total 3156took 0.09s

Criticality revealed through quench dynamics in a many-body systemAug 18 2016We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate and by employing the Loschmidt echo, we see manifestly different dynamics are present if the system is quenched through ... More

Trade-off between speed and cost in shortcuts to adiabaticitySep 15 2016Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous ... More

Equilibration and nonclassicality of a double-well potentialJul 15 2015Jan 29 2016A double well loaded with bosonic atoms represents an ideal candidate to simulate some of the most interesting aspects in the phenomenology of thermalisation and equilibration. Here we report an exhaustive analysis of the dynamics and steady state properties ... More

Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick modelAug 18 2016Oct 19 2016We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate and by employing the time-dependent fidelity, we see manifestly different dynamics are present if the system is quenched ... More

Predominance of entanglement of formation over quantum discord under quantum channelsJul 27 2012Mar 11 2013We present a study of the behavior of two different figures of merit for quantum correlations, entanglement of formation and quantum discord, under quantum channels showing how the former can, counterintuitively, be more resilient to such environments ... More

Criticality, factorization and long-range correlations in the anisotropic XY-modelSep 04 2013Dec 04 2013We study the long-range quantum correlations in the anisotropic XY-model. By first examining the thermodynamic limit we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. ... More

Dynamics and Asymptotics of Correlations in a Many-Body Localized SystemAug 31 2016Sep 05 2016We examine the dynamics of nearest-neighbor bipartite concurrence and total correlations in the spin-1/2 XXZ model with random fields. We show, starting from factorized random initial states, that the concurrence can suffer entanglement sudden death in ... More

Cost of counterdiabatic driving and work outputSep 07 2015Oct 31 2016Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve nonzero power for the practical extraction of work, these processes must be performed within a finite time, which inevitably induces excitations in the ... More

Precursors of non-MarkovianityFeb 08 2019Using the paradigm of information backflow to characterize a non-Markovian evolution, we introduce so-called precursors of non-Markovianity, i.e. necessary properties that the system and environment state must exhibit at earlier times in order for an ... More

Quenching small quantum gases: Genesis of the orthogonality catastropheMay 23 2014Jul 07 2014We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two ... More

Full counting statistics approach to the quantum non-equilibrium Landauer boundApr 04 2017Nov 01 2017We develop the full counting statistics of dissipated heat to explore the relation with Landauer's principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer's ... More

Non-Equilibrium Thermodynamics of Harmonically Trapped BosonsApr 12 2016Jun 28 2017We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions ... More

Multipartite non-locality in a thermalized Ising spin-chainJun 11 2010Oct 22 2010We study multipartite correlations and non-locality in an isotropic Ising ring under transverse magnetic field at both zero and finite temperature. We highlight parity-induced differences between the multipartite Bell-like functions used in order to quantify ... More

Non-Equilibrium Thermodynamics of Harmonically Trapped BosonsApr 12 2016Aug 04 2016We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions ... More

Multipartite quantum and classical correlations in symmetric n-qubit mixed statesSep 03 2014Aug 17 2016We discuss how to calculate genuine multipartite quantum and classical correlations in symmetric, spatially invariant, mixed $n$-qubit density matrices. We show that the existence of symmetries greatly reduces the amount of free parameters to be optimized ... More

Correlation approach to work extraction from finite quantum systemsApr 30 2014Jan 14 2015Reversible work extraction from identical quantum systems via collective operations was shown to be possible even without producing entanglement among the sub-parts. Here, we show that implementing such global operations necessarily imply the creation ... More

Passing quantum correlations to qubits using any two-mode stateJul 28 2009Nov 10 2009We draw an explicit connection between the statistical properties of an entangled two-mode continuous variable (CV) resource and the amount of entanglement that can be dynamically transferred to a pair of non-interacting two-level systems. More specifically, ... More

Global Quantum Correlation in the Ising modelJan 16 2012We study quantum correlations in an isotropic Ising ring under the effects of a transverse magnetic field. After characterizing the behavior of two-spin quantum correlations, we extend our analysis to global properties of the ring, using a figure of merit ... More

How strict is strictification?Feb 21 2018Oct 26 2018The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the $\mathbf{Gray}$-category of $2$-categories and the tricategory of bicategories. We show ... More

A resolution of singularities for Drinfeld's compactification by stable mapsJun 05 2016Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting ... More

