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Verifying the Steane code with QuantomaticJun 19 2013Dec 30 2014In this paper we give a partially mechanized proof of the correctness of Steane's 7-qubit error correcting code, using the tool Quantomatic. To the best of our knowledge, this represents the largest and most complicated verification task yet carried out ... More

Generalised Compositional Theories and Diagrammatic ReasoningJun 11 2015This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely ... More

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculusFeb 08 2019We present a new circuit-to-circuit optimisation routine based on an equational theory called the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, a flexible, lower-level language for describing quantum computations graphically. Then, ... More

A graphical approach to measurement-based quantum computingMar 28 2012Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax directly captures ... More

Generalised Proof-Nets for Compact Categories with BiproductsMar 30 2009Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and biproducts, presented ... More

Linked and knotted synthetic magnetic fieldsAug 10 2018We show that the realisation of synthetic magnetic fields via light-matter coupling in the Lambda-scheme implements a natural geometrical construction of magnetic fields, namely as the pullback of the area element of the sphere to Euclidean space via ... More

Graphs States and the necessity of Euler DecompositionFeb 03 2009Coecke and Duncan recently introduced a categorical formalisation of the interaction of complementary quantum observables. In this paper we use their diagrammatic language to study graph states, a computationally interesting class of quantum states. We ... More

Pivoting makes the ZX-calculus complete for real stabilizersJul 26 2013Dec 30 2014We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the ... More

Interacting Frobenius Algebras are HopfJan 19 2016Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others. Bonchi, Sobocinski, and Zanasi ... More

Interacting Quantum Observables: Categorical Algebra and DiagrammaticsJun 25 2009Apr 21 2011This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatise ... More

A Categorical Quantum LogicDec 15 2005We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with biproducts on a ... More

Graphical Reasoning in Compact Closed Categories for Quantum ComputationFeb 03 2009Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such ... More

Proceedings 9th Workshop on Quantum Physics and LogicJul 29 2014This volume contains the proceedings of the ninth workshop on Quantum Physics and Logic (QPL2012) which took place in Brussels from the 10th to the 12th of October 2012. QPL2012 brought together researchers working on mathematical foundations of quantum ... More

Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational ModelsApr 16 2010In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken ... More

Stellar Populations of Lyman Alpha Emitters at z = 3 - 4 Based on Deep Large Area Surveys in the Subaru-SXDS/UKIDSS-UDS FieldNov 13 2009We investigate the stellar populations of Lyman alpha emitters (LAEs) at z=3.1 and 3.7 in 0.65 deg^2 of the Subaru/XMM-Newton Deep Field, based on rest-frame UV-to-optical photometry obtained from the Subaru/XMM-Newton Deep Survey, the UKIDSS/Ultra Deep ... More

Open Graphs and Computational ReasoningJul 22 2010We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges ... More

The Archimedean limit of random sorting networksFeb 25 2018Mar 19 2018A sorting network (also known as a reduced decomposition of the reverse permutation), is a shortest path from $12 \cdots n$ to $n \cdots 21$ in the Cayley graph of the symmetric group $S_n$ generated by adjacent transpositions. We prove that in a uniform ... More

Search for $WH \to \ell νb\bar{b}$ Final States at the TevatronOct 11 2011Latest results are presented in the search for low mass standard model Higgs production in association with a $W$ boson, based on large luminosity data samples collected at the CDF and D0 Experiments at the Fermilab Tevatron $p\bar{p}$ collider. The selection ... More

Graph theoretic invariants for operator algebras associated to topological dynamicsJul 22 2013We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed graph which can ... More

Oscillations in the Habitable Zone around Alpha Centauri BFeb 06 2012The Alpha Centauri AB system is an attractive one for radial velocity observations to detect potential exoplanets. The high metallicity of both Alpha Centauri A and B suggest that they could have possessed circumstellar discs capable of forming planets. ... More

Twisted forms of toric varietiesAug 18 2014Jan 19 2016We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms rather than just ... More

Equivariant unirationality of del Pezzo surfaces of degree 3 and 4Oct 30 2014Oct 03 2016A variety X with an action of a finite group G is said to be G-unirational if there is a G-equivariant dominant rational map V -> X where V is a faithful linear representation of G. This generalizes the usual notion of unirationality. We determine when ... More

Using prior information to identify boundaries in disease risk mapsAug 24 2012Disease maps display the spatial pattern in disease risk, so that high-risk clusters can be identified. The spatial structure in the risk map is typically represented by a set of random effects, which are modelled with a conditional autoregressive (CAR) ... More

Essential Dimensions of A_7 and S_7Aug 22 2009We show that Y. Prokhorov's "Simple Finite Subgroups of the Cremona Group of Rank 3" implies that, over any field of characteristic 0, the essential dimensions of the alternating group, A_7, and the symmetric group, S_7, are 4.

