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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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

Invasion percolation on the Poisson-weighted infinite treeDec 02 2009Oct 04 2012We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the $\sigma\to\infty$ limit of a representation discovered by Angel et al. [Ann. Appl. ... 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

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

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

Every plane graph of maximum degree 8 has an edge-face 9-colouringDec 24 2009Mar 08 2011An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\Delta\ge10$ ... 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

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

Tight inequalities among set hitting times in Markov chainsSep 01 2012Sep 28 2012Given an irreducible discrete-time Markov chain on a finite state space, we consider the largest expected hitting time $T(\alpha)$ of a set of stationary measure at least $\alpha$ for $\alpha\in(0,1)$. We obtain tight inequalities among the values of ... More

Colouring squares of claw-free graphsSep 27 2016Jul 18 2017Is 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

Unstable products of smooth curvesJun 22 2005Aug 24 2005We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the ... 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

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

Bipartite induced density in triangle-free graphsAug 07 2018Aug 17 2018Any triangle-free graph on $n$ vertices with minimum degree at least $d$ contains a bipartite induced subgraph of minimum degree at least $d^2/(2n)$. This is sharp up to a logarithmic factor in $n$. We also provide a related extremal result for the fractional ... More

Strong chromatic index and Hadwiger numberMay 15 2019We investigate the effect of a fixed forbidden clique minor upon the strong chromatic index, both in multigraphs and in simple graphs. We conjecture for each $k\ge 4$ that any $K_k$-minor-free multigraph of maximum degree $\Delta$ has strong chromatic ... More

Supersaturation in the Boolean latticeMar 18 2013We prove a "supersaturation-type" extension of both Sperner's Theorem (1928) and its generalization by Erdos (1945) to k-chains. Our result implies that a largest family whose size is x more than the size of a largest k-chain free family and that contains ... 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

On r-dynamic Coloring of GridsJul 13 2014An \textit{$r$-dynamic $k$-coloring} of a graph $G$ is a proper $k$-coloring of $G$ such that every vertex in $V(G)$ has neighbors in at least $\min\{d(v),r\}$ different color classes. The \textit{$r$-dynamic chromatic number} of a graph $G$, written ... More

Extension from Precoloured Sets of EdgesJul 16 2014May 27 2018We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree $\Delta$. ... 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

Genus six curves, K3 surfaces, and stable pairsDec 26 2018A general smooth curve of genus six lies on a quintic del Pezzo surface. In \cite{AK11}, Artebani and Kond\=o construct a birational period map for genus six curves by taking ramified double covers of del Pezzo surfaces. The map is not defined for special ... More

Duty-cycle and energetics of remnant radio-loud AGNFeb 15 2018Deriving the energetics of remnant and restarted active galactic nuclei (AGNs) is much more challenging than for active sources due to the complexity in accurately determining the time since the nucleus switched-off. I resolve this problem using a new ... 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

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

The behaviour of galactic cosmic ray intensity during solar activity cycle 24Dec 05 2018We have studied long-term variations of galactic cosmic ray (GCR) intensity in relation to the sunspot number (SSN) during the most recent solar cycles. This study analyses the time-lag between the GCR intensity and SSN, and hysteresis plots of the GCR ... More

Understanding the Heavy Tailed Dynamics in Human BehaviorMay 07 2015The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of data sets, ... 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

Weighted Bergman kernels on orbifoldsJul 30 2009Sep 16 2011We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated to such a line ... More

A study of the Hilbert-Mumford criterion for the stability of projective varietiesDec 29 2004Feb 02 2005We make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties $(X,L)$; in particular for K- and Chow stability. For each type of stability this leads to a concept of slope $\mu$ for varieties ... 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

The M_BH - L_rad Relation for Flat-Spectrum QuasarsFeb 25 2003In this proceedings we summarize our recent letter (Jarvis & McLure 2002) where we suggested that by correcting for the inevitable effects of inclination, the black-hole masses of flat-spectrum quasars (FSQ) with intrinsically powerful radio jets are ... More

The host galaxies of flat-spectrum quasarsFeb 25 2003We present the results of deep VLT-ISAAC Ks-band imaging of four z~1.5 flat-spectrum quasars selected from the Parkes half-Jansky flat spectrum sample. We find that the hosts of these flat-spectrum quasars are consistent with lying on the K-z Hubble relation ... More

Using MgII to investigate quasars and their black-hole massesOct 30 2003We highlight the importance of the MgII emission-line doublet in probing high-redshift quasars and their supermassive black holes. In the SDSS era, where large scale investigations of quasars across the age of the Universe are possible, this emission-line ... More

Orientation dependency of broad-line widths in quasars and consequences for black-hole mass estimationMar 09 2006In this paper we report new evidence that measurements of the broad-line widths in quasars are dependent on the source orientation, consistent with the idea that the broad-line region is flattened or disc-like. This reinforces the view derived from radio-selected ... More

On the black-hole mass -- radio luminosity relation for flat-spectrum radio-loud quasarsAug 21 2002A new analysis of the connection between black-hole mass and radio luminosity in radio-selected flat-spectrum quasars (FSQ) is presented. In contrast to recent claims in the literature, we find no evidence that the black-hole masses of radio-selected ... 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

Finite-time Lyapunov exponents and Lagrangian coherent structures in the infinitesimal integration time limitApr 15 2019Lagrangian diagnostics, such as the finite-time Lyapunov exponent and Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These diagnostics can help illuminate regions where particles transported by a flow will ... 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

Finite-time Lyapunov exponents and Lagrangian coherent structures in the infinitesimal integration time limitApr 15 2019May 10 2019Lagrangian diagnostics, such as the finite-time Lyapunov exponent and Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These diagnostics can help illuminate regions where particles transported by a flow will ... 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

