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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

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

Hopf-Frobenius algebras and a new Drinfeld doubleMay 02 2019The ZX-calculus and related theories are based on so-called interacting Frobenius algebras, where a pair of $\dag$-special commutative Frobenius algebras jointly form a pair of Hopf algebras. In this setting we introduce a generalisation of this structure, ... 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

Hopf-Frobenius algebras and a Simpler Drinfeld doubleMay 02 2019Jul 07 2019The ZX-calculus and related theories are based on so-called interacting Frobenius algebras, where a pair of $\dag$-special commutative Frobenius algebras jointly form a pair of Hopf algebras. In this setting we introduce a generalisation of this structure, ... 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

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

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

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

Finite Groups of Essential Dimension 2Dec 09 2009Sep 25 2010We classify all finite groups of essential dimension 2 over an algebraically closed field of characteristic 0.

Lattice Field Theory Methods in Modern BiophysicsSep 28 2006An effective field theory exists describing a very large class of biophysically interesting Coulomb gas systems: the lowest order (mean-field) version of this theory takes the form of a generalized Poisson-Boltzmann theory. Interaction terms depend on ... More

Null-homologous twisting and the algebraic genusAug 12 2019The algebraic genus of a knot is an invariant that arises when one considers upper bounds for the topological slice genus coming from Freedman's theorem that Alexander polynomial one knots are topologically slice. This paper develops null-homologous twisting ... More

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

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

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

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

Gaps between consecutive untwisting numbersAug 18 2019For $p\geq 1$ one can define a generalization of the unknotting number $tu_p$ called the $p$th untwisting number which counts the number of null-homologous twists on at most $2p$ strands required to convert the knot to the unknot. We show that for any ... More

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

Pauli Fusion: a computational model to realise quantum transformations from ZX termsApr 29 2019We present an abstract model of quantum computation, the Pauli Fusion model, whose primitive operations correspond closely to generators of the ZX calculus (a formal graphical language for quantum computing). The fundamental operations of Pauli Fusion ... More

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

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculusFeb 08 2019Apr 29 2019We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using ... 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

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

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

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

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

Phase Gadget Synthesis for Shallow CircuitsJun 04 2019We give an overview of the circuit optimisation methods used by tket, a compiler system for quantum software developed by Cambridge Quantum Computing Ltd. We focus on a novel technique based around phase gadgets, a family of multi-qubit quantum operations ... More

Number of arithmetic progressions in dense random subsets of $\mathbb{Z}/n\mathbb{Z}$Jul 26 2019We examine the behavior of the number of $k$ term arithmetic progressions in a random subset of $\mathbb{Z}/n\mathbb{Z}$. If $k=3$ and the subset is chosen uniformly at random, then we show that the resulting distribution, while obeying a central limit ... More

Semistability and CAT(0) GeometryMar 20 2017We explain why semistability of a one-ended proper CAT(0) space can be determined by the geodesic rays. This is applied to boundaries of CAT(0) groups.

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

Kan extensions and cartesian monoidal categoriesSep 23 2014The existence of adjoints to algebraic functors between categories of models of Lawvere theories follows from finite-product-preservingness surviving left Kan extension. A result along these lines was proved in Appendix 2 of Brian Day's 1970 PhD thesis. ... More

Searching for Extraterrestrial Intelligence by Locating Potential ET Communication Networks in SpaceJul 10 2019Jul 23 2019There have been periodic efforts in recent decades to search for extraterrestrial intelligence (SETI), especially by trying to find an extraterrestrial (ET) radio signal or other technosignature in space. Yet, no such technosignatures have been found. ... More

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

Span composition using fake pullbacksJul 05 2019The construction of a category of spans can be made in some categories $\CC$ which do not have pullbacks in the traditional sense. The PROP for monoids is a good example of such a $\CC$. The 2012 book concerning homological algebra by Marco Grandis gives ... 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

Step Size in Stein's Method of Exchangeable PairsApr 02 2009Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we analyze how modifying ... More

The core of adjoint functorsDec 01 2011Jan 03 2012There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, ... More

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

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

Weighted Tensor Products of Joyal Species, Graphs, and CharadesMar 10 2015Jan 17 2016Motivated by the weighted Hurwitz product on sequences in an algebra, we produce a family of monoidal structures on the category of Joyal species. We suggest a family of tensor products for charades. We begin by seeing weighted derivational algebras and ... More

Pascual Jordan's resolution of the conundrum of the wave-particle duality of lightSep 24 2007In 1909, Einstein derived a formula for the mean square energy fluctuation in black-body radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1925 Dreimaennerarbeit with Born and Heisenberg, Jordan showed ... More

The subgroup membership problem in amalgamated products of finitely generated free groupsMay 19 2013May 21 2013Stallings folding theory is modified, using double coset representatives, and to applied to the study of subgroups of amalgamated products of finite rank free groups. As a first application the subgroup membership problem for such groups is shown to be ... More

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)Oct 23 2006In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical ... More

E11 and SupersymmetryNov 26 2010Feb 24 2011We introduce fermions into the E11 non-linear realisation. We show, at low levels, that the commutators of the Cartan involution invariant subalgebra of E11 with the known supersymmetry transformations of eleven dimensional supergravity lead to symmetries ... 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.