A necessary and sufficient condition for global convergence of the complex zeros of random orthogonal polynomialsJan 22 2019Consider random polynomials of the form $G_n = \sum_{i=0}^n \xi_i p_i$, where the $\xi_i$ are i.i.d. non-degenerate complex random variables, and $\{p_i\}$ is a sequence of orthonormal polynomials with respect to a regular measure $\tau$ supported on ... More

Classifying all mutually unbiased bases in RelSep 24 2009Sep 25 2009Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the categorical approach ... More

Strong Complementarity and Non-locality in Categorical Quantum MechanicsMar 22 2012Apr 27 2012Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, ... More

Circuit Synthesis of Electrochemical Supercapacitor ModelsMar 30 2016This paper is concerned with the synthesis of RC electrical circuits from physics-based supercapacitor models describing conservation and diffusion relationships. The proposed synthesis procedure uses model discretisation, linearisation, balanced model ... More

Low-Order Mathematical Modelling of Electric Double Layer Supercapacitors Using Spectral MethodsNov 29 2014This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration and conductivity ... More

Cohomology of presheaves with oriented weak transfersMay 01 2014Over a field of characteristic zero, we establish the homotopy invariance of the Nisnevich cohomology of homotopy invariant presheaves with oriented weak transfers, and the agreement of Zariski and Nisnevich cohomology for such presheaves. This generalizes ... More

The monoidal centre as a limitApr 04 2003The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that ... More

Categorical and combinatorial aspects of descent theoryMar 14 2003Mar 20 2003There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and outlined for weak ... More

Fundamentals of Stein's methodSep 09 2011This survey article discusses the main concepts and techniques of Stein's method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its relation to concentration inequalities. The material is presented ... 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

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

Betweenness and NonbetweennessFeb 18 2016The betweenness function $bet(n)$ is the minimum number of total orderings of $n$ objects such that for any three distinct objects $a$, $b$ and $c$, there is an ordering in which $b$ is between $a$ and $c$. The nonbetweenness function $nbet(n)$ is the ... More

PDF/A-3u as an archival format for Accessible mathematicsJun 24 2014Including LaTeX source of mathematical expressions, within the PDF document of a text-book or research paper, has definite benefits regarding `Accessibility' considerations. Here we describe three ways in which this can be done, fully compatibly with ... More

Localization and Gluing of Orbifold Amplitudes: The Gromov-Witten Orbifold VertexSep 27 2011Mar 30 2012We define a formalism for computing open orbifold GW invariants of [C^3/G] where G is any finite abelian group. We prove that this formalism and a suitable gluing algorithm can be used to compute GW invariants in all genera of any toric CY orbifold of ... 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

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.

Recent Progress on D$^3$ -- The Directional Dark Matter DetectorFeb 01 2014Direction-sensitive WIMP dark matter searches may help overcome the challenges faced by direct dark matter detection experiments. In particular, directional detectors should be able to clearly differentiate a dark matter signal from background sources. ... More

The Hilbert-Chow morphism and the incidence divisorSep 29 2010For a smooth projective variety $P$, we construct a Cartier divisor supported on the incidence locus in $\mathscr{C}_a (P) \times \mathscr{C}_{\dim(P)-a-1}(P)$. There is a natural definition of the corresponding line bundle on a product of Hilbert schemes, ... More

The Information Flow Problem on Clock NetworksMay 17 2016The information flow problem on a network asks whether $r$ senders, $v_1,v_2, \ldots ,v_r$ can each send messages to $r$ corresponding receivers $v_{n+1}, \ldots ,v_{n+r}$ via intermediate nodes $v_{r+1}, \ldots ,v_n$. For a given finite $R \subset \mathbb{Z}^+$, ... More

Alexander Polynomials of Periodic Knots: A Homological Proof and Twisted ExtensionNov 12 2009Nov 17 2009In 1971, Kunio Murasugi proved a necessary condition on a knot's Alexander polynomial for that knot to be periodic of prime power order. In this paper I present an alternate proof of Murasugi's condition which is subsequently used to extend his result ... 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

