Results for "Philip Bille"

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Sparse Regular Expression MatchingJul 10 2019We present the first algorithm for regular expression matching that can take advantage of sparsity in the input instance. Our main result is a new algorithm that solves regular expression matching in $O\left(\Delta \log \log \frac{nm}{\Delta} + n + m\right)$ ... More
From Regular Expression Matching to ParsingApr 09 2018Jan 29 2019Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular expression parsing ... More
Fast evaluation of union-intersection expressionsAug 23 2007We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and database systems. ... More
Space-Efficient Re-Pair CompressionNov 04 2016Re-Pair is an effective grammar-based compression scheme achieving strong compression rates in practice. Let $n$, $\sigma$, and $d$ be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original paper, the ... More
Practical and Effective Re-Pair CompressionApr 27 2017Re-Pair is an efficient grammar compressor that operates by recursively replacing high-frequency character pairs with new grammar symbols. The most space-efficient linear-time algorithm computing Re-Pair uses $(1+\epsilon)n+\sqrt n$ words on top of the ... More
Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed TextsSep 15 2006May 03 2007We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms ... More
Time-Space Trade-Offs for Longest Common ExtensionsNov 01 2012Apr 22 2013We revisit the longest common extension (LCE) problem, that is, preprocess a string $T$ into a compact data structure that supports fast LCE queries. An LCE query takes a pair $(i,j)$ of indices in $T$ and returns the length of the longest common prefix ... More
Subsequence Automata with Default TransitionsOct 29 2015Jan 19 2016Let $S$ be a string of length $n$ with characters from an alphabet of size $\sigma$. The \emph{subsequence automaton} of $S$ (often called the \emph{directed acyclic subsequence graph}) is the minimal deterministic finite automaton accepting all subsequences ... More
A Separation Between Run-Length SLPs and LZ77Nov 20 2017In this paper we give an infinite family of strings for which the length of the Lempel-Ziv'77 parse is a factor $\Omega(\log n/\log\log n)$ smaller than the smallest run-length grammar.
Succinct Partial Sums and Fenwick TreesMay 31 2017We consider the well-studied partial sums problem in succint space where one is to maintain an array of n k-bit integers subject to updates such that partial sums queries can be efficiently answered. We present two succint versions of the Fenwick Tree ... More
Mergeable Dictionaries With ShiftsJan 03 2019We revisit the mergeable dictionaries with shift problem, where the goal is to maintain a family of sets subject to search, split, merge, make-set, and shift operations. The search, split, and make-set operations are the usual well-known textbook operations. ... More
Deterministic Indexing for Packed StringsDec 06 2016Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string indexing problem ... More
Tree Compression with Top TreesApr 21 2013May 11 2014We introduce a new compression scheme for labeled trees based on top trees. Our compression scheme is the first to simultaneously take advantage of internal repeats in the tree (as opposed to the classical DAG compression that only exploits rooted subtree ... More
Time-Space Trade-Offs for Lempel-Ziv Compressed IndexingJun 30 2017Jan 09 2018Given a string $S$, the \emph{compressed indexing problem} is to preprocess $S$ into a compressed representation that supports fast \emph{substring queries}. The goal is to use little space relative to the compressed size of $S$ while supporting fast ... More
Random Access to Grammar Compressed StringsJan 11 2010Oct 29 2013Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel grammar representation ... More
Compressed Communication Complexity of Longest Common PrefixesJun 08 2018We consider the communication complexity of fundamental longest common prefix (Lcp) problems. In the simplest version, two parties, Alice and Bob, each hold a string, $A$ and $B$, and we want to determine the length of their longest common prefix $l=\text{Lcp}(A,B)$ ... More
Sparse Suffix Tree Construction with Small SpaceJul 04 2012We consider the problem of constructing a sparse suffix tree (or suffix array) for $b$ suffixes of a given text $T$ of size $n$, using only $O(b)$ words of space during construction time. Breaking the naive bound of $\Omega(nb)$ time for this problem ... More
Finger Search in Grammar-Compressed StringsJul 10 2015Jun 24 2016Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly ... More
Longest Common Extensions in Sublinear SpaceApr 10 2015The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions ... More
Longest Common Extensions in TreesDec 03 2014Jul 09 2015The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In ... More
Dynamic Relative Compression, Dynamic Partial Sums, and Substring ConcatenationApr 29 2015Sep 16 2016Given a static reference string $R$ and a source string $S$, a relative compression of $S$ with respect to $R$ is an encoding of $S$ as a sequence of references to substrings of $R$. Relative compression schemes are a classic model of compression and ... More
Finger Search in Grammar-Compressed StringsJul 10 2015Nov 16 2016Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly ... More
Fast Dynamic ArraysNov 01 2017We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of $n$ elements supporting access in time $O(1)$ and insertion and deletion in time $O(n^\epsilon)$ for $\epsilon > 0$ while using $o(n)$ extra ... More
