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

Charged Many-Electron -- Single Hole Complexes in a Double Quantum Well near a Metal Plate

It has been shown that the presence of a metal plate near a double quantum well with spatially separated electron and hole layers may lead to a drastic reconstruction of the system state with the formation of stable charged complexes of several electrons bound to a spatially separated hole. Complexes of both the Fermi and the Bose statistics may coexist in the ground state and their relative densities may be changed with the change of the electron and hole densities. The stability of the charged complexes may be increased by an external magnetic field perpendicular to the layers plane.Comment: to appear in Phys.Rev.Lett. 77, No.7 (1996). 4 pages, RevTeX, 1 figur

Multiwavelength characterisation of an ACT-selected, lensed dusty star-forming galaxy at z=2.64

We present \ci\,(2--1) and multi-transition $^{12}$CO observations of a dusty star-forming galaxy, ACT\,J2029+0120, which we spectroscopically confirm to lie at $z$\,=\,2.64. We detect CO(3--2), CO(5--4), CO(7--6), CO(8--7), and \ci\,(2--1) at high significance, tentatively detect HCO$^{+}$(4--3), and place strong upper limits on the integrated strength of dense gas tracers (HCN(4--3) and CS(7--6)). Multi-transition CO observations and dense gas tracers can provide valuable constraints on the molecular gas content and excitation conditions in high-redshift galaxies. We therefore use this unique data set to construct a CO spectral line energy distribution (SLED) of the source, which is most consistent with that of a ULIRG/Seyfert or QSO host object in the taxonomy of the \textit{Herschel} Comprehensive ULIRG Emission Survey. We employ RADEX models to fit the peak of the CO SLED, inferring a temperature of T$\sim$117 K and $n_{\text{H}_2}\sim10^5$ cm$^{-3}$, most consistent with a ULIRG/QSO object and the presence of high density tracers. We also find that the velocity width of the \ci\ line is potentially larger than seen in all CO transitions for this object, and that the $L'_{\rm C\,I(2-1)}/L'_{\rm CO(3-2)}$ ratio is also larger than seen in other lensed and unlensed submillimeter galaxies and QSO hosts; if confirmed, this anomaly could be an effect of differential lensing of a shocked molecular outflow.Comment: Accepted for publication in Ap

Welcome to the Twilight Zone: The Mid-Infrared Properties of Poststarburst Galaxies

We investigate the optical and Wide-field Survey Explorer (WISE) colors of "E+A" identified post-starburst galaxies, including a deep analysis on 190 post-starbursts detected in the 2{\mu}m All Sky Survey Extended Source Catalog. The post-starburst galaxies appear in both the optical green valley and the WISE Infrared Transition Zone (IRTZ). Furthermore, we find that post-starbursts occupy a distinct region [3.4]-[4.6] vs. [4.6]-[12] WISE colors, enabling the identification of this class of transitioning galaxies through the use of broad-band photometric criteria alone. We have investigated possible causes for the WISE colors of post-starbursts by constructing a composite spectral energy distribution (SED), finding that mid-infrared (4-12{\mu}m) properties of post-starbursts are consistent with either 11.3{\mu}m polycyclic aromatic hydrocarbon emission, or Thermally Pulsating Asymptotic Giant Branch (TP-AGB) and post-AGB stars. The composite SED of extended post- starburst galaxies with 22{\mu}m emission detected with signal to noise >3 requires a hot dust component to produce their observed rising mid-infrared SED between 12 and 22{\mu}m. The composite SED of WISE 22{\mu}m non-detections (S/N<3), created by stacking 22{\mu}m images, is also flat, requiring a hot dust component. The most likely source of this mid-infrared emission of these E+A galaxies is a buried active galactic nucleus. The inferred upper limit to the Eddington ratios of post-starbursts are 1e-2 to 1e-4, with an average of 1e-3. This suggests that AGNs are not radiatively dominant in these systems. This could mean that including selections able to identify active galactic nuclei as part of a search for transitioning and post-starburst galaxies would create a more complete census of the transition pathways taken as a galaxy quenches its star formation.Comment: 13 pages, 11 figures, accepted for publication in the Astrophysical Journa