On the Existence of a Closed, Embedded, Rotational $λ$-HypersurfaceSep 15 2017In this paper we show the existence of a closed, embedded $\lambda$-hypersurfaces $\Sigma \subset \mathbb{R}^{2n}$. The hypersurface is diffeomorhic to $\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1$ and exhibits $SO(n) \times SO(n)$ symmetry. ... More

The Loop Murnaghan-Nakayama RuleAug 21 2012Jan 08 2015We give a combinatorial proof of a natural generalization of the Murnaghan-Nakayama rule to loop Schur functions. We also define shifted loop Schur functions and prove that they satisfy a similar relation.

Wreaths, mixed wreaths and twisted coactionsOct 24 2016Distributive laws between two monads in a 2-category $\CK$, as defined by Jon Beck in the case $\CK=\mathrm{Cat}$, were pointed out by the author to be monads in a 2-category $\mathrm{Mnd}\CK$ of monads. Steve Lack and the author defined wreaths to be ... More

Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2Oct 23 2015We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective space over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an application, we ... More

Enhancing R with Advanced Compilation Tools and MethodsSep 09 2014I describe an approach to compiling common idioms in R code directly to native machine code and illustrate it with several examples. Not only can this yield significant performance gains, but it allows us to use new approaches to computing in R. Importantly, ... More

On the Possibility of Detecting Class A Stellar Engines Using Exoplanet Transit CurvesJun 07 2013The Class A stellar engine (also known as a Shkadov thruster) is a spherical arc mirror, designed to use the impulse from a star's radiation pressure to generate a thrust force, perturbing the star's motion. If this mirror obstructs part of the stellar ... More

The Effect of Irradiation on the Jeans Mass in Fragmenting Self-Gravitating Protostellar DiscsJan 07 2013When a self-gravitating disc is subject to irradiation, its propensity to fragmentation will be affected. The strength of self-gravitating disc stresses is expected to dictate disc fragmentation: as the strength of these torques typically decrease with ... More

Theoretical electron energy loss spectroscopy of isolated grapheneAug 27 2014A thorough understanding of the electronic structure is a necessary first step for the design of nanoelectronics, chemical/bio-sensors, electrocatalysts, and nanoplasmonics using graphene. As such, theoretical spectroscopic techniques to describe collective ... More

Global Seismic Oscillations in Soft Gamma RepeatersMar 06 1998There is evidence that soft gamma repeaters (SGRs) are neutron stars which experience frequent starquakes, possibly driven by an evolving, ultra-strong magnetic field. The empirical power-law distribution of SGR burst energies, analogous to the Gutenberg-Richter ... More

Globular Cluster Luminosity Functions and the Hubble Constant from WFPC2 Imaging: Galaxies in the Coma I CloudNov 18 1996The membership of some galaxies in the nearby (d ~ 12 Mpc) Coma I cloud is uncertain. Here we present globular cluster luminosity functions (GCLFs) from the HST for two bright ellipticals which may belong to this group. After fitting the GCLF, we find ... More

Native Synthetic Imaging of Smoothed Particle Hydrodynamics density fields using gridless Monte Carlo Radiative TransferApr 16 2010An algorithm for creating synthetic telescope images of Smoothed Particle Hydrodynamics (SPH) density fields is presented, which utilises the adaptive nature of the SPH formalism in full. The imaging process uses Monte Carlo Radiative Transfer (MCRT) ... More

Globular clusters and galaxy fomationMay 08 2006We first discuss recent progress in using the Milky Way globular cluster (GC) system as a `test-bed' for properties derived from integrated spectra and stellar population models. Standard techniques may give rise to spuriously high alpha-element ratios ... More

The trouble with orbits: the Stark effect in the old and the new quantum theoryApr 21 2014The old quantum theory and Schr\"odinger's wave mechanics (and other forms of quantum mechanics) give the same results for the line splittings in the first-order Stark effect in hydrogen, the leading terms in the splitting of the spectral lines emitted ... More

Square free words as products of commutatorsSep 09 2008Elements of the commutator subgroup of a free group can be presented as values of canonical forms, called Wicks forms. We show that, starting from sufficiently high genus g, there is a sequence of words w(g) which can be presented by f(g) distinct Wicks ... More