Fingerprints in Compressed StringsMay 13 2013May 16 2013The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string $S$ of size $N$ compressed by a context-free ... More
Fast Lempel-Ziv Decompression in Linear SpaceFeb 28 2018We consider the problem of decompressing the Lempel-Ziv 77 representation of a string $S\in[\sigma]^n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in optimal $O(n)$ time but requires ... More
Top Tree Compression of TriesFeb 06 2019We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to preprocess ... More
Numerical computation of real or complex elliptic integralsSep 06 1994Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check ... More
Homogenization of Periodic Multi-Dimensional Structures II: The Linearly Elastic/Perfectly Plastic CaseOct 02 2000In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in particular classes of ... More
Disambiguating Noun Groupings with Respect to WordNet SensesNov 29 1995Word groupings useful for language processing tasks are increasingly available, as thesauri appear on-line, and as distributional word clustering techniques improve. However, for many tasks, one is interested in relationships among word {\em senses}, ... More
The Slope of the Upper End of the IMF and the Upper Mass Limit: An Observer's PerspectiveAug 05 2010Aug 08 2010There are various ways of measuring the slope of the upper end of the IMF. Arguably the most direct of these is to place stars on the H-R diagram and compare their positions with stellar evolutionary models. Even so, the masses one infers from this depend ... More
Massive Stars in the Local Group: Star Formation and Stellar EvolutionJul 30 2003The galaxies of the Local Group that are currently forming stars can serve as our laboratories for understanding star formation and the evolution of massive stars. In this talk I will summarize what I think we've learned about these topics over the past ... More
Wild Character Varieties, points on the Riemann sphere and Calabi's examplesJan 05 2015Jul 19 2016We will give several descriptions of some basic examples of wild character varieties, including a discussion of links to work of Sibuya, Calabi and Euler, amongst others.
Operations in the homology spectral sequence of a cosimplicial infinite loop spaceJan 19 2011Oct 03 2012Consider the mod 2 homology spectral sequence associated to a cosimplicial space X. We construct external operations whose target is the spectral sequence associated to E\Sigma_2 \times_{\Sigma_2} (X\times X). If X is a cosimplicial E_\infty-space, we ... More
X-Ray PolarimetryAug 25 2014Jan 08 2016We review the basic principles of X-ray polarimetry and current detector technologies based on the photoelectric effect, Bragg reflection, and Compton scattering. Recent technological advances in high-spatial-resolution gas-filled X-ray detectors have ... More
A note on Iwasawa-type decompositionOct 02 2010We study the Iwasawa-type decomposition of an open subset of SL(n,C) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on the space of admissible elements in AN. We also show that the space of admissible elements is a multiplicative ... More
A Generalised Stern-Brocot Tree from Regular Diophantine QuadruplesMar 06 1999Diophantine quadruples are sets of four distinct positive integers such that the product of any two is one less than a square. All known examples belong to an infinite set which can be constructed recursively. Some observations on these regular solutions ... More
Some Rational Diophantine SextuplesFeb 13 1999A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six such numbers are presented and the computational algorithm used to find them ... More
Synchrotron-radiation studies of topological insulatorsOct 09 2012Jun 28 2013Topological insulators (TIs) are a recently discovered class of quantum materials that are currently attracting considerable attention. The most interesting aspect of the TIs is, in fact, not that they are bulk insulators but that their surfaces support ... More
Anomalous gamma gamma interactionDec 17 2007Data from LEP2 on hadron production in gamma gamma interactions at high pT exceed the predictions of QCD by about an order of magnitude. The amplitude for the process is asymptotically proportional to the sum of the squares of the charges of quarks. The ... More
Programming Complex SystemsOct 15 1997Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex ... More
The lambda-q calculus can efficiently simulate quantum computersFeb 26 1997We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We conclude by noting ... More
Forward W + c, b-jet and Top Measurements with LHCbNov 02 2015Inclusive c and b-jet tagging algorithms have been developed to utilize the excellent secondary vertex reconstruction and resolution capabilities of the LHCb detector. The validation and performance of these tagging algorithms are reported using the full ... More
Mottness: Identifying the Propagating Charge Modes in doped Mott InsulatorsJan 28 2010Mar 16 2010High-temperature superconductivity in the copper-oxide ceramics remains an unsolved problem because we do not know what the propagating degrees of freedom are in the normal state. As a result, we do not know what are the weakly interacting degrees of ... More
Stability in the homology of Deligne-Mumford compactificationsJan 11 2018Using the the theory of FS^op modules, we study the asymptotic behavior of the homology of $\overline M_{g,n}$, the Deligne--Mumford compactification of the moduli space of curves, for $n >> 0$. An FS^op module is a contravariant functor from the category ... More
