Results for "Ross Duncan"

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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
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
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
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
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
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
Optimising Clifford Circuits with QuantomaticJan 29 2019We present a system of equations between Clifford circuits, all derivable in the ZX-calculus, and formalised as rewrite rules in the Quantomatic proof assistant. By combining these rules with some non-trivial simplification procedures defined in the Quantomatic ... 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
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
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
Daughter Fragmentation is Unlikely To Occur in Self-Gravitating Circumstellar DiscsFeb 22 2016Circumstellar discs are thought to be self-gravitating at very early times. If the disc is relatively cool, extended and accreting sufficiently rapidly, it can fragment into bound objects of order a few Jupiter masses and upwards. Given that the fragment's ... 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.
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
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
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
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculusFeb 08 2019Feb 26 2019We present the theoretical foundations for a new quantum circuit optimisation technique based on an equational theory called the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing ... 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
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
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
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
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
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
Vector product and composition algebras in braided monoidal additive categoriesDec 10 2018This is an account of some work of Markus Rost and his students Dominik Boos and Susanne Maurer. We adapt it to the braided monoidal setting.
Polynomials as spansMar 10 2019The paper defines polynomials in a bicategory $\mathscr{M}$. Polynomials in bicategories $\mathrm{Spn}\mathscr{C}$ of spans in a finitely complete category $\mathscr{C}$ agree with polynomials in $\mathscr{C}$ as defined by Nicola Gambino and Joachim ... More
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
Monoidal categories in, and linking, geometry and algebraJan 14 2012Oct 04 2012This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a link between knot ... More
The 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
Transience/Recurrence and the speed of a one-dimensional random walk in a "have your cookie and eat it" environmentFeb 06 2009Jun 07 2009Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $\omega(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$, from which ... More
Compactness results for neck-stretching limits of instantonsDec 07 2012May 07 2015We prove that, under a suitable degeneration of the metric, instantons converge to holomorphic quilts. To prove the main results, we develop estimates for the Yang-Mills heat flow on surfaces and cobordisms.
Higher-rank instanton cohomology and the quilted Atiyah-Floer conjectureNov 21 2013May 07 2015Given a closed, connected, oriented 3-manifold with positive first Betti number, one can define an instanton Floer group as well as a quilted Lagrangian Floer group. The quilted Atiyah-Floer conjecture states that these cohomology groups are isomorphic. ... More
The Galactic Millisecond Pulsar PopulationOct 09 2012Among the current sample of over 2000 radio pulsars known primarily in the disk of our Galaxy, millisecond pulsars now number almost 200. Due to the phenomenal success of blind surveys of the Galactic field, and targeted searches of Fermi gamma-ray sources, ... More
A rigorous and efficient asymptotic test for power-law cross-correlationSep 16 2013Sep 17 2013Podobnik and Stanley recently proposed a novel framework, Detrended Cross-Correlation Analysis, for the analysis of power-law cross-correlation between two time-series, a phenomenon which occurs widely in physical, geophysical, financial and numerous ... More
Extrasolar Asteroid Mining as Forensic Evidence for Extraterrestrial IntelligenceMar 28 2011The development of civilisations like ours into spacefaring, multi-planet entities requires significant raw materials to construct vehicles and habitats. Interplanetary debris, including asteroids and comets, may provide such a source of raw materials. ... More
What is a Galaxy? Cast your vote here...Jan 17 2011Jan 22 2011Although originally classified as galaxies, Ultra Compact Dwarfs (UCDs) share many properties in common with globular star clusters. The debate on the origin and nature of UCDs, and the recently discovered ultra-faint dwarf spheroidal (dSph) galaxies ... More
The Jeans Mass as a Fundamental Measure of Self-Gravitating Disc Fragmentation and Initial Fragment MassJul 05 2011As a formation route for objects such as giant planets and low-mass stars in protostellar discs (as well as stars in AGN discs), theories of self-gravitating disc fragmentation need to be able to predict the initial masses of fragments. We describe a ... More
Searching for Gravitational Radiation from Binary Black Hole MACHOs in the Galactic HaloMay 10 2007The Laser Interferometer Gravitational Wave Observatory (LIGO) is one of a new generation of detectors of gravitational radiation. The existence of gravitational radiation was first predicted by Einstein in 1916, however gravitational waves have not yet ... More
Pushing the limit on neutron star spin ratesAug 25 2006Millisecond X-ray pulsars consist of a rapidly-spinning neutron star accreting from a low-mass stellar companion, and are the long-sought evolutionary progenitors of millisecond radio pulsars, as well as promising candidate sources for gravitational radiation. ... More
Triggers of magnetar outburstsJan 21 2004Bright outbursts from Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are believed to be caused by instabilities in ultramagnetized neutron stars, powered by a decaying magnetic field. It was originally thought that these outbursts were ... More
Globular Clusters and Galaxy FormationJun 20 2002Globular clusters provide a unique probe of galaxy formation and evolution. Here I briefly summarize the known observational properties of globular cluster systems. One re-occurring theme is that the globular cluster systems of spirals and ellipticals ... More
Fixed points of a finite subgroup of the plane Cremona groupAug 18 2014Jan 04 2016We classify all finite subgroups of the plane Cremona group which have a fixed point. In other words, we determine all rational surfaces X with an action of a finite group G such that X is equivariantly birational to a surface which has a G-fixed point. ... More
Why Do We Believe in the Second Law?Aug 14 2002Claims of exceptions to the second law of thermodynamics are generally met with extreme skepticism that is quite reasonable given the great confidence placed in the second law. But what specifically is the basis for that confidence? The perspective from ... More
On the components of the gauge group for PU(r)-bundlesNov 21 2013We discuss a general procedure for using characteristic classes to study the components of the gauge group for a principal G-bundle. To illustrate this, we work out the case where G is the projective unitary group.
