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Why do These Match? Explaining the Behavior of Image Similarity ModelsMay 26 2019Explaining a deep learning model can help users understand its behavior and allow researchers to discern its shortcomings. Recent work has primarily focused on explaining models for tasks like image classification or visual question answering. In this ... More

The existence of optimal bang-bang controls for GMxB contractsFeb 19 2015Nov 04 2015A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the admissible ... More

Weakly chained matrices, policy iteration, and impulse controlOct 13 2015Sep 24 2017This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) ... More

Big but Imperceptible Adversarial Perturbations via Semantic ManipulationApr 12 2019Machine learning, especially deep learning, is widely applied to a range of applications including computer vision, robotics and natural language processing. However, it has been shown that machine learning models are vulnerable to adversarial examples, ... More

Learning Type-Aware Embeddings for Fashion CompatibilityMar 25 2018Jul 27 2018Outfits in online fashion data are composed of items of many different types (e.g. top, bottom, shoes) that share some stylistic relationship with one another. A representation for building outfits requires a method that can learn both notions of similarity ... More

Weakly chained matrices, policy iteration, and impulse controlOct 13 2015Mar 26 2016This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) ... More

Swapout: Learning an ensemble of deep architecturesMay 20 2016We describe Swapout, a new stochastic training method, that outperforms ResNets of identical network structure yielding impressive results on CIFAR-10 and CIFAR-100. Swapout samples from a rich set of architectures including dropout, stochastic depth ... More

SafetyNet: Detecting and Rejecting Adversarial Examples RobustlyApr 01 2017Aug 15 2017We describe a method to produce a network where current methods such as DeepFool have great difficulty producing adversarial samples. Our construction suggests some insights into how deep networks work. We provide a reasonable analyses that our construction ... More

CDVAE: Co-embedding Deep Variational Auto Encoder for Conditional Variational GenerationDec 01 2016Problems such as predicting an optical flow field (Y) for an image (X) are ambiguous: many very distinct solutions are good. Representing this ambiguity requires building a conditional model P(Y|X) of the prediction, conditioned on the image. It is hard ... More

Structural Consistency and Controllability for Diverse ColorizationSep 06 2018Colorizing a given gray-level image is an important task in the media and advertising industry. Due to the ambiguity inherent to colorization (many shades are often plausible), recent approaches started to explicitly model diversity. However, one of the ... More

CDVAE: Co-embedding Deep Variational Auto Encoder for Conditional Variational GenerationDec 01 2016Mar 28 2017Problems such as predicting a new shading field (Y) for an image (X) are ambiguous: many very distinct solutions are good. Representing this ambiguity requires building a conditional model P(Y|X) of the prediction, conditioned on the image. Such a model ... More

Detecting Anomalous Faces with 'No Peeking' AutoencodersFeb 15 2018Detecting anomalous faces has important applications. For example, a system might tell when a train driver is incapacitated by a medical event, and assist in adopting a safe recovery strategy. These applications are demanding, because they require accurate ... More

Dense domains, symmetric operators and spectral triplesJun 07 2013This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). We present counterexamples to claims in the literature that Fredholm modules can be obtained from these weaker variations of ... More

Authoring image decompositions with generative modelsDec 05 2016We show how to extend traditional intrinsic image decompositions to incorporate further layers above albedo and shading. It is hard to obtain data to learn a multi-layer decomposition. Instead, we can learn to decompose an image into layers that are "like ... More

A Visual Representation for Editing Face ImagesDec 02 2016We propose a new approach for editing face images, which enables numerous exciting applications including face relighting, makeup transfer and face detail editing. Our face edits are based on a visual representation, which includes geometry, face segmentation, ... More

NO Need to Worry about Adversarial Examples in Object Detection in Autonomous VehiclesJul 12 2017It has been shown that most machine learning algorithms are susceptible to adversarial perturbations. Slightly perturbing an image in a carefully chosen direction in the image space may cause a trained neural network model to misclassify it. Recently, ... More

An Approximate Shading Model with Detail Decomposition for Object RelightingApr 20 2018We present an object relighting system that allows an artist to select an object from an image and insert it into a target scene. Through simple interactions, the system can adjust illumination on the inserted object so that it appears naturally in the ... More