Defining Subrings in Finitely Generated Fields of Characteristic Not TwoOct 22 2018We give a construction of a family of definable subrings of finitely generated fields $K$ of characteristic not two. We deduce that for any such $K$ there exists a first-order sentence $\varphi_K$ characterising $K$ in the class of finitely generated ... More
Origin of the Correspondence Rules of Quantum TheoryOct 13 2009Feb 14 2010To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the correspondence rules of ... More
An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum FormalismMay 19 2008In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few elementary features ... More
Completely Quantized Collapse and ConsequencesJun 21 2005Promotion of quantum theory from a theory of measurement to a theory of reality requires an unambiguous specification of the ensemble of realizable states (and each state's probability of realization). Although not yet achieved within the framework of ... More
Wavefunction Collapse and Conservation LawsApr 17 2000Jun 06 2000It is emphasized that the collapse postulate of standard quantum theory can violate conservation of energy-momentum and there is no indication from where the energy-momentum comes or to where it goes. Likewise, in the Continuous Spontaneous Localization ... More
Nonlinear elliptic equations and systems with linear part at resonanceMay 13 2016The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and no examples ... More
A Roadmap to Interstellar FlightApr 05 2016Oct 31 2016In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with ... More
Krawtchouk-Griffiths Systems II: As Bernoulli SystemsDec 02 2016We call Krawtchouk-Griffiths systems, KG-systems, systems of multivariate polynomials orthogonal with respect to corresponding multinomial distributions. The original Krawtchouk polynomials are orthogonal with respect to a binomial distribution. Here ... More
Tetraplectic structures, tri-momentum maps, and quaternionic flag manifoldsMar 06 2001Jun 25 2001The purpose of this note is to define tri-moment maps for certain manifolds that carry closed non-degenerate 4-forms and an $Sp(1)^n$-action. Examples include quaternionic vector spaces and flag manifolds. We show how this map can be used ro reduce such ... More
M87 and the Dynamics and Microphysics inside the Blazar ZoneJul 02 2010The blazars provide a considerable opportunity to peer into the workings within a few tens of parsecs of the central engine in AGN. This considerable opportunity involves significant challenges as different macroscopic dynamical processes and microscopic ... More
Families of solution curves for some non-autonomous problemsMay 05 2016The paper studies families of positive solution curves for non-autonomous two-point problems \[ u"+\lambda f(u)-\mu g(x)=0, \;\; -1<x<1, \;\; u(-1)=u(1)=0 \] depending on two positive parameters $\lambda$ and $\mu$. We regard $\lambda$ as a primary parameter, ... More
Explicit solutions and multiplicity results for some equations with the $p$-LaplacianJun 24 2016We derive explicit ground state solutions for several equations with the $p$-Laplacian in $R^n$, including (here $\varphi (z)=z|z|^{p-2}$, with $p>1$) \[ \varphi \left(u'(r)\right)' +\frac{n-1}{r} \varphi \left(u'(r)\right)+u^M+u^Q=0 \,. \] The constant ... More
Varieties with Ample Tangent SheavesApr 01 2017Sep 23 2017This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic to the complex ... More
Diophantine Quadruples and Cayley's HyperdeterminantJul 28 2001Sep 09 2001A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Such Diophantine sets have been used to construct high rank elliptic curves. Here I demonstrate ... More
Strict Local Martingales with JumpsJul 09 2013Mar 25 2014A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, ... More
Equivariant Motivic Homotopy TheoryDec 01 2013In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by Voevodsky and ... More
Hurwitz Theory of Elliptic Orbifolds, IISep 20 2018An elliptic orbifold is the quotient of an elliptic curve by a finite group. In 2001, Eskin and Okounkov proved that generating functions for the number of branched covers of an elliptic curve with specified ramification are quasimodular forms for $SL_2(\mathbb{Z}).$ ... More
Propagation and stability of flames in inhomogeneous mixturesFeb 07 2018We investigate the effect of thermal expansion and gravity on the propagation and stability of flames in inhomogeneous mixtures. We focus on laminar flames in the simple configuration of an infinitely long channel with rigid porous walls in order to understand ... More
Massive Stars in the Galaxies of the Local GroupMay 25 2013The star-forming galaxies of the Local Group act as our laboratories for testing massive star evolutionary models. In this review, I briefly summarize what we believe we know about massive star evolution, and the connection between OB stars, Luminous ... More
Higher-order semantics for quantum programming languages with classical controlNov 26 2013This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact ... More
Maximum Entropy Production and Non-Gaussian Climate VariabilityMar 16 2016Earth's atmosphere is in a state far from thermodynamic equilibrium. For example, the large scale equator-to-pole temperature gradient is maintained by tropical heating, polar cooling, and a midlatitude meridional eddy heat flux predominantly driven by ... More
Soft QCD Measurements at LHCbSep 01 2014Studies in the forward region of charged particle multiplicity and density, as well as energy flow, are presented. These measurements are performed using data from proton-proton collisions at a center-of-mass energy of 7 TeV, collected with the LHCb detector. ... More
