Differentially Private Data Releasing for Smooth Queries with Synthetic Database Output

We consider accurately answering smooth queries while preserving differential privacy. A query is said to be $K$-smooth if it is specified by a function defined on $[-1,1]^d$ whose partial derivatives up to order $K$ are all bounded. We develop an $\epsilon$-differentially private mechanism for the class of $K$-smooth queries. The major advantage of the algorithm is that it outputs a synthetic database. In real applications, a synthetic database output is appealing. Our mechanism achieves an accuracy of $O (n^{-\frac{K}{2d+K}}/\epsilon )$, and runs in polynomial time. We also generalize the mechanism to preserve $(\epsilon, \delta)$-differential privacy with slightly improved accuracy. Extensive experiments on benchmark datasets demonstrate that the mechanisms have good accuracy and are efficient

Exploring the Transient Radio Sky with ASKAP

Many types of astronomical objects show variability at radio wavelengths. While several dedicated transient surveys at other wavelengths have already yielded fruitful results, there are only a few transient surveys at radio wavelengths. In this thesis, we explored a range of radio transient phenomena with the Australian Square Kilometre Array Pathfinder (ASKAP). In Chapter 2, we present the results of a radio transient and polarisation survey towards the Galactic Centre, conducted as part of the ASKAP Variables and Slow Transients (VAST) pilot survey. As part of the search, we identified a highly-variable, highly-polarised source, ASKAP J173608.2-321635. In Chapter 3, we present detailed follow-up observations of this source. We used a range of facilities over a wide frequency range (from radio to X-ray) to investigate the nature of the source. However, there is no type of source that can fully explain the observational properties of the source. The properties of the source indicate that this could be a newly discovered Galactic Centre Radio Transient (GCRT), whose nature is still unknown. In Chapter 4, we explored the capability of ASKAP to detect fast radio bursts from neutron star mergers. We simulated the slew time of ASKAP for different scenarios and found that the chance of such a detection in coming years would be low. However, with the upgrade of the gravitational wave detector network in the next few years, we suggest that it will be more likely to make such detections. In conclusion, the work in this thesis demonstrates the ability of ASKAP to explore a variety of transient phenomena. Further transient surveys with ASKAP, MeerKAT, the Deep Synoptic Array (DSA), the next-generation VLA (ngVLA) and the Square Kilometre Array (SKA) will enable us to have comprehensive understanding of the radio transient sources population, and may reveal new types of sources in the future

Topologically protected vortex transport via chiral-symmetric disclination

Vortex phenomena are ubiquitous in nature, from vortices of quantum particles and living cells [1-7], to whirlpools, tornados, and spiral galaxies. Yet, effective control of vortex transport from one place to another at any scale has thus far remained a challenging goal. Here, by use of topological disclination [8,9], we demonstrate a scheme to confine and guide vortices of arbitrary high-order charges10,11. Such guidance demands a double topological protection: a nontrivial winding in momentum space due to chiral symmetry [12,13] and a nontrivial winding in real space arising from collective complex coupling between vortex modes. We unveil a vorticity-coordinated rotational symmetry, which sets up a universal relation between the topological charge of a guided vortex and the order of rotational symmetry of the disclination structure. As an example, we construct a C3-symmetry photonic lattice with a single-core disclination, thereby achieving robust transport of an optical vortex with preserved orbital angular momentum (OAM) that corresponds solely to one excited vortex mode pinned at zero energy. Our work reveals a fundamental interplay of vorticity, disclination and higher-order topological phases14-16, applicable broadly to different fields, promising in particular for OAM-based photonic applications that require vortex guides, fibers [17,18] and lasers [19].Comment: 11 pages, 4 figure

A matched-filter approach to radio variability and transients: searching for orphan afterglows in the VAST Pilot Survey

Radio transient searches using traditional variability metrics struggle to recover sources whose evolution timescale is significantly longer than the survey cadence. Motivated by the recent observations of slowly evolving radio afterglows at gigahertz frequency, we present the results of a search for radio variables and transients using an alternative matched-filter approach. We designed our matched-filter to recover sources with radio light curves that have a high-significance fit to power-law and smoothly broken power-law functions; light curves following these functions are characteristic of synchrotron transients, including "orphan" gamma-ray burst afterglows, which were the primary targets of our search. Applying this matched-filter approach to data from Variables and Slow Transients Pilot Survey conducted using the Australian SKA Pathfinder, we produced five candidates in our search. Subsequent Australia Telescope Compact Array observations and analysis revealed that: one is likely a synchrotron transient; one is likely a flaring active galactic nucleus, exhibiting a flat-to-steep spectral transition over $4\,$months; one is associated with a starburst galaxy, with the radio emission originating from either star formation or an underlying slowly-evolving transient; and the remaining two are likely extrinsic variables caused by interstellar scintillation. The synchrotron transient, VAST J175036.1$-$181454, has a multi-frequency light curve, peak spectral luminosity and volumetric rate that is consistent with both an off-axis afterglow and an off-axis tidal disruption event; interpreted as an off-axis afterglow would imply an average inverse beaming factor $\langle f^{-1}_{\text{b}} \rangle = 860^{+1980}_{-710}$, or equivalently, an average jet opening angle of $\langle \theta_{\textrm{j}} \rangle = 3^{+4}_{-1}\,$deg.Comment: 20 pages, 6 figures; accepted for publication in MNRA