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Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)Oct 24 2014Jun 20 2015Explicit solutions of the cubic Fermat equation are constructed in ring class fields $\Omega_f$, with conductor $f$ prime to $3$, of any imaginary quadratic field $K$ whose discriminant satisfies $d_K \equiv 1$ (mod $3$), in terms of the Dedekind $\eta$-function. ... More

Skein theory and the Murphy operatorsFeb 13 2001The Murphy operators in the Hecke algebra H_n of type A are explicit commuting elements whose sum generates the centre. They can be represented by simple tangles in the Homfly skein theory version of H_n. In this paper I present a single tangle which ... More

Closed-Loop Policies for Operational Tests of Safety-Critical SystemsJul 25 2017May 19 2018Manufacturers of safety-critical systems must make the case that their product is sufficiently safe for public deployment. Much of this case often relies upon critical event outcomes from real-world testing, requiring manufacturers to be strategic about ... More

Imitating Driver Behavior with Generative Adversarial NetworksJan 24 2017The ability to accurately predict and simulate human driving behavior is critical for the development of intelligent transportation systems. Traditional modeling methods have employed simple parametric models and behavioral cloning. This paper adopts ... More

An Efficient Automated Validation Procedure for Exoplanet Transit CandidatesJun 07 2012Oct 03 2012Surveys searching for transiting exoplanets have found many more candidates than they have been able to confirm as true planets. This situation is especially acute with the Kepler survey, which has found over 2300 candidates but has confirmed only 77 ... More

An estimate of the circulation generated by a bluff bodyMay 30 2006Mar 01 2008A loss in circulation is sometimes cited in connection with bluff-body wakes as a result of comparing the circulation actually observed downstream with a well-known theoretical estimate of the total circulation generated by a cylinder. In an effort to ... More

A Complete Set of Invariants for LU-Equivalence of Density OperatorsJul 13 2015Nov 21 2016We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants below a certain degree. This implicitly gives a finite complete set of invariants for local unitary equivalence. ... More

Comment on Ghost imaging with a single detector [arXiv0812.2633v2]Feb 11 2009Computational ghost imaging has been demonstrated experimentally recently. In this comment we wish to clarify the difference between pseudothermal ghost imaging (PGI) and computational ghost imaging (CGI). In particular, to emphasize the physics that ... More

Comment on a paper by Lapaire and SipeAug 08 2006In a recent paper [quant-ph/0607008] Lapaire and Sipe argue that one can discuss interference experiments using entangled photons in terms of single photon wave functions. Furthermore, they argue that contrary to the claim of the authors of the postponed ... More

Entanglement and State PreparationJan 26 1999Jan 27 1999When a subset of particles in an entangled state is measured, the state of the subset of unmeasured particles is determined by the outcome of the measurement. This first measurement may be thought of as a state preparation for the remaining particles. ... More

Probability of Physical Association of 104 Blended Companions to \textit{Kepler} Objects of Interest Using Visible and Near-Infrared Adaptive Optics PhotometrySep 29 2016We determine probabilities of physical association for stars in blended Kepler Objects of Interest, and find that $14.5\%^{+3.8\%}_{-3.4\%}$ of companions within $\sim4\arcsec$ are consistent with being physically unassociated with their primary. This ... More

Ghost Interference with Optical Parametric AmplifierJul 21 2004The 'Ghost' interference experiment is analyzed when the source of entangled photons is a multimode Optical Parametric Amplifier(OPA) whose weak limit is the two-photon Spontaneous Parametric Downconversion(SPDC) beam. The visibility of the double-slit ... More

The Robo-AO KOI Survey: laser adaptive optics imaging of every Kepler exoplanet candidateAug 01 2016The Robo-AO Kepler Planetary Candidate Survey is observing every Kepler planet candidate host star (KOI) with laser adaptive optics imaging to hunt for blended nearby stars which may be physically associated companions. With the unparalleled efficiency ... More

Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behaviorDec 23 2009Jun 25 2010Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus reverse-engineering attempts. ... More

Convexity and the Separability Problem of Quantum Mechanical Density MatricesMar 08 2001A finite dimensional quantum mechanical system is modeled by a density rho, a trace one, positive semi-definite matrix on a suitable tensor product space H[N] . For the system to demonstrate experimentally certain non-classical behavior, rho cannot be ... More