Quantum Darwinism as a Darwinian processJan 05 2010The Darwinian nature of Wojciech Zurek's theory of Quantum Darwinism is evaluated against the criteria of a Darwinian process as understood within Universal Darwinism. The characteristics of a Darwinian process are developed including the consequences ... More

Effect of inter-particle interaction in a free oscillation atomic interferometerFeb 15 2013Nov 27 2013We investigate the dynamics of two interacting bosons repeatedly scattering off a beam-splitter in a free oscillation atom interferometer. Using the inter-particle scattering length and the beam splitter probabilites as our control parameters, we show ... More

Cost of transitionless driving and work outputSep 07 2015Mar 04 2016Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve non-zero power for the practical extraction of work, these processes must be performed within a finite-time, which inevitably induces excitations in ... More

Photon production from gluon mediated quark-anti-quark annihilation at confinementApr 07 2015Jun 20 2015Heavy ion collisions at RHIC produce direct photons at low transverse momentum, $p_{T}$ from 1-3 GeV/c, in excess of the $p$$+$$p$ spectra scaled by the nuclear overlap factor, $T_{AA}$. These low $p_{T}$ photons have a large azimuthal anisotropy, $v_{2}$. ... More

Exactness of free and amenable groups by the construction of Ozawa kernelsSep 15 2004Jun 01 2005Using properties of their Cayley graphs, specific examples of Ozawa kernels are constructed for both free and amenable groups, thus showing that these groups satisfy Property O. It is deduced both that these groups are exact and satisfy Yu's Property ... More

Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equationsJul 05 2000We present a very simple proof of the global existence of a $C^\infty$ Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with boundary) which has $C^\infty$ dependence on initial data $u_0$ in the ... More

Short Homotopically independent loops on surfacesOct 04 2013In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that for every closed Riemannian surface of genus $g \geq 2$ and area normalized ... More

Moving liquids with light: Photoelectrowetting on semiconductorsAug 24 2011Liquid transport in microchip-based systems is important in many areas such as Laboratory-on-a-chip, Microfluidics and Optofluidics. Actuation of liquids in such systems is usually achieved using either mechanical displacement11 or via energy conversion ... More

Ergodicity and intersections of nodal sets and geodesics on real analytic surfacesOct 02 2012We consider the the intersections of the complex nodal set of the analytic continuation of an eigenfunction of the Laplacian on a real analytic surface with the complexification of a geodesic. We prove that if the geodesic flow is ergodic and if the geodesic ... More

On the density of primes with a set of quadratic residues or non-residues in given arithmetic progressionApr 08 2013Jul 25 2013Let $\mathcal{A}$ denote a finite set of arithmetic progressions of positive integers and let $s \geq 2$ be an integer. If the cardinality of $\mathcal{A}$ is at least 2 and $U$ is the union formed by taking certain arithmetic progressions of length $s$ ... More

Spectral determination of analytic axi-symmetric plane domainsJan 03 1999Apr 07 1999Let ${\cal D}$ denote the class of bounded real analytic plane domains with the symmetry of an ellipse. We prove that if $\Omega_1, \Omega_2 \in {\cal D}$ and if the Dirichlet spectra coincide, $Spec(\Omega_1) = Spec(\Omega_2)$, then $\Omega_1 = \Omega_2$ ... More

Statistical Modeling in Continuous Speech Recognition (CSR)(Invited Talk)Jan 10 2013Automatic continuous speech recognition (CSR) is sufficiently mature that a variety of real world applications are now possible including large vocabulary transcription and interactive spoken dialogues. This paper reviews the evolution of the statistical ... More

Strategies for observing extreme mass ratio inspiralsApr 27 2006Aug 26 2006I review the status of research, conducted by a variety of independent groups, aimed at the eventual observation of Extreme Mass Ratio Inspirals (EMRIs) with gravitational wave detectors. EMRIs are binary systems in which one of the objects is much more ... More

Addendum: Level Spacings for Integrable Quantum Maps in Genus ZeroFeb 04 2000In this addendum we strengthen the results of math-ph/0002010 in the case of polynomial phases. We prove that Cesaro means of the pair correlation functions of certain integrable quantum maps on the 2-sphere at level N tend almost always to the Poisson ... More

Precision and Casimir Force Measurements in Superfluid and Vacuum with Silicon Nitride MembranesAug 28 2008The recent discovery that silicon nitride membranes can be used as extremely high Q mechanical resonators makes possible a number of novel experiments, which include improved long range vacuum Casimir force measurements, and measurments of the properties ... More

