 2015Sep 27 2015This paper proposes a Fast Region-based Convolutional Network method (Fast R-CNN) for object detection. Fast R-CNN builds on previous work to efficiently classify object proposals using deep convolutional networks. Compared to previous work, Fast R-CNN ... More

Cohomology theories with supportsJul 11 2012For $E$ a presheaf of spectra on the category of smooth $k$-schemes satisfying Nisnevich excision, we prove that the canonical map from the algebraic singular complex of the theory $E$ with quasi-finite supports to the theory $E$ with supports intersecting ... More

Law of large numbers for increasing subsequences of random permutations and an approximation result for the uniform measureJul 21 2004Jul 25 2005Let the random variable $Z_{n,k}$ denote the number of increasing subsequences of length $k$ in a random permutation from $S_n$, the symmetric group of permutations of $\{1,...,n\}$. We show that $Var(Z_{n,k_n})=o((EZ_{n,k_n})^2)$ as $ n\to\infty$ if ... More

Trees, permutations and the tangent functionMar 21 2003This is a report on a talk to high school mathematics students. It gives some combinatorial connections for the entries of the boustrophedon triangle whose sides are the Taylor coefficients for the tangent and secant functions.

Pointwise extensions and sketches in bicategoriesSep 23 2014We make a few remarks concerning pointwise extensions in a bicategory which include the case of bicategories of enriched categories. We show that extensions, pointwise or not, can be replaced by extensions along very special fully faithful maps. This ... More

Kan extensions and cartesian monoidal categoriesSep 23 2014The existence of adjoints to algebraic functors between categories of models of Lawvere theories follows from finite-product-preservingness surviving left Kan extension. A result along these lines was proved in Appendix 2 of Brian Day's 1970 PhD thesis. ... More

Fourier spaces and completely isometric representations of Arens product algebrasMay 29 2018Motivated by the definition of a semigroup compactification of a locally compact group and a large collection of examples, we introduce the notion of an (operator) "homogeneous left dual Banach algebra" (HLDBA) over a (completely contractive) Banach algebra ... More