The Search for Directed IntelligenceApr 07 2016Jun 18 2016We propose a search for sources of directed energy systems such as those now becoming technologically feasible on Earth. Recent advances in our own abilities allow us to foresee our own capability that will radically change our ability to broadcast our ... More
Polygons in Minkowski space and Gelfand-Tsetlin for pseudounitary groupsMar 18 2007Apr 23 2007We study the symplectic geometry of the moduli spaces of polygons in the Minkowski 3-space. These spaces naturally carry completely integrable systems with periodic flows. We extend the Gelfand-Tsetlin method to pseudo-unitary groups and show that the ... More
Logarithmic forms with twisted coefficientsFeb 01 1998Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings and a unitary local system V on it. We consider a differential graded Lie algebra (DGLA) of forms with holomorphic logarithmic singularities and vanishing ... More
Elliptic Curves and Hyperdeterminants in Quantum GravityOct 20 2010Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely ignored over a period of 100 years before once again being recognised as ... More
Krawtchouk-Griffiths Systems I: Matrix ApproachNov 21 2016We call \textsl{Krawtchouk-Griffiths} systems, or KG-systems, systems of multivariate polynomials orthogonal with respect to corresponding multinomial distributions. The original Krawtchouk polynomials are orthogonal with respect to a binomial distribution. ... More
Inflation from a Non-Local Theory of GravityAug 19 2009This paper studies the inflationary dynamics of a Non-Local Theory of gravity. This theory, based around derivatives of the Ricci Scalar in the Einstein-Hilbert action, was previously found to be Ghost free, and to give rise to a bouncing cosmology. Perturbation ... More
Observations from Australasia using the Gravitational Microlensing TechniqueAug 18 1999The new astronomical technique of gravitational microlensing enables measurements of high precision to be made in certain circumstances. Useful advances have been made in the fields of galactic astronomy, stellar astronomy and planetary science. The technique ... More
Non-existence of solutions for non-autonomous elliptic systems of Hamiltonian typeOct 26 2016We extend the classical Pohozaev's identity to semilinear elliptic systems of Hamiltonian type, providing a simpler approach, and a generalization, of the results of E. Mitidieri [6], R.C.A.M. Van der Vorst [14], and Y. Bozhkov and E. Mitidieri [1].
A new link between Boson and Fermion algebras: an alternative to supersymmetryOct 08 2006In this paper we describe a new family of algebras which in the case of n = 2 reduces to the Fermion algebra and in the limiting case of n tends to infinity reduces to the Boson algebra. These generalized algebras describe particles which obey a generalized ... More
Four-fermion production and limits on anomalous couplings at LEP-2Jul 19 2003Electroweak processes with four fermions in the final state were measured extensively at LEP-2 in e+e- collisions with centre-of-mass energies up to 209 GeV. By combining the results obtained by Aleph, Delphi, L3 and Opal, the predictions from the Standard ... More
From Information Geometry to Quantum TheoryMay 19 2008Feb 14 2010In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, ... More
An Information-Theoretic Approach to Quantum Theory, II: The Formal Rules of Quantum TheoryFeb 15 2007In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a correspondence principle, ... More
An Information-Theoretic Approach to Quantum Theory, I: The Abstract Quantum FormalismFeb 13 2007In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we formulate an ... More
Informational Approach to Identical Particles in Quantum TheorySep 02 2013Jun 08 2014A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via the symmetrization ... More
Simple Derivation of the Lindblad EquationApr 10 2012The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is hermitian, trace 1, positive and completely positive. Some elementary examples ... More
Quasirelativistic quasilocal finite wave-function collapse modelFeb 11 2005A Markovian wave function collapse model is presented where the collapse-inducing operator, constructed from quantum fields, is a manifestly covariant generalization of the mass density operator utilized in the nonrelativistic Continuous Spontaneous Localization ... More
Topology of the Stokes phenomenonMar 29 2019Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate category between ... More
Constructing doubly-pointed Heegaard diagrams compatible with (1,1) knotsOct 25 2011A (1,1) knot K in a 3-manifold M is a knot that intersects each solid torus of a genus 1 Heegaard splitting of M in a single trivial arc. Choi and Ko developed a parameterization of this family of knots by a four-tuple of integers, which they call Schubert's ... More
On eigen-structures for pseudoAnosov mapsSep 15 2010We investigate various structures associated with the hyperbolic Markov and homological spectra of a pseudoAnosov map $\phi$ on a surface. Each unstable eigenvalue of the action of $\phi$ on first cohomolgy yields an eigen-cocycle that is transverse and ... More
A periodic model for the dynamics of cell volumeMay 04 2016We prove the existence and uniqueness of positive periodic solution for a model describing the dynamics of cell volume flux, introduced in Julio A. Hernandez \cite{H}. We also show that the periodic solution is a global attractor. Our results confirm ... More
Eigenvalues of sums of pseudo-Hermitian matricesMay 08 2008We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.