Mutually Unbiased Bases, Generalized Spin Matrices and SeparabilityAug 26 2003Apr 21 2004A collection of orthonormal bases for a complex dXd Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: |<v,w>| ^{2}=1/d. The MUB problem is to prove or disprove ... More

Note on Separability of the Werner states in arbitrary dimensionsJan 30 2000Feb 25 2000Great progress has been made recently in establishing conditions for separability of a particular class of Werner densities on the tensor product space of $n$ $d$--level systems (qudits). In this brief note we complete the process of establishing necessary ... More

Complete Separability and Fourier representations of n-qubit statesDec 28 1999Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these two bases and ... More

Discerning Exoplanet Migration Models Using Spin-Orbit MeasurementsOct 19 2010We investigate the current sample of exoplanet spin-orbit measurements to determine whether a dominant planet migration channel can be identified, and at what confidence. We use the predictions of Kozai migration plus tidal friction (Fabrycky and Tremaine ... More

On the Low False Positive Probabilities of Kepler Planet CandidatesJan 28 2011Jun 10 2011We present a framework to conservatively estimate the probability that any particular planet-like transit signal observed by the Kepler mission is in fact a planet, prior to any ground-based follow-up efforts. We use Monte Carlo methods based on stellar ... More

Separability and Fourier representations of density matricesJan 07 2000Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d) $ is a basis for $d\times d$ matrices. If $N=d_{1}\times d_{2}\times...\times d_{b}$ and ... More

The mildly nonlinear imprint of structure on the CMBDec 03 1999Dec 05 1999I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included ... More

Are pre-main-sequence stars older than we thought?Jul 14 2009We fit the colour-magnitude diagrams of stars between the zero-age main-sequence and terminal-age main sequence in young clusters and associations. The ages we derive are a factor 1.5 to 2 longer than the commonly used ages for these regions, which are ... More

On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnetJun 28 1999The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schr\"odinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izergin ... More

A Structured Variational Auto-encoder for Learning Deep Hierarchies of Sparse FeaturesFeb 28 2016In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian units allow spike-and-slab ... More

What Bell DidAug 08 2014On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier arguments of Einstein, Podolsky and Rosen. ... More

Reply to WernerAug 08 2014Reinhard Werner authored a comment on my paper "What Bell Did", disputing the conclusion and argumentation of the paper. This is my reply.

Euclidean-valued group cohomology is always reducedOct 11 2013Nov 25 2013If G is a countable discrete group acting linearly on a finite-dimensional vector space over any topological field, then the groups of coboundaries are closed for the product topology in all degrees, and hence the cohomology is reduced in all degrees. ... More

Correlation functions, null polygonal Wilson loops, and local operatorsOct 18 2011Jul 30 2012We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By ... More

The LSST Data Processing Software Stack: Summer 2015 ReleaseNov 20 2015The Large Synoptic Survey Telescope (LSST) is an 8-m optical ground-based telescope being constructed on Cerro Pachon in Chile. LSST will survey half the sky every few nights in six optical bands. The data will be transferred to NCSA and within 60 seconds ... More

A Geometric Embedding for Standard Analytic ModulesMar 28 2005Jun 11 2007In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector bundle defined ... More

The elementary obstruction and the Weil restrictionDec 20 2007Mar 31 2009In this text we investigate the good behaviour of the elementary obstruction, introduced by Colliot-Thelene and Sansuc. This is an obstruction to the existence of a rational points on certain algebraic varieties. Assuming some conditions on the Picard ... More

On the regularity over positively graded algebrasDec 20 2006Aug 30 2007We study the relationship between the Tor-regularity and the local-regularity over a positively graded algebra defined over a field which coincide if the algebra is a standard graded polynomial ring. In this case both are characterizations of the so-called ... More

Uniform stability of linear evolution equations, with applications to parallel transportsFeb 12 2015I prove the bistability of linear evolution equations $x' = A(t)x$ in a Banach space $E$, where the operator-valued function $A$ is of the form $A(t) = f'(t)G(t,f(t))$ for a binary operator-valued function $G$ and a scalar function $f$. The constant that ... More