Automatic 3D modelling of craniofacial formJan 21 2016Three-dimensional models of craniofacial variation over the general population are useful for assessing pre- and post-operative head shape when treating various craniofacial conditions, such as craniosynostosis. We present a new method of automatically ... More

Slingshot Dynamics for Self Replicating Probes and the Effect on Exploration TimescalesJul 05 2013Interstellar probes can carry out slingshot manoeuvres around the stars they visit, gaining a boost in velocity by extracting energy from the star's motion around the Galactic Centre. These maneouvres carry little to no extra energy cost, and in previous ... More

Automorphisms of cubic surfaces in positive characteristicDec 04 2017Oct 12 2018We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that the moduli space ... More

Locally adaptive spatial smoothing using conditional autoregressive modelsMay 16 2012Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The spatial correlation ... More

Finite dimensional point derivations for graph algebrasAug 22 2006This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of ... More

Limit theorems for the Zig-Zag processJul 29 2016Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained ... More

Pebble accretion in self-gravitating protostellar discsFeb 14 2019Pebble accretion has become a popular component to core accretion models of planet formation, and is especially relevant to the formation of compact, resonant terrestrial planetary systems. Pebbles initially form in the inner protoplanetary disc, sweeping ... More

Boundary detection in disease mapping studiesAug 09 2011In disease mapping, the aim is to estimate the spatial pattern in disease risk over an extended geographical region, so that areas with elevated risks can be identified. A Bayesian hierarchical approach is typically used to produce such maps, which models ... More

On calculating the slice genera of 11- and 12-crossing knotsAug 05 2015Nov 09 2016This paper contains the results of efforts to determine values of the smooth and the topological slice genus of 11- and 12-crossing knots. Upper bounds for these genera were produced by using a computer to search for genus one concordances between knots. ... More

Classification and clustering for samples of event time data using non-homogeneous Poisson process modelsMar 06 2017Jan 07 2018Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to multiple independent ... More

The co-evolution of black hole growth and star formation from a cross-correlation analysis between quasars and the cosmic infrared backgroundJun 27 2014We present the first cross-correlation measurement between Sloan Digital Sky Survey (SDSS) Type 1 quasars and the cosmic infrared background (CIB) measured by Herschel. The distribution of the quasars at 0.15<z<3.5 covers the redshift range where we expect ... More

Veloce Rosso: Australia's new precision radial velocity spectrographJul 05 2018Veloce is an ultra-stable fibre-fed R4 echelle spectrograph for the 3.9 m Anglo-Australian Telescope. The first channel to be commissioned, Veloce 'Rosso', utilises multiple low-cost design innovations to obtain Doppler velocities for Sun-like and M-dwarf ... More

Stellar Populations of Lyman Alpha Emitters at z~6-7: Constraints on the Escape Fraction of Ionizing Photons from Galaxy Building BlocksApr 06 2010Sep 18 2010We investigate the stellar populations of Lyman alpha emitters (LAEs) at z=5.7 and 6.6 in a 0.65 deg^2 sky of the Subaru/XMM-Newton Deep Survey (SXDS) Field, using deep images taken with Subaru/Suprime-Cam, UKIRT/WFCAM, and Spitzer/IRAC. We produce stacked ... More

Monolayer sorption of neon in mesoporous silica glass as monitored by WAXSJan 29 2008We report measurements of the x-ray scattering intensity as mesoporous glasses are filled with Neon. We outline a simple model to account for the non-linear increase in the intensity of the first peak in a liquid-like diffraction pattern as a monolayer ... More

Numerical evolution of Brill wavesJun 20 2000Oct 20 2000We report a numerical evolution of axisymmetric Brill waves. The numerical algorithm has new features, including (i) a method for keeping the metric regular on the axis and (ii) the use of coordinates that bring spatial infinity to the edge of the computational ... More

Optical Absorption Spectra and Excitons of Dye-Substrate Interfaces: Catechol on TiO$_2$(110)Jun 14 2016Optimizing the photovoltaic efficiency of dye-sensitized solar cells (DSSC) based on staggered gap heterojunctions requires a detailed understanding of sub-band gap transitions in the visible from the dye directly to the substrate's conduction band (CB) ... More

Model-Based Bayesian Reinforcement Learning in Large Structured DomainsJun 13 2012Model-based Bayesian reinforcement learning has generated significant interest in the AI community as it provides an elegant solution to the optimal exploration-exploitation tradeoff in classical reinforcement learning. Unfortunately, the applicability ... More