Rotation Blurring: Use of Artificial Blurring to Reduce Cybersickness in Virtual Reality First Person ShootersOct 06 2017Users of Virtual Reality (VR) systems often experience vection, the perception of self-motion in the absence of any physical movement. While vection helps to improve presence in VR, it often leads to a form of motion sickness called cybersickness. Cybersickness ... More

Standard detectors aren't (currently) fooled by physical adversarial stop signsOct 09 2017Oct 26 2017An adversarial example is an example that has been adjusted to produce the wrong label when presented to a system at test time. If adversarial examples existed that could fool a detector, they could be used to (for example) wreak havoc on roads populated ... More

Learning Diverse Image ColorizationDec 06 2016Colorization is an ambiguous problem, with multiple viable colorizations for a single grey-level image. However, previous methods only produce the single most probable colorization. Our goal is to model the diversity intrinsic to the problem of colorization ... More

Quantitative Evaluation of Style TransferMar 31 2018Style transfer methods produce a transferred image which is a rendering of a content image in the manner of a style image. There is a rich literature of variant methods. However, evaluation procedures are qualitative, mostly involving user studies. We ... More

Distinct differences in the nanoscale behaviors of the twist-bend liquid crystal phase of a flexible linear trimer and homologous dimerOct 02 2017Feb 19 2018We synthesized the liquid crystal dimer and trimer members of a series of flexible linear oligomers and characterized their microscopic and nanoscopic properties using resonant soft x-ray scattering and a number of other experimental techniques. On the ... More

Learning Diverse Image ColorizationDec 06 2016Apr 27 2017Colorization is an ambiguous problem, with multiple viable colorizations for a single grey-level image. However, previous methods only produce the single most probable colorization. Our goal is to model the diversity intrinsic to the problem of colorization ... More

Where's My Drink? Enabling Peripheral Real World Interactions While Using HMDsFeb 16 2015Head Mounted Displays (HMDs) allow users to experience virtual reality with a great level of immersion. However, even simple physical tasks like drinking a beverage can be difficult and awkward while in a virtual reality experience. We explore mixed reality ... More

Fast, Diverse and Accurate Image Captioning Guided By Part-of-SpeechMay 31 2018Apr 11 2019Image captioning is an ambiguous problem, with many suitable captions for an image. To address ambiguity, beam search is the de facto method for sampling multiple captions. However, beam search is computationally expensive and known to produce generic ... More

Max-Sliced Wasserstein Distance and its use for GANsApr 11 2019Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional ... More

Factorisation of equivariant spectral triples in unbounded KK-theoryMay 12 2015We provide sufficient conditions to factorise an equivariant spectral triple as a Kasparov product of unbounded classes constructed from the group action on the algebra and from the fixed point spectral triple. Our results are for the action of compact ... More

Piecewise Constant Policy Approximations to Hamilton-Jacobi-Bellman EquationsMar 19 2015Jan 20 2016An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different control ... More

A new technique for determining Substorm Onsets and Phases from Indices of the Electrojet (SOPHIE)Jun 07 2016We present a new quantitative technique that determines the times and durations of substorm expansion and recovery phases and possible growth phases based on percentiles of the rate of change of auroral electrojet indices. By being able to prescribe different ... More

Self-Similarity of ICME Flux Ropes: Observations by Radially Aligned Spacecraft in the Inner HeliosphereMay 17 2019Interplanetary coronal mass ejections (ICMEs) are a significant feature of the heliospheric environment and the primary cause of adverse space weather at the Earth. ICME propagation, and the evolution of ICME magnetic field structure during propagation, ... More

Dawn-dusk asymmetries in the coupled solar wind-magnetosphere-ionosphere system: a reviewJan 17 2017Dawn-dusk asymmetries are ubiquitous features of the coupled solar-wind-magnetosphere-ionosphere system. During the last decades, increasing availability of satellite and ground-based measurements has made it possible to study these phenomena in more ... More

Itinerant Antiferromagnetism in FeGe_2Oct 01 1996FeGe_2, and lightly doped compounds based on it, have a Fermi surface driven instability which drive them into an incommensurate spin density wave state. Studies of the temperature and magnetic field dependence of the resistivity have been used to determine ... More

Interplanetary Coronal Mass Ejections observed by MESSENGER and Venus ExpressNov 24 2015Interplanetary coronal mass ejections (ICMEs) observed by the MESSENGER (MES) and Venus Express (VEX) spacecraft have been catalogued and analysed. The ICMEs were identified by a relatively smooth rotation of the magnetic field direction consistent with ... More

