Privately Estimating a Gaussian: Efficient, Robust and Optimal

In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP setting, we give an efficient algorithm that estimates an unknown $d$-dimensional Gaussian distribution up to an arbitrary tiny total variation error using $\widetilde{O}(d^2 \log \kappa)$ samples while tolerating a constant fraction of adversarial outliers. Here, $\kappa$ is the condition number of the target covariance matrix. The sample bound matches best non-private estimators in the dependence on the dimension (up to a polylogarithmic factor). We prove a new lower bound on differentially private covariance estimation to show that the dependence on the condition number $\kappa$ in the above sample bound is also tight. Prior to our work, only identifiability results (yielding inefficient super-polynomial time algorithms) were known for the problem. In the approximate DP setting, we give an efficient algorithm to estimate an unknown Gaussian distribution up to an arbitrarily tiny total variation error using $\widetilde{O}(d^2)$ samples while tolerating a constant fraction of adversarial outliers. Prior to our work, all efficient approximate DP algorithms incurred a super-quadratic sample cost or were not outlier-robust. For the special case of mean estimation, our algorithm achieves the optimal sample complexity of $\widetilde O(d)$, improving on a $\widetilde O(d^{1.5})$ bound from prior work. Our pure DP algorithm relies on a recursive private preconditioning subroutine that utilizes the recent work on private mean estimation [Hopkins et al., 2022]. Our approximate DP algorithms are based on a substantial upgrade of the method of stabilizing convex relaxations introduced in [Kothari et al., 2022]

Some hygrothermal effects on the mechanical behaviour and fractography of glass-epoxy composites with modified interface

The mechanical behaviour of glass fibre-reinforced epoxy composites with introduced layers of materials and with fibre coating is studied. The role of aerosil powder as a filler material is investigated, and the fracture mode is analysed by scanning electron microscopy. The nvestigation shows a considerable drop in interlaminar shear stress for the higher fibre volume fraction, whereas the introduction of filler materials to the composite causes no change. Surface mat-reinforced samples show a marginal increase in shear stress. Exposure to moisture reduces the interlaminar shear stress value faster for the higher fibre volume fraction, thereby highlighting the role of the interracial area. Impact values for coated and uncoated fibres show an identical trend with exposure to dry heat, the former always recording lower values. The impact value decreases faster with moisture absorption for the composite with the higher fibre content. Fractography reveals poor adhesion in the coated laminates

High Peak Power Ytterbium Doped Fiber Amplifiers

We have tested a series of Ytterbium doped large core fibers operating near 10Kpps and producing pulses of approximately 1ns. We have achieved 850μJ/pulse resulting in peak powers in excess of 2MW with 0.4ns pulses and near diffraction limited beams. In another fiber, we have achieved over 1.5mJ/pulse with pulses of 900ps corresponding to 1.65MW of peak power and M 2 of 2.5. In the latter case, wall-plug efficiencies, excluding cooling of the pump diode lasers, in excess of 15% were also achieved. This fiber amplifier has operated for 2 months without any degradation or observed optical damage

Reliability and photodarkening in 790nm-pumped 2μm fiber lasers

Recent progress on high efficiency Tm-doped silica fibers pumped at 790nm has enabled the demonstration of a 2μm CW fiber laser operating at the 1kW power level and with single mode beam quality [1]. In addition to this state-of-the-art high power research, Tm-doped fibers are now starting to find applications in lasers with nsec [2] and psec [3] pulsed operation, as well as lower power CW lasers (50-100W) in the 1940nm wavelength region for medical use [4]. As with Yb-doped fibers, the question of photodarkening needs to be addressed to ensure the long term fiber reliability is appropriate for the application. In a recent paper [5], we proposed that the up-conversion process in highly doped Tm-fibers was significantly quenched when compared with lower concentration fibers, under 790nm pumping. This trend was also observed in the photodarkening rate as measured in a CW 2μm fiber laser cavity operating around 20W output power. In this controlled experiment, the rate of photodarkening dropped from 15% per 1000 hours in low concentration fiber to less than 1% in a fiber doped with 4.6% Tm. In this paper we review the 20W results of our earlier work and then confirm the long term reliability of 1940nm CW fiber lasers operating at higher (40W) output power, presenting results for a laser operating for 1200 hours without significant loss of output power (around 12% total power variation). Over any given 24-hour period during this experiment the laser operates open loop with around 8% total power variation in an air cooled configuration. We believe these results confirm the appropriate level of long term reliability of Tm-doped fibers for CW fiber lasers at the ∼50W power level suitable for medical laser applications.6 page(s

Mitigation of photodegradation in 790nm-pumped Tm-doped fibers

9 page(s