Quantum ergodicity of C* dynamical systemsFeb 03 2000This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a convexity inequality ... More

Two-particle self-consistent approximation, pseudogap and superconductivity in the attractive Hubbard modelDec 15 2000In this thesis, I present a non-perturbative approach to the single-band attractive Hubard model which is an extension of previous work by Vilk and Tremblay on the repulsive model. Exact results are derived in the general context of functional derivative ... More

Neutrino Factory and Muon Collider R&DNov 05 2001European, Japanese, and US Neutrino Factory designs are presented. The main R&D issues and associated R&D programs, future prospects, and the additional issues that must be addressed to produce a viable Muon Collider design, are discussed.

Dirac phase leptogenesisOct 02 2007I present here a concise summary of the preprint arXiv:0707.3024, written in collaboration with A. Anisimov and P. Di Bari. There we discuss leptogenesis when {\em CP} violation stems exlusively from the Dirac phase in the PMNS mixing matrix. Under this ... More

The Optimal Sample Complexity of PAC LearningJul 02 2015Feb 07 2016This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the sample complexity ... More

Park City lectures on EigenfunctionsOct 29 2013This is an expository article based on my lectures on eigenfunctions of the Laplacian for the 2013 IAS/Park City Mathematics Institute (PCMI) summer school in geometric analysis. Many of the results are based on joint work with H. Christianson, J. Jung, ... More

Wetting of soap bubbles on hydrophilic, hydrophobic and superhydrophobic surfacesMar 26 2013Wetting of sessile bubbles on solid and liquid surfaces has been studied. A model is presented for the contact angle of a sessile bubble based on a modified Young equation - the experimental results agree with the model. A hydrophilic surface results ... More

Logarithmic lower bound on the number of nodal domainsOct 18 2015We prove that the number of nodal domains of a density one subsequence of eigenfunctions grows at least logarithmically with the eigenvalue on negatively curved `real Riemann surfaces'. The geometric model is the same as in prior joint work with Junehyuk ... More

Asphericity for certain groups of cohomological dimension 2Jan 27 2015Mar 16 2015A finite connected 2-complex K whose fundamental group is of cohomological dimension 2 is aspherical iff the subgroup \Sigma_K of H_2(K) consisting of spherical 2-cycles is zero. A finite connected subcomplex of an aspherical 2-complex is aspherical iff ... More

Off-diagonal decay of toric Bergman kernelsMar 28 2016We study the off-diagonal decay of Bergman kernels $\Pi_{h^k}(z,w)$ and Berezin kernels $P_{h^k}(z,w)$ for ample invariant line bundles over compact toric projective \kahler manifolds of dimension $m$. When the metric is real analytic, $P_{h^k}(z,w) \simeq ... More

Verifying black hole orbits with gravitational spectroscopyNov 29 2007May 08 2009Gravitational waves from test masses bound to geodesic orbits of rotating black holes are simulated, using Teukolsky's black hole perturbation formalism, for about ten thousand generic orbital configurations. Each binary radiates power exclusively in ... More

Inverse Spectral Problem for Surfaces of RevolutionFeb 05 2000This paper concerns the inverse spectral problem for analytic simple surfaces of revolution. By `simple' is meant that there is precisely one critical distance from the axis of revolution. Such surfaces have completely integrable geodesic flows with global ... More

Neutrino Experiments: Status, Recent Progress, and ProspectsNov 19 2007Nov 28 2007Neutrino physics has seen an explosion of activity and new results in the last decade. In this report the current state of the field is summarized, with a particular focus on progress in the last two years. Prospects for the near term (roughly 5 years) ... More

Characterization and properties of weakly optimal entanglement witnessesJul 03 2014Jul 12 2015We present an analysis of the properties and characteristics of weakly optimal entanglement witnesses, that is witnesses whose expectation value vanishes on at least one product vector. Any weakly optimal entanglement witness can be written as the form ... More

Analyzing the Low State of EF Eridani with Hubble Space Telescope Ultraviolet SpectraMay 13 2010Time-resolved spectra throughout the orbit of EF Eri during its low accretion state were obtained with the Solar Blind Channel on the Advanced Camera for Surveys onboard the Hubble Space Telescope. The overall spectral distribution exhibits peaks at 1500 ... More

Topology of the Standard Model, I: FermionsJun 16 2013Dec 26 2015The Harari-Shupe model for fermions is extended to a topological model which contains an explanation for the observed fact that there are only three generations of fermions. Topological explanations are given for $\beta$-decay and for proton decay predicted ... More