Exponential Genus Problems in one-relator products of groupsJun 03 2005Exponential equations in free groups were studied initially by Lyndon and Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution ... More
Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2Oct 23 2015Nov 09 2017We 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
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
Optimality in Quantum Data Compression using Dynamical EntropyApr 10 2019Apr 15 2019In this article we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared to be encoded ... 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
Detecting fast radio bursts at decametric wavelengthsSep 04 2016Nov 07 2016Fast radio bursts (FRBs) are highly dispersed, sporadic radio pulses that are likely extragalactic in nature. Here we investigate the constraints on the source population from surveys carried out at frequencies $<1$~GHz. All but one FRB has so far been ... More
On the nonlinearity of quantum dynamical entropyOct 12 2018Oct 20 2018Linearity of a dynamical entropy means that the dynamical entropy of the n-fold composition of a dynamical map with itself is equal to n times the dynamical entropy of the map for every positive integer n. We show that the quantum dynamical entropy introduced ... 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
On the qubit routing problemFeb 21 2019We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present empirical results ... 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
On the qubit routing problemFeb 21 2019Feb 28 2019We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present empirical results ... 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
How else can we detect Fast Radio Bursts?May 05 2016May 26 2016We discuss possible electromagnetic signals accompanying Fast Radio Bursts (FRBs) that are expected in the scenario where FRBs originate in neutron star magnetospheres. For models involving Crab-like giant pulses, no appreciable contemporaneous emission ... More
Scaling of curvature in sub-critical gravitational collapseFeb 24 1998Aug 12 1998We perform numerical simulations of the gravitational collapse of a spherically symmetric scalar field. For those data that just barely do not form black holes we find the maximum curvature at the position of the central observer. We find a scaling relation ... More
Accreted versus In Situ Milky Way Globular ClustersJan 25 2010Here we examine the Milky Way's GC system to estimate the fraction of accreted versus in situ formed GCs. We first assemble a high quality database of ages and metallicities for 93 Milky Way GCs from literature deep colour-magnitude data. The age-metallicity ... More
Word Hyperbolic SemigroupsApr 30 2002The study of word hyperbolic groups is a prominent topic in geometric group theory; however word hyperbolic groups are defined by a geometric condition which does not extend naturally to semigroups. We propose a linguistic definition. Roughly speaking ... More
The Giant Flare of 1998 August 27 from SGR 1900+14: II. Radiative Mechanism and Physical Constraints on the SourceOct 30 2001(ABBREVIATED) The extraordinary 1998 August 27 giant flare places strong constraints on the physical properties of its source, SGR 1900+14. We make detailed comparisons of the published data with the magnetar model. The giant flare evolved through three ... More
Limit sets for modules over groups on CAT(0) spaces -- from the Euclidean to the hyperbolicJun 14 2013Apr 17 2014The observation that the 0-dimensional Geometric Invariant $\Sigma ^{0}(G;A)$ of Bieri-Neumann-Strebel-Renz can be interpreted as a horospherical limit set opens a direct trail from Poincar\'{e}'s limit set $\Lambda (\Gamma)$ of a discrete group $\Gamma ... More
Quantum categories, star autonomy, and quantum groupoidsJan 20 2003Apr 04 2003A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. We define the term "quantum category". The definition of antipode for a bialgebroid is less resolved ... More
Wilson's ratio and the spin splitting of magnetic oscillations in quasi-two-dimensional metalsMay 05 1999Sep 07 1999A simple consistency check is proposed for the Fermi liquid description of the low-temperature properties of quasi-two-dimensional metals. In a quasi-two-dimensional Fermi liquid the Zeeman splitting of magnetic oscillations can be used to determine g^*, ... More
Ginzburg-Landau theory of phase transitions in quasi-one-dimensional systemsJan 18 1995A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition. It is shown ... More
Doubles for monoidal categoriesNov 13 2007In a recent paper, Daisuke Tambara defined two-sided actions on an endomodule (= endodistributor) of a monoidal V-category A. When A is autonomous (= rigid = compact), he showed that the V-category (that we call Tamb(A)) of so-equipped endomodules (that ... More