Multi-phonon Resonant Raman Scattering Predicted in LaMnO3 from the Franck-Condon Process via Self-Trapped Excitons

Resonant behavior of the Raman process is predicted when the laser frequency is close to the orbital excitation energy of LaMnO3 at 2 eV. The incident photon creates a vibrationally excited self-trapped ``orbiton'' state from the orbitally-ordered Jahn-Teller (JT) ground state. Trapping occurs by local oxygen rearrangement. Then the Franck-Condon mechanism activates multiphonon Raman scattering. The amplitude of the $n$-phonon process is first order in the electron-phonon coupling $g$. The resonance occurs {\it via} a dipole forbidden $d$ to $d$ transition. We previously suggested that this transition (also seen in optical reflectivity) becomes allowed because of asymmetric oxygen fluctuations. Here we calculate the magnitude of the corresponding matrix element using local spin-density functional theory. This calculation agrees to better than a factor of two with our previous value extracted from experiment. This allows us to calculate the absolute value of the Raman tensor for multiphonon scattering. Observation of this effect would be a direct confirmation of the importance of the JT electron-phonon term and the presence of self-trapped orbital excitons, or ``orbitons''.Comment: 8 pages and 3 embedded figures. The earlier short version is now replaced by a more complete paper with a slightly different title. This version includes a caculation by density-functional theory of the dipole matrix element for exciting the self-trapped orbital exciton which activates the multiphonon Raman signal

First-principles calculations of the self-trapped exciton in crystalline NaCl

The atomic and electronic structure of the lowest triplet state of the off-center (C2v symmetry) self-trapped exciton (STE) in crystalline NaCl is calculated using the local-spin-density (LSDA) approximation. In addition, the Franck-Condon broadening of the luminescence peak and the a1g -> b3u absorption peak are calculated and compared to experiment. LSDA accurately predicts transition energies if the initial and final states are both localized or delocalized, but 1 eV discrepancies with experiment occur if one state is localized and the other is delocalized.Comment: 4 pages with 4 embeddded figure

Bone turnover markers are correlated with total skeletal uptake of 99mTc-methylene diphosphonate (99mTc-MDP)

ABSTRACT: BACKGROUND: Skeletal uptake of 99mTc labelled methylene diphosphonate (99mTc-MDP) is used for producing images of pathological bone uptake due to its incorporation to the sites of active bone turnover. This study was done to validate bone turnover markers using total skeletal uptake (TSU) of 99mTc-MDP. METHODS: 22 postmenopausal women (52-80 years) volunteered to participate. Scintigraphy was performed by injecting 520 MBq of 99mTc-MDP and taking whole body images after 3 minutes, and 5 hours. TSU was calculated from these two images by taking into account the urinary loss and soft tissue uptake. Bone turnover markers used were bone specific alkaline phosphatase (S-Bone ALP), three different assays for serum osteocalcin (OC), tartrate resistant acid phosphatase 5b (S-TRACP5b), serum C-terminal cross-linked telopeptides of type I collagen (S-CTX-I) and three assays for urinary osteocalcin (U-OC). RESULTS: The median TSU of 99mTc-MDP was 23% of the administered activity. All bone turnover markers were significantly correlated with TSU with r-values from 0.52 (p = 0.013) to 0.90 (p < 0.001). The two resorption markers had numerically higher correlations (S-TRACP5b r = 0.90, S-CTX-I r = 0.80) than the formation markers (S-Total OC r = 0.72, S-Bone ALP r = 0.66), but the difference was not statistically significant. TSU did not correlate with age, weight, body mass index or bone mineral density. CONCLUSION: In conclusion, bone turnover markers are strongly correlated with total skeletal uptake of 99mTc-MDP. There were no significant differences in correlations for bone formation and resorption markers. This should be due to the coupling between formation and resorption