The Energetics and Lifetimes of Local Radio Active Galactic NucleiApr 20 2015We present a model describing the evolution of Fanaroff-Riley type I and II radio AGN, and the transition between these classes. We quantify galaxy environments using a semi-analytic galaxy formation model, and apply our model to a volume-limited low ... More

Magnetic Polarization Currents in Double Quantum Dot DevicesJan 26 2002We investigate coherent electron transport through a parallel circuit of two quantum dots, each of which has a single tunable energy level. Electrons tunneling via each dot from the left lead interfere with each other at the right lead. It is shown that ... 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

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

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

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

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

An invariance principle for semimartingale reflecting Brownian motions in domains with piecewise smooth boundariesApr 03 2007Semimartingale reflecting Brownian motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for some stochastic networks. In this paper, ... 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

A 3x10^9 solar mass black hole in the quasar SDSS J1148+5251 at z=6.41Mar 03 2003We present near-infrared H and K-band spectra of the z=6.41 quasar SDSS J114816.64+525150.3. The spectrum reveals a broad MgII 2799 emission line with a full-width half-maximium of 6000 km/s. From the peak wavelength of this emission line we obtain a ... More

Ideal triangulations of 3-manifolds II: taut and angle structuresFeb 21 2005This is the second in a series of papers in which we investigate ideal triangulations of the interiors of compact 3-manifolds with tori or Klein bottle boundaries. Such triangulations have been used with great effect, following the pioneering work of ... More

Addendum to ``Canonical bases for quantum generalized Kac-Moody algebras''Nov 13 2007We provide some necessary details to several arguments appearing in our previous paper ``Canonical bases for quantum generalized Kac-Moody algebras''. We also make the link with some other work on the same subject.

Higher-Order Angular Galaxy Correlations in the SDSS: Redshift and Color Dependence of non-Linear BiasApr 19 2007We present estimates of the N-point galaxy, area-averaged, angular correlation functions $\bar{\omega}_{N}$($\theta$) for $N$ = 2,...,7 for galaxies from the fifth data release of the Sloan Digital Sky Survey. Our parent sample is selected from galaxies ... More

A Reduction of Imitation Learning and Structured Prediction to No-Regret Online LearningNov 02 2010Mar 16 2011Sequential prediction problems such as imitation learning, where future observations depend on previous predictions (actions), violate the common i.i.d. assumptions made in statistical learning. This leads to poor performance in theory and often in practice. ... More

Precision Measurements of Higher-Order Angular Galaxy Correlations Using 11 Million SDSS GalaxiesMay 31 2006We present estimates of the N-point galaxy area-averaged angular correlation functions wN for N = 2,...,7 from the third data release of the Sloan Digital Sky Survey (SDSS). The sample was selected from galaxies with 18 < r < 21, and is the largest ever ... 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

Exploring the Use of Attention within an Neural Machine Translation Decoder States to Translate IdiomsOct 10 2018Idioms pose problems to almost all Machine Translation systems. This type of language is very frequent in day-to-day language use and cannot be simply ignored. The recent interest in memory augmented models in the field of Language Modelling has aided ... More

Graphical Methods in Device-Independent Quantum CryptographyMay 25 2017Jan 09 2018We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography ... More

Magnetic Skyrmions at Critical CouplingDec 18 2018Feb 07 2019We introduce a family of models for magnetic skyrmions in the plane for which infinitely many solutions can be given explicitly. The energy defining the models is bounded below by a linear combination of degree and total vortex strength, and the configurations ... More

The Icosahedral (H$_2)_{13}$ SupermoleculeAug 02 2018We investigate a range of possible materials containing the supermolecular form of hydrogen comprising 13 hydrogen molecules arranged in an icosahedral arrangement. This supermolecule consists of freely rotating 12 hydrogen molecules in an icosahedral ... More

An analytic solution of the BFKL equation with momentum cutoffsJan 16 1995We outline a general method for obtaining the solution to the ($t=0$) BFKL equation in the presence of transverse momentum cutoffs. A lower cutoff allows one to avoid integration over nonperturbative momenta and an upper one is needed from energy-momentum ... More

SPINVERT: A program for refinement of paramagnetic diffuse scattering dataFeb 12 2013We present a program (SPINVERT; http://spinvert.chem.ox.ac.uk)for refinement of magnetic diffuse scattering data for frustrated magnets, spin liquids, spin glasses, and other magnetically disordered materials. The approach uses reverse Monte Carlo refinement ... 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

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

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

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

Compressibility of random walker trajectories on growing networksNov 22 2018Jan 28 2019We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability distribution ... More

Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs$_2$CuCl$_4$ and to the layered organic superconductors $κ$-(BEDT-TTF)$_2$XDec 13 2000Apr 27 2001We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials ... More

Face Detection in Repeated SettingsMar 20 2019Face detection is an important first step before face verification and recognition. In unconstrained settings it is still an open challenge because of the variation in pose, lighting, scale, background and location. However, for the purposes of verification ... More

Inference of epidemiological parameters from household stratified dataSep 29 2016Mar 21 2017We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household transmission, recovery, ... More

Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov ExponentsAug 16 2018Sep 19 2018This paper proposes a Lagrangian data-driven reduced order model (ROM) for an efficient and relatively accurate numerical simulation of the finite time Lyapunov exponent (FTLE) field. To generate the ba- sis, the new Lagrangian ROM explicitly uses Lagrangian ... More

Scattering processes and resonances from lattice QCDJun 20 2017The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers ... More