Stability of exponential utility maximization with respect to market perturbationsJul 14 2011Dec 11 2012We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, ... More
Exploiting Subgraph Structure in Multi-Robot Path PlanningOct 31 2011Multi-robot path planning is difficult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of abstraction that allows ... More
Low-shot Visual Recognition by Shrinking and Hallucinating FeaturesJun 09 2016Nov 30 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
Connectivity properties of group actions on non-positively curved spaces I: Controlled connectivity and openness resultsNov 03 1998Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the space R := Hom(G, ... More
Overcoming the language barrier in mobile user interface design: A case study on a mobile health appMay 16 2016This research report proposes a structured solution to address the need for awareness of cultural and language in user design. It will include evaluated research on established methods that already exist. Discussed ideas about how to address this situation ... More
Training Machine Learning Models by Regularizing their ExplanationsSep 29 2018Neural networks are among the most accurate supervised learning methods in use today. However, their opacity makes them difficult to trust in critical applications, especially when conditions in training may differ from those in practice. Recent efforts ... More
Torsors, herds and flocksDec 23 2009Sep 23 2010This paper presents non-commutative and structural notions of torsor. The two are related by the machinery of Tannaka-Krein duality.
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
Extremal Distances for Subtree Transfer Operations in Binary TreesSep 02 2015Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection ($TBR$), subtree prune and regraft ($SPR$) and rooted subtree prune and regraft ($rSPR$). For a pair of leaf-labelled ... 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
Uniqueness/nonuniqueness for nonnegative solutions of the Cauchy problem for $u_t=Δu-u^p$ in a punctured spaceDec 13 2004Consider classical solutions to the following Cauchy problem in a punctured space: $ &u_t=\Delta u -u^p \text{in} (R^n-\{0\})\times(0,\infty); & u(x,0)=g(x)\ge0 \text{in} R^n-\{0\}; &u\ge0 \text{in} (R^n-\{0\})\times[0,\infty). $ We prove that if $p\ge\frac ... 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
The speed of a general random walk reinforced by its recent historySep 07 2017Mar 28 2019We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed as the "history ... More
Real setsApr 28 2017Jan 16 2018After reviewing a universal characterization of the extended positive real numbers published by Denis Higgs in 1978, we define a category which provides an answer to the questions: \begin{itemize} \item what is a set with half an element? \item what is ... More
Genus six curves, K3 surfaces, and stable pairsDec 26 2018A general smooth curve of genus six lies on a quintic del Pezzo surface. In \cite{AK11}, Artebani and Kond\=o construct a birational period map for genus six curves by taking ramified double covers of del Pezzo surfaces. The map is not defined for special ... More
Extremes for the inradius in the Poisson line tessellationJan 31 2015A Poisson line tessellation is observed within a window. With each cell of the tessellation, we associate the inradius, which is the radius of the largest ball contained in the cell. Using Poisson approximation, we compute the limit distributions of the ... More
Dynamic Multi-Factor Clustering of Financial NetworksMay 07 2015We investigate the tendency for financial instruments to form clusters when there are multiple factors influencing the correlation structure. Specifically, we consider a stock portfolio which contains companies from different industrial sectors, located ... More
Unified description of hydrogen bonding and of proton transfer by a two-state effective HamiltonianSep 10 2011Sep 21 2011An effective Hamiltonian is considered for hydrogen bonding between two molecules due to the quantum mechanical interaction between the orbitals of the H-atom and the donor and acceptor atoms in the molecules. The Hamiltonian acts on two diabatic states ... More
Exact results for quantum phase transitions in random XY spin chainsSep 20 1996The effect of disorder on the quantum phase transitions induced by a transverse field, anisotropy, and dimerization in XY spin chains is investigated. The low-energy behavior near the critical point is described by a Dirac-type equation with a random ... More
Marching in squaresMar 13 2015In this articles we consider very mathematical (if not very plausible) geometric marching. Our marchers will exhibit beautiful mathematics, some familiar and some less so. In a final summary section we discuss the point of all the fancy footwork.