Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds

"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and raise a few new questions. We also unify this approach with approximate differential privacy by giving an appropriate definition of "approximate concentrated differential privacy.

Fast rates in statistical and online learning

The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast rates in online and statistical learning has led to the discovery of many conditions in learning theory under which fast learning is possible. We show that most of these conditions are special cases of a single, unifying condition, that comes in two forms: the central condition for 'proper' learning algorithms that always output a hypothesis in the given model, and stochastic mixability for online algorithms that may make predictions outside of the model. We show that under surprisingly weak assumptions both conditions are, in a certain sense, equivalent. The central condition has a re-interpretation in terms of convexity of a set of pseudoprobabilities, linking it to density estimation under misspecification. For bounded losses, we show how the central condition enables a direct proof of fast rates and we prove its equivalence to the Bernstein condition, itself a generalization of the Tsybakov margin condition, both of which have played a central role in obtaining fast rates in statistical learning. Yet, while the Bernstein condition is two-sided, the central condition is one-sided, making it more suitable to deal with unbounded losses. In its stochastic mixability form, our condition generalizes both a stochastic exp-concavity condition identified by Juditsky, Rigollet and Tsybakov and Vovk's notion of mixability. Our unifying conditions thus provide a substantial step towards a characterization of fast rates in statistical learning, similar to how classical mixability characterizes constant regret in the sequential prediction with expert advice setting.Comment: 69 pages, 3 figure

Quantum entanglement distribution with 810 nm photons through telecom fibers

We demonstrate the distribution of polarization entangled photons of wavelength 810 nm through standard telecom fibers. This technique allows quantum communication protocols to be performed over established fiber infrastructure, and makes use of the smaller and better performing setups available around 800 nm, as compared to those which use telecom wavelengths around 1550 nm. We examine the excitation and subsequent quenching of higher-order spatial modes in telecom fibers up to 6 km in length, and perform a distribution of high quality entanglement (visibility 95.6%). Finally, we demonstrate quantum key distribution using entangled 810 nm photons over a 4.4 km long installed telecom fiber link.Comment: 5 pages, 5 figures, 1 tabl

Studying Free-Space Transmission Statistics and Improving Free-Space QKD in the Turbulent Atmosphere

The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD experiments. We implement a signal-to-noise ratio filter (SNRF) in our QKD system which rejects measurements during periods of low transmission efficiency, where the measured quantum bit error rate (QBER) is temporarily elevated. Using this, we increase the total secret key generated by the system from 78,009 bits to 97,678 bits, representing an increase of 25.2% in the final secure key rate, generated from the same raw signals. Lastly, we present simulations of a QKD exchange with an orbiting LEO satellite and show that an SNRF will be extremely useful in such a situation, allowing many more passes to extract a secret key than would otherwise be possible.Comment: 9 pages, 6 figure

Inappropriate Implantable Cardioverter-Defibrillator Shocks Incidence, Predictors, and Impact on Mortality

ObjectivesThe purpose of this study was to assess the incidence, predictors, and outcome of inappropriate shocks in implantable cardioverter-defibrillator (ICD) patients.BackgroundDespite the benefits of ICD therapy, inappropriate defibrillator shocks continue to be a significant drawback. The prognostic importance of inappropriate shocks outside the setting of a clinical trial remains unclear.MethodsFrom 1996 to 2006, all recipients of defibrillator devices equipped with intracardiac electrogram storage were included in the current analysis and clinically assessed at implantation. During follow-up, the occurrence of inappropriate ICD shocks and all-cause mortality was noted.ResultsA total of 1,544 ICD patients (79% male, age 61 ± 13 years) were included in the analysis. During the follow-up period of 41 ± 18 months, 13% experienced ≥1 inappropriate shocks. The cumulative incidence steadily increased to 18% at 5-year follow-up. Independent predictors of the occurrence of inappropriate shocks included a history of atrial fibrillation (hazard ratio [HR]: 2.0, p < 0.01) and age younger than 70 years (HR: 1.8, p = 0.01). Experiencing a single inappropriate shock resulted in an increased risk of all-cause mortality (HR: 1.6, p = 0.01). Mortality risk increased with every subsequent shock, up to an HR of 3.7 after 5 inappropriate shocks.ConclusionsIn a large cohort of ICD patients, inappropriate shocks were common. The most important finding is the association between inappropriate shocks and mortality, independent of interim appropriate shocks

Detector decoy quantum key distribution

Photon number resolving detectors can enhance the performance of many practical quantum cryptographic setups. In this paper, we employ a simple method to estimate the statistics provided by such a photon number resolving detector using only a threshold detector together with a variable attenuator. This idea is similar in spirit to that of the decoy state technique, and is specially suited for those scenarios where only a few parameters of the photon number statistics of the incoming signals have to be estimated. As an illustration of the potential applicability of the method in quantum communication protocols, we use it to prove security of an entanglement based quantum key distribution scheme with an untrusted source without the need of a squash model and by solely using this extra idea. In this sense, this detector decoy method can be seen as a different conceptual approach to adapt a single photon security proof to its physical, full optical implementation. We show that in this scenario the legitimate users can now even discard the double click events from the raw key data without compromising the security of the scheme, and we present simulations on the performance of the BB84 and the 6-state quantum key distribution protocols.Comment: 27 pages, 7 figure

Cln5 represents a new type of cysteine-basedS-depalmitoylase linked to neurodegeneration

Genetic CLN5 variants are associated with childhood neurodegeneration and Alzheimer’s disease; however, the molecular function of ceroid lipofuscinosis neuronal protein 5 (Cln5) is unknown. We solved the Cln5 crystal structure and identified a region homologous to the catalytic domain of members of the N1pC/P60 superfamily of papain-like enzymes. However, we observed no protease activity for Cln5; and instead, we discovered that Cln5 and structurally related PPPDE1 and PPPDE2 have efficient cysteine palmitoyl thioesterase (S-depalmitoylation) activity using fluorescent substrates. Mutational analysis revealed that the predicted catalytic residues histidine-166 and cysteine-280 are critical for Cln5 thioesterase activity, uncovering a new cysteine-based catalytic mechanism for S-depalmitoylation enzymes. Last, we found that Cln5-deficient neuronal progenitor cells showed reduced thioesterase activity, confirming live cell function of Cln5 in setting S-depalmitoylation levels. Our results provide new insight into the function of Cln5, emphasize the importance of S-depalmitoylation in neuronal homeostasis, and disclose a new, unexpected enzymatic function for the N1pC/P60 superfamily of proteins