Holography for asymptotically locally Lifshitz spacetimesJul 22 2011May 12 2014We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We identify the ... More

Pair production of black holes in a $U(1) \otimes U(1)$ theoryJan 26 1994Mar 21 1994Charged dilaton black hole solutions have recently been found for an action with two $U(1)$ gauge fields and a dilaton field. I investigate new exact solutions of this theory analogous to the C-metric and Ernst solutions of classical general relativity. ... More

Correlations in Quantum PhysicsAug 24 2012We provide an historical perspective of how the notion of correlations has evolved within quantum physics. We begin by reviewing Shannon's information theory and its first application in quantum physics, due to Everett, in explaining the information conveyed ... More

A Provenance Tracking Model for Data UpdatesAug 22 2012For data-centric systems, provenance tracking is particularly important when the system is open and decentralised, such as the Web of Linked Data. In this paper, a concise but expressive calculus which models data updates is presented. The calculus is ... 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

Estimation of an Origin/Destination matrix: Application to a ferry transport dataMay 30 2013The estimation of the number of passengers with the identical journey is a common problem for public transport authorities. This problem is also known as the Origin- Destination estimation (OD) problem and it has been widely studied for the past thirty ... More

Modeling Financial Volatility in the Presence of Abrupt ChangesDec 25 2012The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive days, creating ... More

On gauge unification in Type I/I' modelsJan 15 2000Mar 29 2000We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In ... More

Optimal ancilla-free Clifford+V approximation of z-rotationsSep 15 2014Mar 06 2015We describe a new efficient algorithm to approximate z-rotations by ancilla-free Clifford+V circuits, up to a given precision epsilon. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest Clifford+V circuit ... More

Conditions for a Lévy process to stay positive near 0, in probabilityJun 06 2016A necessary and sufficient condition for a L\'evy process $X$ to stay positive, in probability, near 0, which arises in studies of Chung-type laws for $X$ near 0, is given in terms of the characteristics of $X$.

Adams operations on the virtual K-theory of P(1,n)Feb 14 2013We analyze the structure of the virtual (orbifold) K-theory ring of the complex orbifold P(1,n) and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin-Graham. In particular, we identify the group of virtual ... More

Optimal Policies for Simultaneous Energy Consumption and Ancillary Service Provision for Flexible Loads under Stochastic Prices and No Capacity Reservation ConstraintJul 06 2014Flexible loads, i.e. the loads whose power trajectory is not bound to a specific one, constitute a sizable portion of current and future electric demand. This flexibility can be used to improve the performance of the grid, should the right incentives ... More

The Hyperplane is the Only Stable, Smooth Solution to the Isoperimetric Problem in Gaussian SpaceJul 26 2013Dec 08 2014We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $\Sigma^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize ... More

Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphsDec 15 2017Oct 11 2018We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation ... More

Detecting Tampering in a Random HypercubeJan 17 2012Sep 04 2012Consider the random hypercube $H_2^n(p_n)$ obtained from the hypercube $H_2^n$ by deleting any given edge with probabilty $1-p_n$, independently of all the other edges. A diameter path in $H_2^n$ is a longest geodesic path in $H_2^n$. Consider the following ... More

Violation of Bell's inequality in fluid mechanicsMay 28 2013We show that a classical fluid mechanical system can violate Bell's inequality because the fluid motion is correlated over large distances.

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

Explorations in Statistics Research: An Approach to Expose Undergraduates to Authentic Data AnalysisAug 22 2015The Explorations in Statistics Research workshop is a one-week NSF-funded summer program that introduces undergraduate students to current research problems in applied statistics. The goal of the workshop is to expose students to exciting, modern applied ... More

The luminosity function of cluster pulsarsDec 21 2010We study luminosities of millisecond pulsars in globular clusters by fitting the observed luminosity distribution with single and double power laws. We use simulations to model the observed distribution as the brighter part of some parent distribution ... More

Mackey functors on compact closed categoriesJun 20 2007We develop and extend the theory of Mackey functors as an application of enriched category theory. We define Mackey functors on a lextensive category $\E$ and investigate the properties of the category of Mackey functors on $\E$. We show that it is a ... More

Low-shot visual object recognitionJun 09 2016Low-shot visual learning - the ability to recognize novel object categories from very few examples - is a hallmark of human visual intelligence. Existing machine learning approaches fail to generalize in the same way. To make progress on this foundational ... More