Metacommutation as a Group Action on the Projective Line over $\mathbf{F}_\mathbf{p}$Mar 21 2015Cohn and Kumar showed the quadratic character of $q$ modulo $p$ gives the sign of the permutation of Hurwitz primes of norm $p$ induced by the Hurwitz primes of norm $q$ under metacommutation. We demonstrate that these permutations are equivalent to those ... More

Remarks on Privileged WordsNov 28 2013We discuss the notion of privileged word, recently introduced by Peltomaki. A word w is privileged if it is of length <=1, or has a privileged border that occurs exactly twice in w. We prove the following results: (1) if w^k is privileged for some k >=1, ... More

Measured Sensitivity of the First Mark II Phased Array Feed on an ASKAP AntennaSep 02 2015This paper presents the measured sensitivity of CSIRO's first Mk. II phased array feed (PAF) on an ASKAP antenna. The Mk. II achieves a minimum system-temperature-over-efficiency $T_\mathrm{sys}/\eta$ of 78 K at 1.23 GHz and is 95 K or better from 835 ... More

Measured Aperture-Array Noise Temperature of the Mark II Phased Array Feed for ASKAPSep 18 2015Nov 06 2015We have measured the aperture-array noise temperature of the first Mk. II phased array feed that CSIRO has built for the Australian Square Kilometre Array Pathfinder telescope. As an aperture array, the Mk. II phased array feed achieves a beam equivalent ... More

Establishing, versus Maintaining, Brain Function: A Neuro-computational Model of Cortical Reorganization after Injury to the Immature BrainDec 22 2011The effect of age at injury on outcome after acquired brain injury (ABI) has been the subject of much debate. Many argue that young brains are relatively tolerant of injury. A contrasting viewpoint due to Hebb argues that greater system integrity may ... More

On the rate of convergence to stationarity of the M/M/N queue in the Halfin-Whitt regimeMar 10 2010Sep 09 2013We prove several results about the rate of convergence to stationarity, that is, the spectral gap, for the M/M/n queue in the Halfin-Whitt regime. We identify the limiting rate of convergence to steady-state, and discover an asymptotic phase transition ... More

Steady-state $\mathit{GI}/\mathit{GI}/\mathit{n}$ queue in the Halfin-Whitt regimeMar 09 2011Dec 03 2013We consider the FCFS $\mathit{GI}/\mathit{GI}/n$ queue in the so-called Halfin-Whitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by $n^{1/2}$, is tight. ... More

Acceleration of Solar Wind Ions by Nearby Interplanetary Shocks: Comparison of Monte Carlo Simulations with Ulysses ObservationsOct 02 1996The most stringent test of theoretical models of the first-order Fermi mechanism at collisionless astrophysical shocks is a comparison of the theoretical predictions with observational data on particle populations. Such comparisons have yielded good agreement ... More

Boundaries, spectral triples and K-homologyJul 25 2016This paper extends the notion of a spectral triple to a relative spectral triple, an unbounded analogue of a relative Fredholm module for an ideal $J\triangleleft A$. Examples include manifolds with boundary, manifolds with conical singularities, dimension ... More

Non-Negative Networks Against Adversarial AttacksJun 15 2018Jan 03 2019Adversarial attacks against neural networks are a problem of considerable importance, for which effective defenses are not yet readily available. We make progress toward this problem by showing that non-negative weight constraints can be used to improve ... More

Multi-point shock and flux rope analysis of multiple interplanetary coronal mass ejections around 2010 August 1 in the inner heliosphereSep 13 2012We present multi-point in situ observations of a complex sequence of coronal mass ejections (CMEs) which may serve as a benchmark event for numerical and empirical space weather prediction models. On 2010 August 1, instruments on various space missions ... More

Modeling observations of solar coronal mass ejections with heliospheric imagers verified with the Heliophysics System ObservatoryMar 02 2017Jul 07 2017We present an advance towards accurately predicting the arrivals of coronal mass ejections (CMEs) at the terrestrial planets, including Earth. For the first time, we are able to assess a CME prediction model using data over 2/3 of a solar cycle of observations ... More

Stochastic gradient variational Bayes for gamma approximating distributionsSep 04 2015While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key challenge in ... More

Comments on D-brane Dynamics Near NS5-BranesAug 10 2004Sep 16 2004We study the properties of a D-brane in the presence of $k$ NS5 branes. The Dirac-Born-Infeld action describing the dynamics of this D-brane is very similar to that of a non-BPS D-brane in ten dimensions. As the D-brane approaches the fivebranes, its ... More