Fully Implicit Finite Volume Scheme for Transient Conductive-Radiative Heat Transfer: Discrete Existence, Uniqueness, Maximum PrincipleJul 04 2014This article studies a fully implicit finite volume scheme for transient nonlinear heat transport equations coupled by nonlocal interface conditions modeling diffuse-gray radiation between the surfaces of (both open and closed) cavities. The model is ... More
Fifty Years in Fifteen Minutes: The Impact of the Parkes ObservatoryOct 08 2012The scientific output of Parkes over its fifty year history is briefly reviewed on a year-by-year basis, and placed in context with other national and international events of the time.
Representations of sl(2) in the Boolean lattice, and the Hamming and Johnson schemesFeb 02 2011Feb 10 2011Starting with the zero-square "zeon algebra", the regular representation gives rise to a Boolean lattice representation of sl(2). We detail the su(2) content of the Boolean lattice, providing the irreducible representations carried by the algebra generated ... More
A Simple Derivation of AMP and its State Evolution via First-Order CancellationJul 09 2019We consider the linear regression problem, where the goal is to recover the vector $\boldsymbol{x}\in\mathbb{R}^n$ from measurements $\boldsymbol{y}=\boldsymbol{A}\boldsymbol{x}+\boldsymbol{w}\in\mathbb{R}^m$ under known matrix $\boldsymbol{A}$ and unknown ... More
Quantum Observables on a Completely Simple SemigroupNov 22 2017Completely simple semigroups arise as the support of limiting measures of random walks on semigroups. Such a limiting measure is supported on the kernel of the semigroup. Forming tensor powers of the random walk leads to a hierarchy of the limiting kernels. ... More
Transitivity of Surface Dynamics Lifted to Abelian CoversApr 14 2008A homeomorphism f of a manifold M is called H_1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover \tM. Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements of H_1(M). ... More
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in TimeNov 16 2012Feb 14 2014Building on the recent work of C. De Lellis and L. Sz\'{e}kelyhidi, we construct global weak solutions to the three-dimensional incompressible Euler equations which are zero outside of a finite time interval and have velocity in the H\"{o}lder class $C_{t,x}^{1/5 ... More
A New Slant on Lebesgue's Universal Covering ProblemJan 29 2014Feb 19 2014Lebesgue's universal covering problem is re-examined using computational methods. This leads to conjectures about the nature of the solution which if correct could provide a blueprint for a complete solution. Empirical lower bounds for the minimal area ... More
A White Hole Model of the Big BangMar 04 1998A model of the universe as a very large white hole provides a useful alternative inhomogeneous theory to pit against the homogeneous standard FLRW big bang models. The white hole would have to be sufficiently large that we can fit comfortably inside the ... More
An Acataleptic UniverseApr 24 2013John Wheeler advocated the principle that information is the foundation of physics and asked us to reformulate physics in terms of bits. The goal is to consider what we know already and work out a new mathematical theory in which space, time and matter ... More
The dagger lambda calculusJun 06 2014Dec 30 2014We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" ... More
Using Information Content to Evaluate Semantic Similarity in a TaxonomyNov 29 1995This paper presents a new measure of semantic similarity in an IS-A taxonomy, based on the notion of information content. Experimental evaluation suggests that the measure performs encouragingly well (a correlation of r = 0.79 with a benchmark set of ... More