Explicit construction and uniqueness for universal operator algebras of directed graphsOct 12 2004Oct 22 2004Given a directed graph, there exists a universal operator algebra and universal C*-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C*-algebra ... More

Limit theorems for the Zig-Zag processJul 29 2016Jul 25 2017Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained ... More

Versality of algebraic group actions and rational points on twisted varietiesSep 28 2011Jul 10 2013We formalize and study several competing notions of versality for an action of a linear algebraic group on an algebraic variety X. Our main result is that these notions of versality are equivalent to various statements concerning rational points on twisted ... More

The Deep Physics Behind the Second Law: Information and Energy As Independent Forms of BookkeepingJan 03 2005Even after over 150 years of discussion, the interpretation of the second law of thermodynamics continues to be a source of confusion and controversy in physics. This confusion has been accentuated by recent challenges to the second law and by the difficulty ... More

The Yang-Mills flow for cylindrical end 4-manifoldsMar 01 2016We establish various existence and uniqueness results for the Yang-Mills flow on cylindrical end 4-manifolds. We also show long-time existence and infinite-time convergence under certain hypotheses on the underlying data.

Circular support in random sorting networksFeb 25 2018Oct 31 2018A sorting network is a shortest path from $12 \cdots n$ to $n \cdots 2 1$ in the Cayley graph of the symmetric group generated by adjacent transpositions. For a uniform random sorting network, we prove that in the global limit, particle trajectories are ... 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

How large are the globular cluster systems of early-type galaxies and do they scale with galaxy halo properties?Oct 03 2017The globular cluster systems of galaxies are well-known to extend to large galactocentric radii. Here we quantify the size of GC systems using the half number radius of 22 GC systems around early-type galaxies from the literature. We compare GC system ... More

Radial Kinematics of Isolated Elliptical GalaxiesApr 21 2006Ellipticals in very low density environments are extremely rare but hold important clues about galaxy formation and evolution. In this paper we continue our study of isolated elliptical galaxies, presenting results on the radial stellar kinematics for ... 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

Orientable and non-orientable genus $n$ Wicks forms over hyperbolic groupsSep 03 2015Sep 24 2015In 1962 M.J. Wicks gave a precise description of the form a commutator could take in a free group or a free product and in 1973 extended this description to cover a product of two squares. Subsequently, lists of "Wicks forms" were found for arbitrary ... More

Optimality in Quantum Data Compression using Dynamical EntropyApr 10 2019Aug 03 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

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

Asymptotic zero distribution of random orthogonal polynomialsJan 30 2018Mar 22 2018We consider random polynomials of the form $H_n(z)=\sum_{j=0}^n\xi_jq_j(z)$ where the $\{\xi_j\}$ are i.i.d non-degenerate complex random variables, and the $\{q_j(z)\}$ are orthonormal polynomials with respect to a compactly supported measure $\tau$ ... 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

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

Linked and knotted synthetic magnetic fieldsAug 10 2018Apr 29 2019We 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

Discovery of a Giant Lya Emitter Near the Reionization EpochJul 25 2008Feb 21 2009We report the discovery of a giant Lya emitter (LAE) with a Spitzer/IRAC counterpart near the reionization epoch at z=6.595. The giant LAE is found from the extensive 1 deg^2 Subaru narrow-band survey for z=6.6 LAEs in the Subaru/XMM-Newton Deep Survey ... 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

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

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 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

On the structure of globular cluster systems in elliptical galaxiesSep 18 2005It has long been known that the radial density profiles of globular cluster systems (GCSs) in elliptical galaxies vary with the total luminosities of their host galaxies. In order to elucidate the origin of this structural non-homology in GCSs, we numerically ... More

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

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

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

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

Segal operations in the algebraic $K$-theory of topological spacesJul 10 2017Jul 09 2018We extend earlier work of Waldhausen which defines operations on the algebraic $K$-theory of the one-point space. For a connected simplicial abelian group $X$ and symmetric groups $\Sigma_n$, we define operations $\theta^n \colon A(X) \rightarrow A(X{\times}B\Sigma_n)$ ... More

Algebraic and Logical Methods in Quantum ComputationOct 08 2015Feb 15 2017This thesis contains contributions to the theory of quantum computation. We first define a new method to efficiently approximate special unitary operators. Specifically, given a special unitary U and a precision {\epsilon} > 0, we show how to efficiently ... More

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

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

A Convex Primal Formulation for Convex Hull PricingMay 17 2016Apr 10 2017In certain electricity markets, because of non-convexities that arise from their operating characteristics, generators that follow the independent system operator's (ISO's) decisions may fail to recover their cost through sales of energy at locational ... More

A retrieval strategy for interactive ensemble data assimilationSep 08 2010Aug 08 2011As an alternative to either directly assimilating radiances or the naive use of retrieved profiles (of temperature, humidity, aerosols, and chemical species), a strategy is described that makes use of the so-called averaging kernel (AK) and other information ... More

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

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

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

The Size-Luminosity Relationship of Quasar Narrow-Line RegionsApr 16 2018The presence of an active galactic nucleus (AGN) can strongly affect its host. Due to the copious radiative power of the nucleus, the effects of radiative feedback can be detected over the entire host galaxy and sometimes well into the intergalactic space. ... 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

PSD-throttling on TreesJun 14 2019PSD-forcing is a coloring process on a graph that colors vertices blue by starting with an initial set $B$ of blue vertices and applying a color change rule (CCR-$\Zp$). The PSD-throttling number is the minimum of the sum of the cardinality of $B$ and ... More

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

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

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