A Chandra and XMM View of the Mass & Metals in Galaxy Groups and ClustersOct 28 2002X-ray observations with Chandra and XMM are providing valuable new measurements of the baryonic and dark matter content of groups and clusters. Masses of cD clusters obtained from X-ray and gravitational lensing studies generally show good agreement, ... More

X-Ray Evidence for Multiphase Hot Gas with Nearly Solar Fe Abundances in the Brightest Groups of GalaxiesMar 18 1999Aug 27 1999We analyze the ASCA spectra accumulated within ~100 kpc radii of 12 of the brightest groups of galaxies. Upon fitting isothermal models (1T) jointly to the ASCA SIS and GIS spectra we obtain fits for most groups that are of poor or at best marginal quality ... More

On The Origin of Radio Halos in Galaxy ClustersApr 11 2001May 15 2001Previously it has been recognized that radio halos in galaxy clusters are preferentially associated with merging systems as indicated by substructure in the X-ray images and temperature maps. Since, however, many clusters without radio halos also possess ... More

Renormalization Group Flows from Gravity in Anti-de Sitter Space versus Black Hole No-Hair TheoremsMar 06 2000Apr 10 2000Black hole no-hair theorems are proven using inequalities that govern the radial dependence of spherically symmetric configurations of matter fields. In this paper, we analyze the analogous inequalities for geometries dual to renormalization group flows ... More

Constraints on Higher Derivative Operators in the Matrix Theory Effective LagrangianOct 12 1998Oct 13 1998The consistency of Matrix theory with supergravity requires that in the large N_c limit terms of order v^4 in the SU(N_c) Matrix effective potential are not renormalized beyond one loop in perturbation theory. For SU(2) gauge group, the required non-renormalization ... More

Alternating Subgroups of Exceptional Groups of Lie TypeSep 02 2015Jun 07 2016In this paper we examine embeddings of alternating groups and symmetric groups into almost simple groups of exceptional type. In particular, we prove that unless the alternating or symmetric group has degree 6 or 7, there is no maximal subgroup of any ... More

From gauge transformations to topology computation in quantum lattice gas automataMay 17 2001The evolution of a quantum lattice gas automaton (LGA) for a single charged particle is invariant under multiplication of the wave function by a global phase. Requiring invariance under the corresponding local gauge transformations determines the rule ... More

Scale decoherence in inhomogeneous potentialsMay 14 1998Finite precision measurement factors the Hilbert space of a quantum system into a tensor product $H_{coarse} \otimes H_{fine}$. This is mathematically equivalent to the partition into system and environment which forms the arena for decoherence, so we ... More

Quantum lattice gases and their invariantsMar 16 1997The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schroedinger equations, in different continuum limits. By analyzing the discrete analogues ... More

Control-based continuation: bifurcation and stability analysis for physical experimentsJun 12 2015Dec 22 2015Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an experiment it is not ... More

The Hausdorff dimension of a class of random self-similar fractal treesOct 22 2012In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical properties of an ... More

Random walk on the range of random walkOct 23 2012We study the random walk $X$ on the range of a simple random walk on $\mathbb{Z}^d$ in dimensions $d\geq 4$. When $d\geq 5$ we establish quenched and annealed scaling limits for the process $X$, which show that the intersections of the original simple ... More

On Conjugacy of Maximal Subalgebras of Solvable Lie AlgebrasOct 17 2011The purpose of this paper is to consider when two maximal subalgebras of a finite-dimensional solvable Lie algebra $L$ are conjugate, and to investigate their intersection.

Solvable Complemented Lie AlgebrasApr 19 2011In this paper a characterisation is given of solvable complemented Lie algebras. They decompose as a direct sum of abelian subalgebras and their ideals relate nicely to this decomposition. The class of such algebras is shown to be a formation whose residual ... More

The index complex of a maximal subalgebra of a Lie algebraJun 29 2010Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called ... More

Second-order Markov random fields for independent sets on the infinite Cayley treeJan 09 2013Jun 18 2015Recently, there has been significant interest in understanding the properties of Markov random fields (M.r.f.) defined on the independent sets of sparse graphs. When these M.r.f. are restricted to pairwise interactions (i.e. hardcore model), much progress ... More