Electrowetting of a soap bubbleApr 25 2013A proof-of-concept demonstration of the electrowetting-on-dielectric of a sessile soap bubble is reported here. The bubbles are generated using a commercial soap bubble mixture - the surfaces are composed of highly doped, commercial silicon wafers covered ... More

Measure of nodal sets of analytic Steklov eigenfunctionsMar 04 2014Let $(\Omega, g)$ be a real analytic Riemannian manifold with real analytic boundary $\partial \Omega$. Let $\psi_{\lambda}$ be an eigenfunction of the Dirichlet-to-Neumann operator $\Lambda$ of $(\Omega, g, \partial \Omega)$ of eigenvalue $\lambda$. ... More

Type theory and homotopyOct 09 2010The purpose of this survey article is to introduce the reader to a connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Martin-L\"of into homotopy theory, ... More

Science Potential of a Deep Ocean Antineutrino ObservatoryNov 22 2006Dec 15 2006This paper presents science potential of a deep ocean antineutrino observatory under development at Hawaii. The observatory design allows for relocation from one site to another. Positioning the observatory some 60 km distant from a nuclear reactor complex ... More

Heavy Ions Interpretation of Highest Energy Cosmic RaysDec 14 2001A brief review of the energy spectrum of primary cosmic rays above $10^{10}$ eV and the measurement techniques used to investigate the ultra high energy ones is given. This is followed by a discussion of the atmospheric shower profile of the highest energy ... More

Billiards and boundary traces of eigenfunctionsAug 23 2003This is a report for the 2003 Forges Les Eaux PDE conference on recent results with A. Hassell on quantum ergodicity of boundary traces of eigenfunctions on domains with ergodic billiards, and of work in progress with Hassell and Sogge on norms of boundary ... More

Quantum unique ergodicityJan 27 2003Jul 31 2003This short note proves that a Laplacian cannot be quantum uniquely ergodic if it possesses a quasimode of order zero which (i) has a singular limit, and (ii) is a linear combination of a uniformly bounded number of eigenfunctions (modulo an o(1) error). ... More

Fast Markov Chain Monte Carlo Algorithms via Lie GroupsJan 24 2019From basic considerations of the Lie group that preserves a target probability measure, we derive the Barker, Metropolis, and ensemble Markov chain Monte Carlo (MCMC) algorithms, as well as two new MCMC algorithms. The convergence properties of these ... More

Discovering dynamic functional networks in the human neonatal brain with electric source imagingFeb 11 2019When the human brain manifests the birth of organised communication among local and large-scale neuronal populations activity remains undescribed. We report, in resting-state EEG source-estimates of 100 infants at term age, the existence of macro-scale ... More

The art of juggling with two balls or A proof for a modular condition of Lucas numbersApr 24 2010Apr 28 2010In this short note we look at the problem of counting juggling patterns with one ball or two balls with a throw at every occurrence. We will do this for both traditional juggling and for spherical juggling. In the latter case we will show a connection ... More

Geo-neutrinos: recent developmentsDec 11 2014Radiogenic heating is a key component of the energy balance and thermal evolution of the Earth. It contributes to mantle convection, plate tectonics, volcanoes, and mountain building. Geo-neutrino observations estimate the present radiogenic power of ... More

Testing Geological Models with Terrestrial Antineutrino Flux MeasurementsDec 14 2009Uranium and thorium are the main heat producing elements in the earth. Their quantities and distributions, which specify the flux of detectable antineutrinos generated by the beta decay of their daughter isotopes, remain unmeasured. Geological models ... More

Muon Cooling R&DAug 15 2001International efforts are under way to design and test a muon ionization cooling channel. The present R&D program is described, and future plans outlined.

