Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

MVG Mechanism: Differential Privacy under Matrix-Valued Query

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline.Comment: Appeared in CCS'1

Scaling the mid-IR radiation at 7 μm - Two-stage double-pass 195 MHz narrow-bandwidth DFG laser system

We present a laser system based on difference frequency generation (DFG) to produce tunable, narrow-linewidth (<30 pm), and high-energy mid-IR radiation in the 6785 nm region. The system exploits nonlinear crystals (such as LiInS2, LiInSe2 and BaGa4Se7) and nanosecond pulses generated by single-frequency Nd:YAG and Cr:forsterite lasers at 1064 and 1262 nm, respectively. Various experimental configurations are used: single-pass and double-pass through the nonlinear crystal. Additional increments of the output energy can be obtained by performing two stage double-pass geometry

Oms1 associates with cytochrome c oxidase assembly intermediates to stabilize newly synthesized Cox1.

The mitochondrial cytochromecoxidase assembles in the inner membrane from subunits of dual genetic origin. The assembly process of the enzyme is initiated by membrane insertion of the mitochondria-encoded Cox1 subunit. During complex maturation, transient assembly intermediates, consisting of structural subunits and specialized chaperone-like assembly factors, are formed. In addition, cofactors such as heme and copper have to be inserted into the nascent complex. To regulate the assembly process, the availability of Cox1 is under control of a regulatory feedback cycle, in which translation of the COX1 mRNA is stalled when assembly intermediates of Cox1 accumulate through inactivation of the translational activator Mss51. Here we have isolated a cytochromecoxidase assembly intermediate in preparatory scale fromcoa1Δmutant cells using Mss51 as a bait. We demonstrate that at this stage of assembly the complex has not yet incorporated the heme a cofactors. Using quantitative mass spectrometry, we defined the protein composition of the assembly intermediate and unexpectedly identified the putative methyltransferase Oms1 as a constituent. Our analyses show that Oms1 participates in cytochromecoxidase assembly by stabilizing newly synthesized Cox1

HATS-5b: A Transiting hot-Saturn from the HATSouth Survey

We report the discovery of HATS-5b, a transiting hot-Saturn orbiting a G type star, by the HAT-South survey. HATS-5b has a mass of Mp=0.24 Mj, radius of Rp=0.91 Rj, and transits its host star with a period of P=4.7634d. The radius of HATS-5b is consistent with both theoretical and empirical models. The host star has a V band magnitude of 12.6, mass of 0.94 Msun, and radius of 0.87 Rsun. The relatively high scale height of HATS-5b, and the bright, photometrically quiet host star, make this planet a favourable target for future transmission spectroscopy follow-up observations. We reexamine the correlations in radius, equilibrium temperature, and metallicity of the close-in gas-giants, and find hot Jupiter-mass planets to exhibit the strongest dependence between radius and equilibrium temperature. We find no significant dependence in radius and metallicity for the close-in gas-giant population.Comment: 10 pages, submitted to A

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.Comment: Review article, will be published in Journal of Optics B, special issue on Optical Solitons, 6 figure

HATS-3b: An inflated hot Jupiter transiting an F-type star

We report the discovery by the HATSouth survey of HATS-3b, a transiting extrasolar planet orbiting a V=12.4 F-dwarf star. HATS-3b has a period of P = 3.5479d, mass of Mp = 1.07MJ, and radius of Rp = 1.38RJ. Given the radius of the planet, the brightness of the host star, and the stellar rotational velocity (vsini = 9.0km/s), this system will make an interesting target for future observations to measure the Rossiter-McLaughlin effect and determine its spin-orbit alignment. We detail the low/medium-resolution reconnaissance spectroscopy that we are now using to deal with large numbers of transiting planet candidates produced by the HATSouth survey. We show that this important step in discovering planets produces logg and Teff parameters at a precision suitable for efficient candidate vetting, as well as efficiently identifying stellar mass eclipsing binaries with radial velocity semi-amplitudes as low as 1 km/s.Comment: 11 pages, 10 figures, submitted to A

Conformal invariance: from Weyl to SO(2,d)

The present work deals with two different but subtilely related kinds of conformal mappings: Weyl rescaling in $d>2$ dimensional spaces and SO(2,d) transformations. We express how the difference between the two can be compensated by diffeomorphic transformations. This is well known in the framework of String Theory but in the particular case of $d=2$ spaces. Indeed, the Polyakov formalism describes world-sheets in terms of two-dimensional conformal field theory. On the other hand, B. Zumino had shown that a classical four-dimensional Weyl-invariant field theory restricted to live in Minkowski space leads to an SO(2,4)-invariant field theory. We extend Zumino's result to relate Weyl and SO(2,d) symmetries in arbitrary conformally flat spaces (CFS). This allows us to assert that a classical $SO(2,d)$-invariant field does not distinguish, at least locally, between two different $d$-dimensional CFSs.Comment: 5 pages, no figures. There are slight modifications to match with the published versio

The astrometric Gaia-FUN-SSO observation campaign of 99 942 Apophis

Astrometric observations performed by the Gaia Follow-Up Network for Solar System Objects (Gaia-FUN-SSO) play a key role in ensuring that moving objects first detected by ESA's Gaia mission remain recoverable after their discovery. An observation campaign on the potentially hazardous asteroid (99 942) Apophis was conducted during the asteroid's latest period of visibility, from 12/21/2012 to 5/2/2013, to test the coordination and evaluate the overall performance of the Gaia-FUN-SSO . The 2732 high quality astrometric observations acquired during the Gaia-FUN-SSO campaign were reduced with the Platform for Reduction of Astronomical Images Automatically (PRAIA), using the USNO CCD Astrograph Catalogue 4 (UCAC4) as a reference. The astrometric reduction process and the precision of the newly obtained measurements are discussed. We compare the residuals of astrometric observations that we obtained using this reduction process to data sets that were individually reduced by observers and accepted by the Minor Planet Center. We obtained 2103 previously unpublished astrometric positions and provide these to the scientific community. Using these data we show that our reduction of this astrometric campaign with a reliable stellar catalog substantially improves the quality of the astrometric results. We present evidence that the new data will help to reduce the orbit uncertainty of Apophis during its close approach in 2029. We show that uncertainties due to geolocations of observing stations, as well as rounding of astrometric data can introduce an unnecessary degradation in the quality of the resulting astrometric positions. Finally, we discuss the impact of our campaign reduction on the recovery process of newly discovered asteroids.Comment: Accepted for publication in A&

Four Dimensional CFT Models with Rational Correlation Functions

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field $\phi$ of dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of $\phi$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of $L_V$) is proven to be equivalent to $c \in N$.Comment: 28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are correcte