Behaviour of entropy under bounded and integrable orbit equivalenceApr 04 2016Nov 07 2016Let $G$ and $H$ be infinite finitely generated amenable groups. This paper studies two notions of equivalence between actions of such groups on standard Borel probability spaces. They are defined as stable orbit equivalences in which the associated cocycles ... More

Discrete Hashimoto surfaces and a doubly discrete smokering flowJul 25 2000B\"acklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schr\"odinger equation ... More

The structure of low-complexity Gibbs measures on product spacesOct 16 2018Mar 04 2019Let $K_1$, $\dots$, $K_n$ be bounded, complete, separable metric spaces. Let $\lambda_i$ be a Borel probability measure on $K_i$ for each $i$. Let $f:\prod_i K_i \to \mathbb{R}$ be a bounded and continuous potential function, and let $$\mu(d \mathbf{x})\ ... More

Rational group ring elements with kernels having irrational dimensionSep 12 2009Mar 12 2013We prove that there are examples of finitely generated groups G together with group ring elements Q \in \bbQ G for which the von Neumann dimension \dim_{LG}\ker Q is irrational, so (in conjunction with other known results) answering a question of Atiyah. ... More

RectangularityAug 08 2011We introduce a condition on arrays in some way maximally distinct from Latin square condition, as well as some other conditions on algebras, graphs and $0,1$-matrices. We show that these are essentially the same structures, generalising a similar collection ... More

The geometry of model spaces for probability-preserving actions of sofic groupsDec 04 2015Jun 06 2016Bowen's notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the `model spaces'. The metric ... More

Norm convergence of continuous-time polynomial multiple ergodic averagesMar 01 2011Jul 01 2016For a jointly measurable probability-preserving action $\tau:\mathbb{R}^D\curvearrowright (X,\mu)$ and a tuple of polynomial maps $p_i:\mathbb{R}\to \mathbb{R}^D$, $i=1,2,...,k$, the multiple ergodic averages \[ \frac{1}{T}\int_0^T (f_1\circ \tau^{p_1(t)})(f_2\circ ... More

Towards a Noether-like conservation law theorem for one dimensional reversible cellular automataDec 01 2003Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics. We take the ... More

Electroweak Physics Results from NuTeVMay 22 2002NuTeV has performed precise measurements of neutral-current to charged-current cross section ratios using intense high energy neutrino and anti-neutrino beams on a primarily steel target at the Fermilab Tevatron. A null hypothesis test of the standard ... More

Beyond the RPA on the cheap: improved correlation energies with the efficient "Radial Exchange Hole" kernelAug 27 2012The "ACFD-RPA" correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here we present a parameter-free exchange-correlation ... More

Inner Accretion Disk Edges in a Kerr-Like SpacetimeApr 30 2013Jun 06 2013According to the no-hair theorem, astrophysical black holes are uniquely described by the Kerr metric. In order to test this theorem with observations in either the electromagnetic or gravitational-wave spectra, several Kerr-like spacetimes have been ... More

Beyond the Standard Model Higgs Boson Searches at the TevatronDec 02 2010Results are presented for beyond the Standard Model Higgs boson searches using up to 4.2 fb-1 of data from Run II at the Tevatron. No significant excess is observed in any of the channels so 95% confidence level limits are presented.

Sgr A* and General RelativityDec 11 2015May 09 2016General relativity has been widely tested in weak gravitational fields but still stands largely untested in the strong-field regime. According to the no-hair theorem, black holes in general relativity depend only on their masses and spins and are described ... More

Invariant Set Theory: Violating Measurement Independence without Fine Tuning, Conspiracy, Constraints on Free Will or RetrocausalityJul 07 2015Nov 06 2015Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe $U$ can be considered a deterministic dynamical system evolving precisely on a (suitably constructed) fractal dynamically ... More

Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groupsMay 27 2011Jul 01 2016Let $G$ be a connected nilpotent Lie group. Given probability-preserving $G$-actions $(X_i,\Sigma_i,\mu_i,u_i)$, $i=0,1,...,k$, and also polynomial maps $\phi_i:\mathbb{R}\to G$, $i=1,...,k$, we consider the trajectory of a joining $\lambda$ of the systems ... More

A short extension of two of Spira's resultsDec 05 2013Oct 17 2014Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $\tau$-function are improved through the use of some elementary considerations.