A systematic variation of the stellar initial mass function in early-type galaxies

Much of our knowledge of galaxies comes from analysing the radiation emitted by their stars. It depends on the stellar initial mass function (IMF) describing the distribution of stellar masses when the population formed. Consequently knowledge of the IMF is critical to virtually every aspect of galaxy evolution. More than half a century after the first IMF determination, no consensus has emerged on whether it is universal in different galaxies. Previous studies indicated that the IMF and the dark matter fraction in galaxy centres cannot be both universal, but they could not break the degeneracy between the two effects. Only recently indications were found that massive elliptical galaxies may not have the same IMF as our Milky Way. Here we report unambiguous evidence for a strong systematic variation of the IMF in early-type galaxies as a function of their stellar mass-to-light ratio, producing differences up to a factor of three in mass. This was inferred from detailed dynamical models of the two-dimensional stellar kinematics for the large Atlas3D representative sample of nearby early-type galaxies spanning two orders of magnitude in stellar mass. Our finding indicates that the IMF depends intimately on a galaxy's formation history.Comment: 4 pages, 2 figures, LaTeX. Accepted for publication as a Nature Letter. More information about our Atlas3D project is available at http://purl.org/atlas3

High Quality Early Time Light Curves of GRB 060206: Implications for Gamma Ray Burst Environments and Energetics

The 2-m robotic Liverpool Telescope (LT) reacted promptly to the high-redshift (z=4.048) gamma-ray burst GRB 060206. The afterglow was identified automatically and multicolor r'i'z' imaging was triggered without human intervention. Combining our data with those obtained from later follow-ups provides a well-sampled optical light-curve from 5 minutes to >2d after the gamma event. The light-curve is highly structured with at least three bumps evident in the first 75 minutes, including a major rebrightening (Delta_r'=-1.6 at t=3000s), interpreted as late energy injection. At early time (t=440s), we find evidence for fast (Delta t_(rest)<4s<<t) variability, indicating on-going internal-engine activity. We emphasise that a low redshift GRB (z<1) with similar intrinsic properties would have been interpreted completely differently due to undersampling of the light curve in the rest frame at early times; the light-curve behaviour of GRB 060206 should therefore not be considered peculiar. Finally, although the observed late-time steepening of the optical light curve resembles a jet break if taken in isolation, the lack of a corresponding change in the X-ray slope rules out a jet-break interpretation. Traditionally, GRB jet breaks have been inferred from optical data in the absence of simultaneous X-ray data. We suggest therefore that current estimates of the jet opening angle distribution might be biased by events like GRB060206. Consequently, the GRB explosion energy distribution and event rates may have to be revised.Comment: 9 pages, 5 figures, Submitted to Ap

Black Holes in the Early Universe

The existence of massive black holes was postulated in the sixties, when the first quasars were discovered. In the late nineties their reality was proven beyond doubt, in the Milky way and a handful nearby galaxies. Since then, enormous theoretical and observational efforts have been made to understand the astrophysics of massive black holes. We have discovered that some of the most massive black holes known, weighing billions of solar masses, powered luminous quasars within the first billion years of the Universe. The first massive black holes must therefore have formed around the time the first stars and galaxies formed. Dynamical evidence also indicates that black holes with masses of millions to billions of solar masses ordinarily dwell in the centers of today's galaxies. Massive black holes populate galaxy centers today, and shone as quasars in the past; the quiescent black holes that we detect now in nearby bulges are the dormant remnants of this fiery past. In this review we report on basic, but critical, questions regarding the cosmological significance of massive black holes. What physical mechanisms lead to the formation of the first massive black holes? How massive were the initial massive black hole seeds? When and where did they form? How is the growth of black holes linked to that of their host galaxy? Answers to most of these questions are work in progress, in the spirit of these Reports on Progress in Physics.Comment: Reports on Progress in Physics, in pres