On the steady-state probability of delay and large negative deviations for the $GI/GI/n$ queue in the Halfin-Whitt regimeJun 30 2013Aug 31 2016We consider the FCFS $GI/GI/n$ queue in the Halfin-Whitt heavy traffic regime, and prove bounds for the steady-state probability of delay (s.s.p.d.) for generally distributed processing times. We prove that there exist $\epsilon_1, \epsilon_2 > 0$, depending ... More

Well-posed two-point initial-boundary value problems with arbitrary boundary conditionsApr 29 2011Sep 26 2011We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions ... More

Review of the Solar Array TelescopesAug 11 2006For several years the only experiments sensitive to astrophysical gamma rays with energies beyond the reach of EGRET but below that of the Cherenkov imaging telescopes have been the "solar tower" detectors. They use >2000 m2 mirror areas to sample the ... More

Growth-Algorithm Model of Leaf ShapeApr 25 2010The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape based on a growth ... More

Towards Patterns for Heaps and Imperative LambdasOct 19 2015In functional programming, point-free relation calculi have been fruitful for general theories of program construction, but for specific applications pointwise expressions can be more convenient and comprehensible. In imperative programming, refinement ... More

Simple Modules for Groups with Abelian Sylow 2-Subgroups are AlgebraicJan 17 2008May 18 2008Let G be a finite group and let p be a prime. A module for G over a field of characteristic p is called algebraic if it satisfies a polynomial, with addition and multiplication given by direct sum and tensor product. In some sense, having this property ... More

Perverse Equivalences and Broué's Conjecture II: The Cyclic CaseJun 30 2012We study Brou\'e's abelian defect group conjecture for groups of Lie type using the recent theory of perverse equivalences and Deligne--Lusztig varieties. Our approach is to analyze the perverse equivalence induced by certain Deligne--Lusztig varieties ... More

Equations of Parametric Surfaces via SyzygiesOct 11 2000Feb 22 2001The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.

The Schwinger model on $S^1$: Hamiltonian formulation, vacuum and anomalyJun 18 2012We present a Hamiltonian formulation of the Schwinger model on the circle in Coulomb gauge as a semi-bounded self-adjoint operator which is invariant under the modular group ${\cal M}=\Z$ of large gauge transformations. There is a nontrivial action of ... More

Leibniz A-algebrasMay 24 2019Jun 03 2019A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually ... More

On certain decompositions of solvable Lie algebrasDec 04 2012May 03 2013The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of these classes ... More

Weil-étale Cohomology over $p$-adic FieldsNov 29 2011May 29 2012We establish duality results for the cohomology of the Weil group of a $p$-adic field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil modules, which implies Tate-Nakayama Duality. We define ... More

X-Ray Constraints on Dark Matter in Galaxy Clusters and Elliptical Galaxies: A View from Chandra and XMMOct 20 2003I review constraints on the radial density profiles and ellipticities of the dark matter obtained from recent X-ray observations with Chandra and XMM of elliptical galaxies and galaxy clusters and discuss their implications, especially for the self-interacting ... More

Oxygen Absorption in Cooling FlowsJan 19 2000Feb 04 2000The inhomogeneous cooling flow scenario predicts the existence of large quantities of gas in massive elliptical galaxies, groups, and clusters that have cooled and dropped out of the flow. Using spatially resolved, deprojected X-ray spectra from the ROSAT ... More

X-Ray Evidence for Multiphase Hot Gas with Solar Abundances in the Brightest Elliptical GalaxiesNov 05 1998Jun 22 1999We examine whether isothermal models of the hot gas can successfully describe the ASCA and ROSAT spectra of NGC 1399, NGC 4472, NGC 4636, and NGC 5044. Broad-band spectral fitting of the ASCA SIS and GIS data accumulated within a radius of ~5 arcmin for ... More

Statistical Origin of Black Hole Entropy in Matrix TheoryFeb 24 1998Jun 01 1998The statistical entropy of black holes in M-theory is considered. Assuming Matrix theory is the discretized light-cone quantization of a theory with eleven-dimensional Lorentz invariance, we map the counting problem onto the original Gibbons-Hawking calculation ... More

Conformal Models of Two-Dimensional TurbulenceDec 03 1992Dec 03 1992Polyakov recently showed how to use conformal field theory to describe two-dimensional turbulence. Here we construct an infinite hierarchy of solutions, both for the constant enstrophy flux cascade, and the constant energy flux cascade. We conclude with ... More