Modern Python at the Large Synoptic Survey TelescopeDec 01 2017The LSST software systems make extensive use of Python, with almost all of it initially being developed solely in Python 2. Since LSST will be commissioned when Python 2 is end-of-lifed it is critical that we have all our code support Python 3 before ... More

Free Semialgebraic GeometryFeb 28 2019This is a survey article on the currently very active research area of free (=non-commutative) real algebra and geometry. We first review some of the important results from the commutative theory, and then explain similarities and differences as well ... More

Who discovered positron annihilation?Sep 13 2018In the early 1930s, the positron, pair production, and, at last, positron annihilation were discovered. Over the years, several scientists have been credited with the discovery of the annihilation radiation. Commonly, Thibaud and Joliot have received ... More

Time Symmetric Quantum Theory Without RetrocausalityJul 24 2017In their recent paper "Is a Time Symmetric Interpretation of Quantum Theory Possible Without Retrocausality?", Matthew Leifer and Matthew Pusey argue that the answer to their title question is "no". Unfortunately, the central proof offered in the paper ... More

Counting Cliques in Finite Distant GraphsDec 23 2016We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product decomposition of their ... More

Contrastive Explanation: A Structural-Model ApproachNov 07 2018The topic of causal explanation in artificial intelligence has gathered interest in recent years as researchers and practitioners aim to increase trust and understanding of intelligent decision-making and action. While different sub-fields have looked ... More

The ECMWF Ensemble Prediction System: Looking Back (more than) 25 Years and Projecting Forward 25 YearsMar 16 2018This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast ... More

Double Hall algebras and derived equivalencesSep 22 2008Dec 20 2009We show that the reduced Drinfeld double of the Ringel-Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of [BS1], [BS2], [SVdB], ... More

The one-arm exponent for mean-field long-range percolationNov 11 2014Consider a long-range percolation model on $\mathbb{Z}^d$ where the probability that an edge $\{x,y\} \in \mathbb{Z}^d \times \mathbb{Z}^d$ is open is proportional to $\|x-y\|_2^{-d-\alpha}$ for some $\alpha >0$ and where $d > 3 \min\{2,\alpha\}$. We ... More

Gluing and deformations of asymptotically cylindrical special LagrangiansSep 27 2017We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, ... More

An asymptotic equipartition property for measures on model spacesJan 30 2017Sep 18 2018Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences of measures ... More

Deducing the Density Hales-Jewett Theorem from an infinitary removal lemmaMar 09 2009Apr 19 2011We offer a new proof of Furstenberg and Katznelson's density version of the Hales-Jewett Theorem: For any $\delta > 0$ there is some $N_0 \geq 1$ such that whenever $A \subseteq [k]^N$ with $N \geq N_0$ and $|A|\geq \delta k^N$, $A$ contains a \textbf{combinatorial ... More

High Energy Muon Momentum Estimation from Multiple Coulomb Scattering in Dense DetectorsMay 09 1997A method is described for estimating muon track momentum from the distribution of hits along tracks in dense calorimeters due to multiple Coulomb scattering (MCS). The method requires only well-aligned conventional drift chambers or similar tracking devices ... More

Background field approach to electromagnetic properties of baryonsNov 15 2011Dec 13 2011We investigate the self-energies of particles in an external magnetic field $B$. The dependence is generally of the type $\sqrt{P(B)}$ with $P$ a polynomial in $B$ and the participating masses. The non-analytic point depends on the mass and charge constellations, ... More

On exchangeable random variables and the statistics of large graphs and hypergraphsJan 10 2008May 26 2008De Finetti's classical result of [18] identifying the law of an exchangeable family of random variables as a mixture of i.i.d. laws was extended to structure theorems for more complex notions of exchangeability by Aldous [1,2,3], Hoover [41,42], Kallenberg ... More