Neutrino Factories: PhysicsAug 15 2000The recent evidence for neutrino oscillations opens a new and exciting era in neutrino physics. The next generation of accelerator based neutrino oscillation experiments are expected to confirm the nature of the oscillations, and begin to measure some ... More

A New Era of LeptogenesisJul 09 2008This thesis is devoted to some forefront issues in the field of leptogenesis. After reviewing the simplest picture where flavor effects are neglected and only the lightest right-handed neutrino contributes to the generation of asymmetry, we discuss in ... More

Notes on the Theory of Algebraic NumbersJul 27 2015A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of ... More

Refined Error Bounds for Several Learning AlgorithmsDec 22 2015Sep 10 2016This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error rates of sample-consistent ... More

Virtual Reality: A Definition History - A Personal EssayDec 16 2013This essay, written in 1998 by an active participant in both virtual reality development and the virtual reality definition debate, discusses the definition of the phrase "Virtual Reality" (VR). I start with history from a personal perspective, concentrating ... More

Using twins and scaling to construct cospectral graphs for the normalized LaplacianSep 29 2014Oct 23 2014The spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of twins and scaling ... More

Natural models of homotopy type theoryJun 12 2014Mar 19 2015The notion of a natural model of type theory is defined in terms of that of a representable natural transfomation of presheaves. It is shown that such models agree exactly with the concept of a category with families in the sense of Dybjer, which can ... More

Gaussian beams on Zoll manifolds and maximally degenerate LaplaciansApr 10 2014Gaussian beams exist along all closed geodesics of a Zoll surface, despite the fact that the algorithm for constructing them assumes that the closed geodesics are non-degenerate. Similarly, there exists a global Birkhoff normal for a Zoll Laplacian despite ... More

Random orthonormal bases of spaces of high dimensionOct 07 2012We consider a sequence H_N of Hilbert spaces of dimensions d_N tending to infinity. The motivating examples are eigenspaces or quasi-mode spaces of a Laplace or Schrodinger operator. We define a random ONB of H_N by fixing one ONB and changing it by a ... More

Matrix elements of Fourier Integral OperatorsAug 05 2013This article is concerned with the semi-classical limits of matrix elements $<F \phi_j, \phi_j>$ of eigenfunctions of the Laplacian $\Delta_g$ of a compact Riemannian manifold $(M, g)$ with respect to a Fourier integral operator $F$ on $L^2(M)$. Many ... More

Growth of balls in the universal cover of surfaces and graphsApr 12 2013Apr 16 2013In this paper, we prove uniform lower bounds on the volume growth of balls in the universal covers of Riemannian surfaces and graphs. More precisely, there exists a constant $\delta>0$ such that if $(M,hyp)$ is a closed hyperbolic surface and $h$ another ... More

Significance of Rapid Solutions Development to Business Process ManagementAug 19 2012Business process management (BPM) is moving from a niche market into the mainstream. One of the factors leading to this transformation is the emergence of very powerful rapid solutions development tools for creating BPM solutions (BPM RSD). It has been ... More

Activized Learning: Transforming Passive to Active with Improved Label ComplexityAug 08 2011We study the theoretical advantages of active learning over passive learning. Specifically, we prove that, in noise-free classifier learning for VC classes, any passive learning algorithm can be transformed into an active learning algorithm with asymptotically ... More

Temporal Reasoning About Uncertain WorldsMar 27 2013We present a program that manages a database of temporally scoped beliefs. The basic functionality of the system includes maintaining a network of constraints among time points, supporting a variety of fetches, mediating the application of causal rules, ... More

Coloring the 600 CellFeb 18 2008The 600 cell S has exactly 10 5-colorings. From these colorings we can construct the space of colorings $B(S)$. This complex has 1344 colorings, and is isomorphic to the space of 5 by 5 Latin Squares. These simplices split into 4 copies of a quotient ... More

Scientific goals of the UKIRT Infrared Deep Sky SurveyOct 10 2002UKIDSS is the next generation near-infrared sky survey. The survey will commence in early 2004, and over 7 years will collect 100 times as many photons as 2MASS. UKIDSS will use the UKIRT Wide Field Camera to survey 7500 square degrees of the northern ... More

Geo-neutrinos and the Radioactive Power of the EarthNov 25 2011Sep 11 2012Chemical and physical Earth models agree little as to the radioactive power of the planet. Each predicts a range of radioactive powers, overlapping slightly with the other at about 24 TW, and together spanning 14-46 TW. Approximately 20 % of this radioactive ... More

Geo-neutrinos and Silicate Earth Enrichment of U and ThMay 25 2010Aug 30 2010The terrestrial distribution of U, Th, and K abundances governs the thermal evolution, traces the differentiation, and reflects the bulk composition of the earth. Comparing the bulk earth composition to chondritic meteorites estimates the net amounts ... More

Level Spacings for Integrable Quantum Maps in Genus ZeroFeb 04 2000We consider the eigenvalue pair correlation problem for certain integrable quantum maps on the 2-sphere. The classical maps are time one maps of Hamiltonian flows of perfect Morse functions. The quantizations are unitary operators on spaces of homogeneous ... More

