Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants

The Photonic Band theory and the negative refraction experiment of metallic helix metamaterials

We develop a theory to compute and interpret the photonic band structure of a periodic array of metallic helices for the first time. Interesting features of band structure include the ingenuous longitudinal and circularly polarized eigenmodes, the wide polarization gap [Science 325, 1513 (2009)], and the helical symmetry guarantees the existence of negative group velocity bands at both sides of the polarization gap and band crossings pinned at the zone boundary with fixed frequencies. A direct proof of negative refraction via a chiral route [Science 306, 1353 (2004)] is achieved for the first time by measuring Gooshanchen shift through a slab of three dimensional bona fide helix metamaterial

Experimental realization of a broadband illusion optics device

We experimentally demonstrate the first metamaterial "illusion optics" device - an "invisible gateway" by using a transmission-line medium. The device contains an open channel that can block electromagnetic waves at a particular frequency range. We also demonstrate that such a device can work in a broad frequency range.Comment: 9 pages, 5 figure

Field-Angle and DC-Bias Dependence of Spin-Torque Diode in Giant Magnetoresistive Microstripe

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Finding diamonds in the rough: Targeted Sub-threshold Search for Strongly-lensed Gravitational-wave Events

Strong gravitational lensing of gravitational waves can produce duplicate signals separated in time with different amplitudes. We consider the case in which strong lensing produces identifiable gravitational-wave events and weaker sub-threshold signals hidden in the noise background. We present a search method for the sub-threshold signals using reduced template banks targeting specific confirmed gravitational-wave events. We apply the method to all events from Advanced LIGO's first and second observing run O1/O2. Using GW150914 as an example, we show that the method effectively reduces the noise background and raises the significance of (near-) sub-threshold triggers. In the case of GW150914, we can improve the sensitive distance by $2.0\% - 14.8\%$. Finally, we present the top $5$ possible lensed candidates for O1/O2 gravitational-wave events that passed our nominal significance threshold of False-Alarm-Rate $\leq 1/30$ days