Ranks of elliptic curves in cubic extensionsOct 25 2005For an elliptic curve E over a number field K, we prove that the algebraic rank of E goes up in infinitely many extensions of K obtained by adjoining a cube root of an element of K. As an example, we briefly discuss E=X_1(11) over Q, and how the result ... More

On local search and LP and SDP relaxations for k-Set PackingJul 27 2015Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set problem. In this ... More

How polarizabilities and $C_6$ coefficients actually vary with atomic volumeAug 14 2016In this work we investigate how atomic $C_6$ coefficients and static dipole polarizabilities $\alpha$ scale with effective volume. We show, using confined atoms covering rows 1-5 of the periodic table, that $C_6/C_6^R\approx (V/V^R)^{p_Z}$ and $\alpha/\alpha^R\approx ... More

Photon Rings around Kerr and Kerr-like Black HolesJan 12 2015Very-long baseline interferometric observations have resolved structure on scales of only a few Schwarzschild radii around the supermassive black holes at the centers of our Galaxy and M87. In the near future, such observations are expected to image the ... More

Regular Black Hole Metric with Three Constants of MotionJan 12 2015Dec 15 2015According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric spacetimes which deviate from the Kerr metric have been proposed in order to test ... More

Communication Complexity (for Algorithm Designers)Sep 21 2015This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems that have proved ... More

The shape dynamics description of gravityJan 13 2015Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the ... More

Tackling drug resistant infection outbreaks of global pandemic Escherichia coli ST131 using evolutionary and epidemiological genomicsNov 04 2014Feb 17 2015High-throughput molecular screening is required to investigate the origin and diffusion of antimicrobial resistance in pathogen outbreaks. The most frequent cause of human infection is Escherichia coli, which is dominated by sequence type 131 (ST131), ... More

Beyond the Standard Model Higgs Boson Searches at the TevatronJul 02 2011Results are presented for beyond the Standard Model Higgs boson searches using up to 8.2 invfb of data from Run II at the Tevatron. No significant excess is observed in any of the channels so 95% confidence level limits are presented.

Weak lensing statistics from the Coyote UniverseDec 14 2010Analyzing future weak lensing data sets from KIDS, DES, LSST, Euclid, WFIRST requires precise predictions for the weak lensing measures. In this paper we present a weak lensing prediction code based on the Coyote Universe emulator. The Coyote Universe ... More

Application of Lossless Data Compression Techniques to Radio Astronomy Data flowsMay 22 2014The modern practice of Radio Astronomy is characterized by extremes of data volume and rates, principally because of the direct relationship between the signal to noise ratio that can be achieved and the need to Nyquist sample the RF bandwidth necessary ... More

8-Bit Approximations for Parallelism in Deep LearningNov 14 2015Feb 19 2016The creation of practical deep learning data-products often requires parallelization across processors and computers to make deep learning feasible on large data sets, but bottlenecks in communication bandwidth make it difficult to attain good speedups ... More

Bounds on the number of Diophantine quintuplesJan 19 2015We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of distinct positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on ... More

Stability of Quadratic ModulesJul 28 2008A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by Powers and Scheiderer, ... More

Comparison Theorem and Geometric Realization of RepresentationsDec 22 2003In this paper we generalize the comparison theorem of Hecht and Taylor to arbitrary parabolic subalgebras of a complex reductive Lie algebra and then apply our generalized comparison theorem to obtain results about the geometric realization of representations ... More

Zero-sets of near-symplectic formsJan 13 2006Jan 15 2007We give elementary proofs of two `folklore' assertions about near-symplectic forms on four-manifolds: that any such form can be modified, by an evolutionary process taking place within a finite set of balls, so as to have a prescribed positive number ... More

Computational Power and the Social Impact of Artificial IntelligenceMar 23 2018Machine learning is a computational process. To that end, it is inextricably tied to computational power - the tangible material of chips and semiconductors that the algorithms of machine intelligence operate on. Most obviously, computational power and ... More

Grades of Discrimination: Indiscernibility, symmetry, and relativityAug 07 2014Jun 12 2015There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to ... More

Closed Systems of Invertible MapsDec 21 2015Nov 08 2018We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have connections ... More

Improvements to Turing's Method IIJun 13 2014Oct 17 2014Turing's method uses explicit bounds on $|\int_{t_{1}}^{t_{2}} S(t)\, dt|$, where $\pi S(t)$ is the argument of the Riemann zeta-function. This article improves the bound on $|\int_{t_{1}}^{t_{2}} S(t)\, dt|$ given in an earlier paper by the author.