Semiclassical Approach to Black Hole EvaporationSep 02 1992Black hole evaporation may lead to massive or massless remnants, or naked singularities. This paper investigates this process in the context of two quite different two dimensional black hole models. The first is the original CGHS model, the second is ... More

Quantum strategiesApr 03 1998We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the ... More

Quantum computing classical physicsNov 12 2001In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may ... More

Towards the global: complexity, topology and chaos in modelling, simulation and computationOct 10 1997Oct 17 1997Topological effects produce chaos in multiagent simulation and distributed computation. We explain this result by developing three themes concerning complex systems in the natural and social sciences: (i) Pragmatically, a system is complex when it is ... More

Unitarity in one dimensional nonlinear quantum cellular automataMay 15 1996Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which precludes nontrivial ... More

On the absence of homogeneous scalar unitary cellular automataApr 12 1996Oct 25 1996Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only ``approximately unitary'' CA---which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the one dimensional ... More

Resistance due to vortex motion in the $ν=1$ bilayer quantum Hall superfluidJul 16 2004Jul 07 2005The longitudinal and Hall resistances have recently been measured for quantum Hall bilayers at total filling $\nu=1$ in the superfluid state with interlayer pairing, both for currents flowing parallel to one another and for "counterflowing" currents in ... More

The structure of projective indecomposable modules for $A_n$, $n\leq 12$May 14 2016May 17 2016This article gives the structure of all projective indecomposable modules in blocks with non-cyclic defect group for $n\leq 11$, and almost all in the case of $n=12$, leaving four simple modules for $p=2$ and one simple module for $p=3$.

Scaling limit for the random walk on the largest connected component of the critical random graphOct 22 2012A scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi random graph in the critical window is deduced. The limiting diffusion is constructed using resistance form techniques, and is shown to satisfy the same quenched ... More

The generalised nilradical of a Lie algebraDec 03 2015A solvable Lie algebra L has the property that its nilradical N contains its own centraliser. This is interesting because gives a representation of L as a subalgebra of the derivation algebra of its nilradical with kernel equal to the centre of N. Here ... More

Complements of Intervals and Prefrattini Subalgebras of Solvable Lie AlgebrasApr 19 2011In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gasch\"utz. The approach follows that of P. Hauck and H. Kurtzweil for groups, by first considering complements in subalgebra intervals. ... More

On maximal subalgebras and a generalised Jordan-Hölder Theorem for Lie algebrasSep 23 2015The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan-H\"older Theorem for chief series.

C-sections of Lie algebrasOct 08 2014Dec 02 2014Let $M$ be a maximal subalgebra of a Lie algebra $L$ and $A/B$ a chief factor of $L$ such that $B \subseteq M$ and $A \not \subseteq M$. We call the factor algebra $M \cap A/B$ a $c$-section of $M$. All such $c$-sections are isomorphic, and this concept ... More

Aging and communication in the twin paradoxSep 25 2016The twin paradox of the special theory of relativity has given rise to a large body of literature discussing its implications. In its standard form, the traveler changes velocity only at the destination of the trip, so that he appears to perceive an improbably ... More

Attojoule Optoelectronics for Low-Energy Information Processing and Communications: a Tutorial ReviewSep 18 2016Sep 20 2016Optics offers unique opportunities for reducing energy in information processing and communications while resolving the problem of interconnect bandwidth density inside machines. Such energy dissipation overall is now at environmentally significant levels; ... More

Recent developments in toric geometryJun 25 1996This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic geometry, combinatorics ... More

Erratum to "The Homogeneous Coordinate Ring of a Toric Variety", along with the original paperOct 22 1992Mar 06 2014This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published in 1995. The ... More

The Functor of a Smooth Toric VarietyDec 03 1993Dec 08 1993A map Y -> P^n is determined by a line bundle quotient of (O_Y)^{n+1}. In this paper, we generalize this description to the case of maps from Y to an arbitrary smooth toric variety. The data needed to determine such a map consists of a collection of line ... More

The determinant on flat conic surfaces with excision of disksOct 05 2012Feb 25 2013Let M be a surface with conical singularities, and consider a degenerating family of surfaces obtained from M by removing disks of smaller and smaller radius around a subset of the conical singularities. Such families arise naturally in the study of the ... More

Lower Bounds for Representation GrowthOct 05 2009This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in finite groups, ... More