Robust Geo-neutrino ResultsNov 11 2016Geo-neutrino observations probe the quantities and distributions of terrestrial heat-producing elements uranium and thorium. The quantities of these elements gauge global radiogenic power, offering insights into the origin and thermal history of the Earth. ... More

Reductions of abelian varieties of generalized Mumford typeNov 19 2016We study the reductions of a class of absolutely simple abelian varieties over number fields with endomorphism rings $\mathbb{Z}$ and $l$-adic monodromy groups of low rank. We also study the densities of the places at which the possible reductions occur. ... More

Integrating electricity markets: Impacts of increasing trade on prices and emissions in the western United StatesOct 10 2018This paper analyzes the market impacts of expanding California's centralized electricity market across the western United States and provides the first statistical assessment of this issue. Using market data from 2015-2018, I estimate the short-term effects ... More

Three-dimensional Binary Superlattices of Oppositely-charged ColloidsApr 29 2005We report the equilibrium self-assembly of binary crystals of oppositely-charged colloidal microspheres at high density. By varying the magnitude of the charge on near equal-sized spheres we show that the structure of the binary crystal may be switched ... More

Catalysis and activation of magic states in fault tolerant architecturesOct 01 2010Feb 09 2011In many architectures for fault tolerant quantum computing universality is achieved by a combination of Clifford group unitary operators and preparation of suitable nonstabilizer states, the so-called magic states. Universality is possible even for some ... More

Enhanced fault-tolerant quantum computing in $d$-level systemsJun 11 2014Oct 09 2015Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford gate. Codes ... More

Pinchuk maps, function fields, and real Jacobian conjecturesFeb 14 2012Jan 18 2013Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated extension of rational ... More

Pinchuk Maps and Function FieldsAug 25 2012May 08 2013All counterexamples of Pinchuk type to the strong real Jacobian conjecture are shown to have rational function field extensions of degree six with no nontrivial automorphisms.

D-analogues of q-shifted factorial and the q-Kummer sumDec 10 2012Recently, the concept of a D-analogue was introduced by the author. This is a Dirichlet series analogue for the already known and well researched hypergeometric q-series. we consider the D-analogues of the q-binomial coefficients, and a D-analogue of ... More

Polylogarithm approaches to Riemann Zeta function zeroesDec 10 2012We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results arise from ... More

Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz driftDec 21 2018We introduce an explicit, adaptive time-stepping scheme for simulation of SPDEs with non-Lipschitz drift coefficients. Strong convergence is proven for the full space-time discretisation with multiplicative noise by considering the space and time discretisation ... More

GOGMA: Globally-Optimal Gaussian Mixture AlignmentMar 01 2016Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. ... More

An ANOVA Test for Parameter Estimability using Data Cloning with Application to Statistical Inference for Dynamic SystemsMay 14 2013Oct 01 2013Models for complex systems are often built with more parameters than can be uniquely identified by available data. Because of the variety of causes, identifying a lack of parameter identifiability typically requires mathematical manipulation of models, ... More

Uncertainty Constrained robotic Exploration: An Integrated Exploration PlannerDec 05 2016Efficient robotic exploration of an unknown, sensor limited, global-information-deficient environments poses unique challenges to path planning algorithms. In these difficult environments, no deterministic guarantees on path completion and mission success ... More

An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache SequencesMay 15 2011We present an integral representation of Kekul\'{e} numbers for $P_{2} (n)$ benzenoids. Related integrals of the form $\int_{-\pi}^{\pi} \frac{\cos(nx)}{\sin^{2}x +k} dx$ are evaluated. Conjectures relating double integrals of the form $\int_{0}^{m} \int_{-\pi}^{\pi} ... More

Derived Koszul Duality and Topological Hochschild HomologyJan 21 2014Motivated by a result from string topology, we prove a duality in topological Hochschild homology (THH). The duality relates the THH of an E_1-algebra spectrum and the THH of its derived Koszul dual algebra under certain compactness conditions. The result ... More

The K-Theory Spectrum of VarietiesMay 12 2015Using a construction closely related to Waldhausen's $S_\bullet$-construction, we produce a spectrum $K(\mathbf{Var}_{/k})$ whose components model the Grothendieck ring of varieties (over a field $k$) $K_0 (\mathbf{Var}_{/k})$. We then produce liftings ... More