Updating the error term in the prime number theoremJan 13 2014Oct 17 2014An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the third to a conjecture ... More

Quantitative equidistribution for certain quadruples in quasi-random groupsOct 24 2013Jul 08 2015In a recent paper (arXiv:1211.6372), Bergelson and Tao proved that if $G$ is a $D$-quasi-random group, and $x$,$g$ are drawn uniformly and independently from $G$, then the quadruple $(g,x,gx,xg)$ is roughly equidistributed in the subset of $G^4$ defined ... More

Measure concentration and the weak Pinsker propertyApr 30 2017Feb 16 2018Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less than $\varepsilon$. ... More

On the norm convergence of nonconventional ergodic averagesMay 03 2008Feb 25 2009We offer a generalization of the recent result of Tao (building on earlier results of Conze and Lesigne, Furstenberg and Weiss, Zhang, Host and Kra, Frantzikinakis and Kra and Ziegler) that the nonconventional ergodic averages associated to an arbitrary ... More

Measuring the Recoverability of Close Binaries in Gaia DR2 with the Robo-AO Kepler SurveyJun 26 2018Aug 31 2018We use the Robo-AO survey of Kepler planetary candidate host stars, the largest adaptive optics survey yet performed, to measure the recovery rate of close stellar binaries in Gaia DR2. We find that Gaia recovers binaries down to 1" at magnitude contrasts ... More

Robo-AO Kepler Planetary Candidate Survey III: Adaptive Optics Imaging of 1629 Kepler Exoplanet Candidate Host StarsMay 11 2016Sep 30 2016The Robo-AO \textit{Kepler} Planetary Candidate Survey is observing every \textit{Kepler} planet candidate host star with laser adaptive optics imaging to search for blended nearby stars, which may be physically associated companions and/or responsible ... More

Robo-AO Kepler Planetary Candidate Survey II: Adaptive Optics Imaging of 969 Kepler Exoplanet Candidate Host StarsApr 28 2016We initiated the Robo-AO Kepler Planetary Candidate Survey in 2012 to observe each Kepler exoplanet candidate host star with high-angular-resolution visible-light laser-adaptive-optics imaging. Our goal is to find nearby stars lying in Kepler's photometric ... More

Formal Semantics and Soundness of a Translation from Event-B Actions to SQL StatementsJun 08 2016The EventB2SQL tool translates Event-B models to persistent Java applications that store the state of the model in a relational database. Most Event-B assignments are translated directly to SQL database modification statements, which can then be executed ... More

Black Hole Formation in Lovelock GravityAug 10 2014We first derive the Hamiltonian for Lovelock gravity and find that it takes the same form as in general relativity when written in terms of the Misner-Sharp mass function. We then minimally couple the action to matter fields to find Hamilton's equations ... More

Distribution and Generalized Center in Planar NearringsJul 05 2016Nov 10 2016Planar nearrings play an important role in nearring theory, both from the structural side as being close to generalised nearfields, as well as from an applications perspective, in geometry and designs. We investigate the distributive elements of planar ... More

Closed Systems of Invertible MapsDec 21 2015We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have connections ... More

X-ray Probes of Black Hole Accretion Disks for Testing the No-Hair TheoremJan 12 2015The spins of a number of supermassive and stellar-mass black holes have been measured based on detections of thermal continuum emission and relativistically broadened iron lines in their x-ray spectra. Likewise, quasiperiodic variability has been observed ... More

Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons LearnedJun 26 2014Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines ... More

Implementing and Automating Fixed-Form Variational Posterior Approximation through Stochastic Linear RegressionJan 09 2014We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer details on ... More

Determining the CKM Parameter Vcd from nuN Charm ProductionAug 14 1997The formalism for extracting the CKM parameter $V_{cd}$ from $\nu N$ production of charm is discussed in some detail. The various model assumptions needed are clearly pointed out. A direct determination from neutrino induced dimuon production requires ... More