Differentially Private Distributed Optimization

In distributed optimization and iterative consensus literature, a standard problem is for $N$ agents to minimize a function $f$ over a subset of Euclidean space, where the cost function is expressed as a sum $\sum f_i$. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to the optimal value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve $\epsilon$-differential privacy the accuracy of the algorithm has the order of $O(\frac{1}{\epsilon^2})$

Mesoscopic Theory of Critical Fluctuations in Isolated Granular Gases

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only, that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out

Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes

By using a theoretical formalism able to work in both real and k-spaces, the physical origin of the phenomenon of extraordinary transmission of light through quasi-periodic arrays of holes is revealed. Long-range order present in a quasiperiodic array selects the wavevector(s) of the surface electromagnetic mode(s) that allows an efficient transmission of light through subwavelength holes.Comment: 4 pages, 4 figure

Plasmon-exciton-polariton lasing

Strong coupling of Frenkel excitons with surface plasmons leads to the formation of bosonic quasi-particles known as plasmon-exciton-polaritons (PEPs).Localized surface plasmons in nanoparticles are lossy due to radiative and nonradiative decays, which has hampered the realization of polariton lasing in a plasmonic system, i.e., PEP lasing. These losses can be reduced in collective plasmonic resonances supported by arrays of nanoparticles. Here we demonstrate PEP lasing in arrays of silver nanoparticles by showing the emergence of a threshold in the photoluminescence accompanied by both a superlinear increase of the emission and spectral narrowing. We also observe a reduction of the threshold by increasing the coupling between the molecular excitons and the resonances supported by the array despite the reduction of the quantum efficiency of the emitters. The coexistence of bright and dark collective modes in this plasmonic system allows for a 90?-change of polarization in the emission beyond the threshold

Initial Jitter Analysis of Lynx, a Proposed Future Large Astrophysics Facility

Lynx is an X-Ray telescope large-mission concept for consideration in NASA's 2020 Astrophysics Decadal Survey. A conceptual structural design is evolving that leverages the success and lessons learned from Chandra and that takes into account unique needs of Lynx. Space optics systems require extreme stability. Any motion in-service (thermal effects, structural dynamics, etc.) impacts performance. An initial analysis was performed to predict the first-cut dynamic responses, jitter, at two selected points on the Lynx observatory. One point is on the Lynx X-ray Mirror Assembly (LMA) and the other, on the focal plane Integrated Science Instrument Module (ISIM). Relative motion between these two points was predicted along with vibration spectra. This information will be used in upcoming analyses of the LMA and the ISIM